Are the transformations just observed ones or real ones?

[phyti]

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

The left drawing shows S' moving at .6c with a .5 unit stick contracted to .4 unit, as measured by S. Three photon events occur, Emission, Reflection, and Detection.
S records (x, t) for E as (0,0), calculates* (x, t) for R as (1.0, 1.0), and for D as
(.75, 1.25).
Due to time dilation, S' records (x', t') for E as (0,0), and for D as (0, 1.00), and calculates* (x', t') for R as (.50, .50).
The right drawing shows events from the S' perspective.
At D, S' expects the S distance to be .60 according to his clock, placing him at D'. Since the S distance is .75, he concludes the S frame moving at -.6c is contracted by .80.
The perception of a length contracted S frame is a reciprocal effect of time dilation for S'.

The motion induced effects on the S' frame are real in the sense of being independent of observation. The S' observation of the world beyond his frame is conditioned by those same effects, resulting in an altered perception, that does not correspond to reality outside the mind.

*Dividing the round trip time in half per SR definition of simultaneity.

 

[ghwellsjr]

The left drawing shows S' moving at .6c with a .5 unit stick contracted to .4 unit, as measured by S. Three photon events occur, Emission, Reflection, and Detection.
S records (x, t) for E as (0,0), calculates* (x, t) for R as (1.0, 1.0), and for D as
(.75, 1.25).
Due to time dilation, S' records (x', t') for E as (0,0), and for D as (0, 1.00), and calculates* (x', t') for R as (.50, .50).
The right drawing shows events from the S' perspective.

In the right drawing, why did you label event D as D' and event R as R'?

At D, S' expects the S distance to be .60 according to his clock, placing him at D'.

I don't understand this sentence at all. There is no D in the S' diagram (the one on the right) and I can't tell what you mean by the "S distance".

Since the S distance is .75, he concludes the S frame moving at -.6c is contracted by .80.

Are you actually meaning to say that the a frame is contracted?

The perception of a length contracted S frame is a reciprocal effect of time dilation for S'.

Or are you saying that each frame perceives the other frame to be contracted (due to time dilation)? I don't understand this at all.

The motion induced effects on the S' frame are real in the sense of being independent of observation. The S' observation of the world beyond his frame is conditioned by those same effects, resulting in an altered perception, that does not correspond to reality outside the mind.

*Dividing the round trip time in half per SR definition of simultaneity.

It might help if you provide more details about your diagrams. For example, why is there a segment of a circle in the first diagram? Why isn't there a similar segment in the second diagram?

Why are the events R' and R along the same light beam in the first diagram but not in the second?

There seem to me to be so many extra lines in both drawings with no explanation and no obvious reason for their existence.

I always thought that when you draw two diagrams of the same scenario, every feature in the first diagram would also be present in the second diagram. Maybe you're trying to convey something entirely different in the two diagrams but if so, I wish you'd explain what's going on.

 

[Dale]

IMO, you don't need light rays in a spacetime diagram representing a measurement of length. The position needs to be measured simultaneously at both ends, but that can be done via synchronized clocks rather than light rays. The important part is how the coordinates transform.

 

[Sugdub]

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

What do you mean with “a moving object”? According to the principle of relativity of motion, this wording has no objective meaning. Hence no objective meaning can be assigned to the “length of a moving object”.

The definition you quote may be used to define the “proper length” of an object, assuming the measurement device is at rest in respect to the (remote) object. Please note that the measurement process does not deal directly with the events e1 and e2 you refer to, but with events e'1 and e'2 relevant to the reception, by the (remote) measurement device, of signals which emission coincides with e1 and e2 respectively. If the target object is in relative motion in respect to the measurement device, then the simultaneity between e1 and e2 does not imply the same between e'1 and e'2. So which criterion are you going to apply to justify your claim that the outcome of your measurement reflects a genuine property of the object, a “length”?

 

[Mentz114]

What do you mean with “a moving object”? According to the principle of relativity of motion, this wording has no objective meaning. Hence no objective meaning can be assigned to the “length of a moving object”.

Come on ! At this level of discussion you are hair splitting. From the context it is obvious what is meant. I am entitled to call anything that is in motion wrt to me 'a moving object'. Do you really think stevendaryl does not know the principles of relativity ? There is no difficulty in understanding 'the length of a moving object'.

 

[harrylin]

What do you mean with “a moving object”? According to the principle of relativity of motion, this wording has no objective meaning. Hence no objective meaning can be assigned to the “length of a moving object”. [..]

The objective meaning of a "moving object" can be found in any textbook, as it's an operational definition.
No invariant meaning can be assigned to:
- the speed of a moving object
- the length of a moving object
- the duration of a physical process in a moving object
- the kinetic energy of a moving object
etc.

 

[Sugdub]

Come on ! At this level of discussion you are hair splitting. From the context it is obvious what is meant. I am entitled to call anything that is in motion wrt to me 'a moving object'. Do you really think stevendaryl does not know the principles of relativity ? There is no difficulty in understanding 'the length of a moving object'.

Please consider that my own "level of discussion" is very basic, so that I try to be explicit about the assumptions that are made, in order to detect misunderstandings, as far as possible. In future I'll try to avoid formulations which can be interpreted as a challenging the competence of those who indeed have the knowledge. I accept your swift reaction.
I have no doubts about the competence of Stevendaryl, and this why this author must have a clear answer to propose as to which simultaneity criterion (emission- or detection-events) is used for the definition of the so-called "length of the moving object". Or do you think my question does not make sense?

 

[stevendaryl]

What do you mean with “a moving object”?

Moving is relative to a frame, and so is length.

According to the principle of relativity of motion, this wording has no objective meaning. Hence no objective meaning can be assigned to the “length of a moving object”.

Every frame has a notion of "velocity relative to that frame" and "length relative to that frame" and "simultaneity of events relative to that frame". Those notions are frame-dependent, but they are objective in the sense that given a frame, velocity, length and times are determined.

The definition you quote may be used to define the “proper length” of an object,

No, it's not the proper length of an object, it's the length of an object, relative to a frame. It's the proper length in the special case in which the object is at rest in the frame.

Please note that the measurement process does not deal directly with the events e1 and e2 you refer to, but with events e'1 and e'2 relevant to the reception, by the (remote) measurement device, of signals which emission coincides with e1 and e2 respectively.

That is not true. The definition of a coordinate system is a way of assigning space and time coordinates to events. How you figure out this assignment might involve light signals, but it might not.

 

[stevendaryl]

Please consider that my own "level of discussion" is very basic, so that I try to be explicit about the assumptions that are made, in order to detect misunderstandings, as far as possible. In future I'll try to avoid formulations which can be interpreted as a challenging the competence of those who indeed have the knowledge. I accept your swift reaction.
I have no doubts about the competence of Stevendaryl, and this why this author must have a clear answer to propose as to which simultaneity criterion (emission- or detection-events) is used for the definition of the so-called "length of the moving object". Or do you think my question does not make sense?

Let me illustrate the concept of an inertial coordinate system, so that you can see what "velocity" and "length" relative to an inertial coordinate system mean.

Suppose we have a very, very, very long train. We'll call it the A train. Each train car has length L. The cars are numbered with consecutive integers with car number 0 being the one in the middle. Each car has an identical clock. The clocks are synchronized by the following procedure: Bring all the clocks to car #0, set them to the same time, then walk them to their destination cars.

Now, right outside the A train, on a parallel track, is another train, the B train. The B train has two ends, the right end and the left end. Passengers in car number $n_1$ of the A train note that the left end of the B train is lined up with their car at time $t_1$, according to the clock in car number $n_1$. Passengers in car number $n_2$ of the A train note that the right end of the B train is lined up with their car at time $t_1$, according to the clock in car number $n_2$. When the passengers get together to compare notes, they compute:

The length of the B train at time $t_1$ = $|n_2 - n_1|\times L$

This length is certainly NOT an illusion of any kind. It's dependent on a convention for synchronizing clocks and for measuring distances, etc. But given those conventions, the length of the B train relative to the frame of the A train is perfectly objective.

 

[stevendaryl]

I have no doubts about the competence of Stevendaryl, and this why this author must have a clear answer to propose as to which simultaneity criterion (emission- or detection-events) is used for the definition of the so-called "length of the moving object". Or do you think my question does not make sense?

Your question does not make sense, because coordinates have nothing, necessarily, to do with "emission" or "detection".

 

[Sugdub]

I'm striving to accept your statements, however with serious reservations.

Moving is relative to a frame, and so is length.

You seem to be using the word "length" where I would normally refer to a "distance". I think the word "length" should be used to refer to an intrinsic characteristic of an object.

Every frame has a notion of "velocity relative to that frame" and "length relative to that frame" and "simultaneity of events relative to that frame". Those notions are frame-dependent, but they are objective in the sense that given a frame, velocity, length and times are determined.

Clearly those notions are context-dependent. It means that they are not representative of intrinsic properties or characteristics of the object they point to. When we look at a distant object, it appears to have a smaller size as compared to its proper size. Everybody refers to the "apparent size of the object" and there is no ambiguity that it is not an "illusion", it is the way the object appears from a distance. Here we are no longer debating on objects being far or close, not with their relative position, but with their relative speed. Apart from that the analogy can be made between what you define as the "length of an object relative to a frame" and what I would better call the "apparent length of the object relative to a given frame"

No, it's not the proper length of an object, it's the length of an object, relative to a frame. It's the proper length in the special case in which the object is at rest in the frame.

So for me it is its apparent length of the object, relative to a frame. Let's see however if this is only a difference in wording.

That is not true. The definition of a coordinate system is a way of assigning space and time coordinates to events. How you figure out this assignment might involve light signals, but it might not.

Yes and no. I have no problem with you stating that the representation of events e1 and e2 can be made in any coordinate system. However my statement did not deal with that at all. It referred explicitely to the measurement process targetting a remote object. And I keep stating that the measurement process deals with events which are co-located with the measurement device, i.e. not with e1 and e2 as such which are co-located with the object.

So my question to you still holds: which simultaneity criterion are you going to retain for assessing whether one measures a "length" (according to your definition of that term) in case the object in in relative motion in respect to the measuring device? It it the simultaneity of the events co-located with the object, or the simultaneity of the events co-located with the measurement device?

 

[stevendaryl]

I'm striving to accept your statements, however with serious reservations.



You seem to be using the word "length" where I would normally refer to a "distance". I think the word "length" should be used to refer to an intrinsic characteristic of an object.

Why? The length of an object is the distance between the two ends.

Clearly those notions are context-dependent. It means that they are not representative of intrinsic properties or characteristics of the object they point to. When we look at a distant object, it appears to have a smaller size as compared to its proper size. Everybody refers to the "apparent size of the object" and there is no ambiguity that it is not an "illusion", it is the way the object appears from a distance. Here we are no longer debating on objects being far or close, not with their relative position, but with their relative speed. Apart from that the analogy can be made between what you define as the "length of an object relative to a frame" and what I would better call the "apparent length of the object relative to a given frame"

But there is nothing "apparent" about it. It doesn't have to do with "appearances", so the word "apparent' is not appropriate.

The word "apparent" is appropriate when your senses lead you to believe that something is true that is not, in fact, true. An object that is far away is "apparently" smaller than the same object close up, but its size isn't actually changed.

Yes and no. I have no problem with you stating that the representation of events e1 and e2 can be made in any coordinate system. However my statement did not deal with that at all. It referred explicitely to the measurement process targetting a remote object.

The definition of length is relative to a coordinate system, not to a measuring device. Of course, measuring devices may be involved in figuring out the coordinates of an event.

So my question to you still holds: which simultaneity criterion are you going to retain for assessing whether one measures a "length" (according to your definition of that term) in case the object in in relative motion in respect to the measuring device? It it the simultaneity of the events co-located with the object, or the simultaneity of the events co-located with the measurement device?

I gave you the definition of length relative to a frame: we say that the length of an object in frame F is equal to L at time t if there are a pair of events, $e_1$ and $e_2$ such that

• The events are simultaneous in frame F.
• The distance between the events is L in frame F.
• $e_1$ is co-located with one of the object, and $e_2$ is co-located at the other end.

So the criterion of simultaneity applies to the events at the object, not at whatever measuring device is used to measure the length.

 

[Dale]

You seem to be using the word "length" where I would normally refer to a "distance". I think the word "length" should be used to refer to an intrinsic characteristic of an object.

On this forum you need to use the standard definitions of terms. Length is not an intrinsic characteristic of an object. It is a frame variant quantity.

The quantity you are thinking of is "proper length". Please do not confuse length with proper length. They are different concepts, and in order to communicate effectively it is important that you use them correctly. Do not try to assert that length is frame invariant, and do not use "length" when you mean "proper length".

 

[harrylin]

[..]
I have a similar question to you: which simultaneity criterion are you going to retain for assessing whether one measures a "length" (according to your definition of that term) in case the object in in relative motion in respect to the measuring device? It it the simultaneity of the events co-located with the object, or the simultaneity of the events co-located with the measurement device?

I have a similar question for you, in continuation of my last post: what is your criterion for kinetic energy - is it the kinetic energy of the object in a "co-located" (co-moving) reference system with the object, or is it the kinetic energy according to your measurement system?

And similar for clock rate: a clock that is "ticking slow" according to your measurement system will prove, if it followed a circular path, to have actually lost time (that's an "absolute") compared to a clock that was all the time at rest in your system - see §4 of http://www.fourmilab.ch/etexts/einstein/specrel/www/ .
So, are we allowed to use our measurement system all the time in order to be consistent, or must we use inconsistent measurements, such that we must say that a clock that all the time was ticking at its normal rate magically will be found to be behind? Or do you hold that an object's length is "inherent", but an object's resonance frequency is not?

 

[phyti]

In the right drawing, why did you label event D as D' and event R as R'?


I don't understand this sentence at all. There is no D in the S' diagram (the one on the right) and I can't tell what you mean by the "S distance".


Are you actually meaning to say that the a frame is contracted?


Or are you saying that each frame perceives the other frame to be contracted (due to time dilation)? I don't understand this at all.


It might help if you provide more details about your diagrams. For example, why is there a segment of a circle in the first diagram? Why isn't there a similar segment in the second diagram?

Why are the events R' and R along the same light beam in the first diagram but not in the second?

There seem to me to be so many extra lines in both drawings with no explanation and no obvious reason for their existence.

I always thought that when you draw two diagrams of the same scenario, every feature in the first diagram would also be present in the second diagram. Maybe you're trying to convey something entirely different in the two diagrams but if so, I wish you'd explain what's going on.

Sorry for the confusion. I forget that what's easy for me may not be for someone else.
Following the convention S vs S', the primed (') values correspond to those for the observer in S', and the labels refer to both frame and observer. The light gray horizontal and vertical lines are for measurements.
In the left drawing the vertical line at x = 1.00 represents the fixed object location in the S frame. E, R, D, are events according to S. E', R', D', are events according to S'. As S' moves along the x axis, he records the distance markers for each local event (E and D) he experiences. The arc is a simpler method than the hyperbola to indicate the time on the S' clock (follow the original values from the example).
Let's assume S is an absolute rest frame as drawn. That means the perception of S is not affected by time dilation (td) or length contraction (lc). What S observes is basic physical phenomena, including td and lc (via deformed em fields), both due to extended light paths and a constant c.
The right drawing is the S' perspective, with S moving to the left. Only the necessary elements are transformed from the left drawing. The object at x = 1.00 is now at x' = .80, explained as a reciprocal effect of td for S'. The world of S' outside his frame is smaller by a factor of 1/γ = .80. If .60c was an absolute speed for S', then the magenta path would be the speed of light relative to S', and R the reflection event. Since only the relative speed can be measured, the time and location of R or R' is uncertain. The SR convention resolves this issue by defining the light paths as equal, resulting in the maximum spatial interval equal to γ*(D'-R interval in the S frame). The S' stick still measures .50 relative to his ruler.

In response to windows post 1, all observers have perceptions that are real as images in the mind. Some of the perceptions correspond to physical phenomena outside of and independent of the mind, and some do not. SR is about physical phenomena interacting with human observation and experience, and that makes it also a theory of perception.

There are no known physical phenomena that would cause the universe to instantly contract because a spacecraft launched, or a bunch of particles are accelerated to .9c.
There are however direct and indirect measurable effects implying td and lc on fast moving objects. It's reasonable to assign the change to the object (observer) as a result of its motion. This would explain why no one else perceives what the moving observer perceives. Compare this to someone on hallucinogenic drugs. Their images are real to them, but no one else experiences them, since they are confined to the mind. This analogy is why I use the term altered perception.

 

[nitsuj]

SR is about physical phenomena interacting with human observation and experience, and that makes it also a theory of perception.
There are no known physical phenomena that would cause the universe to instantly contract because a spacecraft launched, or a bunch of particles are accelerated to .9c. There are however direct and indirect measurable effects implying td and lc on fast moving objects. It's reasonable to assign the change to the object (observer) as a result of its motion. This would explain why no one else perceives what the moving observer perceives. Compare this to someone on hallucinogenic drugs. Their images are real to them, but no one else experiences them, since they are confined to the mind. This analogy is why I use the term altered perception.

! It's a long thread to read it all to be sure of the context, that said SR isn't (directly) a theory of perception. In the least a theory that introduces time into geometric structure.

The physical phenomena is causation. The whole universe has contracted from this "fast moving object" perspective. It must for the sake of the fast moving object to see the "happenings" within the universe in the same order as everyone else regardless of comparative motion.

If the comparative time interval of 10 seconds for the fast moving object is much much longer then the "stationary" observer's, the fast moving object must see "happenings" across a much much shorter distance then the "stationary" observer. To the very specific point that both would measure c to have the same value.

It is comparatively altered geometry, not comparatively() altered perception.

 

[ghwellsjr]

Sorry for the confusion. I forget that what's easy for me may not be for someone else.
Following the convention S vs S', the primed (') values correspond to those for the observer in S', and the labels refer to both frame and observer. The light gray horizontal and vertical lines are for measurements.
In the left drawing the vertical line at x = 1.00 represents the fixed object location in the S frame.

I thought you said in post #36 that the stick was moving in the left drawing. Isn't that the only object in this scenario? What do you mean by "the fixed object location in the S frame"?

E, R, D, are events according to S. E', R', D', are events according to S'.

Ok, but what are the D' and R' events in the left drawing and what is the R event in the right drawing?

As S' moves along the x axis, he records the distance markers for each local event (E and D) he experiences.

I presume you mean he records 0 for event E and 0.75 for event D. What does he do with those numbers?

The arc is a simpler method than the hyperbola to indicate the time on the S' clock (follow the original values from the example).

Let me see if I got this right. To determine what time is on the S' clock at D in the left diagram, you draw a horizontal line from D to the left and a vertical line from D down to the bottom. Then you draw a segment of a circle from where the horizontal line intersect the S time axis to the right with the center at the origin. You stop when the segment encounters the previously drawn vertical line. From that point you draw another horizontal line to the left and read the value on the S time axis, in this case, 1.00. Correct?

Let's assume S is an absolute rest frame as drawn. That means the perception of S is not affected by time dilation (td) or length contraction (lc). What S observes is basic physical phenomena, including td and lc (via deformed em fields), both due to extended light paths and a constant c.

By "extended light paths", are you referring to the extension of the reflected light from R to D and continuing up to the S time axis at 2.00? If so, how does the observer at x=0 in S determine td and lc?

The right drawing is the S' perspective, with S moving to the left. Only the necessary elements are transformed from the left drawing. The object at x = 1.00 is now at x' = .80,...

This must be a different object than the 0.5 unit stick you originally mentioned. Is this a different 0.25 unit stick going from x=0.75 to x=1 in S and intersecting the t'=0 axis in S' from x'=0.6 to x'=0.8? Why no mention of the 0.5 unit stick? Isn't it shown by the two parallel lines in S and the two vertical lines in S' at x=0 and x=0.5?

...explained as a reciprocal effect of td for S'.

Why td and not lc?

The world of S' outside his frame is smaller by a factor of 1/γ = .80. If .60c was an absolute speed for S', then the magenta path would be the speed of light relative to S', and R the reflection event.

Are you making the point that R cannot be the refection event because the magenta lines are not at c?

Since only the relative speed can be measured, the time and location of R or R' is uncertain.

Are you making the point that this would be true if we didn't have SR?

The SR convention resolves this issue by defining the light paths as equal, resulting in the maximum spatial interval equal to γ*(D'-R interval in the S frame). The S' stick still measures .50 relative to his ruler.

But isn't the point that S measures the stick to be 0.4, just that he can't do it with only his ruler (because it is moving with respect to him) but S' can measure the stick with only his ruler because it is stationary with respect to him?

Thanks for helping me understand a little more but I'm afraid I still have a long way to go.

 

[phyti]

! It's a long thread to read it all to be sure of the context, that said SR isn't (directly) a theory of perception. In the least a theory that introduces time into geometric structure.

It's many things, thus 'also' a theory of perception. Time was revised from a universal value to an observer dependent value.

The physical phenomena is causation. The whole universe has contracted from this "fast moving object" perspective. It must for the sake of the fast moving object to see the "happenings" within the universe in the same order as everyone else regardless of comparative motion.

All moving observers do not see events in the same order.

If the comparative time interval of 10 seconds for the fast moving object is much much longer then the "stationary" observer's, the fast moving object must see "happenings" across a much much shorter distance then the "stationary" observer. To the very specific point that both would measure c to have the same value.

The fast moving observer sees more events in a shorter time interval, in support of his conclusion of the contracted universe.

It is comparatively altered geometry, not comparatively() altered perception.

The observer, including his mental analysis of sensory input, is modified by td and lc to the same extent as the frame he occupies.

 

[nitsuj]

All moving observers do not see events in the same order.

Who cares and what is the physical significance of non casually connected events. "Happenings" is referring to the specific event(s) of a cause and then effect; and not referring to RoS. I wouldn't retort with some point that has no physical significance so thought what I meant would be clear, specifically by not even using the word event, since that could be merely a position in spacetime.

 

[Sugdub]

Let me illustrate the concept of an inertial coordinate system, so that you can see what "velocity" and "length" relative to an inertial coordinate system mean...
Now, right outside the A train, on a parallel track, is another train, the B train...
This length is certainly NOT an illusion of any kind. It's dependent on a convention for synchronizing clocks and for measuring distances, etc. But given those conventions, the length of the B train relative to the frame of the A train is perfectly objective.

Thank you for proposing this thought experiment. I think there are similar ones in the litterature, which presentation is generally not so clear. Because yours is so straightforward it is easier for me to identify where exactly I fail to follow your reasonning.
Whatever the distance between both parallel tracks, "right outside" or far away, light signals are required between both ends of train B and observers located in train A, respectively, in order for your thought experiment looking "feasible".
Can you please elaborate (in simple words as you perfectly did for presenting this example) on the simultaneity criterion required for the reception events of both signals in train A and on the simultaneity criterion required for the emission events of the same signals in train B in order for them to be representative of the length of train B. Can both criteria be met concurrently if both light rays travel the same distance (parallel tracks)?
A positive answer to my question would imply that a potential observer at rest in train B (this is a slight add-on to the experiment you propose) would measure a different value for the length of train B as compared to those located in train A, this difference being due to their relative motion in respect to each other. I do think it is logically impossible that relative motion of its own triggers changes in observed phenomena. As already stated I believe SR is a wonderful theory but my criticisms relate to the way it is presented, which does not match the spirit of the original presentation made by Einstein in his 1905 paper.

 

[harrylin]

[..] I believe SR is a wonderful theory but my criticisms relate to the way it is presented, which does not match the spirit of the original presentation made by Einstein in his 1905 paper. [..].

I agree; and that's why several people here including myself present it similar to the way he did! He stayed away from making any metaphysical claims.
[edit: I should have added: when first presenting Special Relativity. He did engage in somewhat metaphysical discussions from about 1920 onwards, with such titles as "Ether and the Theory of Relativity"].

And note that I showed with my calculation example that just knowing the change in relative motion between objects is of its own not enough to predict the observed phenomena.

 

[stevendaryl]

Whatever the distance between both parallel tracks, "right outside" or far away, light signals are required between both ends of train B and observers located in train A, respectively, in order for your thought experiment looking "feasible".

Well, not necessarily light signals.

Can you please elaborate (in simple words as you perfectly did for presenting this example) on the simultaneity criterion required for the reception events of both signals in train A and on the simultaneity criterion required for the emission events of the same signals in train B in order for them to be representative of the length of train B. Can both criteria be met concurrently if both light rays travel the same distance (parallel tracks)?

Sure. Let $e_1$ be the emission of a light signal from the left end of the B-train. Let $e_1'$ be the reception of that signal by car number $n_1$ of the A-train. Let $e_2$ be the emission of a light signal from the right end of the B-train. Let $e_2'$ be the reception of that signal by car number $n_2$ of the A-train. The assumption, for the purposes of this thought experiment is that $e_1$ and $e_1'$ have negligible separations in both space and time, and similarly $e_2$ and $e_2'$. So the pairs of events are approximately simultaneous in both frame A and frame B. The thought experiment is assuming that the distance between the tracks is negligible compared with the distance between two cars of either train.

But the simultaneity criterion for $e_1$ and $e_1'$ is completely unconnected with the simultaneity criterion for $e_1'$ and $e_2'$. The first depends on $e_1$ and $e_1'$ being close together in space and time, while the latter depends on clock synchronizations.

A positive answer to my question would imply that a potential observer at rest in train B (this is a slight add-on to the experiment you propose) would measure a different value for the length of train B as compared to those located in train A,

Yes, that's definitely true. Or at least, that's the prediction of Special Relativity.

this difference being due to their relative motion in respect to each other. I do think it is logically impossible that relative motion of its own triggers changes in observed phenomena.

That way of putting things doesn't make any sense. Relative motion can't "trigger" anything, because it's not an event. Events trigger other events. If you want to talk about events causing things to happen, then the relevant event would be the acceleration or deceleration of one of the trains.

So you can imagine that initially both trains are moving in the same direction at the same velocity. Then later, the B-train changes speed (say by braking). A sudden change of speed will cause the cars of B to jerk and strain. You can't brake all points along train B simultaneously. If you tried to, it would be simultaneous according to one frame, but then it wouldn't be simultaneous according to a different frame. But if B is braking, then it is CHANGING frames, so there is no single frame to use. So braking will put stress on the B-train. After the braking stops, the stresses will go away, and the train will re-establish some equilibrium length. But there is absolutely no reason to think that this equilibrium length will be the same (as measured by the frame of the A-train) as it was before braking. SR predicts that it won't be.

But it's not that relative motion triggers a change of length--it's whatever actions put the train into relative motion that triggers a change of length.

As already stated I believe SR is a wonderful theory but my criticisms relate to the way it is presented, which does not match the spirit of the original presentation made by Einstein in his 1905 paper.

That's kind of a ridiculous thing to say. SR has been examined by physicists from more angles and from more different perspectives than just about any other theory of physics. There has been 100 years of thought experiments, paradoxes proposed and resolved, alternative derivations, alternative mathematical formulations, etc. If physicists are unwilling to hear your particular spin on SR criticism, it's because at some point, people have to make a judgment call as to what is worth spending more time on. At this point, SR is about as well-established as Euclidean geometry. Arguing about it is sometimes a good way for a student to learn, but it's not going to be of any benefit to working physicists at this point.

 

[stevendaryl]

I agree; and that's why several people here including myself present it similar to the way he did! He stayed away from making any metaphysical claims.
[edit: I should have added: when first presenting Special Relativity. He did engage in somewhat metaphysical discussions from about 1920 onwards, with such titles as "Ether and the Theory of Relativity"].

And note that I showed with my calculation example that just knowing the change in relative motion between objects is of its own not enough to predict the observed phenomena.

I think that at the time that Einstein wrote his paper on SR, he was under the influence of the positivists, and thought that all concepts of physics should be given operational definitions. He had difficulty maintaining his positivist stance when he turned to GR, because there did not seem to be any nice operational way to define a coordinate system for an observer in the presence of gravity.

 

[phyti]

I thought you said in post #36 that the stick was moving in the left drawing. Isn't that the only object in this scenario? What do you mean by "the fixed object location in the S frame"?

It's a random fixed object located at x = 1.00 in the S frame, for demonstration purposes. It could be a jar of pickles or the distance marker.

Ok, but what are the D' and R' events in the left drawing and what is the R event in the right drawing?

The events to the right are the same events to the left, just different perspectives.
At the left, D' and R' are locations according to S' as determined by his clock. They provide a comparison of where S' thinks he is relative to the locations S assigns for S', D and R.

As S' moves along the x axis, he records the distance markers for each local event (E and D) he experiences.

Yes he records 0 and .75 as x values. He uses the corresponding t' values 0 and 1.00 to calculate the t' value for R', being 1.00/2 = .50. By symmetry x' = ct' = .50.
Now to the .75 distance marker which is fixed in the S frame. By his clock, S' records 1.00 at D when at the .75 marker, yet he calculates distance traveled as .6c*1.00 = .60. How does he reconcile this mismatch? If he cannot detect his frame contraction or his time dilation, since he is also effected by both, he concludes the world outside his frame is length contracted.

Let me see if I got this right. To determine what time is on the S' clock at D in the left diagram, you draw a horizontal line from D to the left and a vertical line from D to the x axis. Then you draw a segment of a circle from where the horizontal line intersect the S time axis to the right with the center at the origin. You stop when the segment encounters the previously drawn vertical line. From that point you draw another horizontal line to the left and read the value on the S time axis, in this case, 1.00. Correct?

Correct (with a minor revision, underlined)j. Make it more specific, as you keep encouraging us to do.

By "extended light paths", are you referring to the extension of the reflected light from R to D and continuing up to the S time axis at 2.00? If so, how does the observer at x=0 in S determine td and lc?

If the stick was at rest in S, light would require 1.00 S time for the round trip. He observes the stick, which has contracted during its acceleration, prior to t = 0. S measures .4 for the stick length using; the radar method shown, simultaneous clock readings on the x axis, or the time for the stick to pass a given position.
Since clocks are frequencies, S and S' observe equal doppler shifts for the other clock.
Extended light paths result from motion of the target object. The light has to compensate for the motion of S'. More time is required on the outbound path, and less time on the inbound path, with the increase always greater than the decrease, i.e. a net increase of time.

I'll finish the response for the rest later (to keep them short).

 

[phyti]

I agree; and that's why several people here including myself present it similar to the way he did! He stayed away from making any metaphysical claims.
[edit: I should have added: when first presenting Special Relativity. He did engage in somewhat metaphysical discussions from about 1920 onwards, with such titles as "Ether and the Theory of Relativity"].

And note that I showed with my calculation example that just knowing the change in relative motion between objects is of its own not enough to predict the observed phenomena.

It's good to find another 'free thinker'. I agree with you, and yes you can demonstrate from a universal fixed frame, that the absolute speed determines lc and td. Despite the limitation on measuring an absolute speed, a relation can be established between relative speed and relative lc and td. It's not magic! In summation, an observer only measures the differences in speed, lc, and td. But that's the principle idea in 'relativity'. In fact all measurement is relative to a standard.

 

[Dale]

I do think it is logically impossible that relative motion of its own triggers changes in observed phenomena.

It is not a change in an observed phenomenon, it is a disagreement about whether or not the observed phenomena constitute a length. Your objection is not pertinent to the topic.

If in my frame I measure that the back of the train is at x=0 and the front of the train is at x=1, both at t=0, then I will say that the length of the train is 1. However, someone moving at v=.6 relative to me will say that my measurement of the front of the train was at x=1.25 and at t=0.75 (in units where c=1). So they will disagree that my measurement constituted a measurement of the length.

Again, length contraction isn't about changes in length, it is about disagreement between frames.

 

[choran]

Hope I'm OK with asking this in this thread--if not, feel free to ignore. I wonder if there is a difference between the length contraction under discussion with the phenomenon involved wherein the light from a moving object reaching the detector (eye, CCD, whatever) of necessity originates at different points along the object, and thus has traveled different distances to the detector from various points on the object, and different times in its path of travel. Hope that's clear enough. I believe it's called, or related to Penrose-Terrell. Question is, is length contraction the same as, different from, in addition to or...?

 

[yuiop]

I wonder if there is a difference between the length contraction under discussion with the phenomenon involved wherein the light from a moving object reaching the detector (eye, CCD, whatever) of necessity originates at different points along the object, and thus has traveled different distances to the detector from various points on the object, and different times in its path of travel. Hope that's clear enough. I believe it's called, or related to Penrose-Terrell. Question is, is length contraction the same as, different from, in addition to or...?

Penrose-Terrell rotation is a purely optical effect. A sphere does not appear length contracted due to the rotation effect and quite a lot people give this as a proof that length contraction is not a physical phenomena. However the length contraction of a long rectangular object is not totally obscured by the PT rotation and can in principle be photographed.

If each photon that lands on the film of a Penrose-Terrell camera had a time stamp with its time of emission, it would be seen that the pixels that make up the photograph would have a wide variety of time stamps. If we took a series of photographs and used a computer to assemble an image made of pixels with exactly the same time stamp, then we would have an image complete with length contraction (and no rotation).

Essentially, length contraction is a mental picture of where all the parts of a moving object are at a given simultaneous instant of time. This assembled picture takes into account any delays due to light travel and removes those delays, so that the resulting calculation has more physical significance than just optical appearance.

I think the best demonstration of the physicality of length contraction is in the Ehrenfest paradox, where the length contraction of the outside edges of a rotating object causes real stresses that would eventually tear the the object apart if the radius was not permitted to alter as the rotational speed varied. The next best demonstration is Bell's rockets paradox, where a string of fixed length (in one reference frame) breaks due to length contraction, but a lot of people don't get the solution to that paradox.

 

[choran]

Would be correct that no Penrose-Terrell photos have been taken, but that the "images" are simply mathematically derived by applying a non-relativistic formula based upon the speed of arrival of light from different portions of the object as it moves through space, as you explain above, by calculating the wide variety of "time stamps"? Is it also correct to state that the Penrose effect or procedure would not capture a length contraction, and is that simply because by definition the length contraction posited in relativity theory is not the one described and measured by the Penrose situation/procedure? Thanks again for your help.

 

[yuiop]

Would be correct that no Penrose-Terrell photos have been taken, but that the "images" are simply mathematically derived by applying a non-relativistic formula based upon the speed of arrival of light from different portions of the object as it moves through space, as you explain above, by calculating the wide variety of "time stamps"?

Every time an ordinary photo is taken of a moving object, it is effectively a Penrose-Terell type image. It is just that the velocities of common objects are usually too low for any relativistic rotation or length contraction effects to visibly noticeable. A hypothetical PT camera has additional sophistications such as curved back to equalise the light path from the lens to the film and an extremely fast shutter. The mathematical calculations of Penrose-Terrell rotation are relativistic, because they take into account the effect of length contraction and then factor in the light delays to calculate what image would be produced on a camera film.

Is it also correct to state that the Penrose effect or procedure would not capture a length contraction,

No. It would capture the length contraction of a long thin rod moving parallel to its long axis. The apparent length of the rod would be changing in successive images, but the one when both ends of the rod are exactly the same distance from the camera lens would show the length contracted length. For the exceptional case of a sphere, the length contraction is hidden by the apparent rotation.

and is that simply because by definition the length contraction posited in relativity theory is not the one described and measured by the Penrose situation/procedure? Thanks again for your help.

Yes, they are two different things. If the leading end of the rod is opposite the lens when the photograph is taken, the light from the trailing edge of the rod must have left much earlier and this makes the rod appear longer on the image.

If the trailing edge of the rod is directly opposite the lens when the photo is taken, then the light from the leading edge must have left much earlier and gives the optical impression of the rod being much shorter.

Length contraction on the other hand is the calculated difference between the positions of the leading and trailing edge, when they are measured simultaneously. This length is constant (for constant velocity) independent of whether the rod is approaching or receding from the observer.

 

[choran]

Last question: Are you saying that Penrose describes a type of relativistic effect, but not the one normally alluded to when people speak of "length contraction"?
Thanks so much.

 

[yuiop]

Last question: Are you saying that Penrose describes a type of relativistic effect, but not the one normally alluded to when people speak of "length contraction"?
Thanks so much.

Yes. Your welcome ;)

P.S. I should probably add that the examples of 'physical' length contraction I gave in post #63 both involve acceleration. The Lorentz transformations usually relate to observers and objects moving with purely inertial motion and then the observed measurements are observer dependent and reciprocal and no tangible physical effects occur purely as a result of transforming reference frames.

 

[harrylin]

It is not a change in an observed phenomenon[..]
Again, length contraction isn't about changes in length, it is about disagreement between frames.

The term "length contraction" has two different meanings; one meaning relates to a reduction in a moving object's or system's equilibrium length according to a system in which that object or system was in rest before. This was also how Einstein used it in 1905: "let a constant velocity v be imparted in the direction of the increasing x of the other stationary system".
I illustrated that with my calculation example and Yuiop next illustrated it as follows:

[..] I think the best demonstration of the physicality of length contraction is in the Ehrenfest paradox, where the length contraction of the outside edges of a rotating object causes real stresses that would eventually tear the the object apart if the radius was not permitted to alter as the rotational speed varied. The next best demonstration is Bell's rockets paradox, where a string of fixed length (in one reference frame) breaks due to length contraction[..].

Just two side notes:
- Ehrenfest: real stresses would not tear a rotating object apart due to length contraction (=inward) but due to inertia (=outward).
- Bell: the change of stress-free length plays a role according to all inertial reference systems .

 

[ghwellsjr]

Penrose-Terrell rotation is a purely optical effect. A sphere does not appear length contracted due to the rotation effect and quite a lot people give this as a proof that length contraction is not a physical phenomena. However the length contraction of a long rectangular object is not totally obscured by the PT rotation and can in principle be photographed.

If each photon that lands on the film of a Penrose-Terrell camera had a time stamp with its time of emission, it would be seen that the pixels that make up the photograph would have a wide variety of time stamps. If we took a series of photographs and used a computer to assemble an image made of pixels with exactly the same time stamp, then we would have an image complete with length contraction (and no rotation).

If these time stamps originate from the moving object, which I presume you mean by "time of emission", then I would assume that they have been synchronized according to the rest frame of that moving object which will result in measurements of the Proper Time and Proper Length of the object.

If you want to be able to measure Length Contraction, then you might be able to do this with a strobe lamp with time stamped photons that is colocated with the camera. The camera would then record reflections with the time stamps for the round-trip timings of the light. This will employ the radar method of establishing relativistic distances to points on moving objects and from this you can determine the lengths of objects according to the frame of the strobe/camera. I'm sure this would work for inline motions and I think it will work for lateral motions.

 

[stevendaryl]

The term "length contraction" has two different meanings; one meaning relates to a reduction in a moving object's or system's equilibrium length according to a system in which that object or system was in rest before. This was also how Einstein used it in 1905: "let a constant velocity v be imparted in the direction of the increasing x of the other stationary system".

Yeah, there are two "length contraction" effects, one having to do with the changes in the measured equilibrium length of an object that is set in motion, and the second having to do with a comparison of distances in two different inertial coordinate systems.

There are similarly two "time dilation" effects: the changes in the measured rate of a clock that is set in motion, and the second having to do with a comparison of elapsed times in two different inertial coordinate systems.

Of course, these pairs of effects are closely related:

• From the assumption that clocks and rods undergo time dilation and length contraction when set into motion, one can show that a coordinate system based on those moving clocks and rods will be related to the original coordinate system through the Lorentz transformations.
• From the assumption that the forces governing rates of clocks and lengths of objects are Lorentz-invariant, one can derive that they must undergo time dilation and length contraction.