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Double-Slit Experiment in Time, Not Space
TheMatt writes "Thomas Young's double-slit experiment is a classic experiment that helped establish the wave-like nature of light. Since then, it has been done with atoms, buckyballs, and biomolecules. It has even been seen in a single molecule, and the single electron version was voted the most beautiful experiment by Physics World readers (covered previously on Slashdot). Now, PhysicsWeb is reporting that Gerhard Paulus and coworkers have conducted the double-slit experiment using a double-slit in time, not space. The "slit" was a crafted femtosecond pulse consisting of one-and-a-half cycles--say, two maxima and one minima--passed through an argon gas. Each maxima has a probability of ionizing an argon atom and producing an electron. The electrons were accelerated to a detector which observed an interference pattern since the detector had no idea which maximum produced the electron."
New look for classic experiment
2 March 2005
Physicists in Europe and the US have performed a novel version of the double-slit quantum-interference experiment with single electrons. In the classic version of the experiment, electrons pass through a mask containing two parallel slits and produce a pattern of bright and dark interference fringes on a screen. Now, Gerhard Paulus of Texas A&M University and co-workers in Berlin, Munich, Sarajevo and Vienna have observed an interference pattern with electrons that pass through a double slit in time, not space, as a result of being ejected from an atom at one of two possible times by a laser pulse.
The double-slit experiment was first performed with light by Thomas Young over 200 years ago.The formation of the fringes can be explained by the interference of waves travelling from the two slits. When the peaks of the two waves coincide on the screen, the interference is constructive and the result is a bright fringe. However, if the peak of one wave coincides with the trough of the other, destructive interference results in a region of darkness.
The spacing between the fringes depends on the wavelength of the light and the separation of the slits. Similar interference fringes have also been observed with electrons, atoms and molecules, with the fringe spacing depending on the de Broglie wavelength of the particles. Experiments have also shown that an interference pattern builds up even if there is only one particle in the apparatus at any time, and that the pattern disappears if we try to determine which slit it passes through. This process is now understood in terms of interference between the two possible paths through the apparatus, rather than between two waves or particles: if we know "which way" the electron passes through the slits, we do not see interference, and vice versa.
The latest experiment is radically different because the slits exist in time not space, and because the interference pattern appears when the number of electrons at the detector is plotted as a function of their energy rather than their position on a screen. The work was performed at the Technical University of Vienna in collaboration with physicists from the Max Born Institute in Berlin, the Max Planck Institute for Quantum Optics in Munich and the University of Sarajevo.
Paulus and co-workers focused a train of pulses from a Ti:sapphire laser into a chamber containing a gas of argon atoms. The pulses were so short - just 5 femtoseconds - that each one contained just a few cycles of the electric field.
The team was able to control the output of the laser so that all the pulses were identical. The researchers could, for example, ensure that each pulse contained two maxima of the electric field (thatis, two peaks with large positive values) and one minimum (a peak with a large negative value). There was a small probability that an atom would be ionized by one or other of the maxima, which therefore played the role of the slits, with the resulting electron being accelerated towards a detector. If the atom was ionized by the minimum, the electron travelled in the opposite direction towards a second detector.
The team registered the arrival times of the electrons at both detectors and then plotted the number of electrons as a function of energy. The researchers observed interference fringes at the first detector because it was impossible to know if an electron counted by the detector was produced during the first or second maximum.
There was no interference pattern at the second detector because all the electrons were produced at the same time at the minimum. However,when the phase of the laser was changed so that there was one maximum and two minima, interference fringes were seen at the second detector but not at the first. "We have complete which-way information and no which-way information at the same time for the same electron," says Paulus. "It just depends on the direction from which
Be better in bed. Wikiafterdark!
"Maximum" is singular. "Maxima" is plural. Minima are similar.
So it's "two maxima and one minimum."
I believe posters are recognized by their sig. So I made one.
For those of you who are unfamiliar with the double-slit experiment, there is a very clear, non-technical explanation here.
This space for rent.
It is a 404 - user-friendly, but only to people who read danish.
In this experiment we have an atom which has a 50% chance of being ionized at time t0 and a 50% chance of being ionized at time t1 (OK, the probablities cannot literally be those values but this is an example) so we have a superposition of two states - one corresponding to an atom ionized at one time and one ionized at another time. As the wavefunction for the atoms is essentially oscillatory it means that as the wavefunctions for these two separate states evolve they are out of phase with each other (or are sums of terms that are out of phase with each other). This means we can expect constructive or destructive interference depending on the exact value of t1-t0. This is what was observed.
Doesn't it make you feel good to know that our freedoms are protected by politicans, lawyers and journalists.
Rough trans: The address of the homepage you wish to find is not here or doesn't exist any longer. You can try the following: Check if the address is spelled correctly. Notice that it has meaning if you use capital or lowercase letters!
Or maybe it says something about a moose.
I thought the meaning of the double slit test was to prove that the single electron actually passed through both slits, and in essence interfered with itself.
But in this case we're dealing with two different electrons fired at different times, so it's not quite the same.
Even so, if the electrons create the interference pattern, that means they must have collided... in time? So the second electron reached the point of collision before it was actually fired.
Does that mean that every electron travels every possible path in space AND in time? So whenever it is possible for an electron to be fired, it does, and interferes with all other electrons fired at all other times?
My head hurts. Damn you, Science.
"Reactionaries must be deprived of the right to voice their opinions; only the people have that right." - Mao
What the double slit experiment did was allow us to show that light is both. In the experiment, one shines a pinpoint of light onto two very thin slits. The physics of waves dictate that waves will interfere in a characteristic pattern. This was later used with any matter of particles to show that the wave/particle duality, that is, all suitable small things act like waves or particles depending on the circumstances.
The experiment depends on the fact that we have no idea which slit any particular particle passes through. This uncertainty, in a certain sense, allows particles to go through both slits, which is why a single electron will interfere with itself. If we do know which slit an particle goes through, then then interference disappears. In this way we can show that particles are a wave until, in Schrödinger terms, we collapse it into a wave. So the experiment can show the duality.
So, to summarize, when the state of any particular particle is left uncertain, and certain other conditions are met, it will interfere as a wave. What they are doing here is introducing the uncertainty through a ultra-short pulse of light. There are two ways that the pulse could interact with the surrounding particles, but the universe does not know exactly which interaction occurred. There, the strange and headache producing phenomenon of the sub atomic world are allowed to manifest. I am not sure how this is time instead of space, but it is neat.
"She's a scientist and a lesbian. She's not going to let it slide." Orphan Black
Basically, you can look at light, or electrons, or whatever, as either a particle or a wave. Sometimes one interpretation will work better (light as a particle explains the photoelectric effect, light as a wave explains interference patterns, diffraction, etc). Current state of play is that the wave interpretation is always the best way to look at things, except when you observe the system everything collapses to particles, and when something mathematically inconvenient happens (you can explain the photoelectric effect in terms of waves, but the maths is horrible).
Classic two slit experiment with light consists of shining laser light on a barrier with two slits; each slit produces a diffraction pattern (http://en.wikipedia.org/wiki/Diffraction), the diffraction patterns interfere to produce the classic two slit pattern, see same link. This basically works because the laser light is coherent, you can (sort of) treat all the photons coming from the laser like one photon.
If you do this with electrons, because electrons are waves, you get the same patterns. Ditto any other particle.
Even if you do this experiment firing only one electron at a time you will get the same two-slit interference pattern, although 'common sense' tells you the electron can only pass through one of the two slits what actually happens is it passes through both at once. If on the other hand you fit a detector over one slit to register the passage of electrons, so you can tell which slit the electron passes through, you lose the interference pattern, you get two overlapping single slit diffraction patterns, which is not the same thing.
Roughly, if you have two slits and whenever an electron is fired at the slits you do not know which slit it went through, but the classical probability (what you'd expect if you didn't know quantum mechanics) of either slit is 0.5, then you will get a two-slit pattern.
This is basically the same experiment, except instead of two slits in space a little distance apart there are two possible source times for the electron, separated by a small time gap. There is no way to know whether a detected electron was produced at the first or second time, so the maths works out (roughly) the same as for the two slits in space case and you would expect to see the classic two-slits pattern. But it is kind of neat that someone's actually found a way to test that idea.
**Skip the first part if you know the basics.
If you pass a water wave through a wall with two slits in it, you will get interference. If you put another solid wall (no slits) beyond and parallel to the first wall, you will see that the water line on the 2nd wall looks like a sinewave with magnitude tapering off as you get further from the slits.
If you pass particles (electrons, photons, etc) at a wall with two slits, and place a "detecting wall" beyond the first wall, then the distribution of electrons hitting the detecting wall would be similar to the wave observed against the 2nd wall in the water example.
--New Experiment--
In the new example, two pulses of light can trigger an electron to be released. Think of these two pulses as pulling a trigger on a gun while playing russian roulette. The electron is the bullet and the detector is your head. If you pulled the trigger at 0 secs and 2 secs, you'd expect to see a person die at 0.01 seconds and/or/neither 2.01 seconds, assuming it took 0.01 seconds for the bullet to reach the person and kill him.
The detector, however sees an interference pattern. This is like seeing deaths at 1 second or 1.5 seconds. The interference pattern is measured as a function of time, and instead of seeing two blips in time, they saw a range.
All the "WAHT?!" posts are understandable, given that I'm a physics major and I still find the article unclear in not showing the interference pattern. Is this exhibited in the plot of energy vs. time? That'd make sense to me, given that they are canonically conjugate variables (like position and momentum.) However, the gist is that, analogous to the interference of spatially separated possible paths in the spatial double slit case, two possible paths separated in time are interfering here.
Cagle has been peddling this theory for quite awhile. Do a quick search on cagle in any of the sci.physics groups and you will see his posts along with extremely patient people who try to point out the flaws in his logic (cough!).
We defeated the Nazis, the next evil: Libertarians
Who is this "We" you refer to?
And since when do people who work hard to support civil liberties get lumped in with people who work even harder to take then away?
I think you need to spend a bit more time at Cato's website and learn what Libertarianism really represents. (Hint: diminished state control of our lives)
"Rocky Rococo, at your cervix!"
Wait, rotating in one dimension? I assume that in layman's terms, one dimension would best described as a line, with a single point being dimensionless. So in order to rotate in one dimension... what? You can move up and down a line with respect to some point, but that's linear movement!
Yeah, I think you're right. No idea of your credentials, but the physicist often is right in such discussions.
The double-slit experiment classically involved sending light through two small slits closely separated, onto a dark screen. If light was particulate, you'd expect to see only two bright spots on the screen. But you see a whole interference pattern, with the brightest spot located between the two slits.
This is because of diffraction, and that light acts like a wave, so you get constructive and destructive interference on the screen.
What we didn't know until the 20th century is that light consists of photons, which are individual quanta of electromagnetic radiation. These photons interfere with each other in space as they go through the slits, to give the characteristic interference pattern on the far screen. Or, that the photons don't go through a single slit, but the photons actually go through both slits, and you don't know where the photon is until you measure it (ie, let it hit the screen).
The current experiment effectively used a laser to create two 'slits' in time. They made two quick laser pulses (really two maxima and one minimum). The pulses have some probability of creating an electron, and by making two discrete pulses in time, there is a similar 'interference pattern' associated with observing the electron at various points in time. This means that the electron wasn't created from one laser pulse or the other, but was effectively created through both slits, the time separation of which created an interference effect.
There's no new quantum mechanics here, but here's an attempt at a layman's explanation of what's called the propagator. In classical mechanics you have a well-defined trajectory from a set of well-defined initial conditions (ie, a ball on a spring has a well-defined position and momentum at some time, and you can exactly predict where the ball will be at future times). See this article for example.
Quantum mechanics extends this because there is a classical path the ball would take, but also infinitely many other 'quantum' paths that can also bring the ball from position X at time 0 to position Y at time T. Many of these are classically impossible. But Quantum Mechanics deals with a wavefunction (which describes the state of the system) which is complex. So you need to consider all these other paths too, but each path has an associated phase with it. When you maintain this phase coherence between all paths, you are basically building a similar interference pattern. So when you take the modulus squared of the wavefunction to find the probability of finding the electron, you have interference from the wavefunction going through either of the two slits in time.
The difficulty is that you have to repeat the experiment many times to see when you measure the electron, just like w/ the classical double-slit experiment you need enough photons to give a relative intensity that can be measured.
Here's a little math for anyone curious. The time progression of a wavefunction looks like
|Psi(t)>=exp(-i*H*t/hbar)|Psi(0)>
where |Psi(t)> is the wavefunction at time t, i is the square root of negative one, H is the Hamiltonian Operator, hbar is the Planck constant. See here for more information on the Hamiltonian for classical and quantum mechanics. In many cases it's the energy operator (expressed in terms of position and momentum), and acts on discrete energy eigenstates.
But you can see that time translation evolves the 'phase' of the wavefunction. And if the wavefunction isn't in a single energy eigenstate but a combination of them, each individual component will have have the phase evolve at a different
You'll be much better off posting in a forum where people don't actually know any real math or physics beyond what they read in Scientific American. Anyone who actually has a clue can see this for the drivel it is just from your abuse of semantics alone.
Jedidiah.
Craft Beer Programming T-shirts
Comment removed based on user account deletion
No, time isn't a wave. As another poster mentioned, time is another dimension.
But it's much more tricky than that, time is very different from space. If you rotate a vector in 3-D space, it's length (x^2+y^2+z^2) will remain the same, even though the x,y, and z components are different and kind of mixed together. What Einstein showed is that in 4-dimension space-time, the quantity (-t^2+x^2+y^2+z^2) is what is conserved if you 'rotate' in 4-D spacetime (in other words, if you change reference frames, like going from standing on the ground to standing on a freigh train). So spatial dimensions look spherical while the time dimension looks hyperbolic.
There are obvious parallels between Space and Time in non-relativistic quantum mechanics, namely a time translation evolves the wavefunction by a factor exp(-i*H*t/hbar) and a spatial translation evolves the wavefunction by a factor exp(-i*p*x/hbar). What this means is that momentum is the 'generator' of space translations, and the 'Hamiltonian' is the generator of time translations.
But making relativity works in quantum mechanics isn't as straightforward as physicists hoped, and involved alot of extra work, which finally culminated as quantum field theory. You can read more detail here . But here's a quick summary :
In quantum mechanics, position and momentum aren't just parameters but are operators. They don't commute, which is why you cannot simultaneously know a position and momentum. But time is NOT an operator, it is a parameter, it's the corresponding Hamiltonian that is the operator. So you have 4-dimensional space, 3 dimensions act like operators, 1 dimension acts as a parameter.
So anyway, back to this experiment, what the physicists did was to show that an electron, with a probability of being created during two discrete times (each of the laser pulses) turns out to have an interference pattern just like photons traveling through two slits in space.
The resulting electrons weren't produced from laser pulse 1 or laser pulse 2, but were produced from a superposition of both pulses, and the complex phase that I showed previously with time evolution causes an interference pattern between the two pulses.
Take everything I'm about to say with a grain of salt; I'm a layman and not a physicist. I'm attempting to translate my layman's understanding of this into clear information that other laymen can understand. I'd appreciate any corrections that will be offered by those who have a better understanding of this and the ability to translate that into plain English.
Wave/Particle Duality is how physicists talk about things on the quantum scale sometimes exhibiting wave-like behavior and other times exhibiting particle-like behavior. Here's an analogy:
Suppose you have a thick metal barrier with two parallel vertical slits, a target a few feet behind the barrier, and a machine gun. You point the gun in the general direction of the target, put it on full auto, and let 'er rip. As you fire, sweep the gun around at random. Many of the bullets will hit the barrier, and many will make it through one slit or the other to make holes in the target behind. After you've emptied a few thousand rounds and examine the target, you'll see a random spray of bullet holes behind the slits. The bullets are like particles, and nothing really surprising comes from this double-slit experiment. Each bullet that hits the target passed through exactly one slit and didn't collide with any other bullet.
Now, visualize a bathtub half full of water, with a vertical barrier separating a quarter of the tub from the other three quarters. Now, use your hands to make waves on the surface of the water in the tub. Watch what happens at the double slit, and the pattern of the water surface at the other end of the tub beyond the barrier. Each wave you make passes through both slits. At both points on the other side where the wave emerges, a new wave effectively starts at each slit individually. As these new waves on the other side of the barrier spread out in a semicircle, they collide and form an interference pattern.
Now, the above two things are easy to visualize because they happen in the macroscopic world of classical physics. A bullet is a discreet object whose position and momentum can both be measured with certainty at any time. A wave on water has measurable properties such as amplitude, wavelength, and speed. In the quantum world, however, it's not so easy. You can't directly observe an atom or an electron or a photon. Instead, you have to bounce electrons and photons and atoms off each other and infer what you can from the results.
This next statement is very important; it's the whole reason QM is so very strange: The bouncing itself invariably transfers energy and therefore changes the object being observed.
Now, we know that quantum objects have particle-like properties. A photon can collide with an atom and either be absorbed or reflected. If they were strictly waves then it would be more like sound waves or waves on a liquid surface; they'd tend to spred out in ever-expanding circles/spheres through the medium that transmits them. You can't create a wave on water that travels in one direction for very long; even the wake of a very large ship disperses over a realtively short distance. However, a laser keeps photons in a tightly focused beam, just like a good sniper rifle can deliver bullets in tight groupings over a mile or more of distance.
On the other hand, quantum particles also act like waves. Light has frequency/wavelength. If you shine a laser through two slits that are close enough and narrow enough, you get an interference pattern on the other side. Atoms, when they have heat, oscillate around a centerpoint; this is called Brownian motion. The frequency of this oscillation (a wave-like property) is a function of its type and temperature.
Electrons are said to "orbit" atoms' nuclei. One way to think of this is with the electron being a tiny particle moving a near lightspeed; at that speed over such tiny distances the electron might as well be a cloud surrounding the nucleus. You'll never be able to take a freeze-frame picture and localize an
...time was not a dimension in the sense that spacial dimensions were. That's going to be a much harder line of reasoning to maintain, now, because clearly time DOES behave in the same way as a spacial dimension, when it comes to diffraction.
I don't think this has anything to do with the properties of time per se. As I understood the effect, it has to do with the spatial "probability field" of tiny objects. If there is *any* uncertainty which path a small object will take, the entire probable space will act as a wave function that determines the actual path.
In theory, you should be able to produce this effect with any setup that induces uncertainty of position at that scale. The experiment proves something about the properties of uncertainty and probability - it doesn't actually say anything about the nature of space, time, or types of particles.
Most of quantum physics isn't as counter-intuitive as some quantum physicists want people to believe. Its reputation is mainly based on the usage of confusing metaphors and misleading statements.
(Like the ambigous implication that observing something changes the outcome, which is not true. They really talk about the theoretical possibility of observing something, which is a moot point in most probability scenarios anyway. Often there is an unqualified human-centric touch to those statements, which are clearly just designed for sensationalism. Particles don't care whether you can actually measure their state or not. Often the real question is, whether that actual state really exists in the first place. Most people don't seem to be able to distinguish between a model of something and the real thing.)
We already knew that particles are also waves... What does this experiment show us that's new? Does it show that two particles are a wave, or something?
It tells us nothing new about waves and particles, but it does confirm that there is no difference between a pair of slits separated by space and a pair of slits separated in time.
IOW it confirms that time is just another dimension.
You make the mistake of thinking you can educate the fundamental stupidity out of people. You can't.
You do sound like a Physicist :)
Actually, Mathematicians don't say that. Mathematicians say that a closed curve is homeomorphic to S^1, and a line to R^1, ie, there exists a bijective, bicontinuous mapping between the sets.
The "topology" of a space is actually the set of all open sets in that space. (Which trivially could not be a set like S^1.) In essense, the thesis of general topology is that all continuity related problems can be redefined in terms of open sets. If you'll recall, in classic analysis an open set is defined as an open ball with respect to the metric of the space in question. This produced spaces that while perhaps not equivalent to R^n were very similar in many ways, in particular because there existed a way to meaningfully define the distance between any two points.
In topology, we do away with the metric definition of an open set entirely, and leave the concept of an open set essentially undefined (well, subject to a few sanity restrictions involving unions and intersections of open sets). This allows mathematicans to study spaces that really are nothing like the ones we experience regularly, and the vast majority of them are really, really unfriendly, which is one of the reasons that topology is the course that scares many math majors away.
However, it gives way to Algebraic Topology, which is without a doubt one of the most beautiful branches of pure math.
Physics is cool and all, if you're not quite bright enough to make it in Math. Ha ha. *jab*
First of all, if you don't know the classic double-slit experiment, read Double-slit experiment at Wikipedia. In the classic experiment, we send something (a photon, an election, whatever) through two slits, and plot the number (of photons, electrons, whatever) vs. the position. Now due to the uncertainty principle we know that Delta x*Delta p>=h-bar/2, where Delta x is the uncertainty of position, Delta p is the uncertainty of momentum, and h-bar is a constant (see Planck's constant for more info). So we can derive the formula lambda/s=x/D, where lambda is the wavelength (of the photon, or the de Broglie wavelength of the electron), s is the slit separation, x is the fringe width, and D is the distance of the slits from the screen.
Now in this new experiment, we send a photon which has a wave consisting of two maxima and one minimum into a cloud of atoms. An electron may be emitted from the cloud and sent to the screen, and we measure the time it arrives at the screen. This electron could have been emitted from the first maxima or the second maxima (ignore the minimum as those electrons get sent to the other screen). If we plot the number of electrons vs time, we should see the exact same interference pattern as with the plot of number of electrons vs. position that we see in the classic experiment. And the uncertainty principle can also be expressed as Delta E*Delta T>=h-bar/2, where Delta T is uncertainty of energy and Delta T is uncertainty of time. So now we should find that E/s~x/D (I'm not sure if this is right, and not sure if I'm missing some constants so I used proportional rather than equal here). E is the energy of the photon, s is now the difference in time between the two maxima, x is still the fringe width (though it's now measure in units of time), and D is still the distance between the screen and the (in this case cloud), but I suppose you have to measure the distance in time (the time it takes the electron to travel that distance).
Anyway, this is all a guess, since the actual experiment doesn't seem to be found. If someone sees a glaring problem, feel free to flame.
"As I interpret this, one of the clocks is slightly in the past relative to the other one."
Why? Both clocks are sitting side by side and can be viewed by the same individual at the same time. A simpler interpretation is that one clock experienced a slower time as demonstrated by it's time display in the here-and-now.
As I have already requested (in a different reply to a different on of your almost entirely redundant posts) a full proof for me to dismantle, I will keep my response to a few key problems (see: fatal flaws) I see in this postulate.
(A) How do you propose to measure velocity using only measurements of the time dimension? Last I checked, velocity is defined as (spatial units translated)/(temporal units translated).
(B) If we simply look at this in two dimensions, restraining spatial coordinates to the x direction, and our second dimension being time, your theory would have the origin of the t axis sliding up and down, while the x axis remains stationary. While this will change the appearance of our visual rendering of the coordinate system (for example, we may draw the x axis intersecting the t axis at t=-4s, for instance), it is simply smoke and mirrors. An event at (t1,6) will always be 4m away from an event at (t1,10). An event at (t2,-5) will always be |t2-t3| away from (t3,-5), no matter how much you shift the numerical origin of your t axis. My point is this: any coordinate system is relative to an arbitrarily chosen origin. While you may renumber your t axis as often as you wish, and thus have it "slide" to and fro relative to your other axes, the relative spacetime differences between events will remain the same.
(C) Sorry, ran a bit long on (B), so i'll make this my last point. This point is one of semantics. You state that the time dimension expands as a spherically symmetric wavefront through space. Thus, you feel the time dimension has spatial components. Therefore, your time "dimension" is not a dimension at all, as it contains an x, y, and z component, each which have a _set_ relationship to one another (they define a sphere, as you explicitly state above). For time to be its own dimension, it must be possible for any relationship of x, y, and z to exist at any point t. Perhaps you stated this in a way you did not intend, or perhaps you simply can't wrap your head around four dimensions.
In any case, please either correct any mistakes or misinterpretations I have made, or shelf your theory until you can make the math work.
A fine summary, but I'm going to nit-pick on the order in which the experiments were done.
What the double slit experiment did was allow us to show that light is both.
The double slit experiment showed us that light was a wave. This understanding allowed a Grand Unified Theory of Optics (not that they called it that) which explained reflection, refraction and diffraction in terms of waves.
We didn't know light was both until Einstein's 1905 paper on the photoelectric effect (for which he won his Nobel.)
For electrons, it was the other way around. First we knew they were particles, then the electron double split experiment proved that they also behaved as waves.
Quattuor res in hoc mundo sanctae sunt: libri, liberi, libertas et liberalitas.
It seems somewhat muddled and misleading to me. Read this (note: Java applet) and this instead.
Dr. Elliot's theory of moving dimenstions stands unrefuted.
A lot of crackpot theories stand unrefuted. Not because they are correct, but because it's just not worth any expert's time to refute them.
It would be great if the detractors could use logic and reason in refuting Dr. E's theory, rather than just refuting it by dismissing it.
OK, I'll give it a shot... Bleah. This is as far as I got.
First off, since the universe is expanding, space-time is also expanding, showing that dimensions are moving and expanding.
Wrong. Anybody who says this clearly hasn't understood college level math (or logic). I suggest taking some classes and bone up on the fundamentals, then rewriting your ideas so that they're comprehensible to other scientists.
I read about that in Brian Greene's The Fabric of the Cosmos. Amazing stuff.
Mod parent "Informative". This is actually true.
Check out the book "Genius: The Life and Science of Richard Feynman" (by James Gleick)
there's no way of determining which of the two bodies will age more quickly and at what rate they will age in relation to each other
Correct, if no one accellerates. So long as they are moving apart then there is no way to determin which is "aging more quickly". For some observers the first one will age faster, and for other observers the second will age faster. The farther apart they get the bigger the discrepance can become. If they are one light-year apart then either one may be seen as up to one year "older" than the other. If they are 10 light years apart then either one may be seen as up to ten years older than the other.
Time can only be compared locally, when they are at the same spot. If they are travenlling at different speeds then they can only be at the same spot once, and then constantly moving apart. Since you only have one time-point you cannot make any "duration" measurments that apply to both. The only way to measure a duration for both of them is to have them at the same location twice, and in order to do that at least one of them needs to accelerate and "return" to the other one. That acceleration will cause that one's space/time axes to "twist". It's hard to explain that "twist" in words, but it's pretty clear in pictures. Anyway, that acceleration and "twist" causes that one to see the other one suddenly age. The one that accelerates and "twists" is the one that has aged less when they get back together. It is acceleration that causes time to "slow down".
Standing here on earth we are constantly accelerated by gravity even though we don't move. That gravitational acceleration causes our clocks to run slower than someone floating out in space. If you could stand just outside a black hole that enormous gravity and enormous acceleration causes your clock to run very slow.
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- - You can't take something off the Internet! That's like trying to take pee out of a swimming pool.
They found that just about everyone could, on a small but repeatable level, affect the output of a random number generator just by concentrating on it. (The implications of that, if true, are staggering enough alone)
Extremely careful analysis is required when looking for very small effects in the midst of large masses of data.
See for example: http://quasar.as.utexas.edu/papers/reg.pdf
Frequentist analysis breaks down in a variety of circumstances, and Bayesian analysis must be used instead. The most familiar case where frequentist analysis breaks down is when there are a very small number (or just one) event(s). But it also breaks down in these large datasets when one goes hunting for very small probability events.
Looked at informally, what is more probable: that humans have a small but significant ability to alter events by thinking about them (that evolution has somehow missed out on improving on) or that the experiments and analysis are somehow flawed? Naively, the latter hypothesis is more plausible, and the paper linked above demonstrates this to be the case.
--Tom
Blasphemy is a human right. Blasphemophobia kills.
lthough mathematics is indeed a very precise language, it still fails to define the number 1.
Try looking in here or here both of which conveniently go to some trouble to very explicitly define 1 and number, etc. Philosophy of mathematics has a much mre solid grounding than you apparently imagine.
Secondly - and I'm being very hypothetical here - even though dimensions are implied to be static, surely a reference point within one dimension can move independently of other dimensions? And aren't our observations based on drift relative to the reference point being used?
Welcome to the world of not understanding dimension as used in special and general relativity. It's on a manifold, which is coordinate system indpendent - that's the whole point really - you're talking about moving the coordinate system, when the whole point is that it doesn't matter.
To me, "rotation in 1 dimension" is possible, with a very limited definition of rotation - freedom to change "forward" from a given direction to its opposite.
Actually think about what you're saying for change. Motion (even in one direction) requires time, which we've already said is just another dimension in spacetime, so to have motion we have 2 dimensions and we're not talking about rotation in 1 dimension any more, but in 2. It helps if you pay attention in class, honest.
Does this make sense?
Not in the least, and I shouldn't even be bothered spending nthe time replying, but I'm bored. Please, go read some books on the subject(s) before shooting your mouth off randomly.
Jedidiah.
Jedidiah.
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