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

[GregAshmore]

Do you think somehow this is not true in the rest frame? The rest frame's view of the rod at a single instant is actually composed of a bunch of different events on worldlines of different parts of the rod, events which occur at different times in some other frame such as S. Unless you think the rod rest frame's definition of simultaneity is more "true" than any other's, the situation seems to be totally symmetric here, each frame's view of "the rod at a single moment" is composed of a set of events which occur at different moments in the other frame.

I do not accept as fact the sentence in bold. That is, I do not accept that a material object is a composite of an infinite number of separate events, events which just happen to be at the same time in the object's rest frame. I don't know how the assertion could be tested. It fact, I'm completely in the dark as to what kind of events you have in mind.

Someone--DaleSpam or GrayGhost, I think--said that my assertion of true length is a matter of semantics, and can never be more than that. I agree, because (as DaleSpam pointed out months ago) there is no way to experimentally test it. For the same reason, your assertion that the rod is a collection of events is also a matter of semantics.

I'm pretty sure that's why bcrowell believes that I am not accomplishing anything meaningful in this thread. If so, I respectfully disagree. I am not of the opinion that the numbers collected in an experiment are an end in themselves. I want to know what the numbers mean; I want to understand the reality of the world I live in. As GrayGhost has mentioned, many others have felt the same way. In every book on relativity and quantum physics that I have read--perhaps ten in all--the author has spent some time on the subject of reality.

I've concluded that there are (for the moment at least) limits to our ability to understand physical reality. From my perspective, it is meaningful to have a sense of what those limits are.

I appreciate the input from all of you. I do try and learn from it.

I'll be back when I get stumped in GR math.

 

[JesseM]

I do not accept as fact the sentence in bold. That is, I do not accept that a material object is a composite of an infinite number of separate events, events which just happen to be at the same time in the object's rest frame. I don't know how the assertion could be tested. It fact, I'm completely in the dark as to what kind of events you have in mind.

Someone--DaleSpam or GrayGhost, I think--said that my assertion of true length is a matter of semantics, and can never be more than that. I agree, because (as DaleSpam pointed out months ago) there is no way to experimentally test it. For the same reason, your assertion that the rod is a collection of events is also a matter of semantics.

I said "The rest frame's view of the rod at a single instant is actually composed of a bunch of different events", I didn't say that "the rod is a collection of events", I don't even know what that would mean. By the frame's "view" of the rod I just meant the set of points in spacetime (each point is identified by a unique set of space and time coordinates, and is termed an 'event' regardless of whether anything physically interesting is happening at those coordinates) that are occupied by the rod at a single moment in that frame. And in any case, I was just responding to your analogous statement:

[2] The view of the rod from frame S (its coordinate length) is horizontal. Therefore, the view is not one view, but a composite of many views.

If you don't agree that "view of the rod from frame S" just means the set of points in spacetime occupied by the rod at a single moment in S, then you need to define what this phrase means in order for your statement [2] not to be hopelessly vague. I can't really imagine a coherent definition of "view of the rod from frame S" where "the view is not one view, but a composite of many views" would not be just as true in the rest frame as it is in any other frame, unless you just make it true-by-definition by defining "one view" to mean the view of the rod's rest frame so that other frames by definition do not have one view.

 

[John232]

Every book I have read that touched on this topic all explained that the observer using the measuring rod would always measure his rod to stay the same length because the measuring rod itself had contracted.

Say your length is contracted, you measure your ship, it is the same length because your rod is also shorter.

The only problem I see with this is that multiple frames of references would require different amounts of length contraction. But, I have came to terms with the fact that no matter what relativistic observers there are you will always measure your rod at rest with you to be the proper length. So then the different observers at different constant speeds would need to measure different amounts of length contraction since the velocity they are traveling is all different. A third party would see it as one ship as being contracted using his proper length to measure less contraction of another ship.

I think that acceleration could be different. You can prove that a body is accelerating. It can't assume that it is at rest. Light will bend due to its motion. If Einstein was traped in an elevator he could prove that it was accelerating by measuring the curvature of a beam of light, similair to what happens in the presence of gravity.

His light clock in the elevator would become distorted by this curvature and then it would seem that he would also be able to measure the decrease in the clocks speed since he is able to detect the longer path the photon takes in the clock when at the same amount of acceleration. In effect, allowing him to measure the difference of how his light clock measures time. But, at constant speeds this would be impossible.

 

[Dale]

I've concluded that there are (for the moment at least) limits to our ability to understand physical reality.

I would go even further. There are limits to our ability to even define "physical reality", let alone understand it.

 

[GregAshmore]

I said "The rest frame's view of the rod at a single instant is actually composed of a bunch of different events", I didn't say that "the rod is a collection of events", I don't even know what that would mean. By the frame's "view" of the rod I just meant the set of points in spacetime (each point is identified by a unique set of space and time coordinates, and is termed an 'event' regardless of whether anything physically interesting is happening at those coordinates) that are occupied by the rod at a single moment in that frame. And in any case, I was just responding to your analogous statement:

If you don't agree that "view of the rod from frame S" just means the set of points in spacetime occupied by the rod at a single moment in S, then you need to define what this phrase means in order for your statement [2] not to be hopelessly vague. I can't really imagine a coherent definition of "view of the rod from frame S" where "the view is not one view, but a composite of many views" would not be just as true in the rest frame as it is in any other frame, unless you just make it true-by-definition by defining "one view" to mean the view of the rod's rest frame so that other frames by definition do not have one view.

As I understand your position, no observer ever sees the rod itself--all observers see a view of the rod. This is where we disagree. I believe that an observer at rest with the rod sees the rod itself. All other observers see a view of the rod.

The problem with your interpretation is that the definition of "the rod" is hopelessly vague, because no one ever sees the rod. The problem with my interpretation is that the definition of "the view of the rod" is hopelessly vague, because no one can tell the difference between a view of the rod and the rod itself.

I am more comfortable with my interpretation because I can identify the rod itself at all times in the spacetime diagram--it is a line parallel to the X axis of the rod's rest frame. So on paper I am able to distinguish between the one rod and the many views of the rod. In practice--in the lab with measuring instruments--that distinction is not verifiable.

Which leads to DaleSpam's contention that we are unable even to properly define physical reality, let alone understand it.

 

[JesseM]

As I understand your position, no observer ever sees the rod itself--all observers see a view of the rod.

I have no idea what "the rod itself" means, and in fact I have repeatedly objected whenever you use this language--"the rod itself" sounds like some sort of metaphysical absolute, like "the soul" or "God". All that science can deal with are measurable properties of things, which I guess is what you mean by "view", although you ignored my request to define this word. Among these measurable properties are the coordinates of the points in spacetime occupied by the rod at some moment in time, and my argument was just that no matter what frame you use, this set of points will be a set of points at different moments in time in some other frame. So again, I don't see why the rest frame has "one view" while other frames do not, this claim seems totally arbitrary as long as you aren't willing to define "one view". As long as you continue to ignore all requests to define your terminology, I don't think this conversation can really go anywhere. Refusing to define is equivalent to refusing to question or think carefully about one's initial vague intuitions, in my opinion.

 

[pervect]

I don't really have time to read this thread, but I thought I'd say a few things about the philosophy of relativity, in the hopes that they might help.

Pre-relativity, length was taken to be a property of an object that was independent of the observer.

Post-relativity, it was realized that length was not independent of the observer. The usual way of describing this is to say that the length depends on the object and the frame of reference.

The proper length of an object is a property of the object itself and independent of the observer - though it can also be viewed as picking out one particular observer, this isn't really the most powerful view of proper length. If one focuses on things that are independent of the observer in relativity, one comes to the conclusion that the Lorentz Interval between points is independent of the observer. Furthermore, though I don't want to get into a detailed discussion, there is a sense in which the proper length of an object is an example of a Lorentz interval.

While there are many ways to interpret relativity philosophically, one of the easiest ways is to focus on observer-independent quantites, in particular the Lorentz Interval (which includes proper length and proper time as specific examples), just because the Lorentz interval IS observer-independent. Because these quantities are observer-independent, we can say they are going to be the fundamental elements of our philosophical system, or in some sense "real". We will calculate observer-dependent quantites when necessary if we have the necessary information (which observer) to do so.

Just because it's easy, "natural", and in general makes things a lot simpler doesn't mean that everyone does this, however. :-).

The general idea is that specifying the Lorentz interval between all possible pairs of points determines the geometry of space-time. The old-style observer-dependent notions of distance and time between points can be recovered from this information about the observer independent Lorentz intervals always when space-time if flat, and with a few ambiguities when space-time is not flat.

 

[GrayGhost]

As I understand your (JesseM's) position, no observer ever sees the rod itself--all observers see a view of the rod. This is where we disagree. I believe that an observer at rest with the rod sees the rod itself. All other observers see a view of the rod.

Greg,

There are basically 4 situ ...

(1) the rod as it presently exists per the observer
(2) the image of the rod per receipt of light signals per the observer
(3) the rod as it presenty exists per itself
(4) the image of the rod per receipt of light signals per itself

You speak of the rest (proper) length as though it is the only true length. However, that is to say ... the LTs predict spacetime solns that are not real, when relative motion is involved. Clearly, this is not the case, given the theory has stood for >100 yr now under intense scrutiny by the finest minds, every inch the way. Therefore, one should always evaluate, and re-evaluate, their disagreements with the theory before assuming the contrary.

Light signals alone cannot be used to determine how a body presently exists within the spacetime. The reason is that the image of the body, moving or not, takes time to reach your eyes (or equipment). Let's consider the body at rest with yourself. Since different points of the body reside at different distances from your eye, the collective image received by your eye at any instant is composed of a collection of photons which have traveled different distances from reflection-points of the body. Since some of these rays travel longer, the image conveyed by said photon must exist from an earlier point in time. Therefore, and generally speaking, no image you ever see is an image as the body existed in either it's own present moment, or your own. You might imagine a rod 1 lt-sec long at rest with yourself, lined with attached-atomic-clocks all in sync per the rod's own frame of reference. The image you receive at your eye at any moment (if magic eyes) would not see rod-clocks all in sync.

That said, to know how a body "presently exists", this must be predicted. It's a prediction of how the body exists NOW from some specific POV. It has nothing to do with light transit time conveying the image. If you and I move relatively, my NOW and your NOW are not the same per SR. In fact, they are angularly rotated wrt one another in spacetime in a non-classical way, just as your illustration has shown. So how is this prediction made? Well, it's made in the way JesseM has explained, because that's how the LTs actually do achieve it. Your euclidean stationary system is a collection of all spacetime points as they presently exist per you. The body (moving or not) has its own coordinate system, a collection of all spacetime points as they presently exist per it. The LTs map every point of one system into the other, which is why JesseM's stated process is accurate. If every point of the moving system is indeed mapped 1:1 into your own stationary system, then it is true (as JesseM says) that every point "of the moving body istelf" is mapped into your own stationary system's POV. IOWs, one really must consider the mapping of each point of the other body (moving or not) into your own POV, to know how it presently exists per oneself. Inherent in that process and its outcome is the meaning of the Special Relativity.

Which leads to DaleSpam's contention that we are unable even to properly define physical reality, let alone understand it.

Well we may never understand everything, and hence the argument that we can never truly define reality. On the other hand, we understand a lot more these days than in the dark ages. I prefer it in this way .. we have an incomplete understanding of reality, but an understanding nonetheless. It improves as we learn more. Yet, we do not even know why time passes, and so the relativity is built upon some things we do not yet fully grasp, so.

GrayGhost

 

[GregAshmore]

I have no idea what "the rod itself" means, and in fact I have repeatedly objected whenever you use this language--"the rod itself" sounds like some sort of metaphysical absolute, like "the soul" or "God". All that science can deal with are measurable properties of things, which I guess is what you mean by "view", although you ignored my request to define this word. Among these measurable properties are the coordinates of the points in spacetime occupied by the rod at some moment in time, and my argument was just that no matter what frame you use, this set of points will be a set of points at different moments in time in some other frame. So again, I don't see why the rest frame has "one view" while other frames do not, this claim seems totally arbitrary as long as you aren't willing to define "one view". As long as you continue to ignore all requests to define your terminology, I don't think this conversation can really go anywhere. Refusing to define is equivalent to refusing to question or think carefully about one's initial vague intuitions, in my opinion.

I believe that I clearly defined the distinction between the true view and the distorted view in the original post. The true view sees the entire rod all at once, at one instant of the rod's proper time. The distorted view sees a collection of individual points on the rod at different instants of the rod's proper time. I maintain that the distortion is the result of the movement of the rod over the time difference, where the time difference = V * L.

I understand that you may not wish to accept that the view in the rest frame is "true", and the view in other frames is "distorted". But I think the distinction between the view in the rest frame and the view from other frames is clear enough.

 

[JesseM]

I believe that I clearly defined the distinction between the true view and the distorted view in the original post. The true view sees the entire rod all at once, at one instant of the rod's proper time.

Only point particles have "proper time". We can talk about the proper time on any given point on the rod like the left end, but there's nothing inherent in the definition of proper time that would tell you which event on the left end occurs at the same proper time as an event on the right end, that's purely a matter of your simultaneity convention. So to use correct terminology, you should say "at one instant in the inertial frame where the rod is at rest". But stated this way, it seems that the "true view" involves that definition of simultaneity only because you have chosen to define it that way, I could just as easily pick a different definition that says "the true view sees the entire rod all at once, at one instant in the inertial frame where the rod is aligned parallel to the x-axis and moving in the +x direction at 0.99c". If you think there is something inherent in your notion of the meaning of the word "true" that would make this definition incorrect (as opposed to just different from your own preferred definition of 'true view', a merely aesthetic matter) then please explain it, otherwise I don't see how you are doing anything other than playing games with semantics.

I understand that you may not wish to accept that the view in the rest frame is "true"

I don't know what you mean by "true", unless "true view" is just an arbitrary term that you are defining in the quote above without claiming it has any connection with the ordinary English associations of the word (in much the same way that words like 'energy' and 'action' had preexisting meanings in English before being used as technical terms in physics, and when physicists use them they don't intend the words to have the same meaning as their colloquial English meanings). If that's the case you could have easily chosen some other arbitrary word, like "I define the 'maroon-colored view' to be the view sees the entire rod all at once, at one instant in the inertial rest frame of the rod", and it would make no difference to your argument.

 

[GregAshmore]

Greg,

There are basically 4 situ ...

(1) the rod as it presently exists per the observer
(2) the image of the rod per receipt of light signals per the observer
(3) the rod as it presenty exists per itself
(4) the image of the rod per receipt of light signals per itself

You speak of the rest (proper) length as though it is the only true length. However, that is to say ... the LTs predict spacetime solns that are not real, when relative motion is involved. Clearly, this is not the case, given the theory has stood for >100 yr now under intense scrutiny by the finest minds, every inch the way. Therefore, one should always evaluate, and re-evaluate, their disagreements with the theory before assuming the contrary.

I'm not challenging the conformation of the measured results with the predictions of the Lorentz transform. I'm trying to understand what the numbers mean. The equations meant one thing to Lorentz, and quite another thing to Einstein.

Light signals alone cannot be used to determine how a body presently exists within the spacetime. The reason is that the image of the body, moving or not, takes time to reach your eyes (or equipment). Let's consider the body at rest with yourself. Since different points of the body reside at different distances from your eye, the collective image received by your eye at any instant is composed of a collection of photons which have traveled different distances from reflection-points of the body. Since some of these rays travel longer, the image conveyed by said photon must exist from an earlier point in time. Therefore, and generally speaking, no image you ever see is an image as the body existed in either it's own present moment, or your own. You might imagine a rod 1 lt-sec long at rest with yourself, lined with attached-atomic-clocks all in sync per the rod's own frame of reference. The image you receive at your eye at any moment (if magic eyes) would not see rod-clocks all in sync.

That said, to know how a body "presently exists", this must be predicted.

If I set up an array of cameras with synchronized clocks, I can collect an image of the resting rod as it is at a given instant. I can then examine at my leisure the rod as it existed at that moment.

It's a prediction of how the body exists NOW from some specific POV. It has nothing to do with light transit time conveying the image. If you and I move relatively, my NOW and your NOW are not the same per SR. In fact, they are angularly rotated wrt one another in spacetime in a non-classical way, just as your illustration has shown. So how is this prediction made? Well, it's made in the way JesseM has explained, because that's how the LTs actually do achieve it.

But no transformation is needed to see the rod "as it was" if one collects the data in the rest frame as described above.

 

[Dale]

I'm not challenging the conformation of the measured results with the predictions of the Lorentz transform. I'm trying to understand what the numbers mean. The equations meant one thing to Lorentz, and quite another thing to Einstein.

The two interpretations are completely equivalent experimentally. In other words, you are free to choose either interpretation and you will not be proven wrong by current evidence. You are even free to switch interpretations on an arbitrary whim, either works fine. I tend to use Lorentz's interpretation only when thinking about the Doppler effect and Einstein's interpretation for everything else.

Personally, I don't think that the interpretations that we use are particularly important for anything other than helping us remember how to correctly apply the formulas for a given situation. So as long as you are consistently able to use the equations to get the right predictions then you are OK, IMO.

 

[GregAshmore]

Only point particles have "proper time". We can talk about the proper time on any given point on the rod like the left end, but there's nothing inherent in the definition of proper time that would tell you which event on the left end occurs at the same proper time as an event on the right end, that's purely a matter of your simultaneity convention. So to use correct terminology, you should say "at one instant in the inertial frame where the rod is at rest".

I did say that. It is the frame M in the diagram.

But stated this way, it seems that the "true view" involves that definition of simultaneity only because you have chosen to define it that way, I could just as easily pick a different definition that says "the true view sees the entire rod all at once, at one instant in the inertial frame where the rod is aligned parallel to the x-axis and moving in the +x direction at 0.99c". If you think there is something inherent in your notion of the meaning of the word "true" that would make this definition incorrect (as opposed to just different from your own preferred definition of 'true view', a merely aesthetic matter) then please explain it, otherwise I don't see how you are doing anything other than playing games with semantics.

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. Even given perfect instruments, it seems to me that there is a difference in principle between a measurement taken in the rod's rest frame and one taken from a frame moving relative to the rod. That difference is hinted at in the way velocities add in SR, and confirmed by the lifting of the speed limit 'c' in GR. (I understand [or think I do] that one can never actually measure a speed greater than c in GR, because our measurements are taken in a projection of the GR spacetime onto a locally flat spacetime where the Lorentz transformations apply. But this supports my argument that measurements taken at speed are distorted--or perhaps better said, less informative--than measurements taken at rest.)

 

[GregAshmore]

The two interpretations are completely equivalent experimentally. In other words, you are free to choose either interpretation and you will not be proven wrong by current evidence. You are even free to switch interpretations on an arbitrary whim, either works fine. I tend to use Lorentz's interpretation only when thinking about the Doppler effect and Einstein's interpretation for everything else.

Personally, I don't think that the interpretations that we use are particularly important for anything other than helping us remember how to correctly apply the formulas for a given situation. So as long as you are consistently able to use the equations to get the right predictions then you are OK, IMO.

For all practical purposes, I agree.

 

[GrayGhost]

I'm not challenging the conformation of the measured results with the predictions of the Lorentz transform. I'm trying to understand what the numbers mean. The equations meant one thing to Lorentz, and quite another thing to Einstein.

Well, to best understand their meaning wrt Einstein, I'd recommend you forget about Lorentz for the moment. Assume that any absolute reference for motion or simultaniety never existed. Then, consider your illustrations at face value.

If I set up an array of cameras with synchronized clocks, I can collect an image of the resting rod as it is at a given instant. I can then examine at my leisure the rod as it existed at that moment. ... no transformation is needed to see the rod "as it was" if one collects the data in the rest frame

By attaching the cameras and clocks to the rest-rod, and photographing the rod they are attached to, one verifies only one thing ... that SR reduces to classical mechanics at non-luminal motion. Well the theory already predicts that, so that won't help you much.

Your test cannot prove whether the rod exists in only its rest state, or not. It only verifies how the rod exists from its own POV. Your cameras must be in luminal relative motion wrt the rod to find the truth to the matter. The photos will either be consistent with your illustrations, or not. Countless tests to date support that they would be consistent. Keep in mind that the desynchronisation of luminally-moving-synchronised-clocks (as your illustration suggests) is neither an optical or illusionary effect per the theory.

GrayGhost

 

[ghwellsjr]

Greg, what do you say about two clocks in relative motion? Do you agree with these comments:

I assert that a clock keeps one true time, its rest time. If so, then the dilated coordinate time which is measured in some other frame must be somehow untrue. I argue that the coordinate time is a distorted view of the true time.

A clock is completely unaffected by acceleration. It is always at rest and keeping its one true time.

I'm not sure what I think about it. My initial reaction is that distance and time are not interchangeable, so the parallelism which you have drawn between true length and true time will perhaps not hold up under scrutiny. For example, what precisely do you mean by "view of time"?

I mean exactly what you mean when you use the expression "view of length".

In case you haven't noticed, I took some of your sentences and changed "rod" to "clock", "length" to "time", and "shorter" to "dilated". (I hope no one thought I was agreeing with the comments I asked you about.)

I'm not suggesting that distance and time are interchangeable. When an observer views a moving rod and a moving clock, he sees the rod as a shorter length (along the axis of relative motion) but the clock as taking a longer (dilated) time.

I'm just wondering since you have a problem with the observer's view of the rod's shorter length if you also have a similar problem with the observer's view of the clock's longer time?

Greg, can I get an answer to my question, please?

 

[GregAshmore]

Greg, can I get an answer to my question, please?

No, not in this thread. I'll need time to think about it, and I don't have much of that right now. Besides, while the problem is certainly of interest (I had asked myself the same question prior to your post), I'm not sure the answer changes anything with respect to my interpretation of length, because I think my argument stands on its own.

Of course I noticed that you substituted time for length. But I wasn't talking about time, I was talking about length. More precisely, the crux of my argument is that each "snapshot" of a point on the rod shows the rod at a different time in the rod's rest frame. Here your analogy by substitution breaks down. It makes no sense to say, "each snapshot of a time on the rod is taken at a different time in the rod's rest frame". So the answer to the question, "Is there a notion of true time which is consistent with the Lorentz transform?" is not to be found by the same sort of analysis on which I based my argument for true length.

 

[ghwellsjr]

That's OK, I don't have time either, except to say I don't have time.

 

[GregAshmore]

That's OK, I don't have time either, except to say I don't have time.

I worked 58 hours last week.

 

[JesseM]

I did say that. It is the frame M in the diagram.

But you also said "The true view sees the entire rod all at once, at one instant of the rod's proper time", and it's incorrect to equate "one instant in frame M" with "one instant of the rod's proper time", because proper time says nothing about simultaneity and only deals with time along the worldline of a point particle.

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.

More circular reasoning, you only call it an "error" because you call the rest frame's measurements "true", but you have given no justification for this terminology which seems to be based on nothing but your own personal aesthetic preferences. You really seem to be completely unable to formulate a rational argument which doesn't simply assume the premises you are trying to argue for! It's a little like trying to argue with a religious fundamentalist who says "I know everything in the Bible must be true, after all it says right here in the Bible that it's all the true word of God", then when you try to say "yes, but what if that statement itself wasn't true?" the fundamentalist just responds "but every statement in here is true, it says so right here!"

Before I asked you:

"the true view sees the entire rod all at once, at one instant in the inertial frame where the rod is aligned parallel to the x-axis and moving in the +x direction at 0.99c". If you think there is something inherent in your notion of the meaning of the word "true" that would make this definition incorrect ... then please explain it

But in your answer you didn't even address this alternate definition of "true view", let alone tell me what you mean by "true" or why this definition wouldn't fit with what you mean by that word. If I start by assuming this definition of "true view", then why can't I equally well say "as a practical matter, the farther one gets from the frame moving at 0.99c relative to the rod, the greater the error in measurement?"

Even given perfect instruments, it seems to me that there is a difference in principle between a measurement taken in the rod's rest frame and one taken from a frame moving relative to the rod.

Maybe you could attempt to justify why you think there is a "difference in principle" as opposed to just asserting it?

That difference is hinted at in the way velocities add in SR

More totally vague language. Why do you think relativistic velocity addition "hints at" a "difference in principle" that would force us to conclude that the rest frame's view is the "true view" while anything departing from that is an "error in measurement"?

and confirmed by the lifting of the speed limit 'c' in GR.

GR does no such thing, it says that the speed of light is c in any locally inertial frame (see this article on the equivalence principle for more on the notion of local inertial frames). It's true that a global coordinate system covering a large region of curved spacetime will not be an inertial frame and thus the coordinate speed of light need not be c in such a frame, but it's equally true that one can come up with non-inertial coordinate systems in the flat spacetime of SR and that light will not have a coordinate speed of c in such systems (one example would be Rindler coordinates)

(I understand [or think I do] that one can never actually measure a speed greater than c in GR, because our measurements are taken in a projection of the GR spacetime onto a locally flat spacetime where the Lorentz transformations apply.

Not true, you can certainly set up a system of rulers and clocks whose measurements define a non-inertial coordinate system where light doesn't move at c, like the family of accelerating clocks used to define Rindler coordinates.

But this supports my argument that measurements taken at speed are distorted--or perhaps better said, less informative--than measurements taken at rest.)

How would it "support" it even if it was correct? You have given no explanation of the connection of any of these ideas to your original claim that the rest frame measurements are "true", which itself is an incoherent claim since you refuse to explain what you even mean by "true" in a non-circular way. Again, if it's purely a matter of definition that the rest frame is the "true view", then it would be just as valid to adopt a different definition which says that the frame moving at 0.99c relative to the rod is the "true view". If the word "true" has some greater meaning to you in this context than just an arbitrary definition of which frame's view we choose to label as "true", then you need to explain that greater meaning. If you continue to make circular arguments without explaining in detail what connotations the word "true" has to you and why you think these connotations imply that your definition of "true view" makes sense while my alternate definition doesn't, then I don't think this conversation can go anywhere and this will be my last post on the subject.

 

[GregAshmore]

You really seem to be completely unable to formulate a rational argument which doesn't simply assume the premises you are trying to argue for! It's a little like trying to argue with a religious fundamentalist who says "I know everything in the Bible must be true, after all it says right here in the Bible that it's all the true word of God", then when you try to say "yes, but what if that statement itself wasn't true?" the fundamentalist just responds "but every statement in here is true, it says so right here!"

I will not address your entire post here because I think the argument presented in the original post is rational enough. Furthermore, I have already acknowledged that the argument is semantic, as it cannot be verified or falsified in the lab. (Your position is in the same category, by the way.)

As to GR, any statements made by me on that subject are purely qualitative in nature--as I had intended to indicate by prefacing them with something like "it seems to me"--because I do not yet know the math for GR.

With regard to the section of your post which I have quoted above, I am becoming impatient with your attempts to draw me into a theological debate. There are places for such a debate--where I would be happy to discuss theological matters with you--but this forum is not one of those places.

 

[JesseM]

I will not address your entire post here because I think the argument presented in the original post is rational enough. Furthermore, I have already acknowledged that the argument is semantic, as it cannot be verified or falsified in the lab.

But at the same time you deny that it is merely a matter of arbitrary definitions, don't you? That's what I took your comment "I don't see it as a matter of aesthetics" to mean, that you don't think it's merely a matter of personal aesthetic preferences that you like the definition "the true view sees the entire rod all at once, at one instant in the inertial frame where the rod is at rest" but you don't like the definition "the true view sees the entire rod all at once, at one instant in the inertial frame where the rod is aligned parallel to the x-axis and moving in the +x direction at 0.99c". If I misunderstand, and you agree there is no reason other than personal aesthetic preferences to prefer the first definition of "true view" to the second, then please say so. But if you don't think it's just a matter of an arbitrary choice of definitions, then you don't really think it's purely a semantic argument.

With regard to the section of your post which I have quoted above, I am becoming impatient with your attempts to draw me into a theological debate. There are places for such a debate--where I would be happy to discuss theological matters with you--but this forum is not one of those places.

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! 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.")

 

[bobc2]

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.

 

[JesseM]

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".

 

[GrayGhost]

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

 

[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.