# Time Dilation in Relativity

Discussion in 'Physics & Math' started by RJBeery, Feb 1, 2017.

1. ### Q-reeusValued Senior Member

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It's the gradient of the potential i.e. Newtonian 'g-field' that sums to zero. Inside, the potential -GM/R is depressed uniformly, where R is the effective radius of the shell. Note that in GR, R is defined in terms of proper surface area or proper circumference. Something needful when dealing with a dreaded black hole. For which the usual definition for R as proper length of a radius vector from centre of a sphere to it's periphery, breaks down completely.

3. ### Q-reeusValued Senior Member

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For the spatial and temporal metric components themselves yes. There is a real issue with transitioning of g_rr across the shell wall in GR, but see my comment later.
Not exactly. Gradients of the spatial metric are zero (zero 'g=field'), but the temporal component is depressed wrt far outside.
Not so. Explicitly, time dilation factor √g_tt = √(1 + 2Φ/c^2), where Φ = -GM/r (r > R), or -GM/R (r =< R) is the Newtonian potential, and has a non-vanishing constant value within the shell interior. Flatness of metric does not necessarily equate to undepressed metric coefficients. There is something 'funny' happening about the g_rr spatial metric when considering a shell, apparently but not actually resolved by working in the so-called isotropic Schwarzschild metric. It led me to abandoning GR way back. But I'd rather not go into that further here - or even in another thread.

5. ### RJBeeryNatural PhilosopherValued Senior Member

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$F = m*a = \frac{G*M*m}{d^2}$
$a = \frac{G*M}{d^2}$
$t_0 = t_f\sqrt{1-\frac{2*G*M}{d*c^2}}=t_f\sqrt{1-\frac{2*a*d}{c^2}}$
We've already established that time dilation is a local phenomenon (e.g. Pound-Rebka, modern gravitometers). It seems ad-hoc to continually restrict the definition of "local" to coincide with technology advances. Doesn't really matter anyway, I'm not trying to disprove the EP. Quite the contrary, I'm predicting a stronger Equivalence Principle in that two bodies under the same conditions would experience reality identically, which includes agreeing on the rate of a remote clock ticking whether they are free-floating or in the center of a massive transparent sphere.
I looked for a long time for this as well. Thanks for the link

7. ### Q-reeusValued Senior Member

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From that your definition of acceleration is proper acceleration. What an observer records as g-forces. Easy to show why it cannot work in general. Later.
Wrong. Local implies an intensive, say pressure, temperature, 'g-force' etc. Pound-Rebka is an extensive phenomena. The relative difference in frequency. As measured between two vertically separated locations. Nowadays, measurable over differences of just centimetres. Still necessarily a relational phenomenon involving differences over a spatial extension.
See above. The definition of local vs non-local can be rubbery in e.g. astronomy/cosmology but is not up for grabs when it comes to defining time dilation. Always an extensive, relational thing.
Your definition of 'the same conditions' restricts to whether or not proper acceleration is experienced. And discounts differences in gravitational potential hence in spacetime metrics. Many times now I have pointed out the temporal metric component g_tt < 1 is depressed inside a spherical matter shell. Unambiguously predicting a laser beam emitted from within such a transparent shell will record as redshifted to a receiver far outside the shell, where notionally g_tt = 1. That is the standard position. Regardless that many physicists otherwise familiar with GR often get it wrong.

What blows your concept out of the water is GPS. The constellation of satellites forming the 'sky' part of GPS system are all free-falling in a zero-g environment, yet the major relativistic correction that has to be made for it all to work is owing to gravitational time dilation:
http://fusion.net/video/205931/why-gps-wouldnt-work-without-einsteins-theory-of-relativity/
http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html
https://www.aapt.org/doorway/TGRU/articles/Ashbyarticle.pdf
Latter gives the explicit calculations - see esp. p9 on. Your idea involving proper accelerations simply cannot work.
I'm tempted to say no problem but it was quite a hunt. The point of that result is though, you have to face the fact one can be immersed in an arbitrarily uniform 'g-field' lacking any tidal field i.e. all 2nd derivatives of metric are zero. So where does that leave your attempt to connect 'tidal forces' to proper acceleration thence to time dilation?

Confused2 likes this.
8. ### RJBeeryNatural PhilosopherValued Senior Member

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Whether the relational phenomena involving differences over a spatial dimension are physically connected or not, I believe this is a distinction without a difference. The model is suggesting that the "intensive g-force" is directly due to the tidal forces causing the Pound-Rebka results; we could easily consider the building a discrete system whose "feet" are aging more slowly than its "head".
I'm not discounting the differences in gravitational potential, I'm questioning that they affect time dilation. There isn't a need to explain what GR predicts because I agree with you on that point.
As mentioned earlier, this presumes that a geodesic path experiences no proper acceleration, but we have already established that a geodesic path does in fact experience such acceleration. The GPS satellites are also under an additional torque as they orbit the Earth which may account for the differential from the gravitational potential prediction.
This is quite possible, but I'm convinced enough to try which is something that any Physicist should respect.
My model would predict that a clock within such a cavity would experience zero time dilation relative to the distant observer. It's difficult for me to grasp a uniform g-field, where the geodesic path would indeed experience zero proper acceleration...

Last edited: Feb 8, 2017
9. ### Q-reeusValued Senior Member

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Well rjb, no point in going round in circles on this. You have a fixed position that in some to me strange way, tidal fields i.e spacetime curvature, are solely and intensively responsible for time dilation. And according to your theory, lowering a clock down a deep bore hole will have it ticking faster not slower relative to one on the surface. An alternative way of saying that is that a laser beam fired from down the bore hole up to the surface will register as blueshifted to a surface receiver. Agreed?
Then I suggest you arrange with your compatriot to carry such an experiment out. Taking all the precautions and consistency checks that would have been observed in say the original Pound-Rebka experiment. In your case, local gravitational 'anomalies' owing to geological mass density concentrations might easily throw your assumptions off. Hence best to consult a geologist as to a suitable location. Please do report back the results - after having it reviewed and commented on by experts in the field.
Good luck. But steel yourself for a letdown.

10. ### RJBeeryNatural PhilosopherValued Senior Member

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Agreed, I was just thinking this may be a quicker experiment than waiting for two atomic clocks to diverge.
The suggestion I made was to have an emitter and receiver both at the surface and in the well, and run two tests in tandem. That may account for any potential atmospheric and temperature anomalies.
Of course! I realize the gravity of what I'm proposing.

Thank-you for the mature banter...

11. ### Q-reeusValued Senior Member

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Quicker maybe but probably too insensitive if trying to compare frequency shifts. Frequency stability for affordable lasers unlikely to be up to scratch. Digital counting of pulsed output may get around that issue but do the sums, figure out what you need, and consult competent people in the field.
Yes, but would not guard against possibility of a local mascon(s) throwing out significantly the assumption of uniform rock density and in turn assumed tidal gravity. Hence the advisability of a geologist's input. One way around that would be to do the experiment in the ocean i.e. submersed atomic clock vs surface atomic clock readings. Hire a spot aboard a deep sea trawler. OTOH a back-of-the-envelope calculation may show typical mascons can be neglected. But do some modelling, or better still ask a geologist familiar with gravimetric surveying.

In either case, one has to allow for the contributions of letting down and hauling up phases, but is easily accounted for. Repeat, but with the only variable being submersion time. The differential in readings between runs eliminates up/down phase issues. How cheap are ultra-stable atomic clocks these days?

Whichever route you take, a thorough accounting for all uncertainties needs be done before embarking. You may find it's financially out of reach to obtain the needed tight control levels. Of course if you can persuade a university physics department somewhere....but that I doubt.
You're welcome.

12. ### Confused2Registered Senior Member

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501
The experiment may already have been done. I suggest recalculating Pound-Rebka using Beery Theory and Einstein and compare to see if the results each lie within the error bar of the other. I wrote the very software for doing this a few years ago but accidentally formatted the disk with it on and haven't had the heart to start again.

13. ### Q-reeusValued Senior Member

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Good idea, but actual formula used by Beery Theory in Pound-Rebka setting predicts the same result to 1st order accuracy, which is all that can be expected.
His implementation postulates that Earth's surface sets the point of maximum redshift hence emitters positioned higher OR lower will be blueshifted as seen from terra firma location. Personally I cannot see any consistency as the simple a.d approach contains no mathematical input at all from tidal gravity. The latter being a somehow governing principle of sorts but just how is beyond my ken.

The least costly approach would be for rjb to enter into a serious personal correspondence with one or more experts in GR and take careful note of his/her/their objections and counterarguments. Sometimes though the only way to shake or confirm a conviction is to go do the experiment.

14. ### RJBeeryNatural PhilosopherValued Senior Member

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I'm out of my element on lab test design. The digital counting sounds great but...I cannot intuit that it would work. How could a receiver ever perpetually receive a signal at a rate faster than it was emitted?
Thanks for the ideas, I am speaking with a couple of folks. An associate told me that "Microsemi's devices are stable to 1 part in 2.5x10^11 or so over a day..." The advantage of clocks is that I could bury one for many years to reach whatever arbitrary divergence was necessary to be convincing to all.
The path I'm taking is: build theory, devise test, spec it out, approach Uni and if they aren't interested then I pay for it myself or seek a donor. Most of my neighbors are pretty wealthy and might perhaps be interested in taking a flier like this.
I arrived at the conclusion that tidal forces are the cause of time dilation from completely disparate, largely philosophical paths. The attempted mathematical justification for it came as an afterthought. If you read the paper you'll see that there are multiple formulas suggested which are similar...but not identical.

If we drop a ball down a well it continues to accelerate. If we think in terms of "dropping a photon" down a well we would expect it to continue to blue-shift. If we think in terms of the gravitational field itself, though, then the photon's shifting may be a consequence of its "stresses". I don't really need anyone to see what I'm seeing in my mind's eye, I'm already committed to pursuing a test on it, but I really do appreciate the feedback.

15. ### Q-reeusValued Senior Member

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For the same reason the laser beam is perpetually redshifted or blueshifted at receiver locale relative to emitter locale. Differing clock-rates. The total cycles counted for a finite wavetrain has to be equal, but the wavetrain duration is correspondingly different at the two locales and there is no paradox.
A quick search and found it: https://www.microsemi.com/product-directory/3425-timing-synchronization#clocks-amp-freq
I'd say that is the way to go. Apart from the mascon issue, be aware of the need to take something else into account. See the article I linked to here: http://www.sciforums.com/posts/3434544/
Especially re assumptions of uniform density ve actual density profile for earth. Of course the time dilation results found there are based on the conventional picture....

The winching down/up phase can be an arbitrarily tiny part of the overall time involved. And as a 'twin paradox' component, it's easy to work out the expected velocity contribution which to 1st order accuracy can well ignore varying metric. I expect it will be negligible. Hence no need for two runs per se. Although multiple runs is sensible just on a repeatability/reliability basis.
If as I'm confident standard theory based on potentials is confirmed, better hope any neighbor who financially supports you remains a good neighbor afterwards!
I predict some soul-searching and a deep reappraisal post experiment.
OK. Let's see how it all works out. A learning experience whatever transpires.

16. ### RJBeeryNatural PhilosopherValued Senior Member

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I get it now. Staring at math does nothing for me, I have to internalize new concepts. An observer loudly counting on the surface of the Earth, once a second, would be heard by a distant observer (who is not experiencing any gravitational time dilation) as counting more slowly than once a second because his clock is moving more quickly between numbers. Does digital counting of pulsed output allow for better resolution than measuring frequency shifts? It's difficult for me to decide that they are any different - measuring the frequency of a laser is basically a counting of its cycles. I'll have to think about it some...
I cannot predict within an order of magnitude how expensive such a lab test will be.
I suspect that's true regardless of the outcome.

Q-reeus, if you PM me your name I'd be happy to mention you in the final paper if the test produces results incompatible with current theory.

17. ### Q-reeusValued Senior Member

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With laser frequencies in optical band, 430–770 THz, electronics to allow a direct count of cycles does not afaik exist. So a direct method must be wavelength based. You will need to ask around as to how accurate that would be, and of course at an affordable price. Another side of that cost is sufficient laser frequency stability. Once found, compare that to the already known values for the atomic clocks sourced at Microsemi etc. Clock method seems less fiddly overall. No need for instance to have to arrange how to carefully aim a laser beam located down a deep well.
(Then again, single-mode optical fibre linkage would overcome that issue. So, overall sensitivity vs cost will be the decider.)
PS - Will PM 'conversation' you.

Last edited: Feb 12, 2017
18. ### RJBeeryNatural PhilosopherValued Senior Member

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I'm in discussion with lab that has a 1.1 km shaft underground. If that would produce a shift of 5x10^-14 and the clocks are accurate to 2.5x10^-11 (per day)...you can see the problem. Fiber optic channel is a great suggestion because the shaft is used regularly; it would also eliminate pathing issues, contaminants, etc. Do fiber optics induce frequency shifting? I just need to find instrumentation on wavelength measurement accuracy (and I'm open to suggestions!).

In my mind the redshift/blueshift is the test to perform. I could set it up and (depending on current technology) have results within a single day. Running two fiber optics cables, so as to look for time dilation in each direction concurrently, should allow our results to be less likely attributed to anomalies.

19. ### Q-reeusValued Senior Member

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Indeed! I had forgotten just how sensitive the Mossbauer method used in Pound-Rebka had to be. So your theory (taking into account actual density profile of earth?) has a change ~ 3 orders of magnitude below noise threshold of available clock? Then scratch both clocks and lasers, given fractional frequency stability of affordable lasers will almost certainly be a considerably worse than for those clocks.
No. Any contribution owing to slight non-linearity should be well below detection levels and besides could only generate harmonics not slight changes in frequency. Only gravity will induce the latter. However a moot point given above issue. In principle beat interference detection for counter-propagating laser signals would be easily sensitive enough. But in practice will be wrecked owing to insufficient frequency stability. You might want to ask around to confirm that though.
Given the above, my only further suggestion is don't give up just yet. Check out possibility of sourcing a relatively affordable and compact Mossbauer setup. One that can handle lowering a source or detector down and up that hole. And maybe a uni dept could be persuaded to do the grunt work and foot the bill - as an interesting exercise for undergrads. Maybe.

20. ### Q-reeusValued Senior Member

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Looks like I was too pessimistic re laser frequency stability:
https://www.rp-photonics.com/stabilization_of_lasers.html
http://www.stablelasers.com/
Price tag? Universities having such?
Allowing adequate laser source stability is achievable, this 'pico priced' wavemeter is way too low in resolution:
http://www.moglabs.com/wavemeter-faq.html
https://www.rp-photonics.com/wavemeters.html
Contacting such vendors and indicating what is required is the way to get an experienced judgement as to feasibility. And further leads.
Mossbauer still looks the better bet imo.

21. ### RJBeeryNatural PhilosopherValued Senior Member

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I was advised by Dr. Rudiger Paschotta (the "RP" in rp-photonics) that wavemeters are too imprecise to use in this application. He recommended atomic clocks but...ugh.

22. ### Q-reeusValued Senior Member

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Hmm....There should be some detector based on beat wave interference that would be up to scratch, given existence (surprise) of sub Hz frequency stability in off-the-shelf lasers. An atomic clock of sufficient stability, given what Microsemi could offer as off-the-shelf, will likely be both prohibitively expensive and too bulky. Have you checked out if commercially available Mossbauer detectors are around?

But here's the thing you should rethink. According to your conception of gravitational time dilation, a clock or laser or whatever, located inside a spherical matter shell, will tick at the same rate as one far outside the shell where gravitational influence is negligible. That is, there will be no recorded redshift by a detector there. Similarly, no recorded blueshift by a detector within the shell receiving light from a remote laser.

This leads to an energy paradox. A very simple way of thinking about gravitational time dilation is to do an overall before/after energy balance. Assembly of final matter shell from initially diffuse dust. No need to even do the simple sums. Just realize that gravitational collapse of the dust to end with a static shell requires inwardly collapsing dust KE be converted to heat energy then radiated away in the process. Hence every atom in that final, cooled shell has reduced energy relative to when part of the diffuse dust.

Similarly, any clock or laser winched down from afar, through a tiny hole in the shell wall say, and ending up stationary in the hollow interior, has given out energy to the winch in the lowering process. Higher to lower gravitational potential. A laser within now fires a beam to the outside for some given duration. According to the consensus view, there must be redshift, just to account for the reduced energy content of everything within the shell. If the laser + energy source is now winched back out to a remote location, the reduced mass owing to laser energy given out, will mean less energy required to winch out than initially given to the winch in the lowering process. All accounted for in an overall energy balance

Whereas you claim there will be no redshift. Is it not obvious now that this permits a cyclic process that is a perpetuum mobile in principle? Can live with that?
If not, a lot of further research and time and expense may be saved.