Are accelerating lines of simultaneity correct?

[Austin0]

Your statements still aren't precise enough to make it crystal-clear to me what you are saying. Please try to be more precise and specific, if you can. Perhaps, just pick one of your numbered items, and try to make your statements absolutely crystal-clear.





Mike Fontenot

Hi Mike I am thinking of a context to make it explicit. In the meantime I have a very simple direct question.
Considering two lines of simultaneity that intersect before reaching Sue and then diverge and meet her worldline. What if both observers at Sues locations at those two events simply send messages to Tom giving their proper time and Sues.
DO you not agree that Tom would receive the message from the later observer [greater proper time reading] before the message from the observer with the lesser proper time?

 

[Mike_Fontenot]

[...]
Considering two lines of simultaneity that intersect before reaching Sue and then diverge and meet her worldline. What if both observers at Sues locations at those two events simply send messages to Tom giving their proper time and Sues.
DO you not agree that Tom would receive the message from the later observer [greater proper time reading] before the message from the observer with the lesser proper time?

Your statements are still imprecise. I'll formulate a specific example, complete with hard numbers, and post it as soon as time permits. Then perhaps there won't be any opportunity for any misunderstandings, or ambiguities.

But I can tell you now that, if the last paragraph of your posting of several days ago is the crux of what's bothering you, that's a typical example of perceived inconsistencies that always disappear as soon as you formulate your statements precisely.

Mike Fontenot

 

[Mike_Fontenot]

Here's a specific, precisely-described scenario for Tom (the accelerating traveler), and his (perpetually inertial) twin Sue:

We'll start at spacetime point A with Tom being about 40 ly from Sue, when Tom is 14 years old, and Sue is about 44.6 years old (all according to Sue). (I'll leave out how they got into this state...those details aren't required here). Their relative velocity is about -0.774c (they are moving toward one another). Tom says Sue is 75.5 when he is 14.

The line tangent to Tom's worldline at point A has the slope v = -0.774, so it slopes gradually downward to the right.

Tom's line of simultaneity at that instant in his life has the slope 1/v = -1/0.774 = -1.3 (approximately). So it slopes steeply downward to the right. The spacetime point (call it point C) where that line intersects Sue's worldline (the t0 axis) gives Sue's age when Tom is 14 (according to Tom). Because of the negative slope of that line, it is easy to see why Tom says Sue is older than she says she is, when he is 14. Sue's lines of simultaneity are all vertical lines. Call the intersection of the vertical line through point A, with Sue's worldline, point E (where Sue is 44.6 years old).

It will help if you plot these lines on the x0 vs t0 plane (Sue's coordinates).

Call the MSIRF at that instant in Tom's life MSIRF1, with coordinates x1 and t1. For simplicity, we can require all the inertial observers in MSIRF1 to be the same age as Tom at that instant (according to all those observers, not to Tom). The MSIRF1 observer momentarily co-located with Tom at that instant is named Toby (he happens to be a dog). For simplicity, we also take Toby's spatial location in MSIRF1 to be at x1 = 0. So the line tangent to Tom's worldline (described above) is the time axis (t1) of MSIRF1. And Tom's line of simultaneity at that instant is one of MSIRF1's lines of simultaneity (parallel to the x1 axis of MSIRF1).

The MSIRF1 observer momentarily co-located with Sue (when all of those observers are 14) is named Sissy (also a dog). Her distance from Toby (measured in the MSIRF1 frame) is 25.3 ly.

I'm not just trying to be funny with those names (although they ARE funny). It's hard to keep track of who's who, so I've chosen to name all the inertial observers, who are ever co-located with Tom during this scenario, with male names starting with "T", like Tom's does. And I've chosen to name all the inertial observers, who are ever co-located with Sue during this scenario, with female names starting with "S", like Sue's does. And, to help distinguish the observers in MSIRF1 from the observers in MSIRF2 (to be defined shortly), I'll use dog's names in MSIRF1 and cat's names in MSIRF2.

Next, Tom accelerates at +1g (in the direction away from Sue) for two years (of his life). At the end of that time (call it spacetime point B), he is the same distance from Sue as before (about 40 ly according to Sue, and about 25.3 ly according to Tom).

Tom is now 16 years old, and Sue is about 46.9 years old (according to Sue). Their relative velocity is about +0.774c (moving away from one another). Tom says Sue is 16.0 when he is 16.

The line tangent to Tom's worldline at this instant in his life has the slope v = +0.774, so it slopes gradually upward to the right.

Tom's line of simultaneity at that instant in his life has the slope 1/v = +1/0.774 = +1.3 (approximately). So it slopes steeply downward to the left. The spacetime point (call it point D) where that line intersects Sue's worldline (the t0 axis) gives Sue's age when Tom is 16 (according to Tom). Because of the positive slope of that line, it is easy to see why Tom says Sue is younger than she says she is, when he is 16. Sue's lines of simultaneity are all vertical lines. Call the intersection of the vertical line through point B, with Sue's worldline, point F (where Sue is 46.9 years old).

It will help if you also plot these lines on the x0 vs t0 plane (Sue's coordinates).

Call the MSIRF at that instant in Tom's life MSIRF2, with coordinates x2 and t2. For simplicity, we can require all the inertial observers in MSIRF2 to be the same age as Tom at that instant (according to all those observers, not to Tom). The MSIRF2 observer momentarily co-located with Tom is named Tabby (he happens to be a cat). For simplicity, we we also take Tabby's spatial location in MSIRF2 to be at x2 = 0. So the line tangent to Tom's worldline at this instant in Tom's life is the time axis (t2) of MSIRF2. And Tom's line of simultaneity at that instant is one of MSIRF2's lines of simultaneity (parallel to the x2 axis of MSIRF2).

The MSIRF2 observer momentarily co-located with Sue (when all of those observers are 16) is named Scratchy (also a cat). Her distance from Tabby (measured in the MSIRF2 frame) is 25.3 ly.

OK, we've got a well-defined and specific scenario now. It is consistent with your example, because the two lines of simultaneity (passing through points A and B) intersect between Tom and Sue.

Using the above scenario I've given, try to formulate the issue you were trying to raise in your posting of several days ago. Anytime you want to refer to an inertial observer, use the names I've given above. If you need other inertial observers, define and name them in a similar way to what I've done above. If you want to refer to an inertial frame, there are three of them above: Sue's frame, MSIRF1, and MSIRF2. Use those names. If you need others, define and name them. And I've identified six important spacetime points in the above description: points A, B, C, D, E, and F. If you want to refer to those spacetime points, use those names. If you need to refer to other spacetime points, define them precisely, and give them capital-letter names. Go for it!

Mike Fontenot

 

[yogi]

No. Simultaneity is a human-invented convention: very useful for doing calculations but of no experimentally-verifiable physical significance.

If you refer to the "one-way" speed of light from A to B, yes it's a convention determined by the definition of simultaneity you choose. But the "two-way" speed of light, from A to B and back to A again, is no convention, it's experimentally measurable and constant.

SIZE]

That is a great short clarifying statement that indentifies the root source of much of the misunderstanding that has evolved around this subject.

 

[Austin0]

Here's a specific, precisely-described scenario for Tom (the accelerating traveler), and his (perpetually inertial) twin Sue:

We'll start at spacetime point A with Tom being about 40 ly from Sue, when Tom is 14 years old, and Sue is about 44.6 years old (all according to Sue). (I'll leave out how they got into this state...those details aren't required here). Their relative velocity is about -0.774c (they are moving toward one another). Tom says Sue is 75.5 when he is 14.

The line tangent to Tom's worldline at point A has the slope v = -0.774, so it slopes gradually downward to the right.

Tom's line of simultaneity at that instant in his life has the slope 1/v = -1/0.774 = -1.3 (approximately). So it slopes steeply downward to the right. The spacetime point (call it point C) where that line intersects Sue's worldline (the t0 axis) gives Sue's age when Tom is 14 (according to Tom). Because of the negative slope of that line, it is easy to see why Tom says Sue is older than she says she is, when he is 14. Sue's lines of simultaneity are all vertical lines. Call the intersection of the vertical line through point A, with Sue's worldline, point E (where Sue is 44.6 years old).

It will help if you plot these lines on the x0 vs t0 plane (Sue's coordinates).

Call the MSIRF at that instant in Tom's life MSIRF1, with coordinates x1 and t1. For simplicity, we can require all the inertial observers in MSIRF1 to be the same age as Tom at that instant (according to all those observers, not to Tom). The MSIRF1 observer momentarily co-located with Tom at that instant is named Toby (he happens to be a dog). For simplicity, we also take Toby's spatial location in MSIRF1 to be at x1 = 0. So the line tangent to Tom's worldline (described above) is the time axis (t1) of MSIRF1. And Tom's line of simultaneity at that instant is one of MSIRF1's lines of simultaneity (parallel to the x1 axis of MSIRF1).

The MSIRF1 observer momentarily co-located with Sue (when all of those observers are 14) is named Sissy (also a dog). Her distance from Toby (measured in the MSIRF1 frame) is 25.3 ly.

I'm not just trying to be funny with those names (although they ARE funny). It's hard to keep track of who's who, so I've chosen to name all the inertial observers, who are ever co-located with Tom during this scenario, with male names starting with "T", like Tom's does. And I've chosen to name all the inertial observers, who are ever co-located with Sue during this scenario, with female names starting with "S", like Sue's does. And, to help distinguish the observers in MSIRF1 from the observers in MSIRF2 (to be defined shortly), I'll use dog's names in MSIRF1 and cat's names in MSIRF2.

Next, Tom accelerates at +1g (in the direction away from Sue) for two years (of his life). At the end of that time (call it spacetime point B), he is the same distance from Sue as before (about 40 ly according to Sue, and about 25.3 ly according to Tom).

Tom is now 16 years old, and Sue is about 46.9 years old (according to Sue). Their relative velocity is about +0.774c (moving away from one another). Tom says Sue is 16.0 when he is 16.

The line tangent to Tom's worldline at this instant in his life has the slope v = +0.774, so it slopes gradually upward to the right.

Tom's line of simultaneity at that instant in his life has the slope 1/v = +1/0.774 = +1.3 (approximately). So it slopes steeply downward to the left. The spacetime point (call it point D) where that line intersects Sue's worldline (the t0 axis) gives Sue's age when Tom is 16 (according to Tom). Because of the positive slope of that line, it is easy to see why Tom says Sue is younger than she says she is, when he is 16. Sue's lines of simultaneity are all vertical lines. Call the intersection of the vertical line through point B, with Sue's worldline, point F (where Sue is 46.9 years old).

It will help if you also plot these lines on the x0 vs t0 plane (Sue's coordinates).

Call the MSIRF at that instant in Tom's life MSIRF2, with coordinates x2 and t2. For simplicity, we can require all the inertial observers in MSIRF2 to be the same age as Tom at that instant (according to all those observers, not to Tom). The MSIRF2 observer momentarily co-located with Tom is named Tabby (he happens to be a cat). For simplicity, we we also take Tabby's spatial location in MSIRF2 to be at x2 = 0. So the line tangent to Tom's worldline at this instant in Tom's life is the time axis (t2) of MSIRF2. And Tom's line of simultaneity at that instant is one of MSIRF2's lines of simultaneity (parallel to the x2 axis of MSIRF2).

The MSIRF2 observer momentarily co-located with Sue (when all of those observers are 16) is named Scratchy (also a cat). Her distance from Tabby (measured in the MSIRF2 frame) is 25.3 ly.

OK, we've got a well-defined and specific scenario now. It is consistent with your example, because the two lines of simultaneity (passing through points A and B) intersect between Tom and Sue.

Using the above scenario I've given, try to formulate the issue you were trying to raise in your posting of several days ago. Anytime you want to refer to an inertial observer, use the names I've given above. If you need other inertial observers, define and name them in a similar way to what I've done above. If you want to refer to an inertial frame, there are three of them above: Sue's frame, MSIRF1, and MSIRF2. Use those names. If you need others, define and name them. And I've identified six important spacetime points in the above description: points A, B, C, D, E, and F. If you want to refer to those spacetime points, use those names. If you need to refer to other spacetime points, define them precisely, and give them capital-letter names. Go for it!

Mike Fontenot

Hi Mike ...I am both amazed and appreciative of the effort you put into this.
Also the nice symmetry of your scenario.

SO Specifically:
1)
a) Scratchy being a specially intelligent cat sends Tom a message at D;
It is year 16 and Sue also turned 16
b) SIssy sends a message at C ; Hi Tom ,,it is year 14 and Sue just turned 75.5

Drawing in the light cones it is clear Tome receives the message from Scratchy sent in year 16 long before receiving the message from Sissy sent in year 14 ,,,,yes??
It is not Sue's reported age that is significant but the temporal reordering with regard to Tom's simultaneous surrogates. What meaning does simultaneity have in this context if it does not represent a coherent relationship of light speed separation and a rational temporal ordering??

2) If you look at the point of Tom's curved accelerating segment where the tangent is parallel to Sue's world line and draw a vertical line this then represents the point where they are at rest wrt each other. Share simultaneity if not proper time readings.

Now draw in the intermediate LoS's between points A and B. These will all intersect at the same point as AC and BD .

From Sue's perspective between points D and C ,which is temporally forward for Sue ,,,she will be colocated with a series SIrens, Sexies, Satanics, etc etc each with a clock around their neck with a decreasing proper time reading.

3) Wait it gets even worse; when you draw in the subsequent parallel LoS's forward in time from point B you find that they overlap the ones from A to B .
Now Sue has an overabundance of transitory petlife colocated with her.

BTW With the scenario you have set up it is a valid diagram of Born rigid acceleration in the section of acceleration. The point where all the lines intersect is what Born called the pivot event. In this case it doesn't completely apply because Tom is being reduced to a dimensionless point but if the frame was extended, the extended locations would all have the same pivot point and share LoS's passing through that point.

In any case this is part of what I am talking about. By choosing a symmmetrical situation you eliminated some of the geometric problems arising from comparison between two points on a unidirectional accelerating frame.
At least this gives you an idea and a basis for discussion.
Again my sincere appreciation for your time and patience Thanks

 

[Mike_Fontenot]

SO Specifically:
1)
a) Scratchy being a specially intelligent cat sends Tom a message at D;
It is year 16 and Sue also turned 16

Careful there! You said "It is year 16". WHOSE YEAR 16? I can GUESS that you MEANT that Scratchy is 16 years old at point D. And, since Tom and Scratchy are momentarily stationary when Tom is 16 (and because of our arbitrary simplifying choice to make all inertial observers in MSIRF2 have the same age as Tom at that instant of stationarity, according to all observers in MSIRF2), Scratchy and Tom mutually agree that they are both 16 then. (Sue also happens to be 16 then, but that is just a quirk of this unusually symmetrical example ... it wouldn't be true for less symmetrical examples, but it's not of any importance in the present issues).

b) SIssy sends a message at C ; Hi Tom ,,it is year 14 and Sue just turned 75.5

Your statement (b) is less ambiguous than statement (a), but the phrase "it is year 14" should have been something like "I am currently co-located with Sue, I am now 14, and Sue is 75.5 now' ". That's the degree of precision that is required to remove all ambiguity.

Drawing in the light cones it is clear Tom receives the message from Scratchy sent in year 16 long before receiving the message from Sissy sent in year 14 ,,,,yes??

Again, the phrases above "in year 16" and "in year 14" are imprecise. I can GUESS that you MEANT "when Scratchy was 16" and "when Sissy was 14"...but you shouldn't make your readers GUESS...that invites misunderstandings. Imprecision in your statements and thoughts can also muddle your own thinking.

But, assuming that my above guess is correct, your conclusion IS correct.

We didn't specify anything about how Tom accelerates after point B, but the answer to your question is the same in any case. An electromagnetic signal sent from point D will have a worldline (a "lightline") of slope +1. Likewise for the lightline from point C. Tom's worldline after point B must everywhere have a slope less than +1 and greater than -1. In all cases, his worldline will intersect the lightline sent from 16-year-old Scratchy (saying that Sue is 16) before his worldline intersects the lightline from 14-year-old Sissy (saying that Sue is 75.5).

It is not Sue's reported age that is significant but the temporal reordering with regard to Tom's simultaneous surrogates. What meaning does simultaneity have in this context if it does not represent a coherent relationship of light speed separation and a rational temporal ordering??

Try to re-formulate your above question, to make it much more specific and much more precise. As it stands now, it is much too vague, and vagueness causes ambiguity and misunderstandings.

[Addendum:] Since some of your questions involve instants in Tom's life beyond age 16 (point B), we should extend the scenario in order to keep everything specific and precise. Let's take the simplest case: immediately after point B, Tom instantaneously changes his velocity so that he is thereafter stationary with respect to Sue...his worldline is therefore horizontal after point B. Let the intersection of his worldline with the lightline from point D be denoted point G. And let the intersection of his worldline with the lightline from point C be denoted point H.

Mike Fontenot

 

[Austin0]

Hi Mike ...I am both amazed and appreciative of the effort you put into this.

It is not Sue's reported age that is significant but the temporal reordering with regard to Tom's simultaneous surrogates. What meaning does simultaneity have in this context if it does not represent a coherent relationship of light speed separation and a rational temporal ordering??

2) If you look at the point of Tom's curved accelerating segment where the tangent is parallel to Sue's world line and draw a vertical line this then represents the point where they are at rest wrt each other. Share simultaneity if not proper time readings.

Now draw in the intermediate LoS's between points A and B. These will all intersect at the same point that AC and BD intersect .

From Sue's perspective between points D and C ,which is temporally forward for Sue ,,,she will be colocated with a series SIrens, Sexies, Satanics, etc etc each with a clock around their neck with a decreasing proper time reading.

3) Wait it gets even worse; when you draw in the subsequent parallel LoS's forward in time from point B you find that they overlap the ones from A to B .
Now Sue has an overabundance of transitory petlife colocated with her.

BTW With the scenario you have set up it is a valid diagram of Born rigid acceleration in the section of acceleration. The point where all the lines intersect is what Born called the pivot event. In this case it doesn't completely apply because Tom is being reduced to a dimensionless point but if the frame was extended, the extended locations would all have the same pivot point and share LoS's passing through that point.

Again, the phrases above "in year 16" and "in year 14" are imprecise. I can GUESS that you MEANT "when Scratchy was 16" and "when Sissy was 14"...but you shouldn't make your readers GUESS...that invites misunderstandings.
But, assuming that my above guess is correct, your conclusion IS correct. Good guess Mike

We didn't specify anything about how Tom accelerates after point B, but the answer to your question is the same in any case. An electromagnetic signal sent from point D will have a worldline (a "lightline") of slope +1. Likewise for the lightline from point C. Tom's worldline after point B must everywhere have a slope less than +1 and greater than -1. In all cases, his worldline will intersect the lightline sent from 16-year-old Scratchy (saying that Sue is 16) before his worldline intersects the lightline from 14-year-old Sissy (saying that Sue is 75.5).



Try to re-formulate your above question, to make it much more specific and much more precise. As it stands now, it is much too vague, and vagueness causes ambiguity and misunderstandings.

[Addendum:] Since some of your questions involve instants in Tom's life beyond age 16 (point B), we should extend the scenario in order to keep everything specific and precise. Let's take the simplest case: immediately after point B, Tom instantaneously changes his velocity so that he is thereafter stationary with respect to Sue...his worldline is therefore horizontal after point B. Let the intersection of his worldline with the lightline from point D be denoted point G. And let the intersection of his worldline with the lightline from point C be denoted point H.

Mike Fontenot

Hi Mike I think your already delineated parameters are perfect. I don't think any more complications are necessary or constructive.
Were my directions for drawing in intermediate LoS's between points A and B in any way unclear?
I think inertial LoS's from B on will be fine. You do see that the parallel lines from B on overlap the previous lines between A and B right?
Meaning two different clocks and observers from different times on Toms worldline, simultaneously colocated with Sue and each other,,Yes?
A whole series of pairs of them, with one set 's clocks advancing and the other set's clocks going backwards in time,
interesting picture no?
Thanks

 

[Mike_Fontenot]

Were my directions for drawing in intermediate LoS's between points A and B in any way unclear?

You do see that the parallel lines from B on overlap the previous lines between A and B right?
Meaning two different clocks and observers from different times on Toms worldline, simultaneously colocated with Sue and each other,,Yes?
A whole series of pairs of them, with one set 's clocks advancing and the other set's clocks going backwards in time,
interesting picture no?

Your statements weren't as precise as they need to be, but I can guess what you were trying to say.

It IS true that all of Tom's lines of simultaneity between his ages 14 and 16 (points A and B) pass through the point of intersection of the AC and BD lines. (That point of intersection is at the "critical distance" that I previously gave a simple equation for). And it IS true that Tom will conclude that Sue is getting younger during that time, while he is getting older. And it IS true, as Sue ages from 16 to 75.5, that she will be momentarily co-located with a sequence of Tom's different MSIRF observers, whose ages are decreasing as Sue ages. And it IS also true that as Sue's age increases from 46.9 to 75.5, she will also be constantly co-located with an additional specific MSIRF observer whose age is increasing from 16 to 44.6 (with the same rate of ageing as Sue's). (This latter statement is true only for the particular choice I made, that Tom's velocity, with respect to Sue, after point B is zero. For other choices of Tom's constant velocity after point B, there would be additional different, momentarily co-located, MSIRF observers with Sue. Sue would see their ages increase as she ages, but at a slower rate than her own.)

Do you see any of the above as a problem? I still can't tell if you believe you are finding inconsistencies. Or, are you just pointing out things that are bizarre? SR IS bizarre. But it's NOT inconsistent. Nothing in the above is inconsistent.

One of your previous comments seemed to clearly indicate that you believe you've identified inconsistencies. You wrote:

A last thought; if you consider a case where two lines intersect and diverge before meeting Sues worldline...what if the proximate observer on the line intersecting Sue at an earlier age shoots her? You then have the choice either she is dead beforealready having seen alive by the earlier CNIF observer or the earlier observer sees her tombstone before a later CMIF observer shoots her.

I think those comments may indicate that you've misunderstood some of what I've been saying. When I say "When Tom is 14, he concludes that Sue is 75.5", that doesn't mean that he knows at that instant what Sue is doing at that instant, or even if Sue is ALIVE at that instant. It means that if Sue IS still alive, she's 75.5. And if it turns out that she died at age 60 (say), then she will have been dead for 15.5 years when Tom is 14 (according to Tom).

Tom can come to his conclusion about Sue's age when he is 14, in three different ways:

(1) He can just use the Lorentz equations, to immediately tell him what Sue's age is when he is 14.

(2) Or, he can (at the instant he is 14) receive a message from Sue, telling her age when she sent the message. In that case, Tom has to COMPUTE how much Sue has aged between when she sent that message, and when he received it. If he has been receiving previous messages for a while, and making the indicated calculation each time, then he will be able to IMMEDIATELY compute her current age, when he receives her message when he is 14. But he won't know yet if she actually lived beyond her just REPORTED age, or if she did, how she has passed her time while the message was in transit.

(3) Or, he can find out later how old Sue was when he was 14, by receiving a message from Sissy giving Sue's (and Sissy's) ages. But in that case, he won't know the answer for a while. This alternative (in addition to being slow) is of value only conceptually...it's too hard to find all those animals willing to accept those jobs.

It seems clear that I haven't convinced you of the necessity of being excruciatingly precise and specific in all of your thinking, and in all of your statements, in SR. And I doubt that I ever will, so I think we'd both be wasting our time to continue trying.

I have a few final comments, that you may or may not already understand. If you don't already understand them, they might be of some help to you:

1) If an inertial observer (say, Tom) is separated at some instant of his life by some non-zero distance from a "home" inertial observer (say Sue), then we can imagine a large number of other inertial observers momentarily co-located with Tom at that instant, with various different velocities relative to Sue (greater than -1c and less than +1c). At that instant, ALL of those observers could receive the same message from Sue, reporting her age when the message was transmitted. Each of those observers can calculate how much Sue aged during the transit of the message. They will all get different answers for that calculation, and so they will all come to different conclusions about her current age. Inconsistent? No. It's nothing but the Lorentz equations. And the Lorentz equations follow from only two assumptions: (1) the speed of any given light pulse will be measured by all inertial observers to have the same value c, and (2) there is no preferred inertial frame.

2) Tom can do a sequence of instantaneous velocity changes, with the amount of his ageing between those changes being some constant amount of his time. And during each of those segments, Tom is inertial (his velocity is constant). We can choose that constant time between those velocity changes to be as small as we like, without changing the sequence of velocities that he goes through. In the limit, the time between velocity changes becomes infinitesimal, but the sequence is still preserved. During each of Tom's infinitesimal inertial segments, Tom has the same velocity (wrt Sue) as one of those perpetually inertial observers in item (1) ... generally a different inertial observer for different segments. I.e., during each segment, Tom is mutually stationary with respect to some (generally different) inertial observer in item (1). And during each segment, Tom must agree, about Sue's current age, with the inertial observer with whom he is mutually stationary. So, in this limiting case, Tom's conclusion about Sue's current age can jump around, back and forth, over a large range of ages for Sue, all while Tom's age hardly changes at all. Bizarre? Yes. Inconsistent? No.

3) If Tom is limited to segments of different constant finite accelerations, then for each instant in his life, there is a definite current age for Sue. I.e, if you ask Tom, "What was Sue's age when you were 23", he will never give you two, or three, or no answers...he will always give you one answer (which will generally be different for different ages of his own). Sue's age (according to Tom), as a function of Tom's age , is a continuous function. But that function is NOT generally a one-to-one function ... i.e., it generally does NOT have an inverse. You can plot the function, with Tom's age on the horizontal axis, and Sue's age (according to Tom) on the vertical axis ... you will get a continuous curve, which is only intersected, by any given vertical line, at a single point. But for any given horizontal line, you may get no intersection, or one intersection, or any number of different intersections. If you ask Tom, "How old were you when Sue was 60", he will generally give you more than one answer. He might say "There were two different times in my life (15.5 and 30) when Sue was 60". Bizarre? Yes. Inconsistent? No.

(4) The fact, that Tom's accelerations cause him to rapidly change his conclusions about Sue's current age, in no way influences the events that occur in Sue's life, nor does it influence her own perception of the progression of her life. The progression and events of her life are analogous to a completed movie reel. Projectionists can run the film forwards and backwards, slow and fast, and it doesn't change the frames on the film in any way. If Sue dies at age 30, no observer can disagree with that.

(5) SR says that events that are space-like separated, i.e., far enough apart in space, and close enough in time, so that there can be no cause-and-effect relationship between them, HAVE NO INHERENT ORDERING. I.e., you can't say, in an observer-independent way, that event A occurs before event B, if A and B are space-like events. Some inertial observers will say A precedes B, but other inertial observers will say that B precedes A. They are both correct, according to their own (correctly performed) elementary measurements and elementary calculations. Bizarre? Yes. Inconsistent? No. It's just SR.

Mike Fontenot

 

[JDoolin]

(5) SR says that events that are space-like separated, i.e., far enough apart in space, and close enough in time, so that there can be no cause-and-effect relationship between them, HAVE NO INHERENT ORDERING. I.e., you can't say, in an observer-independent way, that event A occurs before event B, if A and B are space-like events. Some inertial observers will say A precedes B, but other inertial observers will say that B precedes A. They are both correct, according to their own (correctly performed) elementary measurements and elementary calculations. Bizarre? Yes. Inconsistent? No. It's just SR.

That's correct. By default, that line of simultaneity is at t=0. But as Tom's velocity changes, it can swing from t \to x/c all the way to t \to -x/c. Any of the events in that region can become simultaneous based on Tom's changes in velocity. All of that region where Sue ages from 30 to 70 are events inside that region "outside the lightcone;" neither past nor future.

I don't know if this will help, but I made a demo a few years ago, and you can connect two events, and if they are time-like separated, it puts in the line of simultaneity (unfortunately, the line disappears once you let up on the mouse, and if they are space-like separated, it puts in an appropriate velocity, where the two events are simultaneous.

http://www.wiu.edu/users/jdd109/stuff/relativity/LT.html

I thought maybe my demonstration would aid in this discussion. The demo has time graphed vertically, so (sorry) Mike might have to adjust.

My demo might be what Austin would call a "born rigid" accelerated coordinate system with a single event pivot, but Mike would probably not. (I'm guessing.)

In any case, it's "pivot" is constantly moving in time, because the observer's acceleration must take place at the event where the observer accelerates, and that origin is constantly moving forward in time.

Jonathan Doolin

 

[Austin0]

Your statements weren't as precise as they need to be, but I can guess what you were trying to say.


Do you see any of the above as a problem? I still can't tell if you believe you are finding inconsistencies. Or, are you just pointing out things that are bizarre? SR IS bizarre. But it's NOT inconsistent. Nothing in the above is inconsistent.

One of your previous comments seemed to clearly indicate that you believe you've identified inconsistencies.

I think those comments may indicate that you've misunderstood some of what I've been saying. When I say "When Tom is 14, he concludes that Sue is 75.5", that doesn't mean that he knows at that instant what Sue is doing at that instant, or even if Sue is ALIVE at that instant. It means that if Sue IS still alive, she's 75.5. And if it turns out that she died at age 60 (say), then she will have been dead for 15.5 years when Tom is 14 (according to Tom).



It seems clear that I haven't convinced you of the necessity of being excruciatingly precise and specific in all of your thinking, and in all of your statements, in SR. And I doubt that I ever will, so I think we'd both be wasting our time to continue trying.

I have a few final comments, that you may or may not already understand. If you don't already understand them, they might be of some help to you:

1) If an inertial observer (say, Tom) is separated at some instant of his life by some non-zero distance from a "home" inertial observer (say Sue), then we can imagine a large number of other inertial observers momentarily co-located with Tom at that instant, with various different velocities relative to Sue (greater than -1c and less than +1c). At that instant, ALL of those observers could receive the same message from Sue, reporting her age when the message was transmitted. Each of those observers can calculate how much Sue aged during the transit of the message. They will all get different answers for that calculation, and so they will all come to different conclusions about her current age. Inconsistent? No. It's nothing but the Lorentz equations. And the Lorentz equations follow from only two assumptions: (1) the speed of any given light pulse will be measured by all inertial observers to have the same value c, and (2) there is no preferred inertial frame.

2) Tom can do a sequence of instantaneous velocity changes, with the amount of his ageing between those changes being some constant amount of his time. And during each of those segments, Tom is inertial (his velocity is constant). We can choose that constant time between those velocity changes to be as small as we like, without changing the sequence of velocities that he goes through. In the limit, the time between velocity changes becomes infinitesimal, but the sequence is still preserved. During each of Tom's infinitesimal inertial segments, Tom has the same velocity (wrt Sue) as one of those perpetually inertial observers in item (1) ... generally a different inertial observer for different segments. I.e., during each segment, Tom is mutually stationary with respect to some (generally different) inertial observer in item (1). And during each segment, Tom must agree, about Sue's current age, with the inertial observer with whom he is mutually stationary. So, in this limiting case, Tom's conclusion about Sue's current age can jump around, back and forth, over a large range of ages for Sue, all while Tom's age hardly changes at all. Bizarre? Yes. Inconsistent? No.

3) If Tom is limited to segments of different constant finite accelerations, then for each instant in his life, there is a definite current age for Sue. I.e, if you ask Tom, "What was Sue's age when you were 23", he will never give you two, or three, or no answers...he will always give you one answer (which will generally be different for different ages of his own). Sue's age (according to Tom), as a function of Tom's age , is a continuous function. But that function is NOT generally a one-to-one function ... i.e., it generally does NOT have an inverse. You can plot the function, with Tom's age on the horizontal axis, and Sue's age (according to Tom) on the vertical axis ... you will get a continuous curve, which is only intersected, by any given vertical line, at a single point. But for any given horizontal line, you may get no intersection, or one intersection, or any number of different intersections. If you ask Tom, "How old were you when Sue was 60", he will generally give you more than one answer. He might say "There were two different times in my life (15.5 and 30) when Sue was 60". Bizarre? Yes. Inconsistent? No.

(4) The fact, that Tom's accelerations cause him to rapidly change his conclusions about Sue's current age, in no way influences the events that occur in Sue's life, nor does it influence her own perception of the progression of her life. The progression and events of her life are analogous to a completed movie reel. Projectionists can run the film forwards and backwards, slow and fast, and it doesn't change the frames on the film in any way. If Sue dies at age 30, no observer can disagree with that.

(5) SR says that events that are space-like separated, i.e., far enough apart in space, and close enough in time, so that there can be no cause-and-effect relationship between them, HAVE NO INHERENT ORDERING. I.e., you can't say, in an observer-independent way, that event A occurs before event B, if A and B are space-like events. Some inertial observers will say A precedes B, but other inertial observers will say that B precedes A. They are both correct, according to their own (correctly performed) elementary measurements and elementary calculations. Bizarre? Yes. Inconsistent? No. It's just SR.

Mike Fontenot

Hi Mike I will make another attempt to be precise and specific.
Event C (t'=14.x=25.3) and event D (t'=16,x'=25.3) occur at essentially the same spatial location relative to Tom , the same distance with the same scale of measurement.
Would you agree with this?
Event C at t'=14 is transmitted before Event D at t'=16 correct?

Both transmissions having the same initial distance to travel to reach Tom.
Now I am sure you would agree that SR does have structured temporal ordering of events occurring at a single spatial location , yes?
So do you think it is possible for an EM transmission sent from a single location to arrive after another transmission sent later from the same location to a single location?
Regardless of any possible motion of the system during transit??
Do you think this is consistent with SR principles??

You seem to have the idea that I am alone in perceiving some problems here, but that is definitely not the case.
Many others have noted the disconnection from reality of LoS's for accelerating systems.
They call them coordinate effects , not consistent with what could be observed through a telescope or any other possible observer. Coordinate artifacts etc.
The question is not whether there is a problem but the extent of the problem.
Some have suggested there is simply a limitation of the domain of applicability of LoS's for accelerated frames. That they can only be considered meaningful in the areas without intersections etc. OK this is a rational responce whether I agree or not.
But actually you are the only one I have encountered who seems to feel that it is all meaningful and accurate and consistent with a possible reality .
You seem to think that this question is along the lines of a barn and pole non-issue and simply due to a lack of understanding of basic SR.

Would you agree that a coordinate system ultimately comes down to instruments and rulers??
That the abstract construct is only as valid as it is consistent with a possible real world physical system of measurement.
That in this circumstance, with motion restricted to the x axis, this in practical application means a ruler and system of clocks.
That wrt inertial frames passing in uniform motion this generates a singular, unique set of pairs of events, yes??
That every clock and position colocation (t,x,t'x') occurring in the S set of events will also occur in the S' set of events once and only once.
ANd reciprocally, every event pair occurring in the S' set will also be found once and only once in the S set.
Every t,x and every t',x' will occur only once in the combined set.
This will hold true for any range of spacetime with inertial frames. It is rational and consistent with our fundamental concepts of spacetime.
Would you disagree with any of this??
In principle shouldn't any rational accelerated frame essentially fulfill the same criteria??
Fundamentally it must represent a physical ruler and clocks just like an inertial frame.
With the same constraints of temporality that apply to inertial frames.
Specifically; with passing inertial frames they may totally disagree on clock readings but at all times they are physically colocated and passing forward in spacetime.
Simple rational physics.
So why would you think this should not or would not apply to an accelerated ruler and clocks?
You have said you did not think trying to work with this type of construct would be productive.
Then do you think that simply because the maths are too complex or there are serious complications involved , which there obviously are, that it is just easier to implement an abstract construct like CMIRF's, even if their use does not generate a rationally consistent set of events and is not consistent with any possible actual physical system??