# Are the transformations just observed ones or real ones?

• Windows
In summary, the transformations of time dilation, length contraction, and relativistic mass have all been observed and measured, making them considered as real by most physicists. However, the effect of length contraction has not been directly observed, and is instead a fundamental result of the theory of relativity. Additionally, the concept of relativity of simultaneity suggests that these transformations are not absolute, but rather dependent on the observer's frame of reference.

#### Windows

Hello!
Are the transformations such as time dilation, length contraction and relativistic mass just observed ones or real ones?
Thank you.

What is the difference? How are we supposed to learn about reality other than through observing it?

More explicitly, is there an experiment which could tell the difference between an observed transform and a real one? If not, then the question is not scientific.

Look for a pinned thread rgth at the top of this forum on experimental support for special relativity:https://www.physicsforums.com/showthread.php?t=229034

Time dilation, relativistic mass increase, and length contraction have all been observed and measured.

(And I'm somewhat unclear on what you mean by the difference between "observed" and "real". If by "observed" you mean some sort of optical illusion, they're not illusions, they're real).

I mean we observe things through photons and because relative to us something is traveling then what we see will be different because of the transforms; So what if we could see reality, the object as it is, in other words we use the transforms to somewhat find the real value will it be correct?
I hope you understood what I mean, it has nothing to do with philosophy.

Windows said:
I hope you understood what I mean, it has nothing to do with philosophy.
Then please describe the experiment that you are thinking of. If you can describe the experiment sufficiently then we should be able to figure out the predicted outcome or possibly the actual experimental outcome.

Windows said:
I mean we observe things through photons and because relative to us something is traveling then what we see will be different because of the transforms; So what if we could see reality, the object as it is, in other words we use the transforms to somewhat find the real value will it be correct?
I hope you understood what I mean, it has nothing to do with philosophy.

I don't disagree with the previous answers but I think it might help to state the following: you are at this very moment traveling at .9999c from some frame of reference. From that frame of reference, you are severely time dilated and length contracted. This is a real and measurable fact from that frame of reference. Do you feel any different?

From some other frame of reference, you are now traveling at .9c and are only mildly time dilated and length contracted from that frame of reference.

Are the observations from your frame of reference any more valid than those from the other two frames of reference? No.

You cannot really talk about "real" unless you specify the frame of reference from which you are defining "real".

Windows said:
So what if we could see reality, the object as it is

We do see reality, and reality looks different depending on your point of view, and yet, all the different points of view are consistent with each other. - That's relativity.

Windows said:
I mean we observe things through photons and because relative to us something is traveling then what we see will be different because of the transforms; So what if we could see reality, the object as it is, in other words we use the transforms to somewhat find the real value will it be correct?
I hope you understood what I mean, it has nothing to do with philosophy.

Perhaps you are referring to the fact that light takes a finite amount of time to reach us from any event, and our view may be distorted by this delay? If so, the answer is that length contraction, time dilation and so on are effects that remain even after you account for the finite travel time of the light that you are using to see things with.

Here's an example to make this clear: muons are particles that, when at rest, live for about 2 * 10^-6 seconds before they decay. Given that lifetime and the fact that nothing can go faster than c, it might seem like they shouldn't be able to travel more than about c * (2 * 10^-6 seconds) = 600 meters before they decay. But in fact muons that are traveling near the speed of light can travel much farther than 600 meters before they decay. The reason is that the "internal clock" of a fast muon is slowed down by time dilation, so they live much longer than 2 * 10^-6 seconds. Whatever you mean by "real," this seems to me to be a clear indication that time dilation is "real" and not just a deceptive appearance.

Are the transformations such as time dilation, length contraction and relativistic mass just observed ones or real
ones?

The time dilation (see the example above) and increase in effective mass (Kaufmann's experiments and later ones) have been observed, and thus considered as real. The effect of length contraction has not been observed, as far as I know. The theory, by the way, predicts that the moving bodies would appear to stationary observer as if they were rotated, not contracted (due to high speed). The length contraction is basic result of the theory of relativity, so in light of other successes of that theory, most physicists believe it exists, but as I said we do not have direct evidence so we do not know for sure if it is real.

Windows said:
Hello!
Are the transformations such as time dilation, length contraction and relativistic mass just observed ones or real ones?
Thank you.
Neither, if between inertial frames: they are not real in the sense that they are not "absolute", and they are not just observed in the sense that really something changed when an object changed speed.
Non-inertial motion breaks the symmetry in observations: a clock that is moved fast around will be found to have lost time relatively to a clock that is kept steady (ignoring gravitational effects etc). One just can't say that a fast moving clock is "really slow", as that would imply the observation of absolute speed in the sense of "really going fast through space".

[addendum] An important clue to understanding is relativity of simultaneity: depending on how you decide to synchronize your clocks, you "observe" that a relatively to you moving clock is ticking slow or fast. It all boils down to your free choice to pretend that you are "really in rest" or "really moving"; you cannot say that it's true. Consequently we cannot, as you put it, say that we see the object "as it really is". According to you, if you take yourself to be in rest, a relatively to you fast moving object is length contracted; but you may instead hold that object to be in rest and therefore not length contracted.

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Windows said:
Hello!
Are the transformations such as time dilation, length contraction and relativistic mass just observed ones or real ones?
Thank you.
This, to me, is a trick question because the coordinate effects as a result of transformation are not observable. What's real are all the observations and measurements that anyone makes and they don't change when a transformation is performed.

Your question is ambiguous, leading to unclear responses. I suggest a different wording which avoids the word “real”.

I can use light rays and a clock to measure the length of a remote object which is at rest in respect to me. However the same experimental protocol will deliver a different numerical outcome if the object is moving in respect to me, all things equal. Does that mean:
i) that the so-called “length of the object" varies due to its relative motion in respect to me? ... or does that mean that
ii) the measurement protocol I used delivers a “biased value” for the length of the object due to its relative motion in respect to me?

In the first case the length should not be considered as an attribute of the object, it is an attribute of my relationship to it (likewise the color) . In the second case, the length can be assigned as an attribute of the object, although its appearance may vary depending on experimental conditions (likewise the shape).

Hopefully physicists will clarify the SR view on this alternative.

Sugdub said:
Your question is ambiguous, leading to unclear responses. I suggest a different wording which avoids the word “real”.

I can use light rays and a clock to measure the length of a remote object which is at rest in respect to me. However the same experimental protocol will deliver a different numerical outcome if the object is moving in respect to me, all things equal. Does that mean:
i) that the so-called “length of the object" varies due to its relative motion in respect to me? ... or does that mean that
ii) the measurement protocol I used delivers a “biased value” for the length of the object due to its relative motion in respect to me?

In the first case the length should not be considered as an attribute of the object, it is an attribute of my relationship to it (likewise the color) . In the second case, the length can be assigned as an attribute of the object, although its appearance may vary depending on experimental conditions (likewise the shape).

Hopefully physicists will clarify the SR view on this alternative.

I'm afraid that I don't understand your phrasing better than that of the OP; nevertheless I guess that I and others already answered it (in different phrasings). Note that SR describes not motion relative to people but motion relative to inertial reference systems.

Rephrasing your questions I would say that:
i) the so-called “length of the object" varies as function of variation of its motion as measured with any inertial reference system; and that
ii) the measurement protocol that you use delivers a “biased value” for the length of the object as function of your free choice of clock synchronization.

Probably it would be useful if we give an example of the effect of clock synchronization (ii) on the measurement (i).

Sugdub said:
Your question is ambiguous, leading to unclear responses. I suggest a different wording which avoids the word “real”.

I can use light rays and a clock to measure the length of a remote object which is at rest in respect to me. However the same experimental protocol will deliver a different numerical outcome if the object is moving in respect to me, all things equal. Does that mean:
i) that the so-called “length of the object" varies due to its relative motion in respect to me? ... or does that mean that
ii) the measurement protocol I used delivers a “biased value” for the length of the object due to its relative motion in respect to me?

In the first case the length should not be considered as an attribute of the object, it is an attribute of my relationship to it (likewise the color) . In the second case, the length can be assigned as an attribute of the object, although its appearance may vary depending on experimental conditions (likewise the shape).

Hopefully physicists will clarify the SR view on this alternative.
The mainstream SR philosophical view is clearly the first. The reason that the second doesn't work is that "bias" implies that one frame is right and the others are wrong. This is opposed to the principle of relativity.

However, there is no experimental way to distinguish between the first and second, so it is a matter of philosophical preference. I tried to get the OP to recognize that by thinking about possible experiments.

harrylin said:
... Note that SR describes not motion relative to people but motion relative to inertial reference systems.

Rephrasing your questions I would say that:
i) the so-called “length of the object" varies as function of variation of its motion as measured with any inertial reference system; and that
ii) the measurement protocol that you use delivers a “biased value” for the length of the object as function of your free choice of clock synchronization.

Probably it would be useful if we give an example of the effect of clock synchronization (ii) on the measurement (i).

Thank you for your input. I do think the precise wording of question/answers is a key element for non-physicists like me grasping the about-ness of this non-intuitive theory. However I must say that in this particular case the expressions “ inertial reference system” and “free choice of clock synchronization” look inappropriate to me.
To be precise I wish to add that the value returned by the measurement protocol in the specific case where the target object is at rest in respect to the inertial-system-from-which-the-measurement-is-exercised can be assigned as an attribute of the object: physicists refer to the “proper length” of the object.
However, the value returned by the same measurement protocol (no change to the clock synchronization process) in the general case where the target object is in constant motion in respect to the inertial-system-from-which-the-measurement-is-exercised, being different from the proper-length, can be considered :
1) either as tracing a “length contraction”, which seems to refer to something happening to the target object itself, not to the way it “appears” from a given perspective...
2) or as an apparent-length of the target object, which means that in such experimental conditions the protocol delivers a biased value of the proper-length and therefore cannot be considered as a valid method for measuring it.

Eventually the initial question relates to the actual meaning SR assigns to an expression like “length contraction”: does it refer to something happening to the target object or to the way the (unaffected) object is “perceived” from a different “perspective”?
Hopefully the “OP” (as you say) will tell us whether this wording matches his/her concerns... but anyway I'm curious to learn about the answer.

DaleSpam said:
The mainstream SR philosophical view is clearly the first. The reason that the second doesn't work is that "bias" implies that one frame is right and the others are wrong. This is opposed to the principle of relativity. ...

In my understanding the principle or relativity of motion tells that it does not make sense to state that a physical object is at rest better than in constant motion (from an absolute perspective) or the other way round. This is not what is at stake here.
An experimental protocol may be appropriate to measure a physical quantity under certain experimental conditions and the same protocol may be inappropriate if these constraints are not met. Hence the “biased value”. As you can read from my previous input, I'm trying to understand whether “length contraction” refers to something which affects the target object itself or the way it is “perceived” through a non-invasive measurement process.

Sugdub said:
Eventually the initial question relates to the actual meaning SR assigns to an expression like “length contraction”: does it refer to something happening to the target object or to the way the (unaffected) object is “perceived” from a different “perspective”?
Yes.

Sugdub said:
In my understanding the principle or relativity of motion tells that it does not make sense to state that a physical object is at rest better than in constant motion (from an absolute perspective) or the other way round. This is not what is at stake here.
I think that is exactly what is at stake here. If A and B are two inertial observers moving relative to each other and each performs the same experimental measurement but you say that A's is biased and B's is not then you are certainly violating the principle of relativity.

does it refer to something happening to the target object or to the way the (unaffected) object is “perceived” from a different “perspective”?
No, in the theory of relativity the length contraction has nothing to do with perception. The inter-molecule distances and the electromagnetic field pattern around them actually contract. If that was no so, the molecules would not be in equilibrium positions and the material would be in a state of tension, which would manifest as length extension in the the co-moving frame and could lead to breaking of the body into pieces.

An object moving fast with respect to the Earth actually contracts in the frame of the Earth, so for example, fast moving limousine of rest length 10m could fit into garage 5 m long and in principle you could close the door. The other thing is, what happens next... such car would have very high energy.

Jano L. said:
An object moving fast with respect to the Earth actually contracts in the frame of the Earth, so for example, fast moving limousine of rest length 10m could fit into garage 5 m long and in principle you could close the door.
If that's true, then don't you think that you should also point out that in the frame of the limousine, it's the garage that actually contracts? And if you agree, then how does this help resolve the OP's question?

Sugdub said:
[...] in this particular case the expressions “ inertial reference system” and “free choice of clock synchronization” look inappropriate to me.
They are essential for a good understanding. When I have time I'll give a numerical example that may clarify it better than 100 words (I think that I gave one in the past, if I can find it back that will save time).

[..] 1) [..] something happening to the target object itself, not to the way it “appears” from a given perspective...
Yes, that's what I said. Whatever changes state is affected; what does not change state cannot be affected by the non-change. And the example to-be-given will clarify how the measured value depends on your free of choice of clock synchronization.
2) or as an apparent-length of the target object, which means that in such experimental conditions the protocol delivers a biased value of the proper-length and therefore cannot be considered as a valid method for measuring it. [..]
Once more, see above! Length is "relative" and proper length is "absolute".

DaleSpam said:
I think that is exactly what is at stake here. If A and B are two inertial observers moving relative to each other and each performs the same experimental measurement but you say that A's is biased and B's is not then you are certainly violating the principle of relativity.

Your statement would be correct if it were true that the relative motion between observers can cause a divergence of measurement results, but this cannot be. If A and B obtain different outcomes when running analogue measurement protocols (i.e. the phenomena they observe are different), it must be due to an objective difference in their respective experimental conditions (otherwise we would be debating on non-determinist patterns, which is not the case here). One cannot attribute this difference in results to observers being “moving relative to each other” since this would indeed breech the principle of relativity of motion. The relative motion between observers cannot, of its own, cause a difference in observed phenomena since it would mean that one of both observers goes objectively faster than the other one, and this is precisely what the above principle forbids: in spite of their relative motion in respect to each other, none of them can be said “moving faster” than the other one, none of them can be said “in absolute rest”.
In the debate at stake, the rationale for the difference in the outcome of the observations is that one observer is at rest in respect to the target object whereas the other one is in motion in respect to the same object. Their relative speed in respect to the target object is different, and that is an objective difference in their respective experimental conditions. It is the cause for the divergence of their experimental results. And there is no breech to the principle of relativity.
Indeed the relative motion between observers is a possible consequence of that fact, but there is no equivalence: it could be that both observers move away from the target object with the same relative speed but in opposite directions. This counter-example shows that in spite of being in relative motion between each other, both observers could have the same speed in respect to the target object, in which case it is impossible that they obtain different results: this would breech the principle of isotropy of the propagation of light in space (may I recall that the scenario at stake assumes that observers measure the propagation time of light rays and then convert it into distances using the factor c).
One must trace the difference in experimental results to a proper cause, to an objective difference in experimental conditions, to something which holds for an observer but not for the other one, to an asymmetry between their respective experimental conditions. The “motion between observers” is a symmetrical and reciprocal clause which cannot make it.
Very appropriately the generic title given to this forum reads: “Special & General Relativity - Dependence of various physical phenomena on relative motion of the observer and the observed objects. Exp. & theo. theories of relativity”.

harrylin said:
... Length is "relative" and proper length is "absolute".

So the “length” is “relative” to what? To the measurement process? This is precisely what we would normally call the “apparent length”, a biased value of the “proper length”. What is the “apparent diameter” of the moon if not an effect of the observation conditions, a biased value of its “proper diameter”? Certainly the moon itself is not affected.
You seem to indicate that the observed object “changes state” (changes length?) as a consequence of being observed … how long is this change effective? Is the “length contraction” of the object caused / provoked / induced by the incoming light ray from the measurement device? How is the information transmitted which triggers the magnitude of the contraction? ... I'm afraid your statement will induce more questions than answers.
Obviously you make a difference between relativistic and non-relativistic patterns. We are looking for a proper wording to make the nature of this difference understandable by non-experts. You don't need to invent anything, just tell us what the SR theory says.

Sugdub said:
In the debate at stake, the rationale for the difference in the outcome of the observations is that one observer is at rest in respect to the target object whereas the other one is in motion in respect to the same object.
Ah, OK, I had misunderstood what you were saying previously. However, your concern is not relevant here. Length is a defined quantity, specifically length is defined as the distance between the front and back of an object at one instant in time. The velocity of the object is not relevant to the definition of length.

You are thinking about the distinction between proper length and length. Proper length is defined as the length of an object in its rest frame, so the speed of an object is relevant for the definition of proper length. It is a different concept than length.

An object's length in some frame may differ from its proper length, but that does not imply bias: they are both unbiased measurements of different quantities. Similarly, the object's length may differ in different frames, but that also does not imply any bias because of the prinicple of relativity.

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Sugdub said:
So the “length” is “relative” to what? To the measurement process? [..]
You seem to indicate that the observed object “changes state” (changes length?) as a consequence of being observed …[..].
No and no. As I said before, I believe that sound bites are insufficient to explain these things; physics requires calculation examples to clarify the meaning of sentences. So here's my (totally unrealistic) numerical example:

1. A space shuttle with a 10m long ruler (let's call it the "Moving Ruler") and two linear CCD arrays with clocks at its ends is accelerated to 0.1c relative to the launch site. The detectors function thus as combined position and time detector arrays. After one turn around the Earth it passes at that speed very close to CCD detectors that are situated on a 10m long ruler on the launch site; let's call that the Stationary Ruler.
0.1c -> γ ≈ 1.005
The length of such an object is defined as the distance between two extremities as determined at the same time.
Let's suppose that you are standing there doing the measurements. You had synchronized your clocks to the launch frame shortly before the shuttle took off and that synchronization is still valid (let's assume negligible rotation of the Earth during the mesurements). According to your measurements, the length of the Moving Ruler was 9.95m at fly-by.

Now, suppose that the astronauts synchronized their clocks only before departure; then their clocks should be nearly* synchronous with each other according to the launch pad frame. Consequently they will measure that the stationary ruler is 10.05m long. Now they scratch their heads and wonder if they should announce that they disproved relativity theory (remember CERN). But then one of them suddenly realizes that they had forgotten to synchronize their on-board clocks to the moving frame. They quickly do so, and at the next fly-by they measure that - as expected - the Stationary Ruler "has" a length of 9.95m.
Of course, they always measure the length of their own 10m long ruler to be 10m long, as measured with a co-moving ruler of 1m. And also you agree with them that the proper length of the Moving Ruler is and was 10m.

[addendum:] Note also that according to the inertial frame in which the flying shuttle is in rest, the "Moving Ruler" expanded from 9.95m to 10.00m.

I hope that with the understanding that follows from the above example, my earlier comments will be clear upon a second reading.

*only nearly, due to slightly different v(t) profiles

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harrylin said:
I believe that sound bites are insufficient to explain these things; physics requires calculation
+1 on that!

I thank you for your attempt to clarify the meaning of the expression “length contraction”. I must tell it did not convince me. I think physics requires clear concepts more than complex calculous which can easily hide many kinds of traps.
harrylin said:
According to your measurements, the length of the Moving Ruler was 9.95m at fly-by...Consequently they will measure that the stationary ruler is 10.05m long. ... the Stationary Ruler "has" a length of 9.95m. ...the "Moving Ruler" expanded from 9.95m to 10.00m.
First I wish to point out that the expressions above just miss the issue at stake. An objective statement would be of the kind “The outcome of the measurement process toward the “Moving Ruler” expanded from 9.95m to 10.00m”. And precisely the issue at stake is to clarify whether that means that the Ruler has expanded or not.
harrylin said:
You had synchronized your clocks to the launch frame ... ... they had forgotten to synchronize their on-board clocks to the moving frame.
Also I don't understand the meaning of these expressions. I can't assess whether they are any meaningful, but I'll just note that they seem to be made necessary because the physical systems from which the measurements are performed are in relative motion to each other. Had you presented the same experiments by comparing measurements toward a target object which is either at rest, or in motion, in respect to the physical system from which both measurements are performed, as I did in the example you criticized, then there would be no need, as I told you, for this “synchronization”, whatever it means. By introducing two observers in relative motion to each other instead of objects in relative motion or at rest in respect to an observer, you have introduced a degree of complexity which could have been avoided, in addition to creating the conditions for a major logical error whereby the relative motion between the observers could be the cause of the divergence of their measurements (see above my recent input). Differences in measurement outputs can only be caused by an objective difference in the experimental conditions, and the relative motion between observers does not match this requirement. This parameter can only add confusion since it masks the actual cause of the difference in measurements, i.e. the change of the relative speed between the observer and the target object.

Sugdub said:
I thank you for your attempt to clarify the meaning of the expression “length contraction”. I must tell it did not convince me. I think physics requires clear concepts more than complex calculous which can easily hide many kinds of traps.
I agree, that's why I gave not a complex but a simple, basic example to explain why the choice of options was a false choice.

Note: please examine the insertion of [/quote] for correct rendering of quotes.

First I wish to point out that the expressions above just miss the issue at stake. An objective statement would be of the kind “The outcome of the measurement process toward the “Moving Ruler” expanded from 9.95m to 10.00m”. And precisely the issue at stake is to clarify whether that means that the Ruler has expanded or not.
Sorry, I cannot parse your first sentence. However, I already clarified that the Moving Ruler appeared to expand or shrink depending on how you had synchronized your clocks. Nevertheless, all inertial reference system agree that it changed shape.
Also I don't understand the meaning of these expressions. I can't assess whether they are any meaningful,
I'm sorry to hear that; the way clocks are used for the measurement of moving lengths and the way clocks are synchronized, are essential for the measurement outcomes that you are discussing.
Einstein emphasized that also in the introduction of his 1905 paper, as follows:
"the assertions of any such theory have to do with the relationships between rigid bodies (systems of co-ordinates), clocks, and electromagnetic processes. Insufficient consideration of this circumstance lies at the root of the difficulties which the electrodynamics of moving bodies at present encounters." - http://www.fourmilab.ch/etexts/einstein/specrel/www/
I'll just note that they seem to be made necessary because the physical systems from which the measurements are performed are in relative motion to each other. Had you presented the same experiments by comparing measurements toward a target object which is either at rest, or in motion, in respect to the physical system from which both measurements are performed, as I did in the example you criticized, then there would be no need, as I told you, for this “synchronization”, whatever it means.
It is true that in a single system things may appear simpler. However in such a system one cannot test the requirements of the relativity principle, which relates to the impossibility to detect the system's inertial motion. Moreover my elaborations included three of such systems; the conclusions for a single system follow from it.
Interestingly, the famous E=mc2 (which is for a single system) was also derived from such considerations about systems in relative motion.
By introducing two observers in relative motion to each other instead of objects in relative motion or at rest in respect to an observer, you have introduced a degree of complexity which could have been avoided,
I doubt that: the OP's questions were not merely concerned with such a system - the transformation equations concern two systems in relative motion. My example was intended to answer all the questions that were raised in this thread. But if a full answer is too complex, we can split it up in parts: one piece of calculation referring to one piece of question. :tongue2:
in addition to creating the conditions for a major logical error whereby the relative motion between the observers could be the cause of the divergence of their measurements (see above my recent input). [..]
I can understand that phrase of yours in two ways, one which is correct and one which is erroneous. And my example answers it:
Differences in measurement outputs can only be caused by an objective difference in the experimental conditions, and the relative motion between observers does not match this requirement. This parameter can only add confusion since it masks the actual cause of the difference in measurements, i.e. the change of the relative speed between the observer and the target object.
I highlighted the cause of difference in measurements. The measurements of standard systems S and S' in relative inertial motion disagree with each other, as I set forth, without any acceleration during the measurement, and without any "target object". At least, that is what SR predicts - and explaining how to use SR (as well as GR) is what this forum is meant for.

 in order to end wasting time with words, I'll not anymore reply in this thread to discussions about words instead of measurement methods and predicted measurement outcomes.

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Sugdub said:
I think physics requires clear concepts more than complex calculous which can easily hide many kinds of traps.
Reality is complex and full of many kinds of hidden traps. An accurate model of reality is therefore likely to require complex calculations which can hide many kinds of traps. Physics requires experimentally accurate calculations much more than clear concepts.

I think that it is a clear mistake to expect that the universe in all of its complexity should be modeled easily.

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harrylin said:
...The measurements of standard systems S and S' in relative inertial motion disagree with each other, as I set forth, without any acceleration during the measurement, and without any "target object". At least, that is what SR predicts ...
I'm sorry but this statement is logically flawed. If one could demonstrate that the value obtained by S is larger than the value obtained by S', all things equal apart from their relative motion in respect to each other, then one could equally demonstrate that S' will obtain a larger value than S: the relative motion is symmetrical. It cannot sort out which one, from S and S', must obtain the largest value. It cannot be the cause of the divergence of their measurement outcomes. I gave above in this thread a counter-example showing that your statement cannot be true. If S and S' obtain different experimental results, it must be due to an objective difference in their respective experimental conditions and the principle of relativity of motion forbids that their relative motion in respect to each other be considered as such. If your statement actually reflects what SR predicts, I feel more than uncomfortable with it.

May be you could consider presenting things in a different way: whereas the outcome of a single run of the aforementioned experimental protocol can be interpreted as delivering the “measured length” of a unique object (e.g. the diameter of a sphere) at rest in respect to the inertial-system-from-which-the-measurement-is-performed, the same numerical outcome could equally be interpreted as the “measured length” for a range of objects of a different shape (e.g. a continuous range of ellipsoids derived from the same sphere), each of them being assigned an appropriate constant relative speed in respect to the inertial-system-from-which-the-measurement-is-performed. Each combination (ellipsoid – relative speed) would lead to the same “measured length” as compared to the sphere in relative rest (i.e. phenomena are NOT affected).
When one explores the world using light rays and clocks according to an ad-hoc experimental protocol, the unique set of phenomena resulting from this exercise is compatible with a continuous range of “images” of the world, the Lorentz transformation enabling to swap between physically equivalent representations. For objects which length is already known, it enables computing their relative speed and the other way round for those objects which relative speed is already known. Otherwise a range of indeterminacy will remain open.
I think this is the only way one can explain the conductor-and-magnet experiment in Einstein's original paper "on the electronics of moving bodies": one single experiment, one single value for the observed current (i.e. no change in phenomena) but a range of descriptions of the EM field compatible with the measured current, all being equivalent as per the Lorentz transformation as established by SR. Had the Lorentz transformation of SR predicted a change in phenomena, it would have been inconsistent to invoke it for resolving the conductor-and-magnet issue.

Eventually, only the phenomena we observe in given experimental conditions can be said “real”. Anything else is a conventional interpretation about the kind of world they might reflect. Stating that the same set of phenomena is compatible with a range of physically equivalent “images” of the world is substantially different than claiming that the relative speed between observers can affect the phenomena each one observes, which contradicts the principle of relativity of motion. That suggestion being made, it remains up to physicists to propose a logically consistent presentation of SR.

All reference frames will predict the same value for any experimental measurement. However, a given measurement can only be "length" in one frame. Different frames will thus disagree about the length. They will agree on the outcome of a measurement, but they will disagree on whether or not that measurement is a length.

See above for the definition of length. Again, note that the velocity of the object whose length is being measured is not part of the definition, however, note also that the definition requires that the distance between the front and back be measured "at the same time". That is the part that different frames disagree on and the part which will cause a measurement of length in one frame to not be a measurement of length in another frame.

Sugdub said:
[..] If S and S' obtain different experimental results, it must be due to an objective difference in their respective experimental conditions and the principle of relativity of motion forbids that their relative motion in respect to each other be considered as such. If your statement actually reflects what SR predicts, I feel more than uncomfortable with it.
As suggested, I will now split up some of the aspects of my illustration, adding a little more precision with [].

I first recalled that The length of such an object is defined as the distance between two extremities as determined at the same time.
Next I emphasized with a numerical example how they will approximately agree on the relative lengths of their rulers if the clock synchronization in the frame that changed velocity is not adapted to the new velocity. And then I explained the objective difference in standard experimental conditions as follows:

one of them suddenly realizes that they had forgotten to synchronize their on-board clocks to the moving frame. They quickly do so [that is, they changed their clock synchronization], and at the next fly-by they measure that - as expected - the Stationary Ruler "has" a length of 9.95m.

May be you could consider presenting things in a different way: whereas the outcome of a single run of the aforementioned experimental protocol can be interpreted as delivering the “measured length” of a unique object (e.g. the diameter of a sphere) at rest in respect to the inertial-system-from-which-the-measurement-is-performed, the same numerical outcome could equally be interpreted as the “measured length” for a range of objects of a different shape (e.g. a continuous range of ellipsoids derived from the same sphere), each of them being assigned an appropriate constant relative speed in respect to the inertial-system-from-which-the-measurement-is-performed. Each combination (ellipsoid – relative speed) would lead to the same “measured length” as compared to the sphere in relative rest (i.e. phenomena are NOT affected). [..]
If I understand what you say, then I presented your "same measured length" as follows:

Of course, they always measure the length of their own 10m long ruler to be 10m long, as measured with a co-moving ruler of 1m. And also you agree with them that the proper length of the Moving Ruler is and was 10m.

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DaleSpam said:
All reference frames will predict the same value for any experimental measurement. However, a given measurement can only be "length" in one frame. Different frames will thus disagree about the length. They will agree on the outcome of a measurement, but they will disagree on whether or not that measurement is a length.

See above for the definition of length. Again, note that the velocity of the object whose length is being measured is not part of the definition, however, note also that the definition requires that the distance between the front and back be measured "at the same time". That is the part that different frames disagree on and the part which will cause a measurement of length in one frame to not be a measurement of length in another frame.

Thanks for your attempt in producing a clear statement. In spite of some progress I think we are still circling round in non-conclusive statements in the absence of a thorough control of the phrasing. Just let me explain: most physicists (if not all) use the word “frame” in two different contexts with two radically different meanings. That might not be an issue internally (although …) but that makes their explanations hardly understandable to outsiders.

In your second paragraph you are dealing with the measurement process, using the word “frame” as a designation for the “inertial-system-from-which-the-measurement-is-performed”. In this context, a change of “frame” would relate to a change in the actual experimental conditions, which would trigger a change of the numerical value delivered by the measurement process. May be I should point out again that in this context, changing “frame” deals with a concrete change of the relative speed between the target object and the “inertial-system-from-which-the-measurement-is-performed” and therefore it should not be confused with a “change of galilean (or inertial) reference frame” through which, by definition, the relative speed between any pair of physical objects is left unaffected (see below). Unfortunately most physicists (if not all) make this confusion.

Conversely the first sentence in your first paragraph “All reference frames will predict the same value for any experimental measurement” can only be discussed in the context where a theoretician analyses the experiments (as referred to above) and their outcome, e.g. in order to establish a comparison and a theoretical justification for the change in (past or future) observed phenomena. Indeed the theoretician who performs his/her analysis two years after the actual experimentation took place is not going to change anything to the conditions of the past experiments. Indeed the theoretician is free to adopt any inertial physical system as a hook for the “reference frame” in which all experiments to be compared will get described (otherwise no comparison would be possible). When one deals with the various (and physically equivalent) perspectives offered to the theoretician, changing the “reference frame” is not going to affect in any way his/her theoretical conclusions/predictions since physics laws will lead to conclusions which are structurally transparent to any choice for the coordinate system (space and time coordinates) and any choice for the inertial reference frame (rest/motion).

It is correct to state that the measurement protocol we are dealing with, based on measuring the propagation time of light rays and converting this value into a distance in space (using c), if applied to both ends of the target object, will deliver a numerical outcome which can be considered as a measurement of the “length of the objet” (a spatial “length” always relates to something) IFF the said object was in relative rest in respect to the aforementioned “inertial-system-from-which-the-measurement-is-performed”. If this condition is met (it depends on the actual experimental conditions at the time the measurement was performed but in no way on the inertial reference frame chosen by the theoretician for describing the experiment), then the requirement on synchronous measurements for both ends can be waived since there is no dependency on time. If not, then the requirement on synchronism cannot be waived and there is no objective way to define the meaning of “simultaneous” measurements because the measurement process we are dealing with is not instantaneous (in particular it does not take the same time for both experiments we are considering, all things equal). Then the outcome of the experiment cannot be considered as a measurement of the “length of the object”. I'm quite satisfied that we seem to agree upon this at last. However, should the Lorentz transformation deal with observed phenomena (i.e. to the outcome of experimental measurements), the only possible logical consequence would be that the “contracted length” is not “real” and that the “length contraction” is a misleading expression.

So the about-ness of SR is still to be clarified and in this respect I invite you to comment on my recent response to Nugatory, in the light of my comment on the "conductor and magnet" issue: does the Lorentz transformation apply to observed phenomena, or does it apply to theoretical descriptions of the (necessarily non-observable) “imagined world” compatible with the observed phenomena? In the latter case only, an object of a given length in relative rest in a given “image of the world” could equally be replaced with another object of a different length, “contracted” as compared to the previous value, but in relative motion, as part of another “image of the world”. The Lorentz transformation would then apply to the description of the "imagined world", transforming one image into another one, exclusive but physically equivalent in respect to its compatibility with phenomena. The “length contraction” would then become meaningful in a very acute way.

Sugdub said:
Thanks for your attempt in producing a clear statement. In spite of some progress I think we are still circling round in non-conclusive statements in the absence of a thorough control of the phrasing.
That is one reason why math is so important in physics.

Sugdub said:
Just let me explain: most physicists (if not all) use the word “frame” in two different contexts with two radically different meanings. ...

In your second paragraph you are dealing with the measurement process, using the word “frame” as a designation for the “inertial-system-from-which-the-measurement-is-performed”. ...

Conversely the first sentence in your first paragraph “All reference frames will predict the same value for any experimental measurement” can only be discussed in the context where a theoretician analyses the experiments (as referred to above) and their outcome
I do use the word "frame" with two subtly different meanings in general, but not here. In general I either use the word "frame" to refer to a coordinate system or to a frame field (aka tetrad, aka vierbein).

In this post, however, I was consistently referring to a coordinate system. I had only a single usage of the term. All coordinate systems will agree on the outcome of any measurement, however not all coordinate systems will agree that a given measurement is a measurement of length.

Sugdub said:
Then the outcome of the experiment cannot be considered as a measurement of the “length of the object”. I'm quite satisfied that we seem to agree upon this at last.
Your satisfaction is strange since I have given you no reason to think that I would agree. The definition of "length" is quite clear, as I identified above. The length of the object is well-defined regardless of the velocity of the object and different coordinate systems disagree on the value.

Sugdub said:
So the about-ness of SR is still to be clarified
"About-ness"? If you cannot handle math, then at least stick to standard terms, preferably ones with accepted scientific meanings. I have never seen the word "about-ness" before, and I have no idea why we should care if SR has clear "about-ness" or not.

Sugdub said:
It is correct to state that the measurement protocol we are dealing with, based on measuring the propagation time of light rays and converting this value into a distance in space (using c), if applied to both ends of the target object, will deliver a numerical outcome which can be considered as a measurement of the “length of the objet” (a spatial “length” always relates to something) IFF the said object was in relative rest in respect to the aforementioned “inertial-system-from-which-the-measurement-is-performed”. If this condition is met (it depends on the actual experimental conditions at the time the measurement was performed but in no way on the inertial reference frame chosen by the theoretician for describing the experiment), then the requirement on synchronous measurements for both ends can be waived since there is no dependency on time. If not, then the requirement on synchronism cannot be waived and there is no objective way to define the meaning of “simultaneous” measurements because the measurement process we are dealing with is not instantaneous (in particular it does not take the same time for both experiments we are considering, all things equal). Then the outcome of the experiment cannot be considered as a measurement of the “length of the object”. I'm quite satisfied that we seem to agree upon this at last. However, should the Lorentz transformation deal with observed phenomena (i.e. to the outcome of experimental measurements), the only possible logical consequence would be that the “contracted length” is not “real” and that the “length contraction” is a misleading expression.

Why can't such an experiment be considered to be a measurement of the length of an object? It's essentially a DEFINITION of the length of a moving object:

If
• Event $e_1$ takes place at one end of a moving object.
• Event $e_2$ takes place at the other end of a moving object.
• Events $e_1$ and $e_2$ are simultaneous in some frame $F$
then the length of the object in frame $F$ is defined to be the distance between $e_1$ and $e_2$ in frame $F$.

So "length" is explicitly dependent on the notions of "simultaneous in frame F" and "distance between points in frame F". (Frame here can be taken to mean "coordinate system", although people don't usually consider rectangular coordinates to be a different "frame" than spherical coordinates).

With this definition of "length of a moving object", then SR implies that:

If light signals are used to synchronize clocks within a frame, and also to measure distances within a frame, then the length of a moving object will be length-contracted compared to its length when at rest in that frame.

There is actually another assumption at work here, which is that "length of an object" has to be well-defined. The object has to have some "equilibrium length" that it will be restored after you perturb the object by pushing or pulling it.