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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)

Hmmm. It appears we should find a common understanding about what is being measured and how, as a matter of priority. A large part of the problem is due to the weird/fuzzy language used by physicists, the "contraction of lengths" being a typical example.

1- Yes I've read the section you refer to on time dilation and I'll use it as a support to give you a first hint about where the problem lies. As we have already discussed, and I personally believe you are not going to step back since you now understand what lies behind, the difference in values obtained by both observers is not due to their relative motion, but to the fact that they have a different speed in respect to the target object. From that point, it must be equivalent to present the time dilation/length contraction discussion either by referring to two distinct observers and two distinct reference frames S and S' in relative motion, as physicists have always done (first paradigm), or to shrink this down to one observer and therefore one single reference frame, distinguishing however two different experiments for which, all things equal, the target object is either at rest or in relative motion to the observer (second paradigm). It is quite obvious that it will be easier to keep control of the logical flow if one adopts the second paradigm. Had Einstein properly identified the cause of the change in value, all this weird concept of "reference frames in relative motion" would have never existed. From now, you know that it is not needed and that one could store it on the shelves of a museum of obsolete concepts in science. Waiting for the opening ceremony, we must preserve a way to transpose the discussion between both paradigms, ensuring that the physical conclusions (time dilation, length contraction) be identical irrespective of the preferred paradigm. Now let's consider an event which coordinates in S and S' are (x,t) and (x',t') respectively (first paradigm). How do you convert this into the second paradigm? Is there any alternative but referring to two events (x,t) and (x',t'), both expressed in the unique reference frame of the unique observer, both events describing the same thing according to the conditions of the experiment (rest/motion)? So alongside the second paradigm, you will conclude that the event (x,t) you refer to in the first experiment (rest) will be transformed into a different event (x',t') in the second experiment (motion). It means that something taking place at a given place and a given time when running the first experimental conditions will actually take place at another place and another time if you run the same experiment in different conditions: nothing mysterious. This has no bearing at all to any kind of "length contraction". Length contraction is just a loaded view induced when reasoning alongside the first paradigm, because this paradigm typically masks the fact that there are two independent experiments being conducted.

2- An event is not a physical object, it is not located somewhere in space and time, it cannot be in motion and one cannot be in motion toward it. One cannot "measure the coordinates" of an event. An event is a record. It records what has happened to a given physical object at a given time and a given location. First of all, an event (x,t) traces the fact that a physical object was located at position x at time t, in addition to recording what happened to the object (e.g. it emitted, received or reflected a pulse of light). And of course the values x and t which are recorded as "the coordinates of the event" actually reflect the position x of the object at the time t something noticeable happened to it. When physicists indicate that "S measures coordinates x1 and x2 to these firecracker events", that cannot mean anything else than measuring or assessing the position of each firecracker according to a given measurement/assessment protocol. On that point, it seems possible to reconcile our divergent wordings. However, in this particular example, there is a problem concerning which events are actually looked at, and another problem concerning which measuring protocol is involved, as I will explain in the next two sections.

3- Most "events" are not directly accessible to an observer. Generally speaking an event belongs to the history file of a physical object, and an "observer" can only access events that belong to his/her own history file (including those of the measuring instruments and detectors he/she carries with him/her. The example of a "firecracker" is symptomatic of this issue: indeed its explosion can be recorded into an event, but a remote observer has no direct experimental access to it. The assumption is that the observer is co-moving with the rod, not that he/she is riding it. He/she can only access another event relating to the reception, at a remote place, of the light emitted by the explosion. Between both "events", emission and reception of the light ray, there may be a lot of time and space, as can easily be understood with the example of a supernova. So some events can be directly "observed" and some other events can only be "inferred" from observations thanks to a theory, in this context a theory of the propagation of light. From the coordinates of the event tracing the reception of the light by the observer, one cannot infer what were the coordinates of the explosion event unless you already know the distance to the firecracker. The example of the firecracker might reveal being ill-fated. Ultimately, the wording "S measures coordinates x1 and x2 to these firecracker events" is meaningless: what do you actually measure and how is this done? Which experimental protocol is involved? As indicated above, the position of an event is nothing else than the distance to the object it relates to, so that we are back to square one: if you wish to measure the length of a remote object, you first must find a proper way to assess or measure the distance to each end of this object. Anyway very few objects are equipped with firecrackers.

4- According to the above, you can't escape clarifying which protocol will be used for this measurement. As indicated in my previous input, you won't be able to invoke the postulate on the invariance of the speed of light unless you actually use the light as a measuring device. Why is it appropriate to use a light pulse sent by the observer, reflected back to him/her by the object and finally captured by the observer? Because this protocol generates a reflection event of the light by the object, because the duration of the two-way trip enables inferring (under appropriate conditions) the coordinates of the reflection event, because these coordinates indicate the position of the object at a given time. It is fit to purpose and there is no equivalent.

5- How does it work? In the static case where the object is at rest in respect to the observer, and assuming the observer measures the two-way propagation time of the light, it is easy to compute the coordinates (x,t), in the observer's reference frame, of the reflexion event of the light onto the target object. It is clear that x holds as a proper measure of the (static) distance between the observer and the object. The same experimental process can be run twice, once for each end of the object (let's say a rod), leading by difference to a proper measure of the length of the rod (I fully agree there would be an easier way if the rod were at hand, but here we are dealing more generally with remote objects). In the dynamic case, however, the light will reach the object at a different place and a different time as compared to the static case, actually closer and earlier if the object moves toward the observer (because the measurement process, using the light, is not instantaneous), so that the reflection event is not the same event as in the static case (see paragraph 1 above). The coordinates (x',t') of this reflection event actually indicate that the object was located at a distance x' of the observer at time t', and although x' will in this case be smaller than x, this has no bearing to a "contraction" of anything: all things equal, the position of the moving object is captured at a different time and place depending on the relative speed of the object (magnitude and direction). Again this measurement process can be run twice, once for each end of the rod, generating two different reflection events which will now (in the non-static case) have different time coordinates. Therefore, the gap in the position coordinates of these two events cannot be considered delivering a proper measure for the length of the rod (as you can read we are in full agreement about the importance of Δt' = 0 however there is still no rationale for stating a "contraction of lengths").

6- In summary, the two-way measurement protocol based on light has the potential for delivering a genuine measure of the distance to the object, including in the non-static case, provided the relative velocity of the object is known. However different position measurements will hold at different times and therefore one cannot directly infer, by difference of such positions, neither the length of an object nor the relative distance between two objects, unless they are at rest in respect to the observer. In order for this to become possible, and assuming the relative motion to the observer is known, one must use an appropriate transformation formula to re-calibrate all reflection events (x',t') at a common date t, leading to a corresponding set of calibrated reflection events (x,t) from which one can now compute by difference the length of objects and the relative distances between objects. This is why we need SR to produce the appropriate transformation formula.

Once you have "digested" this, you might read again my previous input. I accept that I had skipped some explanations that are necessary, in order to keep it short. You will also remember, since this is still the scope of our debate, that physicists haven't so far produced any kind of explanation as to why SR predicts that x' should be smaller than x. The explanation I provided is fully integrated in the above. It reads easily if you adopt the second paradigm. Just consider again the interest for a museum of obsolete scientific concepts.Sugdub (talk) 16:57, 7 December 2011 (UTC)

Re your phrase "... you will conclude that the event (x,t) you refer to in the first experiment (rest) will be transformed into a different event (x',t') in the second experiment".

Here I had to stop reading, as it is clear to me that you do not understand what is meant by an "event in physics", and that you obviously have no idea about the physical meanings of the variables in the cited coordinate transformations. It is clear to me that you cannot possibly have understood anything in the section Special relativity#Time dilation and length contraction (*), or anything that I have been explaining here. Before we can possibly continue, you will have to understand what an event is in physics and how coordinates are used —in physics— and what they mean. See (at the very least) the two sections in Special relativity immediately preceeding (*), where you also find a pointer to the article where events are explained (Spacetime#Basic concepts). DVdm (talk) 17:56, 7 December 2011 (UTC)