The case for True Length = Rest Length

[GrayGhost]

ghwellsjr,

To refocus this discussion, I previously posted this illustration ...

scenario description here ...

https://www.physicsforums.com/showpost.php?p=3182687&postcount=235"​

Illustration here ...

https://www.physicsforums.com/attachment.php?attachmentid=32982&d=1299884366"​

The question was never anything more than this ... How does twin A map into the twin B system IF everyone flew as such?

My goal was to show that twin A must wildly jump thru space (per B) when B undergoes virtually instant proper accelerations. Again, this is per B's POV as the result of B's own proper acceleration, not any energy expenditure on A's behalf. Hand in hand with that, the twin A clock-readout must jump wildly per B. Add, the doppler effect changes abruptly as well. Now, I assume here that either twin may apply the LTs as they usually do, even if non-inertial, except that they must apply it to infitesimally small segments and sum the solns (solutions) over the interval. Of course, none of that matters given I've reduced the duration of acceleration to a virtual zero, for sake of simplicity and point.

You've raised a number of issues that you seem to think others disagree with. Just to mention a few ...

(1) observers cannot know how others move until light signals arrive revealing such.
(2) observers in relative motion disagree on the measure of space and time.
(3) The LTs were designed for the all-inertial case.

No relativist disagrees with these statements, I included. Now I have addressed each of these issues, more than once, yet you continue to come back with statements time and time again suggesting I disagree. I'm not sure why you do that, but it does slow down the discussion.

A couple other matters you (or JesseM) raised ...

(4) non-inertial observers may use any convention-of-simultaneity that they feel is valid.
(5) the LTs do not apply to non-inertial POVs.

IMO, whether (4) is true depends on what convention you are talking about. In SR, one may use a different sense-of-simultaneity, but then the 1-way speed of light is not c, although the 2-way speed may be c. When non-inertial though, the convention JesseM raised whereby the observer assumes the reflection event (of emitted radar EM) occurred at the roundtrip's-center-point, is no good in my opinion. Far as (5) goes, I remain unconvinced that this is true, assuming the LTs are applied for infitesimal segments and summed over the interval. It seems to me that the LTs apply within any instant of time, even though they were designed under the simple all-inertial case.

Make no mistake, I understand that no one can predict with certainty where a moving vessel might be in the present moment. Yet, the body does indeed exist "at some specific location NOW", and time will tell the story. My discussion has never been about "guessing" where the moving vessel is at present, but rather how it must map into twin B own's system "wherever it really is". I merely provided one axample whereby twin A remains always inertial, and that was for sake of simplicity and point. My point was merely to show the related required SPACE-JUMP and TIME-JUMP that I mentioned prior here.

GrayGhost

 

[ghwellsjr]

JesseM already addressed your linked post and its diagram. I was never involved in that discussion. It's torture to me.

But I will address your persistent claim of twin B's POV. I asked you some questions about it in post #275 which you ignored. I sincerely don't know what you are talking about and I need you to address my concerns. Here is a repeat of what I said in that post:

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?)​

So when you say POV, do you mean one of the three that I described or something else?

 

[Mike_Fontenot]

Excellent summary of the situation, GrayGhost.

Mike Fontenot

 

[Dale]

In SR, one may use a different sense-of-simultaneity, but then the 1-way speed of light is not c, although the 2-way speed may be c.

The naieve simultaneity convention does not preserve the 1-way speed of light to be c.

 

[GrayGhost]

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?

rjbeery,

Are you still out and about here? If so, I have a few comments that may help if you are interested.

GrayGhost

 

[rjbeery]

GrayGhost, I had planned on unsubscribing from this thread but hadn't done so yet. Anyway I'm all ears...

 

[GrayGhost]

JesseM already addressed your linked post and its diagram.

Indeed, but not to satisfaction.

I was never involved in that discussion. It's torture to me.

Could have fooled me. However, if you prefer not to discuss it then I'm OK with that. I'm happy to discuss whatever you wish, assuming time (and other factors) permit.

But I will address your persistent claim of twin B's POV. I asked you some questions about it in post #275 which you ignored. I sincerely don't know what you are talking about and I need you to address my concerns. Here is a repeat of what I said in that post:

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".​

Well, it was JesseM (or DaleSpam) who injected the term "natural" in relation to frame-of-reference.

I realize that there are different types of reference-frames, eg inertial, rotating, and accelerating. In SR, we use euclidean coordinate systems, and it is "natural" IMO to assign yourself "the origin" of the system you elect to use. This is because all inertial observers are obliged to assume "the stationary", which is always the most convenient choice. I personally assign B a euclidean system, himself the origin, initially at rest in the twin A frame. As he accelerates, remote moving bodies relocate in space and their clocks tick uncharacteristically (wrt the all-inertial case) during periods of B's own proper acceleration. I realize there are other ways of doing it, but that's what I personally envisioned in my stated scenario and illustration.

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?)

So when you say POV, do you mean one of the three that I described or something else?

From a navigation standpoint, here's what would be natural IMO ...

The CAPT of the ship spins up his navigation-gyro. The onboard computer system would align the x, y, and z-axes per reference-markers built within the ship. The x-axis might be the centerline bow-to-stern, z-axis top-to-bottom, y-axis portside-to-starboard. Etc. Then it would not matter which way the CPTN turns his head within the ship.

GrayGhost

 

[GrayGhost]

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?

rjbeery,

Here's my 2 cents ...

Relativistic effects exist when relative motion exists, and they are measurable. The only reason folks debate at length over whether they are real vs illusionary effect, is because ... although relative motion produces measurable length-contractions (and time-dilation), no body ever changes in-and-of-itself due to another's observational POV. This also suggests that no body ever changes in-and-of-itself due to its own proper acceleration. Relativists generally say that contractions "are real per the observer", because they are measurable. Others argue that the measured contractions are something-less-than-real, because the body never changed in-and-of-itself. IMO, it's just 2 ways of looking at the very same mechansim, and therefore comes down to semantics.

My view on "time being absolute in any way" is this ... Inherent in the special theory is that we all pass thru the 4d continuum at the rate of c. As an inertial observer, you experience this only as the passage of "proper time" while you sit there stationary, ie the rate at which time passes yourself per yourself. That may be considered an invariant IMO. However, the theory also requires that moving clocks tick slower, and each inertial observer is obliged to assume the stationary. The relative rate of clocks is about "relative time", which is something more than "proper time" alone, the result of "space and time" being interwoven into a single fused entity as the result of the 2 relativity postulates being true.

EDITED: Consider the 1st half of the classic twins sceanrio. The defined interval is A/B-to-A/X, X being planet X of the A frame (B's turnabout point). B begins and ends colocated with A, and of the A frame. Assume the proper separation between A and X to be length S, a length at rest in the A frame. Twin B must record this separation in motion, and thus length contracted at x = S/gamma. Assuming the rate of proper time is the same for all, then he who travels the shorter pathlength must accrue the least proper time, and thus age the least. That be twin B.

EDITED: In the all-inertial scenario, B travels inertially from A to X. The same mechanism applies there. All observers agree that B experiences less proper time than A (or X) wrt the defined interval A/B-to-X/B. However A & B do NOT agree on who aged the least. Each claims the other to have aged less, because of relative simultaneity and the fact that moving clocks tick slower. In the classic twins scenario, B ages less because his acceleration brings him back into the A frame, and since relativistic effects vanish at v=0, then disagreements (including who aged less) due to relative-simultaneity vanishes as well. So while you are correct in that acceleration forces "agreement" between the observers (which you refer to as absolute), the extent of aging over the interval depends entirely on the time spent in each inertial frame of reference (LTs depend on v, not dv/dt). Because the LTs use v and not acceleration, the twins must run the LTs for infitesimals and sum the results as they go.

GrayGhost

 

[Dale]

(4) non-inertial observers may use any convention-of-simultaneity that they feel is valid.
...

IMO, whether (4) is true depends on what convention you are talking about. In SR, one may use a different sense-of-simultaneity, but then the 1-way speed of light is not c, although the 2-way speed may be c. When non-inertial though, the convention JesseM raised whereby the observer assumes the reflection event (of emitted radar EM) occurred at the roundtrip's-center-point, is no good in my opinion.

Hi GrayGhost, I mentioned this briefly today, but now I have time to make a more complete response. Special relativity is based on two postulates, the first being that the laws of physics are the same in all inertial frames, and the second being that the (one way) speed of light is the same in all inertial frames. Now, unless you express things in terms of tensors, in non-inertial frames the first postulate is violated.

However, it is possible to make non-inertial coordinate systems which do not violate the second postulate (in flat spacetime). That is what the Dolby and Gull simultaneity convention does, it enforces the one-way speed of light postulate at all points. The usual naive simultaneity convention (aka Mike Fontenot's CADO convention) does not preserve the second postulate. This doesn't mean that it cannot be used, just that if maintaining the second postulate is one of your decision factors then you would probably opt for Dolby and Gull instead.

 

[ghwellsjr]

I realize that there are different types of reference-frames, eg inertial, rotating, and accelerating. In SR, we use euclidean coordinate systems, and it is "natural" IMO to assign yourself "the origin" of the system you elect to use. This is because all inertial observers are obliged to assume "the stationary", which is always the most convenient choice. I personally assign B a euclidean system, himself the origin, initially at rest in the twin A frame. As he accelerates, remote moving bodies relocate in space and their clocks tick uncharacteristically (wrt the all-inertial case) during periods of B's own proper acceleration. I realize there are other ways of doing it, but that's what I personally envisioned in my stated scenario and illustration.

What do you mean "obliged"? Is this something you think is a forced requirement of SR? Or is it just because you think it "is always the most convenient choice"? Or something else?

And what if there are two inertial observers in relative motion--how do they both assume "the stationary"?

From a navigation standpoint, here's what would be natural IMO ...

The CAPT of the ship spins up his navigation-gyro. The onboard computer system would align the x, y, and z-axes per reference-markers built within the ship. The x-axis might be the centerline bow-to-stern, z-axis top-to-bottom, y-axis portside-to-starboard. Etc. Then it would not matter which way the CPTN turns his head within the ship.

GrayGhost

But what about when the ship gets to its final position and starts coming back home--does the direction of the X-axis remain the same as it was before so that the ship is now progressing in the opposite direction or does the entire coordinate system flip around so that the ship continues in a positive X direction throughout the whole trip? I'm trying to figure out which of the first two options I previously mentioned you are describing.

 

[GrayGhost]

Hi GrayGhost, I mentioned this briefly today, but now I have time to make a more complete response. Special relativity is based on two postulates, the first being that the laws of physics are the same in all inertial frames, and the second being that the (one way) speed of light is the same in all inertial frames. Now, unless you express things in terms of tensors, in non-inertial frames the first postulate is violated.

Thanx DaleSpam. My reasoning has been conceptual, and based upon an extrapolation of the special theory to the non-inertial case. In my reasoning, I do not see how either postulate would be violated. It seems to me that the same laws of nature should be upheld. However, my line of reasoning requires that twin A advance (or digress) along his worldline more (or less) than the usual case when inertial, and (only) per twin B as he undergoes proper acceleration. In my view, such an interpretation should allow the laws of nature to be unscaved. I'm not using any math model of my own, just an extrapolation of the special theory to the accelerational case. I realize that when B undergoes proper acceleration, that the heavens do not expend energy to move just for him and his POV. I envision the heavens moving as B accelerates similarly as the stars move at nightime, except that relative velocity plays an equal role in the POV's relative orientation change.

I have found that when you make a statement online here, one can generally take it to the bank, so I suppose studying the general theory would help immensely. Just so I know, when you get a chance, can you state in a short brief para how the 1st postulate is violated w/o the use of tensors? I'm just curious as to whether what I'm envisioning can stand up against the violations. If not, I would then have to reconsider it.

However, it is possible to make non-inertial coordinate systems which do not violate the second postulate (in flat spacetime). That is what the Doby and Gull simultaneity convention does, it enforces the one-way speed of light postulate at all points. The usual naive simultaneity convention (aka Mike Fontenot's CADO convention) does not preserve the second postulate. This doesn't mean that it cannot be used, just that if maintaining the second postulate is one of your decision factors then you would probably opt for Doby and Gull instead.

Can you please post me a reference for that Doby and Gull convention? I can't recall if you posted that link in the past, and I'd like to take a look at it. Thanx.

GrayGhost

 

[Dale]

Just so I know, when you get a chance, can you state in a short brief para how the 1st postulate is violated w/o the use of tensors? I'm just curious as to whether what I'm envisioning can stand up against the violations. If not, I would then have to reconsider it.

It is actually essentially a tautology. The first postulate says that the laws of physics have the same mathematical form in all inertial frames. This is essentially a definition of an inertial frame, i.e. an inertial frame is one in which the laws of physics takes their standard form. Therefore, if you find a coordinate system where the first postulate holds, then that coordinate system is inertial. So conversely, in all non-inertial coordinate systems, the laws of physics do not take their standard form, by definition.

The reason I mention tensors is simply that in tensor notation all laws take their standard form regardless of the coordinate system. So there is no distinction between inertial and non-inertial coordinate systems that way.

Can you please post me a reference for that Doby and Gull convention? I can't recall if you posted that link in the past, and I'd like to take a look at it.

Certainly, here is the arxiv article by Dolby and Gull:
http://arxiv.org/abs/gr-qc/0104077

 

[bobc2]

GrayGhost, I had planned on unsubscribing from this thread but hadn't done so yet. Anyway I'm all ears...

Glad to see you are still all ears, rjbeery. I still cannot reconcile your idea that acceleration of the round-trip twin causes the difference in aging.

I've plagarized DrGreg's original graphics illustrating the 4-dimensional motion of three observers. I don't think you ever satisfactorily responded to DrGreg's post. However, I'd like to break the analysis down into two steps:

1) Do you maintain, or can you demonstrate that the changing instantaneous 3-D cross-section views of observer A below actually changes the rate of aging of observer C (remaining at rest in the black coordinate system)? Because you can see that manifestly C ages at a uniform rate as he moves along the tC (C's time axis) at the speed of light. Yes, A's view of C's clock is not consistent with the actual aging of C along C's world line. But, just because A views the C clock does not physically cause it to tick slower or faster. If A closed his eyes and decided not to observe C's clock, would C age faster during A's acceleration period? Of course not. A observing C has no effect on C's aging process.

Thus, the aging rate of C is fixed.

2) Now, what about the aging rate of A? Does A's rate of aging change while he is accelerating? As measured in the black coordinates, you can see clearly the variation in proper time increments along the world line of A. The rate of aging is very slow during the outgoing and return world line segments corresponding to constant relativistic speeds. During the turnaround negative acceleration portion of A's worldline, A's aging actually speeds up (with respect to black coordinates)--you see the proper time increments are much more closely spaced over that curved part of A's worldline.

Thus, even in the black coordinate system, C is actually aging much faster than A during A's constant speed (straight line) portion of A's worldline. And of course, A is always moving at the speed of light along his world line--thus, it is the fact that A is following a much shorter path through 4-dimensional space that accounts for the spaced out proper time increments.

Having said all of that, I return to my original analysis of many posts back that if you are going to compare aging processes, you should be comparing proper distance lengths of the world lines (remembering each observer moves along his worldline at the speed of light). And in this analysis the observer taking the shorter worldline path is the younger of the two observers when they meet again.

p.s. I included the worldline for observer B in case you wished to comment on DrGreg's original observations. If A and B both undergo the same acceleration, why is it that the age differences were not the same for A compared to C and then B compared to C? And did C's aging change two times, once for A and then again for B?

 

[GrayGhost]

What do you mean "obliged"? Is this something you think is a forced requirement of SR? Or is it just because you think it "is always the most convenient choice"? Or something else?

Obliged = is allowed to, if one desires to. The stationary POV is not a forced requirement in SR, however it is almost always the case that one desires to assume such, because of the convenience that results. It should also be pointed out that the LTs are designed for an observer who assumes the stationary POV. They transform spacetime coordinates in your own stationary system into coordinates of the moving observer's system (also deemed as stationary per he).

And what if there are two inertial observers in relative motion--how do they both assume "the stationary"?

Each assigns himself a euclidean coordinate system with himself assigned "always the origin".

But what about when the ship gets to its final position and starts coming back home--does the direction of the X-axis remain the same as it was before so that the ship is now progressing in the opposite direction or does the entire coordinate system flip around so that the ship continues in a positive X direction throughout the whole trip? I'm trying to figure out which of the first two options I previously mentioned you are describing.

Well, I suppose it depends on what you might be calling the x,y,z axes. There are a number of sets-of-axes involved aboard a ship. The gyro spin-axis is related to the gyro system's axes. The navigation system will relate the gyro system's axes to both "ship's-axes and spatial-axes". The ship's axes are fixed wrt the ship-hull itself. The spatial-axes are fixed wrt some unchanging reference in space ... true north for military vessels, but some fixed star(s) assuming deep space travel. So to cut to the chase, the navigation system will present a dynamic ship-coordinate-system (which rotates as the ship turns) within a fixed star-coordinate-system (which never rotates).

GrayGhost

 

[ghwellsjr]

Obliged = is allowed to, if one desires to.

What dictionary did you get that out of? Can you point me to an online reference that provides that definition, please?

Each assigns himself a euclidean coordinate system with himself assigned "always the origin".

According to the wikipedia article on Lorentz Transformation, "the origins of both coordinate systems are the same" (in order to be in the Standard Configuration which is what you used in your diagram). What do you think that means?

Well, I suppose it depends on what you might be calling the x,y,z axes. There are a number of sets-of-axes involved aboard a ship. The gyro spin-axis is related to the gyro system's axes. The navigation system will relate the gyro system's axes to both "ship's-axes and spatial-axes". The ship's axes are fixed wrt the ship-hull itself. The spatial-axes are fixed wrt some unchanging reference in space ... true north for military vessels, but some fixed star(s) assuming deep space travel. So to cut to the chase, the navigation system will present a dynamic ship-coordinate-system (which rotates as the ship turns) within a fixed star-coordinate-system (which never rotates).

GrayGhost

I'm asking you what you mean by POV and now you are suggesting that there are at least two coordinate systems in use by the traveling twin at the same time. Can you understand how I still don't know what you mean by POV?

 

[GrayGhost]

rjbeery,

I noticed that I butchered the last (long) paragraph in my prior post to you, as I made it in haste. I've redited that final para, which is now 2 paras. If you already read it before I edited it, please see it again. Sorry about that. The hyperlink is here ...

hyperlink above

When you say "acceleration makes time absolute", I take it that you mean all observers agree as to how much twin A and B aged, and who aged the least. I agree with you on that matter. However, I'd state it this way ... the age disgreement vanishes because they begin and end in the same frame of reference, because relative simultaneity (the cause of disagreement) vanishes when v=0. I suppose that's to say the same thing, but just in a different way.

GrayGhost

 

[GrayGhost]

What dictionary did you get that out of? Can you point me to an online reference that provides that definition, please?

Well, you got me there, lol. Call it the dictionary of GrayGhost ...

http://www.thefreedictionary.com/obliged"​

Each "does himself a favor" by assuming the stationary because it is convenient :)

According to the wikipedia article on Lorentz Transformation, "the origins of both coordinate systems are the same" (in order to be in the Standard Configuration which is what you used in your diagram). What do you think that means?

Man, you're picky :) OK then ... Of course the system origins are the same. However, "each possesses a vertical worldline" that intersects x=0 at t=0, and their worldlines are not colinear.

I'm asking you what you mean by POV and now you are suggesting that there are at least two coordinate systems in use by the traveling twin at the same time. Can you understand how I still don't know what you mean by POV?

OK, prior you said ...

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?)

Well, there are multiple sets of axes involved in any navigation system. However if I picked a coordinate system to act as the ship's POV, I figure the POV highlighted here could apply to the ship. That is, the positive X direction coming out of the bow, the +Y direction coming out of the starboard side, and the +Z direction coming out the roof of the ship. These are standard fixed-ship-axes. If the ship turns or accelerates, the heavens appear to move while it maintains itself the stationary.

The reason I've been focused on twin B, is because his POV is more complex than twin A's. Twin A's is far easier. The heavens do not move wildly within the A-system when twin B accelerates. So applying the LTs to infitesimals is a little more complex for B than A. Both have to account for the fact that velocity can change during any infitesimal. However, twin B also has to account for the heavens moving during the infitesimal segments considered, which affects his LT solns (when transforming to the twin A system) because his sense of simultaneity rotates. The smaller the infitesimal, the less the error.

GrayGhost

 

[ghwellsjr]

Well, you got me there, lol. Call it the dictionary of GrayGhost ...

http://www.thefreedictionary.com/obliged"​

Each "does himself a favor" by assuming the stationary because it is convenient :)

Chalk it up to "semantics".

Man, you're picky :) OK then ... Of course the system origins are the same. However, "each possesses a vertical worldline" that intersects x=0 at t=0, and their worldlines are not colinear

GrayGhost, have you seen any description or explanation of the Lorentz Transform that says that the "observer" for each frame is even in the frame, let alone forever fixed at the origin? I believe the intent is that the observer for each frame is as a super-observer like you or me looking at all parts of the frame at the same time. We are not bound by the speed of light or energy or anything else. We can pop down clocks, spaceships, rulers, and even people any where we want at any fraction of the speed of light.

OK, prior you said ...



Well, there are multiple sets of axes involved in any navigation system. However if I picked a coordinate system to act as the ship's POV, I figure the POV highlighted here could apply to the ship. That is, the positive X direction coming out of the bow, the +Y direction coming out of the starboard side, and the +Z direction coming out the roof of the ship. These are standard fixed-ship-axes. If the ship turns or accelerates, the heavens appear to move while it maintains itself the stationary.

The reason I've been focused on twin B, is because his POV is more complex than twin A's. Twin A's is far easier. The heavens do not move wildly within the A-system when twin B accelerates. So applying the LTs to infitesimals is a little more complex for B than A. Both have to account for the fact that velocity can change during any infitesimal. However, twin B also has to account for the heavens moving during the infitesimal segments considered, which affects his LT solns (when transforming to the twin A system) because his sense of simultaneity rotates. The smaller the infitesimal, the less the error.

GrayGhost

What would happen if twin B decelerated when he got to his maximum distance away from twin A until he was stopped with respect to twin A and came to rest? What would his POV be and what would he see?

 

[GrayGhost]

GrayGhost, have you seen any description or explanation of the Lorentz Transform that says that the "observer" for each frame is even in the frame, let alone forever fixed at the origin?

The LTs are designed with a starting reference event, ie the intersection of the 2 system origins. That's where the 2 worldlines intersect. There may be an observer anywhere at rest in either of the 2 frames. However, the cooridinate system itself is a POV whether any observer resides at its origin "to behold of it" or not. It's natural for an observer to assign himself the origin of the system he assigns to himself, and so it's also natural (in thought) to assume an observer located at the origin of a system.

I believe the intent is that the observer for each frame is as a super-observer like you or me looking at all parts of the frame at the same time. We are not bound by the speed of light or energy or anything else. We can pop down clocks, spaceships, rulers, and even people any where we want at any fraction of the speed of light.

I figure that the intent of the LTs is to map coordinates in spacetime between 2 inertial systems that move relatively. I don't see the need for "super", myself. It's just the way it is. Indeed, any material thing may be anywhere and of v<c, and in thought we might imagine anything that "could exist". Far as not being bound by c, all is possible in the imagination. That is, we can imagine the guy is "over there right now", even though light signals have not yet proven such. Time tells the story :)

What would happen if twin B decelerated when he got to his maximum distance away from twin A until he was stopped with respect to twin A and came to rest?

He'd be at rest with twin A, but remotely located.

What would his POV be and what would he see?

Depends. Do you define POV as what he sees per his own eyes, or the vessel he's in that got him there? I mean, let's say the CAPT turns his head for a moment while the ship's in transit. Should the POV change here? From an SR standpoint, coordinate systems are inertial and do not rotate.

In real life, granted, it's another matter and becomes much more complex. But from an SR standpoint, the origin of a coordinate system has a POV. If an inertial observer is at said origin, he beholds the same POV. Twin B's POV at the turnabout point, when back in the A frame, is defined by the LTs (amongst other things).

GrayGhost

 

[ghwellsjr]

Back in post #271, you defined your use of POV to be a specific FOR in which the observer is at the origin:

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).

Now you are saying that it's still a POV even if there is no observer located at the origin:

The LTs are designed with a starting reference event, ie the intersection of the 2 system origins. That's where the 2 worldlines intersect. There may be an observer anywhere at rest in either of the 2 frames. However, the cooridinate system itself is a POV whether any observer resides at its origin "to behold of it" or not. It's natural for an observer to assign himself the origin of the system he assigns to himself, and so it's also natural (in thought) to assume an observer located at the origin of a system.

And then you ask me how I define POV:

Do you define POV as what he sees per his own eyes, or the vessel he's in that got him there? I mean, let's say the CAPT turns his head for a moment while the ship's in transit. Should the POV change here? From an SR standpoint, coordinate systems are inertial and do not rotate.

In real life, granted, it's another matter and becomes much more complex. But from an SR standpoint, the origin of a coordinate system has a POV. If an inertial observer is at said origin, he beholds the same POV. Twin B's POV at the turnabout point, when back in the A frame, is defined by the LTs (amongst other things).

GrayGhost

I never use POV except in this thread when trying to figure out what you mean by it. You will note in my first quote above, I said:

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.​

You are the one who insists on putting a non-inertial observer at the origin of some kind of non-inertial FOR or at the origins of a series of inertial FOR's or whatever it is you have in mind that you don't seem to be able to communicate precisely. So that is why I'm asking you to consider the observer (twin B) after he has come to rest with respect to his twin at the halfway point of his trip. Please describe his POV that you think is natural for him and decribe what he sees of his twin, the twin's clock, the heavens, and all the other descriptions that you gave earlier when the traveling twin did not stop but instead reversed direction.

Please understand, I am not debating you, I'm trying to understand you, but you have to be precise and clear and not turn my questions back on me.

 

[GrayGhost]

Please understand, I am not debating you, I'm trying to understand you, ...

OK, I appreciate that, thanx.

Back in post #271, you defined your use of POV to be a specific FOR in which the observer is at the origin:

Now you are saying that it's still a POV even if there is no observer located at the origin:

And then you ask me how I define POV:

Indeed.

I said:

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.​

Well, I agree with your second sentence here. I disagree with the first sentence ... The measurement made by one's own ruler is related to the ruler itself, and the units-of-measure wrt said ruler is related to the units-of-measure wrt one's own assigned coordinate system axes. The frame-of-reference assigned to oneself is the (say) cartesian cooridnate-system assigned to oneself. So I see them all as related. Now, I do realize that a measurement may be made w/o the consideration of mapping said measurements into a coordinate system. Normally you would want to map it, but maybe you only wish to know (say) the separation and do not care about the mapping within the system. Yet, this does not mean the coordinate system and the measurements made by rulers are not related, IMO.

You are the one who insists on putting a non-inertial observer at the origin of some kind of non-inertial FOR or at the origins of a series of inertial FOR's or whatever it is you have in mind that you don't seem to be able to communicate precisely.

I'm not sure how else to communicate it. I tweeked an old illustration and posted it, and provided a narrative description of it. The debates here have been over side-issues, mainly semantics, and not my specific point at hand.

At one point or another here, I think everyone has agreed that I consider ... twin B's experience during non-inertial motion is the "collective equivalent" of an infinite number of contiguous corresponding inertial frames-of-reference of which twin B momentarily occupies. I do not see this as the frankenstein-force-fit description, as DaleSpam suggested prior. IMO, twin B's POV "actually is" the very same as said collective equivalent. However, twin B must sum the LT solutions for each of those infitesimal segments considered (over the interval), and this summing is what allows the LTs that were designed for the all-inertial case to apply to the non-inertial POV.

So that is why I'm asking you to consider the observer (twin B) after he has come to rest with respect to his twin at the halfway point of his trip. Please describe his POV that you think is natural for him and decribe what he sees of his twin, the twin's clock, the heavens, and all the other descriptions that you gave earlier when the traveling twin did not stop but instead reversed direction.

When twin B comes to rest with A at the turnabout point, his POV is the same as A's in these respects ...

wrt A (and thus B), the following apply ... Bodies in motion are length-contracted and clocks in motion tick slower than his own. No doppler effects are existent wrt EM radiated by inertial sources stationary wrt A (and thus B). Otherwise, the EM is doppler shifted per the doppler eqn of speical relativity. The effects of gravitation are "considered ignorable" in my responses here.​

GrayGhost

 

[ghwellsjr]

The measurement made by one's own ruler is related to the ruler itself, and the units-of-measure wrt said ruler is related to the units-of-measure wrt one's own assigned coordinate system axes. The frame-of-reference assigned to oneself is the (say) cartesian cooridnate-system assigned to oneself. So I see them all as related. Now, I do realize that a measurement may be made w/o the consideration of mapping said measurements into a coordinate system. Normally you would want to map it, but maybe you only wish to know (say) the separation and do not care about the mapping within the system. Yet, this does not mean the coordinate system and the measurements made by rulers are not related, IMO.

OK, you're saying that after an observer makes measurements, he has the option of mapping them to a coordinate system. That part I get and agree with. I'm still unclear about which coordinate system you think is assigned to the observer.

At one point or another here, I think everyone has agreed that I consider ... twin B's experience during non-inertial motion is the "collective equivalent" of an infinite number of contiguous corresponding inertial frames-of-reference of which twin B momentarily occupies. I do not see this as the frankenstein-force-fit description, as DaleSpam suggested prior. IMO, twin B's POV "actually is" the very same as said collective equivalent. However, twin B must sum the LT solutions for each of those infitesimal segments considered (over the interval), and this summing is what allows the LTs that were designed for the all-inertial case to apply to the non-inertial POV.

(It was JesseM, not DaleSpam, that made that suggestion. See post #236.)
Here's another thing I don't understand. You keep talking about an observer using Lorentz Transforms to solve for something involving summing but you have not made it clear what the starting inertial frame is that he is working with, nor the set of events (1 time and 3 spatial coordinates) in that frame, nor the relative speed between that first FOR and the FOR he wants to convert the events in to. And after doing that for one FOR and he does it again for the next FOR, what is it that he sums and what is the significance of the sum? I just have no idea what you are thinking. Please elaborate instead of just repeating the same general recipe.

When twin B comes to rest with A at the turnabout point, his POV is the same as A's in these respects ...

wrt A (and thus B), the following apply ... Bodies in motion are length-contracted and clocks in motion tick slower than his own. No doppler effects are existent wrt EM radiated by inertial sources stationary wrt A (and thus B). Otherwise, the EM is doppler shifted per the doppler eqn of speical relativity. The effects of gravitation are "considered ignorable" in my responses here.​

GrayGhost

Well, since we only have twin A and twin B with no relative motion, then the only thing in your list that might apply is "No doppler effects are existent wrt EM radiated by inertial sources stationary wrt A (and thus B)", but I'm not sure if you meant that to also apply to both A and B or if you meant to only apply it to other potential objects/observers and specifically exclude twin A and twin B.

But what I need to know is the differences between the POV for the two twins. Do they share any of the coordinates between their two FOR's? Do they have the same time coordinate? Do they share any of their spatial axes? Do all their axes point in the same direction?

Can you please fill in these details even if you think they are obvious, because they are not obvious to me.

Thanks.

 

[Dale]

twin B's experience during non-inertial motion is the "collective equivalent" of an infinite number of contiguous corresponding inertial frames-of-reference of which twin B momentarily occupies. I do not see this as the frankenstein-force-fit description, as DaleSpam suggested prior. IMO, twin B's POV "actually is" the very same as said collective equivalent.

You certainly can arbitrarily adopt that convention and define B's POV in that way. But that is merely a personal choice and is not a standard convention. That convention has some problems, such as the fact that the one way speed of light is not c in it, and that it assigns multiple coordinates to the same event. But you are certainly free to use it anyway.

The point is that the phrase "B's POV" unambiguously refers to the reference frame where B is at rest if B is inertial, but if B is non-inertial it is ambiguous unless you specify what convention you are using.

 

[GrayGhost]

You certainly can arbitrarily adopt that convention and define B's POV in that way. But that is merely a personal choice and is not a standard convention. That convention has some problems, such as the fact that the one way speed of light is not c in it, and that it assigns multiple coordinates to the same event. But you are certainly free to use it anyway.

Well, the twin B POV is not an always-inertial POV. Your 2 points here are valid, however whether that's any real problem depends on how you look at the overall-picture there. Where you figure the 1-way speed of light cannot be c, I figure it differently ... that events move in spacetime (per B) while he himself undergoes proper acceleration. They must move in a way that ensures the 1-way speed of light is always c, during-any-single-moment-considered anywhere in space (per B). The LTs define the spacetime relation between the twin A and B POVs, and since the LTs require the 1-way speed of light to be c, then never can the speed of light "not be c" for-any-moment-considered at-any-location-in-space.

During twin B's own proper acceleration, events move, and bodies move thru space and time non-linearly, IOWs differently than what would be expected in an all-inertial case (in which case events don't even move). Twin A is inertial, and at any point during twin B's traversal, B exists at some specific location in space and time (per A). If twin A is diligent enough, then at any said moment, twin A can determine (by summing LTs solns for infitesimal segments as he goes) how A himself must exist in space and time per twin B, and also what twin B's clock should then read. When we later look at twin B's clock, nav data, and track data, twin B should hold twin A precisely where twin A predicted he would. Both observers are bound by the LTs, and the spacetime coordinates are invariant under rotation.

The point is that the phrase "B's POV" unambiguously refers to the reference frame where B is at rest if B is inertial, but if B is non-inertial it is ambiguous unless you specify what convention you are using.

Well, therein lies the problem IMO. I'd say by Einstein's convention, in the sense that the 1-way speed of light is c across the all-of-space in any single moment considered (per B). However, the Einstein convention is ... T₁ = 1/2*(T₀+T₂). This convention cannot apply (per B) in-the-usual-all-inertial-way during B's own proper acceleration, because events, including emission, reflection, and reception move as his own acceleration continues. Yet, what is upheld is this ... light's speed is always c in-any-moment-considered at-any-point-in-space. Also, add that there is no convention that can consistently correctly guess where anyone is in space (now), given said-other has the ability to undergo proper acceleration and his flight is not preplanned. However, each twin does have the ability to determine where-the-other-twin-was when his own radar's reflection event occurred (off the other twin), although that would be a more difficult thing for twin B to determine compared to the ease of the all-inertial observer (ie A) or the all-inertial scenario. The fact is, each observer exists at some specific location in spacetime, and if the convention used does not accurately figure it, then the convention is somewhere between less-than-perfect and unsatisfactory IMO.

GrayGhost

 

[Mike_Fontenot]

[...]The LTs define the spacetime relation between the twin A and B POVs, and since the LTs require the 1-way speed of light to be c, then never can the speed of light "not be c" for-any-moment-considered at-any-location-in-space.
[...]

Just FYI:

When I wrote my original relativity paper (which derives and explains the CADO equation), I referred to the quantity "v" (or its nondimensional version beta) as "the velocity of the traveler, relative to the home twin", without specifying "according to WHOM?". It is well known that any two inertial frames will always agree about their relative velocity ... it is not necessary to specify "according to WHOM?" in that case.

The CADO reference frame is DEFINED by requiring that the accelerating traveler, at each instant of his life, always agree (about remote distances and times) with the inertial frame with which he is momentarily stationary at that instant. I call that the "MSIRF(t)", for "Momentarily Stationary Inertial Reference Frame" at the instant "t" in the traveler's life.

And since the home twin's inertial frame always agrees about relative velocity with each of those MSIRF's, I thought that the accelerating traveler must also agree. That's why I didn't feel the need to specify "according to WHOM?" when I referred to the quantity "v" or "beta" in my paper.

But I later realized that I was incorrect: the accelerating traveler does NOT agree about velocities with his current MSIRF. They agree about distances and times at that instant, but not about velocities at that instant. The reason lies in the fact that velocities always by definition are based on changes of a distance during a very small change in time. I.e., the velocity of the home twin, relative to the traveler, according to the traveler, at some instant t of his life, refers to how that distance changes for two very closely-spaced times of his life very near the instant t. And the MSIRF's at those two different times in his life AREN'T the SAME inertial reference frame. THAT'S why the traveler generally won't agree about relative velocities with his current MSIRF.

Fortunately, this omission on my part didn't affect the results in my paper, because all the results were correct when the quantity "v" and "beta" in my equations referred to the velocity of the traveler, relative to the home twin, ACCORDING TO THE HOME TWIN. I.e., it WAS necessary for me to specify "according to WHOM" when I referred to a relative velocity.

Mike Fontenot

 

[GrayGhost]

Just FYI:

But I later realized that I was incorrect: the accelerating traveler does NOT agree about velocities with his current MSIRF. They agree about distances and times at that instant, but not about velocities at that instant. The reason lies in the fact that velocities always by definition are based on changes of a distance during a very small change in time. I.e., the velocity of the home twin, relative to the traveler, according to the traveler, at some instant t of his life, refers to how that distance changes for two very closely-spaced times of his life very near the instant t. And the MSIRF's at those two different times in his life AREN'T the SAME inertial reference frame. THAT'S why the traveler generally won't agree about relative velocities with his current MSIRF.

Indeed. Thanx for the correction there Mike. I've been thru this before, but it has been a very long time. So, while it makes the overall spacetime predictions more complex, it in no way makes it undo'able. Each twin has the added burden of predicting what the other holds as "the current" instantaneous-relative-velocity, which of course must be done to determine the gamma factor at that instant. So during periods of relative acceleration, the current "instantaneous velocity and gamma factor" are personal per POV. By "per POV", I mean "per twin A and per twin B".

GrayGhost

 

[Dale]

Where you figure the 1-way speed of light cannot be c, I figure it differently ... that events move in spacetime (per B) while he himself undergoes proper acceleration. They must move in a way that ensures the 1-way speed of light is always c, during-any-single-moment-considered anywhere in space (per B).

I am not following your description, I don't think that it is possible to avoid both of the problems that I mentioned above this way. Could you put it mathematically for clarity?

Say that you have an inertial unprimed frame:
$$(t,x)$$

And in that inertial frame there is an observer B with a timelike worldline:
$$(t_B(\lambda),x_B(\lambda))$$

What is the expression or operation to determine B's coordinates:
$$(t',x')$$

 

[GrayGhost]

Just FYI:

But I later realized that I was incorrect: the accelerating traveler does NOT agree about velocities with his current MSIRF (Momentarily Stationary Inertial Reference Frame). They agree about distances and times at that instant, but not about velocities at that instant. The reason lies in the fact that velocities always by definition are based on changes of a distance during a very small change in time. I.e., the velocity of the home twin, relative to the traveler, according to the traveler, at some instant t of his life, refers to how that distance changes for two very closely-spaced times of his life very near the instant t. And the MSIRF's at those two different times in his life AREN'T the SAME inertial reference frame. THAT'S why the traveler generally won't agree about relative velocities with his current MSIRF.

Mike,

I'll have to rethink my last response on this matter. I figure your paper may have had it right in the first place. I'll repost a new response on this soon.

GrayGhost

 

[GrayGhost]

I am not following your description, I don't think that it is possible to avoid both of the problems that I mentioned above this way. Could you put it mathematically for clarity?

I was wondering when you were going to get around to asking that question. Patience is a virtue :)

GrayGhost

 

[ghwellsjr]

I was wondering when you were going to get around to asking that question. Patience is a virtue :)

GrayGhoat

I was wondering when you are going to get around to answering my questions from post #302. I only have so much patience :)

 

[Mike_Fontenot]

[...]
So, while it makes the overall spacetime predictions more complex, it in no way makes it undo'able.
[...]

Actually, the calculations required to determine simultaneity according to the accelerating traveler, beyond those required to determine simultaneity according to the home-twin, are very simple and easy: basically, only one multiplication and one addition (or subtraction) are needed. Those simple arithmetic operations are performed on three quantities, all of which are as concluded by the (unaccelerated) home-twin. So those three quantities must be determined (for each instant of the accelerated traveler's life) regardless of whether you want to determine the traveler's "point-of-view", or the home-twin's "point-of-view".

The two additional simple arithmetic operations, that are required to determine the traveler's conclusions about simultaneity, are just those specified in the CADO equation, which is given here:

https://www.physicsforums.com/showpost.php?p=2934906&postcount=7 .

The three quantities that are needed in the CADO equation are defined in the above posting. All three quantities are computed using a single inertial frame: the frame of the home-twin.

In the idealized cases of instantaneous velocity changes, the determination of those three quantities is trivial.

For the more realistic cases of accelerations which are "piece-wise constant", the determination of the three quantities is more complicated, but they all still DO have closed-form analytic solutions, which are fairly widely known and will probably be familiar to almost everyone with a thorough understanding of special relativity (at the level of Taylor & Wheeler, for example).

For completely general acceleration profiles, the three quantities can still be determined, but numerical integration is required. Fortunately, those cases are rarely needed.

The CADO equation is valid for ALL situations where the "home-twin" is perpetually unaccelerated. It IS possible, if necessary, to determine simultaneity, according to each of two observers, who are BOTH accelerating, in completely arbitrary ways. But that again requires iterative numerical methods, and the simple CADO equation is not generally applicable in those cases.

Mike Fontenot

 

[GrayGhost]

I was wondering when you are going to get around to answering my questions from post #302. I only have so much patience :)

Touche^'

 

[GrayGhost]

Mike Fontenot,

My position is that the LTs must apply per twin B, even during his proper acceleration. If twin B and the momentarily colocated MSIRF-observer disagree on the instantaneous relative velocity of twin A (as you contend), then a problem arises. I've determined the root of this problem, and how to resolve it. Your contention that they must disagree, is half correct but incomplete IMO. I'll need some time to figure how to articulate this in a "cut to the chase" manner. That said, I am not sure as yet whether this has any impact on your paper.

GrayGhost

 

[Mike_Fontenot]

[...]
My position is that the LTs must apply per twin B, even during his proper acceleration.
[...]

The Lorentz equations DO apply. But the quantity "v" that appears in the Lorentz equations needs to be "the relative velocity between the home-twin and the traveler, according to the home-twin", NOT according to the traveler. Or, since the MSIRF(t) at any given instant "t" in the traveler's life, always agrees with the home-twin about their relative velocity, you can equally well specify the velocity "v" in the Lorentz equations as "the relative velocity between the home-twin and the MSIRF(t), according to the MSIRF(t)" ... it's the same number in either case.

Here's something for you to think about, while you are mulling all this over:

Take the standard twin "paradox" scenario, with gamma = 2. Suppose that immediately before the turnaround, their separation according to the home-twin, is L lightyears. The traveler says their separation is L/2 lightyears then.

Half way through the turnaround (when the home-twin says their relative velocity is zero), the home twin says their separation is still L, and the traveler NOW also says their separation is L lightyears. So the traveler says that their separation has changed by L/2 lightyears, during an infinitesimal amount of his ageing, so he says that their relative velocity during that first half of the turnaround has been infinitely large.

Denote the age of the traveler at the beginning of the turnaround as t1, and the age of the traveler at the midpoint of the turnaround as t1+delta, where delta is infinitesimally small, but non-zero). Denote the MSIRF at the beginning of the turnaround as MSIRF(t1), and the MSIRF at the midpoint of the turnaround as MSIRF(t1+delta) ... they are DIFFERENT inertial frames.

Ask yourself this: what do MSIRF(t1) and MSIRF(t1+delta) say about THEIR own separation (with respect to the home-twin) during the first half of the turnaround? Do either of them agree with the traveler, that the separation changes by L/2 during the infinitesimal time delta, and thus that the velocity during the time delta is infinitely large?

Mike Fontenot

 

[GrayGhost]

...

For reference ...

https://www.physicsforums.com/attachment.php?attachmentid=32982&d=1299884366"​

I've already thought thru all the points you mentioned in your last post here Mike, and I do not disagree with them. It does not change my opinion that your assumption of the instantaneous twin A velocity (per B) is incomplete.

(1) There is the relative twin B velocity recorded by twin A thru A-space over A-time.
(2) There is the relative twin A velocity recorded by twin B thru B-space over B-time.​

Wrt (2), there are 2 components of the relative velocity. Over a twin B virtually-instant-acceleration ...

component one ... is the relative velocity between B and an observer of the A-frame momentarily colocated with B. B will (virtually) agree with said inertial observer's assessment. This is the very same relative velocity that twin A holds of the remotely located luminal twin B.

component two ... is the added relative velocity (over and above component one) which results from the angular rotation of B's own sense-of-simultaneity, and this velocity component increases in conjunction with increased range (eg twin A range). This superpositional effect is why the inertial twin A can move superluminally wrt B per B, during B's rapid enough proper acceleration. It is not the result of any energy expenditure by (or upon) the always-inertial twin A. The further away twin A is, the faster twin A must traverse B-space per B, which in theory (unlikely in practice) could exceed speed c and approach infinite. However, this velocity component does not affect the slope of the twin A worldline, no matter how far away A might be from B.​

I submit that the instantaneous velocity of twin A per B (at some B-time) "is equivalent to" the slope of the B-worldline per A (at that same B-time).

The instantaneous velocity of twin A (from component one) is what must be used by twin B when B applies the LTs to any instant of his own time. He cannot use the collective velocity (both components added) within the LTs.

You said ...

Mike_Fontenot: The Lorentz equations DO apply. But the quantity "v" that appears in the Lorentz equations needs to be "the relative velocity between the home-twin and the traveler, according to the home-twin", NOT according to the traveler.​

So while you agree with me in that v must be that as recorded by twin A, you disagreed (prior) that "the instantaneous twin A velocity" as recorded by B can agree with the MSIRF-observer colocated with B. On the one hand I agree with you, given B is calculating twin A velocity in the classical way, ie change in recorded position over time. However on the other hand, the slope of the worldline is indicative of a velocity different from the classical calculation ... because classically, events (eg. the location of the A clock per B upon commencement of B acceleration) do not move in space and time with accelerated POVs.

So are we (maybe) saying the very same thing and I do not quite realize it, or is there anything in what I say that you disagree with?

GrayGhost