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

[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?

 

[bobc2]

.

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.

Greg,

It occurs to me that your description of the situation would be consistent with a concept of the 4-dimensional universe with a 4-dimensional rod existing somewhere in that universe. I'm not trying to propose a cosmology here (and certainly don't have a metric in mind for it), but am just trying to present a picture to see if you identify with it some way.

With this picture I think you could make a case for the length of the rod in the context you seem to be communicating, i.e, a 4-dimensional rod with definite dimensions that are independent of any observers (although an observer would have to be comoving with the rod to be able to observe the actual 4-dimensional "length" (of course a more significant length would be the really long length along X4).

I thought of this when I noticed your mention of "...independent of time."

I'm probably way off base again, but it's the only thing I could imagine that would be consistent with your description. Perhaps you would agree with the picture mathematically but would reject the reality of the 4-dimensional world while retaining the mathematical implication of a "true" rod length (nevertheless, within the context of the picture).

Maybe I've just thrown in too much meaningless double talk here.

 

[Dale]

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.

No. Once you introduce time the rod is characterized by duration as well as length.

 

[JesseM]

Or, it could be that you are so sure you are right that you are not listening to me.

I doubt that's it, because instead of explaining that I misunderstood something you said earlier, in this post you simply introduce a new argument that you hadn't made before. It's also pretty clear that you are not listening to me when you completely ignore the substance of my criticisms as you did in your previous post #81, and are now doing again, failing to address any of the things I said and just making a vague psychological accusation about my being too sure I am right. And I also made a request in that previous post, you either didn't see it because you skimmed my post again without reading carefully, or just chose to ignore it:

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.

If you aren't willing to address this alternate definition of "the rod" and tell me specifically what's wrong with it, then again please don't bother responding at all, I'm only interested in a genuine back-and-forth discussion here.

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.

But you can't just assume that when you "introduce time", the rod is at rest! That is exactly equivalent to assuming "the rod" is a 3D cross-section of the 4D world-tube using the rest frame's definition of simultaneity, and assuming that is just another way of assuming what you are trying to prove, i.e. yet another variation on the same circular argument. If you start with "only space" and a rod of length L aligned parallel to the X-axis in one instant, why shouldn't it be possible that when you "introduce time", you now find that rod of length L is moving at 0.99c along the X axis, so that L is not the rest length but rather the length in frame F where the rod is moving at 0.99c?

 

[phyti]

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.
...

Greg is correct on this.
Upon return by the space traveler, his clock is behind the Earth clock, and he is younger, a permanent change.
Their measurement of distance to the the turn around is the same, i.e.,what it was before he left.
The odometer reading is only a temporary record.

 

[GregAshmore]

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?

I'm working on the assumption that there is one reality which encompasses all coordinate systems, and in that reality there is just one rod. Your question seems to imply that there is a separate reality within each 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)?

I think this question boils down to, "Is perception reality?" In principle I would say no. The OP attempts to explain how the perception of the rod differs from the real rod.

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?

I'm not sure what you mean by c x with reference to proper time. The definition of proper time is the change in time in a frame in which there is no change in x. Can you explain?

 

[GregAshmore]

I doubt that's it, because instead of explaining that I misunderstood something you said earlier, in this post you simply introduce a new argument that you hadn't made before.

No, not a new argument. The OP is based on this conception of the rod.

If you aren't willing to address this alternate definition of "the rod" and tell me specifically what's wrong with it, then again please don't bother responding at all, I'm only interested in a genuine back-and-forth discussion here.

I've been trying to address your proposition. It seems to me that this definition of the rod is fundamentally different than the one I am using, because time is an integral component of it. That's what I meant when I said that time and distance are not the same thing. The rod, for the purposes of this discussion, is entirely defined by distance--its length. (I say, "for the purposes of this discussion", because there are only two parameters in the LT, time and distance.)

But you can't just assume that when you "introduce time", the rod is at rest!

Whether the rod is at rest or not has nothing to do with the definition of the rod. The rod is entirely defined by its length. Movement involves time, which by definition is not a component of the rod. In other words, the rod is unaffected by its motion. Or, more to the point in a discussion of relativity, the rod never moves; it is always at rest.

That is exactly equivalent to assuming "the rod" is a 3D cross-section of the 4D world-tube.

No, it is not, for the reason given above. The 4D world-tube is not the rod; it is the rod plus time.

 

[GregAshmore]

No. Once you introduce time the rod is characterized by duration as well as length.

Well, here is where we disagree. By my definition, the rod exists (or in principle could exist) apart from time. Both definitions are rational.

btw, my definition does not clear up the murky water of "reality". It solves a particular problem in the interpretation of the spacetime diagram. I suspect that if I pursue it to its logical limit, I will run into trouble in some other area.

 

[bobc2]

I'm not sure what you mean by c x with reference to proper time. The definition of proper time is the change in time in a frame in which there is no change in x. Can you explain?

Sorry. That was a typo error. It was intended to be cT (speed of light times rod time duration--time from manufacture of rod until disentigration at the end of its life). I was wondering if you considered it to have a 4th dimension (a static 4-dimensional existence), even without the flow of time?

 

[Dale]

By my definition, the rod exists (or in principle could exist) apart from time.

How so? In your 2D spacetime universe in what way does "the rod exist apart from time"? From your description it seems to me that the number of dimensions in which the rod exists depends on the space, not the rod. Look at your justification for why it exists independent of time: "the rod is completely independent of time, for the simple reason that time does not exist". That justification is a property of the space, not the rod.

The only way you can say that it could exist apart from time is by considering a "toy universe" without time. In any universe with time, in what sense does "the rod exist apart from time"?

 

[bobc2]

How so? In your 2D spacetime universe in what way does "the rod exist apart from time"? ...
...The only way you can say that it could exist apart from time is by considering a "toy universe" without time. In any universe with time, in what sense does "the rod exist apart from time"?

What if Greg prepares a toy universe in his 3-D world with time added? It's like a 16' long 2x4 transparent beam with various bundles of fine fibers (optical fibers maybe?) extending from one end to the other, configured in such a way as to present a geometric causality and having 2-D cross-sections that are consitent with some sort of physics (as you look along the length of the beam with emerging fiber patterns in a continuous sequence of cross-section views). But the 2x4 is just sitting there static in his 3-D space. It exists as a 3-D structure, independent of time as it were. He arranges one collection of nano optical fibers in a configuration that presents itself as a sub-sub miniature 3-D rod inside of his toy universe--in this 3-D configuration it has a rectangular cross-section (maybe 5 nanoinch x 50 nanoinch) extruded along the 3rd dimension, perhaps for a distance along the 3rd dimension of .01 inch (not long compared to the 16' length of his universe.

Now he passes a light sheet (they use them a lot in manufacturing inspection systems these days) along the length of the beam at constant velocity, starting at one end and finishing at the other end. He smiles as he sees a plane of light penetrating his universe beam, lighting up a new cross-section at each new instant (could the excitation of electrons within special fiber groups give rise to consciousness--but I digress). He identifies that with the flow of time. He could even use some nanotechnology to engrave subminiature pictures of clocks spaced along the beam with time readings that correspond to the position along the beam divided by the light sheet velocity. So, now he can tell you the proper time at any point along the beam (which is really his own elapsed time in his own hyperspace 3-D world). His beam just sits there as a 3-D structure, independent of the passing of his simulated flow of time. The rod inside of his toy universe exists with unique cross-section dimensions and an extruded length along the 3rd dimension. Could the long side of a cross-section of the sub-sub-miniature beam be Greg's absolutness of rod length?

He could have several light sheets, each slanted at different angles wrt the length of the beam, all sheets starting together and moving at the same rate along the beam, simulating different observer cross-section views. If his optical fibers have been arranged sufficiently cleverly, he might even have something similar to Lorentz invariance--he's got to be clever enough to produce a pattern that yields groups of transformations with physically interesting invariances.

But, does this picture change the argument in any way? The universe beam maintains the absolute 2"x4"x16' dimensions but still has cross-section views. Likewise for the embedded sub-sub-miniature beam. Does the perpendicular cross-section view of the miniature embedded beam have more claim to a 2-D cross-section reality than the slanted views of that beam? However, all observers correponding to the different light sheet movements could develop an understanding that there existed a 2-D cross-section sub-sub-miniature beam extruded along the 3rd dimension. Or could they? But would they all agree about the "true" length of the beam?

Sitting out here with our birds eye view of it all, do we even agree about the "true" length of that subminiature 2-D beam at some instant of time?

 

[ghwellsjr]

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.
...

Greg is correct on this.
Upon return by the space traveler, his clock is behind the Earth clock, and he is younger, a permanent change.
Their measurement of distance to the the turn around is the same, i.e.,what it was before he left.
The odometer reading is only a temporary record.

Are you saying that an odometer taken on a trip loses its reading after it returns?

 

[JesseM]

No, not a new argument. The OP is based on this conception of the rod.

The OP didn't say anything about considering a single frozen snapshot of the rod with no time like you did in your last post.

I've been trying to address your proposition.

But you haven't explained why, when we "introduce time", we might not find that the rod is moving along the X-axis, and thus that the length L that we saw when we just looked at at a single frozen snapshot was not the rest length, but rather the length in a different frame.

Whether the rod is at rest or not has nothing to do with the definition of the rod. The rod is entirely defined by its length.

Yes, and that length needn't be the rest length. If we take a snapshot of a single instant in frame F, this snapshot includes no time, only 3D spatial extension, and in this snapshot the rod's length is shorter than what we'd see if we took a snapshot of a single instant in the rod's rest frame. You have not given a single non-circular reason why this snapshot in frame F isn't just as valid as the snapshot in the rest frame.

Movement involves time, which by definition is not a component of the rod. In other words, the rod is unaffected by its motion.

A velocity of 0 is every bit as much a "state of motion" as a velocity of 0.99c, both involve considering how the position varies with time (a state of being at rest over time cannot be conflated with the fact that the rod shows no motion if you just take a snapshot of space a single instant and ignore time; in such a timeless snapshot, obviously the rod shows no motion regardless of whether the snapshot was taken from the rod's rest frame or the frame where it moves at 0.99c). If we define the "true length" of "the rod" to be the length in frame F where the rod is moving at 0.99c, then "the rod is unaffected by its motion" just means the true length doesn't change when we pick a frame where the rod has a different state of motion than it does in frame F, like the frame where the rod's position stays the same over time.

That is exactly equivalent to assuming "the rod" is a 3D cross-section of the 4D world-tube.

No, it is not, for the reason given above. The 4D world-tube is not the rod; it is the rod plus time.

Er, I didn't say "the 4D world-tube is the rod", I said you are assuming the rod is a 3D cross-section of that world-tube, i.e. a frozen snapshot that includes only space but no time. Anytime you consider how things are arranged in space in a single frozen snapshot without time, the set of events in that snapshot by definition constitute a 3D cross-section of the whole 4D spacetime.

 

[PAllen]

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).

Since I like ghwellsjr's idea, I'll try to give another definition. I agree there are not invariant ways of defining it. So, 'natural', with big quotes, will have to suffice.

Consider that we are talking about an observer taking a trip (that's what an odometer is all about). Let's specify, further, a round trip. You pick a reference object stationary in your start/end frame. During your journey, you use some standard coordinate convention (e.g. Fermi-normal, allowing inertial and accelerated motion). Your odometer simply integrates total spatial coordinate movement of the reference object in your coordinates.

This captures the idea that when you travel to/from star in a short time (relative to your Earth twin), your odometer will show a short distance as well (when you return).

[Edit: most natural reference object? Your start/end point. ]

 

[GregAshmore]

How so? In your 2D spacetime universe in what way does "the rod exist apart from time"? From your description it seems to me that the number of dimensions in which the rod exists depends on the space, not the rod. Look at your justification for why it exists independent of time: "the rod is completely independent of time, for the simple reason that time does not exist". That justification is a property of the space, not the rod.

I'm having trouble following your logic here. In the "minimal world" scenario, there is no such thing as time. How then can the existence of the rod be dependent on time? Isn't that like saying that the existence of the rod is dependent on unicorns?

The only way you can say that it could exist apart from time is by considering a "toy universe" without time. In any universe with time, in what sense does "the rod exist apart from time"?

The illustration was intended to make clear the idea that the rod in and of itself, being characterized solely by its length, is entirely independent of time. The rod exists in time, but does not "mix with" time. This was in response to the charge that my premise is somehow dependent on my conclusion. If the existence of the rod (which is defined as its length) is not tied to, or affected by time, then there is no circularity in my reasoning.

 

[JesseM]

The illustration was intended to make clear the idea that the rod in and of itself, being characterized solely by its length, is entirely independent of time. The rod exists in time, but does not "mix with" time. This was in response to the charge that my premise is somehow dependent on my conclusion. If the existence of the rod (which is defined as its length) is not tied to, or affected by time, then there is no circularity in my reasoning.

Of course it's circular, because for no good reason you just assume that the rod's "length" in this minimal timeless world is equal to its length in a single moment of the inertial frame where the rod has a velocity of 0. You could just as consistently assume that the length in the timeless snapshot is equal to its length in a single moment of the inertial frame where the rod has a velocity of 0.99c, and thus that the rest frame has a "distorted view" of its "true length".