When physics is geometry: a new proof for general relativity through geometric interpretation of Mössbauer rotor experiment. Celebration of the 100th anniversary of general relativity by Christian Co

Dear Christian,

Your essay is very interesting even though I am not sure I perfectly understood everything.

I agree with you that geometry is the key.

In my essay, I propose an intriguing list of equations for fundamental constants that show the recurrence of Phi (the golden ratio) and 8Pi-1 (a ratio I have discovered).

If you have the time, please take a look and let me know if you think these are just coincidences.

All the best,

Patrick

Dear Christian Corda,

I very much enjoyed your essay. Your treatment of the Mossbauer experiment was one I had not seen previously. However, in your essay I did not find as clearly stated your reply to Jacek above, specifically:

"The idea that not only gravitation but all fundamental interactions and matter are manifestations of space-time geometry is indeed my dream of research and the first motivation bringing me to my job of scientist."

I too share essentially this vision and I'm optimistic that we are not that far from seeing results of this approach. I wonder how you reconcile 'instantaneous' entanglement with this view? I do not. I have, in my current essay, discussed a novel approach to Bell that I hope you will read and find interesting. I would appreciate any questions or comments you might have on this topic, as I believe entanglement to be completely incompatible with the fundamental approach you outline above.

My best regards,

Edwin Eugene Klingman

It is my understanding that the equivalence principle works both ways. A frame in flat spacetime, say far out in interstellar space, and another frame falling in a radial gravity field or being frame dragged by any sort of gravity field have equivalent physics. Similarly a body on the hard surface of a body that is the source of a gravity field is equivalent to some accelerated frame in distant flat spacetime. By sitting in my chair the local physics is equivalent to being in an accelerated frame with g = 9.8m/s^2. If there exists a deviation this would be the same as saying the gravitational mass of a body is different from the inertial mass.

If there is a difference in the application of the EP to inertial and accelerated frames it would be news to me. It would be profoundly disappointing as well. I think a more general form of the EP is to say that the quantum vacuum is equivalent in different frames. Further I think that ultimately inertial and accelerated frames are themselves equivalent in quantum gravity.

Cheers LC

I'd like to sit down, maybe today or tomorrow, and see if the k_1 and k_2 could be derived as k = k_1 k_2 in a single derivation.

We can think of this rotating system as a model for a rotating QCD string, such as a meson, in a Regge trajectory, or a superstring. In this latter case the extreme rotation approaches the condition for a black hole by the Regge pole or trajectory J ~ E^2. At some point the system is rotating so enormously the particle horizon according to an observer riding with the frame, say on one arm of the thing. approaches that frame.

LC

Hi Christian,

"The idea that not only gravitation but all fundamental interactions and matter are manifestations of space-time geometry is indeed my dream of research and the first motivation bringing me to my job of scientist."

I agree with this idea because I have the proof of it. In my system space, time, matter, energy and interaction laws are all arise naturally from basically random numbers. That leads to reality manifesting in Geometric Probability.

You can run the programs and see the results and the code is visible. Please do not be discouraged by the grand claims, they are natural outcome of the simulation. I just did what I was allowed to do with all the possible relations between these random numbers.

Essay

Thanks and good luck.

There are two standard forms of the equivalence principle. The Weak form states the equivalence of inertial and passive gravitational mass, which implies that all massive particles will fall along the same space-time trajectories in the presence of only gravitational effects. The Weak Principle is what is tested by the experiments of, e.g. Eötvos. Note that it has no consequences for the behavior of light. The Strong principle states the empirical equivalence of experiments done "at rest" in a constant gravitational field and in a constantly linearly accelerating lab with no gravity. That principle does have implication for light. But the Strong equivalence principle is restricted to comparing constant linear acceleration to a constant field. It does not even properly hold for labs on Earth, where the gravitational field is not constant, although the differences are of second order. (Consider stretching your hands apart and dropping two masses, measuring the distance between the hands and the distance between the place where they hit the floor. In a linearly accelerated system in flat space-time, those distances will be identical. In a lab on the Earth, they will not, since the gravitational field is not constant (they will hit slightly closer together, as they are both falling toward the center of the Earth, as it were. Similarly, a water droplet in a space station orbiting the Earth will be slightly elongated by tidal effects, and one in inertial motion in flat space-time will not. So not all "free-fall" is the same.)

The Strong Principle does not have any application at all for rotating systems. If you check your own reference (Misner, Thorne and Wheeler) you will verify this. Check Wald (for example) as well.

In the first part of this paper, two coordinate systems are laid down on flat space-time. Obviously, these coordinate systems do not change the space-time geometry at all: it is flat in both. The line element, of course, takes a different algebraic form relative to the different coordinates, as it must. This is just the same as using different coordinate systems on Euclidean space, and has no connection to the Equivalence Principle.

To clarify the situation, one cannot just talk about "accelerating" systems: the Strong Principle compares linearly accelerating systems in flat space-time to systems with a constant field. But rotation is not a linear acceleration. There is no gravitational field that will will mimic, as it were, the apparent effects of rotation. It you think any gravitational field can produce a "centrifugal" force, try to specify how. No stress-energy tensor will produce the same apparent physics is a non-rotating lab as there is in a rotating lab.

I see what Kündig states, but the claim is not accurate.

Regards,

Tim

Dear Christian,

As usual you wrote an interesting essay. I also believe with your conclusion remark that "Mathematics is Truth instead of Trick". However, I do subscribe that Geometry is also a "Force" like Newton's gravitational Force. In my essay, KQID prescribes that Existence is geometrical and it is a mere Einstein complex coordinate points(numbers as in Pythagoras') or in this mathematical expression Ψ(iτLx,y,z, Lm). I am surely derived my theory from a very different paradigm however the outcomes must be about the same especially in our experiences and scientific experiments. KQID must also be able to explain and predict more than the dominant paradigm of today.

As usual, well deserved high score and best wishes,

Leo KoGuan

Dear Ch,

I think I know how to do this k_1 + k_2 within a single treatment of the metric. We go back to the metric

ds^2 = Adt^2 - 2ωr^2dφdt - dr^2 - r^2dφ^2

for A = 1 - (ωr)^2. Now divide this entire equation by dt so that

(ds/dt)^2 = A - 2ωr^2(dφ/dt) - (dr/dt)^2 - r^2(dφ/dt)^2

This is the gamma factor for the system with ds/dt = 1/γ. The Lorentz gamma factor is then approximately after binomial theorem etc

γ =~ 1 + ½[(ωr)^2 + v_r^2 + 2ωr^2Ω + r^2Ω^2],

where v_r is the radial velocity and Ω is the angular velocity of the particle.

The particle is a photon and in the experimental set up it is set in a radial direction. The standard gamma factor for a particle does not pertain to a photon, but we are using that here with the idea that v_r is the speed of light or very close to that. We might consider the beam of photons to be just a highly relativistic beam of electrons, where these behave approximate to massless particles. We now consider that the photons are constrained to remain in a type of photon guide or fiber optic. This means the photons have an angular velocity component to them with

c^2 = v_r^2 + (ωr)^2.

The radial part we just write as c or unity as an approximation and we substitute this into the gamma factor, here modified to account for a photon that makes this different from the standard definition, to get

γ =~ ½ + 2(ωr)^2

This is then used to compute the time dilation dτ = γdt. We let dt -- > dr and the time dilation integrate along the radial direction

τ = ∫^R(½ + 2(ωr)^2)dr = R/2 + (2/3)ω^2R^3 = R(1/2 + (2/3)v^2R).

The R/2 can be eliminated if we just consider the difference in gamma factors as the relevant factor so that δγ = 2(ωr)^2 is the relevant factor to compute redshift factors.

Cheers LC

Dear Christian,

Thank you for reading my essay and glad that you liked it. I went through that link that you posted and it was very interesting, I also need to go through your essay very thoroughly because I have not gotten the right results for the gravity as I have for the others.

Indeed the exotic results that I am getting is even surprising to me and I am not too sure what to make of them, but I do have a general idea. I did rate your essay and I may have some questions for you later.

Thanks

Dear Christian,

A rotating laboratory is not "freely falling", i.e. subject to only gravitational effects. Put otherwise, a body "at rest" in a rotating frame (i.e. with constant spatial coordinates) is not following a geodesic. That is why it isn't an inertial frame.You are not separating linear acceleration from rotation, which are quite different. The Strong Equivalence Principle is confined comparisons between effects in various circumstances, none of which include rotating labs or rotating frames. (The physical effects of rotation were, of course, whole point of Newton's bucket experiment, which gets the same explanation in relativity as it does for Newton: rotation is an objective feature of some motions.)

One application of the principle is this: experiments done in a lab "at rest in a constant gravitational field" (to a good approximation, a *non rotating* lab on the surface of the Earth, but that is only approximate) will display the same phenomena as a *linearly accelerating* lab in flat space-time. That gives the "bending of light". Another is the (approximate) equivalence of a non-accelerating lab in flat space-time to a *non rotating* lab in "free fall" on Earth (again this is only to first order since the field on Earth is not constant). There is no principle equating a rotating lab with a non-rotating lab in any gravitational field. Phenomena in a rotating lab will not even be spatially isotropic (referring to the rotating coordinates).

It is kind of odd that you say I cited MTW, I only brought it up because you cited it as one source for the application of the Equivalence Principle to rotational situations. Since you seem to concede that they nowhere make such a claim, perhaps you should remove that citation. Now you say you do not trust textbooks. If so, then don't cite them, especially when they do not make the claim you are trying to establish.

There is a reason that the SLAC was built as a linear accelerator, rather than a closed circuit like the LHC, and that reason has to do with the difference between linear acceleration and non-linear acceleration. Your claim that rotation is the same as linear acceleration is not accurate. And no Equivalence Principle, including the one you cite above, equates rotating labs or rotating frames to non-rotating labs or non-rotating frames.

Regards,

Tim