# Time Dilation in Relativity

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

1. ### RJBeeryNatural PhilosopherValued Senior Member

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As written, the winch will require less energy to haul the laser back out of the gravity well whether there was redshifting or not. I think you are on to something though, so let's keep exploring the idea. Perhaps something related to Bondi's perpetual motion... (copied from: https://arxiv.org/pdf/1307.1441.pdf)

3. ### Q-reeusValued Senior Member

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Yes Bondi's paradox with the bucket conveyor is essentially just another variant of what I gave in #59. The unstated assumption in #59 was the laser contained it's own power supply, and to streamline it, I should have just focused on cyclically raising and lowering the power supply - say a battery.

The only other thing to clinch the matter is to remind that for the shell, gravity in the Newtonian g = -∇φ sense, goes from a maximum at the shell outer surface, monatonically to zero at the shell inner surface and everywhere further in. See e.g. derivation second part p3 here: https://www.math.ksu.edu/~dbski/writings/shell.pdf
Or under ""mass within a gravitating shell" here: http://www.sparknotes.com/physics/gravitation/potential/section3.rhtml
There is no paradox if redshift is based on potential difference (we assume zero KE's at end point locations). Your notion will automatically violate it.

I will add there is an issue remaining when the full stress-energy-momentum tensor of GR is included, but that issue is a delicate one and will not substantially impact what is being considered here.

5. ### Confused2Registered Senior Member

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Beautiful - thank you.

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7. ### Q-reeusValued Senior Member

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And thanks in return. So rare to ever get a compliment here at SF for yours truly.

8. ### RJBeeryNatural PhilosopherValued Senior Member

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Well let's not sign the death certificate just yet, see this as an opportunity to get creative. A good theorist can take a premise as true and study the physical consequences without actually believing the premise, so I invite you to do so. Make sure your ethos is not stifling your creativity.

Last edited: Feb 15, 2017
9. ### RJBeeryNatural PhilosopherValued Senior Member

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I'm going to do a bit of live-streaming of my thoughts here, just to get the creativity going.

ASSUME time dilation is a function of acceleration and distance. We take Bondi's machine and straddle the surface of the Earth such that the emission and absorption frequencies (above and below ground) are equal. The atoms at the top of the machine absorb photons coming from below and, due to their increased mass, cause the contraption to rotate in seeming perpetuity. If over-unity machines are not acceptable what other concepts could be abandoned in order to rectify this scenario?

- mass / energy equivalence?
- inertial / gravitational mass equality?
- does the time dilation differential along the machine's length affect it somehow? What does it even mean to have a loop (i.e. chain) rotating at different rates throughout it's system?
- is Bondi's machine unphysical for some reason? Are there other assumptions being made that perhaps don't extend below the surface of a mass?

...

10. ### Q-reeusValued Senior Member

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Abandoning either will simply allow more 'genuine' over-unity devices to be concocted. Just try it. Might be fun as long as it also being fantasy is kept in mind.
At any given observation point, there is simply a measured steady rate of motion. Measured at the top, the rpm will be less than measured at the bottom. Which does not lead to any kind of 'pile-up' paradox since it's a matter of clocks running at different rates. Everything redshifts, not just photons. A vertical shaft rotating at a steady rate will for instance register a slower rpm at the top than observed at the bottom, without any buildup of twist in the shaft occurring.
That obviously unrealistically ideal machine will still quickly grind to a halt. But only because on each succeeding round trip the probability of iteratively increasing net redshifted photon emission-then-absorption lessens, owing to finite and actually quite narrow atomic spectral line-width.
My example of lowering/raising through a hole in the static shell suffices to show you either accept redshift is a function of Newtonian gravitational potential there, or posit violation of conservation of energy.

You could push on and still try an experiment. Incidentally, the value for Pound-Rebka mentioned in that article suggests you may 'only' need resolution of ca one part in 10^13. Personally I would put that to bed and just chalk it all up to an interesting thought experiment.

11. ### RJBeeryNatural PhilosopherValued Senior Member

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There's a theory called Quantized Inertia which clefts gravitational and inertial mass. I think it has tremendous potential. McCulloch's book is very readable.
http://physicsfromtheedge.blogspot.com/

https://www.technologyreview.com/s/...ry-separates-gravitational-and-inertial-mass/
Ironically, not with my model. I purposely straddled the Earth's surface for this very reason. It would be a true perpetual motion machine unless there's something else preventing it.
The experiment is going to happen, regardless. Not having a plausible explanation for a potential perpetual motion machine just takes the Uni's endorsement off the table.

12. ### RJBeeryNatural PhilosopherValued Senior Member

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Q, I was hoping you could reword this because I'm having a problem following. The battery-powered laser has given out energy (and therefore mass) whether there was red-shifting or not. Maybe I'm just being lazy in thought.

13. ### Confused2Registered Senior Member

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501
Going to an extreme..
Lower down a mass m to a point where the energy of the photons at the surface is (conveniently) reduced by a factor of 2. Let half the mass be converted into photons directed at the surface. Then haul the remaining mass back up to the surface. The mass has lost (1/2)mc² J and the surface has gained (1/4)mc² J. Is the difference in mechanical work done (going down - coming up) equal to (1/4)mc²J ?

14. ### Confused2Registered Senior Member

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501
As I seem to be alone with this... (the above post)
To reduce the energy of each photon by a factor of 2 I think we need a time dilation factor of 2. <--- e=hf should work????????
Or [1]
sqrt(1-2U/c^2) = 0.5
squaring
1-2U/c^2=0.25
2U/c^2=0.75
U=0.375c^2
Going down work done on winch is
0.375c^2m
Coming up work done by winch is
0.5*0.375c^2m
Difference 0.5*0.375c^2m
which is clearly not
0.5mc^2
?

[1]Unfortunately my 'reference' for this is me ... http://www.sciforums.com/threads/is...e-r-2m-singularity.156144/page-3#post-3379123

15. ### Q-reeusValued Senior Member

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Fascinating to study no doubt, but bottom-line admission is WEP, EEP have never been found to be violated, so far to better than ca 1 part in 10^13.
Like plausible metric theories for instance.
As there is an obvious determination to do the experiment regardless, try hard to source an affordable Mossbauer setup. We've already covered why the other alternatives are out.

16. ### Q-reeusValued Senior Member

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Stick with lowering down from radii R2 to R1 then raising up in reverse order for a 100% efficient rechargeable battery. X joules of energy are added while initially up at R2. On lowering to R1, value as 'seen' from R2 is fractionally reduced to X(√(g_tt)/√(g_tt')) joules, where the primed,unprimed temporal metric factors apply at R2, R1. The balance, X[1-(√(g_tt)/√(g_tt'))], was delivered to the notionally 100% efficient winch. That simply assumes conservation of energy but an explicit direct calculation based on Schwarzschild metric will agree with it. It's been done many times without outcry.

Proper value at R1 of course remains X battery joules. Beamed back out as light by the 100% efficient laser so powered, in standard picture, at R2 the received frequency thus photon energy has therefore a relative redshift of √(g_tt)/√(g_tt'). The energy difference between no redshift and redshift is thus X[1-(√(g_tt)/√(g_tt'))] joules.
Precisely the negative of the energy given to the winch during lowering. Add them together, we get zero net change. As required for conservation of energy.

As all we care about was what happened to that X initial joules, winching back up 0 joules is irrelevant. Battery 'dead weight' doesn't figure in the sums. The balance has already been done. Being based on gravitational potentials, a consistent result is independent on such details as being inside or outside a matter shell, or being in a borehole.

Beery theory would have no redshift for when laser+battery is inside shell, despite it being a maximum at just outside the shell! Similarly no delta redshift for emission & reception locations equally straddling the surface (assuming delta r's << earth radius R). Which is guaranteed to violate conservation of energy in general.

17. ### Q-reeusValued Senior Member

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Yes. See my #73.

18. ### Q-reeusValued Senior Member

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Why? See my #73

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19. ### river

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time dilation is a relative consequence of speed .

to other objects in space , your speed does not affect other objects .

inotherwords , time dilation is a perspective consequence of the observer only.

20. ### RJBeeryNatural PhilosopherValued Senior Member

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If that were true then it would always be a relative phenomenon. Time dilation is absolute is many scenarios.

21. ### RJBeeryNatural PhilosopherValued Senior Member

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Update: looks like clocks are the best way to go. Wavemeter tech isn't precise enough and the Mossbauer setup would require a tremendous amount of effort and money. The good news is that my dilation estimate for 1 km beneath Earth's surface was off so I think this may actually be practical and may not even take that long.

22. ### Q-reeusValued Senior Member

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Can't see how you will meet the sensitivity criteria. From your #51:
No, given drift issue and e.g. varying temperatures over an extended time span. Appears that stability value is merely one of gradual frequency drift. Better find out how much temperature variation contributes to that. Also what the clock noise floor is. My suggestion is run through the details of proposed experiment with someone tech savvy at Microsemi or equivalent. One issue is how to sync two clocks then maintain a continuous differential readout throughout the test run(s). Obviously, one would check how that goes when they are adjacent. If random fluctuations would swamp any theorized value owing to gravity, no point proceeding to stage II - sending one down a borehole. Same thing if it's found that a temperature differential corresponding to surface vs down borehole effects clock rate much more than gravity would....

23. ### RJBeeryNatural PhilosopherValued Senior Member

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I'm discussing thing with various groups (some tech companies, physicists, labs etc.) So far, by far, the best resource as been a mailing group called 'time-nuts' which includes a guy who has already done this experiment above ground(!)

http://leapsecond.com/time-nuts.htm