Rest Length, Coordinate Length, and an argument for True Length

[JesseM]

JesseM,

Lorentz's LET assumes apriori that an aether exists, that it does not move, and that all motion is relative to it as a master reference. Also, that light moves at c only wrt this aether frame. Einstein's SR requires that no frame is preferred even if an aether does exist, and light moves invariantly at c per each and all.

In this thread, it was mentioned that LET and SR are indistinguishable by measurement, because they possesses the very same transformations. Some readers will assume the one theory is as good as the other. Are the following true wrt the LET theory ...

If 2 clocks are synchronised by the Einstein/Poincare sync method, they are not in true synchronisation per Lorentz unless they are at rest with the aether. It doesn't matter what any other frame thinks.

Yes, in a LET there is such a thing as absolute simultaneity, and it corresponds to the definition of simultaneity in the aether frame, not in other frames.

If 2 events occur, they are simultaneous only if deemed such per the aether frame's POV. It doesn't matter what any other frame thinks.

In an absolute sense yes, although different frames can still have their own definitions of coordinate simultaneity which differ from absolute simultaneity.

Tau is local time, which is not true time. True time is determined only by synchronised clocks at rest in the aether.

Yes, in the LT there is such a thing as absolute time.

One question ... how is the principle of relativity upheld under LET, given a master frame?

The principle of relativity deals only with the measurable laws of physics, not with absolute metaphysical truths. In LET (at least the version I was talking about) there is absolutely no experimental way to determine which frame is the aether frame, because the laws of physics obey the same equations in the coordinates of each frame (the equations are Lorentz-invariant, meaning if you know the equations in one frame and then transform into a different frame, you get back the same equations). This implies that if you have any experimental apparatus and you record the results in terms of the coordinates of the apparatus rest frame, the results will be the same regardless of which frame the apparatus happens to be at rest in (so if you are in a windowless rocket, there's no experiment you can do that will give a different result depending on whether the rocket is at rest relative to the aether frame or moving at some large constant velocity relative to the aether frame).

 

[GrayGhost]

Is the following true wrt the LET theory? ...

Tau is local time, which is not true time. True time is determined only by synchronised clocks at rest in the aether.

Yes, in the LT there is such a thing as absolute time.

Just to clarify ... you meant LET, not LT, yes?

GrayGhost

 

[GrayGhost]

The principle of relativity deals only with the measurable laws of physics, not with absolute metaphysical truths. In LET (at least the version I was talking about) there is absolutely no experimental way to determine which frame is the aether frame, because the laws of physics obey the same equations in the coordinates of each frame (the equations are Lorentz-invariant, meaning if you know the equations in one frame and then transform into a different frame, you get back the same equations). This implies that if you have any experimental apparatus and you record the results in terms of the coordinates of the apparatus rest frame, the results will be the same regardless of which frame the apparatus happens to be at rest in (so if you are in a windowless rocket, there's no experiment you can do that will give a different result depending on whether the rocket is at rest relative to the aether frame or moving at some large constant velocity relative to the aether frame).

Interesting. That's what I've read, but I've always had a hard time believing that. I'd expect the kinematics to be invariant under rotation, but I was never so sure about the laws of force. For example ...

Let's say a weighing scale with dbl platform sits balanced atop a moving train, one platform fwd of the other. Two identical weights fall out of the sky vertically downward striking the center of each platform and simultaneously per the train passengers. One would imagine that train passengers wouldn't see the scales tip. However, spectators at rest in the aether frame witness what is real. Per them, the weights do not strike the platforms simultaneously, but rather one after the other. Since their perspective is the only real perspective, should not the scale tip per them, and thus per all?

GrayGhost

 

[ghwellsjr]

JesseM,

Lorentz's LET assumes apriori that an aether exists, that it does not move, and that all motion is relative to it as a master reference. Also, that light moves at c only wrt this aether frame. Einstein's SR requires that no frame is preferred even if an aether does exist, and light moves invariantly at c per each and all.

In this thread, it was mentioned that LET and SR are indistinguishable by measurement, because they possesses the very same transformations. Some readers will assume the one theory is as good as the other. Are the following true wrt the LET theory ...

If 2 clocks are synchronised by the Einstein/Poincare sync method, they are not in true synchronisation per Lorentz unless they are at rest with the aether. It doesn't matter what any other frame thinks.

If 2 events occur, they are simultaneous only if deemed such per the aether frame's POV. It doesn't matter what any other frame thinks.

Tau is local time, which is not true time. True time is determined only by synchronised clocks at rest in the aether.​

One question ... how is the principle of relativity upheld under LET, given a master frame?

GrayGhost

In SR, you pick anyone arbitrary inertial frame to describe and analyze your entire scenario. In LET, you also pick one inertial frame to describe and analyze your entire scenario, it's just that you treat it as a preferred frame. Oh, and by the way, no one knows where this frame is but LET assumes that it exists.

So, prior to Einstein, everyone assumed that we must always be in motion relative to the one true preferred absolute ether rest frame (due to the constant acceleration of the surface of the earth) and so we are always experiencing length contraction and time dilation. However, in the ether rest frame, there is no time dilation or length contraction and only in this frame is the speed of light a constant in all directions. It exhibits the absolute truth about all of physics, even though there is no way to identify it.

After Einstein, the issue of where the absolute ether rest frame was became a moot point because Einstein said that you could treat any inertial frame as if it were the absolute ether rest frame. Now, if we pick one in which we are at rest, we will not be experiencing length contraction or time dilation and the speed of light is a constant in all directions and all of physics can be treated as absolutes.

 

[GrayGhost]

In SR, you pick anyone arbitrary inertial frame to describe and analyze your entire scenario. In LET, you also pick one inertial frame to describe and analyze your entire scenario, it's just that you treat it as a preferred frame.

Well, I understand how SR works. But wrt LET, what you say here raises another question ...

What's the difference between any frame being able to be preferred, versus no frame being preferred?​

I mean, the same LTs are used, and presumedly the principle of relativity is upheld.

GrayGhost

 

[GregAshmore]

Greg, I'm interested in your response to JesseM's observation that you can't have your true rod definition both ways, i.e., your proper time picture and your "horizontal" rest system view. Below are sketches illustrating the situation. The left just shows a rest system and a moving system with calibration curves for proper times and proper distances (the hyperbolas are not sketched accurately, but they should convey the point). The two sketches on the right present your two different representations of the "true" rod (represented with red curves) that you've mentioned.

I'm sorry, bobc, but I must stick by my resolve not to get into this question in this thread. I have saved your post and sketch to my hard drive for later consideration.

I will observe that the matter is not cut and dry. Born, for example, says that the length of a rod in any given frame is merely a matter of perspective, and does not involve any physical change in the rod itself. Yet a few pages later he says that the atoms in a clock vibrate at a slower pace, and indeed life itself proceeds at a slower pace, for the younger twin in the twin paradox. Why would the physical characteristics of an object be changed with respect to time, but not with respect to length? I don't have an answer; I'm just asking.

btw, my use of the word "horizontal" was less than optimal in that sentence. The point was that the line of simultaneity in some other frame is not parallel to the X axis in the rod's rest frame, and therefore is not the rod.

 

[GregAshmore]

The quote you mention was not an attempt to get into a theological debate at all, I thought it was pretty obvious I was merely making an analogy between some of your circular arguments and the circularity of the arguments of certain fundamentalists who think they can use quotes in the Bible (such as the one mentioned here which I have seen some fundamentalists point to, 'All Scripture is God-breathed and is useful for teaching, rebuking, correcting and training in righteousness') to justify the truth of the Bible itself. I wasn't trying to say anything about whether anything in the Bible is in fact right or wrong, just making the point that you can't use circular reasoning to prove it's true. Whatever your opinion of the Bible, hopefully you don't actually think that a single quote in the Bible saying "All Scripture is God-breathed" is by itself enough to prove beyond all doubt that everything in the Bible is true!

My study of relativity is a subset of a larger quest. I spent roughly fifteen years considering the truth of the Bible. You can read my thoughts on the matter http://www.how-do-i-know-its-true.net/", if you wish. (Be forewarned that the "science" section of the "published text" has many problems; problems which I am attempting to clear up by submitting my ideas for criticism on this forum. The entire section will be rewritten.)

I assumed that regardless of your religious beliefs you would understand such a basic point about how rational argument works, and that maybe this would get you to look more carefully at your arguments about "true length" and see how there might be an element of circularity there too (for example, if you start out by defining the "true length" as the rest length, then just by definition it will be true that "the closer one gets to light speed, the greater the error in the measurement", but it would be totally circular to use that to try to prove that there are non-aesthetic reasons to say the "true length" should be defined as the rest length as opposed to the length in some other frame, which is what you seemed to do when you said "I don't see it as a matter of aesthetics. As a practical matter, the closer one gets to light speed, the greater the error in the measurement.")

No, I meant as a practical matter, not as a matter of aesthetics. The measurement error, which is fixed, becomes more significant as the object measured approaches light speed. So, for example, if one wants to know the rest length of a rod, the uncertainty increases to near 100% as the object approaches light speed. That is why a frame at 0.99c is not as good a reference frame (for determining length) as the rest frame.

The rationality of my argument for true length is based on the observation that the rod is a line on the spacetime diagram, drawn parallel to the X axis of the rod's rest frame. There is no circularity in the argument. Neither is the argument based on an arbitrary aesthetic. The rod is a line, not a parallelogram, because time and distance are not the same thing.

 

[GrayGhost]

I will observe that the matter is not cut and dry. Born, for example, says that the length of a rod in any given frame is merely a matter of perspective, and does not involve any physical change in the rod itself. Yet a few pages later he says that the atoms in a clock vibrate at a slower pace, and indeed life itself proceeds at a slower pace, for the younger twin in the twin paradox. Why would the physical characteristics of an object be changed with respect to time, but not with respect to length? I don't have an answer; I'm just asking.

GregAshmore,

When Born says "life itself proceeds at a slower pace, for the younger twin", what he meant is that "in collective over the entire roundtrip, one twin ages less than the other".

Wrt your question, here's how I'd state it ...

Twin B ages less than the all-inertial twin A, wrt the roundtrip interval. This is required per SR, since moving clocks must tick slower per any inertial POV. Both twins must agree as to who ages less, or the theory is rediculous. Therefore, twin B must experience relativistic effects that twin A does not, and its during his proper acceleration that he does so. One of these effects is this ... twin B can record twin A's clock to tick faster than his own. There's a reason for this, one which I doubt you will like, yet its true. The net result is that twin A ages more than twin B collectively, from either POV. It turns out that SR predicts this, even though it was originally defined for all inertial scenarios. IMO it's not a topic you should consider disecting until you work out the all inertial case first, because it is much more complex and likely would cloud your progress here. That said, that's why twin B ages less than twin A, and how both can agree.

Upon twin B's return to earth, the reason time differentials exist while length contractions do not is this ...

Bodily length contractions are in fact witnessed by both twins before twin B's return. However, per the classic twins scenario, when twin B arrives back on Earth for clock comparison, he first decelerates to the twin A frame. Since they are at rest with each other, there can be no bodily length contractions, because their relative v = 0. So the length contractions that existed prior, no longer exist on reunion. Also, clock "rate" differentials no longer exist after return, and for the same reason. However the differential in "proper time experienced" (ie relative aging) is always captured, because the time readout (and date) of any clock is the result of its own ticking over the prior period, ie over the defined interval. So the accrued proper-time of either clock is not lost, and the clocks may be compared for relative aging.

GrayGhost

 

[Dale]

However, spectators at rest in the aether frame witness what is real. Per them, the weights do not strike the platforms simultaneously, but rather one after the other. Since their perspective is the only real perspective, should not the scale tip per them

You are neglecting the finite speed of sound in the device.

 

[bobc2]

bobc2, why do you have the yellow line labeled "now"? That seems to be a calibration curve, it's definitely not a surface of simultaneity in any inertial frame. My point about proper time wasn't that this was an alternative way of defining simultaneity to the frame-dependent version, it was that talking about "one instant of the rod's proper time" doesn't specify any definition of simultaneity, not along a calibration curve or anything else, since proper time is only defined in terms of the difference in proper time between two events on the worldline of a single point particle, there's no meaningful answer to the question of which pair of events on two different worldlines (like the worldlines of two ends of a rod) occur at the "same proper time".

I should have explained that. I was creating a straw man ficticious proper time "simultaneity" in an attempt to represent an implication of Greg's proper time beam. He seemed to be suggesting that there should be a beam for which the proper time was the same from one end of the beam to the other--unwittingly implying some kind of proper time simultaneity. You correctly pointed out that each point along the beam has its own world line and its own proper time. That of course gives you a different 3-D beam object than that of the rest system.

 

[ghwellsjr]

In SR, you pick anyone arbitrary inertial frame to describe and analyze your entire scenario. In LET, you also pick one inertial frame to describe and analyze your entire scenario, it's just that you treat it as a preferred frame.

Well, I understand how SR works. But wrt LET, what you say here raises another question ...

What's the difference between any frame being able to be preferred, versus no frame being preferred?​

I mean, the same LTs are used, and presumedly the principle of relativity is upheld.

GrayGhost

The only difference between SR and LET is a philosophical one. SR does not concern itself with the issue of whether or not ether exists. It doesn't matter in SR. LET claims that an ether does exist although it cannot be identified.

But your question: "What's the difference between any frame being able to be preferred, versus no frame being preferred?" implies that LET adherents would be content to pick anyone frame and consider it to be the one and only ether rest frame. They would not. They really believed that there was an ether at rest and they were always moving through it. Therefore, they would never pick their own rest frame as the ether rest frame, that wouldn't make sense to them. Even though they could never identify the ether rest frame, they believed they could identify frames that were not the ether rest frame and certainly they would not keep changing which frame was the ether rest frame like you have to do on the surface of the earth.

So as a practical matter, when they picked their own rest frame as one in which to analyze science, they were always aware that it was an artifact that they could not detect length contraction or time dilation, because, of course their rulers and clocks were similarly contracted and dilated, but they really believed that they were contracted and dilated.

And they never considered that time and distance were relative. They firmly believed that the universe had a single absolute time running it and a single set of space co-ordinates in which it functioned and in which the ether was at rest.

So, although all the principles of relativity are upheld in LET, they are considered to be artifacts whereas in SR, the concept of an ether is considered to be an artifact. The choice between the two is a philosophical one, either one will work identically.

EDIT: By the way, I gave a fuller presentation of these ideas on this post:

https://www.physicsforums.com/showpost.php?p=3083997&postcount=33

 

[JesseM]

My study of relativity is a subset of a larger quest. I spent roughly fifteen years considering the truth of the Bible.

I'm really not interested in getting into that, I was just making a point about circular reasoning. Assuming you agree that it's a circular argument to prove the truth of the Bible by appealing to a single line in the Bible asserting its own truth (if you disagree and think that's not circular reasoning, be sure and tell me!), then there's no need to discuss anything further about the Bible, I was only bringing this up as an example of circular reasoning as an analogy for what seem to be circular reasoning in your own arguments.

No, I meant as a practical matter, not as a matter of aesthetics.

So you are backtracking from your statement that it's just a matter of semantics, i.e. just a matter of which definitions we find more elegant (an aesthetic matter).

The measurement error, which is fixed, becomes more significant as the object measured approaches light speed.

That seems like circular reasoning again, the measurement in a frame where the rod is moving at high speed can only be called an "error" if you presuppose from the start that the measurement in the rest frame is the 'true' value. If on the other hand you presuppose that the "true" value is the value in the frame F where the rod is moving at 0.99c, then the "error" becomes more significant as you look at frames whose velocity relative to frame F approach light speed (so it's very significant for the rod's rest frame, which is moving at 0.99c relative to F). What we define as "error" depends on what we define as true, so you can't prove that there are non-aesthetic reasons to treat the rest frame's measurements as "true" by using a definition of "error" which assumes from the start what you are trying to prove, namely that the rest frame's measurements are the "true" ones.

So, for example, if one wants to know the rest length of a rod, the uncertainty increases to near 100% as the object approaches light speed.

Why would the "uncertainty" increase? If you know its length in the frame where the rod is moving, and you know its speed in that frame, it's just a matter of using the Lorentz transformation to get its rest length. I suppose if there is uncertainty in your measurements of length or speed then this will translate to uncertainty in the measurement of rest length, but it's also true that if you're at rest relative to the rod and you measure its rest length, then you want to know its length in the frame of an observer moving at high velocity relative to you, any uncertainty in your measurement of the rod's length or in your measurement of the observer's velocity will translate to uncertainty in your estimate of the rod's length in that observer's frame.

The rationality of my argument for true length is based on the observation that the rod is a line on the spacetime diagram, drawn parallel to the X axis of the rod's rest frame. There is no circularity in the argument.

First of all, when you say "the rod" you really seem to mean "the rod at a single instant", most physicists would refer to the entire 4-dimensional world-tube as "the rod", not just a 3-dimensional cross-section like you seem to be doing. Second, here you seem to be defining "the rod" as the 3-dimensional cross-section taken using the rest frame's definition of simultaneity, so to use that to try to prove the rest frame has a "true view" of "the rod" is indeed totally circular. Why can't I define "the rod" to be the 3-dimensional cross-section taken using a surface of simultaneity in the frame F where the rod is moving at 0.99c, and therefore say that only when we draw a spacetime diagram from the perspective of frame F will "the rod" be a horizontal line parallel to the x-axis? For that matter, why can't I just say there is no unique 3D cross-section that qualifies as "the rod", that each frame has there own different definition of "the rod" at a single instant? You really seem to completely fail to understand what a circular argument is, or else you are completely blind to the very obvious circularity in your own arguments!

 

[JesseM]

Just to clarify ... you meant LET, not LT, yes?

GrayGhost

Yeah sorry, meant to write LET there.

 

[JesseM]

Well, I understand how SR works. But wrt LET, what you say here raises another question ...

What's the difference between any frame being able to be preferred, versus no frame being preferred?​

I mean, the same LTs are used, and presumedly the principle of relativity is upheld.

GrayGhost

I think it would be helpful to distinguish between a physically preferred frame (one where the equations of the laws of physics take a different, 'special' form than they take in other frames) and a "metaphysically" preferred frame (whose judgments are deemed 'true' in some absolute metaphysical sense). In the type of LET theory we have been talking about, the aether frame is not physically preferred, it is only preferred in that metaphysical sense.

 

[GrayGhost]

So as a practical matter, when they picked their own rest frame as one in which to analyze science, they were always aware that it was an artifact that they could not detect length contraction or time dilation, because, of course their rulers and clocks were similarly contracted and dilated, but they really believed that they were contracted and dilated.

Thanx, I'll look at your hyperlink reference.

Yes, I have read about that. Per LET theory, moving contracted rulers cannot record contracted lengths because it itself is length contracted. Same for slower clocks measuring contracted durations.

Per LET ... per observers moving thru the aether, isn't the measured 2-way speed of light always c? Is this measurment correct by luck too?

Per LET ... would it be fair to say that the luminally moving observer must witness (eyeball) his own length contractions, even though his measuring apparatus cannot measure them? Or at least, he would have very blurred vision when looking in a direction orthogonal wrt the axis of motion. Yeh or neh?​

GrayGhost

 

[JesseM]

Thanx, I'll look at your hyperlink reference.

Yes, I have read about that. Per LET theory, moving contracted rulers cannot record contracted lengths because it itself is length contracted. Same for slower clocks measuring contracted durations.

Per LET ... per observers moving thru the aether, isn't the measured 2-way speed of light always c? Is this measurment correct by luck too?

Per LET ... would it be fair to say that the luminally moving observer must witness (eyeball) his own length contractions, even though his measuring apparatus cannot measure them? Or at least, he would have very blurred vision when looking in a direction orthogonal wrt the axis of motion. Yeh or neh?​

GrayGhost

The laws of electromagnetism are Lorentz-invariant, so even in LET they work exactly the same in the moving frame as they do in the aether frame, so there won't be any visually observable differences (for some explanation of how specific electromagnetic phenomena make sense when viewed from the perspective of different frames, see this page). Again, as long as all the fundamental laws of physics are Lorentz-invariant, that guarantees mathematically that there can be no empirical way to distinguish the aether frame from any other frame.

 

[GrayGhost]

I think it would be helpful to distinguish between a physically preferred frame (one where the equations of the laws of physics take a different, 'special' form than they take in other frames) and a "metaphysically" preferred frame (whose judgments are deemed 'true' in some absolute metaphysical sense). In the type of LET theory we have been talking about, the aether frame is not physically preferred, it is only preferred in that metaphysical sense.

OK JesseM. You say there are multiple LET theories. Is the type you are talking here, Lorentz's own interpretation, or some subsequent version that later stemmed from his own?

I was wondering whether an observer moving luminally could discern (in any way) whether SR was the correct theory, versus (this) LET? IOWs, for example, would you see your own length contractions even though your ruler cannot measure them?

GrayGhost

 

[JesseM]

OK JesseM. You say there are multiple LET theories. Is the type you are talking here, Lorentz's own interpretation, or some subsequent version that later stemmed from his own?

This is a later version, one which assumes relativity is correct in that all fundamental laws of physics obey Lorentz-invariant equations (Lorentz knew this was true of the laws of electromagnetism, but he didn't suggest this was a general principle that applied to all laws--if he had, he would be credited as the originator of special relativity, not Einstein).

I was wondering whether an observer moving luminally could discern (in any way) whether SR was the correct theory, versus (this) LET? IOWs, for example, would you see your own length contractions even though your ruler cannot measure them?

Not if the laws governing matter are also Lorentz-invariant, as they are in quantum field theory (and of course the laws governing bonds between molecules are just electromagnetic laws). If there were some laws governing matter that weren't Lorentz-invariant, it might be possible to construct a type of ruler that didn't contract when moving relative to the aether, or clock that didn't slow down.

 

[GrayGhost]

No, I meant as a practical matter, not as a matter of aesthetics. The measurement error, which is fixed, becomes more significant as the object measured approaches light speed. So, for example, if one wants to know the rest length of a rod, the uncertainty increases to near 100% as the object approaches light speed. That is why a frame at 0.99c is not as good a reference frame (for determining length) as the rest frame.

So, this all comes down to your assumption that rest length is the only true length, and your argument is based upon that apriori assumption.

Greg, let me ask you this though ...

Lasers (attached to a processing system) could be set up to fire along axes orthogonal to the direction of motion of some luminally moving vessel of known rest length (ie proper length). The passing vessel breaks the laser beams, one after the other. Per your own illustration, the lasing system should be able to determine the vessels' moving length. Given the light sinals reveal the vessel's moving length to be less than its rest length, how can you then assert that this length measurment is not real or true?

Your likely answer ... because not's not the way body's measure in everyday experience.

However, what if one could fly about luminally everyday? Then relativistic effects would become everyday experience, and folks would say "of course its contracted, because its moving". Of course, no one ever expects that a body changes in length in-and-of-itself.

GrayGhost

 

[DrGreg]

GregAshmore, how would you determine what you call the "true length" of an elastic band that is in the process of being stretched, i.e. the two ends are moving away from each other, so there is no frame in which all parts of the band are at rest, and so the "rest length" is undefined?

 

[GregAshmore]

So you are backtracking from your statement that it's just a matter of semantics, i.e. just a matter of which definitions we find more elegant (an aesthetic matter).

I don't want to get into an argument about the definition of "semantics", or of "aesthetics". I acknowledged at the end of the OP that the measured length in any frame will be the same, regardless of the interpretation one assigns to the measurement. Neither my interpretation of "rest length as the one true length" nor your interpretation of "rest length as no more special than the length measured in any other frame" can be verified or falsified by experiment.

That seems like circular reasoning again.

No not circular, I was referring to the uncertainty in measurement.

Why would the "uncertainty" increase? If you know its length in the frame where the rod is moving, and you know its speed in that frame, it's just a matter of using the Lorentz transformation to get its rest length. I suppose if there is uncertainty in your measurements of length or speed then this will translate to uncertainty in the measurement of rest length,
[\QUOTE]
Exactly.

but it's also true that if you're at rest relative to the rod and you measure its rest length, then you want to know its length in the frame of an observer moving at high velocity relative to you, any uncertainty in your measurement of the rod's length or in your measurement of the observer's velocity will translate to uncertainty in your estimate of the rod's length in that observer's frame.

Yes. Which means that the best way to refer to the rod's length, and to measure it, is while the rod is at rest. That does not mean that the rest length is "true"; it just means that the rest length has the least measurement uncertainty associated with it.

First of all, when you say "the rod" you really seem to mean "the rod at a single instant", most physicists would refer to the entire 4-dimensional world-tube as "the rod", not just a 3-dimensional cross-section like you seem to be doing.

Yes. I take this position because time and distance are not the same thing. That distinction is rational, though not popular.

Second, here you seem to be defining "the rod" as the 3-dimensional cross-section taken using the rest frame's definition of simultaneity, so to use that to try to prove the rest frame has a "true view" of "the rod" is indeed totally circular.

In the rod's rest frame, the time is the same at all points on the rod. This condition is unique to the rest frame. I argue that because of this uniqueness, the length measured in the rest frame is "true" (or "special", or "preferred", or in some sense "absolute"). I then provide an explanation for the "untrue" (or "compressed", or "distorted") view of length as measured in other frames. There is nothing circular in the argument.

For that matter, why can't I just say there is no unique 3D cross-section that qualifies as "the rod", that each frame has there own different definition of "the rod" at a single instant?

Again, the rest frame of the rod is unique. You are free to define the rod's length any way you wish. I will disagree, on a rational and non-circular basis; that is all.

You really seem to completely fail to understand what a circular argument is, or else you are completely blind to the very obvious circularity in your own arguments!

I enjoy a good discussion, and I think I've shown over several threads that I am able to take correction. But I'm getting tired of being yelled at.

 

[GregAshmore]

GregAshmore,

When Born says "life itself proceeds at a slower pace, for the younger twin", what he meant is that "in collective over the entire roundtrip, one twin ages less than the other".

Wrt your question, here's how I'd state it ...

Twin B ages less than the all-inertial twin A, wrt the roundtrip interval. This is required per SR, since moving clocks must tick slower per any inertial POV. Both twins must agree as to who ages less, or the theory is rediculous. Therefore, twin B must experience relativistic effects that twin A does not, and its during his proper acceleration that he does so. One of these effects is this ... twin B can record twin A's clock to tick faster than his own. There's a reason for this, one which I doubt you will like, yet its true. The net result is that twin A ages more than twin B collectively, from either POV. It turns out that SR predicts this, even though it was originally defined for all inertial scenarios. IMO it's not a topic you should consider disecting until you work out the all inertial case first, because it is much more complex and likely would cloud your progress here. That said, that's why twin B ages less than twin A, and how both can agree.

Upon twin B's return to earth, the reason time differentials exist while length contractions do not is this ...

Bodily length contractions are in fact witnessed by both twins before twin B's return. However, per the classic twins scenario, when twin B arrives back on Earth for clock comparison, he first decelerates to the twin A frame. Since they are at rest with each other, there can be no bodily length contractions, because their relative v = 0. So the length contractions that existed prior, no longer exist on reunion. Also, clock "rate" differentials no longer exist after return, and for the same reason. However the differential in "proper time experienced" (ie relative aging) is always captured, because the time readout (and date) of any clock is the result of its own ticking over the prior period, ie over the defined interval. So the accrued proper-time of either clock is not lost, and the clocks may be compared for relative aging.

GrayGhost

The point I was trying to make is that time and distance do not behave the same way in SR. The fact that the time difference persists while the length difference does not (quite aside from how it happens "physically") underscores that difference.

 

[JesseM]

No not circular, I was referring to the uncertainty in measurement.

Why do you think there is more "uncertainty in measurement" about a moving rod's length than a rod's rest length? It would depend on your precise measurement techniques, this wouldn't be automatically true regardless of how you perform the measurements.

Why would the "uncertainty" increase? If you know its length in the frame where the rod is moving, and you know its speed in that frame, it's just a matter of using the Lorentz transformation to get its rest length. I suppose if there is uncertainty in your measurements of length or speed then this will translate to uncertainty in the measurement of rest length,

Exactly.

but it's also true that if you're at rest relative to the rod and you measure its rest length, then you want to know its length in the frame of an observer moving at high velocity relative to you, any uncertainty in your measurement of the rod's length or in your measurement of the observer's velocity will translate to uncertainty in your estimate of the rod's length in that observer's frame.

Yes. Which means that the best way to refer to the rod's length, and to measure it, is while the rod is at rest.

Huh? I just got through saying it can work either way--you may be more certain of the length in the frame where the rod is moving and therefore less certain of the rest length, but you may also be more certain of the rest length and therefore less certain of the moving length. How can you use that symmetry to say "yes, therefore we should use the rest length?" As always, it seems like you aren't really reading what I write carefully and thoughtfully, but are just skimming it, quoting it and then going on to repeat some knee-jerk assertion that I just got through giving a critique of.

Second, here you seem to be defining "the rod" as the 3-dimensional cross-section taken using the rest frame's definition of simultaneity, so to use that to try to prove the rest frame has a "true view" of "the rod" is indeed totally circular.

In the rod's rest frame, the time is the same at all points on the rod.

Sigh. I just explained that it was circular reasoning to define "the rod" as the 3-dimensional cross-section of the rod's 4D world-tube using the rest frame's definition of simultaneity, and then try to use this definition of "the rod" to prove that the rest frame has the "true view" or whatever. Did you completely ignore everything I just said about the fact that you are defining the phrase "the rod" in a circular way that assumes what you are trying to prove? Your ridiculous response, which just ignores the criticism and makes another circular statement about "the rod", suggests the answer is yes.

You also blithely ignored my counterexample, illustrating why your assumptions are circular:

Why can't I define "the rod" to be the 3-dimensional cross-section taken using a surface of simultaneity in the frame F where the rod is moving at 0.99c, and therefore say that only when we draw a spacetime diagram from the perspective of frame F will "the rod" be a horizontal line parallel to the x-axis?

Do you deny that if I define "the rod" in this way, then it follows from my definition that "In frame F (the one where the rod is moving at 0.99c), the time is the same at all points on the rod"? And likewise if we adopt this definition of "the rod", then the rod's rest frame is not seeing "the rod" at a single instant, but rather a collection of points on "the rod" at different instants? Please don't bother responding unless you have actually thought about this alternate definition of "the rod" and can explain in a non-circular way why anything other than aesthetic preferences should lead us to see your definition as more valid than this one.

This condition is unique to the rest frame.

Only by the circular reasoning that involves defining "the rod" in reference to the rest frame's definition of simultaneity. If we define "the rod" in reference to simultaneity in frame F where the rod moves at 0.99c, then this condition is unique to frame F.

I enjoy a good discussion, and I think I've shown over several threads that I am able to take correction. But I'm getting tired of being yelled at.

Well, I'm getting tired of making a critique of your argument, only to have you completely ignore it and then blithely repeat the exact same type of assertion I just critiqued without explaining anything about why the critique was wrong or showing any evidence that you actually thought about it or understood it.

 

[bobc2]

GregAshmore,...Therefore, twin B must experience relativistic effects that twin A does not, and its during his proper acceleration that he does so...

GrayGhost

GrayGhost, I hope I'm not sounding argumentative. I just wanted to point out an alternate interpretation for accounting for the difference in aging. To get the proper emphasis, I'm going to do a sketch that's a little different than what you normally see in spacetime diagram renditions for the twin paradox.

For the first part of the journey I choose a rest coordinate system that is not on the earth, but rather situated such that each twin is moving in opposite directions from the rest system with the same speed (twin A is on the Earth moving to the left--earth is actually represented as the red rocket in my sketch, and twin B is moving to the right in a blue rocket). This symmetric spacetime diagram for the initial leg of the trip allows us to have the same graphical scale for both red and blue rockets. When they both reach their respective position number 9 we have the usual time dilation situation--each sees the other's clock running slower, but the proper times are the same for red and blue at their respective number 9 positions. Thus, you can see the proper times are the same for red and blue on the first leg of the trip. So, now we just deal with the return trip for B.

When twin B begins his return trip, we no longer have a symmetric spacetime diagram. B must move much faster to catch up with Red. So, I start a new origin for B and measure his proper time using the proper time calibration curves (a new boosted rest system, same hyperbolic functions as would be used in the original rest system).

This graphical presentation shows clearly the reason for B's younger age: By traveling much faster than A, he is taking a much shorter path through spacetime than the path of the continued straight line for A. Red reaches his proper position number 17 while blue reaches his cumulative proper time postion 13 (each incremental change in position number corresponds to equal increments in proper time).

While B is decelerating and accelerating, his cross-section view of the red rocket is changing very rapidly, and he is seeing rapid changes in red's clock, but that is not affecting his age significantly. It's the length of his world line through spacetime compared to the length of A's worldline through spacetime that accounts for their difference in age when they meet up again.

 

[GrayGhost]

GrayGhost, I hope I'm not sounding argumentative.

Don't worry about that Bob. You won't offend me even if you want to argue. I like hearing it straight up, and I appreciate your comments.

Make no mistake, the twin who ages the least is the twin who travels the shorter path thru the continuum. For those present at both events, transitioning frames of reference produces a shorter path wrt those who do not. That's the way I see it as well, so we agree there. I agree that that point should always be stated, even if briefly.

Wrt your illustration ... it shows all this just fine. You do not show the BLUE line-of-simultaneity at the moment he completes the turnaround. Per BLUE, during his rapid turnabout, RED's clock will advance wildly from 8 to about 14 in virtually no time at all. So your illustration also supports my comments to Greg as well.

I should qualify the above ... Time does not speed up for RED per RED during BLUE's turnabout. RED merely advances faster along his worldline "per the BLUE POV", because BLUE's sense-of-NOW rotates during his frame transitioning. The further away RED is, the more wild the effect. Nonetheless, whatever the RED clock reads (per LTs) at any moment per BLUE is real, and not illusionary effect. This puts the meaning of "continuum" into perspective. thanx.

GrayGhost

 

[GrayGhost]

The point I was trying to make is that time and distance do not behave the same way in SR. The fact that the time difference persists while the length difference does not (quite aside from how it happens "physically") underscores that difference.

Well kinda, but that's not entirely accurate either. Each twin accrues a duration over his trip, twin B's being less than twin A's. The duration differential is (of course) the aging differential. Technically, the duration is numerically identical to the distance traveled thru 4-space, twin B's pathlength being contracted wrt twin A's pathlength. In this way, the clock readouts not only reveal the contraction of time, but also the contraction of space.

GrayGhost

 

[ghwellsjr]

The point I was trying to make is that time and distance do not behave the same way in SR. The fact that the time difference persists while the length difference does not (quite aside from how it happens "physically") underscores that difference.

But time and distance both persist, you only think they don't because you are making an invalid comparison of a clock to a ruler. Time dilation does not directly affect the time on a clock, it directly affects the tick rate of a clock and then the clock integrates (or counts) the ticks to keep track of elapsed time.

To get similar behavior, we should use a metronome (which does not count ticks) and a ruler. Take them both on a high speed trip, during which the metonome slows down and the ruler contracts, and when we come back to the starting point, the ruler is the same length as one that did not take the trip and the metronome ticks at the same rate as one that did not take the trip.

Now if you want to get similar behavior to a clock, you need an odometer. This will integrate distance traveled just like the clock integrates time. And you could have a speedometer which calculates divides the (contracted) distance traveled by the (dilated) time.

For example, let's suppose that we take a vehicle with a clock, an odometer and a speedometer. We accelerate the vehicle to 0.6c and take it on a round trip for 50 years according to the starting frame. It's speedometer will read 0.6c and from the point of view of an observer that was stationary with the vehicle before it left, the vehicle's speed is also 0.6c. The gamma factor at this speed is 1.25 which means the clock will be running slow by 1/1.25 according to the rest frame. Its lengths along the direction of motion will also be contracted to 1/1.25 of what the observer in the rest frame sees.

So in our example, the vehicle will take 50/1.25 or 40 years to make the complete trip and this is what will be indicated on its clock. Similarly, the distance traveled according to the rest frame is 0.6*50 or 30 light-years. But according to the on-board odometer, it has traveled 24 light-years. And the speedometer will have read 24/40 = 0.6c during the trip.

 

[JesseM]

Now if you want to get similar behavior to a clock, you need an odometer. This will integrate distance traveled just like the clock integrates time. And you could have a speedometer which calculates divides the (contracted) distance traveled by the (dilated) time.

The two are not exactly analogous, since the proper time along a timelike worldline is frame-invariant (and that's the time a clock moving along the worldline would measure), while there is no frame-invariant notion of the distance traveled along a timelike worldline (though along a spacelike worldline there is a frame-invariant proper distance). When you say the odometer integrates "distance traveled", distance of what in what frame? It can't be the distance traveled by the vehicle itself in the vehicle's rest frame, since of course the vehicle is stationary in that frame and doesn't travel at all! To make your comment about the odometer more precise, I guess we could imagine that the vehicle is traveling along some surface (rather than traveling through empty space), and if we draw closely-spaced dots on the surface along the path of the vehicle, then for any two nearby dots on the surface that the vehicle passes in sequence, the odometer will increase by the same amount as the distance between the dots in the vehicle's rest frame as it passes between them (and if the separation between nearby dots is infinitesimal we don't have to worry about the vehicle's velocity relative to the dots changing during the time it's passing between them).

 

[GregAshmore]

As always, it seems like you aren't really reading what I write carefully and thoughtfully, but are just skimming it, quoting it and then going on to repeat some knee-jerk assertion that I just got through giving a critique of.

Or, it could be that you are so sure you are right that you are not listening to me. We'll never get anywhere with this sort of approach. How about we leave off the recriminations and try to figure out why we are not communicating?

I'll try to develop my concept of what "the rod" is from scratch. This will, I believe, demonstrate that my starting point is fully independent of my conclusion.

In defining the rod, I begin with a minimal world. In this world there is only one parameter, distance. There is just one dimension of distance, which is represented in the usual way by an axis, X. By definition, the rod is fully described by its length. Thus, the rod is independent of its X coordinates.

This conception of the rod is completely independent of time, for the simple reason that time does not exist.

If we now introduce time into the world, the rod is not changed; it is still fully described by its length. If we wish to represent the rod on a two dimensional graph, one axis for distance and the other for time, the rod must be drawn parallel to the X axis of the graph, because by definition the rod is defined by its length only. We can draw the rod at various times, but in every case the rod must be represented by a line drawn parallel to the X axis.

By definition then, any line which crosses the X axis cannot be the rod. It must be something else.

 

[bobc2]

Or, it could be that you are so sure you are right that you are not listening to me. We'll never get anywhere with this sort of approach. How about we leave off the recriminations and try to figure out why we are not communicating?

I'll try to develop my concept of what "the rod" is from scratch. This will, I believe, demonstrate that my starting point is fully independent of my conclusion.

In defining the rod, I begin with a minimal world. In this world there is only one parameter, distance. There is just one dimension of distance, which is represented in the usual way by an axis, X. By definition, the rod is fully described by its length. Thus, the rod is independent of its X coordinates.

This conception of the rod is completely independent of time, for the simple reason that time does not exist.

If we now introduce time into the world, the rod is not changed; it is still fully described by its length. If we wish to represent the rod on a two dimensional graph, one axis for distance and the other for time, the rod must be drawn parallel to the X axis of the graph, because by definition the rod is defined by its length only. We can draw the rod at various times, but in every case the rod must be represented by a line drawn parallel to the X axis.

By definition then, any line which crosses the X axis cannot be the rod. It must be something else.

Fascinating point of departure, Greg. Now, what do you have to say about someone else's perception of that same rod (someone moving at relativistic speed with respect to your rod's rest system)? Does the rod in its rest system have more claim to reality than that rod existing in the other coordinate system? Does the length of the rod in the moving system not represent a fundamental property of the rod (as perceived by a moving observer--notwithstanding the practical difficulty of actually observing it directly)?

You seem to want to ascribe something more special beyond what everyone on this thread has acknowledged as a unique length, i.e., its rest length.

By the way, there is of course something special about the world line length of the rod as well, i.e., c x (proper time) = millions of miles long (considering the time at the creation of the rod and the time that it disintegrates). Do you consider that a fundamental property of the rod as well?