Relative Velocity Experiment - A Matter of Discussion

[alionalizoti]

A simple experiment can be build to demonstrate a possible contradiction between thinking theory and reality.

Use two hand electrical light torches set upon a table and back to back. Switch them on simultaneously, and calculate the relative velocity of their opposite leaving flashes.


←c← O= =O →c→
←2c→

Solution
In this case, the relative velocity between two leaving flashes is twice the speed of light.
A matter of discussion
Well, now put yourself in a teacher position and try to explain to your students, how this could be possible?
I leave this answer to you!

 

[Dale]

Well, now put yourself in a teacher position and try to explain to your students, how this could be possible?

These should be a part of any introductory relativity course:
http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/einvel.html
https://www.physicsforums.com/showthread.php?t=511170

 

[Doc Al]

Solution
In this case, the relative velocity between two leaving flashes is twice the speed of light.

No, the separation rate of the two flashes (according to you) is 2c. But that's not the velocity of anything.

Further: There's no problem at all with having two things separate at a rate greater than c (as observed by a third frame), but their relative velocity will always be less than c.

 

[phinds]

A simple experiment can be build to demonstrate a possible contradiction between thinking theory and reality.

Use two hand electrical light torches set upon a table and back to back. Switch them on simultaneously, and calculate the relative velocity of their opposite leaving flashes.


←c← O= =O →c→
←2c→

Solution
In this case, the relative velocity between two leaving flashes is twice the speed of light.
A matter of discussion
Well, now put yourself in a teacher position and try to explain to your students, how this could be possible?
I leave this answer to you!

As DaleSpam and Doc Al have stated, you misunderstand the technical meaning of "relative velocities". Google "relativistic velocity addition"

 

[ghwellsjr]

Furthermore, we cannot use light as the thing that we measure or define the velocity of anything else relative to. We can use any speed short of c but not c. It would be a lot easier to explain and understand if you start with two objects traveling in opposite directions at a speed of something less than c but for which their simple addition is c or more such as 50% c which results in a velocity of one object relative to the other of 80% c. Or if you want something closer to c you could have the two objects move at 75% c in opposite directions with a resultant relative speed of 96% c between them. If you follow the progression, you can see that no matter how close to c the two objects are moving in opposite directions, their relative velocity never reaches c.

 

[ghwellsjr]

Here are some spacetime diagrams to illustrate the first example that I gave. In all the diagrams, the thick blue lines represents the table or other object from which the other two objects in black and red start off moving at 50% c in opposite directions:

First, we see how the blue object measures the speed of the red object. To do this he needs to know the distance away that the red object is at some particular time which is marked off in seconds by the blue dots. I'm showing one example where he sends a radar signal at his time of 4 seconds (count the blue dots from the bottom up starting with zero) which hits the red object and reflects back to him at his time of 12 seconds. The difference between these two times is 8 seconds and since the radar signal made a round trip, he divides that by two to get 4 light-seconds as the distance. Now the question is what time does he assume that measurement applies to? The answer according to Special Relativity is that it is the average or midpoint of the two times which is 8 seconds. Since the red object started out at his time of 0 seconds at a distance of 0 light-seconds, he establishes that the object has moved 4 light-seconds in 8 seconds for a speed of 50% c.

The blue object can do the same thing for the black object to establish its speed at 50% c in the opposite direction.

Now let's see how the black object would measure the speed of the red object relative to himself. He does exactly the same thing that the blue object did as shown in this diagram:

He sends a radar signal at his time of 1 second which reflects back to him at his time of 9 seconds (count the black dots from the bottom up). Since the difference is 8 seconds, he concludes that the red object was 4 light-seconds away and he establishes the time to be the average of 1 and 9 which is 5 seconds and since the red object was coincident with him at his time zero, he establishes that the red object has moved 4 light-seconds in 5 seconds for a speed of 80% c.

If we want, although it is not necessary, we can transform this diagram to the rest frame of the black object which more directly shows the established speed:

The red object can also measure the speed of the black object relative to himself and will establish the same speed of 80% c in the opposite direction.

We could do the same thing with my second example but that will result in either a very large diagram or one where everything is scrunched together so I'll leave that exercise up to you.

 

[DiracPool]

A simple experiment can be build to demonstrate a possible contradiction between thinking theory and reality.

Use two hand electrical light torches set upon a table and back to back. Switch them on simultaneously, and calculate the relative velocity of their opposite leaving flashes.


←c← O= =O →c→
←2c→

Solution
In this case, the relative velocity between two leaving flashes is twice the speed of light.
A matter of discussion
Well, now put yourself in a teacher position and try to explain to your students, how this could be possible?
I leave this answer to you!

I actually started a thread on this exact same topic not too long ago. You can review it for some supplementary discussion..

https://www.physicsforums.com/showthread.php?t=765845

 

[Sugdub]

No, the separation rate of the two flashes (according to you) is 2c. But that's not the velocity of anything.

Further: There's no problem at all with having two things separate at a rate greater than c (as observed by a third frame), but their relative velocity will always be less than c.

I've no doubt you are right, but this is typically an example where the wording used by physicists triggers misunderstandings. Why is it so difficult to explain that there are two formulas which both hold in SR for combining / composing speeds?

One formula deals with the transformation of the speed of a single object as represented in a reference frame R into the speed of the same object if represented in another frame R' (ONE OBJECT / TWO FRAMES). It is precisely analogous to the Lorentz transformation which transforms the coordinates (space and time) of the object as represented in R into its coordinates in R'. Hence it should be called a “speed transformation formula” in order to highlight this analogy.

The second formula combines the speeds of two different objects if both are represented in the same reference frame R (TWO OBJECTS, ONE FRAME): a simple addition as is the case in Newtonian physics (the “relative speed between both objects in R”), it being noted that since each of the incoming speeds is necessarily lower than c, the result of their addition is necessarily lower than 2c.

A meaningful exercise would be to discuss how the “relative speed between both objects in R” evolves for various choices of R.
Thanks.

 

[ghwellsjr]

I've no doubt you are right, but this is typically an example where the wording used by physicists triggers misunderstandings. Why is it so difficult to explain that there are two formulas which both hold in SR for combining / composing speeds?

One formula deals with the transformation of the speed of a single object as represented in a reference frame R into the speed of the same object if represented in another frame R' (ONE OBJECT / TWO FRAMES). It is precisely analogous to the Lorentz transformation which transforms the coordinates (space and time) of the object as represented in R into its coordinates in R'. Hence it should be called a ?speed transformation formula? in order to highlight this analogy.

The second formula combines the speeds of two different objects if both are represented in the same reference frame R (TWO OBJECTS, ONE FRAME): a simple addition as is the case in Newtonian physics (the ?relative speed between both objects in R?), it being noted that since each of the incoming speeds is necessarily lower than c, the result of their addition is necessarily lower than 2c.

A meaningful exercise would be to discuss how the ?relative speed between both objects in R? evolves for various choices of R.
Thanks.

I think this exercise seems meaningful to you because you are limiting the transformations to be in line with the motion between the objects, aren't you? What if you considered transformations at other angles? Would you still see meaning in the exercise?

 

[Dale]

I do agree that the terminology is confusing. The terminology developed historically, and could certainly be improved with the benefit of hindsight. However, that never seems to work. We are still trying (unsuccessfully) to get rid of relativistic mass. In the end, students need to learn the bad terminology.

 

[Sugdub]

I think this exercise seems meaningful to you because you are limiting the transformations to be in line with the motion between the objects, aren't you? What if you considered transformations at other angles? Would you still see meaning in the exercise?

I feel it is important to show that various quantities which were considered as “physical quantities” in the Newtonian paradigm (I mean quantities characterising intrinsic properties of physical objects or of the relations between those) must at best be considered as features of the representation scheme in the SR paradigm (length, mass, speed, period,...). Their statute is pretty much the same as the statute of coordinates: they provide different but equivalent descriptions of the (simulated) world depending on the selected representation scheme (coordinate system for position and orientation, frame of reference for velocities,...). Features such as “time dilation” and “length contraction” stem from / relate to ... the degree of freedom for choosing a frame of reference for velocities, they do not relate to any intrinsic physical process taking place in the (simulated) world. In this respect, I highly praise the way you separate, in your diagrams and explanations, the layer of “observations” or “measurements” on top of the pure representation layer. I believe all this is easier to explain if the transformations of the reference frame are chosen in line with the motion between the objects, nothing more.

…. and since we are looking at improper wordings which have disastrous consequences in terms of misunderstandings, I would mention as well that there are no such things as “relativistic effects”: there are phenomena which can be properly explained and predicted in the SR paradigm, whereas they can't be properly explained or predicted in the Newtonian paradigm. In the same way, there is no “relativistic Doppler effect”: the classical formula holds in all cases, provided the emitted and the received periods are expressed in the same representation scheme.
Thanks.

 

[phinds]

... there are no such things as “relativistic effects”: there are phenomena which can be properly explained and predicted in the SR paradigm ...

And how are such phenomenon NOT "relativistic effects"? I'm not following your reasoning here. You seem to be saying that they are relativistic effects but you don't like calling them relativistic effects.

 

[Sugdub]

And how are such phenomenon NOT "relativistic effects"? I'm not following your reasoning here. You seem to be saying that they are relativistic effects but you don't like calling them relativistic effects.

SR explains the non-decaying of muons until they reach the ground, whereas the Newtonian theory fails to provide a correct explanation. The discovery of the SR theory did not change anything to the behaviour of muons. Phenomena are not “relativistic” of their own and a theory has no physical effects: it does not effect the world. It has consequences insofar it can or cannot explain or predict specific phenomena. Because it derives the full consequences of the compulsory need for a physical speed limit for any physical object, SR enables a more consistent modelling of the world than the Newtonian paradigm, essentially by providing a space-and-time framework which structurally prevents any possibility of involving instantaneous actions at a distance. On that basis, the “time dilation” feature assigns a different value to the mean lifetime of a muon depending on the reference frame chosen for analysing its behaviour. Nothing changes in the world and nothing changes in the behaviour of muons due to your decision to select one or the other frame of reference for performing this analysis. But representing both the distance covered by the muon over its lifetime and the thickness of the atmosphere in one and the same reference frame has remarkable consequences in respect to the predictions that can be derived in the SR paradigm as opposed to the Newtonian paradigm. SR has no physical “effects”; its “consequences” relate to improving our ability to explain or predict phenomena.
Thanks

 

[Quantum Braket]

...

 

[Dale]

I think I will keep on using the term "relativistic effects".

 

[phinds]

OK, I see what you mean now, but your attempt at changing standard terminology to suit your liking is doing what in the military is called "pissing up a rope".

 

[ghwellsjr]

I think this exercise seems meaningful to you because you are limiting the transformations to be in line with the motion between the objects, aren't you? What if you considered transformations at other angles? Would you still see meaning in the exercise?

I feel it is important to show that various quantities which were considered as “physical quantities” in the Newtonian paradigm (I mean quantities characterising intrinsic properties of physical objects or of the relations between those) must at best be considered as features of the representation scheme in the SR paradigm (length, mass, speed, period,...). Their statute is pretty much the same as the statute of coordinates: they provide different but equivalent descriptions of the (simulated) world depending on the selected representation scheme (coordinate system for position and orientation, frame of reference for velocities,...). Features such as “time dilation” and “length contraction” stem from / relate to ... the degree of freedom for choosing a frame of reference for velocities, they do not relate to any intrinsic physical process taking place in the (simulated) world. In this respect, I highly praise the way you separate, in your diagrams and explanations, the layer of “observations” or “measurements” on top of the pure representation layer. I believe all this is easier to explain if the transformations of the reference frame are chosen in line with the motion between the objects, nothing more.

Thanks for the praise, and high praise at that!

I agree that in line scenarios are easier to explain, especially if we want to make spacetime diagrams but we don't want to jump to the conclusion that only in line transformations are preferred.

I'm also concerned that since Time Dilation and Length Contraction are purely coordinate effects, you seem to have come to the conclusion that changing times and lengths associated with objects as a result of their accelerations are not physical. Is that the case?

…. and since we are looking at improper wordings which have disastrous consequences in terms of misunderstandings, I would mention as well that there are no such things as “relativistic effects”: there are phenomena which can be properly explained and predicted in the SR paradigm, whereas they can't be properly explained or predicted in the Newtonian paradigm. In the same way, there is no “relativistic Doppler effect”: the classical formula holds in all cases, provided the emitted and the received periods are expressed in the same representation scheme.
Thanks.

Another concern: the classical Doppler formula does not hold in all cases. There is a "relativistic Doppler effect" which is different from the classical Doppler effect. The classical formula incorporates two speeds whereas the relativistic formula has only one and you can't get it by just setting one of the speeds in the classical formula to zero. And like all "observations" or "measurements", it doesn't matter which representation layer you use to depict a scenario involving Doppler, they all work equally well.

Please explain your position on Doppler.

 

[Sugdub]

...I'm also concerned that since Time Dilation and Length Contraction are purely coordinate effects, you seem to have come to the conclusion that changing times and lengths associated with objects as a result of their accelerations are not physical. Is that the case?...

Thanks for challenging my views.

I need to be careful with the wording and English is a foreign language for me... First I'll address my understanding of the background of your question. I understand that we both agree that Time Dilation and Length Contraction relate to our formal representation of the physical time and space, so according to SR they “effect” (I would better say “constrain”) delta-time and delta-space quantities in a variable way depending on the selected reference frame. An analogy with space “coordinates” can be found with the representation of a rectangular stick in a 2D coordinate system, for which the values of the delta-x and delta-y projections of the stick onto the x and y coordinate axes will depend on the relative orientation of the axes system in respect to the stick. The delta-x and delta-y values are attributes to the representation of the stick for a given choice of the coordinate system (its “image”, if you prefer), they are not directly attributes to the stick itself. They are not "physical" as per your wording. The only direct attributes to the stick are its “proper” length and width, independent of any representation scheme. There are however a few peculiar cases where the values of the attributes to the image of the stick match the values of the “proper” attributes to the stick, I mean when the axes are selected to be parallel to the rectangle lines. But please note that the matching of the values does not imply the identity of the concepts behind them: an attribute to the image in a given coordinate system shall not be confused with an attribute to the object itself.

My statement is that SR constrains the changing values of delta-time and delta-space associated with (or which are attributes to) the formal representation (the image), in any given representation scheme, of the physical objects. According to SR, the only viable representations of the physical world which are compatible with the existence of a speed limit must constrain the attributes to the representations (images) of the physical objects according to the Time Dilation and the Length contraction formulas. Valid predictions can only be derived in the framework of a valid representation scheme. SR does not tell anything else and this is enough to reach predictions which are verified by experiments.

Let's now come to your wording. You are “concerned” about my suspected “conclusion” whereby “changing times and lengths associated with objects as a result of their accelerations are not physical”. First I hope that the two paragraphs above have convinced you that my conclusion is not in line with your wording, for two reasons: i) “changing times and lengths” are not “associated with objects”, but are attributes to their representations, just like the delta-x and delta-y are attributes to the representation of the stick in the example above; ii) SR only deals with those indirect attributes and does not constrain the direct ("physical") attributes to objects, just like my choice for the orientation of the coordinate system does not "effect" the “proper” ("physical") dimensions of the stick. Second, I will in turn challenge your wording insofar I believe it can be interpreted as if you consider that SR constrains the physical attributes of objects. How is that possible unless you think (contrary to my expectations) that my choice of a representation scheme “effects” the physical world? I'm quite convinced that your wording goes beyond what you actually think. Is that the case?

 

[ghwellsjr]

Thanks for challenging my views.

I need to be careful with the wording and English is a foreign language for me...

Your English (spelling, grammar, etc.) betrays the fact that it is foreign to you. However, I believe you have made one common mistake that even people for whom English is their native tongue often make which is mixing "effect" and "affect". Most of the time, "effect" is a noun and "affect" is a verb. It would make more sense to me if your three uses of the word "effect" were replaced with "affect".

First I'll address my understanding of the background of your question. I understand that we both agree that Time Dilation and Length Contraction relate to our formal representation of the physical time and space, so according to SR they “effect” (I would better say “constrain”) delta-time and delta-space quantities in a variable way depending on the selected reference frame. An analogy with space “coordinates” can be found with the representation of a rectangular stick in a 2D coordinate system, for which the values of the delta-x and delta-y projections of the stick onto the x and y coordinate axes will depend on the relative orientation of the axes system in respect to the stick. The delta-x and delta-y values are attributes to the representation of the stick for a given choice of the coordinate system (its “image”, if you prefer), they are not directly attributes to the stick itself. They are not "physical" as per your wording. The only direct attributes to the stick are its “proper” length and width, independent of any representation scheme. There are however a few peculiar cases where the values of the attributes to the image of the stick match the values of the “proper” attributes to the stick, I mean when the axes are selected to be parallel to the rectangle lines. But please note that the matching of the values does not imply the identity of the concepts behind them: an attribute to the image in a given coordinate system shall not be confused with an attribute to the object itself.

My statement is that SR constrains the changing values of delta-time and delta-space associated with (or which are attributes to) the formal representation (the image), in any given representation scheme, of the physical objects. According to SR, the only viable representations of the physical world which are compatible with the existence of a speed limit must constrain the attributes to the representations (images) of the physical objects according to the Time Dilation and the Length contraction formulas. Valid predictions can only be derived in the framework of a valid representation scheme.

You have just restated the position which we agree on that Time Dilation and Length Contraction are coordinate effects. In other words, given the coordinates in one frame of a scenario, we can use the Lorentz Transformation process to establish the coordinates in another frame moving with respect to the original frame.

SR does not tell anything else and this is enough to reach predictions which are verified by experiments.

And this is your conclusion which we don't agree on. One of the most important aspects of Special Relativity is that the Lorentz Transformation process applies not just to coordinates but also to the formulas and equations of physics. They must remain unchanged after undergoing the Lorentz Transformation. For example, under Newtonian physics, the force equation is F=ma but this does not transform unchanged using the Lorentz Transformation. SR revolutionized all of physics by requiring all laws to be changed so that they remain intact through the Lorentz Transformation process. Maxwell's equations already fit the requirement.

As a result, all objects will undergo some sort of physical deformation during acceleration which can approximate the same effects that Time Dilation and Length Contraction yield but it's not exactly the same and Special Relativity is inadequate to predict exactly what will happen.

Let's now come to your wording. You are “concerned” about my suspected “conclusion” whereby “changing times and lengths associated with objects as a result of their accelerations are not physical”. First I hope that the two paragraphs above have convinced you that my conclusion is not in line with your wording, for two reasons: i) “changing times and lengths” are not “associated with objects”, but are attributes to their representations, just like the delta-x and delta-y are attributes to the representation of the stick in the example above; ii) SR only deals with those indirect attributes and does not constrain the direct ("physical") attributes to objects, just like my choice for the orientation of the coordinate system does not "effect" the “proper” ("physical") dimensions of the stick. Second, I will in turn challenge your wording insofar I believe it can be interpreted as if you consider that SR constrains the physical attributes of objects. How is that possible unless you think (contrary to my expectations) that my choice of a representation scheme “effects” the physical world? I'm quite convinced that your wording goes beyond what you actually think. Is that the case?

As I explained earlier, the choice of a representation scheme does not affect the physical world but there is more to it than that. Let me use a couple of scenarios to explain what I mean.

If we take a clock and express its Proper Time according to a frame in which it is at rest and then transform to a second frame in which it is moving, we will see that it is Time Dilated in this new frame. Nothing physical has happened as a result of this process.

But let's take that same clock that is at rest in the first frame and accelerate it so that it acquires the same speed that it had when we transformed it to the second frame. Now something physical has happened to it and we have to ask ourselves if it is now Time Dilated in exactly the same way as in the first scenario? In one sense we can answer "yes" because otherwise it doesn't fit the definition of a clock but in a more practical sense we have to answer "we don't know" because depending on how we accelerated it, we may have stressed it to a degree that it is now deformed and ticks at a different rate or we could have even destroyed it.

Take for example an ideal light clock that we accelerate along the axis of the propagating light. The two mirrors have to be supported by some structure. We could accelerate one end of the structure such that we initially compress the structure or we could accelerate the other end resulting in an initial stretching of the structure. Then when we end the acceleration, the opposite stresses would apply. In either case, SR can't tell us if the structure ends up with all the stresses removed or whether the clock has been compromised.

For the second scenario, consider a meter stick that has been calibrated against the old official meter stick standard. We can verify that its length is one meter using the new official meter standard using a cesium atomic clock and measuring how long it takes for light to propagate from one end of the meter stick to the other (where we have attached a mirror) and back to the starting point.

Now we accelerate the meter stick along its length and again verify its length. Will it be the same? Depending on how we accelerate it, probably not or definitely not. Again, SR is inadequate to answer that question precisely but we do know that it will have undergone a physical deformation.

Hopefully, this clears up any confusion in my wording.

Now what about my concern over your understanding of Doppler?

 

[Sugdub]

As a result, all objects will undergo some sort of physical deformation during acceleration which can approximate the same effects that Time Dilation and Length Contraction yield but it's not exactly the same and Special Relativity is inadequate to predict exactly what will happen.

I think I now understand what you had in mind in #17 with the expression: “changing times and lengths associated with objects as a result of their accelerations” but this is clearly a non-issue. If a physical acceleration or any other physical process has altered the proper length of the stick or the proper period of the clock, the same length contraction and time dilation factors as beforehand will apply to their representation as “in motion” in a given IRF, but they will of course apply to the new proper (“physical”) characteristics of the objects. SR does not describe physical processes, it only provides a consistent framework for representing their effects. So I invite you to reconsider your statement whereby “... SR is inadequate to predict exactly what will happen ...” since asking whether the proper length is affected by a physical acceleration is clearly out of scope of SR.

And this is your conclusion which we don't agree on. One of the most important aspects of Special Relativity is that the Lorentz Transformation process applies not just to coordinates but also to the formulas and equations of physics. They must remain unchanged after undergoing the Lorentz Transformation. For example, under Newtonian physics, the force equation is F=ma but this does not transform unchanged using the Lorentz Transformation. SR revolutionized all of physics by requiring all laws to be changed so that they remain intact through the Lorentz Transformation process. Maxwell's equations already fit the requirement.

The Newtonian mechanics had the same requirements, except that it invoked the galilean transformation. For me, part of the “revolution” brought by SR was to generalise the concept of “invariance through a change of the coordinate system” into the concept of “invariance through a change of the representation scheme”, the latter also encompassing a change of the inertial frame of reference for velocities. The consequence is indeed that “laws of physics” must now be understood as “laws of Newtonian mechanics” and “laws of SR mechanics” respectively, since their expression is necessarily theory-laden, due to the difference in the invariance criterion (combined with the existence in SR of a max speed limit). In both cases it is clear that equations and formulas describing the effects of “physical” processes must be invariant through the relevant transformations. So I don't see any matter for a serious disagreement there.

My statement in #18: “SR does not tell anything else and this is enough to reach predictions which are verified by experiments.” … (to which you negatively reacted) purposely insisted on the fact that SR does not make any statement about the “physical” behaviour of (e.g.) clocks: it does not state that they physically “slow down” when being “in motion”, it only states that their coordinate-like period when they are represented “in motion in respect to an IRF" must comply with the Time Dilation formula. Here I see a potential for disagreement since most (if not all?) textbooks on SR at best leave this issue open and very often display an ambiguous wording, if not worse. Please comment.

I'll come back to you about the Doppler effect asap. Thanks.

 

[harrylin]

A simple experiment can be build to demonstrate a possible contradiction between thinking theory and reality.

Use two hand electrical light torches set upon a table and back to back. Switch them on simultaneously, and calculate the relative velocity of their opposite leaving flashes.


←c← O= =O →c→
←2c→

Solution
In this case, the relative velocity between two leaving flashes is twice the speed of light.
A matter of discussion
Well, now put yourself in a teacher position and try to explain to your students, how this could be possible?
I leave this answer to you!

As others pointed out, there is no problem with 2c; the problem is due to incompatible terminologies. See also the following thread in which this came up as well:

https://www.physicsforums.com/showthread.php?t=644480

 

[ghwellsjr]

As a result, all objects will undergo some sort of physical deformation during acceleration which can approximate the same effects that Time Dilation and Length Contraction yield but it's not exactly the same and Special Relativity is inadequate to predict exactly what will happen.

I think I now understand what you had in mind in #17 with the expression: “changing times and lengths associated with objects as a result of their accelerations” but this is clearly a non-issue. If a physical acceleration or any other physical process has altered the proper length of the stick or the proper period of the clock, the same length contraction and time dilation factors as beforehand will apply to their representation as “in motion” in a given IRF, but they will of course apply to the new proper (“physical”) characteristics of the objects. SR does not describe physical processes, it only provides a consistent framework for representing their effects. So I invite you to reconsider your statement whereby “... SR is inadequate to predict exactly what will happen ...” since asking whether the proper length is affected by a physical acceleration is clearly out of scope of SR.

No, I won't reconsider my statement but I will give you some more scenarios.

First, consider a clock that is traveling in a circle at a constant speed (which means that it is constantly accelerating) and periodically passing by an identical inertial clock. Einstein predicted in article 4 of his 1905 paper introducing SR that the accelerating clock will be running slower than the inertial clock and by how much. Newtonian physics and the Galilean Transformation do not make this prediction of this purely physical effect.

Second, consider an elastic material like a "string" whose ends are attached to two rockets so that it is not limp or having any stress. Then in the rest frame of this system we accelerate both rockets identically up to some speed along the axis of the "string" such that the "string" does not break or lose its mechanical characteristics. SR predicts that there will be a physical, measurable stress in the string. Newtonian physics does not make this prediction. What SR does not predict is how the stress develops in the string during the acceleration.

And this is your conclusion which we don't agree on. One of the most important aspects of Special Relativity is that the Lorentz Transformation process applies not just to coordinates but also to the formulas and equations of physics. They must remain unchanged after undergoing the Lorentz Transformation. For example, under Newtonian physics, the force equation is F=ma but this does not transform unchanged using the Lorentz Transformation. SR revolutionized all of physics by requiring all laws to be changed so that they remain intact through the Lorentz Transformation process. Maxwell's equations already fit the requirement.

The Newtonian mechanics had the same requirements, except that it invoked the galilean transformation. For me, part of the “revolution” brought by SR was to generalise the concept of “invariance through a change of the coordinate system” into the concept of “invariance through a change of the representation scheme”, the latter also encompassing a change of the inertial frame of reference for velocities.

Both the Galilean Transformation and the Lorentz Transformation encompass "a change of the inertial frame of reference for velocities" so I don't know what you are trying to say here. Both transformations have the same goal, it's just that the Galilean one does not match reality precisely whereas the Lorentzian one does match reality precisely.

The consequence is indeed that “laws of physics” must now be understood as “laws of Newtonian mechanics” and “laws of SR mechanics” respectively, since their expression is necessarily theory-laden, due to the difference in the invariance criterion (combined with the existence in SR of a max speed limit). In both cases it is clear that equations and formulas describing the effects of “physical” processes must be invariant through the relevant transformations. So I don't see any matter for a serious disagreement there.

You have already stated in post #13 that "Newtonian theory fails to provide a correct explanation" so it appears to me that you have a serious disagreement with yourself here.

My statement in #18: “SR does not tell anything else and this is enough to reach predictions which are verified by experiments.” … (to which you negatively reacted) purposely insisted on the fact that SR does not make any statement about the “physical” behaviour of (e.g.) clocks: it does not state that they physically “slow down” when being “in motion”, it only states that their coordinate-like period when they are represented “in motion in respect to an IRF" must comply with the Time Dilation formula. Here I see a potential for disagreement since most (if not all?) textbooks on SR at best leave this issue open and very often display an ambiguous wording, if not worse. Please comment.

I can't defend any textbooks that you have a problem with since I can't see them but Einstein's paper that I referenced earlier clearly does make a statement about the "physical" behaviour of clocks slowing down while in motion. In fact the title of his article is "Physical Meaning of the Equations Obtained in Respect to Moving Rigid Bodies and Moving Clocks". So I don't see how your opinion can be defended.

I'll come back to you about the Doppler effect asap. Thanks.

Please do.

 

[Sugdub]

I can't defend any textbooks that you have a problem with since I can't see them but Einstein's paper that I referenced earlier clearly does make a statement about the "physical" behaviour of clocks slowing down while in motion. In fact the title of his article is "Physical Meaning of the Equations Obtained in Respect to Moving Rigid Bodies and Moving Clocks". So I don't see how your opinion can be defended.

Thanks. My purpose is not to challenge Einstein's views and neither yours, but to understand what SR can actually “state” about the physical world. Let's take two identical clocks A and B moving toward each other at a constant speed. SR assigns different coordinate-like periods to the clocks depending of the IRF where they are both represented. Considering the Time Dilation formula, one may select an IRF in which the coordinate-like period of A is lower than the coordinate-like period of B, but one may as well select a second IRF inverting those values and finally it is possible to select a third IRF in which both clocks have the same coordinate-like period. Since there is no preferred IRF one may ask on which ground SR can state whether both clocks physically tick at different rates and which formula determines their respective “physical periods”?

Let's now imagine that both clocks cross over close to each other and that nothing more happens to clock A whereas clock B reverts its motion after some time and comes back to join clock A. SR predicts, and this is fully confirmed by experiments, that once both clocks meet again, clock B will have registered a shorter elapsed time than clock A since their previous meeting event. I'm not challenging this. But how and when does the difference between elapsed times build up? Is it during the first leg of the journey of B, during the second leg, at a constant rate during the full journey, or any other way? Once you know that A and B have met again, it is possible to imagine several “consistent stories” to justify the outcome of the experiment. Each of these stories will at best match the values of coordinate-like periods for one single IRF and will not match the corresponding values for other IRFs. But in the absence of a preferred IRF, what are we going to conclude?

I can't see how and on which ground the SR theory can assign a physical period to a clock in motion. Please help.

 

[ghwellsjr]

Thanks. My purpose is not to challenge Einstein's views and neither yours, but to understand what SR can actually “state” about the physical world. Let's take two identical clocks A and B moving toward each other at a constant speed. SR assigns different coordinate-like periods to the clocks depending of the IRF where they are both represented. Considering the Time Dilation formula, one may select an IRF in which the coordinate-like period of A is lower than the coordinate-like period of B, but one may as well select a second IRF inverting those values and finally it is possible to select a third IRF in which both clocks have the same coordinate-like period. Since there is no preferred IRF one may ask on which ground SR can state whether both clocks physically tick at different rates and which formula determines their respective “physical periods”?

Unlike the prevailing theories when Einstein published his revolutionary theory, Einstein affirmed the "physical period" of each clock, no matter what its history, which means that coordinate time is not physical. Each IRF assigns different coordinate times and coordinate locations to the physical clocks and other objects in a consistent way so that the Proper Times of each clock represent physical time. The other prevailing theories regarded Coordinate Time and Coordinate Locations as physical and it sounds like that is what you are trying to do too.

Let's now imagine that both clocks cross over close to each other and that nothing more happens to clock A whereas clock B reverts its motion after some time and comes back to join clock A. SR predicts, and this is fully confirmed by experiments, that once both clocks meet again, clock B will have registered a shorter elapsed time than clock A since their previous meeting event. I'm not challenging this. But how and when does the difference between elapsed times build up? Is it during the first leg of the journey of B, during the second leg, at a constant rate during the full journey, or any other way? Once you know that A and B have met again, it is possible to imagine several “consistent stories” to justify the outcome of the experiment. Each of these stories will at best match the values of coordinate-like periods for one single IRF and will not match the corresponding values for other IRFs. But in the absence of a preferred IRF, what are we going to conclude?

We conclude that the coordinate times in any IRF are not physical but the Proper Times of the clocks are physical. SR provides a consistent way to establish Coordinates for any scenario that will yield the same physical observations and measurements that any object experiences, including Doppler effects which I'm still waiting for your exposition.

I can't see how and on which ground the SR theory can assign a physical period to a clock in motion. Please help.

SR theory affirms the physical time displayed on each and every clock no matter what its motion.

 

[Dale]

IMO this recent discussion is an indirect semantic discussion about the meaning of the word "physical".

 

[Sugdub]

...The other prevailing theories regarded Coordinate Time and Coordinate Locations as physical and it sounds like that is what you are trying to do too.

No. I've made clear that SR deals with coordinate-like quantities, quantities which are attributes to the formal representation of physical objects, not direct attributes to those objects. I've even insisted that SR does not tell anything else, and this is what you challenged.

We conclude that the coordinate times in any IRF are not physical but the Proper Times of the clocks are physical.

Fair enough, but you don't answer my question: Which formula determines the evolution of the Proper Time during the journey of each clock in the twins scenario? How does the gap between “Proper Times” build up alongside their journey (between the first collocation event and the final one)? My understanding is that SR predicts the value of the final gap when clocks A and B are collocated again, but that it has nothing to tell about the way this gap builds up during the journey. If I'm wrong, there must be a clear answer to my question above.

SR theory affirms the physical time displayed on each and every clock no matter what its motion.

Not understood.

 

[vanhees71]

ghwellsjr just says that a "physical" quantity is one that can be measured with a real apparatus in the real world, and the proper time of a moving clock is one thing you can measure.

Also, it is very important in physics (and all exact sciences) to stick to clear definitions. Relative velocity of (massive) particles is always understood as the velocity of one of the particles as measured in the rest frame of the other particle.

To get an idea what that might mean for massless particles, we have to formulate this concept in terms of the momenta of the particles and in a covariant way. So we look at massive particles first and express the concept of "relative velocity" in a covariant way. So let $p$ and $q$ be the four-momenta of the two particles 1 and 2 and let particle 2 be at rest. Then we have
$$q=(m_2,0,0,0)$$
and the relative velocity is
$$v_{\text{rel}}=\left |\frac{\vec{p}}{p^0} \right|.$$
Now a covariant expression we can built from the two on-shell momenta is
$$p \cdot q=m_2 p^0.$$
Further we have
$$\vec{p}^2=(p^0)^2-m_1^2=\frac{(p \cdot q)^2}{m_2^2}-m_1^2=\frac{(p \cdot q)^2-m_1^2 m_2^2}{m_2^2}.$$
So the relative velocity is given in a covariant way by
$$v_{\text{rel}}^2=\frac{\vec{p}^2}{(p^0)^2} = \frac{(p \cdot q)^2-m_1^2 m_2^2}{(p \cdot q)^2}.$$
I've set $c=1$ in the whole calculation.

In the limit $m_1 \rightarrow 0$ or/and $m_2 \rightarrow 0$ we get
$$v_{\text{rel}}=1,$$
as it should be, since massless particles always go with the speed of light (which is 1 in my units) wrt. to any inertial reference frame.

 

[ghwellsjr]

...The other prevailing theories regarded Coordinate Time and Coordinate Locations as physical and it sounds like that is what you are trying to do too.

No. I've made clear that SR deals with coordinate-like quantities, quantities which are attributes to the formal representation of physical objects, not direct attributes to those objects. I've even insisted that SR does not tell anything else, and this is what you challenged.

Maybe so but it appears that you are demanding that I produce for you an explanation that claims a physical interpretation of the Coordinates.

We conclude that the coordinate times in any IRF are not physical but the Proper Times of the clocks are physical.

Fair enough, but you don't answer my question: Which formula determines the evolution of the Proper Time during the journey of each clock in the twins scenario? How does the gap between “Proper Times” build up alongside their journey (between the first collocation event and the final one)? My understanding is that SR predicts the value of the final gap when clocks A and B are collocated again, but that it has nothing to tell about the way this gap builds up during the journey. If I'm wrong, there must be a clear answer to my question above.

SR addresses your question in exactly the same way it addresses the speed of an object. It is frame dependent. Once you know the speed, you know the Time Dilation. It can be different in different frames just like the speed is different. I don't see what is so hard or confusing about this.

I already gave you an example of the twins scenario from Einstein's paper (except they weren't called twins, just clocks). In the rest frame of the inertial clock, the other clock is always moving at a constant speed and therefore its Proper Time is Time Dilated to a constant extent and the "build up" of Proper Time each time it visits the inertial clock indicates the difference in the Proper Times between the two clocks. Isn't that simple?

We can transform that simple scenario into one where the inertial clock is moving and now the speed of the other clock is not steady but we can always calculate the instantaneous rate at which the clock is ticking and we "build up" the Proper Time just like before and arrive at the same answer, keeping in mind that the inertial clock is also Time Dilated. That is also simple in concept, although it is more complicated to calculate.

For the more traditional in line twin scenario, the calculations are also simple because we assume instantaneous accelerations so that the non-inertial twin is always traveling at the same speed (between his departure and return). So in the rest frame of the inertial twin, the calculation is just like for the circular scenario.

But we can transform to the frame in which the non-inertial twin is at rest during the first leg of his "journey" and only the inertial twin's clock is Time Dilated for the first "half", based on his speed, then during the second leg, the non-inertial twin is traveling back at an even higher speed resulting in more Time Dilation so that when they reunite, the difference in their Proper Times is the same when analyzed in the first frame.

There is never any gap in time in either twin's Proper Time, they always progress at a steady rate, although that rate can change as a result of an acceleration but it never results in a discontinuity in the "build up" of Proper Time.

SR theory affirms the physical time displayed on each and every clock no matter what its motion.

Not understood.

It seems a very simple concept to me. What don't you understand about a clock displaying time?

 

[CKH]

Sugdub,

Don't let "it's simple" bother you. Plenty of us have trouble working through scenarios in SR. In fact physicists make mistakes as evident in the controversies concerning analysis of rotation and the Sagnac effect.

I believe SR defines time as what a clock measures in the clock's rest frame (whether that frame is inertial or not). So I suppose that makes time "physical" in the clock's rest frame.

Is that correct?

 

[ghwellsjr]

Sugdub,

Don't let "it's simple" bother you.

Einstein called his theory "simple" in his 1905 paper and he ought to know, don't you think?

Plenty of us have trouble working through scenarios in SR. In fact physicists make mistakes as evident in the controversies concerning analysis of rotation and the Sagnac effect.

We were talking about the Time Dilation of a moving clock in an Inertial Reference Frame. Actually, any clock, moving or not.

I believe SR defines time as what a clock measures in the clock's rest frame (whether that frame is inertial or not). So I suppose that makes time "physical" in the clock's rest frame.

Is that correct?

Time is what a clock measures. It doesn't matter whether the clock is associated with any frame or not. All clocks always measure time (we call it Proper Time). If we want to build a frame around the clock and use it as the Coordinate Time of its rest frame, we are free to do that but we don't have to do that if we don't want to. We can just as well consider it to be moving (inertially or not) in an arbitrary inertial frame. Remember, one of the tenants of SR is that no frame is preferred, not even the rest frame of an object.