Are accelerating lines of simultaneity correct?

[Austin0]

No, there is no inconsistency.

In the example I gave in my previous posting, I indicated that Tom's acceleration could be chosen so that the intersection between Tom's two lines of simultaneity (before and after his acceleration) would occur directly on Sue's time axis...which means that Tom would say that Sue is the SAME age before and after his acceleration. Sue, of course, doesn't agree.

There isn't any inconsistency there...Sue and Tom NEVER agree about the correspondence between their ages, unless their relative speed is zero, or unless they are co-located.

The above scenario is an example of a more general result:

I prove, toward the end of my paper, that for any given acceleration A, and initial speed v at the beginning of that acceleration, that there is a critical separation L_c such that the distant object's (Sue's) age won't change at all, regardless of how long the acceleration persists, if their separation at the beginning of the acceleration is L_c.

The equation is

L_c = gamma / A,

where gamma is the usual time-dilation factor (which is a function of the absolute value of the speed), and A is in units of ly/y/y. (1 ly/y/y is about 0.97 g).

(For simplicity, I omitted a factor of c*c in the above equation, which is needed for dimensional correctness, but since I'm using units where c has the value 1, the omission doesn't affect the numerical values being computed).

So not only is Sue's age the same (according to Tom) at the beginning and at the end of his acceleration, it remains constant during his whole segment of acceleration.

Bizarre? Yes, but it's not inconsistent. It is REQUIRED by the combination of the Lorentz equations and my proof that the accelerating traveler must always adopt the simultaneity of his current MSIRF, if he is to avoid contradicting his own elementary measurements and elementary calculations.

I gave a reference early in this thread for my paper that I referred to several times above. In case you missed it before, the reference is:

"Accelerated Observers in Special Relativity",
PHYSICS ESSAYS, December 1999, p629.

Mike Fontenot

Hi Mike I tried accessing your paper. unfortunately I am living in S E Asia and my crdit card has lapsed.
Though in actuality I have no questions regarding your conclusions as your premise makes complete sense.
I do have one question; In the case where Toms CMIF's remain temporally constant with Sues time during acceleration do the colocated (with Sue) coordinate positions in Tom's CMIF's remain constant also ?

What you are describing seems the same as the Born hypothesis picture of constant simultaneity with a single spacetime pivot point. Would you agree ??
Of course I agree that there will never be agreement between Sue and Tom and no actual temporality can be ascribed to any of these calculations.
But I don't think that this question is just an abstract exersize either.

In priciple. is there any reason against positing Tom's frame as a physical system extended beyond Sue's location so there will at all times be a proximate clock and observer from his frame for direct comparison with Sue's clock?

 

[Austin0]

I mean that the lines of simultaneity in a diagram are graphical representations of the frame itself. If the physical size of the frame is limited in extent the graph is of virtual observers and clocks of the frame at those distant locations. That there is no significant difference between the two. YOu can just consider the frame extending however long you want.
The graph is just portraying what the fundamental Lorentz math would tell you about the
clocks at that specific point on the hyperplane/line. It gives direct temporal readings and spatial location in x and geometrically correct spatial locations in x' , but to read this requires the transform (gamma).
QUOTE]

Yes, but the time coordinate t' assigned by frame S to be simultaneous with t is convention, not directly observed until a later time t, unless the clock (or event) is local. Lines of simultaneity connect t with t' by using the SR simultaneity convention.

Certainly clocks are synched by "convention" but relative simultaneity appears to be inherent in the fundamental Lorentz transforms.
Certainly the math is consistent with the invariance of c but do you think the clock convention determined the math ?
As such isn't it implicit that it also relates to elementary particles in electrodynamics whose clocks and temporal relationships are physical not conventional??
Or do you think it is only a matter of synching the lab clocks by convention to achieve corrospondence??

Yes lines of simultaneity are used where there is no direct observation but do you disagree, that in principle in all cases, we can consider the frame itself extended to include that disparate region and the relationships would be exactly the same? Actual observers??

DO you think there is no real problem with the implications of intersecting lines and diverging lines i.e. the simultaneous colocations of observers from the same frame, temporal reordering etc.?
Is the relationship of clocks at relative velocities the result of convention or is the convention an accomodation of a real relative simultaneity implicit in the physics it is describing??

 

[Mike_Fontenot]

[...]
I tried accessing your paper. Unfortunately, I am living in S E Asia and my credit card has lapsed.

I had figured you must be many time zones away from me, because we're never on line at the same time!

Did you try to get my paper from the journal publisher...i.e., is that why you needed your credit card? I didn't know if they would supply an individual paper or not, and if so, how much they would charge.

Are you anywhere near a university library? At least in the U.S., I think any university library can get a journal volume (or maybe even a copy of a specific paper) via an inter-library loan from another university. But I don't know if that's true internationally or not.

I do have one question: In the case where Tom's CMIFs remain temporally constant with Sue's time during acceleration, do the co-located (with Sue) coordinate positions in Tom's CMIFs remain constant also ?

At each instant during Tom's acceleration, there is a different MSIRF. You can imagine that each of those MSIRFs has its own large number of inertial observers spread out along the spatial axis. In each MSIRF, one of those inertial observers is (momentarily) co-located with Sue, at the given instant of Tom's life. That observer can directly observe Sue's age, and the answer he gets is exactly the same answer given by the Lorentz equations (and, much easier and quicker, by my CADO equation). But each of the MSIRFs has its own set of inertial observers, so the observer who happens to be momentarily stationary next to Sue, at some instant of Tom's life, is NOT the same observer who is momentarily stationary next to her at a different instant of Tom's life (and, the spatial distance between the Sue-co-located observer and the Tom-co-located observer will generally be different in different MSIRFs) . All of those different momentarily stationary observers, however, will observe that same age for Sue (during the particular constant acceleration by Tom that we are considering in this example).

What you are describing seems the same as the Born hypothesis picture of constant simultaneity with a single spacetime pivot point. Would you agree ??

Sorry, I can't help you there...I don't know anything about that Born hypothesis. Maybe someone else on this forum can comment.

In priciple, is there any reason against positing Tom's frame as a physical system extended beyond Sue's location so there will at all times be a proximate clock and observer from his frame for direct comparison with Sue's clock?

That's definitely not what I'm doing. Although each of those MSIRFs has observers stationed at all spatial locations, the observers in different MSIRFs are completely different observers. There isn't any kind of permanent, spatially-extended structure attached to Tom in my approach (not even conceptually). I suspect that any attempt to set up some kind of permanent spatially-extended frame, all or which is accelerating together somehow, is either doomed to failure, or, at best, is an inferior way to proceed.

It's important to understand that the MSIRF at tau1 of Tom's life, which has a momentarily stationary observer next to Sue, who observes that she is age t1, will conclude (using another of its observers) at a slightly later instant tau2 in Tom's life, that Sue's age is NOT t1 then. Once an inertial frame is no longer momentarily stationary wrt Tom, it is of no value to Tom at that later instant in Tom's life.

It is probably a good idea to try to always refer to an MSIRF of Tom's as "MSIRF(tau1)" or as "MSIRF(tau2)", to emphasize that there is generally a different MSIRF at each instant of Tom's life.

Mike Fontenot

 

[Al68]

Certainly clocks are synched by "convention" but relative simultaneity appears to be inherent in the fundamental Lorentz transforms.
Certainly the math is consistent with the invariance of c but do you think the clock convention determined the math ?

Of course, since the math assumes the convention.

Yes lines of simultaneity are used where there is no direct observation but do you disagree, that in principle in all cases, we can consider the frame itself extended to include that disparate region and the relationships would be exactly the same? Actual observers??

DO you think there is no real problem with the implications of intersecting lines and diverging lines i.e. the simultaneous colocations of observers from the same frame, temporal reordering etc.?
Is the relationship of clocks at relative velocities the result of convention or is the convention an accomodation of a real relative simultaneity implicit in the physics it is describing??

I'm not sure what you mean by any of this.

 

[Mike_Fontenot]

[...]
At each instant during Tom's acceleration, there is a different MSIRF. You can imagine that each of those MSIRFs has its own large number of inertial observers spread out along the spatial axis. In each MSIRF, one of those inertial observers is (momentarily) co-located with Sue, at the given instant of Tom's life. That observer can directly observe Sue's age, and the answer he gets is exactly the same answer given by the Lorentz equations (and, much easier and quicker, by my CADO equation).
[...]

I should have also added that the answer obtained by the MSIRF(tau1) observer who is momentarily co-located with Sue, is also exactly the same answer obtained by the MSIRF(tau1) observer who is momentarily co-located with Tom. That observer obtains the answer by having received transmissions from Sue giving her age (at the instant when she transmits the message), and then correctly allowing for Sue's ageing that occurred while that message was in transit.

Mike Fontenot

 

[Mike_Fontenot]

I encourage anyone, who has never done it, to spend some quality time PLOTTING the Lorentz equations, and trying to wring as much out of them (geometrically) as you can.

Just start with the simplist form of the equations (one spatial dimension, and the one time dimension), that everyone has seen. I.e., start with the set of two equations, which give x2 and t2 as functions of x1 and t1 (and with the simplist initial condition x2 = x1 = 0 when t2 = t1 = 0). For simplicity, use units where c = 1 (like years and lightyears).

Plot the x1 and t1 coordinates on perpendicular axes. (I prefer to plot x1 vertically, and t1 horizontally, but you may prefer to stick to convention and do the opposite). Put in "tic" marks, for those axes, with equal spacing on both axes.

With a little thought, you should be able to draw in the x2 and t2 axes, and also to determine the location of the "tic" marks along each of those axes. How are the angles of those axes related to each other, with respect to the horizontal and vertical axes? And you should be able to determine the lines of simultaneity and stationarity that pass through any spacetime point (for both the x1, t1 frame AND the x2, t2 frame). And you should be able to see that the intersection of a line of simultaneity with the time axis of the other frame gives the current time in that other frame, according to the frame "owning" that line of simultaneity.

All of the above stuff comes purely from those Lorentz equations...nothing else is needed.

Once you've done the above (and really understand it), it should be easy to see how I originally inferred my CADO equation while staring at such diagrams (called Minkowski diagrams)...the CADO equation just does the geometry for you.

I remember seeing this process of plotting done many years ago, in one of the many books I've used to learn SR...maybe Taylor and Wheeler, but I'm not sure. But it's very important to mess around with it yourself. It'll be time well spent.

Mike Fontenot

 

[Austin0]

I encourage anyone, who has never done it, to spend some quality time PLOTTING the Lorentz equations, and trying to wring as much out of them (geometrically) as you can.

And you should be able to determine the lines of simultaneity and stationarity that pass through any spacetime point (for both the x1, t1 frame AND the x2, t2 frame). And you should be able to see that the intersection of a line of simultaneity with the time axis of the other frame gives the current time in that other frame, according to the frame "owning" that line of simultaneity.

All of the above stuff comes purely from those Lorentz equations...nothing else is needed.

Once you've done the above (and really understand it), it should be easy to see how I originally inferred my CADO equation while staring at such diagrams (called Minkowski diagrams)...the CADO equation just does the geometry for you.

But it's very important to mess around with it yourself. It'll be time well spent.

Mike Fontenot

Hi Mike I am in total agreement here. I did exactly this myself years ago from the opposite direction. Took diagrams for two inertial systems and went through them and applied the math and checked the correspondences , It was through this exercise that I realized both the geometric spatial correspondence and accuracy of lines of simultaneity as well as the fact that it was really the frame itself that was being graphed.
I think perhaps it is this point that is at the root of our failure to communicate.
I have told you from the beginning that I understood and agreed with your system but you seem stuck thinking that because you don't understand what I am talking about that it stems from a lack of understanding on my part or disagreement.

 

[Austin0]

Of course I agree that there will never be agreement between Sue and Tom and no actual temporality can be ascribed to any of these calculations.
But I don't think that this question is just an abstract exersize either.

At each instant during Tom's acceleration, there is a different MSIRF. You can imagine that each of those MSIRFs has its own large number of inertial observers spread out along the spatial axis. In each MSIRF, one of those inertial observers is (momentarily) co-located with Sue, at the given instant of Tom's life. That observer can directly observe Sue's age, and the answer he gets is exactly the same answer given by the Lorentz equations (and, much easier and quicker, by my CADO equation). But each of the MSIRFs has its own set of inertial observers, so the observer who happens to be momentarily stationary next to Sue, at some instant of Tom's life, is NOT the same observer who is momentarily stationary next to her at a different instant of Tom's life (and, the spatial distance between the Sue-co-located observer and the Tom-co-located observer will generally be different in different MSIRFs) . All of those different momentarily stationary observers, however, will observe that same age for Sue (during the particular constant acceleration by Tom that we are considering in this example).

OK we seem to be in agreement here and I assume we would agree this all applies to inertial frames as well.
In the case of inertial frames it should be easy to see that the clocks and observers for the succeeding instants of Tom's passage through spacetime [i.e. lines of simultaneity]
are in fact a single system of clocks. Each instant [LoS] is the same system with an infinitesimal change in proper time.
WHen graphing an accelerating system it is the convention to consider each succeeding instant as a separate, different system of clocks and observers. But this is just an abstraction , arising as far as I can see, from the idea that an accelerating system is not a valid frame of reference so must be replaced by a series of "valid " instantaneous inertial frames.

In priciple. is there any reason against positing Tom's frame as a physical system extended beyond Sue's location so there will at all times be a proximate clock and observer from his frame for direct comparison with Sue's clock?

That's definitely not what I'm doing. Although each of those MSIRFs has observers stationed at all spatial locations, the observers in different MSIRFs are completely different observers. There isn't any kind of permanent, spatially-extended structure attached to Tom in my approach (not even conceptually). I suspect that any attempt to set up some kind of permanent spatially-extended frame, all or which is accelerating together somehow, is either doomed to failure, or, at best, is an inferior way to proceed. Mike Fontenot

I understand that is not what you are doing.
It is also clear that an accelerating system as a singular extended reference frame has problems computationally as well as conceptually. I don't think anyone thinks a Rindler coordinate system is particularly neat and tidy.
I am not suggesting that.
Only that in principle , if our coordinate system and concepts are to have any real meaning related to the real spacetime , we should be able to make that conceptual shift and have it conform to a possible reality. We can do this with inertial frames without reservation.
However extended in space the events graphed by lines of simultaneity [the frame] will correspond to actual frame agreed colocations of clocks.
This is not the case with accelerated lines of simultaneity. They indicate colocations, as you have detailed above, that could not take place with an actual system. I.e. various clocks and observers from different locations and times , simultaneously colocated with SUe at a single time [event].
To simply say; that is not a problem because you are talking about different, only instantaneously existing, clocks and observers is just to admit that they are meaningless abstractions with no relation to any actual system or the real world.

Number two: as you know, in an inertial diagram a geometric line segment of a line of simultaneity, indicates a clock at a specific location in that frame. Wrt the moving frame this requires the gamma transformation to derive a quantitaive value but it is always accurate.
True?
WIth an accelerated system every line has a different gamma factor so how could the segment lengths of succeeding lines be geometrically accurate as defining a specific location in the frame?

Three: Even as abstractions, succeeding CMIF's in the real world are congruent to the path of the system , true?
All the clocks in each succeeding CMIF must be advanced some infinitesimal amount forward in time from the last one. true?
Then I ask you how , without time going backward, could one CMIF be colocated with another at a different proper time?

 

[Passionflower]

It is also clear that an accelerating system as a singular extended reference frame has problems computationally as well as conceptually. I don't think anyone thinks a Rindler coordinate system is particularly neat and tidy.
I am not suggesting that.
Only that in principle , if our coordinate system and concepts are to have any real meaning related to the real spacetime , we should be able to make that conceptual shift and have it conform to a possible reality. We can do this with inertial frames without reservation.
However extended in space the events graphed by lines of simultaneity [the frame] will correspond to actual frame agreed colocations of clocks.
This is not the case with accelerated lines of simultaneity. They indicate colocations, as you have detailed above, that could not take place with an actual system. I.e. various clocks and observers from different locations and times , simultaneously colocated with SUe at a single time [event].
To simply say; that is not a problem because you are talking about different, only instantaneously existing, clocks and observers is just to admit that they are meaningless abstractions with no relation to any actual system or the real world.

Just transport tetrads instead! As someone once wrote:

"The physics is more transparent when expressed in a locally inertial frame (or some other frame adapted to the physics), as opposed to the coordinate frame, where Salvador Dali rules."

As a final thought, it is worth pointing out that in an accelerating frame, even the two-way speed of light needn't be constant.

So you are talking about the two-way instantaneous speed not being constant here?

When physicists or mathematicians say "speed" they mean "instantaneous speed" unless they explicitly say "average speed". Nothing wrong with average speed, but if that's what one is talking about, one needs to insert the word "average" otherwise one will be misunderstood.

 

[Austin0]

Just transport tetrads instead!

I'll expose my ignorance here...what are tetrads? Tropical fish perhaps??

As someone once wrote:

"The physics is more transparent when expressed in a locally inertial frame (or some other frame adapted to the physics), as opposed to the coordinate frame, where Salvador Dali rules."
?

Well you have turned my question on its head here. In this case it is with instantaneously co-moving inertial frames that the Daliesque effects are in full reign.
Unless you find temporal reordering as transparent and rational physics.

So you are talking about the two-way instantaneous speed not being constant here?

Speed of light has absolutely no bearing on this question nor do any of the other questions of length etc. that are problematic in accelerating frames

 

[Mike_Fontenot]

[...] but you seem stuck thinking that because you don't understand what I am talking about that it stems from a lack of understanding on my part or disagreement.

I just haven't been able to understand your concerns, despite my best efforts. I've done my best to at least guess at your concerns, and I've tried to supply some specific examples that I think might address those (presumed) concerns.

I think one way that might let me understand your concerns, would be for you to take that previous scenario I outlined (with the two lines of simultaneity (owned by the two different MSIRFs at the two specific instants of Tom's life in that example) intersecting at the same spacetime point in Sue's life), and try to formulate a extremely precise question, that exactly captures your concern, about that scenario.

I've learned the hard way that, in SR, all statements must be stated in an excruciatingly precise way...in a way that would seem ridiculously overdone and unnecessarily verbose in Newtonian physics. Any wiggle-room at all in the statements can create all sorts of perceived contradictions and paradoxes that don't actually exist.

When I gave that scenario previously, I didn't provide any specific numbers...they weren't necessary then, for the argument I was making. But if you need specific numbers in order to give a precise formulation of your concern, I'll be glad to supply them.

Mike Fontenot

 

[Mike_Fontenot]

When graphing an accelerating system it is the convention to consider each succeeding instant as a separate, different system of clocks and observers. But this is just an abstraction , arising as far as I can see, from the idea that an accelerating system is not a valid frame of reference so must be replaced by a series of "valid " instantaneous inertial frames.

I would say that there IS a valid frame for an accelerating observer.

That frame consists of the (infinite) collection of inertial frames (the MSIRFs), one for each instant of the accelerating observer's life, each of which being momentarily stationary wrt the accelerating observer at that given instant in his life.

This frame is a well-defined...there is no ambiguity or inconsistency at all. And it is NOT a "convention": there are no other reasonable alternatives, because it is the ONLY possible frame for the accelerating observer which doesn't contradict his own elementary measurements and elementary calculations.

This frame certainly does NOT consist of any spatially-extended collection of permanently identifiable clocks and rulers that are being dragged around with the accelerating observer as he (and they) accelerate. I don't think any such approach would be productive.

Of course, in practice you obviously wouldn't want to have to actually construct that infinite set of infinite collections of inertial clocks and rulers to "build" the accelerating observer's frame. But that practical impossibility is of no importance. The accelerating observer can simply CALCULATE what all those MSIRFs would tell him, if they DID exist. Those calculated results provide everything he needs from his frame.

(As far as the other questions in your above posting, I wasn't able to understand them. I think the only way forward is for you to construct the kind of extremely precise statement of your concerns that I described in my last response).

Mike Fontenot

 

[DrGreg]

As a final thought, it is worth pointing out that in an accelerating frame, even the two-way speed of light needn't be constant.

So you are talking about the two-way instantaneous speed not being constant here?

When physicists or mathematicians say "speed" they mean "instantaneous speed" unless they explicitly say "average speed". Nothing wrong with average speed, but if that's what one is talking about, one needs to insert the word "average" otherwise one will be misunderstood.

OK, I was a bit vague in my choice of words in the first quote, but to be fair I did say "in an accelerating frame", so I had in mind non-local instantaneous two-way "coordinate speed" rather than "locally measured speed" (="physical speed" in the terminology of Anamitra in the "On the Speed of Light Again!" thread).

 

[Austin0]

I would say that there IS a valid frame for an accelerating observer.

That frame consists of the (infinite) collection of inertial frames (the MSIRFs), one for each instant of the accelerating observer's life, each of which being momentarily stationary wrt the accelerating observer at that given instant in his life.

This frame is a well-defined...there is no ambiguity or inconsistency at all. And it is NOT a "convention": there are no other reasonable alternatives, because it is the ONLY possible frame for the accelerating observer which doesn't contradict his own elementary measurements and elementary calculations.

This frame certainly does NOT consist of any spatially-extended collection of permanently identifiable clocks and rulers that are being dragged around with the accelerating observer as he (and they) accelerate. I don't think any such approach would be productive.

Of course, in practice you obviously wouldn't want to have to actually construct that infinite set of infinite collections of inertial clocks and rulers to "build" the accelerating observer's frame. But that practical impossibility is of no importance. The accelerating observer can simply CALCULATE what all those MSIRFs would tell him, if they DID exist. Those calculated results provide everything he needs from his frame.

(As far as the other questions in your above posting, I wasn't able to understand them. I think the only way forward is for you to construct the kind of extremely precise statement of your concerns that I described in my last response).

Mike Fontenot

Hi Mike We are agreed on the difficulties if removing any possible ambiguity.

So I will try again with your parameters.
We have the accelerating frame. For illustration let's assume the set of inertial frames moving at greater velocities along the x axis, not as instantaneously ephemeral abstractions
but as a permenent set or bundle of clocks and rulers. Spatially extended and sharing the same space, conguent or intimately cojacent or whatever as long as they can all mutually observe each other. Then as the frame accelerates it simply comes into phase with successive frames with greater velocities, Of course all these frames have different spatial metrics , clock rates and synchronization but they all are moving though time and their clocks are all positively incrementing.
From this it is axiomatic : #1) No local observer in whatever location in any of these frames can possible observe the passing clocks in any other frame at whetever velocity decreasing in displayed proper time. Agreed?
#2) No local observer in any frame can possibly coexist and be colocated with any observer from any point in any frame at a previous time in that frame or in the past time of the complete set.
Is this understood and agreed?
No matter what may be calculated from comparisons with other observers at separated locations in the same frame with the same clock reading all the clocks are moving forward in time.
Objective reality in this case rests with local observations. It is fundamental to SR that any notions of simultaneity wrt spatially separated events is without any real temporal meaning in any frame.
If this is understood it is clear that the mapping within Minkowski with its convention of differing slopes for CMIF's cannot correspond with reality. Because that is exactly what is indicated by intersections etc. Not only that, as the lines converge it is equivalent to local observers in the set of congruent frames observing passing clocks in another frame with decreasing displayed proper times. Which we know is not possible.

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

 

[Mike_Fontenot]

[...]

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.

It is fundamental to SR that any notions of simultaneity wrt spatially separated events is without any real temporal meaning in any frame.

I don't agree at all. For any given inertial frame, the simultaneity specified by the Lorentz equations is completely meaningful for the observers in that frame. In fact, it is the ONLY simultaneity that IS meaningful for those observers, because it corresponds to what any of the observers in that frame can observe and calculate on his own, using only elementary, fundamental methods. (In my paper, I spell out in detail exactly how those elementary observations and calculations are accomplished).

Different inertial frames don't agree about simultaneity. In that sense, simultaneity isn't absolute. But simultaneity is perfectly meaningful for any GIVEN inertial frame, for the observers in that frame.

And simultaneity is also perfectly meaningful for any given ACCELERATING observer, because at any instant in his life, he COULD (if he chose) quit accelerating. At that instant, it can be shown (see my paper) that he will IMMEDIATELY be in agreement with the inertial observers with whom he is now stationary. It follows that the accelerating observer must, at each instant of his life, adopt the simultaneity of the inertial frame with which he is momentarily stationary at that instant, if he wants to avoid contradicting his own (potential) elementary observations and calculations.

Mike Fontenot

 

[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 [tex]t \to x/c[/tex] all the way to [tex]t \to -x/c[/tex]. 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??