Andromacus

I know it is assumed. My point is that by the same logic that with Einstein's new concepts of time and velocity he considerered that he needed to define a certain synchronization based on the second postulate for the distant clock because we cannot "fix the time, by means of this clock, of an event whose distance from the clock is not negligible; for there are no "instantaneous signals" that we can use in order to compare the time of the event with that of the clock", it seems we should not be able to "fix" by assumption the state of motion, the frame of a distant event unless we use the light potulate that assumes c is invariant in all frames. I mean frames have time coordinates so they involve time. Well a lightlike geodesic interval made of events in that interval is being analyzed here using rest frames as literally called in the text, the local clocks that measures the departure time is at rest and the distant clock is supposed to be in the same frame at rest with K.

Very good point, thanks. (.At least somebody is following my reasoning even if in disagreement, I was about to get really pessimistic) This is sensible and in accordance with how Einstein referred to this issue, which he clearly contemplated. Let me use an excerpt of the book by Einstein "The meaning of relativity", where he addresses precisely my point in 101#: "Before we draw any conclusions from these two principles we must first review the physical signicance of the concepts "time" and "velocity." It follows from what has gone before, that co-ordinates with respect to an inertial system are physically defined by means of measurements and constructions with the aid of rigid bodies. In order to measure time, we have supposed a clock, U, present somewhere, at rest relatively to K. But we cannot fix the time, by means of this clock, of an event whose distance from the clock is not negligible; for there are no "instantaneous signals" that we can use in order to compare the time of the event with that of the clock. In order to complete the definition of time we may employ the principle of the constancy of the velocity of light in a vacuum. Let us suppose that we place similar clocks at points of the system K, at rest relatively to it, and regulated according to the following scheme. A ray of light is sent out from one of the clocks, Um, at the instant when it indicates the time tm, and travels through a vacuum a distance rmn, to the clock Un; at the instant when this ray meets the clock Un the latter is set to indicate the time tn = (tm+ rmn)/c. The principle of the constancy of the velocity of light then states that this adjustment of the clocks will not lead to contradictions. With clocks so adjusted, we can assign the time to events which take place near any one of them. It is essential to note that this denition of time relates only to the inertial system K, since we have used a system of clocks at rest relatively to K. The assumption which was made in the pre-relativity physics of the absolute character of time (i.e. the independence of time of the choice of the inertial system) does not follow at all from this definition." Einstein felt the need to stress in the last paragraph that the absolute character of time doesn't follow from his definition because it relates only to one rest inertial frame K, just like you argue in your reply. So maybe you could help me with the questions that could prompt these reasoning or perhaps indicate me where I'm not using the right premises. Einstein justified the absence of contradiction in his sync method and his not really using a global time in the fact that the distant spacetime point where he set his second clock(ray arrival clock) was in the same rest inetial frame K as the local departure clock. But how exactly can one ascertain that the distant clock is in the same inertial frame as the local clock?, it seems like the same reasoning Einstein used to justify the use of his synchronization: "In order to measure time, we have supposed a clock, U, present somewhere, at rest relatively to K. But we cannot fix the time, by means of this clock, of an event whose distance from the clock is not negligible; for there are no "instantaneous signals" that we can use in order to compare the time of the event with that of the clock.", that he solves by using the second postulate, would be needed here to declare the distant event to be in the same inertial frame. Certainly the same solution is given since the reason it is assumed to be in the same frame is the second postulate, that c is invariant in any frame. So we see we can use the same second postulate to solve the issue of the sync of distant clocks, and to rest assure that to assume that the distant clock is in the same frame as the local clock is a non-issue and therefore there is no problem with the Galilean equation that uses newtonian time. Another problem that I see with Einstein's argument is that all this refers to a light ray wich is by definition not supposed to have a rest frame neither at departure nor at arrival points. It seems that for the purposes of deriving the null interval and the Lorentz transformations from Einstein postulates it is alright to consider light has rest frame. For any other purposes is forbidden.

1. Yeah, if you could read you'd realize that I'm refering to the t used by Einstein to derive the null interval for a ray of light in one frame, not the one used in the Lorentz transformation between the obserber in the train and the observer in the embankment. 3. You obviously are not grasping the simple explanation in my last post. Your last paragraph is just hilarious if it weren't because it might mean you are unstable, or simply a psycho, none of the alternatives is funny. I reported you to the moderators without response so far, but I see you have already been suspended once.

Going back to my original question in post #1 and leaving aside the confusing discussions about distant simultaneity(that don't have empirical solution so they are quite useless) , maybe I can formulate it in a way that is easier to understand and get specific answers. My first post highlighted the fact that Einstein used the same time and distance used in galilean transformations for the distance travelled by a light ray in vacuum from spacetime point1 to spacetime point 2, both points measured with global time t i the equation d=ct, to derive the null interval and from it the general minkowskian interval and the Lorentz transformations that leave it invariant. Only using the Einstein synchronization can this be done. So much for conventionality of clock sync. postulated by Einstein himself. The very idea of a standard synchronization establishes the existence of a global time valid at a distance from the clock one has locally. So the contradiction lies in that Einstein needs both to use a single standard synchronization or global time to derive the Lorentz transformations with his postulates, and at the same time declare his choice a convention because he is promoting a local time that is different from frame to frame, from spacetime point (event) to spacetime point. The contradiction would be that it is necessary to have the Einstein sync as conventional and not conventional at once for the arguments of Einstein seminal 1905 paper to hold. If we could just center on this, I would appreciate any input.

So my issue in 4. with the Minkowski diagram is a problem with the representation only, since the boost in one direction is obviously a linear transformation, because it may lead to the wrong physical conclusions in higher dimensions.

Yes I meant inertial observers and also I was trying to make a distinction between the passive transformation and the Minkowski diagrams where one observer is stationary while the other is moving. Probably not the most fortunate phrase to express what I was trying to convey. Precisely the "there's no outside view where both are stationary" issue is discussed in the next points 2. and 3.

This is fair criticism to some extent, thanks. Everyone here talks as if if they were such relativity experts that I thought talking about lorentz transfromations as (hyperbolic)rotations wouldn't invite confusion. However, I'm not making up new terminology, passive Lorentz transformations is terminology in use, a quick internet search gives this example: http://physics.stackexchange.com/questions/135112/a-few-questions-on-passive-vs-active-lorentz-transformations I would also appreciate a more substantial criticism of the content besides the form(wich is fine)

Ok, let me try again then. 1.It's what I'm calling a passive Lorentz transformation, in which we are just looking at the same event, just from different point of view, i.e. from different coordinate systems that are rotated by an imaginary angle. So we are alternating the rest train point of view coordinates and the rest embankment point of view coordinates, so both use perpendicular time and distance coordinate axes. We can do this because velocity is relative and in relativity we can arbitrarily consider each observer at rest with respect to the other. I hope we can agree so far. This is the sense in wich both observers can be considered stationary in the passive Lorentz trasformation. 2.There is a problem when trying to show such passive transformation with a diagram, because both coordinate systems are orthogonal and they would superpose unless they were represented like the right diagram in my analogy with active and passive real rotations, but then somebody could say we are trying to represent imaginary angle rotations, so why use real angle rotations of the axes. So it would seem we are stuck at representing either one of the observers perspective of the event but not both observers at once in a diagram. 3.What is usually done to represent a Lorentz transformation is using the regular Minkowski diagram wich in my analogy could be related to an active rotation (but please not literally, I'm just drawing analogies between imaginary and real angle rotations). To be able to do this with a hyperbolic rotation one must recurr to skewing the grid to express the different velocities of the moving observer with respect to the observer at rest. So we can represent the observer at rest with orthogonal axes and the moving one with oblique axes and the angle between them as the velocity boost. 4.There is a problem if one takes this representation literally, we are either not talking about inertial frames anymore or we are no longer representing a linear transformation. So you'll reply(if you have followed me this far): Don't take it literally. Well, ok, what's your alternative? 5. My point, (and I'm not asking you anymore to agree with me here, just presenting my view) is that Einstein did indeed find this skewing of the grid(although he only did it algebraically, not geometrically at the time) as his solution to what he presented as the apparent irreconcibility of his first and second postulates. I'm saying that mathemaically it is incompatible with keeping observers inertial. Please critizice each of the points specifically all you want, but don't just dismiss it globally as word salad.

The rotations I've been talking about are obviously those including the time coordinate,either active or passive rotations by an imaginary angle. Since hyperbolic rotations have even been mentioned twice wich I took to mean it was understood I'm still a bit perplexed at the reaction.

To clarify, the 2 transformations shown above, the passive and the active are rotations, basically in flat space with cartesian/inertial coordinates active and passive transformations are equivalent, from this comes that the distinction between covariant and contravariant vectors is not necessary in this case. This should be also the case for Lorentz transformations that use inertial coordinates since Minkowski space is flat. However the indefinite signature of the pseudo inner product is supposed to justify the distinction between the active and the passive rotation. So what is called a boost or rotation free Lorentz transformation is just a passive rotation of the axes that includes the time axis(so not a real or active rotation). You are deliberately misinterpreting my words, I was evidently not talking about the regular 3-space rotation when I say rotation. There is no point discussing about science with someone with your attitude. I am asking you to leave and you come back insulting. I pity you but I'm not here to deal with people with such evident personal issues. Take them somewhere else. I ask you again not to come back unless your attitude is constructive

1. Of course, I didn't imply otherwise, was just describing your setting. Axes can rotate clockwise or counterclockwise. 2.No, I'm not. I'm saying actually that they can be deceiving as to what is really going on. In fact they are not mathematically consistent. It's specially deceiving for the amateur, one needs to know some sophisticated math to know what they are really about. But it is a fact that they are very often used to justify the physics of SR in a sort of automatic fast and easy way not only by amateurs but by relativists in general. 3. Actually I'm not claiming that. I'm not suggesting a preferred frame. I admit I should have qualified better what I meant by saying that time is absolute in this context. I was referring to the time in each stationary frame separately as written by you d/t=c, this formula is preserved by axes d(x) and t remaining orthogonal, fixing an absolute simultaneity for light speed. 4. I think you should have quoted the next sentence in that paragraph too. There I tried to justify my claim by explaining that a passive transformation, i.e. rotating the axes while keeping the relative speed line fixed, leads to the numbers you calculated in relation with the new position of the speed line with respect to the rotated coordinate system. Why do you think the mathematically inconsistent Minkowski diagrams are used all the time to ilustrate the physical consequences of SR? Because a 2D diagram of a Lorentz transformation like the one you showed the calculation of, just shows a euclidean rotation of coodinates. This diagrams are taken from wikipedia page about passive transformations vs active transformations. The transformation you described correspond to the image on the right. A minkowski diagram would correspond to the image on the left of an active transformation if it wasn't because the axes are no longer perpendicular in the transformed frame of the M.diagram, and the transformation is no longer linear so the change in speed is purely coordinate just like in the passive transformation. Now this is not easy to understand if one doesn't have some clear notion of geometry. The usual explanation is that one must abandon the Euclidean concepts and adopt the minkowski geometry. The problem is all this is happening in a flat plane(R2) and there is no way out of this. Some reason as if picturing a circle in a plane should make the geometry of the plane "circular", and as if graphing a hyperbola in R2 should transform the geometry of the plane, Well, it doesn't. Well, it's a bit tricky, but all it means is the notion that rest is equivalent to uniform motion if one is to talk about inertial frames. So a linear transformation in flat space is just a coordinate rotation, that in Euclidean terms leaves points invariant. But, and this is the tricky part in SR it is not interpreted like this, the special pseudo inner product of minkowski space leaves room to interpret the Euclidean rotation as a velocity boost like shown in Minkowski diagrams. This thread is about how and why this is mathematically inconsistent. The problem has always been that two realms are maintained: the formal plane of the calculation posted by david345 which is formally consistent but that simply expresses a passive coordinate rotation in wich one of the axes happens to be called ct, and a physical plane that is not consistent(Minkowski diagram using a nonlinear transform to represent a linear transform) that is used to justify the relativity of simultaneity effects and that when questioned sends the questioner to the formal plane and shows how the numbers fit.

That's nice. Of course if you consider spatial distance as absolute you don't need clocks, just measuring length and translating it to meters per second, but for this translation whether you believe it or not you are using the standard synchronization, so basically what you are saying is that this is the only possible synchronization. That's fine with me. Right, that is a Lorentz transformation from the train's frame to the ground's frame that is indeed linear, but that is not what is usually shown in a Minkowski diagram. Your example shows a transform from an observer at rest with the train frame to an observer at rest with the ground frame. It doesn't show the relativity of simultaneity. It is just a rotation of the axes that shows a velocity boost. While a Minkowski diagram shows a transformation from the oberver at rest in the train to an observer moving with respecto him in the ground as perceived by the former, or viceversa. Here the relativity of simultaneity is evident, while in your transform we just see a change of speed, the relative velocity between train and ground, but time is absolute, and no time dilation-length contraction are shown, so the physical properties associated with SR are not shown. It's a transformation between stationary observers that are disconnected, with their velocity boosted.The fact that one sees flashes simultaneous and the other not is just the logical consequence of rotating the coordinates. So the key here is acknowledging that the formal linear transformations can only be made between stationary observers. While a Minkowski diagram that is used to show the physical consequences of Lorentz transformations is done bewtween stationary and moving observers and requires the use of skew noninertial frames for the moving observer.

No, not for a synchronization, I'm talking about the regular Lorentz transformation between frames as seen in the usual Minkowski diagram. Ok, so this is the usual minkowski diagram of a lorentz transformations. The black axes represent the inertial frame at rest and it's compatible with isotropy of light and Einstein sync. The red axes represent in theory the Lorentz transformed inertial frame. But it is evident that non-orthogonal coordiantes cannot represent an inertial frame. This is usually dodged by saying the non-orthogonal coodinates are actually how one observer perceives the other. And symmetrically if we go to the rest frame of the red axes observer they are also orthogonal. But this clearly is not mathematically demonstrable since we cannot put both observers at rest except at the origin, however we are drawing conclusion about simultaneity from this diagram with the miixed coordinates, that should only be used for ilustrative purposes, not to draw physical conclusions. The red axes that give an anitropic c are giving a coordinate velocity that cannot be used to extract physical consequences about simultaneity. Some will say this is just a drawback of the 2D representation but when going to 4-space the restriction persists that the time coordinate must be orthogonal to the spatial hypersurface(Minkowski space is static wich implies this).

From post one I have been saying the contradiction lies in the relativity of simultaneity. It is of couse related to the different synchronization in the different frames, not in the same frame. Read the title of the thread. I don't know what you want me to say nor why it is so important to you to talk about homogeneity. Isotropy is spherical symmetry, a point property in Euclidean geometry as you said. Homogeneity refers to space translation invariance and therefore involves more than one point. The isotropy and homogeneity in classical mechanics and in SR results from using flat geometry. Cartesian, and inertial minkowski coordinates are naturally orthonormal and homogeneous and isotropic and this must be preserved by linear transformations.

The mixing is of inertial and noninertial coordinates when both should be inertial frames, it consist of performing a supposedly lorentz transformation that should preserve orthogonality(isotropy of light with Einstein sync) and getting anisotropic, non-Eisntein sync, non-orthogonal coordinates.for the transformed frame. I thought this was clear enough as written, they are standard definitions. I tried to include a Minkowski diagram but the system won't let me.

As I said inertial coordinates being orthogonal and normalized are both homgeneous and isotropic, and these properties must be preserved by the Lorentzian inertial frame (linear) transformations. But if you look at a minkowski diagram of a frame transformation it is clear that isotropy(i.e. synchronization) is not preserved, changing to non-orthogonal coordinates in one of the frames. This is not a linear transformation. Agree so far?

A clear explanation of how SR's relativity of simultaneity requires the different frames to disagree about sync chronization of clocks(alternative simultaneities) can be read here:http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/Special_relativity_rel_sim/index.html Orthonormality refers to both the time and space axis(inertial coordinates) in a minkowski diagram. We are restricting here to the one dimensional case for simplicity, by isotropy we refer to the perpendicularity of the axes that allows the standard synchronization, that is isotropic(speed from A to B in the x axis is eqaul to that from B to A).. I'm not sure what you mean by isotropy or anisotropy of just one axis, one needs two axes to define perpendicularity.

your examples of alternative simultaneities, and claims that the Lorentz transformation require them, contradict SR. At best I think you'll have to show an alternative simultaneity is in agreement with experimentally verified predictions of SR. This shows you haven't understood what I'm saying(I'll be more tolerant than you and refrain from saying that means you don't have a clue about what you are saying or SR). Try my previous post. I'm willing to carry the blame for your(or others) not understanding my point anyway. Communication in a forum has its drawbacks.

I'm intrigued about your position in this thread. Sometimes I think you are quite aware of the contradiction I'm bringing in like in this post you seem to. Other times it seems you are saying the opposite and in the meantime you bash everyone in sight. I truly don't know yet what your position is.

I think it would indeed help to use math arguments. Basically a simultaneity convention is no more than the choice of coordinate systems one decides to use for a certain problem. The Einstein sync amounts to the usual inertial coordinates of Newtonian mechanics. These are orthonormal coordinates and are the natural ones in a flat space. Other choices of simultaneity are no more than choosing other coordinates, it shouldn't be a problem what coordinates to use except some may adapt better to certain problems or geometries, in this sense as I commented inertial coordinates are the best suited for flat spacetime. As long as one is consistent with the use of coordinates of course, one cannot mix different coordinates for the same problem or risks getting contradictory answers. This mixing of coordinates is happenning here, as can be seen in any Minkowski diagram of a change of frames.. Now for instance non-inertial coordinates are curvilinear, we'll left those aside as this issue doesn't concern non-inertial frames(there is no accelerations or gravity involved). We also have non-orthogonal coordinates like the ones used in Minkowski diagrams to depict the frames not at rest. So these non-orthogonal coordinates are the ones used when a simultaneity convention different to the one required by Einstein's sync (that had to be orthogonal remember?). This is the case everytime a change of frame(Lorentz transformation) is invoked, in order to have relative simultaneities for each frame. Now since here we are always dealing with inertial frames, and transformation between frames must preserve the Lorentzian concept of orthogonality wich is differetnfrom the euclidean concept it is usually accepted the use of non-orthogonal axes in Minkowski diagrams for the frame not considered at rest, but again what characterizes an inertial frame is the orthonormality i,e. perpendivular axes for x and t. So one of the frames in the transformation must use non-orthogonal coordinates(giving anisotropic speed of light), and please realize what this implies, this implies that for the frame not using orthogonal coordinates the one-way speed cannot be equal to the round-trip speed of light, and this forces us to say that the one-way speed is unmeasurable to avoid direct contradiction, since the round-trip speed is considered isotropic. We may gree that light speed shouldn't be at the same time isotropic and anisotropic right? Now this simple fact has been repeatedly ignored by all those who claim they are fine with a non-conventional standard Einstein sync, and don't find any problem with sayin one-way speed is perfectly measurable. The reason SR is contradictory is that both sides can find arguments within the theory to say they are right, but we all know this cannot be true, it is much more likely both sides(conventionalists and non-conventionalists) and therefore SR are wrong somewhere. Edit I was going to include a Minkowski diagram but it seems I'm not allowed.

Can you elaborate this into a more physical argument about the specific issue discussed here? I've got the feeling many of your arguments are appeals to authority rather than physics And it would help if you explained in wich sense is a one-way speed, because the only option I see is that you are using absolute time and distance, and yet I'm sure you realize newtonian(galilean) and SR concepts of time are different.

Well, it will depend on whether you are a conventionalist or a non-conventionalist what answer you give, because each ahas a different answer to the question if the one-way speed can be measured in principle. The contradiction I'm highlighting is precisely that both views are compatible with SR(thus the endless and undecidable debate is still going on, although more quietly of late). If the theory wasn't contradictory on this point an inmediate solution satisfying everyone would have been found.

This seems mostly a discussion on semantics. I started by saying that the train passenger can infer, not know, that the events were not simultaneous, my point is that all that observers have is elements to make inference, because the whole point here, and I think we should agree on it, is that there is not an absolute simultaneity so nobody can "know" if the events(striking) are simultaneous or not, in fact by the relativity of simultaneity it makes no sense to even ask or declare any of the observers know if the events were "really" simultaneous. My reply to md65536 was in the context of her apparently implying that distances were different from the fact that the train observer could infer that the events were not simultaneous. On rereading I can see how my emphasis to reject that idea might lead to some confusion. So in fact the common misconception is deriving from the inference that the distances between lightning A and B are different for the two observers.