A Dissident View of Relativity Theory

mangaroosh

*10. Jefimenko, O.D. 1997. Electromagnetic Retardation and Theory of Relativity, Electret Scientific Co., Star City, W. Virginia, Chapter 10

I came across this article and I was just wondering about the above comment about clocks. It seems to suggest that clocks will slow down by a rate equivalent to the Lorentz factor as a result of gravitational effects acting on time-keeping mechanisms, without the need to invoke "time" dilation.

I was just wondering about the veracity of that statement.

russ_watters

That isn't true. Different clocks show different errors and I don't think that's what the author meant anyway. Sounds to me like he's just clarifying that mechanical clock errors are not relativistic time dilation.

His actual argument appears to be that the differences are errors, not actual differences in the rate of passage of time.

mangaroosh

thanks russ.

I think you're right, that the argument is that the differences are errors, not actual differences in the passage of time; but I think the line "time-keeping mechanisms do slow down when moving at high speed, and that in most instances, they obey the time dilation formula of Lorentz and Poincaré" suggests that mechanical clocks in motion will slow down, compared to clocks at rest*, by a factor calculable using the Lorentz formula; but that such slowing is attributable to gravitational effects on the time keeping mechanisms, as opposed, as you mention, to an actual difference in the passage of time.

*I think we can presume motion and rest are relative to the earth in this case


I'm just wondering by how much a pendulum clock would be expected to slow down if it was accelerated with respect to a similar pendulum clock at rest on earth; or a wrist watch perhaps; or wather clock; or any such mechanical clock? Have any such clocks been used in time dilation experiments?

russ_watters

Proximity to a reference to Relativity in the next sentence may seem to suggest that, but I can't imagine he could possibly believe it, so that's why I think they were more separate. Such clocks are nowhere close to accurate enough to show the effects of time dilation we are capable of producing. For example, GPS clock rate deviation due to GR is 46,000 ns/day. Setting aside the fact that a pendulum clock depends on acceleration due to gravity and will work very poorly in any vehicle not moving at constant velocity or not at all without gravity, the altitude of a gps satellite alone would result in a 4 seconds per second deviation.

Calc:
GPS satellite altitude: 20,000 km
Gh=9.81(6353/(6353+20000)^2=0.57m/s^2
Pendulum Period = 2pi*sqrt (L/g)
deviation: sqrt(1/(.57/9.8)=4.1x

Of course, for an astronaut in orbit, the non-moving pendulum clock would tell him time has stopped while his growing beard and filling bladder would provide much more accurate timekeeping to tell him it hasn't.

For unaccelerated motion however, the principle of Relativity - even as understood by Galileo - demands that there be no deviation. This must be true since there is no experiment you can do in your frame to detect your speed and there are an infinite number of speeds you could assign yourself depending on the frame of reference you choose to measure yourself against.

mangaroosh

Thanks Russ.

Just on the last paragraph; in the case of the pendulum clock at rest on earth and the one on the train, is it possible that the one on the train would tick slower? From the perspective of the observer on the train, or on Galileo's ship, there is no experiment they could conduct to determine if the clock is actually ticking slower; it could be ticking at the same rate as a pendulum clock at rest on earth; equally it could be ticking slower or it could be ticking faster; but the observer on the train or ship would have nothing to compare it to, and therefore no way to determine if its rate had changed.

Presumably, given the equivalence principle, a pendulum clock on a moving train would experience some form of gravitational effect that the clock on earth wouldn't; which would affect its rate - or the opposite effect perhaps. Would you have any idea what that effect would amount to; would it be close to the Lorentz factor or anything?

russ_watters

A pendulum clock is, of course, subject to the effects of relativity, but they are nowhere close to accurate enough to measure those effects.

Nugatory

[emphasis mine]
Moving, no. Accelerating, yes.

James_Harford

If you are interested in relating the Lorentz formula slowing of a moving mechanical clocks to a gravitational effect, you are unlikely to succeed. This formula is a product of special relativity which has no predictive value in discussions about pendulum clocks or any other gravitationally dependent effect.

So if your goal is to better understand some aspect of special relativity, try to forget about the gravitational field of the earth. Better yet, relocate your thought experiments to some distant region of empty space. Hope that helps.