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Effect of acceleration and gravity on clocks
Kant was wrong to take time and space as the fundamental intuitions. Relative station and motion are more fundamental; causality is of course the most fundamental. Time a space are distinct and intuitive for inertial motions, and for certain generalisations of inertial motions; time and space are notions derived from the more primitive intuitions of station and motion. Looking for a start in studying relative station (with slow movements permitted, with respect to an inertial frame), Euclid told us about a geometry that is one of the main foundation stones of our civilisation. But Euclid's geometry does not work for observers who travel near light speed with respect to the objects that they observe (keeping to constant velocity motions in inertial frames for the present exercise). They cannot practically put metre rods next to the objects, nor can they compare times without regard to their speed. They have to observe the moving objects by other methods. Radar and photography are the obvious methods to use. Effectively, light speed has become a new standard of motion. We find that moving straight edges look like arcs of hyperbolas. Minkowski geometry is a hyperbolic geometry. It describes the nature that we know, at least far from heavy objects, when we are looking at fast inertial motion.
Going to accelerated relative motions, we need a new standard: a standard that tells us about acceleration. Inertia is the obvious one. Mass tells us about the force needed to cause acceleration. But how does acceleration affect clocks and measuring rods? It seems that the size of a clock governs how it will be affected by acceleration.
Who can educate me about the effect of acceleration on clocks? Circular motion is about acceleration at right angles to the velocity. Do we have to rotate the accelerated clock to make it keep time? What happens if we don't rotate the clock in time with the circular motion? What about acceleration that stays in the same direction as the unrotated clock, not at right angles to it? It seems that there is no need to rotate A.D. Fokker's spherical light clock. Differential geometry tells us that we can't deform a spherical material surface without making it buckle. Its size affects its performance. Does the size of an atomic clock affect its response to acceleration? To gravity?
Submitted by Christopher Joh... on Sun, 2008-02-17 15:16.
ReX: Effect of acceleration and gravity on clocks
Hi Christopher, I think I have answered these questions on the other current thread:
http://www.scienceblog.com/cms/one-way-speed-light-convention-15507.html...
The link given above by "Anonymous" is also interesting...
Regards,
Burt Jordaan (www.Relativity-4-Engineers.com)
Re: Effect of acceleration and gravity on clocks
"Do you know of someone who has kept and compared two bevies of several identical atomic fountain clocks at the top and bottom of a mountain for a long time? Are those clocks good enough to make that interesting? I find the Rebka and Pound Mossbauer-and-tower experiment hard to feel happy about as a complete guide."
You can see this with a standard cesium beam clock. Elevation changes have to be accounted for — it's about a third of a nanosecond per hour.
Even amateur timekeepers have done it:
http://www.wired.com/science/discoveries/news/2007/12/time_hackers
Re: Effect of acceleration and gravity on clocks
Hi Burt.
Thank you for this.
I will think about Goy and Selleri. Thank you for the reference.
Assuming that the force of gravity doesn't affect an 'ideal' clock for our purposes, then it has to be that the apparent effect of gravity on a distant observer's observations of such a clock are determined by the slowing of light's travel speed in a strong gravitational field, as it curves in a hyperbolic path around the heavy object. Of course it is a sign of empty-headedness or more seriously of heresy to say this; one should say that time itself is slowed and that the "curve" is a matter of a "straight" line in bent space-time with the metaphor that a geodesic is a "straight line". But in any case, the apparent slowing of the clock is a result of the method of observation with light as a reference standard of motion, not an effect on the clock, since it is position and not field intensity that decides the outcome. Again this is verging on heresy, of course, because the religion has it that there is "no such thing as a gravitational force or field".
The price of accepting the general relativity system of thought is loss of inertial references and loss of the principle of conservation of energy. Too expensive, I think. More worrying still is the loss of a coherent notion of causality itself, I think. The notion of cause and effect is emptied by the general relativistic religion, which nevertheless was founded and built on that notion.
More to think about. That includes the finite size of a Fokker spherical light clock as against the near infinitesimal size of some atomic or particle clocks.
Do you know of someone who has kept and compared two bevies of several identical atomic fountain clocks at the top and bottom of a mountain for a long time? Are those clocks good enough to make that interesting? I find the Rebka and Pound Mossbauer-and-tower experiment hard to feel happy about as a complete guide.
Considering the technical precariousness of the gravity probe B and its mighty expense, it seems that a network of one-way measurements of the speed of light, say near the sun, might not be such a bad investment, even though we think we know the answer in advance. The network could be realised by a few artifical solar satellites near the sun. It seems to me that the results can and should be interpreted in terms of a Minkowski space surveyed by radar by several communicating artificial solar satellites far enough but not too far from the sun. I think clocks for this kind of work are now becoming available. A nice remote pulsar time reference and a suitably remote astronomical direction reference would be good.
Sincerely,
Christopher
Re: Effect of acceleration and gravity on clocks
Hi Christopher.
I hope others will join in to do as you requested: "Who can educate me about the effect of acceleration on clocks?"
You asked: "Circular motion is about acceleration at right angles to the velocity. Do we have to rotate the accelerated clock to make it keep time?"
Only if it's a pendulum clock, I think. ;) Experiments on the effects of velocity, acceleration and gravity are normally done with either atomic clocks or particles with known decay times. Neither of them care about the orientation of the clock relative to the acceleration. They also do not care about the magnitude of the acceleration, provided it is not so high that the structural integrity of the clock is compromised.
There are only two relativistic issues that affect the rate of clocks: (i) relative movement with a change in inertial frames somewhere during a journey and (ii) the depth of the gravitational well at the location of the clock. Acceleration or the "force of gravity" does not affect atomic clocks. The latter is proportional to the slope of spacetime and it is the depth rather than the slope that affects clocks.
As far as acceleration is concerned, here is one paper that I found with some data and good references:
http://arxiv.org/PS_cache/gr-qc/pdf/9702/9702055v1.pdf
Regards,
Burt Jordaan (www.Relativity-4-Engineers.com)
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