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Special relativity

Your comments at Talk:Special relativity#How does it work? indicate that you are assuming things about special relativity which are not true. All your questions are loaded questions which explains why we are having such a hard time answering them. Special relativity is much more similar to classical physics than you are giving it credit for being.

Perhaps you were confused by the fact that the usual derivation of the formulas of special relativity makes use of simplifying assumptions, to wit, that both observers have the same origin for their reference frames and that the axes of their frames are parallel and that the relative motion is in the x-direction. These simplifying assumptions are just there for teaching purposes and are not in the theory itself.

"... the relative motion between two observers is the key explanation of their difference of appreciation of their respective distance to a material target (e.g. a firecracker)." No. You might have gotten this mistaken impression due to the simplifying assumption that the origins are the same.

Measurements by the observers are supposed to be independent of each other.

There is no reason why any criterion is needed to determine "which observer will find the larger value". As I said before, the result depends on the factual situation of the observers.

If "two observers moving away from the firecracker in opposite directions at ... the same constant speed v/2" having started together with their origins at the firecracker, then indeed they will measure the distance to the firecracker when it explodes to be the same. You need to be careful about specifying the time here since in special relativity the simultaneity of two events (not at the same location) depends on the observer. JRSpriggs (talk) 00:53, 21 November 2011 (UTC)

This is only bla-bla. On which ground can one predict whether x will be larger or smaller than x'? Which physical parameter is the trigger? Sugdub (talk) 19:51, 26 November 2011 (UTC)

Hi, Sugdub, as we're off the article talk page now, perhaps I might be able to help. You asked questions about how special relativity decides about x being smaller or larger than x' and likewise about t being larger or smaller than t'. I assume you are referring to length contraction (smaller) and time dilation (larger). If that is indeed what you have in mind, then please have a look at the detailed explanation in the section Special relativity#Time dilation and length contraction. There you see exactly how it works, and under which circumstances the contraction ("smallerness") and the dilation ("largerness") manifest themselves. Is this helpful in any way? - DVdm (talk) 12:09, 27 November 2011 (UTC)

Perhaps you meant to ask "What is the locus of events for which x<x' ?". If so, here is the answer. In the unprimed coordinate system (with the usual simplifying assumptions),

${\displaystyle x<x'={\frac {x-vt}{\sqrt {1-{v^{2} \over c^{2}}}}}}$

from which a little algebraic manipulation gives

${\displaystyle t<x{\frac {\left(1-{\sqrt {1-{v^{2} \over c^{2}}}}\right)}{v}}\,.}$

In the primed coordinate system,

${\displaystyle {\frac {x'+vt'}{\sqrt {1-{v^{2} \over c^{2}}}}}=x<x'}$

and thus

${\displaystyle t'<x'{\frac {\left({\sqrt {1-{v^{2} \over c^{2}}}}-1\right)}{v}}\,.}$

I hope this helps. JRSpriggs (talk) 06:30, 2 December 2011 (UTC)

Thank you Folks, all this is highly informative. The issue I've raised was extremely clear:

1- if two observers A and B looking at the same remote object are in relative motion to each other, SR predicts that one of them will measure a sorter distance (x') to the object than the value (x) obtained by the other;

2- if the only information available about observers is that A is moving in respect to B and B is moving in respect to A, what good reason is invoked to substantiate that B will measure a lower value than A ? Is there anything one can sate about observer A which could not be stated as well about observer B?

Whereas the issue at stake has been stripped down to its pure logical essence which anybody equipped with basic common sense can address, physicists' brains have remained wide shut. Fair enough. Their deafening silence tells a lot more than many reluctant acknowledgements. It cannot be censored either.Sugdub (talk) 20:46, 2 December 2011 (UTC)

It appears to me that you are just an anti-relativity troll. However, if you are really still confused, then notice that there is a difference between the two observers under the simplifying assumptions used. That is, the primed observer is moving in the positive-x direction relative to the unprimed observer. The reverse is not true. JRSpriggs (talk) 21:57, 2 December 2011 (UTC)

Definitively: NO. The predicted outcome of a measurement cannot depend on the choices made for the mathematical representation of a physical context. Neither the choice of the origin of axes (placing it here better than one meter aside), of their orientation, of the positive direction on each axis (this one better than the opposite), of the mathematical speed assigned to the point representing a physical object (at rest better than in stable motion), … none of these choices which purely affect the mathematical representation of a given physical context can have any impact on the predictions of physics theories. What we are dealing with in this debate is which physical parameter (irrespective of its mathematical representation) triggers the measurement made by observer B being smaller than the measurement performed by observer A. Resolving this issue does not require any equation. Obviously you did not grasp the distinction between a physical concept and its mathematical representation. To conclude, I'm neither pro- or against- special relativity. I just cannot accept a physics theory which appears to be irrational or inconsistent, whoever produced it.

You might learn something by reading my response below to DVdm.Sugdub (talk) 15:03, 3 December 2011 (UTC)

Re 1: This is not only the case in special relativity. It is also true in Galilean relativity (the one of Newton, before Einstein came along, so to speak), where coordinates of events are transformed like x' = x - vt. Note that, depending on when an event takes place (t), and whether S' is approaching S or receding from it (sign of v, combined with sign of t), x' can be smaller or larger than x. So it all crucially depends on the specific event that you have in mind. If you don't provide the specifics of what you have in mind, nobody will be able to know what you have in mind, let alone to help you with it.

Re 2: The symmetry is complete, as you can see in Special relativity#Time dilation and length contraction (quoted from article):

• "... the length (Δx') of the rod as measured in the frame in which it is moving (S'), is shorter than its length (Δx) in its own rest frame (S)."

and vice versa, (with the primed and unprimed notation interchanged),

• "...the length (Δx) of the rod as measured in the frame in which it is moving (S), is shorter than its length (Δx') in its own rest frame (S')."

which, independently of coordinates —as nature does not care about coordinates— combines to:

• "...the length of the rod as measured in the frame in which it is moving, is shorter than its length in its own rest frame."

Be careful with "basic common sense". That is a bad guide. According to basic common sense this is impossible, and it has nothing to do with special relativity. But it does happen. - DVdm (talk) 22:02, 2 December 2011 (UTC)

Very interestingly the statements you quote deal with the relative motion between the observer and the object he/she is looking at. You assume the first observer is at rest in respect to this object and once combined with the statement whereby both observers are in relative motion to each other, this necessarily means that the second observer is NOT at rest in respect to the object. Although you were not conscious of it, you assume that both observers have a different velocity in respect to the object they both look at: one moves and the other one does not. This is a clear objective difference in the experimental conditions of both observers.

It is obvious that you (and other physicists) make an additional assumption (observer A is at rest in respect to the target object) which was not contained in the statement whereby A and B are in relative motion to each other. Thanks to this additional assumption, the magnitude of the velocity of each observer in respect to the target object is known (zero for observer A and v for observer B).

As you might now understand, it is this objective difference in their experimental conditions (their different velocities in respect to the target object) which will trigger both observers obtaining different values when measuring their distance to the object. It is irrational to believe that it is due to the reciprocal relative motion of both observers.Sugdub (talk) 15:03, 3 December 2011 (UTC)

Yes, one observer is at rest with respect to the object, and the other is moving w.r.t. it. Of course both observers have a different velocity with respect to the object: one of the observers is rest w.r.t. the object, so his velocity w.r.t. it is zero. I am very conscious of that. The objective difference in the experimental conditions of both observers is indeed that one of them carries the stick, so to speak. These are not just assumptions, these are part of the setup.

But you seem to have something wrong. This is not at all about the "distance to the object". It is about the "length of the object". That length is measured by taking the "difference between two distances to events". These events take place at the two endpoints of some imaginary object (a rod). The observers' relative motion, combined with the way they measure the distance between events, really causes the difference. Just look very carefully at Special relativity#Time dilation and length contraction again:

• The rod is moving for observer S'. Two firecrackers are ignited at the end points of the rod, simultaneously for S' (t'1 = t'2, so Δt' = 0). S' measures spatial coordinates x'1 and x'2 for these firecracker events. So S' decides that the lenght is the absolute value of x'2-x'1 = Δx'
• The rod is a rest for observer S, for whom these same firecracker evets are not simultaneous (t1 # t2, so Δt # 0) but that does not matter, because the rod is not moving for S. S measures coordinates x1 and x2 to these firecracker events and gets that the length is the absolute value of x2-x1 = Δx
• When things are compared, it turns out that Δx' < Δx, by a factor γ, that has a value that depends on the relative speed between the observers, and that can be derived from the basic assumptions of the theory.

So there is nothing in here that says something about, like you say, "observers obtaining different values when measuring their distance to the object." - DVdm (talk) 15:46, 3 December 2011 (UTC)

Well, we might have progressed somehow insofar we have identified an objective difference in the experimental conditions of the observers, upon which one could elaborate in order to demonstrate (a hook is not a proof) that it actually explains that both observers obtain different results for similar measurements and that it certifies which one will find the lowest value. For that we'll certainly need to reach a common understanding on what is being measured and on what the measurement process consists in.

But before coming to this discussion, I must say that I'm not convinced you have abandoned the view whereby the difference in the measured values is due to the relative motion of observers. Your statement: "… it turns out that Δx' < Δx, by a factor γ, that has a value that depends on the relative speed between the observers..." still points to that view. May be this is just a remnant expression...

There is a simple way to sort this out: if the relative motion between observers is NOT the cause (and I insist that it cannot be from a logical standpoint), we can simply eliminate one of the observers and envisage demonstrating that "all things equal, the outcome of the measurement performed by an observer varies according to his/her relative speed (v) in respect to the target object". Although the magnitude of the change in experimental conditions (as compared to the pivotal case where the object it at rest in respect to the observer) is still equal to v, the conceptual error about what v stands for has been eliminated.

We'll see whether we can consolidate or not this first step and I believe we can't go much further until this is done.Sugdub (talk) 17:59, 4 December 2011 (UTC)

If you don't want a 'second observer', then perhaps you might think of Δx as "the proper length of the rod" (by definition the length that someone at rest w.r.t. the object would measure). Then the conclusion of Special relativity#Time dilation and length contraction is:

• The length of the object as measured by someone for whom the object is moving with velocity v, is shorter than the object's proper length, by a factor γ, that has a value that depends on v,

or expressed in slightly careless language:

• A moving object is measured to be shorter than its proper length by a factor that depends on the velocity of the object.

One observer. One object. One velocity. - DVdm (talk) 20:40, 4 December 2011 (UTC)

Here we are. Having got rid of the relative motion between observers, the conclusion you propose reads much better. There are however two caveats: on the one hand the validity conditions of your conclusion must be spelled out, since they are extremely peculiar; on the other hand, any wording suggesting that the length of objects "contracts" under certain circumstances is misleading.

Let's start with the latter. In proper words, it is the outcome of the experimental process, i.e. the value it delivers, which gets contracted, not the length of the object, and this value only matches the length of the object in the static case. I hope you will appreciate the clarity of the concept, whereas expressions like "contraction of lengths" are just intrinsically meaningless.

Let's now switch to the validity conditions applicable to the new wording you propose.

1- the first validity condition is that the observer uses pulses of light propagating in the empty space and his/her own clock to measure the propagation time of the light between him-/her-self and the object, and then converts the measured values into distances using always the same conversion factor c (actually only the time for a two-way trip of the light can be measured using the observer's clock). Should the observer use a projectile, or the propagation of sound or whichever other experimental protocol, physicists would need to take into account the appropriate characteristics of the propagation of signals through the physical medium, and this would obviously have an impact on the theory. There would be no reason for invoking the postulate on the invariance of the speed of light... whereas this invariance plays a key role in SR reasoning. So this first validity condition cannot be waived.

2- the second validity condition is that in the non-static case, you assume that the object moves TOWARD the observer at a velocity v. Because the experimental protocol based on pulses of light is not instantaneous (it takes time), the distance which remains to be covered by the light at any time decreases during the measurement process itself, leading to a lower measured propagation time and therefore to a lower distance to the object as compared to the static case. But the reasoning which justifies the "contraction" of the output value when the object moves toward the observer will equally justify a "dilatation" of the measured value for objects moving away from the observer, all things equal. SR only deals with the first case and this is why it always concludes to a "contraction". If you don't agree with that you are left with no explanation to justify why the outcome of the measurement for the non-static case is lower better than larger as compared to the static case. So the conclusion reached by special relativity is only valid under extremely peculiar conditions and to be honest the way it is currently spelled out is totally misleading, not to say totally absurd in the absence of its validity conditions. You might notice that it was not possible to identify this second validity condition as long as the cause for the change of value was considered to be the relative motion between two observers. It is therefore not a surprise if physicists have so far never been able to explain what is the actual trigger for x' being smaller than x better than the opposite. So the second validity condition cannot be waived either. You are now in a position to correct this error.

3- Finally, the experimental protocol relying on measuring the propagation time of the light between the observer and the object is intrinsically limited to values of v lower than c. This is an absolute limit to the validity conditions of any conclusions derived in this context.Sugdub (talk) 10:46, 6 December 2011 (UTC)

It is not assumed "that the object moves TOWARD the observer at a velocity v". Furthermore, it is not true that "the distance which remains to be covered by the light at any time decreases during the measurement process itself", because the process explictly measures the spatial coordinates (x'1 and x'2) to the endpoints of the object at the same time (t'1=t'2 or Δt'=0) for the person for whom the object is moving. It would be very stupid to first (1) measure the distance to the front of a moving train now, to then (2) measure the distance to the rear a number of minutes later, and to finally (3) call the absolute value of the difference between the distances the length of the train. It looks like you haven't understood the very essence of the measurement process, although it was spelled out a few times now — see highlight above, and, again, the section Special relativity#Time dilation and length contraction. Did you have a look at that section? Do you understand it? Do you see the place where it says Δt' = 0 ? Do you understand these equations? Can you explain in your own words what you think the physical meanings are of the symbols x, x', t, t', Δx, Δx', Δt, Δt' and v? - DVdm (talk) 11:21, 6 December 2011 (UTC)

See this illustration from the commons. It compares the effect of rotation in Euclidean space with the effect of a boost in Minkowski space on the cross section (width) of a square slab. In the picture on the right, the vertical direction represents time. JRSpriggs (talk) 17:38, 6 December 2011 (UTC)