Andromacus

You are right. It is just frustrating not to be able to get what I mean across. I'll give it another try: a) This thread is about the relativity of simultaneity, let's agree about its definition as the assignment of different simultaneities for different inertial frames in relative motion with respect to each other related by Lorentz transformations, so that what is simultaneous in one is not in the other and viceversa. b) The different simultaneities for each frame(let's call them frame A and frame B) are defined by a synchronization for frame A and a different(as seen from A) one for frame B and viceversa. Of course from its own frame both A and B think their clocks are the ones correctly synchronized according to Einstein synch and the other as seen from their frame to be the incorrect one. . c)The general formula the 2 synchronization followed within each frame is tQ=tP+e(tP' - tP) where tP is the time at which a light signal is sent from point P in a frame, tQ is the time it is recieved at point Q in the same frame, tP' is the time the light signaled reflected at Q arrives back at P and e(epsilon) is the coefficient from 0 to 1 that gives the different times from P to Q and from Q to P(e=0.5 corresponds to Einstein synch). d)The different synchronizations between the frames that give rise to different simultaneities(relativity of simultaneity) vary in the value of e(the value of e in the moving frame depends on the relative speed between the 2 frames:e in moving frame=rest frame e times(v/c), and it's usually represented by tilting axes(or plane depending on the dimensionality of the representation) in spacetime diagrams. This description of the relativity of simultaneity is consistent with mainstream SR AFAIK, before I go on I would like to have some consensus that it is so. Any comments are welcome.

I wrote the formula that defines the synchronization for a given simultaneity in SR. I thought it was simple enough to understand Wouldn't you have to define what you mean by "synchronization protocol" for me to answer? But that is because you apparently claim you ignore the existence of null intervals and their definition in SR and the fact they require their simultaneity defined in terms of the synchronization tB=tA+1/2(tA'-tA), and that it doesn't allow any other simultaneity with a factor different from 1/2 as would be required by the different simultaneities postulated by the relativity of simultnaneity , no matter how I write it, or the references to Einstein's papers or books I give. Could you maybe try giving an argument from SR that shows what I say about the null interval in different frames is wrong, instead of just replying "I am not aware of it", or "it is not obvious to me"?. I tend to think you should be aware of it or it should be obvious to you a way to counter what I say if it is wrong.

I don't quite follow what you mean. The synchronization protocol is always the same: tB=tA+e(tA'-tA) where only e varies being 1/2 in the Einstein synch, and taking any value between 0 and 1 for the different simultaneities in the transformed frames(for intervals different from zero) depending on the relative velocity bewteen the frames.. The invariance of the null interval means that the only simultaneity compatible with it for any inertial frame is the standard Einsteinian where the time it takes light to go from A to B is the same it takes to go from B to A (the simultaneity is absolute here). While the relativity of simultaneity is the assertion that any simultaneity, that is, any combination of times from A to B and from B to A are allowed as long as the round-trip is constant. Would you say it is possible to have both relative and absolute simultaneity in SR(other than by the unphysical way of re-scaling the units I mentioned above)?

I'm under the impression that the term causing problems here is "conventional". And it is in part my fault as I'm not using the usual meaning of conventioal synchronization as used in the conventionalist versus non-conventionalists debates. For them conventional synchronization refers to different synchronizations within one frame,but I'm not using that meaning I'm using the word conventional referring to the different simultaneities allowed by definition by the relativity of simultaneity, but I see that this invites confusion. So let me rephrase(wich makes the demand almost a tautologic redefinition): the relativity of simultaneity obviously admits different simultaneities for different inertial frames related by change of frames, and different simultaneities means different synchronizations for different frames are valid in the theory. So the theory is obviously compatible with different clock synchronizations by its central feature:the relativity of simultaneity. At the same time the invariant null interval, wich is also a key part of the theory because it is the mathematical statement of the second postulate and is also required to hold thru for the definition of minkowski space line element, only allows the standard Einstein synchronization, that is only agrees with one simultaneity, the one in wich the 3 dimensional euclidean distance equals the constant c times the time that takes a light ray in vacuum to traverse that distance measured by clocks at rest with each other in the euclidean space. So the theory allows the contradiction of being compatible with different simultaneities and with only one. There is of course a way to dodge the contradiction, wich is making all simultaneities equivalent, but this takes away the physical content of the Lorentz transformations and time dilations by making the meters and second change their scale in the change of frame. Experiments seems to indicate that the Lorentz transformations and the time dilation corresponds to something physical, not a simple rescaling of the time and length units, so I don't buy that way out of the inconsistency. Note that Lorentz theory didn't have this inconsistency as the length contraction was considered both real and to ocurr only in the ether absolute frame of the direction of motion. Of course the explanation was clearly hard to justify since it was not measurable and completely ad hoc. So we have the math of the Lorentz transformations wich works to the best our experiments can tell, but i wonder how the Einstein explanation is an improvement to the already faulty Lorentz theory explanation if it just introduces inconsistency.

Ok, here it is in the simplest terms I can: The relativity of simultaneity is the demand that simultaneity and therefore synchronzation of clocks must be conventional between frames in a transformation. This is necessary to comply with both the SR postulates, and it is equivalent to saying that Einstein's synchronization is not the only one valid. Different values for c in one direction and its opposite are allowed in the theory for the formula of synchronization of clocks, not just the standard 1/2. On the other hand the definition of the null interval in SR, wich is an invariant, meaning that it must be preserved under any change of frames, is done using the equation ct=x that is only compatible with the Einstein synchronization, any other synch will not give the null interval c2t2-x2-y2-z2=0. It is not relevant if the derivation is done in one frame because the interval is meant to be invariant to change transformations.

No, you wrote "A time-independent rest frame is clearly an absolute(rest) motion or preferred frame" I chose the wrong word to copy. Does that have that much of an effect on the argument? There is no absolute motion or preferred frame involved here. Agreed. What is a null transformation? What is a Galilean transformation for light? (The follow up may be "what's the relevance", depending on the answer) Not a null transformation, but a Lorentz transformation of an EM wave that leaves the null interval c2t2-x2-y2-z2=0 invariant. This is the first step in many SR books when deriving the LT. Edited: Actually the idea of such a galilean transformation is quite irrelevant to the discussion. "In the case of massive particles" covers 100% of what the Lorentz transform addresses, Actually the LT can be applied to photons in two inertial frames K and K' according to Einstein's "Relativity:the special and the general" and these are the corresponding transformations, they follow simply from substituting x by ct in the usual LTs and technically the units are not changed, it is the magnitude of the values that change as a result of c being invariant. This is debatable. physically it is usually argued as you say, but formally it is clear by looking at the transformations that all there is is a rescaling of the time and length units by contrancting the latter and dilating the former. Geometrically the "squeeze mapping" (see wikipedia about it) is the equivalent of a rotation but using hyperbolic or imaginary angles, it is a linear transformation that preserves the areas formed by the x and t coordinates(hyperbolic sectors) in a LT. In other words one uses c as measuring unit and change x and t units accordingly(compensating one with the other:x contracts what t dilates), see picture taken from wikipedia.

Exactly. A time-independent rest frame is clearly an absolute(rest) motion or preferred frame So Einstein's synchronization is just a condition to use the constancy of c as premise of the transformations , starting from the time-independent galilean inertial coordinates and transforming to another frame keeping c constant wich logically implies changing lengths and times in accordance. Of course in the new frame one can once again use the equivalence between inertial frames to Einstein synchronize again, since an observer in that new frame can consider himself at rest and all distant clocks can be assumed at rest with him again. It is hard not to see here that the second postulate is basically used to change length and time units(so that c remains constant after the transformation), and the Einstein synchronization is just readjusting to the original time-independent or absolute units. Basically making c constant in all frames makes gallilean trnasformations equivalent to Lorentz transformations in the caseof light. It doesn¡t look a very physical way to keep the theory formally contradiction free.

Then that would indicate it is not a prerequisite, as you know clocks are not synchronized between the new transformed frame and the old frame, so for one of them it is not a prerequisite. However it can always be re-adjusted to the Einstein synch precisely because the principle of constancy of c in any inertial frame guarantees it. This is an example of the circular reasoning SR allows, as I said you can conclude from the theory that sinchronization is a fixed prerequisite or that is purely conventional. There scholars and relativity specialists holding both views. You hold that it is a prerequisite, that is fine with me, I cannot convince you of the contrary using the theory itself. BTW, could you address the question in my previous post?

Right, it puts you into a different frame, and in that NEW frame what guarantess that Einstein synch is still working IN THAT NEW frame, NOT BETWEEN frames obviously, is the second postulate thru the Lorentz transformation.

That's ok, no problem.

You edited your post to add the bit about pseudo-euclidean" after I replied without making note of it, that doesn't seem to be fair play.

If you insist on that I would ask you to start a new thread with the claim that flat spacetime is euclidean, but it will probably be sent to speculations as it is well known it is Minkowski space that represents the flat spacetime of special relativity.

Einstein synch is compatible with galilean relativity because it is also based in the Euclidean homogeneous and isotropic space, but there is a key difference, galilean inertial frames are independent of time, while the Einstein synch is precisely used to construct the relativistic inertial frames that are not time independent, but assign different times to different inertial frames. It is in this sense that the Einstein synch is crutially dependent on the second postulate to avoid contradiction when applying this adjustment because the adjustment hinges on the fact that c is invariant in all inertial frames. At least this is Einstein's view AFAIK. The trick is that in order to do this Einstein needs to define light's null interval in terms of the galilean prerelativistic inertial frame and with this he can adjust clocks with finite speed signals. The galilean and relativistic inertial frames(that are different) are arbitrarily used here as if they were interchangeable for the sake of reconciling the first and second postulate. The relativistic inertial frames are derived from a galilean frame. Mathematical consistency requires a single form of inertial frames IMO.

I disagree. A lack of mathematical consistency depending on its kind, doesn't necessarily lead to such heavy-handed consequences. You are missing that there are degrees of inconsistency and certain inconsistencies allow to have incredible approximations to nature. Take for example quantum theory, that is agreed by most not to have complete or rigurous mathematical consistency. Or to go back in time, theories so mathematically inconsistent as Ptolomeus epicycles obtained results that were very close to the newtonians. Newtonian phsics itself is not free from mathematical inconsistency (think of the diverging integrals for mass density at spatial infinity in newtonian gravitation) and yet it is a great approximation.

Ok, that amounts to saying that it's an assumption arbitrarily postulated, but as it is not explicitly either of the well known postulates of SR, you either adscribe it to any of them(I say it is the second postulate in disguise) or add it as a new postulate Hmm, you are the one that says we have one frame by definition for light. So I'm not sure what other frame you mean by "not in our frame". On the other hand we usually measure properties of moving objects by being at rest in their frame. For instance we make measurements on the earth(an approximate inertial frame), being at rest in its frame, we make measurement on the uniform velocity train by being at rest with its frame. Being at a frame at rest with respect to something doesn't mean that something is not moving. I'd say this is quite clear. And we don't "measure motion", we compute it from measures of time and lengths for wich we need clocks and rods at rest in the frame where we want to perform that measurement. Remember the equivalence of inertial frames, we cannot distinguish motion from rest of our own frame without external references. Maybe you should reconsider if the assertion "to measure something you have to be in the frame where that something is" is so obviosly incorrect after all.

We are discussing precisely why can one assert that they are in the same frame, that is, not moving, at a distance without making any mention of the distant synchronization of the second clock. Einstein wrote:"It is essential to note that this definition of time relates only to the inertial system K, since we have used a system of clocks at rest relatively to K." And this assured that " The assumption which was made in the pre-relativity physics of the absolute character of time does not follow at all from this definition." What he doesn't say is that only local frames can be considered at rest a priori unless we use the pre-relativity absolute character of time. To apply a Lorentz transformation of timelike paths the distant frame is always assumed to be different, but for lightlike paths they must be assumed to be the same frame,.There is no logical justification for this double standard other than for the principle of relativity for inertial frames and the second postulate to be compatible. This is arbitrary. Ok, I won't insist, as this is collateral to my main argument, I just was under the impression that to measure something you have to be in the frame where that something is, but you claim a measurement is made (in a rest frame of the clock), of a ray light (moving at c by the second postulate) if I understand what you are saying?

Not only its position, a frame includes its time(a frame includes the state of motion so both spatial and time coordinates i.e. both rods and clocks), we saw that Einstein was concerned with determining distant times and he used the second postulate to introduce his synchronization procedure. But as you say he instead stipulates that the frame of the second event is the same as the first to make clear he is not using an absolute time. But it seems clear he is using his synchronization to decide this (because the frame includes time and clocks), and therefore the second postulate. So it is the second postuate of invariance of c what prevents us from considering this ray of light to have a rest frame, And yet we have two clocks at rest measuring a speed c according to the newtonian equation c=d/t, where c is an absolute speed, d is an absolute distance and t a global time and that implies there exists a rest frame.

I don't remember talking about position being fixed, don't understand this bit. Wait, you are morphing now having a rest frame into light being at rest whatever that means. When we have an observer in a train moving relative to the embankment we say this observer is at rest with respect to the train's frame regardless of the speed of the train and we consider it the rest frame of the train. The local clock measuring the departure time of the ray of light in the galilean equation d=c(t2-t1) seems to imply a rest frame, In any case galilean equations involving time and velocity always have an implicit absolute rest frame. This is usually not allowed for light.