2

To save expert's time: "In GR, is jerk relative?"

As I understand it, "Special Relativity" applies only for (in a word) objects which are not accelerating.

Einstein thought about this hellova' hard for some years and came up with General Relativity:

which covers the case of objects (in a word) accelerating.

So - that's the first two derivatives of position covered.

The third derivative of position is usually called "jerk".

Much as Special Relativity fails with acceleration, in fact, does General Relativity fail with the next derivative, and the following derivatives? What's the situation here?

(Don't even mention circular movement - does this cause extra-special problems when you have, perhaps, higher derivative change in circular motion?) Cheers.

Fattie
  • 1,048
  • 1
    You may want to read this Physics.SE post about acceleration in SR. – Kyle Kanos Nov 06 '14 at 16:24
  • Joe, in GR a body moving in a gravitational field has coordinate acceleration only. It's in freefall and an accelerometer shows nothing. This allowed Einstein to treat such movement as inertial (while a body at rest on the surface of the source of gravitation is treated as accelerating upwards according to Einstein's Eqivalence Principle). – bright magus Nov 09 '14 at 07:41

2 Answers2

4

You understand wrongly I'm afraid.

It's commonly said (by non-relativists) that special relativity doesn't describe acceleration but this is quite incorrect. Accelerating frames can be described perfectly well by special relativity. As an example look at my Q/A How long would it take me to travel to a distant star?. This analyses the motion of an accelerating spaceship, and it does it just using special relativity - no GR to be seen. Alternatively look at the last part of my answer to Is gravitational time dilation different from other forms of time dilation?, which analyses circular motion (i.e. acceleration towards the centre) again using just special relativity.

So I'm afraid your argument that jerk might cause GR to fail is based on an incorrect premise. Both SR ad GR can handle jerk and all higher time derivatives of acceleration without failing.

There is a fundamental difference in the way SR and GR treat acceleration because acceleration is absolute in SR but relative in GR. However this is unrelated to the issue you're asking about.

Community
  • 1
John Rennie
  • 355,118
  • @JoeBlow: yes, in GR all motion of any form is relative. – John Rennie Nov 06 '14 at 16:41
  • Disappointingly, Einstein's brain looked pretty much the same as everyone else's brain. – John Rennie Nov 06 '14 at 17:11
  • @John Rennie, I'm not sure I agree with the remark at the end of your answer. Acceleration is absolute in both SR and GR. In both cases it is measured through a comoving accelerometer and all local observers agree on this measured proper acceleration. It's just that in SR the standard of non-acceleration is a global inertial frame whereas in GR it is a local inertial frame i.e. a freely falling frame. – FenderLesPaul Nov 06 '14 at 23:43
  • @JohnRennie: When considering acceleration in SR can you claim that the accelerated frame is stationary and that the other one is moving? Because the lack of preferred frames is the axiom of SR, one of those the whole theory is based on. – bright magus Nov 09 '14 at 07:33
  • @brightmagus: no. There is no way to determine the velocity of an accelerating observer, only the relative velocity compared to another observer. However an accelerating observer can determine their acceleration by a local measurement (e.g. using an accelerometer) without reference to any other frame. Note FenderLesPaul's comment above, which I agree with. – John Rennie Nov 09 '14 at 07:59
  • @JohnRennie, this is not what I am asking. Let me rephrase. Can you treat accelerated frame (i.e. the one in which acceleration can be locally determined) as stationary, and assume the other frame as accelerating? Sometime ago I discussed such case (you removed then your comment referring to John Baez' claim about accelerating clocks in your comments there), an apparent paradox, and the results were different depending on the frame, showing a problem with switching frames. – bright magus Nov 09 '14 at 08:12
  • @brightmagus: no. In one frame an accelerometer will show a non-zero reading while in the other frame it will show a zero reading. There is a fundamental asymmetry. – John Rennie Nov 09 '14 at 08:52
  • @JohnRennie, and that's why acceleration in SR smells badly ... – bright magus Nov 09 '14 at 08:59
1

General relativity describes measurement and observations for a general observer. Theoretical problems with it lie mainly in its interaction with quantum mechanics and statistical mechanics, and there are no experiments that disagree with its predictions.

Zo the Relativist
  • 41,373
  • 2
  • 74
  • 143