New Atomic Clock Reaches the Boundaries of Timekeeping

SonicSpike sends an article from NPR about a high-tech clock being built at the University of Colorado Boulder. It's more precise than any clock before, able to keep perfect time for five billion years. "At the heart of this new clock is the element strontium. Inside a small chamber, the strontium atoms are suspended in a lattice of crisscrossing laser beams. Researchers then give them a little ping, like ringing a bell. The strontium vibrates at an incredibly fast frequency. It's a natural atomic metronome ticking out teeny, teeny fractions of a second." But this precision leads to a problem: the relativistic differences between keeping the clock on the floor versus hanging it on the wall now introduce more significant fluctuations than the clock itself. "Tiny shifts in the earth's crust can throw it off, even when it's sitting still. Even if two of them are synchronized, their different rates of ticking mean they will soon be out of synch. They will never agree. The world's current time is coordinated between atomic clocks all over the planet. But that can't happen with the new one."

Comments

Old saying

[plover]

A man with one watch always knows what time it is.
A man with two watches is never sure.

Re:Old saying

[SJHillman]

A man with an atomic watch won't shut up about it.

Re:Old saying

[fustakrakich]

A man with an atomic watch better not keep it in his pocket.

Re:Old saying

[Anonymous Coward]

Another old saying I like, from sailors:

When going to sea, take one clock or three, but never two.

(Knowing the time was essential for navigation, to figure out longitude, back in the days before GPS navigation.)

Re:Old saying

[Anonymous Coward]

yeah and GPS absolutely doesn't rely on clocks...

Re:Old saying

[lgw]

A further problem with hyper-accurate clocks is relativity. TFS mentions the issues with general relativity - strength of gravity affects timekeeping. But there's a more profound issue once you get crazy-precise: only co-moving clocks can be synchronized in the first place. The concept of synchronization simply doesn't apply to clocks moving at different velocities - and two clocks at different positions on the rotating, orbiting Earth will never quite be moving with the same velocity. That relativistic effect is tiny, but it's not even hypothetically reconcilable: there are only so many significant digits of time possible to share between clocks in different locations.

Re:Old saying

[Anonymous Coward]

yeah and GPS absolutely doesn't rely on clocks...

GPS doesn't have much to do with a saying from the 1800's.

If you thought you were raising a valid point, YOU FAIL IT.

If you thought you were being funny, YOU FAIL IT.

HTH, HAND

Re:Old saying

[Sarten-X]

Thanks to GPS, the accuracy has improved, but now you need four clocks to get a 3-dimensional fix, and more to improve accuracy. Fortunately, on the open sea there isn't much blocking your view of the sky.

Re:Old saying

[wagnerrp]

Why can't we compute what the relativistic slew rate between two different locations will be and compensate?

Re: Old saying

[DigiShaman]

And the man with a broken watch can still say the right time twice a day.

Re:Old saying

[wisnoskij]

OK, but then time really is happening at different rates in the two different places. Would you want the clocks to show the same amount of time passing when it simply isn't? Should a second in China be minusculy shorter than one in America?

Re: Old saying

[mpoulton]

Because it would be meaningless to "compensate" for the time difference between clocks moving and accelerating differently. Time literally moves at different rates in different reference frames. The clocks are correct; the problem is that the concept of similtaneity is fundamentally flawed.

Re: Old saying

[Anonymous Coward]

Because it would be meaningless to "compensate" for the time difference between clocks moving and accelerating differently. Time literally moves at different rates in different reference frames. The clocks are correct; the problem is that the concept of similtaneity is fundamentally flawed.

wouldn't that make the concept of time fundamentally flawed?

Re:Old saying

[tgeller]

A man with an atomic watch is better than two in the bush.

Re: Old saying

[Oligonicella]

Only on that level. For most everything else, it's fine. So not so much "fundamentally", you just need to apply it appropriately, much like Newtonian physics. You don't need to factor in QM to build a plane.

Re:Old saying

[complete loony]

This is not a new problem, suddenly created by this clock. It already exists with our standard definition of time.

TAI as a time scale is a weighted average of the time kept by over 200 atomic clocks in over 50 national laboratories worldwide

So now we'll be averaging due to relativity differences as well as precision errors.

Re:Old saying

[Jane Q. Public]

"Whoever said a bird in the hand is worth two in the bush hasn't been putting his bird in the right bushes." -- Gallagher

Re: Old saying

[jouassou]

wouldn't that make the concept of time fundamentally flawed?

In any given reference frame, time is a well-defined quantity. The fundamentally flawed concept here is the idea of some kind of universal time that passes at the same rate everywhere in the universe, because relativity tells us that the observed passage of time is affected by things like velocity, acceleration, and gravitation, and therefore varies between different reference frames -- and we have no objective reason to say that any particular reference frame in the universe is inherently superior.

So while the atomic clock might measure the local passage of time with near perfect accuracy in the reference frame where we place it, the results will just be approximate in any other reference frame.

Re:Old saying

[Jane Q. Public]

We had this discussion a while ago, and I looked it up.

3 satellites for a basic fix. The 4th element is a ground station that corrects for most error. Further satellites can add a bit to accuracy but only with diminishing returns.

Re:Old saying

[WuphonsReach]

Best practice in the real world is four reference clocks or only one. With just three configured you run into the problem of ending up in the "just two clocks situation" more often then not. At which point, NTP is likely to oscillate between the two remaining good candidates (without the "prefer" keyword).

How you choose to configure NTP is a tricky art depending on how resilient you want to be and whether you have a local time source or need less then 5ms accuracy. For most situations (99% of servers), being within 500ms of the "internet time" is enough. Your goal is mostly to avoid the issue where the clock is off by tens of seconds or worse.

Re:Old saying

[__aaltlg1547]

No, that's wrong. Four satellites are needed to get a unique position solution. The ground stations only broadcast correction data that can move your position solution by a few meters at most.

Re: Old saying

[Jane Q. Public]

Because it would be meaningless to "compensate" for the time difference between clocks moving and accelerating differently.

It isn't "meaningless", it's just not very useful.

The real problem is that with "clocks" this precise, there must be an acceleration standard in addition to the other standards.

I suggest that 3 be placed on the same fixed level surface, at some kind of "elevation" standard based on effective gravity, so that tectonic changes. Because this is an obvious source of potential error. Just for one example, a recent media article was all about "sea level rise" on the East U.S. coast, when in fact most if not all of what they actually observed (according to official figures) was not sea rise at all, but land subsidence.

Since rise and subsidence tends to occur very slowly, any adjustments in "effective gravity" should be doable via simple low-mass spacers under the equipment. But again, elevation should start at some "standard", such as mean sea level, so that comparisons can be made. Obviously MSL is an artificial figure but I am not aware of a better standard.

Re:Old saying

[Anonymous Coward]

because that would rely on a precise understanding of gravitational fluctuations caused by differing sea-levels (including tides), minor alterations of the earths rotational axis.

I don't think many people here realize just how precise this is, and how uncertain our knowledge of some things are.

Re: Old saying

[Jane Q. Public]

s/so that tectonic changes/so that tectonic changes are accounted for

Re:Old saying

[lgw]

In general relativity, you can paint a coherent picture. Both the observer deep in a gravity well and a distant observer agree that higher gravity makes clocks run slower. But that's not true of special relativity at all. Given two clocks moving relative to one another, each observer thinks the other's clock is running slower and they're equally right. There's simply no universal clock, no standard that's more right than any other clock.

Re:Old saying

[Jane Q. Public]

Should a second in China be minusculy shorter than one in America?

No. It should be slightly longer.

Re:Old saying

[Sam36]

GPS works by having many satellites in an egg shaped orbit around the Earth all broadcasting an atomic time. Your hand held radio receives these signals,and based on the time difference between the individual (and visible) satellites, the location of the satellites is then mapped out mathematically and thus you can triangulate the exact lat and long coordinates of the hand held radio based on that.

Re: Old saying

[techno-vampire]

...the problem is that the concept of similtaneity is fundamentally flawed.

I don't think so. When it comes to physics, I'm an informed layman at best, but I don't think that the concept itself is flawed. The flaw comes in when people try to apply it in a situation where it just doesn't apply. As an example, it certainly doesn't apply at astronomical distances; we can't know exactly where Alpha Centauri is and what's happening there right this minute; we can only know what was going on 4.366 years ago. The idea of simultaneity simply doesn't apply, and most people understand that. The problem here is that most people don't understand relativity deeply enough to understand that when it comes to clocks this accurate the same thing is true: simultaneity just isn't relevant.

Re: Old saying

[RightwingNutjob]

I thought that TAI was supposed to be a hypothetical clock on an idealized (spherical? oblate?) earth that's computed from the a bunch of real atomic clocks. So wouldn't it still be possible to synthesize a time like that to more decimal digits using better actual clocks?

Re:Old saying

[Jane Q. Public]

No, it is NOT wrong. Your assertion is a common misconception. I assure you: I looked into this technology in depth.

Just as basic geometry would normally dictate, 3 satellites are sufficient to find your basic location and elevation. (There are actually 2 solutions to the equation, but one of them makes no sense because it's at some point out in space.)

The 4th element is what is known as a "ground segment", which is used to increase the accuracy of the 3-satellite triangulation. Any further satellite signals are used only to further increase accuracy.

The 4th element is gradually being moved into orbit, which WILL make it a 4-satellite lock for accuracy boost. But the fact remains that your basic geolocation including elevation is still fundamentally based on 3 satellites. The 4th signal is only to improve accuracy for civilians, as they do not have access to the military-accurate signals.

Re:Old saying

[Anonymous Coward]

Three satellites plus some basic assumptions about altitude will work fine, outside of some really unlucky alignments.

Re:Old saying

[Jane Q. Public]

Three satellites plus some basic assumptions about altitude will work fine, outside of some really unlucky alignments.

Exactly. Throw out the nonsense solution of the two that triangulation in 3D gives you with 3 sats, and you have basic location. The 4th signal, which until now has been served by ground stations, is to add accuracy that isn't normally available in the civilian signal. Newer GPS can make use of more satellite signals to improve accuracy, but they are not strictly necessary for decent resolution.

The good news is that civilian-aimed signals are being built into the new generations of satellites, though it will still be a few years until they are deployed.

Re:Old saying

[Anonymous Coward]

Three are needed if you know your altitude and the shape of the earth, which you generally do when you're on the open sea.

Re: Old saying

[Anonymous Coward]

No, it becomes nearly meaningless, because you can't just define a standard acceleration or even position. The offset of clocks relative to any other observer or clock would depend not just on the relative position, but the whole accumulated relative movement history since any point of synchronization. And there is a standard gravity already defined, by the way.

Re: Old saying

[wagnerrp]

Because it would be meaningless to "compensate" for the time difference between clocks moving and accelerating differently. Time literally moves at different rates in different reference frames. The clocks are correct; the problem is that the concept of similtaneity is fundamentally flawed.

I'll admit, I don't understand why the arbitrary reference time we use currently is any less valuable now that we have surface clocks whose real time is measurably changing due to relativistic effects.

Re:Old saying

[itzly]

3 satellites are sufficient to find your basic location and elevation

You need a 4th one for the time. Without an accurate time reference, you can't determine distance to satellites.

Re:Old saying

[dotancohen]

I actually addressed this just yesterday on Stack Exchange:
http://astronomy.stackexchange...

Thanks!

Re: Old saying

[Anonymous Coward]

Sorry, that doesn't make sense. It's a 4D problem because you don't know what time it is. Three spheres intersect at a point, but there are still multiple possibilities because you don't know how big the spheres are.

Re:Old saying

[itzly]

My 10 year old Garmin could already track 12 satellites. And yes, it really helps accuracy. With only 4 you're often limited. When one or more are close to the horizon, reception can be easily blocked by buildings or trees. When they are all above you, accuracy is limited by the acute angles of the triangulation.

Re:Old saying

[smallfries]

Actually basic geometry does not say that at all. The receiver does not get given an accurate distance to each satellite, instead it is an inacurrate relative difference in distance. The intersection between the three spheres is a 3d region rather than a point. The extra fix is required to constrain the equations to a single point. There is more info here.

Re: Old saying

[Anonymous Coward]

If I'm getting this correct, then increasing accuracy decreases the size of the effective reference frame for a given clock. And the article talks about a reference frame shrunk to the point that a few feet of elevation makes for a different frame entirely. How is this not making time keeping past a certain accuracy irrelevant?

Re:Old saying

[tehlinux]

"Osama Bin Laden?! They should call him Osama 'been hidin!'" -- Black Gallagher

Re: Old saying

[Anonymous Coward]

It would necessarily follow that the precision of TAI is limited because its not possible to correct for the relativistic drift between clocks past a certain point.

Just another reason why I don't like the idea of ditching leap seconds. At the end of the day, the only meaningful universal reference point for civilian time is the solar year. We use "seconds" to divide it, but only because its a convenient unit for most practical uses. To think we could ditch it to rely only on the second is misguided, as this case proves.

Re:Old saying

[Anonymous Coward]

"If you think a bird in the hand is better than two in a bush, you've never been in the bush with two birds." -- Michael Parkinson (I think)

Re: Old saying

[Hadlock]

As of about 2010 we already had clocks so accurate you could demonstrate relativistic effects by separating them by just a few feet. It sounds like the vibration from walking in the same room as these is enough to knock them out of sync.

Re:Old saying

[Anonymous Coward]

Your link gives the actual formulas that show how to compute the two points. So, how can you say that basic geometry does not say that at all?

The figure in your reference shows that things go differently when the distances are not accurately known, but this is not what the text tells us.

However, given the 3d region that is the intersection of three spheres, please tell me how the extra fix narrows the position to a point, given that the position almost surely is not on the boundary of the 3d region.

Re:Old saying

[SuricouRaven]

GPS doesn't use triangulation. It uses trilateration.

Re:Old saying

[bombman]

Then how do they know its precise?

Re: Old saying

[master_p]

I think it is wrong to say simultaneity is wrong. The fact that the two clocks are correct does not mean simultaneity does not exist, it only means that we cannot measure simultaneity with clocks.

The fact is thinga happen in parallel in the universe, and so simultaneity exists, because for any event another event would have to have happened at the same time.

Re: Old saying

[lgw]

Simultaneity doesn't mean what you want it to mean. There's no arbitrary universal time in which things can be said to happen simultaneously. Even the order of events can be different depending on the frame of reference of the observer (but causality is always protected). You can pick an arbitrary frame, of course, but you can only observe distant events after the speed-of-light delay, which itself depends on relative velocity. Since we're constantly accelerating, even that comes down to arbitrary choices.

Or in other words, if you and I are moving relative to one another, each of us can have a definition of simultaneity, but we can't agree on what events are simultaneous. Two atomic clocks at different places on Earth won't have any reference frame in which they keep exactly the same time (though they'll agree to quite a few significant digits).

Re:Old saying

[davester666]

Course, he'll be invited for a private meeting with someone from Homeland Security, followed immediately by a short flight out of the country...

Re: Old saying

[Altrag]

Yes but you can perform a transformation to translate from one reference frame to another, and while the universe may not give special meaning to any particular reference frame, there's nothing stopping us from doing so. So in theory you can define a "universal" time if you want.

Similar to choosing where to place the origin on a sheet of graph paper. It doesn't really matter where you put it (mathematically at least) but once its there you have a perfectly meaningful "universal" point of reference to use when describing the positions of other objects.

The trouble of course is computing the transformation parameters with enough accuracy to matter, which I'm assuming is implausible on our not-mathematically-perfect planet.

Re:Old saying

[itzly]

Thank you, but I was using the word triangulation on purpose so you can imagine the acute triangles in your head, and see that the uncertainty increases as the two long legs of the triangle are getting close together.

Re:Old saying

[ssam]

If you are in a boat you probably have a good idea about your altitude, so a 2d fix is all you really need.

Re:Old saying

[stealth_finger]

yeah and GPS absolutely doesn't rely on clocks...

Kinda does as it based entirely on synced time transmissions and triangulations. I don't think the coverage was that great in the 1800's though so they had to fall back on hand written directions from ye olde google maps I guess.

Re: Old saying

[Anonymous Coward]

This completely misses the point of the discoveries outlined by relativity.

Re:Old saying

[itzly]

Not quite. The altitude depends on the local sea level, which not only depends on the tide, but also on the local gravity field and shape of the Earth. So, yes, you can get a 2D fix, but it won't be as accurate as a full 3D fix.

Re: Old saying

[squizzar]

If your watch is broken and runs at 99% speed then I think you only get the right time every 49.5 days or so...

Re: Old saying

[bloodhawk]

I have a broken watch, can't quite work out when 88:88 is going to roll past though.

Re:Old saying

[psmears]

No, it is NOT wrong. Your assertion is a common misconception. I assure you: I looked into this technology in depth.

Then perhaps you can provide a reference?

Just as basic geometry would normally dictate, 3 satellites are sufficient to find your basic location and elevation.

No: basic geometry dictates that, to find a position in three dimensions, you need three measurements of distance. The trouble is that the signal from one satellite gives you no information about your position: the signal (roughly speaking) tells you where the satellite is, and the time by that satellite's clock - but since you have nothing to compare it against, you have no idea how long that signal took to reach you, so you get no information about your position.

It's similar to if you asked me my height, and I said "I'm a foot taller than Fred". If you don't know how tall Fred is, you're no nearer to knowing how tall I am, even though you've been given one measurement. Sure, if you look at probability distributions of height you can have a good guess at how tall I might be, and this is similar to getting a 2D fix (where you assume that your elevation is "at or near the surface of the Earth"), but you can't know for certain that one of both of us don't have unusual heights.

Once you have a signal from two satellites, you can subtract the timestamps, which doesn't directly tell you position, but tells you which satellite is closer to your position, and by how much. This allows you to constrain your position in one dimension (i.e. you still have two degrees of freedom - a surface rather than a solid), and another satellite's signal will give you another constraint (pinning you down to a line); only with a fourth satellite can you determine your position precisely (well, actually the solution can give more than one point but generally only one is realistic).

Re:Old saying

[Anonymous Coward]

Actually, because you don't have an accurate clock on the ground, you _do_ need four signals to get an exact 3D fix, as you also need to fix your position in time when all you have is a statement of the satellite times at transmission. You can make do with fewer satellites (for example, by constraining the position to lie on some geoid), but if all you see are four satallites and you have no other information, you won't be able to get an exact fix.

The "ground segment" is the control system, which sends the almanac data, without which nothing would make sense. Unless you meant a DGPS station or an AGPS connection.

Re:Old saying

[Millennium]

Because you'd have to do it in realtime, or whatever passes for it when dealing with relativistic effects on this scale. Otherwise, microscopic shifts in the Earth's crust will soon change the slew rate, and then you're back to square one. But calculating the slew rate will inevitably take longer than one tick of the clock, so you can't do it in realtime either.

Though this property isn't entirely useless. For example, you could use two of these clocks to build extremely sensitive seismometers: first you would need to calculate their slew rate at rest, but then whenever that changed, you'd know that their relative position had changed. Then you'd have to calculate the new slew rate, to establish the new baseline, but the temporal resolution of such a device would depend only on how quickly you could do that.

Re: Old saying

[Anonymous Coward]

We already had this problem ("What's the time on Earth?") once in the past and we solved it, or ... we "solved" it for all practical purposes, by arbitrarily choosing one meridian as referent and giving it primacy. We can do something similar again, chose a point on Earth with least own fluctuation in gravity and velocity (or continuously calculate and subtract common-mode fluctuations which appear on all other clock sites around globe), and then claim it to be referent clock. That would allow us to use other stationary and mobile clocks as sensitive scientific instruments which would provide us with new insights if they appear to deviate from what our theories predicts.

Re:Old saying

[CrimsonAvenger]

The 4th signal is only to improve accuracy for civilians, as they do not have access to the military-accurate signals.

Umm, no.

Selective Availability (the coarser signal that used to be available to civilians) was turned off a long time ago. Now everyone gets the military grade signal.

Which doesn't mean that there's no point to that "fourth signal" you refer to. It's called differential GPS, and uses a GPS receiver at a surveyed point to broadcast corrections to (relatively nearby) receivers. However, these days, DGPS really only matters when you need a position that must be correct to within inches (someone doing survey work needs it, pretty much noone else cares).

Oh, and it's not being moved into orbit either. Pretty much can't be, since it requires a known position to work from, and orbits are, pretty much by definition, moving and therefore not known to the precision required (within low single-digit inches).

Re:Old saying

[Chrisq]

yeah and GPS absolutely doesn't rely on clocks...

GPS doesn't have much to do with a saying from the 1800's.

If you thought you were raising a valid point, YOU FAIL IT.

If you thought you were being funny, YOU FAIL IT.

HTH, HAND

You would think so until you hear the full saying:

When going to sea, take one clock or three, but never two
Or a GPS receiver will do

Re: Old saying

[Anonymous Coward]

Simultaneity isn't just about distance or time accuracy, but also about velocity and gravitational difference between observers. For any example of two things being simultaneous, you can come up with an observer that would see them as not being simultaneous. This is why the idea is flawed at a fundamental level, as it is meaningless outside of a single frame. It just happens most of the time on Earth, we're effectively sharing the same frame as everyone else.

Re: Old saying

[Anonymous Coward]

"Should a second in China be shorter than America?"

That's RACIST sir!

Re:Old saying

[nabsltd]

You need a 4th one for the time. Without an accurate time reference, you can't determine distance to satellites.

Every GPS signal is the time...that's how it works.

The signal from different satellites (which includes the time, the satellite ID, and the satellite position) is enough by itself to give you everything you need, and by determining how long each signal took to reach the receiver, the position can be fixed.

You only need 3 satellites if your position is already generally known (i.e., what hemisphere), or if the receiver assumes you are reasonably close to sea level. With 4 satellites, you can get a fix with no previous knowledge of where you were. Four will also give you accurate altitude after a few iterations.

Re:Old saying

[Anonymous Coward]

No. It should be slightly longer.

That's what she said! No.. wait.. oh crap!

Re:Old saying

[Anonymous Coward]

I wonder how they check that the clock is keeping the right time!

Re:Old saying

[lars5]

Find a way to entangle strontium atoms.

Re: Old saying

[Anonymous Coward]

For any two events that you view as being simultaneous, there are an infinite number of frames of reference where those events will be viewed as not simultaneous. It is not just a matter of clocks, but that observers at different speeds will have a difference sense of when things they see happen at the same versus different times.

Re:Old saying

[operagost]

One word: geostationary.

Re: Old saying

[operagost]

Interestingly, that's how long Windows 95 could stay up before crashing. COINCIDENCE?

Re:Old saying

[Anonymous Coward]

You have to solve for 4 variables, x,y,z, and t. If you have a clock you trust you can drop to 3 satellites, or if you can make assumptions about elevation or use an altimeter. But 4 satellites is a true GPS fix with no extra data. Most GPS units have decent clocks, and cell phones get their time from the network.

Re:Old saying

[Anonymous Coward]

You just need to attach a Heisenberg compensator to each of your clocks and you're all set.

Re: Old saying

[hawkinspeter]

You're problem is thinking of time as absolute. "Now" travels at the speed of light, so depending on your frame of reference and distance from the event, your "now" would be different to someone travelling at a different velocity and it's quite possible that you'd disagree about the order of events happening.

In the larger universe, it's more obvious that there is no single frame of reference to which you can pin "simultaneity". "Same time" only makes sense in a single frame of refernce.

Re: Old saying

[hawkinspeter]

That might work if we knew that the Earth was perfectly spherical and uniformly dense. However, it's going to be almost impossible to keep track of all the differences in velocity and gravity at different points on the earth in order to compare the measurement of time at one clock with the measurement of time at another clock. The clocks would be correctly measuring time, they'd just never agree with one another due to their frame of reference being different.

Re: Old saying

[Anonymous Coward]

So while the atomic clock might measure the local passage of time with near perfect accuracy in the reference frame where we place it, the results will just be approximate in any other reference frame.

Which is why you calibrate the clock in the frame it is intended to stay in. If a clock is calibrated in one frame, and moved into another: then yes, expect the clock to no longer be accurate.

Re:Old saying

[possiblywrong]

This is incorrect. (I assure you: I *use* this technology in depth. :) ) The confusion arises from thinking about just the spatial component of the problem you are trying to solve, and not also the temporal. A GPS receiver has a generally *inaccurate* internal clock (which means it can be cheap, one of the brilliant parts of the design, IMO). Think of the "pseudorange" from a single satellite as providing a single equation with *four* unknowns: the three dimensions of position, and the *error* in your internal clock. To solve for all four unknowns, four equations (and thus four measurements) are needed.

Re: Old saying

[skids]

It is not just a matter of clocks, but that observers at different speeds will have a difference sense of when things they see happen at the same versus different times.

This assumes the observer is not capable of measuring the velocity to the observed system and compensating for it. Given enough data, the two observers at different velocities could calculate what time each of the two events would have occured at if at the exact time of the event the system the two observers magically teleported to the same location. The problems are agreeing on a mutual standardized location/frame and acquiring said data. You can construct systems where the former is difficult, but there are far more simple applications where it is not difficult to do so. The latter may indeed be very difficult.

Re:Old saying

[cnaumann]

You need a four dimensional fix. You must solve for X, Y, Z, and t. This requires a fix on four satellites. You can work with three if you assume you are on the surface of the earth and know your elevation.

Re:Old saying

[itzly]

Every GPS signal is the time...that's how it works.

Obviously yes. But the signal you hear from each satellite is offset by an unknown amount (assuming unknown time/position). So, you need to solve for 4 variables (time, x, y, z), so you require 4 satellites, as you said later on. If you know 1 of the variables (for instance, because you have an accurate local clock, or you guesstimate the altitude), you can survive on 3 satellites, but it will be less accurate.

Note that you need to know local time to nanosecond accuracy, so a regular quartz oscillator is only useful for a short time after synchronisation, and will drift away fairly quickly.

Re:Old saying

[cellocgw]

Hey, I have a dozen watches (you insensitive clod) -- and I know how to calculate mean, median, and standard deviations!

So there.

Re:Old saying

[cellocgw]

You need a four dimensional fix.

Mr. B. Banzai would like a little word with you.

Re:Old saying

[Rich0]

Every GPS signal is the time...that's how it works.

Obviously yes. But the signal you hear from each satellite is offset by an unknown amount (assuming unknown time/position). So, you need to solve for 4 variables (time, x, y, z), so you require 4 satellites, as you said later on.

If you know 1 of the variables (for instance, because you have an accurate local clock, or you guesstimate the altitude), you can survive on 3 satellites, but it will be less accurate.

Note that you need to know local time to nanosecond accuracy, so a regular quartz oscillator is only useful for a short time after synchronisation, and will drift away fairly quickly.

I'm pretty sure you don't need to know the time to calculate your position with GPS. The satellites all broadcast their idea of the time, and the only thing that matters for GPS positioning is the difference between them pairwise. If they all broadcast the wrong time, it would work just fine as long as they all broadcast the SAME wrong time.

It would also work fine if every GPS satellite just broadcast a single pulse once a second along with its position, and the receiver could measure the arrivial time difference between the pulses. It just is a lot easier to continuously broadcast the time than build such a receiver.

Once you know your position and the satellites position you can calculate the delay in arrival time and calculate the correct absolute time. If you had a GPS constellation such that one satellite gave you the time and a pulse per second, and the other satellites all gave a pulse per second, you could calculate your position and absolute time from 3 of them if you knew your general location.

Re: Old saying

[mythosaz]

If your watch is broken and runs at 99% speed then I think you only get the right time every 49.5 days or so...

Wut?

If your watch is slow, running 99% of normal speed, it means that the hands on a correct watch "laps" the slow watch every 23 hours 45 minutes and 36 seconds.

Re:Old saying

[Anonymous Coward]

you need three measurements of distance.

Yes, and one of those measurements come from knowing your distance from the center of the Earth.

Sure, if you look at probability distributions of height ...

Except you don't need to look at probability distributions. GPS setups meant for use in areas with possibly limited reception and no nearby ground station/LORAN alternative to help deal with that can use a detailed elevation model of the Earth to narrow things down quite a bit.

Re:Old saying

[Anonymous Coward]

To solve for all four unknowns, four equations (and thus four measurements) are needed.

Yes, four unknowns, one of which: the radius of the Earth, can be measured ahead of time. If a simple spheroid model is not good enough, can also use elevation data to refine things.

Re: Old saying

[Anonymous Coward]

You always know how big one of the "spheres" is: the Earth. It is easy enough to even use much more detailed models of Earth's shape without assuming it is a sphere.

Re: Old saying

[Anonymous Coward]

This assumes the observer is not capable of measuring the velocity to the observed system and compensating for it.

No such assumption is being made. The point is simultaneity is relative to the observer and is not a universal description of a situation. The fact you can figure out what other observers see is irrelevant to the previous post that was arguing there is no flaws or issues with simultaneity.

Re:Old saying

[Russ1642]

A man with one watch always knows what time it is.
A man with two watches is never sure.

A man with two watches out of sync is an idiot.

Re: Old saying

[Anonymous Coward]

If you had two 24 hour clocks that agreed at midnight, and one was 1% slower, the faster one would immediately advance in front of the slower one. After a day, the fast one would read midnight again, while the slow one would read 23:45:36. At no point during that day did the fast clock pass the slow one, it was always head by some amount less than 15 minutes. Each day it would gain by 14.6 minutes before eventually lapping it many days later.

Re:Old saying

[psmears]

you need three measurements of distance.

Yes, and one of those measurements come from knowing your distance from the center of the Earth.

Yes, I know you can do that, I even mentioned it :) But the person I was repying to claimed "3 satellites are sufficient to find your basic location and elevation" (emphasis mine) - i.e. they were claiming you could find the distance from the centre of the Earth, without assuming it.

Sure, if you look at probability distributions of height ...

Except you don't need to look at probability distributions. GPS setups meant for use in areas with possibly limited reception and no nearby ground station/LORAN alternative to help deal with that can use a detailed elevation model of the Earth to narrow things down quite a bit.

You still need to think about probability, because the elevation model only tells you where the ground is - not where you are in relation to it. That said, the asumption "you're probably very close to the surface" is often very good, at least for most people :-)

Re:Old saying

[jfengel]

Yep. Effectively, it's a four-variable problem: x, y, z, and t. If you had a synchronized atomic clock with you, you might be able to do it with just three satellites, but that would be pretty bulky and delicate.

Re:Old saying

[Anonymous Coward]

I don't mean to be flippant, but am genuinely wondering:

At some point doesn't the clock accuracy run up against some variant of the [Heisenberg] uncertainty principle? Maybe not exactly the same principle, but I would think that there would be some limit that would be closely related.

Re:Old saying

[Jane Q. Public]

Obviously yes. But the signal you hear from each satellite is offset by an unknown amount (assuming unknown time/position). So, you need to solve for 4 variables (time, x, y, z), so you require 4 satellites, as you said later on.

As I stated above, the 4th signal is what the ground station is for. Its purpose is to compensate for the slight offsets you mention. It doesn't have an unknown offset because it is a ground station.

Also as I mentioned, as the system has become more sophisticated they have found ways to send the offset signals via the satellites themselves, though they are still calculated via ground stations.

The fact remains that the basic triangulation can be performed with a maximum of 3 satellites. The 4th just improves accuracy. A particular GPS receiver may insist on 4 satellite locks, depending on its own hardware and software. But that doesn't make it strictly necessary for a rough location.

Re:Old saying

[Jane Q. Public]

Actually basic geometry does not say that at all. The receiver does not get given an accurate distance to each satellite, instead it is an inacurrate relative difference in distance. The intersection between the three spheres is a 3d region rather than a point. The extra fix is required to constrain the equations to a single point. There is more info here.

This has all been discussed here on Slashdot before. Technically, you are correct but as a practical matter, you are not.

The intersection of the spheres is obviously a 3-D region. This is not in dispute. The factor in question (as you imply in a subtly incorrect way) is the SIZE of that 3-D region. And all this makes absolutely no difference to what I stated above. An exact solution would be a point in space (proving the comment I made about geometry).

The intersection of 3 spheres is most definitely SUFFICIENT, geometrically, to locate a point. (Which in turn requires 3 satellites.) The issue here is that the 3 satellites are moving and so there is a slight uncertainty, or offset, which expands the possible error. The unique Earth-surface solution PLUS error margins result in a 3-D region, rather than a single point.

And that, again as I stated earlier, is what the 4th signal, historically from a ground station, is for: to compensate for those errors, and reduce that region (as much as possible) to a single point.

So just to make this very clear, and avoid misunderstandings: yes, geometry DOES say you can triangulate a 3-D point on Earth from 3 known points in space. The 3 points have 2 solutions, but one is off in space and is discarded. The ONLY time those 3 points are not (theoretically) sufficient is when the plane formed by those 3 points is parallel to a line drawn from your position, which should never happen with same-altitude satellites visible from the ground.

The only reason GPS doesn't pinpoint based only on 3 points is because of slight positioning error and compensation for relativistic effects, which adds potential error and so expands the solution region from a point to a 3-D space.

The 4th signal is to reduce those errors, thereby reducing the volume of the solution space back toward a point.

Re:Old saying

[Jane Q. Public]

I didn't mean to be quite so repetitive, I was just trying to reinforce the point.

One minor correction:

The only reason GPS doesn't pinpoint based only on 3 points is because of slight positioning error and compensation for relativistic effects, which adds potential error and so expands the solution region from a point to a 3-D space.

The 4th signal is to reduce those errors, thereby reducing the volume of the solution space back toward a point.

Should have been:

The only reason GPS doesn't pinpoint based only on 3 points is because of slight satellite positioning error and relativistic effects, which adds potential error and so expands the solution region from a point to a 3-D space.

The 4th signal is to reduce the positioning error and compensate for relativity, thereby reducing the volume of the solution space back toward a point.

Re: Old saying

[Jane Q. Public]

Sorry, that doesn't make sense. It's a 4D problem because you don't know what time it is. Three spheres intersect at a point, but there are still multiple possibilities because you don't know how big the spheres are.

Yes, it does make sense, because yes, you do know the size of those spheres. That's exactly what GPS calculates!

What GPS satellites send is a TIME signal. The difference in time between what the signal says, and the time at your receiver, is the distance to the satellite, which in turn is the radius of the sphere.

The only reason spheres come into the picture at all is because of errors in the signal. If there were no errors or relativistic effects, it would be a simple problem in triangulation, finding the intersection of 3 lines of known length from 3 known points.

But the positioning and relativistic error add an error factor into the lengths of those lines, so the target region mathematically expands to a 3-D region within the non-point intersection of 3 spheres.

So the basic location -- the area within that region -- is still known, as previously discussed. And it is known to actually a pretty reasonable degree... within about 100 meters, more or less. The 4th signal -- the "ground station" signal -- can be used to largely compensate for the mentioned errors because it is not moving relative you on Earth's surface, so you get a constant time signal mostly immune to those errors.

But make no mistake: the 4th signal is only to improve already-pretty-good accuracy. It is not a 4th "position" signal, per se. It is there to compensate for the errors in the other 3 signals.

Re:Old saying

[Anonymous Coward]

Build a man a fish, keep him warm for a day.
Teach a man to fire, then there are stars in the universe.

Re:Old saying

[Sarten-X]

Just as basic geometry would normally dictate, 3 satellites are sufficient to find your basic location and elevation. (There are actually 2 solutions to the equation, but one of them makes no sense because it's at some point out in space.)

This is a Slashdot discussion regarding how many clocks we need on a boat, planning on using a centuries-old navigation technique, and debating the minimal number of signals we need to receive from space, just in case every timepiece on the vessel fails. The discussion started with pithy sayings.

We cannot assume that "making sense" is a requirement.

Re: Old saying

[Anonymous Coward]

Sorry, that doesn't make sense. It's a 4D problem because you don't know what time it is. Three spheres intersect at a point, but there are still multiple possibilities because you don't know how big the spheres are.

Yes, it does make sense, because yes, you do know the size of those spheres. That's exactly what GPS calculates! What GPS satellites send is a TIME signal. The difference in time between what the signal says, and the time at your receiver, is the distance to the satellite, which in turn is the radius of the sphere.

Are you absolutely certain that's how GPS works? Wouldn't that require that each GPS receiver have an atomic clock so it can calculate the difference in time between what the signal says and the time at your receiver?

If GPS receivers had built-in atomic clocks, then only 3 satellites would be necessary to find your basic location and elevation because in that case you'd know the sizes of those spheres.

The only reason spheres come into the picture at all is because of errors in the signal. If there were no errors or relativistic effects, it would be a simple problem in triangulation, finding the intersection of 3 lines of known length from 3 known points. But the positioning and relativistic error add an error factor into the lengths of those lines, so the target region mathematically expands to a 3-D region within the non-point intersection of 3 spheres.

1. Are you absolutely certain that's how triangulation works? Is it possible that you're actually trying to describe trilateration?

2. Even if there were no errors or relativistic effects, how could a GPS receiver without an atomic clock find your basic location and elevation using only 3 satellites? Sure, a GPS receiver with an atomic clock would know the sizes of those 3 spheres. But imagine, just for a moment, that GPS receivers don't have atomic clocks. Don't you see that (even with no errors/relativistic effects) you don't know the sizes of those 3 spheres?

Re:Old saying

[Anonymous Coward]

As I stated above, the 4th signal is what the ground station is for. Its purpose is to compensate for the slight offsets you mention. It doesn't have an unknown offset because it is a ground station.

No. The offset is the amount of time it takes the signal to travel from the satellite or ground station to your receiver. If you don't know where you are, that offset is unknown even for the ground station's signal.

Re:Old saying

[Anonymous Coward]

A three-satellite fix constrains your position to a hyperbola. A hyperbola and a sphere can intersect in as many as four points.

Further, the angle of the hyperbola at the points of intersection is usually nowhere near vertical. Because of the angles involved, a slight error in altitude can turn into a large error in position -- for example, assuming mean sea level when you're actually sitting on top of a high tide could move your position by miles if the angle is shallow enough. Assuming a simple spheroid while standing on top of Mount Everest could mean the reported position is anywhere in the Tibetan Plateau, or beyond.

Re:Old saying

[innerweb]

Two men, or two watches and which Bush?

Re:Old saying

[Anonymous Coward]

... yes, you do know the size of those spheres. That's exactly what GPS calculates! What GPS satellites send is a TIME signal. The difference in time between what the signal says, and the time at your receiver, is the distance to the satellite, which in turn is the radius of the sphere.

Suppose this is how GPS works. Receiving a signal from one satellite and comparing its time to the GPS receiver's atomic clock reveals the size of the sphere centered around that satellite. So a GPS receiver with an atomic clock only needs one signal to constrain its position to that sphere's 2D surface.

A second signal reveals the size of a second sphere, which usually intersects the first sphere along a circle. This constrains the receiver's position to a 1D circle.

A third signal leads to a third sphere, which usually intersects that circle at two points. One is usually in space so it's discarded in favor of the point nearer the surface.

So if GPS receivers had built-in atomic clocks, then only 3 satellites would be necessary to find your basic location and elevation because in that case you'd know the sizes of those spheres.

But most GPS receivers don't have built-in atomic clocks. So let's think about how GPS actually works. Receiving a signal from one satellite doesn't constrain the receiver's position because a receiver without an atomic clock can't calculate the difference in time between what the signal says and the time at your receiver.

Receiving signals from two satellites does constrain the receiver's position. For instance, if both signals show the same time, the receiver is equally far away from both satellites. This constrains the receiver's position to a 2D plane between the two satellites where every point is equally far away from both satellites.

If a third signal also shows the same time, the receiver's position is constrained to lie on a 1D line where every point is equally far away from all three satellites.

Note that three satellites aren't sufficient to find your basic location and elevation if the GPS receiver doesn't have an atomic clock.

... geometry DOES say you can triangulate a 3-D point on Earth from 3 known points in space.

Just as basic geometry would normally dictate, 3 satellites are sufficient to find your basic location and elevation.

Only for GPS receivers with atomic clocks. Since most GPS receivers don't have atomic clocks, 3 satellites aren't sufficient to find your basic location and elevation. They'd have to assume elevation if only 3 satellites are in view, otherwise your position could be anywhere on a 1D line.

The only reason GPS doesn't pinpoint based only on 3 points is because of slight positioning error and compensation for relativistic effects, which adds potential error and so expands the solution region from a point to a 3-D space.

No. Notice that I never mentioned positioning errors or relativistic effects. All I assumed is that GPS receivers don't have atomic clocks. Even with no positioning errors or relativistic effects, GPS receivers without atomic clocks can't solve for basic location and elevation with only 3 satellites. That solution region isn't a point, it's actually a 1D line even with no positioning errors or relativistic effects.

Re:Old saying

[plover]

Selective Availability wasn't a separate signal; it was the encryption of the least significant bits of the satellite's position found in the C/A data. Only a military grade receiver had the keys to decrypt the signals, allowing the receiver to understand the precise location of the satellite, allowing for a more accurate computation.

The "4th signal" the GP may have been referring to is WAAS, the Wide Area Augmentation System. It's a set of precisely surveyed ground stations that continually measure the amount of timing error they're receiving (generally due to atmospheric interference), which is sent back up to the satellites and included in a set of correction data. It was added to serve the FAA in providing accurate altitude and approach data for aircraft that work at all airports. But it's not a separate signal, it's part of the data sent by each satellite. It's effective, and it's cheap - the receiver doesn't need a separate radio to receive DGPS data.

Unlike WAAS, DGPS data does not go back to the satellite. It is transmitted directly by the ground stations to the user receivers. Its a completely different signal, carried on a terrestrial frequency.

Re:Old saying

[Jane Q. Public]

That only means we were talking about different things, it doesn't make you right.

But the time the signal gets to your GPS receiver, the position of the satellite will have offset by a small distance, and there are also relativistic effects to be compensated for. Those are the offsets I was referring to.

Re:Old saying

[Jane Q. Public]

A second signal reveals the size of a second sphere, which usually intersects the first sphere along a circle. This constrains the receiver's position to a 1D circle.

... and more to the same effect.

But that's NOT how it works. The GPS signal isn't ONLY a time signal, it also contains the position of the satellite.

The other two satellites ALSO contain position information.

It is therefore possible to still make the same 3D computation, using the RELATIVE time signals of the satellites.

I did oversimplify just a bit for the sake of a general audience. But the fact remains that geometrically, if you have 3 known points and the distance to each of them, you can calculate a 3D point in space.

And in turn you can calculate the distances from the 3 known points by the relative time of arrival of the time signals. I don't think anybody here said anything about having to measure the times directly.

But I want to repeat: we've hashed this all out here on Slashdot before, and several of us found detailed references. I do know how it works.

Re: Old saying

[Jane Q. Public]

Are you absolutely certain that's how GPS works? Wouldn't that require that each GPS receiver have an atomic clock so it can calculate the difference in time between what the signal says and the time at your receiver?

Yes, I am absolutely certain. And no, it wouldn't, because the GPS signal ISN'T "only" a time signal. It has position information for the satellite! You have assumed far too much.

Given 3 points and their positions, you can calculate the RELATIVE distance from the satellites by noting the relative differences in the time signals. So all the information you need to make the basic calculation are there:

You have 3 points with coordinates. You can calculate the distance to each of those points from the known coordinates of the satellites and the relative time DIFFERENCES of the signals. No atomic clock needed. With the time differences, and knowing what C is, you can make a very precise calculation of your position.

I repeat: the only reason you need a 4th signal is to compensate for minor satellite positioning errors and relativistic effects.

Are you absolutely certain that's how triangulation works? Is it possible that you're actually trying to describe trilateration?

If you're going to split stupid semantic hairs, you can fuck off right now. The basic principles are the same, and I don't think anybody else here misunderstood what I was saying.

2. Even if there were no errors or relativistic effects, how could a GPS receiver without an atomic clock find your basic location and elevation using only 3 satellites? Sure, a GPS receiver with an atomic clock would know the sizes of those 3 spheres. But imagine, just for a moment, that GPS receivers don't have atomic clocks. Don't you see that (even with no errors/relativistic effects) you don't know the sizes of those 3 spheres?

I explained this above. Maybe if you'd asked a polite question or two earlier, instead of flying off on this rant based on incorrect assumptions , it could have been explained to you more easily.

Re:Old saying

[Jane Q. Public]

Obviously yes. But the signal you hear from each satellite is offset by an unknown amount (assuming unknown time/position)

No. It's not unknown. You're forgetting something. A couple of things, actually.

First, you know C, the speed of light. Second, you aren't just taking one measurement but many. When the satellite sends a signal it sends a position signal as well as time. By knowing 2 consecutive positions, C, and the differences (including time difference) between the 2 signals, you can calculate the distance pretty precisely... or at least as precisely as the quality of your data allows.

But wait... there's more! You actually have THREE known points, and THREE different sets of time signals. And knowing the positions of the 3 satellites, you can also refine your calculations by using the relative differences between different satellite signals.

So you actually do have 3 known points, and all the information you need to calculate the distances to them. Of course, once again there are small errors and some relativistic effects that make your calculation a bit fuzzier than ideal, which we have already discussed.

Re:Old saying

[Jane Q. Public]

No: basic geometry dictates that, to find a position in three dimensions, you need three measurements of distance.

Yes! Why are you assuming there is no distance information? There is!

and the time by that satellite's clock - but since you have nothing to compare it against, you have no idea how long that signal took to reach you, so you get no information about your position.

This is where you're falling down. Of course you have things to compare it to. For each satellite, you have consecutive signals giving you new coordinates and a new time reference. You can calculate the distance between those two points. Then you can calculate the change in the difference between the timestamp in the signal and its arrival time. This actually gives you very good distance information, although of course it isn't static. (It could not be.)

You can also make comparisons between the satellites. That only gives you relative, rather than absolute, distances, but you can use that together with using your absolute distance measurements to refine your accuracy somewhat.

So yes, you do have distance information. At least 2 ways of measuring it: absolute to each satellite, and relative between them.

Re:Old saying

[Jane Q. Public]

Yes, I know you can do that, I even mentioned it :) But the person I was repying to claimed "3 satellites are sufficient to find your basic location and elevation" (emphasis mine) - i.e. they were claiming you could find the distance from the centre of the Earth, without assuming it.

No. You are finding your distance from the satellites. Not from the center of the Earth. But since the 3-D positions of the satellites are known to a fine degree of accuracy, that's all you need.

And yes, 3 points and 3 distances is all you need to find a point in 3D space. It actually defines 2 points, but as mentioned before one is out in space so it obviously doesn't count. The other one is on the surface of the Earth (or in a plane, or whatever).

You still need to think about probability, because the elevation model only tells you where the ground is - not where you are in relation to it. That said, the asumption "you're probably very close to the surface" is often very good, at least for most people :-)

No. Again, the orbits (and therefore positions) of the GPS satellites are known very precisely. As long as you can receive the signals from them, you could be above the ground, or below the ground, or even at the center of the Earth (at least theoretically), and still get your position and "elevation", even though it may be negative. Probability is not a factor at all, though accuracy certainly is. There are errors that have to be accounted for.

Re:Old saying

[psmears]

Yes, I know you can do that, I even mentioned it :) But the person I was repying to claimed "3 satellites are sufficient to find your basic location and elevation" (emphasis mine) - i.e. they were claiming you could find the distance from the centre of the Earth, without assuming it.

No. You are finding your distance from the satellites. Not from the center of the Earth.

Umm... if you're claiming you can find your elevation, then you can find your distance from the centre of the Earth. It's more or less the same thing :-). I agree you can use the measurements from the satellites though (i.e. you don't need to know any information about your elevation a priori).

But since the 3-D positions of the satellites are known to a fine degree of accuracy, that's all you need.

I agree that the position of each satellite is known, to high accuracy. That's not the issue - the issue is that, if you have a signal from one satellite, that doesn't tell you your distance from that satellite. The signal basically says "I am satellite 7, I am at (position), and the time by my clock is (time)", and that is all your receiver receives. Receiving that signal tells you nothing about your position (well, possibly you can tell which hemisphere you're in from the fact that the satellite is visible at all, but that doesn't narrow things down much!). You only start getting information about your position when you have signals from more than one satellite, because then you can compare the timestamps - the difference in the timestamps gives you information about the difference in the distance from you to the two satellites.

And yes, 3 points and 3 distances is all you need to find a point in 3D space. It actually defines 2 points, but as mentioned before one is out in space so it obviously doesn't count. The other one is on the surface of the Earth (or in a plane, or whatever).

I agree that 3 points and 3 distances is all you need. The trouble is that the signal from 3 satellites only gives you 2 distances (unless, as jfengel mentions, you happen to be carrying round an atomic clock with you - which is generally not practical!).

You still need to think about probability, because the elevation model only tells you where the ground is - not where you are in relation to it. That said, the asumption "you're probably very close to the surface" is often very good, at least for most people :-)

No. Again, the orbits (and therefore positions) of the GPS satellites are known very precisely. As long as you can receive the signals from them, you could be above the ground, or below the ground, or even at the center of the Earth (at least theoretically), and still get your position and "elevation", even though it may be negative. Probability is not a factor at all, though accuracy certainly is. There are errors that have to be accounted for.

I mention probability because, even in the absence of 3 distances to give you a full 3D fix, you can use the fact that, statistically speaking, most people spend most of their time very close to the Earth's surface, to give a good estimate for one of the distances (i.e. estimate "I'm probably at or near ground level"), which then generally gives a pretty good estimate of your horizontal position. This is why even a 2D GPS fix is very useful in practice. But even if you have a signal from 4+ satellites, probability still comes into play: you have to account for radio interference, atmospheric effects and multipath effects, inaccuracies in the receiver's clocks, rounding errors, etc. etc., each of which adds uncertainty to the measurements and calculations and hence to the ultimate position readout.

Re:Old saying

[psmears]

No: basic geometry dictates that, to find a position in three dimensions, you need three measurements of distance.

Yes! Why are you assuming there is no distance information? There is!

What I said was that there is no distance information in the message received from the satellite. Of course you can derive distance information, or else GPS wouldn't work at all :-)

and the time by that satellite's clock - but since you have nothing to compare it against, you have no idea how long that signal took to reach you, so you get no information about your position.

This is where you're falling down. Of course you have things to compare it to. For each satellite, you have consecutive signals giving you new coordinates and a new time reference. You can calculate the distance between those two points. Then you can calculate the change in the difference between the timestamp in the signal and its arrival time. This actually gives you very good distance information, although of course it isn't static. (It could not be.)

Right - but there are two problems with this. One is that, by taking measurements over time, you do indeed get more information - but you also introduce more unknowns, because now you have to take into account the fact that you are likely to be moving - so you can't tell what part of the difference in the satellite signal is due to the satellite's motion, and which is due to yours. The other is that, even if you're guaranteed to be stationary, for your different readings from the same satellite to be useful, the satellite has to have moved a substantial distance, or else the errors in measurement will be relatively large compared to the change in timestamp difference - so you can't do an accurate calculation of your position. (This is why receivers won't give you a position readout even if they have 4 satellites, if those 4 satellites are very close together in the sky.) In practice it takes of the order of hours for the satellite to move sufficiently (which then introduces other problems - the quartz-based clocks in typical GPS receivers are not sufficiently accurate over such long periods.)

You can also make comparisons between the satellites. That only gives you relative, rather than absolute, distances,

Yes - which is exactly what I said :-) But differences only give you N-1 measurements for N satellites.

Re:Old saying

[smallfries]

Indeed the addition of a 4th fix does not constrain the equations, I was thinking of a slightly different positioning system when I wrote that.

The 4th signal is not historically from a ground station: most GPS receivers will generate an estimated position with a low-accuracy warning on 3 fixes, but they expect 4 in order to generate a real estimate. That 4th signal is normally another satellite. I did look briefly for the difference in CEP-50 between 3 fixes and 4, but could not find a source. You have not linked to any previous discussion on this subject, or external references, so if you have numbers on what the real difference between 3 and 4 fixes is then they would be interesting.

Ground stations are used in d-GPS, but not only as an extra point of reference. As an known location they can be used to cancel errors in the satellites estimate of its position.

Re:Old saying

[Anonymous Coward]

... that's NOT how it works. The GPS signal isn't ONLY a time signal, it also contains the position of the satellite. The other two satellites ALSO contain position information.

That's why, as I explained, a GPS receiver with an atomic clock could constrain its position to lie on the 2D surface of a sphere around a single satellite. If the GPS receiver didn't know the satellite's position, it wouldn't know where that sphere was centered.

... the fact remains that geometrically, if you have 3 known points and the distance to each of them, you can calculate a 3D point in space.

Sure, if your GPS receiver has an atomic clock then you have 3 known points and the distance to each of them. But as I explained, that's not true for GPS receivers without atomic clocks.

And in turn you can calculate the distances from the 3 known points by the relative time of arrival of the time signals.

Not unless your GPS receiver has an atomic clock. Otherwise, suppose all three time signals read the same time. In that case, you could be anywhere on a line where every point is equally far away from all three satellites. Note that I'm assuming we know exactly where each satellite is, with no positioning errors. Even in that case, you don't actually know your distance to those GPS receivers unless your GPS receiver has an atomic clock.

I don't think anybody here said anything about having to measure the times directly.

You did, when you were trying to explain "exactly what GPS calculates":

... yes, you do know the size of those spheres. That's exactly what GPS calculates! What GPS satellites send is a TIME signal. The difference in time between what the signal says, and the time at your receiver, is the distance to the satellite, which in turn is the radius of the sphere.

This would be "exactly what GPS calculates" if GPS receivers had built-in atomic clocks. In that case 3 satellites actually would be sufficient to find your basic location and elevation.

But most GPS receivers don't have built-in atomic clocks. Receiving a signal from one satellite doesn't constrain the receiver's position because a receiver without an atomic clock can't directly measure the difference in time between what the signal says and the time at your receiver.

Receiving signals from two satellites does constrain the receiver's position. For instance, if both signals show the same time, the receiver is equally far away from both satellites. This constrains the receiver's position to a 2D plane between the two satellites where every point is equally far away from both satellites.

You have 3 points with coordinates. You can calculate the distance to each of those points from the known coordinates of the satellites and the relative time DIFFERENCES of the signals. No atomic clock needed. With the time differences, and knowing what C is, you can make a very precise calculation of your position.

No. If a third signal also shows the same time, the receiver's position is only constrained to lie on a 1D line where every point is equally far away from all three satellites. (As this AC notes, in general, this solution region is a 1D hyperbola.)

Note that three satellites aren't sufficient to find your basic location and elevation for GPS receivers without atomic clocks.

Re: Old saying

[skids]

This argument is as spurious as the frames of reference and definitions needed to support it are extreme. Also the orginal post didn't say there were no flaws with "simultaneity", just that calling it "wrong" was "wrong." It's well known that any causal relationship is preserved from any frame of reference, and furthermore "events" on the macro scale don't happen at a discrete moment in time. If you have a balloon with a chipmunk suspended inside it, and you release the chipmunk so it falls and pops the balloon, it can be said with perfect accuracy that the baloon popped simultaneuously with the chipmunk falling, assuming the balloon was not on a table and the chipmunk continued to fall past the edge of the balloon.

The arguments against "simultaneity" require the precise scientific definition of the term, which should be confined to academic papers.

Do not try the above experiment at home.

The general gist of the matter is it would be technically possible to "synchronize" these clocks in the sense that with enough external data to accurately determine the frames of reference involved, we could know the time on one of the clocks as observed by an individual next to that clock from the value of another a clock next to us, even if that individual could never tell us the time on the clock because by the time any communication reached us, it would be stale. This despite the fact that the clocks are actually running at different rates on most frames of reference, not just different offsets. If that was done bilaterally, and both calculations yielded each other's input value, both parties could agree that, in retrospect, they read the clocks at the same "time".

An external observer to both clocks might see the readings happen at different times, but if they have any intellect they have to account for their perspective not being the only valid one.

It would also be possible to construct an average aggregate clock out of a group of these, the question is merely the utility of such a clock, since instead of a "timezone" you'd have a "framezone" where you'd have both an offset and an ongoing drift, not to mention the parameters of that adjustment would not be constant because phenomina like shifting planetary crust don't play nice.

We would not be able to measure the speed of light without such systems, so they obviously play an important role.

Re:Old saying

[lsatenstein]

If the watches are stopped, they are each right twice a day.

Re:Old saying

[Anonymous Coward]

As others have said you only need 3 to give you two points. One is in space, the other is in the ground. Ignore the one in space ...

Re:Old saying

[dataspel]

Give a man a fish, and he will eat for a day. Teach a man to fish, and he will sit at the wharf all day drinking beer and fishing.

Re: Old saying

[khayman80]

You have 3 points with coordinates. You can calculate the distance to each of those points from the known coordinates of the satellites and the relative time DIFFERENCES of the signals. No atomic clock needed. With the time differences, and knowing what C is, you can make a very precise calculation of your position. I repeat: the only reason you need a 4th signal is to compensate for minor satellite positioning errors and relativistic effects.

No. Even without satellite positioning errors or relativistic effects, GPS receivers without atomic clocks still need 4 satellite signals to solve for location and elevation. Here's why.

At time t, your GPS receiver is at unknown coordinates x, y, z when it receives a signal with timestamp t1 from a satellite at precisely known coordinates x1, y1, z1.

(x - x1)^2 + (y - y1)^2 + (z - z1)^2 = (c*(t - t1))^2

If you know time "t" because your GPS receiver has an atomic clock, this equation only has 3 unknowns. In that case, an additional two equations representing signals from two other satellites would be sufficient to find your basic location and elevation:

(x - x2)^2 + (y - y2)^2 + (z - z2)^2 = (c*(t - t2))^2

(x - x3)^2 + (y - y3)^2 + (z - z3)^2 = (c*(t - t3))^2

If you know time "t" because your GPS receiver has an atomic clock, these 3 equations with 3 unknowns can be solved for your position x, y, z.

But if your GPS receiver doesn't have an atomic clock, you don't know time "t" to anywhere near the required precision. So you actually have 4 unknowns, which means you need another equation:

(x - x4)^2 + (y - y4)^2 + (z - z4)^2 = (c*(t - t4))^2

That's why GPS receivers without atomic clocks require 4 satellite locks.

Re:Old saying

[Jane Q. Public]

That's why, as I explained, a GPS receiver with an atomic clock could constrain its position to lie on the 2D surface of a sphere around a single satellite. If the GPS receiver didn't know the satellite's position, it wouldn't know where that sphere was centered.

Holy crap. Still with this, really?

Do you need me to draw you a DIAGRAM of how the geometry works? Then maybe it will sink in.

Re:Old saying

[khayman80]

Holy crap. Still with this, really? Do you need me to draw you a DIAGRAM of how the geometry works? Then maybe it will sink in.

Equations would work better, as I've explained:

You have 3 points with coordinates. You can calculate the distance to each of those points from the known coordinates of the satellites and the relative time DIFFERENCES of the signals. No atomic clock needed. With the time differences, and knowing what C is, you can make a very precise calculation of your position. I repeat: the only reason you need a 4th signal is to compensate for minor satellite positioning errors and relativistic effects.

No. Even without satellite positioning errors or relativistic effects, GPS receivers without atomic clocks still need 4 satellite signals to solve for location and elevation. Here's why.

At time t, your GPS receiver is at unknown coordinates x, y, z when it receives a signal with timestamp t1 from a satellite at precisely known coordinates x1, y1, z1.

(x - x1)^2 + (y - y1)^2 + (z - z1)^2 = (c*(t - t1))^2

If you know time "t" because your GPS receiver has an atomic clock, this equation only has 3 unknowns. In that case, an additional two equations representing signals from two other satellites would be sufficient to find your basic location and elevation:

(x - x2)^2 + (y - y2)^2 + (z - z2)^2 = (c*(t - t2))^2

(x - x3)^2 + (y - y3)^2 + (z - z3)^2 = (c*(t - t3))^2

If you know time "t" because your GPS receiver has an atomic clock, these 3 equations with 3 unknowns can be solved for your position x, y, z.

But if your GPS receiver doesn't have an atomic clock, you don't know time "t" to anywhere near the required precision. So you actually have 4 unknowns, which means you need another equation:

(x - x4)^2 + (y - y4)^2 + (z - z4)^2 = (c*(t - t4))^2

That's why GPS receivers without atomic clocks require 4 satellite locks.

Re:Old saying

[Jane Q. Public]

Your math doesn't mean squat because it's based on invalid assumptions, as I explained earlier.

There is more information available to your GPS receiver than you are accounting for.

But since you seem so resistant to the very IDEA that you could be wrong, I'll just leave you to your preconceptions. It isn't really worth an hour of my time to draw a decent diagram.

Re:Old saying

[khayman80]

Your math doesn't mean squat because it's based on invalid assumptions, as I explained earlier. There is more information available to your GPS receiver than you are accounting for. But since you seem so resistant to the very IDEA that you could be wrong, I'll just leave you to your preconceptions. It isn't really worth an hour of my time to draw a decent diagram.

An hour? Just write down the three trilateration equations from three satellites that are supposedly sufficient to find your basic location and elevation even if your GPS receiver doesn't have an atomic clock. That would only take a few seconds.

At time t, your GPS receiver is at unknown coordinates x, y, z when it receives a signal with timestamp t1 from a satellite at precisely known coordinates x1, y1, z1.

(x - x1)^2 + (y - y1)^2 + (z - z1)^2 = (c*(t - t1))^2

If you know time "t" because your GPS receiver has an atomic clock, this equation only has 3 unknowns. In that case, an additional two equations representing signals from two other satellites would be sufficient to find your basic location and elevation:

(x - x2)^2 + (y - y2)^2 + (z - z2)^2 = (c*(t - t2))^2

(x - x3)^2 + (y - y3)^2 + (z - z3)^2 = (c*(t - t3))^2

If you know time "t" because your GPS receiver has an atomic clock, these 3 equations with 3 unknowns can be solved for your position x, y, z.

If Jane could write down equations showing that three satellites are sufficient to find your basic location and elevation even if your GPS receiver doesn't have an atomic clock, Jane would've done that years ago. Jane can't, because 3 equations aren't sufficient to solve for 4 unknowns.

But I want to repeat: we've hashed this all out here on Slashdot before, and several of us found detailed references. I do know how it works.

Translation: Jane's gone on a similar rant before, except that last time Jane didn't blame the need for 4 satellites on positioning errors and relativistic effects. Last time, Jane asked: "why do the military only require 3 satellite locks? Eh? Answer me that, you fucking genius. ... you are a moron. ..."

The military would only require 3 satellite locks if their GPS receivers had atomic clocks, which would be ridiculously expensive, bulky, and way too fragile for military use.

Re:Old saying

[RockDoctor]

Same argument, different formulation : with one measurement, you have a datum ; with two measurements you have a disagreement ; with three, you have statistics.

And as I pointed out about 5 minutes ago in a different thread, GPS navigation isn't the be-all and end-all of navigation. It doesn't work underground. It doesn't work in buildings. It doesn't work if you've lost electrical power (which is one of the first things to go when trouble happens). And it depends on some foreigners not switching it off. Some of those problems can be addressed (build another GNS system ; carry spare batteries) but for many, knowing how to work without GPS (or any other GNS) is a damned good idea.

well I thought it'd never happen

[Anonymous Coward]

But I guess it was time it did

Can it be used as an accelerometer?

[Sla$hPot]

If so, could a combination of clocks be used as the ultimate offline-GPS unit?

Re:Can it be used as an accelerometer?

[Em Adespoton]

that was my first thought -- these things, if they could be manufactured to be affordable, would be great for relative positioning -- although I was thinking seismometers, not GPS. If you had a network of them, you could instantly (well,at the speed of light) map out any changes in their positioning.

Which reminds me; as my head is moving faster than my feet relative to the centre of the earth, they age at different rates. Same principle at work here. But it means I should spend more time standing on my head :)

Re:Can it be used as an accelerometer?

[milkmage]

affordable? sure. and the new model comes in a room just under the size of your house.. great for taking on camping trips .. as long as you have a big ass trailer.

Re:Can it be used as an accelerometer?

[Anonymous Coward]

would be great for relative positioning

Absolutely, just what one needs to realign one's TARDIS.

Re:Can it be used as an accelerometer?

[Anonymous Coward]

No, unless you can compare the accelerated clock's time with a reference clock. At which point it's not offline.

Re:Can it be used as an accelerometer?

[Em Adespoton]

Good idea; that would solve the size and energy issues too!

of course, we already knew that...

[turkeydance]

like, 0.0000000000000000003 seconds ago.

First! Oh wait.

[Anonymous Coward]

My atomic watch was out :(

Timey Wimey Thingey

[Anonymous Coward]

No wonder Time Lords are batty

They finally invented a clock so accurate...

[unitron]

...that it can't be used to tell time reliably.

Re:They finally invented a clock so accurate...

[Anonymous Coward]

...that it can't be used to tell time reliably.

Hilarious, You win the internet. Thanks @unitron.

Re:They finally invented a clock so accurate...

[unitron]

...that it can't be used to tell time reliably.

Hilarious, You win the internet. Thanks @unitron.

Thanks, one more and I'll have the complete set!

Re:They finally invented a clock so accurate...

[Marginal Coward]

`Two femtoseconds wrong!' sighed the Hatter. `I told you butter wouldn't suit the works!' he added looking angrily at the March Hare.

`It was the best butter,' the March Hare meekly replied.

Re:They finally invented a clock so accurate...

[Marginal Coward]

Sorry...I just realized that 'butter' should have become 'strontium'. (Still, is strontium really funnier than butter?)

Re:They finally invented a clock so accurate...

[Anonymous Coward]

To a Dutch person like myself, strontium is the most hilarious of the elements.

Problem...

[Lab Rat Jason]

That sounds like a 0th world problem...

Re:Problem...

[Anonymous Coward]

"Tiny shifts in the earth's crust can throw it off"
Sounds like an awesome detector for tiny shifts in earths crust

Clositer Bells at the Center of the Universe

[Anonymous Coward]

Somewhere.. at the Center of Space and Time.. a Big bang has occurred.. only there is so Much Gravity.. the Explosion hasn't reached us yet.. Time is nearly standing still.

The Tardis Cloisture Bells are ringing the Alarm and we're still marveling at this thing we call Time.. pervasive throughout Time and Space.. we get to enjoy it until the end of Time.. when the Big Bang actually catches up to us.. tho.. of course it will take an Eternity.

Re:Clositer Bells at the Center of the Universe

[Anonymous Coward]

The shockwave threw us forward Beyond the Explosion Wave, inverting the Contents of Time and Space.. so that what we see as the Universe is actually what was inside the Big Bang.. turned inside out.. thats why Space appears Vast.. and Time unlimited.. the Balloon turned inside Out.

Only the Big bang anchors the beginning and the end.. its a manifold with only one fixed point in space time.

The Surface curves both inside and outside back to the same point in Space Time.

Re:Clositer Bells at the Center of the Universe

[Anonymous Coward]

"cloister". http://en.wikipedia.org/wiki/C... http://en.wikipedia.org/wiki/L...

That's quite a warranty!

[Ichijo]

able to keep perfect time for five billion years

Re:That's quite a warranty!

[Pope Hagbard]

Not warranted for war, plagues, pestilence, or the power going out for an extended period.

Re:That's quite a warranty!

[PolygamousRanchKid]

Yes, but you probably need to change the battery every few million years or so. That's where they will make their money . . . kinda sorta like printer cartridges or iPhone batteries.

You get the atomic clock cheap, but those extras cost you!

Re:That's quite a warranty!

[Anonymous Coward]

For certain definitions of time, anyway. It's all relative.

Re:That's quite a warranty!

[Arancaytar]

But for one simple payment or $100,000, you can pre-purchase your batteries for the next 500 billion years!

Re:That's quite a warranty!

[Anonymous Coward]

I warned you! I told you about Strontium, dog!

research grade tinfoil

[Anonymous Coward]

gonna make a great hat...

Hmm, says here:

[fustakrakich]

Right now, on the top of Mount Everest, time is passing just a little bit faster than it is in Death Valley. That's because speed at which time passes depends on the strength of gravity. Einstein himself discovered this dependence as part of his theory of relativity, and it is a very real effect.

And here I was thinking that because of the earth's rotation, The top of Mount Everest is moving through space just a little bit faster than a point in Death Valley, and that's what would "slow down" time. Now if the earth has "lumpy" gravity, would moving the clock to a different spot on the floor would also change the rate of time? Great way to map the gravity then, isn't it?

Are space and time really separate?

Re:Hmm, says here:

[fustakrakich]

Great way to map the gravity then, isn't it?

Oh shit! just read further down the article, never mind...

Re:Hmm, says here:

[marcansoft]

Moving faster causes time to slow down (special relativity), but so does beeing in a deeper gravitational well (general relativity). As you move away from the Earth, both effects have opposite (but not equal) magnitude. I'm too lazy to do the math right now, but here's a walkthrough (for the case of GPS satellites, but the same equations hold; you just need to know the distance from Earth's center to Death Valley and to Mount Everest, and work out their linear velocity from that).

Re:Hmm, says here:

[Pax681]

"slow down" time. Now if the earth has "Lumpy" GRAVY,

FTFY.. just needed some Zappa magic :P

Re:Hmm, says here:

[Anonymous Coward]

Moving faster causes time to slow down (special relativity), but so does beeing in a deeper gravitational well (general relativity).

If being in a gravitational field causes time to slow down then why doesn't being in an electromagnetic field also cause time to slow down?

And since a gravitational field can affect an electromagnetic field (e.g. can cause electromagnetic waves to bend) then can an electromagnetic field affect a gravitational field (e.g. cause waves in the gravitational field to bend)?

Re:Hmm, says here:

[Bengie]

Gravity does not cause anything in space to bend, relative to itself. Everything thinks it's still going on a strait path or sitting still. Gravity is the warping of space-time, which only warps relative to itself.

Re:Hmm, says here:

[Anonymous Coward]

Moving faster causes time to slow down (special relativity), but so does beeing in a deeper gravitational well (general relativity). As you move away from the Earth, both effects have opposite (but not equal) magnitude. I'm too lazy to do the math right now ....

Thanks Fermat.

Re:Hmm, says here:

[jouassou]

In general relativity, gravitation is not modeled as a direct force between massive objects. Instead, any form of energy density (mass according to E=mc^2, electromagnetic fields, and so on) causes spacetime to curve, and this curvature of spacetime then alters the motion of particles through spacetime. I've always liked the summary "energy tells spacetime how to bend, and spacetime tells matter how to move".

So yes, it is true that electromagnetic fields also act as a source of gravity. However, you'll need some really crazy field configurations before that effect starts becoming comparable to the gravitation from stars and planets though. For a very rough estimate of the sizes involved, you can try setting the volumetric energy density of an electric field (vacuum permittivity)*(electric field)^2/2 equal to the mean energy density (earth mass)c^2/(earth volume) of the earth, which leads to the result 10^16 V/m for the electric field. This is roughly 10^10 times the electric breakdown voltage of air at standard temperature and pressure...

Re:Hmm, says here:

[Anonymous Coward]

If being in a gravitational field causes time to slow down then why doesn't being in an electromagnetic field also cause time to slow down?

In some sense, because that is the way the universe works, and just because they both have "field" in their name they don't do everything the same way.

And since a gravitational field can affect an electromagnetic field (e.g. can cause electromagnetic waves to bend) then can an electromagnetic field affect a gravitational field (e.g. cause waves in the gravitational field to bend)?

Gravitational field is just create from mass-energy density, whether that is from things like atoms or electromagnetic energy. The impact on gravity would be pretty much the same as matter with the same energy density.

Re:Hmm, says here:

[Anonymous Coward]

...this curvature of spacetime then alters the motion of particles through spacetime. I've always liked the summary "energy tells spacetime how to bend, and spacetime tells matter how to move".

But if we can say that a particle in a gravitational field is accelerating because the gravitational field messed with its notions of space and time then why can't we say that a charged particle in an electromagnetic field is accelerating because the electromagnetic field messed with the charged particle's notions of space and time. Thanks to relativity, what we observe already depends on our velocity and acceleration (and whether we're being messed with by a gravitational field). So why not also say that what a particle observes depends on the sum total of whatever fields are messing with it? I mean, sure a charged particle in an electromagnetic field is going to observe something different than a neutral particle - but if what they are observing already depends on all that other stuff then maybe that's not such a big problem.

Re:Hmm, says here:

[Anonymous Coward]

People have tried to come up with a geometric interpretation of electromagnetic fields. The Kaluza-Klein theory can describe electromagnetism with geometry similar to how GR treats gravity, but it requires five dimensions. And to make it consistent with quantum mechanics requires certain properties of those higher dimensions, similar to how modern string theories discuss how there can be more dimensions then observed on the human scale. So far, no observations have shown any of the extra properties of space predicted by KK theory, or other similar alternatives.

Re:Hmm, says here:

[Anonymous Coward]

"energy tells spacetime how to bend, and spacetime tells matter how to move".

oh god just say it: "and matter tells energy how to flow" ... mmmmm

"More precise than any clock before"

[Anonymous Coward]

If time is a human construct and two identical clocks can't remain synchronized with each other, can they really be said to be precise at all?

Re:"More precise than any clock before"

[NoNonAlphaCharsHere]

Shit, you're right. We should just forget this whole physics thing and go back to building henges.

Re:"More precise than any clock before"

[Anonymous Coward]

At least henges still work when the power goes out.

Re:"More precise than any clock before"

[khellendros1984]

Precision is basically the number of significant values that taking a measurement yields. Accuracy is how close to the true value the measurement is. The clocks are both precise and accurate, to the degree that things that we don't normally need to consider (velocity that the clock is moving, the strength of gravity acting on the clock, etc) can be measured. The "problem" is that time flows at different speeds under different conditions, and the clocks can't remain synchronized with each other because reality doesn't actually remain in synchronicity.

Also, time isn't a human construct any more than the other dimensions are. Measurement of time is a human construct, but it's also designed to reflect reality.

Re:"More precise than any clock before"

[blueg3]

If time is a human construct...

It's not.

...[if] two identical clocks can't remain synchronized with each other, can they really be said to be precise at all?

Yes, because the fact that they can't remain synchronized is a result of the actual behavior of time and space. Both clocks are being perfectly accurate (and precise) -- so accurate and precise that they are measuring effects that would make *any* two clocks drift apart.

So keep it perfectly balanced... in outer space

[Anonymous Coward]

At a Lagrange point perhaps

Direct gravity sensor

[Anonymous Coward]

Could it be used as a direct, precise gravity sensor ?

...and also not true

[Roger W Moore]

It can't keep 'perfect time' for any length of time at all. Perfect means zero error. This might be an astoundingly accurate clock but that does not make it perfect.

Re:...and also not true

[fahrbot-bot]

It can't keep 'perfect time' for any length of time at all. Perfect means zero error. This might be an astoundingly accurate clock but that does not make it perfect.

Time is relative to the imperfect Universe in which it and the clock exist.

Re:...and also not true

[Pope Hagbard]

For these purposes "perfect" is probably something like "accurate to within about a second over 5 billion years".

Re:...and also not true

[Oligonicella]

Only if you're concerned with time at the clock's precise location. Otherwise, it's useless. Even in space there's gravity, so Ye might not be correct at all.

Re:...and also not true

[Bengie]

Since "perfect" is impossible, making it a useless word, lets just redefine it to something useful, like the colloquial usage of "close enough with respect to the current standard margin of error.

Re:...and also not true

[Trogre]

Dammit where are my mod points? You just shot down a whole lot of pedants with that comment.

Re:...and also not true

[Anonymous Coward]

For all intents and purposes, it is perfect.

You will not be able to detect the clock losing time because you have no other instruments capable of detecting it, therefore you cannot prove imperically that it is imperfect.

Re:...and also not true

[BlackPignouf]

A mathematician and an engineer are sitting at a table drinking when a very beautiful woman walks in and sits down at the bar.

The mathematician sighs. "I'd like to talk to her, but first I have to cover half the distance between where we are and where she is, then half of the distance that remains, then half of that distance, and so on. The series is infinite. There'll always be some finite distance between us."

The engineer gets up and starts walking. "Ah, well, I figure I can get close enough for all practical purposes."

Re:...and also not true

[Anonymous Coward]

Perfect does not mean zero error. Reality itself does not have zero error, as we know from Heisenberg's uncertainty relations. So perfect really means an error bound by the limits of physics.

In this case, Heisenberg limits temporal accuracy to energy. I think the clock is cooled to yoctoJoule levels (1E-24) which puts the temporal accuracy limit at the picosecond scale (per molecule). Now statistically these picosecond errors mostly cancel, which explains why the clock performs better than the individual atoms. Still, it shows we're really pushing the limits of physics here. We're certainly getting close to perfect

Re:...and also not true

[Roger W Moore]

...with respect to the current standard margin of error

...and there is your problem. The margin of error depends on what you are doing hence your redefinition of 'perfect' is utterly useless since you need to specify your margin of error...in which case you might as well just skip calling it perfect. Despite you assertion to the contrary even though perfect is not obtainable it is still a useful concept to compare reality against e.g. this clock is closer to perfect time keeping than its predecessors.

Re:...and also not true

[Roger W Moore]

So perfect really means an error bound by the limits of physics.

But since those limits are energy dependent a high energy process could actually have a better time resolution than this clock can provide...hence it is not perfect.

Re:...and also not true

[Roger W Moore]

There is another instrument capable of detecting it: itself. You make the same measurement multiple times and see what the difference is each time you do it.

Re:...and also not true

[JigJag]

"Perfect means zero error"

Years ago, I used to think like you, but now I disagree with this statement. For me, perfect means meeting the requirements. Zero error is a requirement but not a reasonable one. My life got much more pleasant when I realized I should aim for meeting reasonable requirements instead of an elusive zero error target.

Re:...and also not true

[Anonymous Coward]

Um, "perfect" refers to the platonic ideal of zero error. You can't even define a "margin of error" without reference to that platonic ideal. So let's not redefine "perfect" just because you're too stupid to see you used the concept yourself in your post.

Re:...and also not true

[Anonymous Coward]

Or you could just learn that things don't need to be perfect to be adequate, instead of redefining words.

Re:...and also not true

[nephilimsd]

By the same logic, infinite is impossible and therefore useless. So we should just redefine it to some arbitrarily large number that I have a hard time conceptualizing. Let's call it roughly 10 duodectrillion. /sarcasm

Just because something is impossible doesn't make the concept of that thing less meaningful. Perfection, in this case, is just a model of how things would work in an idealized universe. It becomes useful as a comparative term. As clocks approach perfection, relativity becomes a complicating factor in further refinement. That doesn't mean we need to redefine perfect for this context.

Re:...and also not true

[Anonymous Coward]

. So we should just redefine it to some arbitrarily large number that I have a hard time conceptualizing.

Kind of a bad example since a lot of fields of math, infinity is just a place holder for a limit process showing something converges at larger and larger numbers, specifically to avoid talking about or defining an infinite object. Plus there are whole schools of thought within mathematics about avoiding such things that can't actually be reached or constructed.

Re: ...and also not true

[Anonymous Coward]

We already have adequate clocks. That does not mean perfect means zero error. Perfect means the lowest error achievable in this universe. Otherwise how are you going to measure the imperfection?

Five Billion Years?

[lazarus]

"...able to keep perfect time for five billion years."

If they were able to create a device that could actually keep the time for five billion years, perfect or not, I would be pretty damn impressed.

Re:Five Billion Years?

[Trax3001BBS]

"...able to keep perfect time for five billion years."

If they were able to create a device that could actually keep the time for five billion years, perfect or not, I would be pretty damn impressed.

My first thought as well, would take a hell of a Radioisotope to generate power for that long.
Wars and such would disrupt it's power after some time if not on an independent power supply.

But in the end due to the relativistic differences (Earth quakes and such); of anyone looking at the clock for the time it was started or past would make it useless - unless you did the math.

Re:Five Billion Years?

[Anonymous Coward]

...and you are not impressed, therefore they have not created such a device?

Misleading Title

[arobatino]

New Atomic Clock Reaches the Boundaries of Timekeeping

On Earth, maybe. It's not a theoretical limit - the article itself points out that you can put the clocks in space.

Ye suspects the only way we will be able to keep time in the future is to send these new clocks into space. Far from the earth's surface, the clocks would be better able to stay in synch, and perhaps our unified sense of time could be preserved.

Re:Misleading Title

[Anonymous Coward]

On Earth, maybe. It's not a theoretical limit - the article itself points out that you can put the clocks in space.

Ye suspects the only way we will be able to keep time in the future is to send these new clocks into space. Far from the earth's surface, the clocks would be better able to stay in synch, and perhaps our unified sense of time could be preserved.

So what you are saying, is that we need to put a clock between the stars. Perhaps we can call the time from that clock "star date."

Re:Misleading Title

[willy_me]

Space is about the only place such clocks would be of any use. I could see them being used to provide GPS like localization services for any craft designed to leave earth's orbit. For it to work you require synchronized clocks. But, unlike GPS, there is no way to perform such a synchronization. You end up having to rely on the accuracy of the two clocks.

Re:Misleading Title

[TwentyCharsIsNotEnou]

Space is about the only place such clocks would be of any use.

Damn, that's only 99.99...% of the universe!

Re:Misleading Title

[Anonymous Coward]

Nice one on the clocks but we don't really need them for time. What we do need is a very highly sensitive gravity detector though. Please offer them to the right department...

Re:Misleading Title

[cellocgw]

Yeah, but, ... if the clocks have to be up in space to be fully accurate, etc., What is the meaning of the word "today" in the sentence "You will not go to space today" ?
[joke, dammit!!!]

Re:Misleading Title

[grumling]

Pulsars are precision references that could easily be used on a spacecraft with a suitable radio:
http://www.itu.int/pub/R-REP-R...

I'm not quite sure, but it seems like this could..

[Anonymous Coward]

somehow be used for some type of unbreakable cryptography....

either that or it's another case of a solution looking for a problem to solve - and not doing a very good job of it..

But...

[Greyfox]

Would they actually be able to detect the change in the flow of the time with just one clock, or would they need to have a reference clock somewhere and measure another clock relative to it? And if so, where do you keep the reference? Where in the universe is it the "correct" time?

Re:But...

[Anonymous Coward]

Where in the universe is it the "correct" time?

That's like asking, "Where in the universe is the "correct" voltage?" The answer is: whichever set of points you happen to be referring to.

Re:But...

[Greyfox]

Well, yeah, I was being vague there. At some point we decide that somewhere in the universe is where the reference time should be measured. But if we put it in some lumpy gravity well, it'd probably lead to interstellar strife in a couple thousand years. Really, anywhere in the solar system is probably "Bad". Too many things distorting the space-time. I suppose you could put a few clocks around and average them. I think that's what they do with the current ones.

Re:But...

[Altrag]

Where in the universe is it the "correct" time?

Wherever you decide it should be. The universe doesn't have any special reference frame so you just make one up. Similar to how somebody just arbitrarily picked a line of longitude to be GMT+0 back when they were figuring out time zones.

Third option

[Anonymous Coward]

Or you spend thirty seconds on Wikipedia looking up the applications of atomic clocks and see that they're critical for GPS and the Internet.

What if aliens drop in,

[p51d007]

Tell everyone "HEY! your clock is off .03 seconds"...the scientist's heads would explode. ;)

what's the up-time?

[volvox_voxel]

..This looks to be a pretty complicated beast that's built onto a table top and looks very much like a graduate research lab.. I wonder what the up time is?.. Mounts can drift with temperature, the bench does not look sealed, there is the potential for dust and contamination.. The laser power can fluctuate every so slightly and are probably run in optical-power mode.. The lasers can't be constantly up, etc. ..I used to work at a laser company that converted a bench-top tunable femtosecond laser with a lot of knobs that took a graduate student to run, and made it into an OEM product that was controller by a computer. It's hard to make commercial products out of some systems because it's hard to make it reliable (like femtosecond amplifiers).. I'm sure this thing requires a lot of babysitting. I wonder how long the measurement can stay stable?

Keep perfect time for five billion years

[Anonymous Coward]

Cool, where do I plug in the 9V cell for battery backup during black outs?

This Clock is Definitive!

[Irate Engineer]

It's reality that is frequently inaccurate.

Better than cesium

[manu0601]

Right now, atomic clocks use cesium. Why is strontium better?

Re:Better than cesium

[Anonymous Coward]

The limiting factor of atomic clocks isn't the element used. Strontium just has a faster resonant frequency. AFAIK, you do some science magic to these elements, put them in a cloud, and they will emit light at a very specific frequency, based on the structure of the atom itself. And the elements that would work in a clock, and the corresponding frequencies, have been known for awhile.

So building a clock is a matter of building a sensor, etc, that can accurately detect that stream of light. Cesium is used because that is the fastest modern technology supports. At least till this clock came along.

Re:Better than cesium

[Anonymous Coward]

Right now, atomic clocks use cesium. Why is strontium better?

Strontium resonates at a much higher frequency (optical frequencies) than cesium (microwave frequencies), thus providing that much more accuracy.

Re:Better than cesium

[EmagGeek]

I think the word you're looking for is "resolution," not "accuracy."

Re:Better than cesium

[akozakie]

More interesting: so, is it time to change the SI definition of a second again, switching to strontium? It's still defined with cesium, right?

Setting the Clock?

[wisnoskij]

How do you originally set the clock? If this is the first time you will have such an accurate measurement of time, then how do you know what time it is so you can set the clock?

Re:Setting the Clock?

[kaiser423]

You just determine your own new epoch :) you're the only one that accurate to begin with, so make the magic number yourself. Obviously you keep it accurate with respect to other clocks, but you're now setting the specific epoch of that extra precision. Yes, time is relative -- you just need to have an agreement on it.

Re:Setting the Clock?

[jpellino]

Simple. Call (860) JAckson-48123. You even get the temperature.

Old news IEEE Spectrum

[Anonymous Coward]

This is old news. It was listed in IEEE Spectrum over a month ago.

Re:Old news IEEE Spectrum

[Anonymous Coward]

This is old news. It was listed in IEEE Spectrum over a month ago.

That's ok, my subscription lapsed.

Re:Old news IEEE Spectrum

[Anonymous Coward]

Over a month ago is close enough for practical purposes. I suppose you want us to use atomic clocks to measure the timeliness of news?

Old saying

[rekoil]

That feeds into best practice for configuring NTP clients - configure one upstream source, or at least three. Never two.

But

[rossdee]

They still have to change it every 6 months to account for daylight saving or the reverse.

Better than cesium

[Anonymous Coward]

higher base frequency, so you can more accurately slice the second.

Oh no!

[Anonymous Coward]

Better get some monks on this, stat!

Maybe they've made a camera...

[Anonymous Coward]

If it's so accurate that it can measure distortions caused by gravity, then maybe what they've actually made is the first pixel in a camera that could one day take pictures using gravity instead of light.

Really?

[perryizgr8]

The world's current time is coordinated between atomic clocks all over the planet. But that can't happen with the new one.

However precise the clock is, we can still use it to coordinate time all over the earth. Just use the same number of significant digits we use today. Nobody is forcing you to consider ALL the available digits of precision.

4-D Time Cube

[Sir Foxx]

Pretty sure the 4-D Time Cube solves all of this.

Discworld

[dywolf]

http://discworld.wikia.com/wik...

Whats the big deal?

[Anonymous Coward]

If this thing is so accurate what's the big deal? Just calibrate them to within a few femtoseconds of each other and then have them only display time into the nanosecond. If they have the accuracy they claim they should keep perfect time with each other for a least a few hundred years.

Re:Whats the big deal?

[Anonymous Coward]

Are you so dumb you think these things are used as "wall clocks" displaying the current time?

Re:Whats the big deal?

[Anonymous Coward]

Where do you live that wall clocks are calibrated to the femtosecond? Even getting into the "displayed" time a nanosecond is one billionth of a second, more than accurate enough for most atomic clock applications. There is such thing as too much accuracy, I work in mapping and while high resolution datasets are nice they also are exponentially more difficult to deal with as their resolution increases. A 40' resolution LiDAR coverage over a few hundred square miles can have some basic tasks run on it in a few minutes, a dataset in the 12' resolution covering the same area takes hours to run and they are now coming out with sub foot resolutions for 3 dimensional photogrammetric LiDAR which will probably need entirely new ways of storing, retrieving & utilizing the data as even current two dimensional datasets can run into the hundreds of Gigabytes for under a thousand square miles.

Re:Whats the big deal?

[Anonymous Coward]

Wait till we get maps down to the molecular level needed for bio-certified matter-energy transporters.

Answer and a quote.

[B5_geek]

Easy answer, build N+1 of them and use the 'average' value of time that they generate.

One of my favourite quotes applies here:

"When you have a clock you always know what time it is. When you have two you are never quite sure." - Mark Twain.

Re:Answer and a quote.

[Anonymous Coward]

http://en.wikipedia.org/wiki/S...

Segal's law is an adage that states:
"A man with a watch knows what time it is. A man with two watches is never sure."

Gravity

[Triklyn]

I find immense beauty in the fact that they set out to make as perfect a tracker of time they could. And end up creating an improved gravity detector when they ran into a wall. :) tell me again, that basic science doesn't deserve funds.

Incredibly precise time

[haapi]

The Doctor should be arriving any time, so to speak.

Clocks that won't keep the same time?

[arfonrg]

Sounds like a perfect match for Daylight Savings Time..

my old clocks drift

[Anonymous Coward]

Thanks for posting the article.

kinda off topic but my old quarts clock drift a few minutes every two weeks. The same thing happens with my old GSM flip phone. My Virgin Mobile USA smartphone automatically corrects the time when I turn the phone on.

A basic need, I guess...

[putzin]

Does this new clock solve a real problem?

What's it all Mean?

[Anonymous Coward]

Any day now you guys will be telling us that we can never know the time because to check the time is to change it.

Setting the clock

[Anonymous Coward]

So how do they set the clock to begin with?

If all of the Atomic clocks on earth, stopped working, how would a brand new one get set?

No you can't

[Anonymous Coward]

Imagine three points in space, on a line, each one light-hour apart. Call them A, B and C.

At B, the middle point, someone holds up a sign saying "it's 2 p.m. here!" exactly 2 p.m. local time. A and C see that precisely one hour later, and conclude that it must now be 3 p.m. at B and set their clocks at that time also. Now all three points are at the same local time, right?

Well, no, because they are now just in B reference frame. Between A and C is 2 hours worth of time, yet both clocks are giving the same time (as seen from A).

When A holds up a sign saying "it's 4 p.m. now!", one hour later B would see that, check their local clock, add one hour, and find A is correct. One hour later still, C would see the sign and think A is wrong, as it is clearly not 4 p.m. plus 2 hours, in C's local time.

TL;DR: there is no such thing as an independent frame of reference, true simultineity does not exist.

Re:No you can't

[Altrag]

Well, no, because they are now just in B reference frame.

Yes. You defined B as the universal reference time.

One hour later still, C would see the sign and think A is wrong, as it is clearly not 4 p.m. plus 2 hours, in C's local time.

Except presumably C would be smart enough to know that A is not in C's local time and would be able to say to themselves "Yep, it was 4pm in A's local time when A said it was 4pm."

Remember, you wouldn't have a "simple" transformation like saying C = B+1 as we do with timezones on Earth. Your transformation would be more along the lines of "C = L*B" for some Lorentz transformation L (or whatever appropriate equivalent if we need to involve full on GR.) And in that case, "C = L*L*A" would be the appropriate double transformation, not "C = 2*L*A".

Translation for the few that don't speak Ducth

[Anonymous Coward]

Perhaps the element should be renamed to defecatium, it sounds more classy than shittium (which strontium translates to in Dutch).

Poorly formulated statement

[Anonymous Coward]

Academic point maybe but "able to keep perfect time for five billion years"? - no. It is capable of keeping time within detectable and measurable limits for five billion years. It doesn't suddenly lose its timekeeping abilities after that time, just that any error would start to become detectable.