Tim88

Hehe yeah. Well, in fact, of course, as discussed all along since post #8, there is (in principle) an empirical difference with the school of teaching according to which the explanation by Poincare that a moving magnetic field causes atoms and molecules to "contract" in that direction is wrong, because, if you had a series of rods with spaces in between, that would not cause the space in between to equally contract. That school of thought* has died out since the publication of Bell's spaceship paradox. As we now have more than sufficiently discussed here, it has become generally accepted that the space between the rockets will indeed not auto-magically equally contract as the rockets contract (in which case the thin string between the rockets could not break). If, as it seems, the originator of that objection to Poincare won't come back to comment on the discussion that it initiated, then I will also abstain from further comments. *Wikipedia sketches that now defunct school of thought as follows: "they are all subject to the same Lorentz contraction, so the entire assembly seems to be equally contracted in the S frame with respect to the length at the start."

I wrote, following the reasoning of Bell: The picture to which I referred, is exactly what follows from Poincare-Einstein-Bell's physical assumptions. Your "rocket frame" is nothing else but an infinite series of different S' - which is an instantly co-moving inertial frame. There is no empirical difference.

Should I take that as implying that you also cannot come up with an empirical difference between Einstein's interpretation and that of Bell and Poincare? Still, for completeness I'll wrap up the clarification. You may call it nitpicking, but technically speaking contraction relates to a change. Bell's Spaceship "paradox" may look paradoxical due to a common mix-up in the literature between, on the one hand, a change of length, and on the other hand, a comparison of distances between two reference systems. No doubt that sloppy usage is widespread because in most situations it doesn't matter, so that (as far as I know) no special term has been introduced for the second comparison. As nicely illustrated on the picture in Wikipedia, it does matter in such cases as Bell brought up: only the objects contract according to the launchpad system S, as sketched in the top illustration - just as first brought up in post #8. Nevertheless, when the rockets have reached a speed at which the string breaks, all the pictured distances are a factor γ greater according to the instantaneous co-moving frame S' than according to S.

I'm afraid that that's not going to work; and I don't know why you think that it would be needed. SR is supposed to be self consistent, without gravitational fields. SR is based in part on Maxwell's theory, which includes magnetic fields. Further, GR was (and is) not needed for the rotating disc, and there is no need to use a rotating frame, with possibly confusing nomenclature. The rotating disc and length contraction effects are perfectly understood from the point of view of a non-rotating reference system, without invoking any "curvature" or terms like that. That is also the reference frame that I used in my description. In the non rotating frame, a stationary wire is not expected to length contract due to the motion of electrons; and in any case, the ratio of electrons to protons remains the same so that their density would change equally. Meanwhile I thought of an even simpler example: two equal charges moving in parallel, like this: o -> o -> According to SR, the force between those charges decreases with speed. However, the Coulomb force between them does not change with speed (only with distance), and obviously the number of charges does not change with speed.

You misunderstood again: Bell's spaceship paradox is not a self contradiction. I don't think so: please provide a citation of Einstein claiming that ""space itself" does contract". I explained twice that "contracts" is a verb, referring to dynamics as measured in a single reference system such as in Bell's example. In that example there is even nothing that could be physically able to "contract space"; I find that concept nonsensical. Sigh. That specific problem was first designed in 1959; Poincare was then long dead. Bell's explanation is, as I already cited, basically the same as the explanation by Poincare and Lorentz, with which Einstein agreed, but with which HallsofIvy apparently disagreed, as you saw. Maybe you also disagree with it; that still hasn't become clear. Thus, for a last time: if you claim that Bell's (and Poincare's) explanation as cited, leads to different predictions from those by Einstein, please show it. Without anyone trying to show a difference, there is nothing to discuss in this thread.

Thanks, it's an interesting topic! You write: "Since the charge density of a moving charged rod increases with velocity, the free electrons in a conductor wire will also have a higher density when a current circulates in the wire. Indeed, electric current is a moving line of electrons or charge. Thus, the free electrons will have higher density than the positive charge of the wire. So, the wire will appear charged and exert a Coulomb force on a charge located nearby." I have seen such exposes in the past, and they could never convince me; here's why. Before I read any further, please clarify how you think that the charge density in a closed loop can be increased that way. As you surely know, following Lenz law one can induce a current with its corresponding magnetic field in such things as a single current loop or a piece of metal. I suppose that necessarily the total charge - and thus the charge density - cannot be altered.

I explained that: It appears that you continue to misunderstand the issue; in any case, you lost track of the topic. As a reminder, here the first claimed empirical difference between Einstein and Poincare was: I brought it to your attention that this has effectively been treated by Bell who stressed the importance of the physical understanding of the contraction of atoms and molecules using Maxwell's equations, and Bell's lesson is rather nicely shown in an illustration in Wikipedia in which consequently the empty space does not contract together with the rockets, exactly as Poincare would have it. Please stick to the topic at hand and explain how, if indeed you think so, Einstein predicts such a "space contraction" between the series of rods in disagreement with Poincare and Bell. PS. the following citation may be useful to clarify my position, which is on this topic the same as that of Bell: "It is my impression that those with a more classical education, knowing something of the reasoning of Larmor, Lorentz, and Poincare, as well as that of Einstein, have stronger and sounder instincts. I will try to sketch here a simplified version of the Larmor-Lorentz-Poincare approach that some students might find helpful. [..] In so far as microscopic electrical forces are important in the structure of matter, this systematic distortion of the field of fast particles will alter the internal equilibrium of fast moving material. It is to be expected therefore that a body set in rapid motion will change shape. Such a change of shape, the Fitzgerald contraction, was in fact postulated on empirical grounds by G. F. Fitzgerald in 1889 to explain the results of certain optical experiments." - Bell, How to teach Special Relativity

I wrote in particular: It probably did not make sense to you because despite my explicit clarification, you did not catch the difference between a dynamic change according to a single reference system, and a disagreement between two reference systems: for a space traveler the distance of empty space to a star is shorter than it is according to a person at rest with the star. No doubt that linguistic confusion is the only issue that you have, and it is totally unrelated to the topic at hand - thus no reason to elaborate any further. The issue was that no doubt according to both Einstein and Poincare, the space between Bell's rockets which depart simultaneously as determined in the launch platform's reference system, will not shrink according to that same system. After the fuel has run out, the space between them will still be the same but in contrast, the rockets will be length contracted. Once more, to elaborate further: the issue that Bell had with his colleagues was that he immediately understood this outcome as he was following the physical way of reasoning of Lorentz, Poincare and Einstein. His colleagues, who followed a more complex mathematical path, at first disagreed with him but finally conceded that he was right. In such cases, there can be no difference between the predictions following Einstein or Poincare.

Yes, I think that has to be correct, for the simple fact that Poincaré introduced the "Lorentz transformations", that is, the transformations of Lorentz written in the symmetrical form as we know them today. It's hard to see how any empirical difference between predictions can occur when one uses the same calculations for those predictions.

Thanks for the clarification. According to Wikipedia, Ferreira was born in 1968. If so, he wasn't there. And if he produced no source for his claim, it's probably wrong. That kind of popular books often are full of errors.

On this point I don't think that there was disagreement between Einstein and Poincare; can you please elaborate how you think that KTX was an issue for Poincare? As far as I remember, Einstein never held that "space itself" contracted; that would even lead to self contradictions such as with Bell's Spaceship paradox (if one rejects Bell's explanation, as his colleagues first did), which is a variant on "a series of rods with space in-between". Note that it's important to distinguish between contraction of lengths (which is an action, dynamic change), and lengths and distances that are measured to be shorter according to one system than according to another system (which is a difference). "Causing to contract" is dynamic, about things happening. From the point of view of the launch platform's reference system, the rockets and the string contract while the rockets accelerate, but "space" does not contract - else the string should NOT break and magical, contradictory things would happen.Only objects can Lorentz contract, which is consistent with Maxwell's electrodynamics (indeed, that was a central issue in Bell's "How to teach relativity").

I suppose that you referred to this paper: https://en.wikisource.org/?curid=735695 Where does he state something like that?

Indeed, on that explanation we also elaborated at great length. It must have been me who was unclear, when I remarked "However we do have, as you know, other explanations of the twin paradox, which we compared at great length several months ago." With "other explanations" I meant the Lorentzian and the Minkowskian interpretations.

One famous example: the gravitational bending of star light towards the Earth is twice the amount predicted based on Newton's light particle theory. - http://www.einstein-online.info/spotlights/light_deflection

SR is not based on such things. It is purposefully based on generalizations of observed phenomena, so that it does not depend on underlying physical models. Therefore, any explanation or interpretation that is fully compatible with the predicted phenomena, is also compatible with SR. By the way, although Minkowski Spacetime is a theory of an "absolute world" (in contrast with Einstein's original concept), I think that it is debatable to call that an "absolute frame of reference".

Good points (+1). The confusing statements are based on the incorrect statement "Saying that B runs slow would be incorrect as we are making our measurements from B." That corresponds to taking a self-centered point of view as "absolute" so that nothing can happen to the observer. Such an approach leads to contradictions or "multiple realities" as well as magical "instantaneous action at a distance". Instead, one has to conclude that, taken over the whole interval, B runs slow; that is the only logically reasonable conclusion. That the use of pseudo gravitational fields is not justifiable was already explained in "Resolution of the clock paradox", Builder 1957, Austr. J.P. However we do have, as you know, other explanations of the twin paradox, which we compared at great length several months ago.

It seems to me that your question is not right... Perhaps you confuse differences in conventions (definitions) with differences in mathematics and physics. Can you give an example for matter in which (γm) differs from γm, or in which m is unequal to (γm)/γ?

It depends on your definitions of force and energy. If your definition of force is "something that can move and displace matter", then gravity is of course a force. Einstein called gravity a force while others don't call it a force.

According to SR the exchange happens with fields, but that's probably not the issue here (to make sure, pleases stick to SR in this sub forum on relativity). As you write "When they move at the speed of light the photon from A will never reach B and therefore B cannot be accelerated further", it sounds as if you are making exactly the same error that I put my finger on earlier and which is in conflict with theory and measurements, as I also already tried to clarify; probably that clarification needs expansion. My example of an electron that is affected by an electric field is similar to your example of an electron that is affected by the presence of another electron. If at the speed of light the interaction of the electric field never reaches the electron, then it's not pushed anymore. I suppose that you do not claim that Newton's mechanics is followed up to speed c, and then suddenly there is no more acceleration. Consequently you probably mean that the "push" is reduced the closer that the speed is to c. And so we're back to: 1. The fact that the electron is still pushed with force F up to the speed of light according to SR: even with the same F according to both observers (according to both reference systems), no matter what the speed is. 2. We're also back to Bertozzi experiment (Bertozzi 1964). If the electron is practically not pushed further, then also practically zero further work F∆s is done on it by the electric field, because F=0. Energy conservation implies that the kinetic energy of the electron cannot increase if no further energy is given to it. Instead, he demonstrated that the kinetic energy of a fast electron increases just as much as that of a slow electron. As he summarized it (emphasis mine): As an afterthought, it struck me that possibly I misunderstood you, and you think that an electron can escape from the influence of a field if it goes fast enough. However no escape from the electric field between the plates is possible as the electron passes through.

A limit speed implies that the acceleration goes to zero; that's just saying the same thing with other words.

OK. The problem that I see with that is, first of all, that according to SR the force that is experienced by the rocket in a co-moving reference system, is just the everyday reaction force; and the transformation factor of force in that direction is 1. In other words, according to SR, if we use the reference system in which the rocket is moving very fast, the force on the rocket is NOT reduced. Your assertion is therefore in disagreement with SR. For reference you can look up §6 of https://www.fourmilab.ch/etexts/einstein/specrel/www/ Alternatively you can "google" the same in more modern texts, I found for example http://www.sciencebits.com/Transformation-Forces-Relativity (disclaimer: I did not check the derivation there). Further, as far as I know our technology has not yet reached the point of verifying the theory for rockets; but it has been done for a somewhat similar case, that of electrons. Probably you would apply the same reasoning as you did on accelerated electrons, and claim that these cannot reach the speed of light because the "push" of the electric field on the electron becomes infinitely small at speed c. (correct?). That reasoning has effectively been disproved by the Bertozzi demonstration experiment, which verified the added kinetic energy at high speeds by measuring the energy that was released at impact. The electron is, as measured in the lab, truly a "high energy" or "heavy" particle in agreement with the amount of added kinetic energy according to SR.

That sounds good, but I think that I can show that it is incorrect, as Janus remarked. Let's try this: if your reasoning were to -the-point, then this means, if I correctly understand your "there won't be any repulsion", that at say 0.99999c the rocket's push will be very small according to you, and so the push will be ever smaller and smaller when going faster, and that is why the rocket cannot reach c? If yes, then I will continue (or maybe someone else who knows what I'm getting at will do so, that's OK).

Sorry for nitpicking here, but it may be important to note that the above is in fact wrong. It is correct for those who use as "rest system" a system in which they are in rest. And while that is the assumption in Einstein's illustrations, it is in common modern practice rarely the case; usually people in different states of motion all use GPS receivers that calculate the speed of light based on the same ECI system (both the train and the track are moving in it). In other words, as a generalization one has to realize that it's not needed to be actually be on the track (as you said), nor does one have to be at rest with respect to the track in, order to determine the "track animation simultaneity" - one only has to use the track's reference frame as reference. As a matter of fact, that is already clear from the way you phrased your examples, as none of us were in that train or on that track. It is of course undeniable that the average clock rate of B was greater than that of A, by mere definition. And this is agreed upon by any inertial reference system. Similarly, it's indeed safe to say - even undeniable by mathematical necessity - that at least for some part of the trajectory the clock rate of B must have been greater than that of A; however what part that is depends on which reference system you choose as "true". And since no inertial frame can be singled out as "true frame", we cannot determine such a thing. Not so. Twin C merely has a different estimation of distant time than twin B. If twin B chooses upon acceleration to switch reference system and adopts that of twin C, then he will himself make his estimation of A's "now" jump 19 years. Alternatively he may choose to stick calculating with his earlier "rest" reference system. In that case he will conclude that due to his own speed which is now higher than that of A (he has to catch up with A!), his own clock ticks slower than that of A, such that on the average over the whole trip his clock will end up behind that of A. Note also that B's act of suddenly turning around far away from twin A cannot have any effect on the clock rate of A; even the information from his turnaround will reach twin A, long after the turnaround with its imaginary clock jump of clock A.

The others answered correctly about this; you are mistaken about distant simultaneity. Concerning that point, you do well to look more carefully at the given examples. However, don't let yourself be misled: considerations of distant simultaneity have no bearing on local simultaneity, of two clocks side by side (ideally at zero distance, although that's not exactly achievable). Your arguments concerning that outcome stand.

Yes indeed, this a variant of Hafele Keating - https://en.wikipedia.org/wiki/Hafele%E2%80%93Keating_experiment It avoids the gravitational potential complication, but the issue of the rotating Earth is central.