Acceleration/Deceleration in SR

[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?