Questions about Einstein SR interpretation

[Simplyh]

Three simple experiments put to question Einstein's Special Relativity interpretation. It has nothing to do with the formulas. Formulas work pretty well; the BIG problem is interpretation!

1.The most recent particle collisions at CERN:
Two Proton Beams at 3.5 TeV, traveling in opposite directions, collide. I don't known the exact angle but I can assume it is quite close to zero as the energy of the collision is about the sum of the energy of the particles. Calculating the speed of the protons, given their energies, gives a speed of around .96c (SR formulas work here pretty well).
Summing both speeds, according to the theorem of addition of speeds gives a speed of around 0.9993c. Calculating the energy for that speed using SR we get around 25 TeV. So, here, SR formulas don't work at all!
Even if my calculations are quite rough and I lack of exact data, it will be surely impossible to get an energy of 7 TeV from two particles at 3,5 TeV, using SR formulas!
So, why is the energy of the collision only 7 TeV? Why is the energy of the collision roughly the sum of the individual energies, suggesting that the collision takes place at the sum of the speeds? Why can two particles collide at 1,92c when SR “forbids” relative speeds greater than c? Why does SR work perfectly only when calculating the energy and speeds of the particles relatively to Earth?

2.Correction of time on satellite clocks:
If we use SR to calculate the slowing of satellite clocks due to its movement relatively to Earth the results are excelling and we use it all the time. We simply wouldn't have GPS if we didn't have SR equations!
But, if we use the same equations to calculate the correction of the clocks from the perspective of the satellite observer, applying the Principle of Relativity, we get it all wrong! the clocks of the satellite should need no correction at all; the clocks on Earth should be retarded.
So, as for the GR correction corresponding to the lower intensity of the field at orbit altitude, it seams that the movement effect is not relative: it does not depend on the observer; it is exactly the same for all observers!

3.Einstein's thought experiment for de-synchronization on the 1905 paper:
We have a solid device with a light source, an observer and a clock at one extremity and a mirror, an observer and a clock on the other. When the device is at rest (relatively to Earth) the time needed for light to travel AB is equal to the time needed to travel BA. But, when the device is moving (relatively to Earth) in the direction AB, the time needed for the light to travel from AB is greater that the time needed to travel BA.
Earth doesn't play here any role concerning relative speed of the objects on that system and so, the movement relatively to Earth, should be ignored. So, the system is as much at rest as before.
So:
The device's system is as good as Earth to be the reference frame to which the movement is referred, according to SR Principle of Relativity.
Light should travel, in that system, at speed c, in all directions, as in all the other inertial systems, according to the Principal of the Constancy of Light Speed.
So, applying both Principals of SR, the time needed for light to travel AB should match the time needed to travel BA. But it doesn't!

Let's now change the interpretation and, basically, keep the formulas. Let's go back to the beginning when Lorentz factor was calculated from the contraction of the electron moving at high speeds.

1.Particles collisions:
As for the electron, the proton field, when moving, interacts with Earth's field, creating a distortion on the field around the particle, which increases the proton's energy, according to SR formulas, taken from Lorentz formulas, taken from the observation of the moving Electron!
So, it doesn't apply to relative movement of two particles which is independent from their movement on Earth's field; relative movement of two particles can very easily exceed the speed of light. The energy of the collision will be the sum of the energies of the particles and the energies of the particles will depend on their speeds relatively to Earth, ACCORDING TO SR FORMULAS BUT NOT TO SR INTERPRETATION OF THE PHENOMENON!

2.Slow down of clocks of satellites
As for the electron, the particle field, when moving, interacts with Earth's field, creating a distortion on the field around the particle, which decreases the pace of its radiation emissions, according to SR formulas, taken from Lorentz formulas, taken from the observation of the moving Electron!
So it doesn't apply to relative movement of two clocks and its standby observers, one on a satellite and one on Earth. Nothing happens to Earth clocks, which don't move on Earth's electromagnetic field, while satellite clocks, which do move on Earth's field, do slow down for all kinds of observers, ACCORDING TO SR FORMULAS BUT NOT TO ITS INTERPRETATION OF THE PHENOMENON!

3.Speed of light relatively to objects moving relatively to Earth
Electromagnetic radiation is a perturbation of the electromagnetic field! This, I think, is unanimous. So, why shouldn't a perturbation of the field displace on the field? Therefore, radiation displaces in the field, not in vacuum!
If radiation propagates in the field, it's quite natural that it follows the field's movement: that's why its speed is equal in all directions at Earth's surface!
On the referred experiment most of the displacement is done on a non distorted field (though, depending on the construction of the device, some parts of the field could be distorted by speed, according to what was said above).
That's why the speed of light is equal to c relatively to Earth, smaller than c relatively to B and higher than c relatively to A, as expressly recognized by Einstein on his paper, in violation of the Principle of the Constancy of Light Speed in all inertial systems!
This principle is only valid to system Earth in particular and to all homogeneous fields in general, NOT TO SYSTEMS IN MOVEMENT RELATIVELY TO THE FIELD WHERE LIGHT IS DISPLACING!

 

[Mentz114]

Every one of your arguments is logically flawed, or based on misinformation or gobbledegook. For example -

As for the electron, the proton field, when moving, interacts with Earth's field, creating a distortion on the field around the particle, which increases the proton's energy, according to SR formulas

This is not recognizable as anything from SR
I can only think your motivation is to attack SR/GR. Contrary to your claims, SR stands up well to experimental tests. I remain unconvinced.

 

[ghwellsjr]

Concerning #3: You cannot measure the time it takes for light to go from A to B or from B to A. All you can measure is the distance from A to B and the round trip time it takes for light to go from A to B and back to A. Then you can calculate the "average" speed of light for the total trip. It won't matter if you do the measurement at rest on Earth or moving at any speed or direction relative to the earth. You will always get the same answer, as long as you are not accelerating. This is experimental evidence and has nothing to do with special relativity.

Prior to Einstein, people were trying to do what you are now trying to do, which is to postulate that the two one-way trips take the same time on Earth (or some other absolute frame) but different times when moving with respect to that absolute frame, which is a valid postulate to make, but it sure makes science difficult, not to mention all the arguments about which absolute reference frame is the "real" one.

Einstein, on the other hand, started with the postulate that the two one-way trips are the same no matter what frame of reference you use, and that leads to nice simple science.

But neither postulate can be proven or known to be "truer" than the other one, because if they could be, they would no longer need to be a postulate.

 

[Dale]

It has nothing to do with the formulas. Formulas work pretty well

That is all a theory is required to do.

 

[JesseM]

Three simple experiments put to question Einstein's Special Relativity interpretation. It has nothing to do with the formulas. Formulas work pretty well; the BIG problem is interpretation!

1.The most recent particle collisions at CERN:
Two Proton Beams at 3.5 TeV, traveling in opposite directions, collide. I don't known the exact angle but I can assume it is quite close to zero as the energy of the collision is about the sum of the energy of the particles. Calculating the speed of the protons, given their energies, gives a speed of around .96c (SR formulas work here pretty well).
Summing both speeds, according to the theorem of addition of speeds gives a speed of around 0.9993c. Calculating the energy for that speed using SR we get around 25 TeV. So, here, SR formulas don't work at all!

The relativistic velocity addition formula only applies when you know the speed of an object in one frame and then want to find the speed of the same object in a different frame with a known speed relative to the first frame. In this example there is no switching between multiple frames, everything is being calculated in the lab frame, so you don't use the velocity addition formula. If you're calculating the energy of two particles in a single frame and there are no potential fields to worry about so each particle's energy is just (rest mass energy) + (kinetic energy), then the total energy of both particles is just the sum of each particle's individual energy in the same frame.

So, why is the energy of the collision only 7 TeV? Why is the energy of the collision roughly the sum of the individual energies, suggesting that the collision takes place at the sum of the speeds? Why can two particles collide at 1,92c when SR “forbids” relative speeds greater than c?

SR only forbids an individual particle from traveling faster than c in a given frame. The rate at which the distance between two particles shrinks in a given frame, known as the closing speed, can be greater than c; if one particle has a position as a function of time given by x(t) = -0.96c*t and the other has x(t) = 0.96c*t, so they collide at x=0 at time t=0, then it's a simple matter to show that before t=0 the distance between them was shrinking at a rate of 1.92 light-seconds per second (for example, at t=-1 seconds, the first particle was at position x=-0.96 light seconds while the second was at x=+0.96 light seconds, so the distance between them at t=-1 seconds was 1.92 light-seconds, and they collided 1 second later at t=0 seconds). In Newtonian physics the closing speed between two objects would be the same as the speed of one object in the other object's rest frame, so they can both be called "relative speed", but in SR the two notions of "relative speed" are different, the closing speed between two objects can be faster than light in the frame of a third party, but the speed of one object in the other object's rest frame will still be slower than light.

Why does SR work perfectly only when calculating the energy and speeds of the particles relatively to Earth?

2.Correction of time on satellite clocks:
If we use SR to calculate the slowing of satellite clocks due to its movement relatively to Earth the results are excelling and we use it all the time. We simply wouldn't have GPS if we didn't have SR equations!
But, if we use the same equations to calculate the correction of the clocks from the perspective of the satellite observer, applying the Principle of Relativity, we get it all wrong! the clocks of the satellite should need no correction at all; the clocks on Earth should be retarded.

Where do you get that idea? The notion that moving clocks always run slower than clocks at rest only applies in an inertial frame; inertial frames are not possible in large regions of curved spacetime, and even if we ignore the curvature of spacetime due to gravity and imagine that the orbiting satellite is just moving in a circle in flat spacetime, circular motion is not inertial (an object moving in a circle in flat spacetime will experience G-forces, the 'centrifugal force', whereas an inertial observer moving in a straight line at constant speed feels weightless). For more on the lack of symmetry between inertial and non-inertial observers, you might want to read up on the twin paradox.

So, as for the GR correction corresponding to the lower intensity of the field at orbit altitude, it seams that the movement effect is not relative: it does not depend on the observer; it is exactly the same for all observers!

3.Einstein's thought experiment for de-synchronization on the 1905 paper:
We have a solid device with a light source, an observer and a clock at one extremity and a mirror, an observer and a clock on the other. When the device is at rest (relatively to Earth) the time needed for light to travel AB is equal to the time needed to travel BA. But, when the device is moving (relatively to Earth) in the direction AB, the time needed for the light to travel from AB is greater that the time needed to travel BA.
Earth doesn't play here any role concerning relative speed of the objects on that system and so, the movement relatively to Earth, should be ignored. So, the system is as much at rest as before.
So:
The device's system is as good as Earth to be the reference frame to which the movement is referred, according to SR Principle of Relativity.
Light should travel, in that system, at speed c, in all directions, as in all the other inertial systems, according to the Principal of the Constancy of Light Speed.
So, applying both Principals of SR, the time needed for light to travel AB should match the time needed to travel BA. But it doesn't!

Yes it does, in the device's own rest frame! You've missed the fact of the relativity of simultaneity, which means that the clocks at either end of the device are out-of-sync in the frame where the device is moving, so even though the observer who sees the device in motion thinks the light took different times to travel AB than to travel BA, in the device's own frame the time was the same. I gave a numerical example on another thread:

Say there's a ruler that's 50 light-seconds long in its own rest frame, moving at 0.6c in my frame. In this case the relativistic gamma-factor (which determines the amount of length contraction and time dilation) is 1.25, so in my frame its length is 50/1.25 = 40 light seconds long. At the front and back of the ruler are clocks which are synchronized in the ruler's rest frame; because of the relativity of simultaneity, this means that in my frame they are out-of-sync, with the front clock's time being behind the back clock's time by vx/c^2 = (0.6c)(50 light-seconds)/c^2 = 30 seconds.

Now, when the back end of the moving ruler is lined up with the 0-light-seconds mark of my own ruler (with my own ruler at rest relative to me), I set up a light flash at that position. Let's say at this moment the clock at the back of the moving ruler reads a time of 0 seconds, and since the clock at the front is always behind it by 30 seconds in my frame, then in my frame the clock at the front must read -30 seconds at that moment. 100 seconds later in my frame, the back end will have moved (100 seconds)*(0.6c) = 60 light-seconds along my ruler, and since the ruler is 40 light-seconds long in my frame, this means the front end will be lined up with the 100-light-seconds mark on my ruler. Since 100 seconds have passed, if the light beam is moving at c in my frame it must have moved 100 light-seconds in that time, so it will also be at the 100-light-seconds mark on my ruler, just having caught up with the front end of the moving ruler.

Since 100 seconds passed in my frame, this means 100/1.25 = 80 seconds have passed on the clocks at the front and back of the moving ruler. Since the clock at the back read 0 seconds when the flash was set off, it now reads 80 seconds; and since the clock at the front read -30 seconds, it now reads 50 seconds. And remember, the ruler was 50 light-seconds long in its own rest frame! So in its frame, where the clock at the front is synchronized with the clock at the back, the light flash was set off at the back when the clock there read 0 seconds, and the light beam passed the clock at the front when its time read 50 seconds, so since the ruler is 50-light-seconds long, the beam must have been moving at 50 light-seconds/50 seconds = c as well! So you can see that everything works out--if I measure distances and times with rulers and clocks at rest in my frame, I conclude the light beam moved at 1 c, and if a moving observer measures distance and times with rulers and clocks at rest in his frame, he also concludes the same light beam moved at 1 c.

Einstein illustrates why the constant speed of light in all frames implies the relativity of simultaneity in a famous thought experiment about a train, which you can read here and here. If two lightning strikes happen at either end of a train simultaneously in the frame of an observer on the tracks who sees the train in motion, then he must conclude that the light will reach an observer at the center of the train at different moments. But if an observer at the center of the train sees light from each strike at different moments, that needn't contradict the idea that both light beams took the same amount of time to travel from the end of the train to his eyes--he can just disagree that the strikes happened simultaneously! Obviously if the two strikes happened 5 second apart in the train-observer's frame rather than happening simultaneously, then if the light from each strike takes the same amount of time to travel from the end of the train to his eyes, he should see the light from one strike 5 seconds after seeing the other strike. So, it is precisely the postulate that the light is supposed to have traveled at c in both frames that forces us to conclude that simultaneity is relative--two strikes which occurred simultaneously in the track-observer's frame must have happened non-simultaneously in the train-observer's frame.

 

[Vanadium 50]

Calculating the speed of the protons, given their energies, gives a speed of around .96c (SR formulas work here pretty well).
Summing both speeds, according to the theorem of addition of speeds gives a speed of around 0.9993c. Calculating the energy for that speed using SR we get around 25 TeV. So, here, SR formulas don't work at all!

Every number is wrong. This is not because "SR formulas don't work at all!" but because you don't understand how to correctly apply them.

I encourage you to take a look at the PF Rules, particularly those on overly speculative posts, as well as the stciky at the top of this forum.

 

[IsometricPion]

So, why is the energy of the collision only 7 TeV? Why is the energy of the collision roughly the sum of the individual energies, suggesting that the collision takes place at the sum of the speeds? Why can two particles collide at 1,92c when SR “forbids” relative speeds greater than c? Why does SR work perfectly only when calculating the energy and speeds of the particles relatively to Earth?

The energy of a collision is defined as the sum of the kinetic energies of the incident particles. So, if one collides two particles each having a kinetic energy of 3.5 TeV, collision energy is 7 TeV. Note that the sum must take place in one frame of reference (in this case the laboratory frame which is also the center of momentum frame in this instance). Just like in Newtonian mechanics energy is not conserved when one shifts between inertial frames with different speeds, so it is not entirely surprising to find that the energy of the collision is ~26000 TeV in the rest frame of one of the protons.

The distance between two objects in SR can be made arbitrarily small via a sufficiently large lorentz boost in that direction. A number of quantities such as the rest mass, space-time interval, etc. do not change under lorentz transformations, so these are in some sense fundamental quantities. Thus, the spatial distance between two objects is not a relevant quantity in SR (finding its time derivative is like finding the time derivative of (\vec{x})^2-c^2(\Delta t)^2 in Newtonian mechanics; it is certainly possible, but it is not physically significant).

 

[Simplyh]

The energy of a collision is defined as the sum of the kinetic energies of the incident particles. So, if one collides two particles each having a kinetic energy of 3.5 TeV, collision energy is 7 TeV. Note that the sum must take place in one frame of reference (in this case the laboratory frame which is also the center of momentum frame in this instance). Just like in Newtonian mechanics energy is not conserved when one shifts between inertial frames with different speeds, so it is not entirely surprising to find that the energy of the collision is ~26000 TeV in the rest frame of one of the protons.

The distance between two objects in SR can be made arbitrarily small via a sufficiently large lorentz boost in that direction. A number of quantities such as the rest mass, space-time interval, etc. do not change under lorentz transformations, so these are in some sense fundamental quantities. Thus, the spatial distance between two objects is not a relevant quantity in SR (finding its time derivative is like finding the time derivative of (\vec{x})^2-c^2(\Delta t)^2 in Newtonian mechanics; it is certainly possible, but it is not physically significant).

At which speed do the particles collide in the lab reference frame? At ,99c or 1,92c? If, for each proton, “it is not entirely surprising to find that the energy of the collision is ~26000 TeV”; then, does de Proton react as having received such an energy? Or does it just react as having collided at 7 Tev?
All the rest you say is just correct, not arguable, mathematics out of the presumptions of SR. I only put to question the presumptions, not their mathematical development.

 

[Simplyh]

You say that in SR “ the closing speed between two objects can be faster than light in the frame of a third party”. Can you develop on this?
“... but the speed of one object in the other object's rest frame will still be slower than light” - this is said by SR. But the prove is that 1/sqr(1-(v2/c2)) would become undetermined for v=c and irrational for v>c which can indeed prove 3 things: there is no possible relative speed greater than c; the formula is incomplete and does not apply to speeds equal and greater than c; the Principle of the Constancy of light speed, which is the bases for that formula, is not correct.
Anyhow, you are just saying what SR says; not arguing in its favour.

Satellite clocks are effectively corrected using SR equations for the relative movement of the satellite on Earth's inertial frame and GR equations for the Gravitational field, summing both effects. The question is: GR equations do not depend on the observer because they only depend on the intensity of the gravitational field; but SR equations do depend on the observer. So that part of the effect would be null for the observer (on-board computer) beside the satellite clock; and Earth clocks should retard in that reference frame. But we know for sure that this does not happen. The total effect, and so the partial relative movement effect, is EXACTLY THE SAME for the computer on Earth and for the computer on board of the satellite!

As for Einstein's thought experiment. All you say is forgetting that the device reference frame, the observers, the clocks, the light source and the mirror are at relative rest. So, in that reference frame there is NO MOVEMENT, according to the Principal of relativity! So, RESPECTING SR, there can be no de-synchro, no difference of lengths, no difference of paths of light, NO DIFFERENCE AT ALL! But there is!

 

[haushofer]

You say that in SR “ the closing speed between two objects can be faster than light in the frame of a third party”. Can you develop on this?

Well, imagine that you send out one photon to the left, and one photon to the right. They both travel at the speed of light c. Every second the distance between the two photons, from your perspective, becomes 2*c bigger. After t seconds the distance x between the two photons is, according to your frame

<br /> x = 2ct<br />

So naively you would then say that

<br /> v=\frac{dx}{dt} = 2c &gt; c<br />

Do you think this violates Einstein's idea that nothing moves faster than the speed of light (or more correctly: nothing can accelerate from v<c to v>c)?

 

[Dale]

GR equations do not depend on the observer

This is incorrect

they only depend on the intensity of the gravitational field

This is also incorrect.

Before criticizing a theory you actually need to learn what it predicts first. Otherwise you are just spouting an ingnorant and irrelevant opinion as is the case here.

 

[Dale]

does de Proton react as having received such an energy? Or does it just react as having collided at 7 Tev?

7 TeV is the mass energy of the collision. All frames agree on it, and that is what determines which kinds of particles can be produced. In different frames the total energy may be greater than 7 TeV, but the mass energy is always 7 TeV.

I only put to question the presumptions

A person's opinion on the presumptions is not relevant. All that matters is whether or not it accurately predicts the results of experiments: http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html

 

[ghwellsjr]

As for Einstein's thought experiment. All you say is forgetting that the device reference frame, the observers, the clocks, the light source and the mirror are at relative rest. So, in that reference frame there is NO MOVEMENT, according to the Principal of relativity! So, RESPECTING SR, there can be no de-synchro, no difference of lengths, no difference of paths of light, NO DIFFERENCE AT ALL! But there is!

In any reference frame, that is, one that is not accelerating, it is not a thought experiment that is the issue. It is real experiments where there is no difference between what you can measure in one reference frame and what you can measure in another reference frame. If you do a "thought experiment" where there is a difference in what you can measure, then you are at odds with reality. If you are talking about differences in things you can't measure, then all that matters is that you get a foundation for doing science that is consistent with itself, makes accurate predictions, doesn't create ambiguities, is easy to understand, etc.

 

[Simplyh]

haushofer:
What you say is correct but is not what Einstein says.

DeleSpan: You are right. I meant the equations used to correct the gravitational effect on satellite clocks. Thanks for the correction.

"In different frames the total energy may be greater than 7 TeV, but the mass energy is always 7 TeV." Can you explain that? The collision takes place at the Proton's reference frame and explains what particles are produced. It corresponds to 7 TeV! Where does this excess energy on the proton's reference frame goes?

ghwellsjr: This experiment can very easily be done. I think modern physics is consensual about the result which corresponds to what I've said. The question is that, following Einstein, modern physics interprets it as a result of de-synchronization. All I say is that this is interpretations doesn't match SR Principles, because as everything is at rest, no difference of any kind could be detected.

 

[IsometricPion]

All the rest you say is just correct, not arguable, mathematics out of the presumptions of SR. I only put to question the presumptions, not their mathematical development.

The presumptions are that space-time is a minkowski space with maximum speed c, and that the laws of physics are the same/valid in each inertial frame. The second assumption is the same as for Newtonian mechanics, about which I have not yet seen you object. So, I can only conclude that you dispute the first postulate. In order to distinguish the type of metric space in which we live (in the limit of negligible gravity/space-time curvature), we do experiments examining the laws of physics at various distances, velocities, etc. There has never been a single experiment (with repeatable results) that has disagreed with the predictions of relativity (within a reasonable estimation of the experimental error).

As for Einstein's thought experiment. All you say is forgetting that the device reference frame, the observers, the clocks, the light source and the mirror are at relative rest. So, in that reference frame there is NO MOVEMENT, according to the Principal of relativity! So, RESPECTING SR, there can be no de-synchro, no difference of lengths, no difference of paths of light, NO DIFFERENCE AT ALL! But there is!

There is no difference/desynchronization in the frame in which the device, mirrors, observers, and clocks are at rest. However, in frames of reference that are in motion (positive or negative) in the direction in which the light beam is travelling, there is a time difference/desynchronization.

 

[Dale]

"In different frames the total energy may be greater than 7 TeV, but the mass energy is always 7 TeV." Can you explain that? The collision takes place at the Proton's reference frame and explains what particles are produced.

The collision takes place in all reference frames, and all reference frames agree on which particles are produced.

It corresponds to 7 TeV! Where does this excess energy on the proton's reference frame goes?

The excess energy goes into the kinetic energy of the products.

 

[ghwellsjr]

We have a solid device with a light source, an observer and a clock at one extremity and a mirror, an observer and a clock on the other. When the device is at rest (relatively to Earth) the time needed for light to travel AB is equal to the time needed to travel BA. But, when the device is moving (relatively to Earth) in the direction AB, the time needed for the light to travel from AB is greater that the time needed to travel BA.

This experiment can very easily be done.

Is the first quote the experiment that you say "can very easily be done" in the second quote?

 

[JesseM]

As for Einstein's thought experiment. All you say is forgetting that the device reference frame, the observers, the clocks, the light source and the mirror are at relative rest. So, in that reference frame there is NO MOVEMENT, according to the Principal of relativity!

Of course, that's exactly what I assumed! The train is completely at rest, so therefore if the observer at the center receives the light from the flashes at different times, but in this frame both light beams had the same distance to reach him and both traveled at the same speed, then this must mean that the flashes themselves occurred at different times.

So, RESPECTING SR, there can be no de-synchro

Huh? You're not making any sense, why do you think the fact that every part of the train is at rest in this frame implies that this frame's opinions about simultaneity can't differ from those of the ground frame? It's not like clocks in this frame are "desynchronized" in any absolute sense, it's just a difference of opinion--the train frame says that its own clocks are synchronized, but the clocks of the ground observer are desynchronized. So, in the train frame the two lightning strikes "really" occurred at different times (i.e. synchronized clocks at either end of the train read different times when the lightning struck next to them), and it's only because the ground observer was using out-of-sync clocks that both of the ground observer's clocks showed the same time when the lightning strikes occurred next to them.

 

[Simplyh]

IsometricPion: could you please answer the questions put by the three experiments I've posted. There is no point on saying that no experiment with repeatable results disagrees with SR, when I'm posted 3 of them. If you don't agree please tell me where I'm wrong; but please no absolute statements.

According to Einstein and modern physics THERE IS a difference in the reference frame of the device. Only it is interpreted as coming from de-synchronization.
Indeed the result of the experiment is according to what Einstein says, but it can not be interpreted as he did, because it contradicts his own SR, where no de-synchronization can be experimented between two clocks at relative rest. I propose an explanation which can be correct or not. Einstein's surely is not.

DeleSpan: You can check. All energy (kinetic and new particles) is the equivalent to 7 TeV! You are stating a wrong result from the experiment!

 

[JesseM]

According to Einstein and modern physics THERE IS a difference in the reference frame of the device. Only it is interpreted as coming from de-synchronization.

But "desynchronization" isn't absolute, it's relative. The train clocks are desynchronized in the frame of the ground observer, but in the train's own rest frame the train clocks are synchronized, and it's the ground observer's clocks that are "desynchronized". According to SR there is no single "correct" frame-independent truth about whose clocks are synchronized and whose are desynchronized. Do you not understand this?

Indeed the result of the experiment is according to what Einstein says, but it can not be interpreted as he did, because it contradicts his own SR, where no de-synchronization can be experimented between two clocks at relative rest.

Again you talk as though there is some absolute sense in which the train's clocks are "desynchronized!" There isn't, SR says different frames disagree about which pairs of clocks are "synchronized" and which are "desynchronized", and no frame's opinions are "more correct" than any other's.

Also, note that it's purely a matter of choice that Einstein picked a scenario where the two lightning strikes happened simultaneously in the ground frame and non-simultaneously in the train frame--he could have equally imagined a different physical scenario where two lightning strikes happen simultaneously in the train frame and non-simultaneously in the ground frame. You could even have a scenario where one strike A happens at the back of the train and two strikes B and C happen at different times at the front of the train, such that strike A and strike B happened simultaneously in the ground frame (and non-simultaneously in the train frame) while strike A and strike C happened simultaneously in the train frame (and non-simultaneously in the ground frame).

 

[Simplyh]

JesseM: Please read! I'm NOT talking about the train de-synchronization experiment which can be object more discussion. I'm talking about the ruler (piston, whatever) experiment in Einstein's 1905 experiment. Please analyse this experiment.
Anyhow: in the train experiment if lightnings are simultaneous on the ground they should be also synchronized on the train, though the times on the ground and on the train are de-synchronized.
If At is the time of lightning A on the train and Bg the time of lightning B on the ground and the others similar; if F is the conversion factor, from SR, of time on the reference frame Ground to reference frame Train, we get:
At = FAg and Bt = FBg (so they are de-synchronized)
But if Ag = Bg (synchronized at the ground)
Then At = FAg and Bt = FAg and so At = Bt (synchronized on the train's frame).
So, though a little bit more tricky, we can't have de-synchronization on the lightning times on the train frame. But it was not what was being discussed.

 

[Dale]

DeleSpan: You can check. All energy (kinetic and new particles) is the equivalent to 7 TeV! You are stating a wrong result from the experiment!

Only in the lab frame. In other frames the total energy may be greater than 7 TeV.

 

[ghwellsjr]

Simplyh: Are you going to answer my question in post #17?

 

[JesseM]

JesseM: Please read! I'm NOT talking about the train de-synchronization experiment which can be object more discussion. I'm talking about the ruler (piston, whatever) experiment in Einstein's 1905 experiment. Please analyse this experiment.

What specific section of the 1905 paper (viewable here) are you referring to? Can you quote it? In any case the point is the same, each frame has a different definition of which clocks are "synchronized" and which aren't, and both frames are equally valid, neither frame's clocks are "desynchronized" in any absolute sense.

Anyhow: in the train experiment if lightnings are simultaneous on the ground they should be also synchronized on the train, though the times on the ground and on the train are de-synchronized.

No, they shouldn't.

If At is the time of lightning A on the train and Bg the time of lightning B on the ground and the others similar; if F is the conversion factor, from SR, of time on the reference frame Ground to reference frame Train, we get:
At = FAg and Bt = FBg (so they are de-synchronized)
But if Ag = Bg (synchronized at the ground)
Then At = FAg and Bt = FAg and so At = Bt (synchronized on the train's frame).
So, though a little bit more tricky, we can't have de-synchronization on the lightning times on the train frame. But it was not what was being discussed.

You should use the actual SR equations instead of making up imaginary ones. There is no "conversion factor" of the type you suggest: the time coordinate t' of an event in the train's frame depends on both the time coordinate t of that event in the ground frame and the position coordinate x of that event in the ground frame. The correct equation is:

t' = gamma*(t - vx/c^2)

where v is the velocity of the train in the ground frame, and gamma = \frac{1}{\sqrt{1 - v^2/c^2}}

So for example say the train is moving with v=0.6c, meaning gamma=1.25. Then say lightning strike A happens at position x=0 light-seconds, t=0 seconds in the ground frame, while lightning strike B happens further along the x-axis at the same moment, at position x=8 light-seconds, t=0 seconds. In that case the time coordinate t' of strike A in the train frame would be:

t' = 1.25 * (0 - 0.6*0) = 0 seconds

While the time coordinate t' of strike B in the train frame would be:

t' = 1.25 * (0 - 0.6*8) = 1.25*(-4.8) = -6 seconds

So you can see that according to the SR equation above (which is just part of the general Lorentz transformation for relating coordinates in one frame to coordinates in another), strike A and B happened 6 seconds apart in the train frame.

 

[IsometricPion]

it contradicts his own SR, where no de-synchronization can be experimented between two clocks at relative rest.

The relevant quote from the paper JesseM cited is:

Observers moving with the moving rod would thus find that the two clocks were not synchronous, while observers in the stationary system would declare the clocks to be synchronous.

However, earlier in the same paper the clocks are defined thus:

at the two ends A and B of the rod, clocks are placed which synchronize with the clocks of the stationary system

There is no contradiction between the clocks being synchronized in the stationary frame (relative to which the rod is moving) and desynchronized in the moving (rod) frame, or vice versa (synchronized in the moving and desynchronized in the stationary).

1.

The energy of the collision will be the sum of the energies of the particles and the energies of the particles will depend on their speeds relatively to Earth, ACCORDING TO SR FORMULAS BUT NOT TO SR INTERPRETATION OF THE PHENOMENON!

The total kinetic energy of the colliding system will depend on the relative speed of the frame from which it is being observed. However, the total rest mass of the system is independent of frame. Just as in Newtonian mechanics, there is a frame in which the products of an inelastic collision are at rest. It is in this frame that the internal energy of the products is most easily evaluated. In SR this frame is the center of momentum frame of the two particles. Since the internal energy of the products is rest mass, and since rest mass is a relativistic invariant, the effective energy of the collision can be taken as energy of the collision in the center of momentum frame (effective in the sense that the collision dynamics will be dictated by this energy, i.e. the equations take on a particularly "nice" form in this frame). In short, the dynamics of the collision depend solely on the relative velocities of the colliding parts of the system.

2.

Nothing happens to Earth clocks, which don't move on Earth's electromagnetic field, while satellite clocks, which do move on Earth's field, do slow down for all kinds of observers, ACCORDING TO SR FORMULAS BUT NOT TO ITS INTERPRETATION OF THE PHENOMENON!

The formulas of SR do not contain terms involving the electromagnetic field (or any other field for that matter). The SR portion of this effect would be observed on the satellite (if it is taken as stationary) as a slowing of the clocks in the Earth's frame.

3.

... the Principle of the Constancy of Light Speed in all inertial systems!
This principle is only valid to system Earth in particular and to all homogeneous fields in general, NOT TO SYSTEMS IN MOVEMENT RELATIVELY TO THE FIELD WHERE LIGHT IS DISPLACING!

Electromagnetic systems obey the principle of linear superposition, the addition of light to a preexisting electromagnetic field only affects the field linearly (i.e. the preexisting and light-produced electromagnetic fields just add vectorially). The preexisting electromagnetic field is in no way affected by the light (it is the same before the light arrives as after it has gone).

ACCORDING TO SR FORMULAS BUT NOT TO ITS INTERPRETATION OF THE PHENOMENON!

I am not entirely sure I know what you mean here. Given the necessary parameters, the formulas predict results. What is there to interpret? Are you implying that a theory that predicts all the same results, but has a different interpretation, is different in a significant way?

 

[Simplyh]

Only in the lab frame. In other frames the total energy may be greater than 7 TeV.

This has no sense. We can discuss the lab frame but not the Proton's frame. When the proton collides all energy IN HIS FRAME is transformed in new particles and their kinetic energies and this is what researchers on the CERN are looking for and what was informed to have occurred at 7 TeV! If else, please explain what happened in the proton's frame.

 

[Simplyh]

Simplyh: Are you going to answer my question in post #17?

Sorry. Too many questions to answer. Yes, Einstein's thought experiment from 1905 seems to me simple to execute.

 

[ghwellsjr]

It's impossible to execute. Can you cite for me an instance when anyone performed the experiment that you call #3 in your first post, which is determining that "the time needed for light to travel AB is equal to the time needed to travel BA"?

 

[JesseM]

This has no sense. We can discuss the lab frame but not the Proton's frame. When the proton collides all energy IN HIS FRAME is transformed in new particles and their kinetic energies and this is what researchers on the CERN are looking for and what was informed to have occurred at 7 TeV! If else, please explain what happened in the proton's frame.

In the proton's frame the same particles are created, but their kinetic energies are different (because their velocities are different in this frame), so the total energy (the sum of the rest mass energy for each particle plus the kinetic energy of each particle) is different too.

 

[JesseM]

It's impossible to execute. Can you cite for me an instance when anyone performed the experiment that you call #3 in your first post, which is determining that "the time needed for light to travel AB is equal to the time needed to travel BA"?

There have been experiments to measure the one-way speed of light and check that it's still c, see here.

 

[Dale]

This has no sense. We can discuss the lab frame but not the Proton's frame.

You can discuss any frame you like. That is the whole point of the first postulate.

When the proton collides all energy IN HIS FRAME is transformed in new particles and their kinetic energies and this is what researchers on the CERN are looking for and what was informed to have occurred at 7 TeV! If else, please explain what happened in the proton's frame.

In the lab frame a proton from the left has a four-momentum of (3.5, 3.49999987, 0, 0) TeV/c and the proton from the right has a four-momentum of (3.5, -3.49999987, 0, 0) TeV/c so by conservation of four-momentum the product has a four-momentum of (7.0, 0, 0, 0) TeV/c corresponding to a mass of 7.0 TeV/c² and a kinetic energy of 0 TeV.

In the rest frame of the proton from the right a proton from the left has a four-momentum of
(25682.97778423260, 25682.97778423259, 0, 0) TeV/c and the proton from the right has a four-momentum of (0.00095393919, 0, 0, 0) TeV/c so by conservation of four-momentum the product has a four-momentum of (25682.97873817180, 25682.97778423259, 0, 0) TeV/c corresponding to a mass of 7.0 TeV/c² and a kinetic energy of 25675.97873817180 TeV.

 

[ghwellsjr]

There have been experiments to measure the one-way speed of light and check that it's still c, see here.

If we could measure the one-way speed of light and find that it was constant, Einstein would not have needed to postulate that it was constant, or we would not continue to base Special Relativity on that postulate. Your link points out that although these tests "clearly use a one-way light path and find isotropy, they are inherently unable to rule out a large class of theories in which the one-way speed of light is anisotropic".

Prior to Einstein, scientists explained the null result of MMX by concluding that since the surface of the Earth was constantly accelerating, and therefore couldn't always be stationary in the æther, there must be a foreshortening of dimensions in the direction of travel against the æther wind and a slowing down of clocks, and along with that, the one-way speed of light was different in different directions, particularly against versus with the æther wind, although the measured round-trip speed of light was always measured as a constant. They postulated that there was a stationary æther and the speed of light was a constant in that medium and even though the measured round-trip speed of light was always the same, even for moving observers, the assumed one-way speed of light was only constant when an observer was not moving with respect to the æther. That's what your link states and it is absolutely true.

So depending on which postulate you start with, you will come to a different conclusion about the unmeasureable one-way speed of light. If we could actually measure the one way speed of light, independent of any postulate, then we could decide once and for all between an æther theory and the Theory of Special Relativity, but just like we cannot determine where the rest frame of the æther is (if it were to exist), we cannot decide by experiment or measurement between those two theories.

 

[JesseM]

If we could measure the one-way speed of light and find that it was constant, Einstein would not have needed to postulate that it was constant, or we would not continue to base Special Relativity on that postulate.

I would say the "postulates" are predictions about what will be seen in future experiments. Specifically they are saying it is possible to find a family of coordinate systems, each moving at constant coordinate velocity as measured by any other system in the family, such that both postulates are satisfied in this family. We can easily imagine a different set of laws of physics where this wouldn't be possible, where any attempt to define a set of coordinate systems such that light had the same one-way speed in each one would result in the laws of physics working differently in different members of the set. For example, this would be true in a Newtonian universe with a preferred ether frame, in spite of the fact that you could define a set of coordinate systems in such a universe where light always moved at c in each one. One obvious way "laws of physics working differently in different frames" could manifest in this case would be that if you synchronized a pair of clocks at a common location and then moved them apart very slowly in your frame, there would be one preferred frame where they would remain synchronized in the coordinates of that frame, while in other frames they would become significantly out-of-sync as the distance increased regardless of how slowly you moved them, and thus the clocks themselves would not measure the one-way-speed of light to be c even if the coordinate system where they were at rest did. I would guess that experiments to test the one-way speed of light are doing something like this: synchronizing clocks at a common location, moving them apart at low speed, and seeing if the clocks do measure the one-way-speed of light to be c.

Prior to Einstein, scientists explained the null result of MMX by concluding that since the surface of the Earth was constantly accelerating, and therefore couldn't always be stationary in the æther, there must be a foreshortening of dimensions in the direction of travel against the æther wind and a slowing down of clocks, and along with that, the one-way speed of light was different in different directions, particularly against versus with the æther wind, although the measured round-trip speed of light was always measured as a constant. They postulated that there was a stationary æther and the speed of light was a constant in that medium and even though the measured round-trip speed of light was always the same, even for moving observers, the assumed one-way speed of light was only constant when an observer was not moving with respect to the æther. That's what your link states and it is absolutely true.

So depending on which postulate you start with, you will come to a different conclusion about the unmeasureable one-way speed of light. If we could actually measure the one way speed of light, independent of any postulate, then we could decide once and for all between an æther theory and the Theory of Special Relativity, but just like we cannot determine where the rest frame of the æther is (if it were to exist), we cannot decide by experiment or measurement between those two theories.

I'd say the type of ether theory you seem to be discussing is really more of an "interpretation" (like the various 'interpretations' of quantum mechanics) than a theory, since it doesn't make any new predictions, it still says that all observable laws of physics work the same way in all the coordinate systems given by the Lorentz transformation. A true alternative physical theory should predict there are at least some phenomena which behave differently in some inertial frames than others.

 

[Ich]

I'd say the type of ether theory you seem to be discussing is really more of an "interpretation"

But as Simplyh is talking about "interpretations", not theories, ghwellsjr has a point in saying that you can't measure the one way speed.
OTOH, Simplyh's claim that an experiment could decide which interpretation is correct is contradicting himself.

Hopefully someone manages to persuade Simplyh to learn some basic SR (or, for that matter, some basic physics, as his/her problem with the definition of energy is not specific to SR), it's hard to deal with inconsistent belief systems.

 

[ghwellsjr]

I would say the "postulates" are predictions about what will be seen in future experiments.

Did you mean predictions still in the future or predictions in Einstein's future that have now been fulfilled?

Either way, this is the first I have ever heard of this new definition of "postulate" and I totally disagree. Einstein was not making a prediction, he was stating an assumption that could not be proven or measured either then or now. His postulate was the same as saying, "in any inertial frame, you can assume that you are at rest with the æther", which is a ridiculous thing to say, but it works just as well as the previously assumed postulate which was "you can assume that there exists just one inertial frame in which you can be at rest with the æther".

I would guess that experiments to test the one-way speed of light are doing something like this: synchronizing clocks at a common location, moving them apart at low speed, and seeing if the clocks do measure the one-way-speed of light to be c.

Didn't you read your own link? It says: "In all of these theories the effects of slow clock transport exactly offset the effects of the anisotropic one-way speed of light (in any inertial frame), and all are experimentally indistinguishable from SR."

I'd say the type of ether theory you seem to be discussing is really more of an "interpretation" (like the various 'interpretations' of quantum mechanics) than a theory, since it doesn't make any new predictions, it still says that all observable laws of physics work the same way in all the coordinate systems given by the Lorentz transformation. A true alternative physical theory should predict there are at least some phenomena which behave differently in some inertial frames than others.

I wasn't talking about an "interpretation" of SR, I was talking about what scientists believed before SR. You could say SR was the new alternative physical theory to the æther theory that everyone believed in prior to SR. But, as your link pointed out, SR theory and æther theory are indistinguishable from each other.

 

[jtbell]

SR theory and æther theory are indistinguishable from each other.

Better: "SR theory and a particular version of aether theory are indistinguishable from each other."

 

[Simplyh]

What specific section of the 1905 paper (viewable here)


There is no "conversion factor" of the type you suggest: ... The correct equation is:

t' = gamma*(t - vx/c^2)

where v is the velocity of the train in the ground frame, and gamma = \frac{1}{\sqrt{1 - v^2/c^2}}

So for example say the train is moving with v=0.6c, meaning gamma=1.25. Then say lightning strike A happens at position x=0 light-seconds, t=0 seconds in the ground frame, while lightning strike B happens further along the x-axis at the same moment, at position x=8 light-seconds, t=0 seconds. In that case the time coordinate t' of strike A in the train frame would be:

t' = 1.25 * (0 - 0.6*0) = 0 seconds

While the time coordinate t' of strike B in the train frame would be:

t' = 1.25 * (0 - 0.6*8) = 1.25*(-4.8) = -6 seconds

So you can see that according to the SR equation above (which is just part of the general Lorentz transformation for relating coordinates in one frame to coordinates in another), strike A and B happened 6 seconds apart in the train frame.

Any two events with coordinates (x,t) equal to (0,0) and (x,0), with x <>0 are not simultaneous in the same reference frame.
If we have two events at distance, then “... it is not possible without further assumption to compare, in respect of time, an event at A with an event at B. We have so far defined only an ``A time'' and a ``B time.'' We have not defined a common ``time'' for A and B, for the latter cannot be defined at all unless we establish by definition that the ``time'' required by light to travel from A to B equals the ``time'' it requires to travel from B to A. Let a ray of light start at the ``A time'' from A towards B, let it at the ``B time'' be reflected at B in the direction of A, and arrive again at A at the ``A time'' .
In accordance with definition the two clocks synchronize if TB – TA = T'A – TB “(Einstein – 1905 paper).
So, according to this definition from Einstein any events (x,t) are only simultaneous in the same reference frame if tx = x/c. This means that your events would only be simultaneous if one had coordinates (0,0) and the other (8,8/c). Applying now the Lorentz transformation for time we get:
t' = 1,25 * (8/c – 0,6*8/c) = 1,25*8/c(1-,6) = 1,25*8/c*,4 = 4/c
Let's remember that a lightning took place at coordinates (8,8/c) in the platform frame. The same lightning has as coordinates in the train frame (x';t') = (x';4/c). But to be simultaneous with event (0,0) in the train frame, the time at that point must be t' = x'/c. So:
x'/c = gamma* (x-vt)/c = gama*(x-vx/c)/c = 1,25*(8-0,6c8/c)/c = 1,25*(8/c*(1-,6)) = 1,25*8/c*,4 = 4/c
And so both lightenings are simultaneous in both reference frames.
Indeed, this is equivalent to say that if S and S' are two inertial systems and we place the origin of S at any event in space-time, then, the corresponding event on S' will be given by the contraction factor. Or, in other words: for any event in space-time S, with coordinates (x,y,z,t), we'll have a corresponding event (x',y',z',t'), on space time S', whose coordinates are given by the contraction factor.
Let's please go back to the 1905 experiment which is easier to understand because everything happens in the same reference frame.
We have a solid arm with two clocks and two observers at extremities A and B. At A there is a light source; at B a mirror. Let a light beam come from A, be reflected at B and go back to A. Time for light to travel from A to B should always be equal to time for light to travel from B to A because all happens in the same reference frame. But it is not so: if the frame is stationary relatively to Earth this is correct; if the frame displaces relatively to Earth than this is not correct. This obviously means that light does not travel at the same speed in all directions in that inertial system whenever that system travels relatively to Earth. Why?

 

[JesseM]

Any two events with coordinates (x,t) equal to (0,0) and (x,0), with x <>0 are not simultaneous in the same reference frame.

What do you mean "in the same reference frame"? They are certainly simultaneous in the frame where the first event had coordinates (0,0) and the second had coordinates (x,0), because all "simultaneous" means is "same time coordinate", and both have a time coordinate of 0 in this frame. In a second inertial frame in motion relative to this one, the events would be assigned different coordinates and their time coordinates might no longer be equal, in which case they'd be non-simultaneous in the second frame.

If we have two events at distance, then “... it is not possible without further assumption to compare, in respect of time, an event at A with an event at B. We have so far defined only an ``A time'' and a ``B time.'' We have not defined a common ``time'' for A and B, for the latter cannot be defined at all unless we establish by definition that the ``time'' required by light to travel from A to B equals the ``time'' it requires to travel from B to A. Let a ray of light start at the ``A time'' from A towards B, let it at the ``B time'' be reflected at B in the direction of A, and arrive again at A at the ``A time'' .
In accordance with definition the two clocks synchronize if TB – TA = T'A – TB “(Einstein – 1905 paper).
So, according to this definition from Einstein any events (x,t) are only simultaneous in the same reference frame if tx = x/c.

How do you get that from Einstein's definitions? The units in your equation tx = x/c don't make sense since the left side has units of time*distance (unless you mean to write t_x, the x just being a subscript) while the right has units of time. And your equation doesn't seem to make sense as a definition of simultaneity, because it seems to deal only with a single set of x and t coordinates, while simultaneity always deals with a pair of events with different coordinates, we might call them (x1, t1) and (x2, t2). And Einsteins' definition above was really dealing with three different events which could be labeled (XA, TA), (XB, TB) and (X'A, T'A). The first event is light being sent from clock A, the second event is the light beam being reflected from clock B, and the third event is the reflected light being received by clock A. Since these coordinates are supposed to in the rest frame of the clocks, XA = X'A, the distance between clocks A and B is (XB - XA), and if the clocks are synchronized in this frame then TB - TA = (XB - XA)/c. Of course, this assumes the coordinate system we are using to describe the events is the same as the one where the clocks are at rest and we want to synchronize them, if we want to apply Einstein's definition using coordinates of a frame that is not the rest frame of the two clocks, translating the definition into equations involving the frame's coordinates would be more complicated (see below for an example).

This means that your events would only be simultaneous if one had coordinates (0,0) and the other (8,8/c).

You mean, they would be simultaneous in the train frame if those were the coordinates in the platform frame? Again you can only talk about events being "simultaneous" relative to a particular choice of frame, never in an absolute sense!

But even if that is what you meant, your math is wrong. If the train is moving at 0.6c relative to the platform frame, and its length is 8 light-seconds in the platform frame, then the event with coordinates in the platform frame x=12.5, t=7.5 will occur at the front end of the train and will be simultaneous in the train frame with the event at the back end of the train at coordinates x=0, t=0 in the platform frame. In other words, if a clock A at the back of the train reads 0 at x=0, t=0, then a clock B at the front of the train must read 0 at x=12.5, t=7.5 in order for it to be "synchronized" with clock A in the train's own rest frame.

With a little analysis we can show that this does make sense in terms of Einstein's definition. Suppose we have a clock A at the back of the train and a clock B at the front, and their worldlines in the coordinates of the platform frame are giving by x=0.6c*t for clock A, and x=0.6c*t + 8 for clock B (these equations ensure that they are both moving at 0.6c, and that at t=0 clock A is at x=0 while clock B is at x=8). Suppose at t=-12.5 seconds in the platform frame, a light signal is sent from clock A; by the equation x=0.6c*t, clock A must be at position x=-7.5 light-seconds when the signal is sent. We assume that at x=0, t=0 clock A read a time of zero, but clock A is running slow by a factor of \sqrt{1 - 0.6^2} = 0.8 in the platform frame, so 12.5 seconds earlier at t=-12.5 seconds, clock A read a time of 0.8*-12.5 = -10 seconds, and we call this reading TA in Einstein's notation.

If a light beam is emitted at x=-7.5, t=-12.5 in the platform frame, the light beam's position as a function of time in this frame must be x = c*t + 5 (this ensures that the light moves at a coordinate speed of c, and that at t=-12.5 it is at position x=-12.5 + 5 = -7.5). So if the front of the train has position as a function of time given by x=0.6c*t + 8, then to figure out when the light beam will catch up with the front, we set these equal, giving c*t + 5 = 0.6c*t + 8, and solving for t gives t = (8 - 5)/(1c - 0.6c) = 3/0.4c = 7.5 seconds. If you plug this time into either the light beam equation or the equation for the front of the train, you find that the x-coordinate of the light catching up to the front of the train must be x=12.5 light-seconds. And remember, I said above that the clock B should read 0 at exactly these coordinates in the platform frame in order for it to be "synchronized" with clock A in the train frame. So, in Einstein's notation we can say that TB = 0, since TB is supposed to be the time on clock B when the light hits it and is reflected back to A.

If the light beam is reflected at these coordinates, then its speed remains constant but its direction changes, so its new position as a function of time is given by x = -c*t + 20 (this ensures that the light is now moving at -c along the x-axis, and that at t=7.5 it has position x=-7.5 + 20 = 12.5 light-seconds). And the position as a function of time for clock A was x=0.6c*t, so to find when the reflected light gets back to clock A we set them equal, giving -c*t + 20 = 0.6c*t, solving for t gives t = 20/(0.6c + 1c) = 12.5 seconds. Since clock A read 0 at t=0, and it's running slow by a factor of 0.8, at t=12.5 seconds clock A reads a time of 12.5*0.8 = 10 seconds. So in Einstein's notation, we have T'A = 10 seconds.

Putting it all together, with TA = -10 seconds, TB = 0 seconds, and T'A = 10 seconds, you can see that Einstein's equation TB – TA = T'A – TB is indeed satisfied here. Thus, in order for clocks A and B to be synchronized in their own frame, if clock A reads 0 at x=0, t=0 in the platform frame, clock B must read 0 at x=12.5 light-seconds, t=7.5 seconds.

Now to check that this matches the Lorentz transformation. Transforming from the platform frame to the train frame, x=0, t=0 in the platform frame corresponds to x'=0, t'=0 in the train frame. As for x=12.5, t=7.5, plugging into the Lorentz transformation gives:

x' = gamma*(x - vt) = 1.25 * (12.5 - 0.6*7.5) = 10
t' = gamma*(t - vx/c^2) = 1.25 * (7.5 - 0.6*12.5) = 0

So, both events have a time coordinate of t'=0 in the train frame, so they are indeed simultaneous in this frame according to the Lorentz transformation.

Let's please go back to the 1905 experiment which is easier to understand because everything happens in the same reference frame.
We have a solid arm with two clocks and two observers at extremities A and B. At A there is a light source; at B a mirror. Let a light beam come from A, be reflected at B and go back to A. Time for light to travel from A to B should always be equal to time for light to travel from B to A because all happens in the same reference frame.

"time" in what frame? If the device is moving in the direction of B in your frame, then in your frame the time from A to B is not equal to the time from B to A, because B is moving away from the light and A is moving towards the light, therefore the light has a longer distance to travel to go from A to B then it does to go from B to A, and since it travels at the same speed in both directions in your frame, the time to go from A to B must be larger. But if there are clocks attached to A and B, and these clocks are "synchronized" in the device's own frame, then if TA is the reading of the clock at A when the light leaves it, TB is the reading of the clock at B when the light hits it, and T'A is the reading of the clock at A when the light returns to it, the equation (TB - TA) = (T'A - TB) will be satisfied. In your frame this is because the clocks are out-of-sync, so even though the time in your frame between the first pair of events is different than the time in your frame between the second pair, the actual readings on the clocks at each event will satisfy (TB - TA) = (T'A - TB). In the device's own rest frame the clocks are "really" synchronized", and the reason (TB - TA) = (T'A - TB) is that the coordinate time between each pair of events really is the same in the device's frame, since the device is at rest and the light travels the same distance in both directions in this frame.

But it is not so: if the frame is stationary relatively to Earth this is correct; if the frame displaces relatively to Earth than this is not correct. This obviously means that light does not travel at the same speed in all directions in that inertial system whenever that system travels relatively to Earth.

Wrong, see above. The light does travel at the same speed in all directions in the device's rest frame, since that frame defines distance/time in terms of distance as measured by something at rest in the frame (like the device itself), and assigns time coordinates to events using clocks which are considered to be "synchronized" in that frame (like the pair of clocks at either end of the device). So the distance between the two pairs of events above will be equal, and the time between each pair will also be equal since it is true of the clock readings TA, TB and T'A that (TB - TA) = (T'A - TB).

 

[ghwellsjr]

Better: "SR theory and a particular version of aether theory are indistinguishable from each other."

I was paraphrasing the quote from JesseM's link (see post #35) which says "all are experimentally indistinguishable from SR", not just one particular theory.

 

[JesseM]

I was paraphrasing the quote from JesseM's link (see post #35) which says "all are experimentally indistinguishable from SR", not just one particular theory.

But they were referring to a particular class of aether theories (the ones I would call 'interpretations' rather than 'theories') which can't be ruled out by the experiments listed, they weren't saying that all aether theories in general are indistinguishable from SR. From the link:

Note that while these experiments clearly use a one-way light path and find isotropy, they are inherently unable to rule out a large class of theories in which the one-way speed of light is anisotropic. These theories share the property that the round-trip speed of light is isotropic in any inertial frame, but the one-way speed is isotropic only in an æther frame. In all of these theories the effects of slow clock transport exactly offset the effects of the anisotropic one-way speed of light (in any inertial frame), and all are experimentally indistinguishable from SR.

In particular, imagine an aether theory where Lorentz contraction of objects moving relative to the aether frame still happens, but time dilation of clocks moving relative to the aether frame doesn't happen. In this case all experiments which look at the two-way speed of light in different directions, like the Michelson-Morley experiment, would still show it has the same two-way speed in all directions regardless of the motion of the device (without time dilation the precise value of that two way-speed would be different depending on the device's motion but then the Michelson-Morley experiment didn't try to measure the value, just whether it was the same or different along different arms of the device). But experiments like the ones listed, where the clocks were synchronized at a single location and then moved apart, would give different results than SR predicts when the one-way speed was measured.

 

[JesseM]

Did you mean predictions still in the future or predictions in Einstein's future that have now been fulfilled?

Predictions about all possible fundamental laws discoverable by experiment, predictions which have so far proven correct when we look at all the most fundamental laws of physics found since (the standard model of particle physics, for example). In modern terms I would say he was predicting that all the fundamental laws of physics would turn out to be Lorentz-invariant, that is, if you write the equations of the laws of physics in the coordinates of one inertial frame and then apply the Lorentz transformation, the equations in the new frame will be unchanged (and of course the Lorentz transformation can itself be derived from the two postulates of SR). This is a physical prediction which could quite easily be falsified, since it's possible to write down all sorts of equations that are not Lorentz-invariant (Newtonian gravity for example), and thus if you used the Lorentz transformation

Either way, this is the first I have ever heard of this new definition of "postulate" and I totally disagree. Einstein was not making a prediction, he was stating an assumption that could not be proven or measured either then or now.

It's not an "assumption" that the laws of physics are Lorentz-invariant. And if they weren't (if Newton's gravity was correct, say), then it would be impossible to come up with a coordinate transformation giving a family of coordinate systems that satisfied both of the two postulates. Do you disagree?

Didn't you read your own link? It says: "In all of these theories the effects of slow clock transport exactly offset the effects of the anisotropic one-way speed of light (in any inertial frame), and all are experimentally indistinguishable from SR."

See my previous post #40, they weren't talking about all possible aether theories.

I wasn't talking about an "interpretation" of SR, I was talking about what scientists believed before SR. You could say SR was the new alternative physical theory to the æther theory that everyone believed in prior to SR. But, as your link pointed out, SR theory and æther theory are indistinguishable from each other.

No they aren't, since before SR scientists had no reason to suppose that all physical rulers would shrink by gamma when moving relative to the ether (even ones not based on electromagnetic forces), or that all physical clocks would slow down by gamma when moving relative to the ether. If you add these assumptions then aether theories do become experimentally indistinguishable from SR, but they would be rather strange assumptions prior to SR, there's no a priori reason to think they'd be true in an aether theory.

 

[ghwellsjr]

Prior to SR in 1905, time dilation and length contraction were the explanations for the null result of MMX and some follow-on experiments. It was the presumed physical contraction of the apparatus that was believed to have caused the null result.

It is true that Maxwell did not correctly understand the implications of his equations and believed in an absolute æther and that an experiment could have detected an æther wind, but that shouldn't detract from the fact that the prediction could have been made from his equations that there wouldn't have been a detectible æther. Who knows how he would have responded to MMX since he died even before the earlier experiment that Michelson performed. Maybe he would have tenaciously hung on to the idea of an æther or maybe he would have been the one to have invented Special Relativity many years before Einstein. Who knows?

 

[Dale]

JesseM and ghwellsjr, I don't really follow your present argument, but a postulate is an assumption by definition.

 

[JesseM]

Prior to SR in 1905, time dilation and length contraction were the explanations for the null result of MMX and some follow-on experiments. It was the presumed physical contraction of the apparatus that was believed to have caused the null result.

Only length contraction was needed to explain the null result of the MMX--are you saying that anyone had actually proposed that all clocks also experience time dilation when moving relative to the aether? I know Lorentz gave the Lorentz transformation prior to Einstein, but my impression was that he just saw it as a sort of interesting mathematical fact that Maxwell's laws would be invariant under such a transformation, I don't think anyone prior to Einstein proposed that all physical laws would be Lorentz-invariant and thus that it would be absolutely impossible for any experiment to give a different result depending on one's velocity relative to the aether.

It is true that Maxwell did not correctly understand the implications of his equations and believed in an absolute æther and that an experiment could have detected an æther wind, but that shouldn't detract from the fact that the prediction could have been made from his equations that there wouldn't have been a detectible æther.

No, it couldn't. It is perfectly conceivable that purely electromagnetic phenomena will be the same under the Lorentz transformation, but that the forces governing the matter that makes up physical clocks and rulers are not purely electromagnetic, and that the equations for at least some of these non-electromagnetic forces would not be Lorentz-invariant. In this case one might have rulers that didn't shrink when moving relative to the aether, and clocks that didn't slow down. Einstein's insight was in predicting that all fundamental physical laws would turn out to be Lorentz-invariant too, not just electromagnetic ones.

Who knows how he would have responded to MMX since he died even before the earlier experiment that Michelson performed. Maybe he would have tenaciously hung on to the idea of an æther or maybe he would have been the one to have invented Special Relativity many years before Einstein. Who knows?

True, we don't know, but my point is not to denigrate Maxwell, just to point out that in actual history Einstein was the first to publish this idea, and that taken together the two postulates of SR do constitute an actual physical prediction (that all fundamental laws are Lorentz-invariant) and cannot simply be considered "true by definition".

 

[JesseM]

JesseM and ghwellsjr, I don't really follow your present argument, but a postulate is an assumption by definition.

What do you mean by "assumption", are you suggesting that Einstein's postulates don't constitute an actual physical prediction about the way the laws of physics work? As I just said to ghwellsjr, my point is that taken together the two postulates are equivalent to the modern statement that all the fundamental laws of physics are Lorentz-invariant, and I'd say that this is a physical prediction which we could easily imagine being falsified by experiment (in which case it would be impossible to define a set of 'inertial frames' in which both postulates of SR would hold true). Do you disagree?

 

[Dale]

As I just said to ghwellsjr, my point is that taken together the two postulates are equivalent to the modern statement that all the fundamental laws of physics are Lorentz-invariant, and I'd say that this is a physical prediction which we could easily imagine being falsified by experiment (in which case it would be impossible to define a set of 'inertial frames' in which both postulates of SR would hold true). Do you disagree?

I agree that the two postulates are equivalent to the modern statement that all the fundamental laws of physics are Lorentz-invariant. I just don't know why you wouldn't consider that a (testable) assumption.

 

[JesseM]

I agree that the two postulates are equivalent to the modern statement that all the fundamental laws of physics are Lorentz-invariant. I just don't know why you wouldn't consider that a (testable) assumption.

I would definitely consider it testable! If for you an "assumption" can be tested then I have no problem with your use of the word. But ghwellsjr seemed to have been using the words "assumption" and "postulate" differently in post #35, to mean something that is true as a matter of the definitions used, and is not testable:

Either way, this is the first I have ever heard of this new definition of "postulate" and I totally disagree. Einstein was not making a prediction, he was stating an assumption that could not be proven or measured either then or now. His postulate was the same as saying, "in any inertial frame, you can assume that you are at rest with the æther", which is a ridiculous thing to say, but it works just as well as the previously assumed postulate which was "you can assume that there exists just one inertial frame in which you can be at rest with the æther".

This is what the disagreement between myself and ghwellsjr here was about.

 

[Simplyh]

You can discuss any frame you like. That is the whole point of the first postulate.

In the lab frame a proton from the left has a four-momentum of (3.5, 3.49999987, 0, 0) TeV/c and the proton from the right has a four-momentum of (3.5, -3.49999987, 0, 0) TeV/c so by conservation of four-momentum the product has a four-momentum of (7.0, 0, 0, 0) TeV/c corresponding to a mass of 7.0 TeV/c² and a kinetic energy of 0 TeV.

In the rest frame of the proton from the right a proton from the left has a four-momentum of
(25682.97778423260, 25682.97778423259, 0, 0) TeV/c and the proton from the right has a four-momentum of (0.00095393919, 0, 0, 0) TeV/c so by conservation of four-momentum the product has a four-momentum of (25682.97873817180, 25682.97778423259, 0, 0) TeV/c corresponding to a mass of 7.0 TeV/c² and a kinetic energy of 25675.97873817180 TeV.

You are right! I was wrongly assuming that Px would be zero also in the Proton's frame which of course is absurd. I stepped on this and decided to include it with only a brief superficial analyses. This is the result of rushing. Sorry: nothing can be concluded after this experiment about the relative speed of the two particles: according to SR they will continue to have a relative speed minor than c.

 

[Simplyh]

There have been experiments to measure the one-way speed of light and check that it's still c, see here.

I've tried to see where you mention but could not find any experiment measuring speed of light on a frame moving relatively to Earth. Could you please spare me time and identify the experiment? Thanks

 

[Simplyh]

What do you mean "in the same reference frame"? ... will also be equal since it is true of the clock readings TA, TB and T'A that (TB - TA) = (T'A - TB).

You understood me wrong a lot o times. Perhaps it's my fault. Of course in tx the x is a subscript. I don't know how to do subscripts here. Tx was meant to be all of them: t1, t2, …, tn.

You say: “Since these coordinates are supposed to in the rest frame of the clocks, XA = X'A, the distance between clocks A and B is (XB - XA), and if the clocks are synchronized in this frame then TB - TA = (XB – XA)/c.” This is quite correct and means coordinate time of B minus coordinate time of A equals coordinate x of B minus coordinate x of A divided by c. If we are comparing all events synchronized with event (0,0), than A coordinates will be (0,0) and B coordinates (x,(x-0)/c) = (x,x/c).
So, do we agree that, in the same reference frame, all events simultaneous to the origin (0,0) have coordinates (x, x/c)?

Of course I was applying that to the rest frame (the station, not the train). So I will ignore all your development assuming that I was applying it to the train frame which, we both agree, is wrong.

So you must apply the Lorentz transformation to the coordinates of B in S; not to the coordinate x of B and the coordinate t of A as you have done. If you do so and then apply Einstein's concept of simultaneity at distance you will see that events B' and A' are as simultaneous as B and A. But, the time coordinates of A and B are not the same; the same applies to the time coordinates A' and B'.

Let's go to the 1905 experiment. You say: “"time" in what frame? If the device is moving in the direction of B in your frame.” This is not correct: my frame is the devices' frame where everything is at rest even when it displaces relatively to Earth. All the objects in the experiment are at rest relatively to the devices frame! Please don't make any calculations; just tell me what is moving considering the device's frame? The observer in A, clock in A, light source in A? Observer in B, clock in B, mirror in B? My frame can be moving relatively to whatever I want but everything in the experiment will still be at rest relatively to that frame. If everything is at rest how can light speed not be the same on both directions?