If rotation was relative, we could say that the Universe is revolving around the earth. But how could this be true, since at some distant point the speed of a star would be greater than the speed of light ? How does Mach answer to this question ?
Asked
Active
Viewed 425 times
1
-
7Rotation isn't relative in Newtonian mechanics, in Mach's Principle, or general relativity. – David Hammen Dec 19 '17 at 06:11
-
2Mach wasn't aware that there was an upper speed limit, that only came with Einsteins insight; so the question is ahistorical. – Mozibur Ullah Dec 19 '17 at 10:04
-
3There is nothing wrong with exceeding c in a non-inertial frame. There is thus no conflict to resolve. – Dale Aug 06 '21 at 15:09
-
Also, there is nothing wrong with exceeding $c$, which does not involve information transfer, which (superluminal) space expansion is of type. – Agnius Vasiliauskas May 22 '23 at 09:03
3 Answers
0
One answer is: you won't know until you try.
Another answer could be that the aggregate influences of all matter are what create the rotational rest frame. If there were no other matter than our tiny planet in the Universe, would there be any way to detect rotation?
I'm not wording that well, but it might add to your insight.
"It is justified to consider Mach as the precursor of the General Theory of Relativity." Albert Einstein
The Ehrenfest paradox may interest you.
It was one of the thought experiments that help Einstein may the leap the General Relativity.
There is a modified Mach's principle in General Relativity. I haven't read this paper, but it is a topic of great interest to me.
Inertial frame dragging and Mach's principle in General Relativity
"We define a new parameter `cumulative drag index' for a particle in circular orbit in a stationary, axisymmetric gravitational field and study its behaviour in the two well known solutions of general relativity {\it viz.}, the Kerr spacetime and the G"odel spacetime, wherein the inertial frame dragging has an important role. As it shows similar behaviour for both co and counter rotating particles, it may indeed be an indication of the influence of the faraway universe on local physics and thus Machian. "
Steven Thomas Hatton
- 1,965
-
1Thanks for the links. Yes my question is related to the links you sent. But my question is more historical. Why didn't physicists reply to Mach with this argument : if rotation were relative, then some stars would exceed the speed of light. As this is not possible, his view is not tenable. This would have ended the debate. Since this was not the case, I am not sure if the argument is valid, and if so, why isn't it valid ? Maybe it has something to do with Ehrenfests paradox... – Anarchasis Dec 20 '17 at 00:09
-
1Well, when Mach stated his principle, there was no special relativity to challenged the idea of something going faster than the speed of light. So that's the main reason they didn't use that objection. Nonetheless, the objection isn't valid. The principle is that the distant massive bodies determine what rotation means. So if they were all rotating that fast, they would change spacetime in such a way as to make it look exactly the way it looks. – Steven Thomas Hatton Dec 20 '17 at 00:59
0
In your rotating frame the star has a Lorentz Boost $\lambda=\frac {\omega r} {c}$ perpendicular to the radius vector to the star. If $\lambda << 1$, then $\frac{v}{\not{c}} = \frac {\omega r} {\not{c}} $ which is the familiar relation you used to suggest superluminal $v$. However, there is no limit to how large $\lambda$ can be as $\omega r$ increases, but always $v \lt c $ because $\frac{v}{c} =\tanh(\lambda) \lt 1$.
I don't know if Mach answered your question this way. Before Einstein published Special Relativity in 1905, Lorentz transformations were known from the invariance of Maxwell's Equations. Mach and Einstein talked to each other. Mach died in 1916 so he certainly knew about Special Relativity and how velocities add. He knew that successive boosts could not add up to greater than c, so he could have had a similar explanation perhaps without using the words "Lorentz Boost Parameter".
Gary Godfrey
- 3,354
0
Mach used the example of a spinning gyroscope to illustrate his concept of relativity. We say a gyroscope is spinning relative to the universe as a whole rather than say the gyroscope is motionless while the universe spins around the gyroscope because of the absurdity of the considering the distant stars to be spinning at enormous or even infinite speeds. The total mass of the universe as observed by the distant stars and their, as a whole, stationary effect was Mach's only absolute for motion. Mach explained that when a train stops suddenly, the passengers fall forward because their attraction to the distant stars is greater than their attraction to the train. Mach never gave a name to his consideration of the total mass of the universe as an absolute but Einstein called it "Mach's Principle."
