Acceleration/Deceleration in SR

[Mike_Fontenot]

I have had a second take on the scenario.
[...]
What does CADO predict?? :-)

I'm sorry, I wasn't able to follow your statement of the new problem.

 

[Fredrik]

Most people call that inertial frame the "co-moving inertial frame". I don't like that term...it perpetuates the mistaken idea that velocities have some kind of absolute significance. I call it the MSIRF, for "momentarily-stationary inertial reference frame". In general, the MSIRF is not the same inertial frame from one moment of John's life to the next.

If "comoving" suggests that velocities have some absolute significance, then "stationary" suggests that velcocity 0 has some absolute significance. It's also weird to describe the coordinate system as "stationary", because it suggests that something about the coordinate system is stationary in a coordinate system. What coordinate system would that be? The MSIRF itself? Then you seem to be saying that the MSIRF is the coordinate system that's "stationary in itself", but you can describe any coordinate system that way.

On the other hand, adding the word "momentarily" is an improvement. I'm just too lazy to write it every time.

John's result is a "realtime" simultaneity assertion in the sense that he can determine Jane's current age without needing to know anything about what either of them will do in the future. He doesn't have to wait for the historians of the future to tell him what Jane's age was when he received her message.
...
All of the above assumed that Jane and John were inertial. But it is possible for John to determine Jane's current age when he isn't inertial. That extension basically requires proving that, at any instant in John's life, regardless of how he's accelerating, that John MUST adopt the conclusions of the inertial frame that is momentarily stationary with respect to him at that instant.

But is isn't possible to prove that, because it isn't true. The comoving inertial frame is conventional and convenient, nothing more.

 

[Dale]

The simultaneity result that my CADO equation produces is the SAME simultaneity result that the Lorentz equations produce. ... John's result is a "realtime" simultaneity assertion in the sense that he can determine Jane's current age without needing to know anything about what either of them will do in the future. He doesn't have to wait for the historians of the future to tell him what Jane's age was when he received her message.

This is not correct. There is no way for an observer to ascertain the simultaneity of events outside his past light cone. In the case of this specific example, suppose that John and Jane are born at the same time 40 light years apart and at rest wrt each other. When John turns 40 he would receive the news that Jane was born and would conclude that she is now 40. However, suppose that when Jane turned 10 she suddenly accelerated to .6c, then in John's frame she is actually 34 years old when he is 40, but John will not even see her acceleration for another 10 years. You simply cannot determine the simultaneity of events outside your past light cone. In fact, you cannot even know that such events happen.

Your CADO is no more realtime than the D&G convention. And it certainly is no more nor less important for doing physics. They are both just simultaneity conventions.

 

[Mike_Fontenot]

If "comoving" suggests that velocities have some absolute significance, then "stationary" suggests that velcocity 0 has some absolute significance.

The MSIRF is momentarily stationary with respect to John...their relative velocity is momentarily zero.

But is isn't possible to prove that, because it isn't true.

I prove it in my paper.

Mike Fontenot

 

[stevmg]

The MSIRF is momentarily stationary with respect to John...their relative velocity is momentarily zero.



I prove it in my paper.

Mike Fontenot

Where is the CADO paper?

stevmg@yahoo.com

 

[Mike_Fontenot]

In the case of this specific example, suppose that John and Jane are born at the same time 40 light years apart and at rest wrt each other. When John turns 40 he would receive the news that Jane was born and would conclude that she is now 40. However, suppose that when Jane turned 10 she suddenly accelerated to .6c, [...]

The CADO equation assumes that the distant object (Jane, in this case), whose current age is being determined by the observer (John, in this case), is perpetually unaccelerated (perpetually inertial). I stated in my last posting that Jane and John are both inertial. Your above supposition doesn't apply.

Both John and Jane need to be inertial, in order for John to make the elementary calculations to determine Jane's ageing during the message transit. It IS possible for John to determine Jane's current age when he is accelerating, but the elementary calculations have to be done by John's MSIRF at that instant of John's life.

It is actually possible to use the CADO equation for situations where both people accelerate, provided their accelerations don't overlap, and are separated by sufficiently-long inertial periods. But it is fairly complicated to use the CADO equation for these types of problems. For situations where the distant object is inertial, though, the CADO equation is very simple and quick to use.

It is also possible to determine Jane's current age, according to John, when they are both accelerating in a completely arbitrary and independent manner. But the CADO equation can't be generalized to handle that case...those cases have to be handled in a completely different way.

Mike Fontenot

 

[Mike_Fontenot]

Where is the CADO paper?

I gave a reference earlier in this thread.

 

[Fredrik]

...their relative velocity is momentarily zero.

That's what "momentarily comoving" means.

I prove it in my paper.

Not possible. It's a convention, not a necessity.

 

[stevmg]

I can't even think of how, but I do know that with the Einstein train paradigm and the simultaneous front and back lightning flashes that are simultaneous from the ground observer can one "flip" the order of which event the observer on the train itself can see the events. Of course their original simultaneity does make them spacelike.

Again, while you folks were in the next galaxy, was what I wrote correct?

stevmg

 

[Fredrik]

Again, while you folks were in the next galaxy, was what I wrote correct?

Yes, if A and B are spacelike separated events, there's an inertial frame in which A is earlier than B and another in which B is earlier than A. This is really easy to see in a spacetime diagram, if you understand that the simultaneity line of an object moving with speed v is a straight line in the diagram with slope v.

Edit: Also note that A and B are spacelike separated if and only if the slope of a straight line connecting them in the diagram satisfies -1 < slope < 1.

 

[Dale]

The CADO equation assumes that the distant object (Jane, in this case), whose current age is being determined by the observer (John, in this case), is perpetually unaccelerated (perpetually inertial). I stated in my last posting that Jane and John are both inertial.

There is nothing special in that. If motion is assumed then both CADO and D&G can be realtime or even predictive, but only insofar as the assumed motion is correct which can only be verified for events in the past light cone.

You just don't seem to get the idea that simultaneity is purely a matter of convention and any convention is acceptable. Your convention is no better nor worse than any other.

 

[stevmg]

Yes, if A and B are spacelike separated events, there's an inertial frame in which A is earlier than B and another in which B is earlier than A. This is really easy to see in a spacetime diagram, if you understand that the simultaneity line of an object moving with speed v is a straight line in the diagram with slope v.

Love it, love it, love it - I AM learning something. Keep hammering away, folks. I was a genius (you know, a legend in my own mind) when I started and I am getting stupider by the minute. Please keep helping me to avoid that.

 

[Austin0]

You are right. Immediately after Tom's instantaneous speed change, Sue is -4.6 years old (according to Tom)...i.e., Sue's mother-to-be will age another 4.6 years before she gives birth to Sue.

. Also, I think Mike meant that 0 time has elapsed on Tom's clock at the event we're supposed to consider.


I don't feel like doing any calculations right now, but in the diagram I'm drawing in my head, I can see that Sue would be much younger than 30 in Tom's comoving inertial frame (after the boost), because its simultaneity lines have slope v in the diagram, so the boost event is simultaneous with an "early" event on Sue's world line.

.

Suppose two people (say, Tom and Sue) are stationary with respect to one another, when they are both 30 years old, and that they are 40 lightyears apart.

Then suppose that Tom instantaneously changes his speed so that he is moving away from Sue at 0.866c.

.

Prior to Tom's acceleration his frame mate Bob is vacationing at rest 26 ly towards earth.
As Tom initiates acceleration Bob is rudely awaken only to get a last fleeting glimpse of the Earth rushing towards him due to the Earth frame's contraction.
Not only terminating Bob but incidently nailing Sue's mom on the way to the library.

My question is this : ...Does Tom simultaneously lose all memory of Sue or does he wait until the information regardiung her prenatal demise (i.e. history) reachs him at c ?

What does CADO predict?? :-)

Did you really? In which one of his frames? The comoving inertial frame before the boost? The comoving inertial frame after the boost? The radar frame? Why would Bob wake up because someone 26 light-years away is accelerating rapidly? Why would that Lorentz contract the Earth and make him teleport to Earth, nail Sue's mom, teleport back and die? Like I said, your description makes no sense.

Sorry...as I said this was basically a joke. A play on the artificial paradox made possible by the assumption of instantaneous acceleration and resulting instantaneous shifting of simulataneity lines and relative coordinates.

It was not a puzzle or question regarding figuring out those coordinate changes . I assumed that you and most people given the context of this thread would be able to do it in your head or with simple calculation based on the gamma factor. Just as you did in your head the post above.
I also made some assumptions within this contaxt that now appear to be ambiguous.
I assumed that "Toms frame mate Bob" would be taken as Bob at rest in the same frame as Tom. Not Bobs comoving frame was at rest with Toms comoving frame as two separate entities.
Here is the real ambiguity I didn't make clear that Bob unlike SUe was attached to the boosted frame. I assumed from the context and what happened to Bob this would be implicit.
My mistake. Oops

I also assumed the interpretation would be that when this frame was accelerated this would apply to both locations and both people instantaneously.. Without going into details of Born rigid acceleration etc.

SO given an instantaneous change. . Bobs position wrt Tom and his own frame do not change with the boost. Only the relative simultaneity and contraction of the Earth frame.
In Bob and Toms frame the Earth is suddenly closer by the gamma factor . In this case the new position is now between Bob and Tom. The Earth having to pass through Bobs location (and Bob) to get there. No teleportation on Bob's part required.

AS I said the joke was in in the question at the end. I assumed these calculations were trivial and obvious. ANd not to be taken seriously. I am not suggesting that length contraction actually implies a physical translation. I also assumed it would be obvious this was a joke both by the question and the language of the setup.

I now realize I was wrong on all counts. My communication software still needs major upgrade.

On a more serious note: I am not familiar with Mike_Fontenot's program and how it might correlate wht radar methods etc.
But from what I have gotten from his explanation of the basis I would have to agree.

In all cases calculations based on the frame itself must correspond with any results from lines of simulataneity. SPecifically :SImply assuming the frame extended in space to include the point in the other frame and applying the Lorentz tranforms you can derive the spatial coordinate of the proximate observer (virtual) in your frame and the clock time in the other.

This is an assumption I have operated on for years. From this perspective in my mind I derived the correct answer to Mike's question by simply multiplying the 40 ly distance by velocity , Since I did it in my head I only got an approximate answer but a quick calculation on paper would have returned the exact answer but I didn't feel like the effort.

To check my assumption; last year I ran it by DrGreg and now have a thread going to get further feedback. SO far I have gotten no reason to doubt this assumption.

If see any reason for doubt; the thread is frames vs lines of simultaneity.

I will try to be clearer and more explicit in the future. Thanks

 

[Fredrik]

Austin0, regarding the Sue, Tom and Bob scenario. I now take it that Bob's velocity is given the exact same boost as Tom's, at the exact same time in Sue's frame, or equivalently, in a frame that's comoving with either Tom or Bob before the boost. In order to talk about how Tom or Bob would describe these events, we need to specify which coordinate system we have chosen to represent a person's "point of view". Let's use the comoving inertial frame (because it's simple enough for me to do these things in my head). In Tom's comoving inertial frame immediately after the boost, Tom's boost event is simultaneous with a much earlier event on Bob's world line than Bob's boost event. So Bob still won't be given a boost for several years. You're right that distances will be have changed due to Lorentz contraction, but I don't know why you think this will put Bob on the other side of Earth. It won't.

 

[Mike_Fontenot]

Previously, I wrote:

[...]
The simultaneity result obtained by both the CADO equation and the Lorentz equations can also be obtained by an inertial observer using only his own elementary measurements and elementary calculations. Here's the gist of how it's done:

Suppose Jane and John are far apart. Both are inertial. They are moving at a constant relative velocity.
[...]

I should have also used those previous comments, together with the following example, to draw attention to another BIG difference between Dolby & Gull simultaneity and CADO/Lorentz simultaneity:

Suppose John and his neighbor Sam get together once a week to look at a TV transmission coming from Jane, where she reports her age at the time of transmission. They then together do the elementary calculation of the amount of Jane's ageing during the message transit, and thereby get her current age when they received her message. The result they get is the same result obtained from either the Lorentz equations or (more quickly and easily) from the CADO equation.

Suppose that John will remain perpetually inertial (like Jane will), but that Sam has committed to do a spaceflight, which will require that he suddenly change his velocity wrt Jane by some amount.

The date for his flight has been set to occur 10 years from the date that he and John first started doing their weekly determination of Jane's current age.

The fact that Sam will eventually change his velocity means that he must reject the result that he and John calculate every week, because Dolby & Gull require that he use a different value for Jane's current age.

So, for 10 years, John and Sam jointly make the weekly calculation of Jane's current age, and their calculations are based only on first-principles, correctly executed. But Dolby & Gull require that Sam, every week for 10 years, must reject those results.

THAT is what I mean when I say that alternative definitions of simultaneity (other than Lorentz simultaneity) will contradict Sam's own elementary measurements and first-principle calculations.

(In order for Sam's acceleration 10 years in the future to make Dolby & Gulls' result differ from the Lorentz result, I suppose the distance to Jane has to be greater than some minimum...so, in the above description, assume that is the case).

[...]
All of the above assumed that Jane and John were inertial. But it is possible for John to determine Jane's current age when he isn't inertial. That extension basically requires proving that, at any instant in John's life, regardless of how he's accelerating, that John MUST adopt the conclusions of the inertial frame that is momentarily stationary with respect to him at that instant.
[...]

At each instant of his life, John must adopt the simultaneity conclusion of his MSIRF at that instant, in the sense that any other conclusion will contradict his own measurements and first-principle calculations. Exactly how we can determine what he will conclude on his own, when he isn't perpetually inertial, is somewhat complicated to explain. But I treat that issue in detail in my paper.

Mike Fontenot

 

[Mike_Fontenot]

You just don't seem to get the idea that simultaneity is purely a matter of convention and any convention is acceptable. Your convention is no better nor worse than any other.

It is certainly true that, in the spirit of GR, we are always free to use almost any coordinate system (with only a few restrictions), and the equations of nature must be written so as to be valid for any and all of those choices. And we certainly have that freedom-of-choice of coordinates in special relativity (subject to the constraint that the Riemann curvature tensor is zero).

But just because we CAN use a certain coordinate system doesn't mean that we SHOULD, or that all choices are equally good from a practical standpoint.

The standard Lorentz coordinates of special relativity have a BIG advantage over any of the others: the Lorentz time coordinate corresponds to the actual time an observer at rest in that frame reads on his OWN watch. And the Lorentz spatial coordinates correspond to the actual distances that that observer measures with his OWN measuring tape.

The Lorentz equations, which relate the Lorentz coordinates in one inertial frame to the Lorentz coordinates in another inertial frame, fully specify simultaneity between those two inertial frames. And that simultaneity is what the CADO equation computes.

Mike Fontenot

 

[Dale]

The fact that Sam will eventually change his velocity means that he must reject the result that he and John calculate every week, because Dolby & Gull require that he use a different value for Jane's current age.

Yes, it is trivially obvious that different simultaneity conventions disagree on which events are simultaneous. Otherwise they wouldn't be different.

THAT is what I mean when I say that alternative definitions of simultaneity (other than Lorentz simultaneity) will contradict Sam's own elementary measurements and first-principle calculations.

No measurement is contradicted. Your method makes an assumption about unobserved motion and that assumption is simply not made with D&G. Their approach is perfectly consistent with their actual (unassumed) measurements and elementary calculations.

Even if it were not it would not matter. Simultaneity is simply a convention and doesn't need to agree with "measurements and elementary calculations" as long as the metric is known. Consider Rindler coordinates for example. The timelike coordinate is not equal to proper time except for the observer at R=1. That is not a problem.

 

[Dale]

But just because we CAN use a certain coordinate system doesn't mean that we SHOULD, or that all choices are equally good from a practical standpoint.

I agree completely. If you had phrased your earlier statement in terms of a personal preference or a matter of practicality I would have left it at that. But you instead claimed in post 12 that one couldn't even do physics with other simultaneity conventions, that your convention was more than a convention but a physics necessity. That is simply wrong.

There may be many good reasons for picking your convention for a specific situation, there may be many other situations where there are good reasons for picking another. All are equally valid, and the convenience and practical considerations will depend on the specific problem.

 

[Mike_Fontenot]

I recognize that there are some benefits that have come from some of the post-Einstein changes that have been introduced in the way SR is formulated and taught. But I also think there is sometimes a cost to that.

Part of what made Einstein so productive and innovative, I think, was that he always maintained his insistence that the variables used in any equation be clearly defined at the outset, including spelling out exactly how they could be measured (at least in principle), and what they MEANT. I think some of the modern abstractions have moved us away from that view.

Most of us have heard the famous quote by Niels Bohr: "Those who are not shocked by quantum mechanics, have not understood it." I think that quote also applies to special relativity. And I think some of the modernizers of SR put a lot of effort into trying to disguise those shocks, or get them out of sight. It seems to me that's what Dolby & Gull are trying to do, with those embarrassing sudden changes in Lorentz simultaneity caused by accelerations.

Mike Fontenot

 

[Austin0]

Austin0, regarding the Sue, Tom and Bob scenario. I now take it that Bob's velocity is given the exact same boost as Tom's, at the exact same time in Sue's frame, or equivalently, in a frame that's comoving with either Tom or Bob before the boost. In order to talk about how Tom or Bob would describe these events, we need to specify which coordinate system we have chosen to represent a person's "point of view". Let's use the comoving inertial frame (because it's simple enough for me to do these things in my head). In Tom's comoving inertial frame immediately after the boost, Tom's boost event is simultaneous with a much earlier event on Bob's world line than Bob's boost event. So Bob still won't be given a boost for several years. You're right that distances will be have changed due to Lorentz contraction, but I don't know why you think this will put Bob on the other side of Earth. It won't.

Hi Fredrik I like you but in some ways you are a hard nut to crack. When I try to be serious you find my logic amusing, worth a chuckle but when I try to be amusing you take it too seriously and don't get it.
As I mentioned earlier I didn't bother specifying details of Born rigid acceleration , but you can assume that Bob's sector of the frame had a previous agreement to initiate acceleration simultaneously with Tom at a specified time which would be simultaneous by the conventions of their shared frame. Which until initiation would also be by the conventions of Sue's frame.
I also just did the math in my head but Sue's distance from Tom is 40 ly's
Bob's distance from Tom is 26 ly's. ...Looking at v=.866c I ballparked a gamma figure of .56 ?? Definitely less than .6 , so Earths and Sues instantaneous relocation relative to Bob and Tom would be somewhere less than 24 ly's from Tom. I.e. in between Bob and Tom

I will reiterate. I was not proposing a serious paradox. I was making a play on the concepts of instantaneous acceleration and the resulting unrealistic shifts in simultaneity and relative location that ensued. YOu may think that my sense of humor is weird and I wouldn't argue. Certainly a joke that requires diagrams and detailed math to get the punchline is suspect.
Next time I will either provide the diagrams or spare you all my humor completely.

 

[Austin0]

I recognize that there are some benefits that have come from some of the post-Einstein changes that have been introduced in the way SR is formulated and taught. But I also think there is sometimes a cost to that.

Part of what made Einstein so productive and innovative, I think, was that he always maintained his insistence that the variables used in any equation be clearly defined at the outset, including spelling out exactly how they could be measured (at least in principle), and what they MEANT. I think some of the modern abstractions have moved us away from that view.

Most of us have heard the famous quote by Niels Bohr: "Those who are not shocked by quantum mechanics, have not understood it." I think that quote also applies to special relativity. And I think some of the modernizers of SR put a lot of effort into trying to disguise those shocks, or get them out of sight. It seems to me that's what Dolby & Gull are trying to do, with those embarrassing sudden changes in Lorentz simultaneity caused by accelerations.

Mike Fontenot

Well put ,all of the above

 

[Fredrik]

When I try to be serious you find my logic amusing, worth a chuckle but when I try to be amusing you take it too seriously and don't get it.

It's hard to take the claim that Tom is closer to Earth than to Bob as a joke. I'm still not sure if you're taking that part seriously.

As I mentioned earlier I didn't bother specifying details of Born rigid acceleration

There's no need to, since you specified the events where they were both given a boost.

I also just did the math in my head but Sue's distance from Tom is 40 ly's
Bob's distance from Tom is 26 ly's. ...Looking at v=.866c I ballparked a gamma figure of .56 ?? Definitely less than .6 , so Earths and Sues instantaneous relocation relative to Bob and Tom would be somewhere less than 24 ly's from Tom. I.e. in between Bob and Tom

I will reiterate. I was not proposing a serious paradox.

So you do understand that the information you provided implies that Bob "moves closer" to Tom by the exact same factor (gamma) that Sue does?

 

[stevmg]

Autin0, Fredrik -

Hey! Both of you keep up your good work. I (and I would say a whole lot more of us) learn a lot from this!

 

[Austin0]

Sue's distance from Tom is 40 ly's
Bob's distance from Tom is 26 ly's.

a gamma figure of .56 ?? Definitely less than .6 ,

so Earths and Sue's mom instantaneous relocation relative to Bob and Tom
would be somewhere less than 24 ly's from Tom. I.e. in between Bob and Tom

.

It's hard to take the claim that Tom is closer to Earth than to Bob as a joke. I'm still not sure if you're taking that part seriously.

what I actually said : Earth moves to approx 24 lys from Tom.

Bob was located at 26ly's from Tom and so was in the way so now he is intimately involved with Sue's mom and and both are now dead and colocated with the earth.

I did get confused and said Sue was relcated with Earth when I meant Sue's mom.
Well actually it is both as Sue ages backwards and disappears enroute, while her mother just gets younger

So you do understand that the information you provided implies that Bob "moves closer" to Tom by the exact same factor (gamma) that Sue does?

Bob doesn't move at all relative to Tom as they are both in a Born accelerated frame.
WHich started accelerating at both points instantaneously by pre arrangement.

But as this is all instantaneous they haven't yet really moved,, it is only the Earth which instantly shifts location as well as it's simultaneity relationship with Tom and Bob
Because of that it is Sue on the Earth the moment before initiation and it is Sue's mom that is on the Earth that relocates and hits Bob.

Maybe clear now?