Inflaton Field, Cosmological Constants and Spacetime

  • Thread starter rogerl
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  • #1
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I can accept that spacetime has no substantial aspect to it because for General Covariance (Diffeomorphism Invariance) to be true, spacetime "points" can't be real or else General Covariance wont work.

Now question. How does Inflaton Field and the Cosmological Constants for example interact with something that is not substantial. Unless the Inflaton field and Cosmological Constant is also not substantial and just pure geometry too?

I've been confused about this for a couple of days. Hope someone can clarify clearly. Thanks.
 

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  • #2
bcrowell
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I can accept that spacetime has no substantial aspect to it because for General Covariance (Diffeomorphism Invariance) to be true, spacetime "points" can't be real or else General Covariance wont work.
This depends on what you mean by "substantial aspect" and "real."

Now question. How does Inflaton Field and the Cosmological Constants for example interact with something that is not substantial. Unless the Inflaton field and Cosmological Constant is also not substantial and just pure geometry too?
And this also depends on what you mean by "substantial."
 
  • #3
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This depends on what you mean by "substantial aspect" and "real."
Meaning the spacetime points exist in space and time.

And this also depends on what you mean by "substantial."
Meaning is the Inflaton or Cosmological Constant like electric or magnetic field in "essence" or substantial sense? If so, how does it interact with spacetime which is most likely not substantial at all (because spacetime points can't be located in space and time or else General Covariance would fail to work).
 
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bcrowell
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Meaning the spacetime points exist in space and time.
So you're saying spacetime points don't exist in space and time?

Meaning is the Inflaton or Cosmological Constant like electric or magnetic field in "essence" or substantial sense?
This depends on what you mean by "like," "essence," and "substantial."
 
  • #5
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So you're saying spacetime points don't exist in space and time?
Meaning not like an aether where the substance can be manipulated like jello. Spacetime is not like a jello but mathematical points or else diffemorphism invariance won't work.

This depends on what you mean by "like," "essence," and "substantial."
Come on. Inflaton or Dark Energy is akin to electric field. So how can they expand mathematical points?
 
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  • #6
Chalnoth
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Come on. Inflaton or Dark Energy is akin to electric field. So how can they expand mathematical points?
Huh? In terms of their physical properties, they are nothing alike at all. Electromagnetic fields (i.e. photons) cause the expansion of the universe to slow down. Inflation and dark energy do the opposite.
 
  • #7
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Huh? In terms of their physical properties, they are nothing alike at all. Electromagnetic fields (i.e. photons) cause the expansion of the universe to slow down. Inflation and dark energy do the opposite.
So how does dark energy get couple to spacetime. Spacetime is just geometrical relationship we used in our language. It doesn't exist like an aether. So in what sense can dark energy or inflaton expand space when space is not even there??
 
  • #8
Chalnoth
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So how does dark energy get couple to spacetime. Spacetime is just geometrical relationship we used in our language. It doesn't exist like an aether. So in what sense can dark energy or inflaton expand space when space is not even there??
That really depends upon what you mean by "not even there".

But regardless, the geometry of space-time couples to the stress-energy tensor, which contains components such as energy density, pressure, momentum density, and shear. Anything that has any of these things affects the geometry of space-time. And dark energy definitely has energy density and pressure.
 
  • #9
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That really depends upon what you mean by "not even there".

But regardless, the geometry of space-time couples to the stress-energy tensor, which contains components such as energy density, pressure, momentum density, and shear. Anything that has any of these things affects the geometry of space-time. And dark energy definitely has energy density and pressure.
I guess inflaton field also has energy density and pressure (said to be negative). So it affects spacetime by the stress-energy tensor. Spacetime math works most probably because the spacetime manifold subroutine is located on a distant horizon per the holographic principle. This makes better sense and perhaps the solution.
 
  • #10
Chalnoth
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Spacetime math works most probably because the spacetime manifold subroutine is located on a distant horizon per the holographic principle. This makes better sense and perhaps the solution.
I have no idea what you mean by this.
 
  • #11
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I have no idea what you mean by this.

You know Bekenstein Holographic Principle in which all the information in 3D can be modeled on a 2D surface? In String theory AdS/CFT paper for example, all the things in our spacetime can be modeled on a surface of something. This means this universe with spacetime is just projection of some processing occuring in a distant horizon (more like a computer literally calculating using General Relativity equations and how it affects stress-energy tensor in that horizon or processing unit).
 
  • #12
Chalnoth
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You know Bekenstein Holographic Principle in which all the information in 3D can be modeled on a 2D surface? In String theory AdS/CFT paper for example, all the things in our spacetime can be modeled on a surface of something. This means this universe with spacetime is just projection of some processing occuring in a distant horizon (more like a computer literally calculating using General Relativity equations and how it affects stress-energy tensor in that horizon or processing unit).
Well, no, the holographic principle is different from that. Using the Einstein equations to describe how the geometry of space-time interacts with the stress-energy tensor is inherently a four-dimensional calculation (three spatial dimensions, one time dimension). A holographic theory that describes this same behavior but in, say, three dimensions would look quite different. There may be some simple mathematical relationship between, say, the Ricci tensor describing the curvature and the stress-energy tensor describing the matter, but you won't simply use those same exact quantities, nor will the new quantities be related by the Einstein field equations.
 
  • #13
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Well, no, the holographic principle is different from that. Using the Einstein equations to describe how the geometry of space-time interacts with the stress-energy tensor is inherently a four-dimensional calculation (three spatial dimensions, one time dimension). A holographic theory that describes this same behavior but in, say, three dimensions would look quite different. There may be some simple mathematical relationship between, say, the Ricci tensor describing the curvature and the stress-energy tensor describing the matter, but you won't simply use those same exact quantities, nor will the new quantities be related by the Einstein field equations.
Maybe that's why they called it Dualities.
 
  • #14
bcrowell
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Rogerl, you need to define your terms, or there's no way to have a meaningful discussion.

Spacetime math works most probably because the spacetime manifold subroutine is located on a distant horizon per the holographic principle.
Did you really mean "subroutine" here? That doesn't make any sense.
 
  • #15
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Rogerl, you need to define your terms, or there's no way to have a meaningful discussion.



Did you really mean "subroutine" here? That doesn't make any sense.
Oh. I was thinking in terms of programming language where certain tasks are done inside a subroutine.. for example.. spacetime equations being part of a subroutine of a main program that is processed in some distant CPU (or Horizon) as per the Holographic Principle. This is one thing that can make sense theoretical physics.. by assuming that there are actual calculations occuring somewhere.
 

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