The speed of an impulse transmitted along a string

Question

A supernova explosion on the far side of the Sun ejects a mass with approximately the same mass of the Sun directly at the back side of the Sun. If this ejected mass is travelling arbitrarily close to the speed of light, the advance warning of its approach would be arbitrarily close to zero. After it collides with the Sun, there would be a delay of just under 8 minutes before we would become aware of the sudden acceleration of the Sun towards the Earth.

Likewise, if a Sun spot suddenly appeared on the surface of the Sun, it would be approximately 8 minutes before we would would be aware of the Sun spot's appearance as observed from the Earth.

If person A on earth tugs a taught string held by person B located at the sun, would the tug be sensed immediately? (please ignore the obvious mechanical issues such as the earth being in motion, etc.).

This question (v2) seems to be non-mainstream as the Sun cannot suddenly disappear. — Qmechanic, Mar 25 '24 at 16:22
@Qmechanic you can make it mainstream if you assume the sun suddenly starts moving away at close the speed of light due to some unknown reason — Pato Galmarini, Mar 25 '24 at 16:24
Nevertheless, it is a legitimate question from someone who wants to understand. It's the kind of question Einstein asked on the train to work at the patent office. Feynman is rolling in his grave. — L Turner, Mar 25 '24 at 16:38
I also disagree with closing this question, and have voted to reopen. Physics textbooks post physically unrealistic problems all the time, but they are used to gain insight into mainstream physics. This question seem to be in the same vein. — Dargscisyhp, Mar 25 '24 at 16:47
possible/partial duplicate of "Is it possible for information to be transmitted faster than light by using a rigid pole?" — Sten, Mar 25 '24 at 16:52

score 2 · Answer 1 · answered Mar 25 '24 at 16:16

Tugging on a string launches a tension wave down the string. It moves at the speed of sound in the string, perhaps a kilometer per second. That's fast enough that the wave bounces back and forth, damping down to a constant tension "instantaneously" to human perception, when you pull a string in ordinary circumstances. But the Sun is a long way away...

KDP · Answer 2 · 2024-03-26T16:12:22.443

2

The tug propagates at the speed of sound in the string, while the gravitational change in the field, propagates at the speed of light. Since the speed of sound in the string is a lot slower than the speed of light, the tug will take a lot longer than 8 minutes to propagate to the other end.

Relativity prohibits the concept of an infinitely rigid object where impulses can travel from one end of the object to the other, instantly, as it would violate the principles of relativity.

edited Mar 26 '24 at 16:12

answered Mar 25 '24 at 16:19

KDP

3,141

@gerrit Yes I did! Thanks for finding that typo ;-) I will fix that right away. – KDP Mar 26 '24 at 16:11

L Turner · Answer 3 · 2024-03-25T16:48:33.747

1

The "tug" would propagate to the sun at the speed of sound in string. At 100 MPH, that would take 107 years.

edited Mar 25 '24 at 16:48

answered Mar 25 '24 at 16:15

L Turner

257

The speed of an impulse transmitted along a string

3 Answers3