Where Are the Boundaries of General Relativity? by Daniele Malafarina

Dan,

I offer some assumptions open to question: Physics treats time as a measure of duration from one event to the next, but that only re-enforces the perception of time as a series of event, not a dynamic process creating and dissolving such events. To wit, does the earth travel the fourth dimension from yesterday to tomorrow, or does tomorrow become yesterday because the earth rotates? Duration only exists within the present, as what is happening between events, not external to what is present. This goes to the heart of the debate of whether math simply models physics, or it the bedrock on which it is based. Whether information creates the illusion of action, or action creates transitory information.

As for the nails holding that sheet, as the ball deforms it; What if it simply causes the sheet to expand in the areas not weighted down? Much as pushing in the surface of a ballon causes other areas to expand. This would mean that while space in gravity fields contracts, the resulting expansion in the intergalactic voids adds up to an overall flat space. Much like the cosmological constant Einstein proposed to balance gravity in the first place. According to tests by COBE and WMAP, overall space is flat, as gravity and cosmic expansion balance. This suggests there is some form of convective cycle between contracting mass and expanding radiation.

I don't think gravity is so much a property of mass, but an effect of energy condensing into mass and creating a vacuum, much as mass releasing its energy creates pressure. There is no observed dark matter, but there is observed excess of cosmic rays on the perimeters of galaxies. Going from this radiation condensing into interstellar gases, to light being absorbed by matter, all the way down to the cores of stars to where heavy metals condense out of lighter forms of mass, would create a form of fairly even vacuum between all forms of energy and mass, not just that which has apparent weight.

Cosmic redshift would be far easier to explain without the insistence light travels as a point particle. While photons might be measured as points, when they are absorbed by matter, why would they maintain this point-like form when they are just energy? Wouldn't light act more like a gas and expand to fill available space? To assume otherwise would require photons to have gravity, or some force holding them together, when it seems the most elemental feature of light is its tendency to expand. Remember that we only observe light from distant galaxies which has traveled the least dense paths across the universe.

Dan,

Very insightful essay (which I will reread several more times as you cover some topics that I have not yet explored)!

If you would like a mathematical "hook" to hang "Therefore, if we want to talk about the limits of GR, it seems useful to ask once more on what ground can we challenge such a successful theory." and "There are plenty of such pillars that lie unquestioned at the foundations of every theory" you can find my essay here.

Regards,

Jeff Baugher

Dan,

I read your essay through, and will reread it with more focus. My first comment is with your statement about dark energy or cosmic acceleration. Dark energy is the quantum vacuum. The cosmological constant Λ = 8πGρ, where I have set c = 1, which enters into the FLRW equation for spacetime cosmology

(a'/a)^2 = 8πGρ/3, a' = da/dt

where k = 0, or the space is flat. (a'/a)^2 = H, the Hubble parameter, and this is related to the cosmological constant by H = Λ/3. The FLRW equation may be written as

a' = sqrt{8πGρ/3}a,

which has the solution a = a_0 exp(sqrt{8πGρ/3} t). This solution is then one where the space exponentially expands. This is what is observed in the observational universe. In a more complete analysis of the FLRW equation the vacuum energy density is related to the pressure by p = -ρ. This negative pressure is one way of looking at this exponential expansion of the universe.

Dark energy is just a source for the de Sitter spacetime. General relativity works perfectly well. The unknown with dark energy is that we do not know have the vacuum is configured this way. This leads to the 123 order of magnitude issue.

Chers LC

Dear Daniele,

Your Essay is interesting for me. On the question: Where are the boundaries of General Relativity?, I offer other theory, Covariant theory of gravitation . This theory is based with the help of Lagrangian and Hamiltonian. See: Fedosin S.G. The Principle of Least Action in Covariant Theory of Gravitation. Hadronic Journal, February 2012, Vol. 35, No. 1, P. 35 - 70; Fedosin S.G. The Hamiltonian in covariant theory of gravitation. vixra.org, 22 May 2012.

In covariant theory of gravitation some specific problems of general relativity disappear. See more about it in my Essay. For example instead of one mass there is three different mass of body one of them is mass at infinity in absence of proper field energy.

Sergey Fedosin Essay

Dear Michele,

I like your thoughtful essay, though I must admit I was misled by the title. I thought your paper was about what the boundaries of the domain of validity of GR were (which is a central theme of my paper), but in fact, you were referring to the boundary conditions that allow us to understand GR more deeply. I would have liked to read more about your thoughts about the possible candidates you consider. The analogy with the tension in the rubber sheet was interesting, I wonder if anyone has ever pointed that out before.

All the best,

Armin

Hello Daniele,

I enjoyed your essay, thought it was very good. I like the way you are neither prejudiced for GR nor against it, and particularly how you look for clues about the way forward. Would have liked to see a little more wide ranging conceptual thinking in that regard, but your work is very good, and has a detachment I like. It's refreshing to see someone looking for strengths and weaknesses in GR but without an axe to grind about it.

I'd appreciate any thoughts you might have on my essay, there are some overlaps with yours. I'm looking at the clues we have about time, while assuming there are missing pieces of the puzzle, and trying to see what can be deduced about these missing pieces. It seems to me that people often work as if we had all the pieces in front of us, and try to draw conclusions by looking at them that way, when there's a need to allow for the gaps in the picture.

Anyway, best wishes, Jonathan

Daniele,

I was very pleased to read your essay. I agree a "clear and dfinite understanding" of "spatially closed solutions" is needed, an a possible one consistent with SR emerges via physical boundary conditions of matter distribution and mechanism in my essay. Not quite as envisaged, but as found once we know what to look for.

As you describe, this is indeed a 'thin shell' model of matter separating two spacetime manifolds, but with 'fluid (magnetohydro-) dynamic coupling' and simple Raman scattering at local c.

See a cross section through a shell measured by the Cluster (4 probe) mission but not previously 'consistently' interpreted in Richard Kingsly-Nixey's essay Fig 2.

Once background frames are allowed gravity can then resolve analogously with a 'density' model where pressure has been reduced locally by concentration into condensed matter 'particles', probably by perturbation into 'motion' (i.e. toroidal twin spin/vortices). To find the morphology; In your fig 1, extend the semi circles top and bottom of the vortices to full circles, which forms a toroid of which the 'manifolds' are then the central space 'in' the donut. The shell is the surface of the donut, equivalent to (Earth's etc) magnetospheres and bow shocks. If in motion it will also have a 'magnetotail'.

I do hope you'll read my essay constructing the underlying physical ontological basis, and give me your views. It still requires complete mathematical formulation.

Thanks and Best wishes

Peter

After studying about 250 essays in this contest, I realize now, how can I assess the level of each submitted work. Accordingly, I rated some essays, including yours.

Cood luck.

Sergey Fedosin

Dear Daniele,

This is a splendidly written essay and rates very highly in my opinion. Though I have a deep love for GR (it's what kindled my first interest in theoretical physics as a child), nevertheless the subject of its limitations and possible extensions must be boldly faced. I only hope that whatever replaces it will retain some of the conceptual simplicity and deep unifying principles of GR, however awful the mathematics! A few other thoughts:

1. First, I am grateful to you for alerting me to the general importance of boundary information in this context. I was not aware of the properties of matching Schwarzchild solutions across a boundary.

2. I wholeheartedly agree with your quote "Nevertheless, General Relativity has also some internal unresolved philosophical 'problems' and these are the issues we want to concentrate on here, arguing that the third category above [the desire to realize some aesthetic or philosophical principles] can provide some important insights into how a new theory of gravity should look."

3. Perhaps the most striking point, to me, at least is the following on page 4: "What happens is that, if we do not consider the improved variational principle including the boundary terms, as the one considered above, we end up with a matching with two arbitrary Schwarzschild solutions that are described by two different mass parameters which are chosen arbitrarily." This I did not know, and it seems to make the importance of your considerations unavoidable.

4. By the way, my own attempts at fundamental physics involve nonmanifold structures, but are based on principles that find their clearest present form in GR (background independence, causality, covariance). If you're interested, you might take a look at my essay here. It's admittedly speculative, but hopefully interesting.

Thanks for the great read! Take care,

Ben Dribus

If you do not understand why your rating dropped down. As I found ratings in the contest are calculated in the next way. Suppose your rating is [math]R_1 [/math] and [math]N_1 [/math] was the quantity of people which gave you ratings. Then you have [math]S_1=R_1 N_1 [/math] of points. After it anyone give you [math]dS [/math] of points so you have [math]S_2=S_1+ dS [/math] of points and [math]N_2=N_1+1 [/math] is the common quantity of the people which gave you ratings. At the same time you will have [math]S_2=R_2 N_2 [/math] of points. From here, if you want to be R2 > R1 there must be: [math]S_2/ N_2>S_1/ N_1 [/math] or [math] (S_1+ dS) / (N_1+1) >S_1/ N_1 [/math] or [math] dS >S_1/ N_1 =R_1[/math] In other words if you want to increase rating of anyone you must give him more points [math]dS [/math] then the participant`s rating [math]R_1 [/math] was at the moment you rated him. From here it is seen that in the contest are special rules for ratings. And from here there are misunderstanding of some participants what is happened with their ratings. Moreover since community ratings are hided some participants do not sure how increase ratings of others and gives them maximum 10 points. But in the case the scale from 1 to 10 of points do not work, and some essays are overestimated and some essays are drop down. In my opinion it is a bad problem with this Contest rating process. I hope the FQXI community will change the rating process.

Sergey Fedosin

Ciao Daniele,

according to my published results the freedom in plying with boundary terms in relativity (special and general) is the missing link for a unified description with quantum mechanics. BCs represents a quantization condition for elementary particles similarly to the semi-classical quantization of a particle in a box. The result is a generalization of the wave particle duality. Note that this has allowed my to derive gauge interactions form a generalization to the boundary of the equivalence principle.

I have just given you an high rate.

Best regards,

Donatello