The case for True Length = Rest Length

[Dale]

The reason for him to "transition", is that if he bases his conclusions about simultaneity on the conclusions of an inertial frame in which he is not at rest, he will then be forced to ignore his own elementary calculations involving his own elementary measurements.

No he won't. He can use any frame he likes whether or not he is at rest and whether or not the frame is inertial. All frames will predict the same results for all measurements. That is required by the first postulate. Your deliberate and persistent ignorance on this topic is simply astounding.

 

[GrayGhost]

Objects don't have a "sense-of-simultaneity", again it is simply a matter of convention what coordinate system we associate with what object. As I said, even if I am an inertial observer I am perfectly free to use an inertial coordinate system moving at 0.6c relative to me, this goes against the most common convention for what is meant by the words "my perspective" but as long as I explain what I'm doing there is no physical reason why I am "wrong" to use a frame other than my rest frame. Do you disagree?

Well, so long as the eventual receipt of light signals validates the convention, then I don't see that it should matter, also including the prediction and validation of doppler effects. Consider the twins ... (during a controlled flight test) if EM transmitted from twin A contains his own time readout and the relative range of B from A at that time (per A), then the spacetime predictions made by twin B (of A) must comply, after the light transit time is negated and doppler effects accounted for. This must be true no matter what convention B uses, assuming the convention matches reality.

If you use 0.6c as your frame of reference, this requires that you must have the added burden of transforming via the composition of velocities formula. So, it's less convenient. Either that, or the relativistic effects predicted for 0.6c must be defined as your standard (non-proper) POV for all relative motion, which again is inconvenient. Similarly, and worse yet, would be the use of a non-inertial frame for your reference for all motion, given you are always-inertial. Can any of these be done? yes. Would anybody want to? Probably not.

GrayGhost

 

[JesseM]

Well, so long as the eventual receipt of light signals validates the convention, then I don't see that it should matter, also including the prediction and validation of doppler effects. Consider the twins ... (during a controlled flight test) if EM transmitted from twin A contains his own time readout and the relative range of B from A at that time (per A), then the spacetime predictions made by twin B (of A) must comply, after the light transit time is negated and doppler effects accounted for. This must be true no matter what convention B uses, assuming the convention matches reality.

If you use 0.6c as your frame of reference, this requires that you must have the added burden of transforming via the composition of velocities formula. So, it's less convenient. Similarly, and worse yet, would be the use of a non-inertial frame for your reference for all motion, given you are always-inertial. Can it be done? yes. Would anybody want to? Probably not.

OK, so you agree there is no natural sense in which changing velocities causes you to "transition" from one inertial frame to another, that it is just a matter of it being more convenient? Well, that's why I've been objecting to your repeated claims that "according to the LTs" the surface of simultaneity swings around during acceleration, the LTs don't dictate what coordinate system an accelerating observer should use, that's a matter of human choice based on considerations like convenience. I also think that in the case of an accelerating observer, it'd be nonsense to say it's most "convenient" to use a coordinate system where the definition of simultaneity at any given instant always matches the definition in the instantaneous inertial rest frame...calculating this from observations would actually be fairly tricky (because B has to figure out at what point in his past his velocity was such that the surface of simultaneity in his inertial rest frame at that moment would intersect with the event of A sending the signal that B is receiving at this moment), whereas something like the Wheeler-Marzke system would be fairly simple, you just constantly send out radar signals and assign the event of the signal bouncing off A a time-coordinate halfway between the time on your clock when that signal was sent and the time on your clock when it returned to you.

 

[ghwellsjr]

Well, so long as the eventual receipt of light signals validates the convention, then I don't see that it should matter, also including the prediction and validation of doppler effects. Consider the twins ... (during a controlled flight test) if EM transmitted from twin A contains his own time readout and the relative range of B from A at that time (per A), then the spacetime predictions made by twin B (of A) must comply, after the light transit time is negated and doppler effects accounted for. This must be true no matter what convention B uses, assuming the convention matches reality.

If you use 0.6c as your frame of reference, this requires that you must have the added burden of transforming via the composition of velocities formula. So, it's less convenient. Either that, or the relativistic effects predicted for 0.6c must be defined as your standard (non-proper) POV for all relative motion, which again is inconvenient. Similarly, and worse yet, would be the use of a non-inertial frame for your reference for all motion, given you are always-inertial. Can any of these be done? yes. Would anybody want to? Probably not.

GrayGhost

All that you say in terms of convention being validated and the convention matching reality for twin A's rest frame is also true for any other inertial frame. That's the problem. What would you think of Michelson and Morley conducting their experiment one time and announcing to the world that they had discovered the absolute ether rest frame because they detected no ether wind? But we know better, don't we? Every inertial frame will behave exactly like an absolute ether rest frame. You cannot use that "evidence" to claim that a particular inertial rest frame is preferred, just because the convention is validated by reality or because the math is more convenient.

You can use any frame to determine things that are frame invariant, such as the measurements that each twin will make or the things that they see with their own keen eyes because these things leave in the light transit time. But you are presumming to "know" the light transit time in an absolute sense so that you can back it out of the measurement and determine the actual time that the traveling twin can deduce of the stationary twin's clock. This determination is not frame invariant and so no argument based on reality or convenience is valid.

What you can do legitimately is build a scenario where the two twins agree to determine everything from a frame in which they are both at rest to start out and when the trip is finished (is that what you meant by "a controlled flight test"?) but that will completely undermine they "paradox" in the Twin Paradox.

 

[ghwellsjr]

How about "when a clock properly accelerates in a straight line, its tick rate changes relative to all inertial frames."?

Agreed.

OK, good, rjbeery, now do you agree with this statement?

When an object properly accelerates in a straight line, its length along that line changes relative to all inertial frames.​

 

[JesseM]

OK, good, rjbeery, now do you agree with this statement?

When an object properly accelerates in a straight line, its length along that line changes relative to all inertial frames.​

By "properly accelerates" are you specifically talking about Born rigid acceleration? Because it is quite possible for an object to accelerate in such a way that its length in a given inertial frame doesn't change, it all depends on the timing of when different points on the object start accelerating and what proper acceleration they experience (if they all start accelerating simultaneously in a given inertial frame, and they all experience identical proper acceleration at each moment of time in that frame, then the object's length won't change in that frame--see the http://en.wikipedia.org/wiki/Bell's_spaceship_paradox]Bell[/PLAIN] spaceship paradox).

 

[ghwellsjr]

Actually, I only added the word "properly" because DrGreg added it to his modification of your modification of my original statement about an accelerated clock to rjbeery and it's the version that rjbeery agreed to. I really don't care but if it matters concerning the length of an object, why didn't you complain about DrGreg's addition of the word with regard to an accelerated clock?

 

[JesseM]

Actually, I only added the word "properly" because DrGreg added it to his modification of your modification of my original statement about an accelerated clock to rjbeery and it's the version that rjbeery agreed to. I really don't care but if it matters concerning the length of an object, why didn't you complain about DrGreg's addition of the word with regard to an accelerated clock?

Ideal clocks are usually imagined to be point particles, since proper time is well-defined along the worldline of a point particle, so for an ideal clock there is no issue with different parts of the clock having different acceleration profiles. And even if you're dealing with an extended object, as long as the distance between ends (in any inertial frame) measured in light-seconds is very small compared to the time in seconds between the beginning and end of its motion (or the beginning and end of the time window you wish to consider), I think it should be the case that proper time experienced by different points on the object will differ by a very small amount compared to the total proper time experienced by anyone point. In contrast the change in length from the beginning to the end could be quite large compared to the total length at the beginning, if the object is not accelerating in a Born-rigid way.

 

[ghwellsjr]

Would be better to say "when a clock accelerates, its tick rate changes relative to all inertial frames."

Actually, even that statement need not be true. A clock moving at constant speed round a circular path is accelerating, but relative to someone permanently at the centre of the circle, the clock rate is unchanging!

How about "when a clock properly accelerates in a straight line, its tick rate changes relative to all inertial frames."?

DrGreg--why did you insert the word "properly" into JesseM's suggested improvement to my original statement?

 

[DrGreg]

DrGreg--why did you insert the word "properly" into JesseM's suggested improvement to my original statement?

Because what everyone has been calling "acceleration" in this thread should, strictly speaking, be called "proper acceleration" i.e. acceleration measured by a comoving inertial observer, or equivalently as measured by an accelerometer. More generally "acceleration" can be measured relative to any frame, including a non-inertial frame, so without the word "proper", different observers could disagree whether something is accelerating or not. But everyone agrees what "proper acceleration" is, it's frame-invariant.

Actually this has nothing whatsoever to do with the point JesseM raised in post #246. The point here is when you are talking about an extended object rather than a point-like particle, it is possible to (properly) accelerate different parts of the object by different amounts. It would seem that when you put forward the proposition

When an object properly accelerates in a straight line, its length along that line changes relative to all inertial frames​

I would assume you meant that the object's length as measured by itself (or to be more precise as measured in the comoving inertial frame) remains constant over time. This is described as "Born rigid acceleration". And then your proposition is correct and is the space-equivalent of the statement about time previously made. But in general objects might not accelerate in a Born rigid way, and then the proposition might fail.

(For example, if you start to accelerate an object by starting to push from the back, it takes time for the force to travel through the object and the front won't start to accelerate until some time later and the object will necessarily have compressed in its own rest frame, never mind any other frame. This compression has nothing to do with relativity. If instead of pushing the back, you pulled the front, you'd have stretched the object.)

 

[Mike_Fontenot]

[...]
The issue that you (JesseM and GrayGhost) are both "dancing around" (the elephant in the room, really), is this: Whenever a person is NOT accelerating for some segment of his life, WHEN in that segment can he legitimately be considered to be an inertial observer?
[...]

Here's another way to describe that "elephant-in-the-room" issue:

The standard time dilation result of special relativity answers the following question:

"What does an inertial observer conclude about the rate of ticking of some particular distant clock, which is moving at a constant speed relative to the inertial observer?".

The standard answer is:

"The inertial observer will conclude that the distant clock is ticking gamma times slower than his own watch."

But what exactly IS "an inertial observer"? Is it someone who is TEMPORARILY not being accelerated, but who may have accelerated in the past, or who may choose to accelerate in the future? Or is it someone who is PERPETUALLY unaccelerated? If it's the latter, does that mean that each tiny bit of matter making up the observer's body has never accelerated before? Could ANY person meet THAT test?

And, in order to determine the clock rate of the distant clock, does the inertial observer need to know the distance to that clock?

The Dolby& Gull simultaneity, and the Minguizzi simultaneity, answer the above two questions very differently than does my CADO simultaneity.

My CADO simultaneity says that an observer is inertial during any segment of his life in which he is unaccelerated, regardless of the duration of that segment. And my CADO simultaneity says that the tick rate of the distant moving clock does NOT depend on how far away that clock is.

If the observer is NOT perpetually unaccelerated, then both Dolby&Gull and Minguizzi DO require that the distance to the moving clock be specified, before they can determine its tick rate. So anyone who subscribes to either the Dolby&Gull simultaneity, or to the Minguizzi simultaneity (or to ANY simultaneity other than my CADO simultaneity), needs to be clear about the answers to the above two questions, before they can say anything about the tick rate of the distant moving clock. And what they say about that tick rate will often NOT be what the standard time dilation result says.

Mike Fontenot

 

[ghwellsjr]

I would assume you meant that the object's length as measured by itself (or to be more precise as measured in the comoving inertial frame) remains constant over time. This is described as "Born rigid acceleration". And then your proposition is correct and is the space-equivalent of the statement about time previously made.

OK, great, thanks for all the clarifications.

A new question for rjbeery--do you agree with this statement?

When an object properly accelerates in a Born rigid way in a straight line, its length along that line changes relative to all inertial frames.

 

[ghwellsjr]

Here's another way to describe that "elephant-in-the-room" issue:

The standard time dilation result of special relativity answers the following question:

"What does an inertial observer conclude about the rate of ticking of some particular distant clock, which is moving at a constant speed relative to the inertial observer?".

The standard answer is:

"The inertial observer will conclude that the distant clock is ticking gamma times slower than his own watch."

But what exactly IS "an inertial observer"? Is it someone who is TEMPORARILY not being accelerated, but who may have accelerated in the past, or who may choose to accelerate in the future? Or is it someone who is PERPETUALLY unaccelerated? If it's the latter, does that mean that each tiny bit of matter making up the observer's body has never accelerated before? Could ANY person meet THAT test?

And, in order to determine the clock rate of the distant clock, does the inertial observer need to know the distance to that clock?

The Dolby& Gull simultaneity, and the Minguizzi simultaneity, answer the above two questions very differently than does my CADO simultaneity.

My CADO simultaneity says that an observer is inertial during any segment of his life in which he is unaccelerated, regardless of the duration of that segment. And my CADO simultaneity says that the tick rate of the distant moving clock does NOT depend on how far away that clock is.

If the observer is NOT perpetually unaccelerated, then both Dolby&Gull and Minguizzi DO require that the distance to the moving clock be specified, before they can determine its tick rate. So anyone who subscribes to either the Dolby&Gull simultaneity, or to the Minguizzi simultaneity (or to ANY simultaneity other than my CADO simultaneity), needs to be clear about the answers to the above two questions, before they can say anything about the tick rate of the distant moving clock. And what they say about that tick rate will often NOT be what the standard time dilation result says.

Mike Fontenot

The tick rate of a distant moving clock is relative, just like the speed is relative. Why do you persist in claiming that you are the only person who knows how to make it absolute?

 

[rjbeery]

When an object properly accelerates in a Born rigid way in a straight line, its length along that line changes relative to all inertial frames

My answer to this is the same as my answer to the following:

When a cube is rotated, its width changes relative to all observers for whom the axis of rotation is not perpendicular to their visual plane.

 

[GrayGhost]

OK, so you agree there is no natural sense in which changing velocities causes you to "transition" from one inertial frame to another, that it is just a matter of it being more convenient?

Well, I'd say it this way ... in a natural sense, whenever 2 observers are of the same frame of reference, even if momentarily, they measure space and time the very same.

Now you may wish not to consider twin B as transitioning contiguous inertial frames. You might prefer that twin B assumes the stationary with all fully-inertial bodies in curvilinear motion. I see these both as appropriate, and the result should be the same either way.

Well, that's why I've been objecting to your repeated claims that "according to the LTs" the surface of simultaneity swings around during acceleration, the LTs don't dictate what coordinate system an accelerating observer should use, that's a matter of human choice based on considerations like convenience.

Here's the difference though ... Most everyone agrees that twin A can use the LTs with Einstein's convention-of-simultaneity since twin A is always inertial, because his sense-of-simultaneity is unchanging. You disagree that the LTs may be used by twin B, when he is non-inertial, because his sense-of-simultaneity is dynamic ... and therefore you assume the Einstein convention-of-simultaneity inappropriate. I submit that this does not matter, that twin B may use the LTs at any time, and that his calculation is only less convenient (than twin A's) while no less peferred. Obviously, the LT solns will need to be calculated for small segments and summed ... the smaller the better.

I also think that in the case of an accelerating observer, it'd be nonsense to say it's most "convenient" to use a coordinate system where the definition of simultaneity at any given instant always matches the definition in the instantaneous inertial rest frame ... calculating this from observations would actually be fairly tricky (because B has to figure out at what point in his past his velocity was such that the surface of simultaneity in his inertial rest frame at that moment would intersect with the event of A sending the signal that B is receiving at this moment), ...

It would be fairly tricky indeed, however in theory it can be done. So long as twin B always keeps track of his own motion at any instant (and saves it away for LT predictions), in a preplanned flight test he can predict the A-clock readout and the range of B from A per A, at any time. If he's running his calculations based upon twin A track data (vs preplanned flight test), then he can predict the A-clock readout and the range of B from A per A, for any reflection event. Twin A will always agree with B's predictions, because they use the same sense-of-simultaneity. I personally believe they should always agree for any reasonable theory of spacetime, just as they do in SR. They agree on the invariants, and they each correctly predict the other's measurements even though they disagree on the measure of space and time.

OK, so it's more convenient for twin A to make predictions of B than for twin B to make predictions of A, and twin A's prediction is not as convenient as in the case of all-inertial scenarios either. None the less, the predictions should be accurate if the LT solutions are summed for infitesimals, and as the width of infitesimals approach zero, the accuracy of the prediction approaches perfect.

Now if A and B are both undergoing proper acceleration, then it gets even more inconvenient.

whereas something like the Wheeler-Marzke system would be fairly simple, you just constantly send out radar signals and assign the event of the signal bouncing off A a time-coordinate halfway between the time on your clock when that signal was sent and the time on your clock when it returned to you.

Indeed, it would be fairly simple, however I disagree it would be correct. The above convention (during twin B acceleration) produces a reflection event that will NOT match the real location of twin A in B's own spacetime system. Everyone knows it. Such a convention requires that we say ... "who cares if we do not properly locate twin A if the error vanishes when we are colocated again?". Add that any prediction (by B) of the A clock at some point, and of what twin A then holds as the twin B range, will not match what twin A actually held for B at said A-moment. So this is completely unsatifactory IMO JesseM. Now if you have no good track data at hand, then the radar method you cite here would be a practicle and simple alternative, assuming accurate predictions are impossible anyway.

Back to the twin A always-inertial case ... So if I am right in that twin B may use the LTs even though he is non-inertial, his calculations are no less preferred even though they are inconvenient. In the limit where the duration of twin B's momentarly consideration (of A) approaches zero, the inprecision of the twin B prediction approaches zero. I submit that the same fundamental issue exists when twin A makes predictions of twin B ... because the twin B clock is steadily slowing down with B's proper increase in relative velocity.

GrayGhost

 

[ghwellsjr]

Well, I'd say it this way ... in a natural sense, whenever 2 observers are of the same frame of reference, even if momentarily, they measure space and time the very same.

Do you know what's wrong with this sentence?
1) All observers are of all frames of reference all the time, why do you think observers are linked to specific frames even if momentarily?
2) What any observer measures of space and time has no relation to any frame of reference. They don't need to be thinking about a frame of reference or have defined a frame of reference to make a measurement or to make an observation. How many times does this need to be repeated?

Now you may wish not to consider twin B as transitioning contiguous inertial frames.

Twin B does not transition contiguous inertial frames, as I said before, he is always in all frames all the time. You're just turning on and off your realization of different frames in some manner that you think makes sense to you.

You might prefer that twin B assumes the stationary with all fully-inertial bodies in curvilinear motion.

Sorry, can't understand this sentence.

I see these both as being true and appropriate, and the result should be the same either way.

Even if you only picked one frame of reference to analyze distances and times, those values are only "true" in that one frame. If you pick another frame you will get different numbers that are only "true" in that second frame.

Here's the difference though ... Everyone agrees that twin A can use the LTs with Einstein's convention-of-simultaneity since twin A is always inertial, because his sense-of-simultaneity is unchanging.

Unless twin A knows the whole story--twin B's acceleration and deceleration profiles and how far or how long twin B is going to travel--any discussion of a frame of reference for twin A is pointless. Frames of reference are for our convenience, not for the observers in our scenario. And as I keep repeating, it doesn't matter which frame we use to describe our scenario, but the easiest one to use is an inertial one in which both twins start out at rest and end up at rest. The purpose of Lorentz Transforms is to convert all the values of distances and times for both twins from one inertial frame to any other inertial frame. Neither twin "owns" any frame of reference. If they are aware of the whole scenario, like we are, then they could use the LTs to see what things look like in other frames. But if they want to see what things look like to themselves, they don't need frames or LTs, they just look.

You disagree that the LTs may be used by twin B, when he is non-inertial, because his sense-of-simultaneity is dynamic ... and therefore you assume the Einstein convention-of-simultaneity inappropriate.

Anybody can use LTs to convert the values of time/distance events in one inertial frame to any other inertial frame, if they are aware of the entire scenario. They won't help an observer take what he is seeing and measuring and somehow extrapolate to things that he cannot see and measure. The problem is not that twin B is non-inertial, it's that you are linking twin B to a non-inertial frame and trying to use the LT for some purpose that it cannot serve.

I submit that this does not matter, that twin B may use the LTs at any time, and that his calculation is only less convenient (than twin A's) while no less peferred..

See, there you go again, linking frames of reference to observers as if the two twins own different frames. Although the definition and analysis of the Twin Paradox is easiest and most convenient in a frame in which they both start out at rest (neither one owns this frame) it's not a matter of it being a "preferred" frame. Even though I personally would choose that frame, I would not call it that because "preferred" has a distinct meaning in SR which is that a particular frame is more "true" or "right" or "matches reality better" or something along those lines as opposed to my personal arbitrary first choice.

Obviously, the LT solns will need to be calcualted for infitesimal segments and summed..

If I knew what "solns" meant, maybe I could respond, but I doubt that whatever you said is obvious.

It would be fairly tricky indeed, however in theory it can be done. So long as twin B always keeps track of his own motion at any instant (and saves it away for LT predictions), in a preplanned flight test he can predict the A-clock readout and the range of B from A per A, at any time. If he's running his calculations based upon twin A track data (vs preplanned flight test), then he can predict the A-clock readout and the range of B from A per A, for any reflection event. Twin A will always agree with B's predictions, because they use the same sense-of-simultaneity. I personally believe they should always agree for any reasonable theory of spacetime, just as they do in SR. They agree on the invariants, and they each correctly predict the other's measurements even though they disagree on the measure of space and time.

What's this about LT predictions? LTs cannot predict anything, they only convert values from one inertial frame to another. If the twins have a preplanned flight test, then of course they can use that information so that twin B can determine the time on twin A's clock corresponding to the time on his own clock in the previously agreed upon inertial frame in which they both started out at rest. And twin B can similarly use that information to keep track of his distance traveled according to that same frame of reference. But in both cases, these distances and times are not preferred in any way. Pick a different frame and you get different values and if you built a table of the times on the two clocks they would be different for different frames.

OK, so it's more convenient for twin A to make predictions of B than for twin B to make predictions of A, and twin A's prediction is not as convenient as in the case of all-inertial scenarios either. None the less, the predictions should be accurate if the LT solutions are summed for infitesimals, and as the width of infitesimals approach zero, the accuracy of the prediction approaches perfect.

If there's one thing that anyone should learn after studying SR for any length of time, it is that time is relative. Why are you trying to predict or correlate the times on twin B's clock with the times on twin A's clock? The only times you can correlate are the start and end times. All other times can vary all over the place depending on the frame of reference used.

Now if A and B are both undergoing proper acceleration, then it gets even more inconvenient.

I think the proper term is torture, self-inflicted.

Indeed, it would be fairly simple, however I disagree it would be correct. The above convention (during twin B acceleration) produces a reflection event that will NOT match the real location of twin A in B's own spacetime system. Everyone knows it. Such a convention requires that we say ... "who cares if we do not properly locate twin A if the error vanishes when we are colocated again?". Add that any prediction (by B) of the A clock at some point, and of what twin A then holds as the twin B range, will not match what twin A actually held for B at said A-moment. So this is completely unsatifactory IMO JesseM. Now if you have no good track data at hand, then the radar method you cite here would be a practicle and simple alternative, assuming accurate predictions are impossible anyway.

"Real location"? "Properly locate twin A"? "Prediction (by B) of the A clock at some point"? "What twin A holds as the twin B range"? "Twin A actually held for B at said A-moment"? All these phrases show a complete misunderstanding of SR. The only way that any of these phrases can have any merit is in the context of a previously agreed upon frame of reference AND a flight plan that twin B adheres to and twin A does too--he has to remain stationary. But if you're going to do that, why even send twin B off, we already know what will happen? He will follow the flight plan and everything will go exactly as described. Boring.

Back to the twin A always-inertial case ... So if I am right in that twin B may use the LTs even though he is non-inertial, his calculations are no less preferred even though they are inconvenient. In the limit where the duration of twin B's momentarly consideration (of A) approaches zero, the inprecision of the twin B prediction approaches zero. I submit that the same fundamental issue exists when twin A makes predictions of twin B ... because the twin B clock is steadily slowing down with B's proper increased in relative velocity.

GrayGhost

Repeat, repeat, repeat: LTs are not for making predictions, they are for converting information from one inertial frame of reference to another inertial frame of reference, so you are not right. It doesn't matter if he is non-inertial but any other frame that you want to use the LT with must be inertial. There is no imprecision in calculating anything as long as you define everything to begin with.

I hope you will take these criticisms in the right spirit and learn from them instead of digging your heals in deeper to try to defend your incorrect notions. If I weren't interested in helping you learn a correct understanding of SR, I wouldn't bother to take hours responding to your posts.

 

[ghwellsjr]

Rjbeery, you previously agreed to this statement:

How about "when a clock properly accelerates in a straight line, its tick rate changes relative to all inertial frames."?

Agreed.

But you are holding fast to your original view that length changes are an illusion, correct?

When an object properly accelerates in a Born rigid way in a straight line, its length along that line changes relative to all inertial frames.

My answer to this is the same as my answer to the following:

When a cube is rotated, its width changes relative to all observers for whom the axis of rotation is not perpendicular to their visual plane.

But I want to bring the first statement into correspondence with the second one and see if you still agree with it:

When a clock properly accelerates in a Born rigid way in a straight line, its tick rate changes relative to all inertial frames.​

 

[GrayGhost]

ghwellsjr,

Boy, you sure have a lot of complaints there. I figure maybe one is valid. You responded before I could get back to fix the "curvilinear motion" para. Anywho, it's bedtime so I'll address you tomorrow.

GrayGhost

 

[rjbeery]

ghwellsjr, I know where you're going. You're wondering how I can consider time dilation to be absolute under acceleration but that I might still consider length contraction illusory. I must admit that bringing acceleration into the picture complicates things for me because I have little experience with the math involved (I'm neither a physicist nor a mathematician).

That being said, my response is that length contraction is always reciprocal; in other words, I'm not aware of any circumstance in which an inertial observer and an accelerating observer will both agree on which party is length contracted. Are you?

 

[ghwellsjr]

ghwellsjr, I know where you're going. You're wondering how I can consider time dilation to be absolute under acceleration but that I might still consider length contraction illusory. I must admit that bringing acceleration into the picture complicates things for me because I have little experience with the math involved (I'm neither a physicist nor a mathematician).

That being said, my response is that length contraction is always reciprocal; in other words, I'm not aware of any circumstance in which an inertial observer and an accelerating observer will both agree on which party is length contracted. Are you?

No, I'm not aware of any circumstance in which an inertial observer and an accelerating observer, who properly accelerates in a Born rigid way in a straight line, will both agree on which party is length contracted, unless they agree to define their motions relative to a common reference frame. But I would also say the same thing with regard to time dilation.

But you have missed the point of my previous questions. I was not asking about time dilation or length contraction. Look at these two statements:

When a clock properly accelerates in a Born rigid way in a straight line, its tick rate changes relative to all inertial frames.​

When an object properly accelerates in a Born rigid way in a straight line, its length along that line changes relative to all inertial frames.​

I'm presuming that you still agree with the first statement but not with the second.

But let's consider that the clock in the first statement is a light clock. Basicallly, we're talking about a burst of light that bounces between two mirrors a fixed distance apart. You agreed that its tick rate changes when it accelerates (in accord with the previously outlined stipulations). Now don't you agree that however the tick rate changes, it won't matter what the orientation of the mirrors are with respect to the axis of acceleration? And yet, don't you agree that if this is true, the mirrors must change their distance apart in some orientations in order for the tick rate to change independently of the orientation of the light clock?

 

[rjbeery]

No, I'm not aware of any circumstance in which an inertial observer and an accelerating observer, who properly accelerates in a Born rigid way in a straight line, will both agree on which party is length contracted, unless they agree to define their motions relative to a common reference frame. But I would also say the same thing with regard to time dilation.

Whoa, you're unaware of any circumstance (involving acceleration) in which two observers can objectively state which one was experiencing time dilation? Even after their reunion?

But you have missed the point of my previous questions. I was not asking about time dilation or length contraction. Look at these two statements:
When a clock properly accelerates in a Born rigid way in a straight line, its tick rate changes relative to all inertial frames.
When an object properly accelerates in a Born rigid way in a straight line, its length along that line changes relative to all inertial frames.
I'm presuming that you still agree with the first statement but not with the second.

But let's consider that the clock in the first statement is a light clock. Basicallly, we're talking about a burst of light that bounces between two mirrors a fixed distance apart. You agreed that its tick rate changes when it accelerates (in accord with the previously outlined stipulations). Now don't you agree that however the tick rate changes, it won't matter what the orientation of the mirrors are with respect to the axis of acceleration? And yet, don't you agree that if this is true, the mirrors must change their distance apart in some orientations in order for the tick rate to change independently of the orientation of the light clock?

I don't disagree with the second statement, exactly, I would simply qualify the word "length". Also, are we speaking of an accelerated light clock or an accelerating light clock? The constancy of c can be apparently violated with accelerating frames (e.g. Sagnac, etc). To extend my cube analogy, replace the acceleration with a rotation. If the light clock is on the face being rotated away, the "light will appear" to be moving more slowly if the edges of the clock are parallel to the axis of rotation. If they are perpendicular, then the apparent length between them does not change and c remains constant.

 

[ghwellsjr]

Whoa, you're unaware of any circumstance (involving acceleration) in which two observers can objectively state which one was experiencing time dilation? Even after their reunion?

You left off the all-important phrase, "unless they agree to define their motions relative to a common reference frame". And you changed the issue from a single acceleration to three accelerations.

I don't disagree with the second statement, exactly, I would simply qualify the word "length". Also, are we speaking of an accelerated light clock or an accelerating light clock?

We are speaking of an accelerating light clock. And again, I'm not asking you specifically about time dilation (which is a change in a particular direction) or length contraction (which is a change in a particular direction), I'm asking you about any change in the tick rate (it could be ticking faster) and any change in the length (it could be getting longer).

Consider a light clock at rest in some frame. This is the only frame we're going to talk about. Now let it accelerate as defined earlier (Born rigid, straight line). According to our defined frame, the tick rate of the light clock will be changing during the time of acceleration in a decreasing direction. Then we stop the acceleration. Now the tick rate remains constant at a lower value than it was at the start. Now let the light clock decelerate (or accelerate in the opposite direction). What happens to the tick rate? It will be changing in an increasing direction. Remember, this is all according to our one defined frame. If we had chosen other frames, the direction and magnitude of the changing tick rates could be entirely different but in all of them, the tick rate changes during Born rigid, straight line accelerations in some manner.

The reason I'm asking you to think about this two-step acceleration is so that it might be clear to you that if we let the first acceleration happen, we will be in a situation where we have an inertial light clock traveling with respect to our one defined frame in which there could be an observer at rest. Then we let the light clock accelerate like we described earlier which brings it to rest in our defined frame. (If we plan things right, it could come to rest at the location of our observer but they would not have started out together, however, this is of no consequence for what we are considering here.)

So think about this second-half situation: two inertial bodies (one a light clock, the other an observer) traveling at some speed with respect to each other. One of the bodies (the light clock) accelerates but does not experience a decrease in its tick rate but rather an increase according to our defined frame. So neither body would "objectively state which one was experiencing time dilation".

This is all a giant side track to the real question I have for you which is during the time of acceleration, does the light clock experience a change in the distance between the mirrors when they are aligned so that the light bounces back and forth along the direction of acceleration?

The constancy of c can be apparently violated with accelerating frames (e.g. Sagnac, etc).

I'm not asking you to consider any particular frame, let alone an accelerating frame, just an accelerating light clock.

To extend my cube analogy, replace the acceleration with a rotation. If the light clock is on the face being rotated away, the "light will appear" to be moving more slowly if the edges of the clock are parallel to the axis of rotation. If they are perpendicular, then the apparent length between them does not change and c remains constant.

I have lots of reactions to your analogy but I think I better save them for another time. Maybe soon you'll see the light and I won't have to comment on it.

 

[rjbeery]

You left off the all-important phrase, "unless they agree to define their motions relative to a common reference frame". And you changed the issue from a single acceleration to three accelerations.

Now wait a minute, let's handle one thing at a time. The twins don't need to agree on any common reference frame. Also, the twins don't need to be inertial at their point of departure nor their point of reunion; therefore, only a single acceleration is required and BOTH twins shall mutually agree on the nature of their absolute age differential. If you don't like this then we can go back to the orbiting twin scenario that is experiencing only a "single acceleration" and is undoubtedly aging more slowly than the twin sitting at his focus of orbit.

 

[ghwellsjr]

We don't need a reference frame to agree on what observers see and measure on their own instruments. Since they both have their own clocks, it's a simple matter for anyone to look at them from any frame and everyone will agree on what those instruments indicate. And that will always be that the twin who accelerated will have less elapsed time on his clock than his inertial twin has on his clock.

We can say similar things about the orbiting (accelerating) twin and his inertial twin and their two clocks.

But, not all frames will agree that the twins' two clocks have kept time in any absolute sense.

Now, can you please go back and respond to my previous post?

 

[rjbeery]

This is all a giant side track to the real question I have for you which is during the time of acceleration, does the light clock experience a change in the distance between the mirrors when they are aligned so that the light bounces back and forth along the direction of acceleration?

Frankly I'm having a problem following some of your post. I can address this point though.
You explicitly said "when an object accelerates in a Born rigid way", later labeling that accelerating object the clock. By definition

The defining property of Born rigidity is locally constant distance in the co-moving frame for all points of the body in question.

Remember we're talking ABSOLUTE length contraction, and ABSOLUTE distance between the mirrors; you're going to have a hard time establishing anything absolute even without the Born rigid restriction. The answer to your question is no.

Maybe soon you'll see the light

Yes, I'm eager to see it. Do your best.

 

[ghwellsjr]

Look at what you quoted:

"The defining property of Born rigidity is locally constant distance in the co-moving frame for all points of the body in question."​

Notice that phrase "co-moving frame"? In the co-moving frame, there is no time dilation happening either and yet you agreed that a clock under acceleration will experience a change in its tick rate:

How about "when a clock properly accelerates in a straight line, its tick rate changes relative to all inertial frames."?

Agreed.

So we're talking, for example, about the clock's initial inertial rest frame and what happens to its tick rate as it is accelerating. Don't you still agree that it will change? And don't you accept the very common explanation of a light clock's time dilation in which the bouncing spot of light has to traverse diagonal paths which take longer?

 

[rjbeery]

But, not all frames will agree that the twins' two clocks have kept time in any absolute sense.

Two twins after a departure, a single acceleration, and a reunion will without a doubt be able to establish absolutely the nature of their age differential during their mutual trips to which all observers in all frames shall agree. I'm not sure how you can claim otherwise and expect me to continue looking to you for a lesson such that I may "see the light".

In the co-moving frame, there is no time dilation happening either and yet you agreed that a clock under acceleration will experience a change in its tick rate

Then you pointed out a sentence that I agreed to earlier, which was

How about "when a clock properly accelerates in a straight line, its tick rate changes relative to all inertial frames.

Are you claiming there is an inconsistency here?

And don't you accept the very common explanation of a light clock's time dilation in which the bouncing spot of light has to traverse diagonal paths which take longer?

You've been talking about a change in the distance between the mirrors, but now the mirrors are parallel to the direction of acceleration? Ghwellsjr, I'm sorry but frankly it appears that you're changing your story around on each post. You've also been dismissive when you are clearly wrong on a point. Lastly, I'm not finding this conversation particularly engaging.

 

[ghwellsjr]

But, not all frames will agree that the twins' two clocks have kept time in any absolute sense.

Two twins after a departure, a single acceleration, and a reunion will without a doubt be able to establish absolutely the nature of their age differential during their mutual trips to which all observers in all frames shall agree. I'm not sure how you can claim otherwise and expect me to continue looking to you for a lesson such that I may "see the light".

It's not my claim that there is no absolute time in our real world. Clocks traveling at different relative speeds will tick at different rates. I didn't make that up. I learned it. It's one of the lessons of the Twin Paradox and the experimental proofs that back it up. Unfortunately, you reject this common knowledge and instead claim that it's only acceleration that accounts for the difference in the tick rates.

Now I'm beginning to wonder if you even understand such common terms as "acceleration", "co-moving", an "inertial". How else could you account for this posting of yours?

In the co-moving frame, there is no time dilation happening either and yet you agreed that a clock under acceleration will experience a change in its tick rate.

Then you pointed out a sentence that I agreed to earlier, which was

How about "when a clock properly accelerates in a straight line, its tick rate changes relative to all inertial frames.

Are you claiming there is an inconsistency here?

No. The first quote is addressing a frame co-moving with an accelerating clock. That means it's a non-inertial frame. The second quote is addressing inertial frames. Do you want help in understanding the difference between a non-inertial frame and an inertial frame?

And don't you accept the very common explanation of a light clock's time dilation in which the bouncing spot of light has to traverse diagonal paths which take longer?

You've been talking about a change in the distance between the mirrors, but now the mirrors are parallel to the direction of acceleration? Ghwellsjr, I'm sorry but frankly it appears that you're changing your story around on each post.

When the light-clock is oriented so that the mirrors are parallel to the direction of acceleration, there is no change in the distance between the mirrors during the acceleration. When the light-clock is oriented so that the mirrors are perpendicular to the direction of acceleration, there is a change in the distance between the mirrors during the acceleration. But in both cases, there is a change in the tick rate. All inertial frames will agree with this assessment, although they may disagree on the magnitude of the changes.

I'm not changing my story around on each post. Here's where I said the same thing earlier, although more briefly because I thought you would be able to understand a briefer illustration:

Now don't you agree that however the tick rate changes, it won't matter what the orientation of the mirrors are with respect to the axis of acceleration? And yet, don't you agree that if this is true, the mirrors must change their distance apart in some orientations in order for the tick rate to change independently of the orientation of the light clock?

If you are having trouble understanding my verbal illustrations, would you like me to do it graphically?

You've also been dismissive when you are clearly wrong on a point. Lastly, I'm not finding this conversation particularly engaging.

I try hard not to be wrong, especially clearly wrong. I'm not aware of any time that I have been clearly wrong and someone brought it to my attention and I didn't express my appreciation. Maybe someone will do that now.

 

[rjbeery]

I'm not aware of any time that I have been clearly wrong and someone brought it to my attention and I didn't express my appreciation. Maybe someone will do that now.

I've already said this thread is losing my interest but I'll post these simply so you can either clarify what you meant or thank me for pointing them out.

I said it is a relative speed over a period of time that leads to an age difference.

Could you please explain the effect of the orbiting twin aging more slowly than the twin experiencing no acceleration at the orbit's focus? If we say that the orbiting twin has a relative speed then the stationary one also has relative speed by definition, correct? There is something that is different between the twins in this scenario, and it isn't speed...

It's not my claim that there is no absolute time in our real world. Clocks traveling at different relative speeds will tick at different rates. I didn't make that up. I learned it.

Your initial statement, plus the bolded word, imply that you believe in absolute time. However...

But, not all frames will agree that the twins' two clocks have kept time in any absolute sense.

Do you think absolute time exists or not? It would surprise me if you did, but it also surprises me that you made the claim that the nature of the twins' age differential would vary depending upon the observing frame (even after their reunion??). This was another issue that you glossed over when I pointed it out. Speaking of being mistaken on a point, wasn't it you that said there is nothing contradictory in the sentence "I'm shorter than you and you're shorter than me"?

OK enough with the petty stuff. As for your general point...you're asking me whether or not I "really" think light is propagating at an angle between the mirrors or the distance between the mirrors is "really" contracted in a moving light clock (depending on the rotation of the clock), but your attempt to establish that this is the case is equivalent to denying the principle of equivalence. It's almost like you're arguing against my case for "true length" by attempting to assert a preferred frame of clock observation. There will always be a frame in which these things are not occurring.

The basis of my stance is that to have two observers make what are apparently logically contradictory statements (i.e. "both observers claim the others' clock is narrower than their own") then we can assign no absolute truth to those statements. There is only a single circumstance in which both parties agree with the others' assessment of the width of their clock relative to their own, and that is when they are inertial to each other. I've said many times that this is nothing, really, but a semantic convention but I feel the logic contains some merit. Does that make sense?

 

[GrayGhost]

ghWells,

Wrt "frame-of-reference", here's what was stated prior ...

OK, so you agree there is no natural sense in which changing velocities causes you to "transition" from one inertial frame to another, that it is just a matter of it being more convenient?

Well, I'd say it this way ... in a natural sense, whenever 2 observers are OF the same frame of reference, even if momentarily, they measure space and time the very same.

All observers are of all frames OF reference all the time

Here, you are debating the meaning of the word OF. I agree in that all bodies reside within the spacetime cooridinate system used by any observer. I'll restate what I said prior as follows ...

in a natural sense, when the coordinate system of each of 2 observers overlay each other perfectly, even if momentarily, they measure space and time the very same.​

When they overlay "only momentarily", then they measure space and time the same "momentarily", far as the infitesimal segment is concerned and as the infitesimal duration considered approaches zero.

It's not that I disagreed with JesseM. Indeed it is "more convenient" to do so, but I see something more there than JesseM does. Twin B always has his own frame-of-reference he uses. It just seems to me that there is no difference between twin B's own frame-of-reference, and the consideration of an inifinite number of contiguous-momentary-corresponding inertial-frames-of-reference (taken in collective) that twin B resides in "at the origin of each" ... far as spacetime coordinate transformations are concerned. If "said collective" is equivalent, then the SPACE-JUMP and TIME-JUMP in my prior illustration exists ... even though doppler effects do not reveal it casually. I see no reason whatever, as to why the twin B frame-of-reference would differ from said collective inertial frames-of-reference. The LTs were designed for all-inertial motion, but IMO they inherently require the twin B frame-of-reference be equivalent to said collective inertial frames-of-reference. I assume here that twin B uses a euclidean coordinate system as inertial observers do.

GrayGhost