There is a good book of C.Rovelli, "Quantum gravity", where this old issue is very well discussed. Namely, do we have treat the metric as characteristic of real space-time manifold or as pure gravity field which fills the big nothing. Let's assume that the second is true, the metric is a gravity field and consider any vacuum solution of Einstein equations. It must be a source for the metric in this case as well, there is no matter, therefore the simplest conclusion is that the vacuum field has it's own energy, at least locally, which we can call as a positive or negative.
So, as it seems, in this interpretation of the metric, it must be some kind of cosmological constant simply by definition of the what the field is. An another consequence is about the energy conservation. If we have a vacuum with some energy, how it was created and where from the energy did come? Again, the simplest explanation is that initially we had two vacuum states with different signs of the energies equal zero overall, which somehow have been splitted and separated.
Of course this is an issue about how the matter is arising, we can also speculate that the matter is first and the geometry is second and that there is no pure vacuum solutions without matter present. Of course, is it seems, the questions about the energy and entropy of the initial state will remain in this case as well.
Dear Sergey,
You are separating gravity and matter. And there is no separation between the two, both are curvatures.
An example, you could establish that a table is matter and that like all mass-energy it has some gravity, but that is not totally true. since at a certain scale that table is composed of particles each with its own gravity and with empty space between them.
And those particles in the smallest possible scale are not anything "solid", they are simply a curvature in space-time just like gravity.
And that same table would behave like a tiny particle on a planetary scale.
What is matter then? the particle? Table? The planet that contains them? The galaxy that contains the planet?
It is much more comfortable to think about curvature and stop distinguishing between mass and gravity
Oh and forget the fields, the fields do not exist, everything is geometry.
And if you want to know how matter is created, you should not only read, if not, follow and check all the equations of:
https://doi.org/10.13140/RG.2.2.19015.96168
and
https://doi.org/10.13140/RG.2.2.19090.27846
Some metrics are difficult to define: for instance 2 points inside of 2 different galaxies, galaxies themselves do not expand, but the space between does
I would like to clarify the question. The point is simple, is here any technical (experimental) and/or conceptual possibility to clarify the metric as geometric characteristic or gravitational field?
No, metrics depend on several states of matter, or on expanding/ not expanding regions
Dear Sergey Bondarenko
I suppose that the metric you are thinking about is the minimal length scale. Nowadays a lot of theorists are convinced that the minimal length scale is identical to the Planck length (ℓP = 1.616255(18)×10−35 m). But about 80 years ago theorists like Werner Heisenberg (and others) proposed that the metric must be ≈ 1 x10-15 m. Their reasoning was simple: the smallest wave length and the smallest “tangible” particles have the size of ≈ 1 x10-15 m. The Planck length shows an enormous empty gap of 1020 with the smallest particles so its proposed existence is fantasy (there are more objections).
The idea of a minimal length scale goes back to the ancient Greek philosophers who proposed the existence of a spatial dynamical unit that cannot be divided any more. The volume of our universe is tessellated by these spatial dynamical units. Their reasoning was simple: if the universe can reproduce all the observable phenomena in time and place the structure of the universe must have this spatial structure. The strange story about the race between a tortoise and Achilles was meant to show that only equal units can describe reality in a convincing way.
In your description of the discussion you use the term “spacetime”. That is a bit problematic in relation to the topic (the existence of a universal metric). Because spacetime – Einstein’s model that describes phenomenological reality – is what it is: a dynamical model. But the model doesn’t fill the whole universe because it only describes the observable phenomena and the mutual relations between these phenomena. In other words, spacetime cannot have a metric, like spontaneous deformable “rulers” have no metric. Thus a metric is part of Euclidean space and is termed discrete Euclidean space. Therefore Einstein’s spacetime is enveloped by Euclidean space.
Be aware that the proposed metric in quantum gravity is actually a proposed metric of Einstein’s spacetime. So don’t be surprised that all the research during more than 3 decades to find the metric of curved spacetime wasn’t successful (see https://www.youtube.com/watch?v=PRyo_ee2r0U).
There is a short article about the foundational problems in physics: https://iai.tv/articles/why-physics-has-made-no-progress-in-50-years-auid-1292. Anyway most theorists are unwilling to discuss the foundational problems.
With kind regards, Sydney
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