Acceleration/Deceleration in SR

1. Jul 17, 2010

stevmg

I just found out that you can do acceleration/deceleration problems in SR. I didn't know that.

The problem I was thinking of was the classic Terence/Stella problem of recent fame on this Forum. See this post by Jesse M who solves this for constant velocities:
https://www.physicsforums.com/showpost.php?p=2610219&postcount=63

Basically, Terence and Stella are on Earth. Terence stays put while Stella accelerates, to the right, say, at 7 g (about 70 m/sec2 s until achieving a velocity of 0.6c (or 180,000,000 m/sec) to the right and then turns around and decelerates at 7 g's until she reaches or catches up with Terence on Earth. I chose 7 g's because good pilots and reclining astronauts can take that for a while.

I don't know where to get started. I've omitted the "crusing" speed of 0.6c to keep matters simple. In other words, Stella's rocket goes out and immediately turns around to come back.

I don't know if you can use the standard v = at and s= (1/2)70t2 = 35t2 to figure alloted time and distance in Terence's frame and Stella's accelerating, then decelerating frame. I assume you have to bust her travels into two frames - one out and one in.

Please give me a kickstart. I know how to do it at "steady state" (constant v = 0.6 c) for out and back.

Do you calculate first t for the given parameters, then s by using the t already calculated, and using the formula:
f X s = energy expended. Then obtain the v for the energy by KE = (1/2)mv2 and then with the v from the energy equation (not the v = 0.6 c) and the s apply the Lorentz transforms??? I don't think so, although that would be a first good "guess."

Steve G

Last edited: Jul 17, 2010
2. Jul 17, 2010

yuiop

Most of the equations you need to handle acceleration in SR are given in simple form here:

http://www.phys.ncku.edu.tw/mirrors/physicsfaq/Relativity/SR/rocket.html [Broken]

That might help.

Last edited by a moderator: May 4, 2017
3. Jul 17, 2010

starthaus

You can start by reading https://www.physicsforums.com/blog.php?b=1911 [Broken]. I wrote a few files on the subject.

Last edited by a moderator: May 4, 2017
4. Jul 17, 2010

stevmg

Is there an "Acceleration in SR part I? All I see is part II.

Steve G

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5. Jul 17, 2010

stevmg

Hold on - I got to your blog and retrieved the other three .pdf files you wrote on this subject.

Thanks,
SG

6. Jul 17, 2010

starthaus

Yes but it is a https://www.physicsforums.com/blog.php?b=1893 [Broken] that part II (don't ask). So, it is a good idea to start with part II :-)

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7. Jul 18, 2010

stevmg

Ok...

8. Jul 18, 2010

Mike_Fontenot

Years ago, I derived a simple equation (called the "CADO" equation) that explicitly gives the ageing of the home twin during accelerations by the traveler (according to the traveler). The equation is especially easy to use for idealized traveling twin problems with instantaneous speed changes. But it also works for finite accelerations. I've got a detailed example with +-1g accelerations on my webpage:

http://home.comcast.net/~mlfasf [Broken]

And I've published a paper giving the derivation of the CADO equation:

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

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9. Jul 18, 2010

stevmg

Copied it to a .pdf file.

Thanks,

SMG

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

How about a reprint or a site where I can see it?

10. Jul 18, 2010

Staff: Mentor

I also like this arxiv article.
http://arxiv.org/abs/gr-qc/0104077

It explicitly works on the twin paradox for a finite acceleration and gives a reasonable coordinate system to use for the travelling twin at all points.

11. Jul 18, 2010

Mike_Fontenot

As far as I know, it's not online anywhere (and I don't have it in any kind of "emailable" form. And the journal didn't give me any reprints, like some journals (at least used to) do.

I also don't know if you can get a copy of just the single article from "Physics Essays" (they DO have a webpage), or perhaps an entire back issue for a reasonable price.

But most university libraries should either have it, or else be able to get it for you via inter-library loan, so that should work if you're anywhere near a university.

BTW, you were not alone in thinking that special relativity can't handle accelerations...that's a common misconception, even among physicists who should know better.

12. Jul 18, 2010

Mike_Fontenot

From just a quick look at that link, it appears to be a definition of simultaneity such that ALL observers will agree about the simultaneity of two given separated events. If so, that's a big mistake (in my opinion).

The ONLY definition of simultaneity that doesn't contradict the observer's own elementary measurements and elementary calculations, is the one I have given in my previously referenced paper. And with that definition, observers in relative motion with respect to one another WON'T agree about the simultaneity of any two given separated events.

If an observer has to disregard his own elementary measurements and calculations, that involve only first-principles, he simply CAN'T do any physics.

Mike Fontenot

13. Jul 18, 2010

Fredrik

Staff Emeritus
It isn't. It's just a standard way to associate a coordinate system with the motion of an object. (I think this is what MTW calls the object's "proper reference frame"). Take the world line to be the t axis and assign coordinates to other events by generalizing this idea: If light is emitted at x=0 at t=-T, then reflected somewhere, and returned to x=0 at t=T, we assign t=0 (and x=T) to the reflection event. (If we apply this procedure to a timelike geodesic, we get a global inertial frame. If we apply it to the world line of an object doing constant proper acceleration, we get Rindler coordinates. These authors are just applying the same idea to the astronaut twin's world line).

14. Jul 18, 2010

Staff: Mentor

You are mis-reading it. The bulk of the paper describes how the different observers disagree, including plots of the stay-at-home twin's worldline in the travelling twin's frame. It is just a definition of simultaneity that works everywhere in a non-inertial frame.

15. Jul 19, 2010

Mike_Fontenot

That is certainly possible.

But the important question is, for an accelerating traveler, does the value they compute for the current age of the home twin, at any given age of the traverer, ACCORDING TO THE TRAVELER, agree with my result or not?

If it does, then it is just an alternative way of arriving at my result.

If it does not, then their result will contradict the traveler's own elementary measurements, combined with his own elementary calculations. And the traveler CAN'T do any physics, if he is forced to disregard his own measurements.

Mike Fontenot

16. Jul 19, 2010

Staff: Mentor

The idea that physics can only be done using some form of your simultaneity convention is just silly. As long as you know the metric you can do physics using any coordinates and any simultaneity convention.

Last edited: Jul 19, 2010
17. Jul 19, 2010

starthaus

PE is a journal known for publishing fringe or outright incorrect (and/or anti-mainstream) articles. Since Mike is unwilling to provide a copy of the paper, it is impossible to figure out to what extent his paper is correct.

18. Jul 19, 2010

Mike_Fontenot

OK, here's a question that's trivial to answer with my equation:

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.

Tom is still 30 years old. How old is Sue, according to Tom?

Mike Fontenot

19. Jul 19, 2010

starthaus

Not forever

Older. How much older depends on the amount of time elapsed on Tom's clock.
For a complete solution, see here

20. Jul 19, 2010

Fredrik

Staff Emeritus
I think you read the question wrong, or maybe I did. I'd say that the answer is "younger" regardless of whether we use the comoving inertial frame or the radar time notion of simultaneity as in the Dolby & Gull article. 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.

In the coordinate system that Dolby & Gull are using, things are much more complicated. Simultaneity starts getting messed up 40 years before the boost event, because that's how long it takes for light to go from Sue to Tom. I don't seem to be able to work out the details in my head. I think her aging rate just keeps getting slower in (D&G's version of) Tom's frame, for a long time starting 40 years before the boost event, and ending...uh...at the event on Tom's world line that's simultaneous in his comoving inertial frame with Sue age 70. After that, her aging rate in (D&G's version of) Tom's frame is the same as in the comoving inertial frame, i.e. slow by a factor of gamma.