The highest grade I've earned was something around a 114% in Geometry (I hate it, but I can visualize anything).
Clearly, whoever marked the test failed fractions back in the day.
Seriously though, what's with American grading systems? I was deeply bemused when I was researching some of the US standardised tests for grad schools. Over here, when we say we got 99% on a test, we mean we got less than 1 part in 100 wrong. Over in America it means that we fell within whatever particular bit of the grading curve they feel deserved to get 99% (Which, for the GRE exam, seems to be about 80 actual % or higher. Given that, in a test prep for the general math section it said that it was very important to remember the difference between "Positive and negative" and "even and odd", I must confess I'm not too worried).
You really did, didn't you? The process is called -rounding- to N significant figures for a reason y'know. As in the last figure is rounded off using the fire non-significant figure, to give, in this case, 9.
(Wow, I/. doesn't put in a 'pedantic' mod any time soon...)
D'oh... I sorta forgot paragraph breaks. Well doesn't taht look like a complete mess? Here it is with proper formatting, if the above hurts your eyes:
That website makes me want to cry:(
For example: As we all know, perpetual motion machines are impossible, and claims of such devices are a clear sign of bad science. No device (or natural phenomenon) can operate endlessly without draining a power source, and certainly no device can operate without a power source at all. Yet, our science states that an object dropped into a tunnel cut through the Earth would oscillate back and forth endlessly from one end of the planet to the other.
Pretty much anything can sustain perpetual motion if you neglect forces like friction which remove energy... And he doesn't seem to understand the difference between force and energy, or even the basic CONCEPT of a black hole (he explains the fact that light can't escape in terms of the fact that the black hole doesn't produce it's own light...) And this is just in the first couple of blurbs from that page you linked.
Not to mention, his 'simple' derivation is based entirely on conclusions which arise from relativity (i.e. Einstein's own derivation, which he also gleefully 'debunks' in many places) and is only applicable to light.
Once again: If an 'earth-shaking'/'revolutionary' theory is first published in a book, it's usually best to laugh and walk away.
That website makes me want to cry:( For example:
As we all know, perpetual motion machines are impossible,
and claims of such devices are a clear sign of bad science.
No device (or natural phenomenon) can operate endlessly
without draining a power source, and certainly no device can
operate without a power source at all. Yet, our science states
that an object dropped into a tunnel cut through the Earth would
oscillate back and forth endlessly from one end of the planet
to the other.
Pretty much anything can sustain perpetual motion if you neglect forces like friction which remove energy...
And he doesn't seem to understand the difference between force and energy, or even the basic CONCEPT of a black hole (he explains the fact that light can't escape in terms of the fact that the black hole doesn't produce it's own light).
And this is just in the first couple of blurbs from that page you linked.
And not to mention, his 'simple' derivation is based entirely on conclusions which arise from relativity (i.e. Einstein's own derivation, which he also gleefully 'debunks' in many places) and is only applicable to light.
Once again: If an 'earth-shaking'/'revolutionary' theory is first published in a book, it's usually best to laugh and walk away.
It wouldn't surprise me at all if they do introduce support for Open formats soon... and also pop up a nice friendly help box any time anyone opens a document in that format warning of reduced flexibility or what have you, and suggesting the document be converted to a nice reliable.doc...
Read penny-arcade much? They restored the award, and it's been almost all they've talked about in news posts for quite some time (see the new penny arcade/pvp rivalry server on dark iron)
Most of the big early server problems are fixed (my server almost never had any anyhow), so if you want to rant, at least use current information.
I figure that it's because the/. moderation system will hopefully produce some decent questions which don't involve shouts of "BLUE RESPONSE NOW!!1!", "NERF SHAMANS!!!1!", or paranoid rantings about blizzard rifling through your pc and violating your 'constitutional rights', which is the typical response to most blue posts, regardless of their original content.
Quite possibly the downloader's fault - on some connections, it seems to reserve a massive amount of bandwidth for uploading, even though it's only using a fraction of it. Try getting something like NetLimiter and capping its upload bandwidth - you don't even need to be selfish, the cap can be more than your usual upload rate and you'll still see some big improvements - when I was downloading the beta, I jumped from about 10k/s to over 100k/s this way, and didn't significantly affect my upload rate at all.
Neutronium is not particularly related to the periodic table, despite its constituents being listed there. The periodic table deals with electronic relationships primarily, hence forms of matter where EM is not the dominent force are not well described by the information contained in it.
The particle listed in the table is, as you say, a bare neutron - often included in lists of atoms/nuclei primarily because of its use in studies of nuclear properties and interactions. In this realm, it's rather important, so it has a place with the others, even if much of the information usually in the table is absent when dealing with neutrons (e.g. electron orbitals)
The periodic table describes single atoms, not large-scale organisations of matter, so that spot in the middle is not neutronium, but ragher represents a single neutron. Not exactly an atom, but a system with atomic number zero, so it rests in the 'zeroth' spot at the middle of this new table.
Most of the 'complete' string theories are actually quite elegant in their implementation (although it can require some sophisticated mathematical tools to see the elegance, it is still there).
The issues arises when you try to apply them to practical situations, and that's common to pretty much all physical theories - Newtonian mechanics is only exactly solvable for two body problems, QM for specific one body problems, and QED (which most will acknowledge is a neat, elegant theory) isn't even exactly solvable for the no-body vacuum problem.
Mathematical difficulties are common when we try to apply almost any theories, it's not a good reason to dismiss them out of hand.
While CPT is still held to be a symmetry (and would cause all manner of mathematical problems if it isn't) this does not mean time itself is symmetric. In fact, it could be quite the opposite.
It's already well known that Charge and Parity inversions were not truly symmetric (i.e. "left" and "right" are really rather different to many processes), and now there's evidence that their composite operator, CP, is not symmetric either. This would then indicate that Time inversion must also be non symmetric, to preserve full CPT symmetry.
However, this time asymmetry must be very tiny, and as yet we haven't got a method to test it - partly because many of the most basic theories we have gloss over the very things we want to look at. For example, time properties in QM and phenomena like wavefunction collapse (the 'events' we use time to tell apart), are just things that are taken as given. If we can work out some understanding of them, then we may be able to formulate a framework to describe this seemingly fundamental time structure.
It seems to say that, if you expressed your approval of a particular crime in the past, that it may be used as evidence against you if you try to disown it in the future. Which seems to make sense.
(Please don't mod me down just because you don't think it's a crime, the courts still seem to think so, and that's what we're discussing)
Inertia isn't solely the province of mass - consider mass corrections as applied to nuclei as a result of their associated binding energy. Indeed, if we go down to the quark level, most of the mass/inertia effects arise from binding energies.
As you mentioned, mass increase doesn't work in all situations, but it does work well in a simple 1D model which would be used to illustrate the basic ideas. Most simple models run into trouble at higher dimensions anyway - your time slowing example wouldn't immediately work to explain transverse and londitudinal mass either, would it?
For any more detailed study of SR, 4-vectors would probably be the better choice anyhow, and most of these disagreements become moot.
More accurately, what galileo was talking about was the concept of an inertial frame, as it applied to mechanics - specifically, that if you carry out an experiment in any reference frame moving at constant velocity, it will be identical to one carried out at rest.
This was a commonly accepted feature of physics, but only as applied to the laws of mechanics. It took Einstein to ask why it didn't appply to EM laws as well before it evolved into the relativity we all know today (it wasn't quite as simple as postulating a maximum speed, that arises as a result of c being constant in all frames)
There is a relativistic mass effect, if you want there to be. It's not necessary, and in many formulations is counterintuitive, but it can be used in a number of formulations to keep things straight - e.g. its use means that E=mc^2 always holds true, not just for rest states.
Even in the example you cited, relativistic mass still has a place. Specifically, if we choose not to use relativistic mass, we can no longer simply express momentum as mv, because using the rest mass and speed measured from the rest frame, we would obtain incorrect results, since as you say the momentum has effectively increased.
While you're right to say that there is no 'extra mass', it is true to say that the energy of a body affects its inertia (See Einstein's 4th 1905 paper, I believe), which can be expressed as a modified mass term, if we so desire.
Well, I guess you don't appreciate the subtleties and beauty of the laws of nature as much as me.
Claiming the intellectual high ground at the first line, classy...
The details of measurements are somewhat irrelevant - the speed light can be readily measured over a few k with simple equipment, or even in a normal lab with somewhat clunky equipment - I know it's one of the first year experiments at my uni, for example. But high precision measurements of almost any constant tends to become very difficult very quickly, not just c, so in general the whole point is somewhat moot.
Light is something we've known about since the dawn of time. Yet electric and magnetic phenomenon weren't studied scientifically until relatively recently. There really is no reason a priori to assume that light is a propogating electromagnetic disturbance, much less a spin 1 quanta of electromagnetic excitation.
Of course there's no reason to assume that a priori - science is all about getting rid of a priori ideas and only judging things on measurable properties we've observed. And in that view, even a cursory glance at their properties is enough to indicate there's some kind of a connection.
I'll give you that the efforts that went into discovering these facts were quite impressive, but - perhaps I'm being just a bit jaded here from thinking of them this way for so long - now the idea that light == em is simply a fact, and hardly feels remarkable any more...
"This indicates that according to the Lorentz transformation, nothing can have the same speed relative to both K and K' unless it is a ray of light"
You then calmly assert that this is nonsense and claim certain mathematical assumptions are to blame. However, even a moment's thought about this indicates that this makes perfect sense - The two frames are in relative motion to one another, and thus for any object the observed velocity would be V = Vframe+Vobject (or it's relativistic correction, for high velocities). So, unless both frames have the same Vframe (i.e they are the same frame), nothing but two rays of light can have the same velocity in both frames - as in the postulates of special relativity.
In effect, you have proved that Lorentz transformations are the ones which are consistent with SR.
In a way, he did make things simpler too - most of the transformations arising from SR had already beeen derived elsewhere (e.g. when trying to explain the Michleson-Mosley experiment), but Einstein produced a simple rule (i.e. that physical constants are invariant) which led directly to those results - and several other interesting ones, too
For examle, the permittivity (epsilon_0) and permeability (mu_0) of free space are two constants that can be measured in the laboratory rather easily. Yet Maxwell's equations in vacuum describe waves travelling at speeds 1/sqrt(epsilon_0*mu_0), which is exactly the speed of light in vacuum (although in Gaussian units this connection is far more obvious). It's pretty amazing to think how these are related.
Really, it's not that amazing... light is an electromagnetic wave, of course it's going to depend on the electric and magnetic constants of the space around it. And besides, that relation arises entirely from classical EM, and has no particular bearing on SR beyond the general invariance of physical constants across reference frames...
Actually, time (by itself) no longer appears to be a symmetry, although we don't have any observations to verify that yet.
You are right that CPT invariance is a crucial part of modern physics, but you seem to forget that the constituent factors do not need to be symmetric - indeed, it has been known for some time that C and P were not symmetries by themselves, although it was thought that their composite operator (CP) was, which would preserve time symmetry.
Of course, science being what it is, there is now evidence that CP is not truly symmetric either, which would then require T to be somewhat antisymmetric also, to preserve CPT. This would mean that there is indeed a distinction between interactions happening in different time directions, thus giving us a measurable 'arrow of time' at the most fundamental levels. The bias is believed to be tiny though, and as yet no-one has came up with a way to observe it.
Slashdot Mirror
Clearly, whoever marked the test failed fractions back in the day.
Seriously though, what's with American grading systems? I was deeply bemused when I was researching some of the US standardised tests for grad schools. Over here, when we say we got 99% on a test, we mean we got less than 1 part in 100 wrong. Over in America it means that we fell within whatever particular bit of the grading curve they feel deserved to get 99% (Which, for the GRE exam, seems to be about 80 actual % or higher. Given that, in a test prep for the general math section it said that it was very important to remember the difference between "Positive and negative" and "even and odd", I must confess I'm not too worried).
You really did, didn't you? The process is called -rounding- to N significant figures for a reason y'know. As in the last figure is rounded off using the fire non-significant figure, to give, in this case, 9.
/. doesn't put in a 'pedantic' mod any time soon...)
(Wow, I
For example: As we all know, perpetual motion machines are impossible, and claims of such devices are a clear sign of bad science. No device (or natural phenomenon) can operate endlessly without draining a power source, and certainly no device can operate without a power source at all. Yet, our science states that an object dropped into a tunnel cut through the Earth would oscillate back and forth endlessly from one end of the planet to the other.
Pretty much anything can sustain perpetual motion if you neglect forces like friction which remove energy... And he doesn't seem to understand the difference between force and energy, or even the basic CONCEPT of a black hole (he explains the fact that light can't escape in terms of the fact that the black hole doesn't produce it's own light...) And this is just in the first couple of blurbs from that page you linked.
Not to mention, his 'simple' derivation is based entirely on conclusions which arise from relativity (i.e. Einstein's own derivation, which he also gleefully 'debunks' in many places) and is only applicable to light.
Once again: If an 'earth-shaking'/'revolutionary' theory is first published in a book, it's usually best to laugh and walk away.
That website makes me want to cry :( For example:
As we all know, perpetual motion machines are impossible,
and claims of such devices are a clear sign of bad science.
No device (or natural phenomenon) can operate endlessly
without draining a power source, and certainly no device can
operate without a power source at all. Yet, our science states
that an object dropped into a tunnel cut through the Earth would
oscillate back and forth endlessly from one end of the planet
to the other.
Pretty much anything can sustain perpetual motion if you neglect forces like friction which remove energy...
And he doesn't seem to understand the difference between force and energy, or even the basic CONCEPT of a black hole (he explains the fact that light can't escape in terms of the fact that the black hole doesn't produce it's own light).
And this is just in the first couple of blurbs from that page you linked.
And not to mention, his 'simple' derivation is based entirely on conclusions which arise from relativity (i.e. Einstein's own derivation, which he also gleefully 'debunks' in many places) and is only applicable to light.
Once again: If an 'earth-shaking'/'revolutionary' theory is first published in a book, it's usually best to laugh and walk away.
It wouldn't surprise me at all if they do introduce support for Open formats soon... and also pop up a nice friendly help box any time anyone opens a document in that format warning of reduced flexibility or what have you, and suggesting the document be converted to a nice reliable .doc...
Read penny-arcade much? They restored the award, and it's been almost all they've talked about in news posts for quite some time (see the new penny arcade/pvp rivalry server on dark iron) Most of the big early server problems are fixed (my server almost never had any anyhow), so if you want to rant, at least use current information.
I figure that it's because the /. moderation system will hopefully produce some decent questions which don't involve shouts of "BLUE RESPONSE NOW!!1!", "NERF SHAMANS!!!1!", or paranoid rantings about blizzard rifling through your pc and violating your 'constitutional rights', which is the typical response to most blue posts, regardless of their original content.
Quite possibly the downloader's fault - on some connections, it seems to reserve a massive amount of bandwidth for uploading, even though it's only using a fraction of it.
Try getting something like NetLimiter and capping its upload bandwidth - you don't even need to be selfish, the cap can be more than your usual upload rate and you'll still see some big improvements - when I was downloading the beta, I jumped from about 10k/s to over 100k/s this way, and didn't significantly affect my upload rate at all.
Neutronium is not particularly related to the periodic table, despite its constituents being listed there. The periodic table deals with electronic relationships primarily, hence forms of matter where EM is not the dominent force are not well described by the information contained in it.
The particle listed in the table is, as you say, a bare neutron - often included in lists of atoms/nuclei primarily because of its use in studies of nuclear properties and interactions. In this realm, it's rather important, so it has a place with the others, even if much of the information usually in the table is absent when dealing with neutrons (e.g. electron orbitals)
The periodic table describes single atoms, not large-scale organisations of matter, so that spot in the middle is not neutronium, but ragher represents a single neutron. Not exactly an atom, but a system with atomic number zero, so it rests in the 'zeroth' spot at the middle of this new table.
The issues arises when you try to apply them to practical situations, and that's common to pretty much all physical theories - Newtonian mechanics is only exactly solvable for two body problems, QM for specific one body problems, and QED (which most will acknowledge is a neat, elegant theory) isn't even exactly solvable for the no-body vacuum problem.
Mathematical difficulties are common when we try to apply almost any theories, it's not a good reason to dismiss them out of hand.
It's already well known that Charge and Parity inversions were not truly symmetric (i.e. "left" and "right" are really rather different to many processes), and now there's evidence that their composite operator, CP, is not symmetric either. This would then indicate that Time inversion must also be non symmetric, to preserve full CPT symmetry.
However, this time asymmetry must be very tiny, and as yet we haven't got a method to test it - partly because many of the most basic theories we have gloss over the very things we want to look at. For example, time properties in QM and phenomena like wavefunction collapse (the 'events' we use time to tell apart), are just things that are taken as given. If we can work out some understanding of them, then we may be able to formulate a framework to describe this seemingly fundamental time structure.
(Please don't mod me down just because you don't think it's a crime, the courts still seem to think so, and that's what we're discussing)
As you mentioned, mass increase doesn't work in all situations, but it does work well in a simple 1D model which would be used to illustrate the basic ideas. Most simple models run into trouble at higher dimensions anyway - your time slowing example wouldn't immediately work to explain transverse and londitudinal mass either, would it?
For any more detailed study of SR, 4-vectors would probably be the better choice anyhow, and most of these disagreements become moot.
This was a commonly accepted feature of physics, but only as applied to the laws of mechanics. It took Einstein to ask why it didn't appply to EM laws as well before it evolved into the relativity we all know today (it wasn't quite as simple as postulating a maximum speed, that arises as a result of c being constant in all frames)
Even in the example you cited, relativistic mass still has a place. Specifically, if we choose not to use relativistic mass, we can no longer simply express momentum as mv, because using the rest mass and speed measured from the rest frame, we would obtain incorrect results, since as you say the momentum has effectively increased.
While you're right to say that there is no 'extra mass', it is true to say that the energy of a body affects its inertia (See Einstein's 4th 1905 paper, I believe), which can be expressed as a modified mass term, if we so desire.
Claiming the intellectual high ground at the first line, classy...
The details of measurements are somewhat irrelevant - the speed light can be readily measured over a few k with simple equipment, or even in a normal lab with somewhat clunky equipment - I know it's one of the first year experiments at my uni, for example. But high precision measurements of almost any constant tends to become very difficult very quickly, not just c, so in general the whole point is somewhat moot.
Light is something we've known about since the dawn of time. Yet electric and magnetic phenomenon weren't studied scientifically until relatively recently. There really is no reason a priori to assume that light is a propogating electromagnetic disturbance, much less a spin 1 quanta of electromagnetic excitation.
Of course there's no reason to assume that a priori - science is all about getting rid of a priori ideas and only judging things on measurable properties we've observed. And in that view, even a cursory glance at their properties is enough to indicate there's some kind of a connection.
I'll give you that the efforts that went into discovering these facts were quite impressive, but - perhaps I'm being just a bit jaded here from thinking of them this way for so long - now the idea that light == em is simply a fact, and hardly feels remarkable any more...
"This indicates that according to the Lorentz transformation, nothing can have the same speed relative to both K and K' unless it is a ray of light"
You then calmly assert that this is nonsense and claim certain mathematical assumptions are to blame. However, even a moment's thought about this indicates that this makes perfect sense - The two frames are in relative motion to one another, and thus for any object the observed velocity would be V = Vframe+Vobject (or it's relativistic correction, for high velocities). So, unless both frames have the same Vframe (i.e they are the same frame), nothing but two rays of light can have the same velocity in both frames - as in the postulates of special relativity.
In effect, you have proved that Lorentz transformations are the ones which are consistent with SR.
In a way, he did make things simpler too - most of the transformations arising from SR had already beeen derived elsewhere (e.g. when trying to explain the Michleson-Mosley experiment), but Einstein produced a simple rule (i.e. that physical constants are invariant) which led directly to those results - and several other interesting ones, too
Really, it's not that amazing... light is an electromagnetic wave, of course it's going to depend on the electric and magnetic constants of the space around it. And besides, that relation arises entirely from classical EM, and has no particular bearing on SR beyond the general invariance of physical constants across reference frames...
Actually, time (by itself) no longer appears to be a symmetry, although we don't have any observations to verify that yet.
You are right that CPT invariance is a crucial part of modern physics, but you seem to forget that the constituent factors do not need to be symmetric - indeed, it has been known for some time that C and P were not symmetries by themselves, although it was thought that their composite operator (CP) was, which would preserve time symmetry.
Of course, science being what it is, there is now evidence that CP is not truly symmetric either, which would then require T to be somewhat antisymmetric also, to preserve CPT. This would mean that there is indeed a distinction between interactions happening in different time directions, thus giving us a measurable 'arrow of time' at the most fundamental levels. The bias is believed to be tiny though, and as yet no-one has came up with a way to observe it.