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Does Special Relativity contain contradictions?

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Halc
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Re: Does Special Relativity contain contradictions?

Post by Halc » October 2nd, 2018, 8:28 am

Steve3007 wrote:
October 2nd, 2018, 7:57 am
Gravitational time dilation fits in because a basic principle of General Relativity is that acceleration and gravity are equivalent (the "equivalence principle").
That principle says you can't tell the difference between the two with a local test, but it doesn't mean that non-gravitational time dilation is caused by acceleration. It is caused by speed.
In my trampoline turnaround, the acceleration is off the scale, yet maybe one second passes in Earth frame, and 3/4 second passes in ship accelerated frame. The 1/4 second difference isn't going to make much difference when they compare clocks back home and find years difference between them.

I can have 3 clocks, one one a stationary Earth (1G), one on a smallish spinning wheel in space (1G), and one in a rocket that moves in a long circle at 1G over 10 years. When reunited 10 years later, the spinning wheel one will read the greatest value (negligible dilation due to negligible speed), the Earth one close behind (slowed due to gravitational dilation), and the one that actually achieved some velocity will be way behind. All three experience 1G.

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Re: Does Special Relativity contain contradictions?

Post by Halc » October 2nd, 2018, 8:38 am

Tamminen wrote:
October 2nd, 2018, 8:04 am

So the relation is 10 -> 5 in one direction and 5 -> 2.5 in another direction, which means that it is not symmetric in this sense.
Well, it is a 2-1 ratio either way. You just happened to choose to compare with a more nearby event in the one case than in the other. It is not a comparison between the same two events in each frame, so you're getting smaller numbers in the second case.

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Re: Does Special Relativity contain contradictions?

Post by Steve3007 » October 2nd, 2018, 8:40 am

Halc wrote:That principle says you can't tell the difference between the two with a local test, but it doesn't mean that non-gravitational time dilation is caused by acceleration. It is caused by speed.
My understanding of General Relativity (which could be wrong) is that it's not just that you can't tell the difference between them, but that they are literally equivalent. So any object undergoing acceleration would undergo gravitational time dilation with respect to an observer who is not in the same non-inertial reference frame as it. Therefore (as I understand it) the twin paradox can be described accurately using Special Relativity, but it can also be described by invoking General Relativity.

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Re: Does Special Relativity contain contradictions?

Post by Halc » October 2nd, 2018, 8:43 am

Steve3007 wrote:
October 2nd, 2018, 8:06 am
Since force is rate of change of momentum (F = d(mv)/dt) and momentum is mass X velocity (mv) the force, from the point of view of the original reference frame, increases as the mass increases (WRT that frame).
Agree, but I was responding to your reference to constant acceleration, not constant rate of change of momentum.
But WRT the rocket's current rest frame the force stays the same because the mass, as measured in that frame, remains the same. so the people don't get crushed.
Again, only if the ship's mass is constant. I think a Bussard ramjet would fit the bill since it doesn't carry its reaction mass.

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Re: Does Special Relativity contain contradictions?

Post by Halc » October 2nd, 2018, 8:48 am

Steve3007 wrote:
October 2nd, 2018, 8:40 am
My understanding of General Relativity (which could be wrong) is that it's not just that you can't tell the difference between them, but that they are literally equivalent. So any object undergoing acceleration would undergo gravitational time dilation with respect to an observer who is not in the same non-inertial reference frame as it.
I disagree. I put the second clock on the wheel to illustrate exactly that. Same acceleration as the other two, but no gravity and almost no speed. The 3rd clock might get dilated by 25% (just a guess, I only made it a 10 year low-G trip), so shouldn't the second one as well given identical acceleration? That would be a trivial test to do in a lab.

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Re: Does Special Relativity contain contradictions?

Post by Steve3007 » October 2nd, 2018, 8:55 am

This is why an object in free fall in a uniform gravitational field is regarded as being in an inertial reference frame.

I had a quick look at good old Wikipedia:

https://en.wikipedia.org/wiki/Gravitati ... e_dilation

The article says this:

"According to the general theory of relativity, gravitational time dilation is copresent with the existence of an accelerated reference frame. An exception is the center of a concentric distribution of matter, where there is no accelerated reference frame, yet clocks are still supposed to tick slowly. Additionally, all physical phenomena in similar circumstances undergo time dilation equally according to the equivalence principle used in the general theory of relativity."

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Re: Does Special Relativity contain contradictions?

Post by Steve3007 » October 2nd, 2018, 9:05 am

I can have 3 clocks, one one a stationary Earth (1G), one on a smallish spinning wheel in space (1G), and one in a rocket that moves in a long circle at 1G over 10 years. When reunited 10 years later, the spinning wheel one will read the greatest value (negligible dilation due to negligible speed), the Earth one close behind (slowed due to gravitational dilation), and the one that actually achieved some velocity will be way behind. All three experience 1G.
To clarify: When you talk about the acceleration of the clocks attached to wheels, are you talking about their centripetal acceleration? Is their rotational speed constant?

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Re: Does Special Relativity contain contradictions?

Post by Steve3007 » October 2nd, 2018, 9:13 am

I also found this article about gravitational time dilation and the equivalence principle:

https://thecuriousastronomer.wordpress. ... elativity/

It seems to show that time dilation occurs between the top and bottom ends of an accelerating rocket. Intriguing.

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Re: Does Special Relativity contain contradictions?

Post by Tamminen » October 2nd, 2018, 9:54 am

Halc wrote:
October 2nd, 2018, 8:38 am
Tamminen wrote:
October 2nd, 2018, 8:04 am

So the relation is 10 -> 5 in one direction and 5 -> 2.5 in another direction, which means that it is not symmetric in this sense.
Well, it is a 2-1 ratio either way. You just happened to choose to compare with a more nearby event in the one case than in the other. It is not a comparison between the same two events in each frame, so you're getting smaller numbers in the second case.
I think we have a confusion of how we use the term 'symmetric', and I think you are right in that the situation is symmetric in the sense of the ratio being the same in both directions, and perhaps this is the normal use of the term in physics. But if the observer in D reads 5 in the clock in T1 and 10 in his own clock, and if it were so that the observer in T1, reading 5 in his own clock, would also read 10 in the clock in frame D, this would be another meaning of 'symmetry'. And symmetry in this sense is true between two events stationary in a frame. What term would you use for this strange "behaviour" of simultaneity?

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Re: Does Special Relativity contain contradictions?

Post by Halc » October 2nd, 2018, 10:03 am

Steve3007 wrote:
October 2nd, 2018, 8:55 am
This is why an object in free fall in a uniform gravitational field is regarded as being in an inertial reference frame.
Things don't accelerate in such a field, so of course this can be regarded as an inertial frame, since it is one, no?. This being within a concentric distribution of matter is exactly such a uniform gravitational field, and clocks within one are gravitationally dilated compared to a stationary clock well outside that field. Neither can locally detect which is which, but if you compare the two (a non-local test), they'll read different values and then each will know which it is.
I had a quick look at good old Wikipedia:

https://en.wikipedia.org/wiki/Gravitati ... e_dilation

The article says this:

"According to the general theory of relativity, gravitational time dilation is copresent with the existence of an accelerated reference frame. An exception is the center of a concentric distribution of matter, where there is no accelerated reference frame, yet clocks are still supposed to tick slowly. Additionally, all physical phenomena in similar circumstances undergo time dilation equally according to the equivalence principle used in the general theory of relativity."
This seems poorly worded if not wrong. I see a lot of commentary on the web taking apart the wording of exactly the part you've quoted here. I think it would be more correct if it talked about being in the gravitational field of exactly one point gravitational source, in which case there would be no exception. Me standing on a planet with the ground exerting a force keeping me stationary in Earth's gravitational field is the same as being in an accelerating ship with the deck exerting the same force keeping me stationary in the ship's accelerated reference frame. That's what the GR rule is, but I thought it was about local forces and physics, not time dilation.

Am I wrong about that? If I put a clock in a centrifuge and whir it up to 1000G, will it dilate the same as being on a star with that sort of gravity? I mean more than it would dilate just from the linear speed of being in that centrifuge? I tried to keep that to a minimum in my example, but there would be no ignoring SR dilation in a centrifuge that violent.


The wiki talks about an exception within (not necessarily at the center like it says) a concentric distribution of matter, where you also cannot locally detect the difference, but any non-point gravitational source would be an exception. Add more points in different places, and the dilation goes up, but the acceleration might go up or down, depending on the distribution of the points. Gravitationally, clocks run slowest on Earth when the moon is full and we're sandwiched between it and the sun, but our acceleration there is the least since the pull is in opposite directions.

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Re: Does Special Relativity contain contradictions?

Post by Halc » October 2nd, 2018, 10:50 am

Steve3007 wrote:
October 2nd, 2018, 9:05 am
To clarify: When you talk about the acceleration of the clocks attached to wheels, are you talking about their centripetal acceleration? Is their rotational speed constant?
Yes to all. I just wanted G forces equivalent to the gravity-bound clock.

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Re: Does Special Relativity contain contradictions?

Post by Halc » October 2nd, 2018, 11:24 am

Steve3007 wrote:
October 2nd, 2018, 9:13 am
I also found this article about gravitational time dilation and the equivalence principle:

https://thecuriousastronomer.wordpress. ... elativity/

It seems to show that time dilation occurs between the top and bottom ends of an accelerating rocket. Intriguing.
There cannot be dilation difference between the top and the bottom since they both accelerate with each other.

Sounds like a variation of the barn-pole paradox fallacy. So I looked at it a little closer:

The description seems not to state what frame in which the measurements are being taken. On the one hand it seems to use an accelerating frame since the height of the rocket is constant, but on the other hand it seems to use an inertial frame since it talks about Bob's absolute position instead of his fixed position there at the tail. The clocks are presumed to be synced, which isn't true once the rocket changes frames.

Anyway, it seems to describe a brief acceleration, not departing much from the inertial frame in which I've decided the author is using. Bob accelerates after the light is emitted from above and moves a little, meeting the signal after a short time. That is expected even in classic physics.

So I read: "Because the rocket is accelerating, the distance travelled by the second pulse will not be same (as it would be if the rocket were moving with a constant velocity)."

That is correct I suppose from an inertial POV, but the clocks measuring the durations are not inertial any more. That's not a different dilation of one clock vs the other, it is the same situation as the first measurement, but done in a reference frame where the rocket is no longer stationary. Everything changes: h is less, and the two clocks need to be synced in the new frame if they are to be compared again. But all the measurements are being taken using clocks outside the rocket, stationary in the reference frame chosen, and these clocks are no longer in sync with the ones depicted on the ship.

At least that's what I read from it. Maybe I'm interpreting it wrong. I'm no expert in the GR rules, but this seems to be going about it with some reasoning flaws. Relativity says there should be zero difference in the two situation, which differ only in frame at which say the pulse emission is from a stationary Alice. Both pulses are emitted in an identical accelerating environment, so the two test runs are completely equivalent and should yield the exact same elapsed time as measured by Alice and Bob. This seems not to be the case in the article, so the author is making mistakes.

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Re: Does Special Relativity contain contradictions?

Post by Halc » October 2nd, 2018, 11:33 am

Tamminen wrote:
October 2nd, 2018, 9:54 am
I think we have a confusion of how we use the term 'symmetric', and I think you are right in that the situation is symmetric in the sense of the ratio being the same in both directions, and perhaps this is the normal use of the term in physics. But if the observer in D reads 5 in the clock in T1 and 10 in his own clock, and if it were so that the observer in T1, reading 5 in his own clock, would also read 10 in the clock in frame D, this would be another meaning of 'symmetry'. And symmetry in this sense is true between two events stationary in a frame. What term would you use for this strange "behaviour" of simultaneity?
You are comparing different pairs of events. In the T1 frame, the U event is not simultaneous with the D clock reading 10. It is simultaneous with an event much closer by (only 4.33 light years away), so the clock at that event is going to be off by only 2.5 years instead of the 5 that would have been computed if the guy in the ship had waited the full 10 years like the D guy did.

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Re: Does Special Relativity contain contradictions?

Post by Tamminen » October 2nd, 2018, 12:00 pm

Halc wrote:
October 2nd, 2018, 11:33 am
Tamminen wrote:
October 2nd, 2018, 9:54 am
I think we have a confusion of how we use the term 'symmetric', and I think you are right in that the situation is symmetric in the sense of the ratio being the same in both directions, and perhaps this is the normal use of the term in physics. But if the observer in D reads 5 in the clock in T1 and 10 in his own clock, and if it were so that the observer in T1, reading 5 in his own clock, would also read 10 in the clock in frame D, this would be another meaning of 'symmetry'. And symmetry in this sense is true between two events stationary in a frame. What term would you use for this strange "behaviour" of simultaneity?
You are comparing different pairs of events. In the T1 frame, the U event is not simultaneous with the D clock reading 10. It is simultaneous with an event much closer by (only 4.33 light years away), so the clock at that event is going to be off by only 2.5 years instead of the 5 that would have been computed if the guy in the ship had waited the full 10 years like the D guy did.
I know all this. What I mean is this: There are these 3 events: (1) the clock in D ticking for 10 years, (2) the clock in T1 ticking for 5 years and (3) the clock in D ticking for 2.5 years. All these events are real. Event 2 is simultaneous with event 1 for D, but not for T1. I just called this 'asymmetry', which was perhaps a misleading expression. 'Asynchrony of clocks' might be better?

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Re: Does Special Relativity contain contradictions?

Post by Halc » October 2nd, 2018, 12:22 pm

Tamminen wrote:
October 2nd, 2018, 12:00 pm
I know all this. What I mean is this: There are these 3 events: (1) the clock in D ticking for 10 years, (2) the clock in T1 ticking for 5 years and (3) the clock in D ticking for 2.5 years.
None of those are events. The 3 events are the D clock reading 10, the T clock reading 5, and the D clock reading 2.5. A 4th event is D clock at 17.5, and 5th event at D reading 20. Those other events have come up. No frame is necessary to specify those events. Not sure if you meant this.
All these events are real. Event 2 is simultaneous with event 1 for D, but not for T1.
I just called this 'asymmetry', which was perhaps a misleading expression. 'Asynchrony of clocks' might be better?[/quote]But events 2 and 3 are simultaneous in frame T1, so the symmetry is back. Events 2 and 4 are simultaneous in T2, and the same separation as the prior case, so even more symmetrical.
Yes, events are ordered differently in different frames. Relativity is very up front about that. It is symmetrical (else you'd be able to determine the preferred frame), but asynchronous, sure.

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