# Equivalence of Matter Energy and Space-Time?

## Main Question or Discussion Point

This is probably a stupid question, but is there an equivalence between matter, energy and space time? Like for instance if you had a ball of 1 kilogram, could you convert it into volumetric space and have everything around it be further away? When two or more objects are going further away from one another, how do you know whether they are being repelled by one another in mutual Newtonian fashion and not that the space between them is like a growing entity?

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That's an interesting question actually. Unfortunately I have no idea, but I would like to hear the opinion of people with more knowledge about this.
Is it not Dark Energy (silly name) that is said to be cause behind the expansion of space? You'd might think any energy could contribute to this, for example the energy stored in the 1-kilogram ball.

Dale
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In geometrized units mass has the same units as distance. I am not sure if that is what you are looking for.
how do you know whether they are being repelled by one another in mutual Newtonian fashion and not that the space between them is like a growing entity?
What do you mean by "repelled in mutual Newtonian fashion"?

PeterDonis
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Is it not Dark Energy (silly name) that is said to be cause behind the expansion of space?
No. It is only said to be the cause behind the acceleration of the expansion of space. Without dark energy, the expansion would be decelerating, not accelerating, because of the mutual gravity of the ordinary matter and energy in the universe.

mfb
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In geometrized units mass has the same units as distance. I am not sure if that is what you are looking for.
Do you mean inverse distance? With $\hbar = c = 1$, mass, energy, inverse time and inverse distance have the same unit.

Khashishi
There are certainly ways of associating a certain volume with a certain energy, but I doubt that any of these has too much significance. There are several choices to choose from. You can associate mass with length using the Schwarzschild radius.
You can associate energy with the volume that contains that amount of dark energy, since dark energy is thought to be proportional to volume.
You can use geometrized units as above (which might give the same result as the schwarzschild radius).

Dale
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Do you mean inverse distance? With $\hbar = c = 1$, mass, energy, inverse time and inverse distance have the same unit.
The geometrized units start with G=c=1. With that the mass is a distance equal to 1/2 the Schwarzschild radius of a black hole of that mass.

http://en.wikipedia.org/wiki/Geometrized_unit_system

mfb
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Ah, okay. I was thinking of particle physics, but that has a different convention.

In geometrized units mass has the same units as distance. I am not sure if that is what you are looking for. What do you mean by "repelled in mutual Newtonian fashion"?
What I mean is the interpretation that objects are moving away from each other due to a force, instead of seeing the distance between them as an entity that is growing. I suppose it doesn't matter how you interpret it, but if the distinction could be made how would you know a motion is the result of a force and not of the change in volumetric space time. I am risking violating the crackpottery rule, but what if you saw distance or better yet volumetric space as an entity onto itself capable of flux and somehow equivocated to both matter and energy. My goal is not to say that is the way it is, but to suppose it as a possibility. Maybe energy can convert into space-time and vice versa. Is there some reason this can't be the case?

mfb
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but if the distinction could be made how would you know a motion is the result of a force and not of the change in volumetric space time.
Simple: Other objects nearby are not moving away from each other. Also, you cannot just "insert new space[time]" somewhere, in general it would not fit.

PeterDonis
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Maybe energy can convert into space-time and vice versa.
Spacetime doesn't work this way in classical GR. You don't have some spacetime, and then wait a while and have some more. Spacetime is the entire 4-D geometry describing the entire history of the universe; "how much" of it there is does not change, because any "change" that happens in the history of the universe is just a geometric feature of the 4-D geometry, which doesn't "change", it just is.

What energy (actually stress-energy, which includes mass, energy, momentum, pressure, and other stresses) does is determine the curvature of the spacetime geometry. But it doesn't do this by "adding spacetime" in some places; it just determines the curvature of the 4-D geometry, which, again, doesn't change, it just is.

There are various attempts to try to model spacetime as an emergent phenomenon with something simpler underlying it (the various candidates for a theory of quantum gravity). But those models go beyond classical GR (and you'll find plenty of discussion of them in the sub-forums of PF that are more focused on quantum gravity).

No, mass and energy is something and space and time is something else

Dale
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With that, I think this thread is done.