Comparing Lorentz and Einstein: Questions Answered

[hprog]

I have recently learned the basics special relativity and it is amazing!, but I still have a few questions and I will be thankful if one can answer me.
(I will rather open an extra thread for each question that bothers me, so each question can be handled independently.)

So I would like to get more understanding on the difference between Lorenz and Einstein.

1)What caused Einstein to drop the ether, if Lorentz has explained it so well, was anything wrong with Lorentz calculations?

2) Since Lorentz was the first to propose time dilation and space contraction, and Galileo was to the first to propose the principle of relativity, so what had Einstein invented?

3) how does SR explains the Michelson-Morly experiment?, after all the Earth is not an inertial frame of reference and it is constantly moving in a non linear motion.

 

[jtbell]

1)What caused Einstein to drop the ether, if Lorentz has explained it so well, was anything wrong with Lorentz calculations?

It's basically a philosophical preference to avoid reference to entities that cannot be observed or measured even in principle. See the discussion in this thread:

https://www.physicsforums.com/showthread.php?t=408772

 

[hprog]

What about my other questions?.
What had Einstein invented, and how does SR explain the Michelson-Morley experiment? is SR actually explaining it the same as Lorentz?.

 

[ghwellsjr]

The Earth moves so slowly compared to the time over which the Michaelson-Morley Experiment was performed and the gravitational effects were so small that the experiment could have detected the æther wind, if there was any to detect. In fact Michaelson was so confident in his experiment that he believed the Earth must have been dragging the æther along with it (just like it drags air so that we don't have 1000 mph winds all the time at the equator) and so he proposed redoing the experiment at the top of a high mountain to minimize the drag in hopes of detecting at least a small portion of the æther wind.

Later, Lorentz and Fitzgerald "explained" the null result of the experiment by claiming that there really was an æther wind but it caused dimensions of physical objects in the direction of the wind to shrink and it caused the experience of time to slow down so that the measurements done by the experiment would be the same for the direction lined up with the wind to be identical to the measurements made at right angles to the wind.

Later still, Poincaré developed this even futher and added E=mc² to the explanation, but they all continued to believe that there was a fixed æther somewhere and that dimensions were constantly changing during the rotation of the MMX apparatus to produce the null result. In other words, they believed there was an absolute, fixed, æther reference frame and that light traveled at c in all directions only in this one frame. Their theories explained why whenever you attempted to measure the round-trip speed of light you would always get c even when the one-way speed was not c.

So what did Einstein do that gives him all the credit for Special Relativity even when all the details had already been worked out by others? He said, in effect, to Michaelson, the reason why you could never measure the æther wind is because you were always stationary in the æther. Wherever you are, as long as you are not accelerating, or as long as you are accelerating very slowly compared to the speed of light, you can assume that you are stationary with the æther and that is why you cannot measure any æther wind. He said the reason why your experiment gave a null result is not because the dimensions of your apparatus were constantly changing as you rotated it around but because the one-way speed of light was c in every direction everytime you did your experiment, no matter how much the Earth had accelerated between your measurements and because of that, dimensions were not changing and time was not slowing down while you were doing your experiment.

Now this was an absolutely crazy notion which is why nobody else proposed it but it was also absolutely brilliant because it freed the scientists up from trying to explain everything in terms of a single elusive fixed reference frame that nobody could detect or find and let them assume that they were in this fixed reference frame wherever they were.

Now Einstein didn't explain it the way I did in terms of believing that everyone was at rest with the æther but he did postulate that the speed of light is c in any reference frame and by that he meant the unmeasureable one-way speed of light, not the measureable round-trip speed of light which was already known to be a constant. And claiming that the one-way speed of light is c in a reference frame is exactly the same thing as saying that that reference frame defines the absolute æther rest frame--there is no difference.

So it turns out that the concept of a single absolute æther rest frame is a waste of time. Thinking in Einstein's new way allows scientists to not worry about that which cannot be determined and focus instead on progressing further. If Einstein had not proposed Special Relativity, General Relativity probably wouldn't have been proposed either and we would be embroiled in all kinds of arguments trying to decide whose candidate for the absolute æther rest frame was the best one.

 

[Histspec]

So I would like to get more understanding on the difference between Lorenz and Einstein.

1)What caused Einstein to drop the ether, if Lorentz has explained it so well, was anything wrong with Lorentz calculations?

Because in Lorentz's theory, there is a stationary aether as a preferred but undetectable frame of reference. On the other hand, the principle of relativity tells us that a preferred frame should not exist at all. So Einstein removed this asymmetry by rejecting the aether hypothesis and by deriving the theory from two principles. See:
http://en.wikipedia.org/wiki/History_of_special_relativity

2) Since Lorentz was the first to propose time dilation and space contraction, and Galileo was to the first to propose the principle of relativity, so what had Einstein invented?

Einstein invented a kinematic theory, which is based on the principle of relativity and light speed constancy. (In contrast, Lorentz's theory is an electrodynamic model, and Galileo's principle does not include light speed constancy.)

3) how does SR explains the Michelson-Morly experiment?, after all the Earth is not an inertial frame of reference and it is constantly moving in a non linear motion.

The acceleration of Earth is too small to influence the MM-experiment, so for this experiment the Earth can be regarded as at rest in an inertial frame.[/url]

Regards,

 

[ghwellsjr]

Because in Lorentz's theory, there is a stationary aether as a preferred but undetectable frame of reference.

In Lorentz's theory, the stationary æther is not merely a preferred frame of reference, it is the only frame of reference. But since it is also undetectable, it puts the theory on tenuous ground.

On the other hand, the principle of relativity tells us that a preferred frame should not exist at all.

Although this is true, it is not the same as saying that a stationary æther frame should not exist. SR merely says that it is a moot point to be concerned about a stationary æther frame, not that it should not or could not or cannot or does not exist, because if it does exist, it would merely be another one of the infinite valid frames of reference, we just can never know which one it is.

So Einstein removed this asymmetry by rejecting the aether hypothesis and by deriving the theory from two principles. See:
http://en.wikipedia.org/wiki/History_of_special_relativity

And the very nice thing that Einstein's theory does is it derives all the features like length contraction, time dilation and E=mc² from those two postulates rather than using them to explain the surprising results of experiments for some unknown reason.

Einstein invented a kinematic theory, which is based on the principle of relativity and light speed constancy. (In contrast, Lorentz's theory is an electrodynamic model, and Galileo's principle does not include light speed constancy.)

But always remember, the light speed constancy that Einstein postulated for any reference frame was the unmeasurable one-way speed of light, not the round-trip measured speed of light which was already known to be a constant.

The acceleration of Earth is too small to influence the MM-experiment, so for this experiment the Earth can be regarded as at rest in an inertial frame.[/url]

Regards,

 

[PhilDSP]

2) Since Lorentz was the first to propose time dilation and space contraction, and Galileo was to the first to propose the principle of relativity, so what had Einstein invented?

Just for the record, Fitzgerald was the first to propose time dilation and space contraction, but he didn't take the idea especially seriously himself and encouraged Lorentz to develop the idea further.

 

[Histspec]

Just for the record, Fitzgerald was the first to propose time dilation and space contraction, but he didn't take the idea especially seriously himself and encouraged Lorentz to develop the idea further.

Only length contraction, not time dilation. The following little paper is Fitzgerald's one and only contribution:

http://en.wikisource.org/wiki/The_Ether_and_the_Earth's_Atmosphere

So in my view, Fitzgerald's contribution was nearly zero - it was Lorentz (and Larmor) who developed a complete theory between 1892-1904.

http://en.wikisource.org/wiki/The_Relative_Motion_of_the_Earth_and_the_Aether (1892)
http://de.wikisource.org/wiki/Versu...d_optischen_Erscheinungen_in_bewegten_Körpern (1895)
http://en.wikisource.org/wiki/Simpl...rical_and_Optical_Phenomena_in_Moving_Systems (1899)
http://en.wikisource.org/wiki/Electromagnetic_phenomena (1904)

 

[grav-universe]

Lorentz envisioned an absolute frame for an aether by which objects physically contract in the line of motion and clocks slow with motion through the aether, but he never quite pinpointed by precisely what degree, only stating that the contraction should be on the magnitude of 1 - n (v/c)^2 when brought to the second order. That still allows some room to detect the aether, although Lorentz knew that all such attempts had so far failed. While Lorentz's approach was more scientifically correct by allowing the possibility that measurements made by experiment might just be too small to detect it, Einstein assumed a precisely null result for all such experiments and proceeded to describe the one and only mathematical description that can be obtained in order to produce this result. He found the exact magnitude for length contraction and time dilation that would always lead to precisely null results for experiments after also providing a description about how observers should synchronize their clocks within each frame when considering that light will be measured in the same round-trip time over the same distance in any direction as also determined by the M-M experiment. Then he went even further by determining the addition of speeds and working through electro-magnetic effects accordingly. In addition to all of this, Einstein's 1905 paper was much more concisely written than Lorentz's 1904 paper, which is barely readable. So all in all, Einstein deserves the credit, although built up from the works of many others who also deserve acknowledgment.

After Einstein's SR is accepted, even if only in terms of the mathematics involved, we can then turn back and have a look at what that would mean when applied in terms of an aether. First of all, it would mean that there is no absolute frame for an aether. All observers' points of view in the aether would be exactly the same as any other. Every frame would measure the same motions of each other, the same time dilation, length contraction, simultaneity differences when applying the Einstein simultaneity convention, and the same isotropic speed of light. There would no longer be an absolute frame for the aether, but any preferred frame would be the same as any other preferred frame. That means that the aether would appear isotropically to every inertial frame. That is, if it were detectable. The null result of any experiment that can be performed also means that any absolute motion relative to the aether cannot be determined, since any preferred inertial frame will be at rest to the aether and observe the same time dilation and length contraction of other frames as other frames observe of the preferred frame. Another problem is that this precise time dilation and length contraction imposed by an aether would seem to be only coincidental. There is no specific mechanical reason that the aether should constrain itself to these exact values of sqrt[1 - (v/c)^2] in order to render it undetectable. If it does so, then it would seem that the aether is bound to impose similar conditions upon itself as it does objects that move through it, such that it also abides by the mathematics of SR, whereby the mathematics of SR then supercede LET. So although the idea of an aether does have the advantage of allowing a mechanical reason for time dilation and length contraction to take place rather than just strange distortions of reality according to each frame, the mathematics of SR still becomes predominant and so is more important, at least unless or until someone can show why the aether should maintain such precise conditions as would be necessary.

 

[Simplyh]

1.We can understand that the interaction between two physical entities can result on a mutual distortion.
2.We can also understand that if we use a token, time and space on a moving frame relatively to us will seem to be distorted, because we have to “discount” the limited speed of the physical entity we use as our the testimony of what happens away.
3.But we can not assume that a real physical distortion can happen without a physical interaction; and we can not assume that the “discount” we must use in our calculations means any physical change on the observed object (we are assuming a despicable influence of the token upon the observed object).
Yet:
1.For SR, some physical changes (space contraction; time dilatation) happen just because of relative motion, that is, without any physical interaction. SR also says that these changes are only experienced on the observers frame, not on the moving frame. If this would just come from the limited speed of light used as a token, there would be no objections. For example: if a light source emits a light ray every second, viewed from an observer who gets apart from the source, at a constant speed, lightnings will be received at always growing intervals, because light had to travel a longer distance for every second. But this only has to do with the use of light acting as the testimony of what happens on the away object, not with light itself. If we simply send a walking fellow, with a constant speed on the observer's reference frame, we'll get the same results (of course distances and speeds must be much smaller but the principals and calculations will be exactly the same).
Till now all makes sense but it's not much: just the need for measurement corrections!
2.Now, if we just take off all physical entities we wouldn't be able to explain real physical changes, which are the ones which really concern Physics. Yet, physical changes happen: clocks of satellites and astronauts do slow down on the astronaut and satellite frames, Mercury's perihelion really happens on Mercury's frame, etc. To make things acceptable, SR, introduces space-time: “Just as it was consistent from the Newtonian standpoint to make both the statements, tempus est absolutum, spatium est absolutum, so from the standpoint of the special theory of relativity we must say, continuum spatii et temporis est absolutum. In this latter statement absolutum means not only ‘physically real’, but also ‘independent in its physical properties, having a physical effect, but not itself influenced by physical conditions’.
As long as the principle of inertia is regarded as the keystone of physics, this standpoint is certainly the only one which is justified. But there are two serious criticisms of the ordinary conception. In the first place, it is contrary to the mode of thinking in science to conceive of a thing (the space-time continuum) which acts itself, but which cannot be acted upon.” (Einstein: “Meaning of Relativity”).
3.Space-time is physically indistinguishable from the ether: both are absolute, continuous and have no detectable properties. In this sense, SR is nothing but an ether theory, were the name “ether” has been changed by “space-time”. Though quite similar to ether, space-time is less consistent theoretically because, as grav-universe stated: “the idea of an aether does have the advantage of allowing a mechanical reason for time dilation and length contraction to take place rather than just strange distortions of reality according to each frame”.
4.In my view the advantage of Einstein regarding Lorentz is that he tries to get away from this absolute reference frame; this ever present “wish” that all would come only from matter-energy, is already a great step forward on itself.
But SR also introduces other great advantages already cited before: a) simplification ; b) Mathematical consistency: as stated by grav-universe; c) Symmetry and d) generalization: as stated by Histspec.
5.Yet, it is quite inconsistent theoretically!

 

[PhilDSP]

Only length contraction, not time dilation. The following little paper is Fitzgerald's one and only contribution:

http://en.wikisource.org/wiki/The_Ether_and_the_Earth's_Atmosphere

Fitzgerald was basically an ideas guy and a very, very good one at that. Most of his contributions were in the form of letters and discussions with others. And that he did with Lorentz in such a way that certainly gave Lorentz a boost he would never have had otherwise.

But Lorentz of course pulled things all together, refined and documented the current understanding of EM more comprehensively than anyone else at the time with the possible exception of Becker and Hertz who unfortunately passed on before his theory and understanding had developed to completion. We might have inherited a very different viewpoint on relativity if he had lived longer.

 

[Mentz114]

...gave Lorentz a boost ...

very amusing, even if you didn't mean it like that.

We might have inherited a very different viewpoint on relativity if he had lived longer.

Pure speculation. I must disagree. Whoever did it, I think we would have got SR. Nobody has found anything better in 100 years.

 

[ghwellsjr]

...
After Einstein's SR is accepted, even if only in terms of the mathematics involved, we can then turn back and have a look at what that would mean when applied in terms of an aether. First of all, it would mean that there is no absolute frame for an aether. All observers' points of view in the aether would be exactly the same as any other. Every frame would measure the same motions of each other, the same time dilation, length contraction, simultaneity differences when applying the Einstein simultaneity convention, and the same isotropic speed of light. There would no longer be an absolute frame for the aether, but any preferred frame would be the same as any other preferred frame. That means that the aether would appear isotropically to every inertial frame. That is, if it were detectable. The null result of any experiment that can be performed also means that any absolute motion relative to the aether cannot be determined, since any preferred inertial frame will be at rest to the aether and observe the same time dilation and length contraction of other frames as other frames observe of the preferred frame.
...

I'm having trouble with your term "preferred frame". By that do you mean the frame which is at rest with the æther (for the sake of argument)? If so, wouldn't it mean exactly the same thing as "absolute frame for an æther"? But then it gets confusing because you talk about "any preferred frame would be the same as any other preferred frame" and you talk about "every inertial frame" and then "any preferred inertial frame". So I don't know if each of these terms means something different or if they are all the same or what.

Would you mind rewriting this paragraph, with consistent terms and define the terms ahead of time, please?

 

[Fredrik]

Only length contraction, not time dilation. The following little paper is Fitzgerald's one and only contribution:

http://en.wikisource.org/wiki/The_Ether_and_the_Earth's_Atmosphere

So in my view, Fitzgerald's contribution was nearly zero - it was Lorentz (and Larmor) who developed a complete theory between 1892-1904.

http://en.wikisource.org/wiki/The_Relative_Motion_of_the_Earth_and_the_Aether (1892)
http://de.wikisource.org/wiki/Versu...d_optischen_Erscheinungen_in_bewegten_Körpern (1895)
http://en.wikisource.org/wiki/Simpl...rical_and_Optical_Phenomena_in_Moving_Systems (1899)
http://en.wikisource.org/wiki/Electromagnetic_phenomena (1904)

I never found the history of relativity interesting in the past, but I've started to think that it's at least somewhat interesting lately. I'll make a note of the link to this thread, so I can read those articles later.

I came across this article recently, by following a link from a Wikipedia page about the ether. It ends with a translation and commentary of an article by Poincaré, which makes me doubt that Lorentz and Larmor had a complete theory. It starts on page 241. Poincaré corrected some of Lorentz's mistakes there, and introduced the principle of relativity.

 

[jtbell]

For example: if a light source emits a light ray every second, viewed from an observer who gets apart from the source, at a constant speed, lightnings will be received at always growing intervals, because light had to travel a longer distance for every second.

This is incorrect. The "moving" observer receives the light pulses at an interval longer than one second, but this interval remains constant so long as the relative speed of the source and observer remains constant. This is simply the Doppler effect which has a well-known relativistic version:

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/reldop2.html

which discusses it in terms of the frequency rather than the period.

 

[grav-universe]

I'm having trouble with your term "preferred frame". By that do you mean the frame which is at rest with the æther (for the sake of argument)? If so, wouldn't it mean exactly the same thing as "absolute frame for an æther"? But then it gets confusing because you talk about "any preferred frame would be the same as any other preferred frame" and you talk about "every inertial frame" and then "any preferred inertial frame". So I don't know if each of these terms means something different or if they are all the same or what.

By preferred frame, I mean an arbitrary frame that an observer remains stationary to and all observations and measurements are made with respect to that frame. For instance, with the twin paradox, with one twin accelerating away and back and the other remaining inertial without accelerating at all, the preferred frame of observation is usually the inertial twin's because the mathematics is easier. With an absolute frame of an aether, the preferred frame would be that of the aether. However, the mathematics of SR render the aether undetectable and the observations from any inertial frame are the same as any other, so there is no longer any absolute frame of the aether, they are all the same, any inertial preferred frame then being the same as any other.

A similar analogy might be observers co-moving with the expansion of the universe, whereas even though they are moving relative to each other, they remain stationary to the CMB and measure the CMB isotropically, because the CMB is also expanding with the universe. That is not a precise analogy, though, of course, and observers that are not co-moving with the expansion of the universe and therefore traveling through the CMB will observe areas of overall redshift and blueshift along the line of motion through the CMB, although they will still measure the local speeds of the individual photons that make it up isotropically. With SR applied to an aether, one should not detect any differences with observations made from within any inertial frame, rendering the aether undetectable. However, when extending SR to GR, even Einstein came to eventually lean back toward the idea of an aether. With acceleration the aether might become detectable in some fashion, perhaps in terms of rotating bodies or some relation to Mach's principle, which Einstein tried to work out, but the details will depend upon the precise modelling of such an aether and that of GR, which is still evolving.

 

[HallsofIvy]

One very fundamental distinction between Lorentz and Einstein was that Lorentz's theory only allowed for the contraction of physical objects in the direction of motion- which he saw as a "real" contraction caused by the increased magnetic pull of protons and electrons in that direction. Einstein's theory requires a contraction of the space between physical objects as well.

 

[grav-universe]

One very fundamental distinction between Lorentz and Einstein was that Lorentz's theory only allowed for the contraction of physical objects in the direction of motion- which he saw as a "real" contraction caused by the increased magnetic pull of protons and electrons in that direction. Einstein's theory requires a contraction of the space between physical objects as well.

That is an interesting insight. If only applying a length contraction of objects that travel through the aether, observers that travel with the object will measure inversely greater distances than measured within the aether frame. However, if the same mathematics applies for LET as with SR, including time dilation and simultaneity issues when synchronizing using the Einstein simultaneity convention, then any observations and measurements work out precisely in the same way as with SR when applying contracted rulers as well as time dilating and unsynchronized clocks as viewed from the aether frame in order to measure distances since the distances within a moving frame cannot be measured directly with a ruler without also employing clocks, even if only to mark off points upon the ruler simultaneously within the measuring frame. I'm not sure whether or not Lorentz considered applying such a simultaneity convention to clocks, however. If the two way time for a pulse of light to travel away from a clock and back is the same over the same distance in any direction, as the M-M experiment also implies, then it is a simple matter to synchronize clocks within that frame to measure an isotropic speed of light.

 

[Simplyh]

This is incorrect. The "moving" observer receives the light pulses at an interval longer than one second, but this interval remains constant ...

You're right. Thanks for the correction

 

[Saw]

I'm not sure whether or not Lorentz considered applying such a simultaneity convention to clocks, however.

At least Poincaré did. That is why it is called the Einstein - Poincaré convention:

Let us suppose that there are some observers placed at various points, and they synchronize their clocks using light signals. They attempt to adjust the measured transmission time of the signals, but they are not aware of their common motion, and consequently believe that the signals travel equally fast in both directions. They perform observations of crossing signals, one traveling from A to B, followed by another traveling from B to A. The local time t is the time indicated by the clocks which are so adjusted. If [c] is the speed of light, and v is the speed of the Earth which we suppose is parallel to the x axis, and in the positive direction, then we have: t'=t-vx/c².

(from The Theory of Lorentz and The Principle of Reaction)

 

[ghwellsjr]

By preferred frame, I mean an arbitrary frame that an observer remains stationary to and all observations and measurements are made with respect to that frame.

I'm afraid you have taken a well defined term "preferred frame" and made up your own definition that isn't even consistent. Look at Histspec's use of the phrase in this post where he uses it correctly:

Because in Lorentz's theory, there is a stationary aether as a preferred but undetectable frame of reference. On the other hand, the principle of relativity tells us that a preferred frame should not exist at all.

A preferred frame is one that corresponds to an absolute stationary æther frame. SR states that there is no preferred frame. You can't just say that it is the frame you prefer to use because the mathematics is easier:

For instance, with the twin paradox, with one twin accelerating away and back and the other remaining inertial without accelerating at all, the preferred frame of observation is usually the inertial twin's because the mathematics is easier.

And what follows seems very confusing to me:

With an absolute frame of an aether, the preferred frame would be that of the aether. However, the mathematics of SR render the aether undetectable and the observations from any inertial frame are the same as any other, so there is no longer any absolute frame of the aether, they are all the same, any inertial preferred frame then being the same as any other.

In SR, it is not correct to say that the observations from any inertial frame are the same as any other. They may all view the speed of light the same but most everything else is different.

And your original post, even with your definition of "preferred frame" doesn't make any sense to me:

All observers' points of view in the aether would be exactly the same as any other. Every frame would measure the same motions of each other, the same time dilation, length contraction, simultaneity differences when applying the Einstein simultaneity convention, and the same isotropic speed of light. There would no longer be an absolute frame for the aether, but any preferred frame would be the same as any other preferred frame. That means that the aether would appear isotropically to every inertial frame. That is, if it were detectable. The null result of any experiment that can be performed also means that any absolute motion relative to the aether cannot be determined, since any preferred inertial frame will be at rest to the aether and observe the same time dilation and length contraction of other frames as other frames observe of the preferred frame.

Could you please elaborate on what you meant by these statements?

 

[grav-universe]

At least Poincaré did. That is why it is called the Einstein - Poincaré convention:

(from The Theory of Lorentz and The Principle of Reaction)

Thank you for the link, Saw. That transformation he comes up with for time is interesting. I cannot tell how he derived it and I have been trying to work it through. It seems he set up the same synchronization as with the Einstein simultaneity convention, and length contraction falls out of the formula leaving only time dilation, but the time dilation would have to be 1 - (v/c)^2 in order to result with t' = t - v x / c^2 as far as I can tell, so I'm curious about how he came up with that.

 

[grav-universe]

A preferred frame is one that corresponds to an absolute stationary æther frame. SR states that there is no preferred frame.

There is no absolute frame in SR, certainly, so there is no reason to prefer observations to be made from one frame over another. That is all I meant, that any frame of reference can be chosen as arbitrarily as any other.

In SR, it is not correct to say that the observations from any inertial frame are the same as any other. They may all view the speed of light the same but most everything else is different.

I was speaking in general there, knowingly so, but figuring my statements would be understood, sorry. I suppose it might be more correct to state that the same observations will be made equally from any inertial frame in terms of the time dilation, length contraction, and simultaneity differences measured, as a function of relative speed.

Could you please elaborate on what you meant by these statements?

I will rewrite it.

All observers' points of view from a particular inertial frame would be exactly the same as from any other inertial frame. In other words, observers within any inertial frame will measure the same time dilation, length contraction, and simultaneity differences as a function of the relative speed when applying the Einstein simultaneity convention with the same isotropic speed of light. There would no longer be an absolute frame for the aether, but any inertial frame of reference would be the same as any other inertial frame of reference, so the aether would appear isotropically to every inertial frame. That is, if it were detectable. The null result of any experiment that can be performed also means that any absolute motion relative to the aether cannot be determined, since any arbitrarily chosen inertial frame will be at rest to the aether and observe the same time dilation and length contraction of any other inertial frame as the other frame observes of the initial frame.

 

[Histspec]

That transformation he comes up with for time is interesting. I cannot tell how he derived it and I have been trying to work it through. It seems he set up the same synchronization as with the Einstein simultaneity convention, and length contraction falls out of the formula leaving only time dilation, but the time dilation would have to be 1 - (v/c)^2 in order to result with t' = t - v x / c^2 as far as I can tell, so I'm curious about how he came up with that.

You only have to consider the "aether wind", than you will notice that this results in an error when synchronizing clocks. To first order, this "error" corresponds with Lorentz's "local time" t' = t - v x / c^2.

See (http://en.wikipedia.org/wiki/History_of_Lorentz_transformations" ), especially the section "Poincaré (1900, 1905)".

Regards,

 

[Histspec]

I came across this article recently, by following a link from a Wikipedia page about the ether. It ends with a translation and commentary of an article by Poincaré, which makes me doubt that Lorentz and Larmor had a complete theory. It starts on page 241. Poincaré corrected some of Lorentz's mistakes there, and introduced the principle of relativity.

It's true that Lorentz made some mistakes that were corrected by Poincaré, as it was admitted by Lorentz himself (see http://en.wikisource.org/wiki/Two_Papers_of_Henri_Poincar%C3%A9_on_Mathematical_Physics" ). However, Poincaré always spoke of "the theory of Lorentz" and considered his own contributions as of minor importance compared to the achievements of Lorentz.

BTW: It's curious, but Poincaré never mentioned Einstein, as well as Einstein never mentioned Poincaré...

Regards,

 

[grav-universe]

You only have to consider the "aether wind", than you will notice that this results in an error when synchronizing clocks. To first order, this "error" corresponds with Lorentz's "local time" t' = t - v x / c^2.

See (http://en.wikipedia.org/wiki/History_of_Lorentz_transformations" ), especially the section "Poincaré (1900, 1905)".

Regards,

If only considering it to the first order, that is true, yes, thank you. I think Poincare should have mentioned that, then. Otherwise, we have t' = z (t - v x / c^2) / (1 - (v/c)^2), where z is the time dilation. With the Lorentz transformation, we have z = sqrt[1 - (v/c)^2], giving t' = (t - v x / c^2) / sqrt[1 - (v/c)^2]. Even if we don't figure in time dilation or length contraction, although length contraction falls out anyway so it doesn't matter here, then z = 1 and we would still have t' = (t - v x / c^2) / (1 - (v/c)^2) in that case, but all do indeed reduce to t' = t - v x / c^2 to first order only, so would be very close to that as as long as the time dilation is some function of v/c away from unity and v/c is small.

 

[Saw]

If only considering it to the first order, that is true, yes, thank you. I think Poincare should have mentioned that, then. Otherwise, we have t' = z (t - v x / c^2) / (1 - (v/c)^2), where z is the time dilation. With the Lorentz transformation, we have z = sqrt[1 - (v/c)^2], giving t' = (t - v x / c^2) / sqrt[1 - (v/c)^2]. Even if we don't figure in time dilation or length contraction, although length contraction falls out anyway so it doesn't matter here, then z = 1 and we would still have t' = (t - v x / c^2) / (1 - (v/c)^2) in that case, but all do indeed reduce to t' = t - v x / c^2 to first order only, so would be very close to that as as long as the time dilation is some function of v/c away from unity and v/c is small.

Humm. I had not interpreted the formula that way. I thought it was not an approximation, that it was exact… about what it is, i.e. just one phase of the reasoning process leading to the Lorentz Transformation.

Let us see it with an example. I use natural units (c = 1). A train car has been measured as 2 light-seconds long when at rest with the ground. Now the train starts moving at v = 0.5 c wrt the ground. A light beam is flashed from the mid-point of the train in both directions.

An observer from the ground can reason as follows (putting herself in the shoes of the train observer and assuming that wrt the train light does not travel at c):

• the forward-looking light, traveling wrt the train at c-v (0.5 c), traverses the 1 ls path and hits the train Front after 2s (t1 = x’/v = 1/0.5 = 2 s) ,
• while the backward-looking light, traveling wrt the train at c+v (1.5 c), hits the Back after 0.667 s. (t2 = x’/v = 1/1.5= 2/3= 0.667 s).

Also to be noted, the distances traversed by the light beams in the ground frame (where light travels at c = 1) until their respective targets are:

• the forward-looking light travels x1 = ct1= 2 ls.
• the backward-looking light travels x2=ct2 = 0.667 ls.

But “locally” (on the train) one will not measure that. On the train, the car is a valid clock. If the train was 2 ls long, it is still so when “moving”. So each path from the middle point to the Front or the Back must take 1 second for light to traverse, traveling at c. Hence both t1’ and t2’ are 1 s. And the formula gives precisely those results:

t1’ = t1 – vx1 = 2 – 0.5 * 2 = 2 -1 = 1 s
t2’= t2 + vx2 = 0.67 + 0.5*0.67 = 0.67 + 0.33 s = 1 s

Of course, the question is then: would the train clock really measure 2 s at the return of the light pulses to the mid-point?

To this effect, you need the two other factors. First, the train clock slows down by the factor resulting from the light clock thought experiment, sqr(1-v^2) = 0.86, so the light pulses will not return after 2.66 s but after 2.309 s in the ground measurement. Second, the light pulses have a shorter path to traverse, due to length contraction, by the same factor.

 

[grav-universe]

Here is how to derive the formula for that. In Alice's frame, light travels in all directions at some speed c. A ship is moving past Alice at a speed v with Bob at the front and Carl at the back. Bob and Carl measure a proper length d of the ship, while Alice measures a length contraction L of the ship, as well as a time dilation of z for the ship's clocks, and notices that Carl's clock is set ahead of Bob's by a time tl. These are all of the factors that Alice can observe of the length and time that Bob and Carl measure directly as long as the speed, length, and rate of ticking of clocks within an inertial frame are always observed to remain steady and constant, so are independent of whether we use Lorentz theory or SR or even ballistic theory as well as any others as long as we use this definition of an inertial frame as observed from another inertial frame, that none of the variables v, z, L, or tl will be observed to change over time, so are independent of the kinematic model being considered.

Bob and Carl synchronize their clocks to measure light pulses isotropically. According to the null result of the M-M experiment, they should be able to do this without any contradiction. We don't need to assume that Bob and Carl will measure the same speed of the pulses that Alice measures, however, which cannot be determined directly without postulating that all frames measure the same speed c of light, but only that they measure the same difference in times for the light pulses to travel from Bob to Carl as from Carl to Bob. From Alice's perspective, a pulse will travel from Carl to Bob in a time c t1 = L d + v t1, since the ship travels forward at v over the same time t1 that the pulse traverses it, so t1 = L d / (c - v). Carl's clock reads tl greater than Bob's according to Alice, so let's say that when the pulse leaves Carl, tC = tl and tB = 0. When the pulse reaches Bob, z t1 will have passed upon Bob's clock, so Bob's clock reads tB' = z t1 when receiving the pulse. The difference in times between the readings upon Bob and Carl's clocks is tB' - tC = z t1 - tl = z L d / (c - v) - tl. All observers within any frame will agree with those readings since the light pulses coincide with the clocks at those points, so this is the difference in time that Bob and Carl measure according to their own frame. For the light pulse to travel from Bob to Carl as Alice measures it, we have c t2 = L d - v t2, since Carl is traveling toward the pulse at v over the time t2, whereas t2 = L d / (c + v). If the pulse leaves Bob at tB = 0 and tC = tl, then Carl will receive it at tC' = tl + z t2, and the difference in time that Bob and Carl measure will be tC' - tB = tl + z L d / (c + v). Now, since Bob and Carl synchronize their clocks to measure the same time for a light pulse to travel in either direction, so with the same difference between the readings upon their clocks, then

tB' - tC = tC' - tb

z t1 - tl = tl + z t2

z L d / (c - v) - tl = tl + z L d / (c + v)

2 tl = z L d [1 / (c - v) - 1 / (c + v)]

2 tl = z L d [(c + v) - (c - v)] / ((c - v) (c + v))

tl = z L d v / (c^2 - v^2)

Now for the transformation for time. The ship travels past Alice along the x-axis at v and as Bob passes Alice, they synchronize their clocks to T = 0. After a time t according to Alice, an event occurs at a distance x. Let's say that the back of the ship coincides with the event. Therefore, whatever time Carl's clock reads directly while at the same place as the event will be the time that the event took place according to the frame of the ship. Alice observes that the front of the ship has traveled a distance v t over the time t when the event occurs, and the event occurs at a distance x, so let's say that according to Alice, the length of the ship is L d = v t - x. The difference between Carl and Bob's time as Alice observes them, then, is tl = z (v t - x) v / (c^2 - v^2). So after at time of t passes for Alice, Bob's clock reads z t according to Alice, and Carl's clock is set a time of tl greater than Bob's according to Alice as well, which is the actual time of the event according to the frame of the ship since the event coincides with Carl's clock, so

t' = z t + tl

= z t + z (v t - x) v / (c^2 - v^2)

= z [(c^2 - v^2) t + v^2 t - v x] / (c^2 - v^2)

= z [c^2 t - v x] / (c^2 - v^2)

= z [t - v x / c^2] / (1 - (v/c)^2)

If considering that no time dilation takes place between frames, then z = 1 and we have t' = [t - v x / c^2] / (1 - (v/c)^2). With a time dilation of z = sqrt[1 - (v/c)^2], we get t' = [t - v x / c^2] / sqrt[1 - (v/c)^2].

 

[grav-universe]

Of course, the question is then: would the train clock really measure 2 s at the return of the light pulses to the mid-point?

The time that a clock at the midpoint measures will just be the time dilated factor that the ground frame measures between the midpoint sending and receiving the pulse. To see this using the transformation, we can just find the difference in the times between the two events of the pulse leaving the midpoint and the pulse returning. According to the ground frame that measures c isotropically for the speed of light, the pulse leaves the midpoint at some time ta, travels some distance L d forward along the length of the train in a time t1 = L d / (c - v), then travels back to the same point in a time t2 = L d / (c + v), so arriving back at the same point at a time tb = ta + t1 + t2 = ta + L d [1 / (c - v) + 1 / (c + v)] = ta + L d [(c + v) - (c - v)] / ((c - v) (c + v)) = ta + 2 L d v / (c^2 - v^2). The time will also be the same for a pulse to travel back the same distance L d and forward to the midpoint again. Okay, so the difference in time that passes between the pulse leaving the midpoint and arriving again according to the ground observer will be tb - ta = 2 L d v / (c^2 - v^2). The distance from the ground observer that each event occurs, occurring at the same point upon the train while the train moves forward at v, then, is xa and xb = xa + v (tb - ta), whereas xb - xa = v (tb - ta). According to the train observers, the difference in times between the events is

tb' - ta'

= z [tb - v xb / c^2] / (1 - (v/c)^2) - z [ta - v xa / c^2] / (1 - (v/c)^2)

= z [(tb - ta) - v (xb - xa) / c^2] / (1 - (v/c)^2)

= z [(tb - ta) - v^2 (tb - ta) / c^2] / (1 - (v/c)^2)

= z (tb - ta) [1 - (v/c)^2] / (1 - (v/c)^2)

= z (tb - ta)