The case for True Length = Rest Length

[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 tommorrow.

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

 

[GrayGhost]

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?

My understanding is that a frame-of-reference is equivalent to a spacetime coordinate system. Twin B assigns the origin of a coordinate system to himself, and that represents his own frame-of-reference. I've generally referred to this as a point-of-view (POV). I have always assumed that the coordinate system assigned to oneself, is in essence equivalent (in part) to one's own ruler. I'm presuming you will disagree with this, yes? I mean, in thought experiment, the cooridinate system could be considered of rigid axes. In that case, what then would the difference between the coordinate system and the measuring ruler?

GrayGhost

 

[Mike_Fontenot]

I think one of the "disconnects" in these recent exchanges, is this:

1) Any object or person exists in ALL reference frames, and

2) Anyone can choose to ANALYZE the motion of any other person, by using ANY reference frame,

BUT

3) When GrayGhost refers to "the reference frame OF a particular person", I think he intends that it be a reference frame in which that person is permanently at rest at the spatial origin. Such a frame describes what the given observer concludes about the world surrounding him. [ADDENDUM #2: In particular, the reference frame OF a particular person DIRECTLY tells him how far away all objects are from him, AND what the current age of each of those objects is (and how the age of each of those objects is currently changing).]

[ADDENDUM: I hadn't seen GrayGhost's above post when I wrote the above comments (we were typing at the same time!) ... his above post says essentially what I was trying to get at above.]

Mike Fontenot

 

[GrayGhost]

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. 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.

Hmmm. I would think that twin A assigns a coordinate system to himself (as origin) regardless as to whether twin B exists, or whether he's considering twin B motion vs any other observer's motion. So I do not see it as pointless. Also, I don't see why either twin has to wait until the roundtrip is completed to use the LTs. They work no matter when they are applied by either twin, including for times after twin B departure and before twin B return.

Wrt your last sentence, I cannot understand why you are telling me this. I doubt anyone would disagree that "to see, you look".

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.

Wrt the 1st sentence here, please see my prior response above. Wrt the 2nd sentence here, SR is a local theory and no one can foresee the future. One might try to predict the future flight profile of another fellow, but it's nothing more than an educated guess. Wrt your 3rd sentence here, I am considering the twin B frame-of-reference equivalent to the collection of corresponding momentary-contiguous-inertial-frames-of-reference, and I figure the LTs work just fine as they always do. The only difference is that the LTs must be applied to infitesimal segments and summed (as you go), whereas in all-inertial scenarios you just run the LTs once because the motion never changes.

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 ... 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.

I have never even remotely suggested that any frame is preferred. In fact, I've stated many times over that the non-inertial POV is less convenient but no less preferred.

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

Easy ... LT solns = the results of LT calculations.

What's this about LT predictions? LTs cannot predict anything, they only convert values from one inertial frame to another.

Indeed the LTs transform, but they are run using the best known track data currently at hand. All systems have resolution limits, which thereby affects the precision of calculations. Observers attain LT results based upon imperfect input data. As the error in the input data approaches zero, the observer's prediction via Lorentz transformation approaches reality.

If there's one thing that anyone should learn after studying SR for any length of time, it is that time is relative.

I agree.

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.

Indeed, observers of relative v >0 are allowed (and expected) to disagree on simultaneity, which means the relativity of simultaneity allows observers to agree on their disagreements...

At some twin A hypothetical moment, let's say twin A determines the twin B clock should read 1.275 hr-B (post twin-B departure), and that twin B should then hold twin A currently at 2.115 lh-B downrange, with current velocity at 0.922c. If twin A later asks twin B ... hey, when you were at 1.275 hr by your own clock, how far downrange was I and what was my speed? ... if twin B does not say 2.115 lh at 0.992c, then twin A either screwed up his LT calculation of B, or the input data he used was inaccurate. Every observer, and no matter what his frame of reference, must agree that B will say "2.115 lh at 0.992c", assuming that all data used for predictions are precise and accurate.

GrayGhost

 

[GrayGhost]

Mike_Fontenot,

I'd say you summed it up well there, thanx.

GrayGhost

 

[ghwellsjr]

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'm debating the meaning of the word OF? You're the one that used it, I was just using your wording. I have no idea why you are saying that or why you bolded your first occurrence of the word OF and my second occurrence. I just don't know what this is all about.

I agree in that all bodies reside within the spacetime cooridinate system used by any observer.

It's not just that all bodies reside within the spacetime coordinate system used by any observer, it's that you should analyze the whole situation from one single spacetime coordinate system and it doesn't have to be one that is "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..

You seem to have this idea that there is a single natural coordinate system of any observer, but if natural is a meaningful term in this context, there are in fact many and I can think of several that might be considered "natural" but I have no idea if one of them is what you would consider "natural".

For example, in the Twin Paradox, it might be natural to define the X axis in the direction that twin B starts out and keep it that way for the whole trip, but it might also be natural to rotate it when twin B turns around so that he is always going in a positive X direction. Or maybe to be a little more like the Point Of View (POV) of an observer, we should place the positive X direction coming out of his nose, the Y direction going through his ears and the Z direction going out the top of his head. And, of course, after we get done doing this for twin B, we should do it all over again for twin A. (Why are you focusing so much on twin B?)

A while back, you made this statement:

I might add ... not only does twin A's distant luminal clock spin wildly during B's own rapid proper acceleration, eg the turnabout point, but twin A also flies wildly across the heavens (per B). Twin A doesn't do this on its own, but rather only because twin B's POV has changed while rapidly accelerating. The always inertial observer never experiences (or records) any such effect, because their sense-of-simultaneity never rotates since they never undergo proper acceleration.

But then you decided that twin B doesn't actually get to see twin A behaving this way but rather he has to determine that it is actually happening by calculation [I corrected a couple typos]:

First, a ways back, I made a misleading statement that suggested that the visual experience of twin B would witness the "time jump" (no time is ever missing though) during B's rapid turnabout. In fact, B will only observe the rapid doppler shift, not the A-time-jump. The A-time-jump exists, but must be determined because it cannot be seen visually. I believe I corrected that mis-statement in subsequent posts. The LTs reveal to twin B that the A clock advanced wildly during B's own rapid turnabout, even though the light signals show only a doppler shift ... and the doppler shift requires that twin A jumped wildly across space per B. In addition to the rapid doppler shift, if twin A was emitting pulses at periodic intervals, B (upon completion of his rapid turnabout) would note that the rate of receipt of said pulses increase by a factor of gamma.

Now this is really out of my realm because I don't like the torture of non-inertial frames but it seems to me that if you are using the first natural POV that I listed above, when twin A flies wildly across the heavens, that the heavens are also flying wildly and as soon as twin B's acceleration is finished, and he is back to his original speed (in the opposite direction), twin A has flown wildly back to his original position, along with the heavens. Since twin A has remained inertial during the entire trip and never experiences any acceleration, your frame of reference, POV, spacetime coordinate system, whichever term you like to use must calculate that twin A experienced no acceleration and therefore no wild flying or jumping. But I could be wrong. I don't like torture, especially self-inflicted.

But if you used the second POV, then twin A would not only fly across the heavens from far behind twin B but he would end up in front of him along with the heavens, because twin A never accelerates. But I could be wrong.

Now did you ever consider what would happen if twin A were using the third natural POV method going through the nose, ears and top of the head and he looked down at his feet? All of a sudden, wouldn't twin B go flying across the heavens (along with the heavens, of course)? I could be wrong. I hate torture.

I asked you before but never got a response: where did you come up with the factor of gamma in the last sentence of the previous quote?

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 as a collective POV) that twin B resides in "at the origin of each" ... far as spacetime coordinate transformations are concerned. If said collective POV 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

As stated earlier over and over again, you can use any frame of reference, even an arbitrary non-inertial one like "twin B's own frame-of-reference" (whatever that means) but twin B can't use it because he does not have the information that we have. He has to wait for the information concerning twin A to get to him (or rely on a prior agreement that twin A will not accelerate). And twin A can't use his "own frame-of-reference" (unless he relies on a prior agreement on when twin B will turn around and with what profile) because he certainly has no knowledge based on information available to him in real time of what twin B is doing. But whichever frame of reference you use, you must include both twins in it. After you figure out everything that is going on according to your favorite frame of reference, you can do it all over again with another one. If you had picked in inertial FOR, you could use the LT to convert from one FOR to another FOR, but that's even torture for me. I recommend picking the FOR that requires the least amount of calculation and that is one in which both twins start out at rest and end up at rest. You can use Relativistic Doppler to calculate what each twin sees and everything is soooo simple. I like that. Not that there is anything wrong with torture, I just don't like it.

 

[ghwellsjr]

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?

I already did in post #264.

If we say that the orbiting twin has a relative speed then the stationary one also has relative speed by definition, correct?

No, the orbiting twin has a relative speed and a non-relative or an absolute acceleration. That means we cannot consider the stationary one to be relative to the accelerating one, just like in the classic Twin Paradox when the traveling twin accelerates to take off, turn around or land at the end of the journey. It's only when the traveling twin is inertial that we can consider the stationary twin's speed to be relative to the traveling twin but the orbiting twin is never inertial so the stationary one cannot have a speed relative to him.

There is something that is different between the twins in this scenario, and it isn't speed...

That's right--it's acceleration.

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??

No and I apologize for being so unclear. I thought when I said

"It's not my claim that there is no absolute time in our real world."​

you would understand that I was not claiming credit for the idea and that I didn't make it up but that I learned it. Oh, but I already said that.

I'm curious, what is the issue with your bolding my word "will"? How does that imply that I believe time is absolute?

Now how about you, rjbeery? 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.

This is like SR101. Clocks slow down in a frame where they have a speed. Please understand, this other frame will see the same time difference on their clocks that they see when the reunite, but since the two twins' clocks are running slow then their age difference will be smaller, according to this other frame. Do I need to defend this fact? I guess until I apologize for being "clearly wrong" on this point, you are going to continue claiming that I am dismissive and glossing over your points.

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"?

Maybe you should provide a link or a post # when you want to quote me instead of just making things up. Are you thinking of post #213?

OK enough with the petty stuff.

No, that's not enough. I have sincerely tried to address your claims of when you thought I clearly wrong on a point. I asked you a question here:

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?

And you were dismissive, not even acknowledging the question. Please click on the link button (the little arrow to the right of your name) and tell me how you are not clearly wrong in the quotes following my question or thank me for pointing out your error. Otherwise, it is clear that you have no intention of playing by your own rules.

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.

It's truly a shame that you continue to misquote me. I have put in bold words that you claim I said that I didn't say. Why do you do that?

You have to pay careful attention to what I was saying. I was talking about an accelerating (not just moving) light clock. And there is no inertial frame in which the tick rate is not changing (I didn't say time dilation because that is a change in a particular direction) and then I said if the light clock were reoriented so that instead of the mirrors being parallel to the direction of accleration, they were perpendicular to the direction of acceleration, then I said the distance between the mirrors must change while the light clock is accelerating in order to maintain the same changing tick rate as it would have had in the first orientation. I know this is somewhat complicated when expressed in words but I would appreciate it if you would ask for clarification instead of just arguing it down.

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?

It's not a matter of whether it makes sense, the issue should be does it comport with reality. Even though you are now claiming that the only time the width of objects carried by two observers can only be compared when they are at rest with each other, that's not how you started out this thread. You started out by saying that two rods in relative motion have the same true length equal to their rest length. Don't you see the difference between these two claims?

Here's what you should learn and understand: when you have two rods in relative motion and the rods are aligned along the direction of relative motion, each rod will see, measure, observe, conclude, etc. that the other one is shorter than itself. But this assessment is just like the assessment of the relative speed. Nobody claims that when you have two object/observers/rods/clocks in relative motion that both of them at the same time are traveling at the same speed but in opposite directions. You recognize what each of them observes but then you assign an inertial frame of reference. As soon as you do that, the lengths of the rods take on an absolute nature for that frame of reference. If you choose a frame in which one of the rods is at rest, it will have what is called its rest length, but the other one will be shorter, not just as an illusion but absolutely for that frame of reference. Then you can stop using that frame of reference and switch to a frame of reference in which the second rod is at rest. Now it will be what is called its rest length and the first one will be shorter, both according to the frame of reference that is in effect. Now you can pick another frame of reference, say one in which both rods are moving in opposite directions but at something more than half of their relative speed. Now both rods will be the same length but shorter than their rest lengths for that frame of reference.

I sincerely hope this helps you, rjbeery.

 

[ghwellsjr]

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?

My understanding is that a frame-of-reference is equivalent to a spacetime coordinate system. Twin B assigns the origin of a coordinate system to himself, and that represents his own frame-of-reference. I've generally referred to this as a point-of-view (POV). I have always assumed that the coordinate system assigned to oneself, is in essence equivalent (in part) to one's own ruler. I'm presuming you will disagree with this, yes? I mean, in thought experiment, the cooridinate system could be considered of rigid axes. In that case, what then would the difference between the coordinate system and the measuring ruler?

GrayGhost

Yes, as I said in my reply to your previous post, a frame of reference is a spacetime coordinate system. It's used by those of us who are creating and using the thought experiments. It is sometimes thought of as a system of rigid rulers placed in all three dimensions with synchronized clocks at each junction. Or we could just draw it on a piece of paper or a screen in some approximation to 3-D. Or we could eliminate the Z-axis and illustrate just 2-axes of space and have it animated to provide the time axis in real time. Or we could eliminate one more axis of space and end up with a spacetime diagram. But do people do that in real-life? I've never seen it done. Astronomers probably have the closest thing to this streching out into space so that they can locate heavenly objects at any given time.

This kind of coordinate system is usually not too useful to the pretend observers in the thought experiment because we know everything that is going on from one end of the area of space under considertion to the other and our poor observers can only experience what they are aware of as it is made aware to them. I'm talking about the light travel time which is what these thought experiments are all about.

If you want to have your observers also have their own POV, or if you want to use their POV as the coordinate system for your scenario, then you are complicating matters immensely and for no good reason, in my opinion. But if you do, you should not think that because we can plop down information that we know into the coordinates system that that information is readily available to the observer. He can only know what comes to him by way of light signals when they reach him. This is the essence of the problem that Special Relativity addresses. You cannot sidestep that problem and allow the observer to know things ahead of time. It's important that we observe how that information is made available to the observer or otherwise, I don't see the point in doing the thought experiment.

I hope I have addressed your concerns. If not, please ask again.

 

[ghwellsjr]

I think one of the "disconnects" in these recent exchanges, is this:

1) Any object or person exists in ALL reference frames, and

2) Anyone can choose to ANALYZE the motion of any other person, by using ANY reference frame,

BUT

3) When GrayGhost refers to "the reference frame OF a particular person", I think he intends that it be a reference frame in which that person is permanently at rest at the spatial origin. Such a frame describes what the given observer concludes about the world surrounding him. [ADDENDUM #2: In particular, the reference frame OF a particular person DIRECTLY tells him how far away all objects are from him, AND what the current age of each of those objects is (and how the age of each of those objects is currently changing).]

[ADDENDUM: I hadn't seen GrayGhost's above post when I wrote the above comments (we were typing at the same time!) ... his above post says essentially what I was trying to get at above.]

Mike Fontenot

I think I have addressed most of these issues in my previous post to GrayGhost.

The real problem with what I see you attempting to do is promoting the idea that an observer can answer questions about things remote from him (times and distances) before information concerning those things has propagated to him via light signals. And the other problem is that you don't seem to grasp the concept of such things as the relativity of time. You seem to think that there are answers to questions like what time is on the one person's clock for every moment on the other person's clock. These questions do not have unique answers but are frame dependent and, of course, when you use a non-inertial frame or switch between frames, you can end up claiming that clocks go backwards or race forwards. It wouldn't be so bad if you would always bring up your first two points and just say, hey look what happens when you use my CADO technique, instead of claiming that it is the only correct way to do it (when there is no correct way).

 

[rjbeery]

ghwellsjr, the general demeanor of this thread has become, in my opinion, nonconstructive. I've made my case as best I can and we continue to have disagreements on many issues. Therefore I am bidding you adieu, thanks for your thoughts.

 

[ghwellsjr]

I would like to respond to some of your questions and concerns in this post but since you were composing it while I was composing post #275 where I addressed many of your concerns, I will not address them again here unless you call them to my attention again.

But if they want to see what things look like to themselves, they don't need frames or LTs, they just look.

Wrt your last sentence, I cannot understand why you are telling me this. I doubt anyone would disagree that "to see, you look".

Here's an example:

Your statement: The overall experience per twin B is twin A's wildly spinning distant clock during periods of twin B's own proper acceleration is not correct. Twin B (the traveling twin) never experiences twin A's clock wildly spinning and by that I mean twin B never observes twin A's clock wildly spinning.

In this you are mistaken, and so we disagree. The twins graphic rjbeery just threw up tells the story there. Not only can twin A's clock spin wildly per B "per the math" during B's own rapid proper accelerations (pos or neg), but twin B will also observe this similarly.

Now I realize that you have since changed your mind about this but I think it is a common mistake that many people make thinking that the information we have coming from a frame of reference is somehow available to an observer in our scenario if he is at the origin of the FOR.

Wrt the 2nd sentence here, SR is a local theory and no one can foresee the future. One might try to predict the future flight profile of another fellow, but it's nothing more than an educated guess.

I never liked the word "predict". I never thought it applied to LTs and never understood your use of the term.

Easy ... LT solns = the results of LT calculations.

So "solns" is an abbreviation for "solutions"?

Indeed the LTs transform, but they are run using the best known track data currently at hand. All systems have resolution limits, which thereby affects the precision of calculations. Observers attain LT results based upon imperfect input data. As the error in the input data approaches zero, the observer's prediction via Lorentz transformation approaches reality.

The Lorentz Transform is a mathematical process that perfectly converts events (space-time coordinates) from one frame of reference to another frame of reference. It does not make any kind of prediction. It does not give anybody any additional information that they did not already know. It only changes the four numbers that identify the X, Y, Z, and T values in one frame to their equivalent values in another frame.

At some twin A hypothetical moment, let's say twin A determines the twin B clock should read 1.275 hr-B (post twin-B departure), and that twin B should then hold twin A currently at 2.115 lh-B downrange, with current velocity at 0.922c. If twin A later asks twin B ... hey, when you were at 1.275 hr by your own clock, how far downrange was I and what was my speed? ... if twin B does not say 2.115 lh at 0.992c, then twin A either screwed up his LT calculation of B, or the input data he used was inaccurate. Every observer, and no matter what his frame of reference, must agree that B will say "2.115 lh at 0.992c", assuming that all data used for predictions are precise and accurate.

GrayGhost

I'm sure you have mistakes in this exercise. Could you please look it over and fix them, this doesn't make any sense at all. It appears that you have twin B traveling at faster than the speed of light.

But beyond that, the whole idea of trying to answer the question of how far twin B has traveled is frame dependent and you haven't specified the frame in which to answer the question. Or are you just assuming that it's obvious which frame should be used? Also, relative speeds are not frame dependent and yet you listed two different speeds but I suspect that is a typo.