Holographic principle responsible for life?

[Mike2]

The holographic principle claims that physics on the surface of a sphere determines the physics inside the volume enclosed by that sphere. And in particular, the entropy calculated from the surface of the sphere limits the entropy inside the sphere. If so, then entropy per unit volume would go as the surface area of a sphere divided by the volume of the sphere, or ~r^2/r^3 = 1/r. So if the entropy per volume must diminish when considering larger and larger volumes, then does this imply that with a large enough universe, there must exist improbable complexities such as life? Does the expansion of the universe force a lower entropy state/volume on the average?

 

[Mike2]

The holographic principle claims that physics on the surface of a sphere determines the physics inside the volume enclosed by that sphere. And in particular, the entropy calculated from the surface of the sphere limits the entropy inside the sphere. If so, then entropy per unit volume would go as the surface area of a sphere divided by the volume of the sphere, or ~r^2/r^3 = 1/r. So if the entropy per volume must diminish when considering larger and larger volumes, then does this imply that with a large enough universe, there must exist improbable complexities such as life? Does the expansion of the universe force a lower entropy state/volume on the average?

If the result of considering larger volumes means that the entropy/volume must be less, could this be responsible for the reduction of quantum states and the collapse of wave functions from the a superposition of many possibilities when considering small regions to one choice of eigenstate measured by larger systems? Throw in some thoughts if you have them.

 

[Mike2]

If the result of considering larger volumes means that the entropy/volume must be less, could this be responsible for the reduction of quantum states and the collapse of wave functions from the a superposition of many possibilities when considering small regions to one choice of eigenstate measured by larger systems? Throw in some thoughts if you have them.

Now we suppose that spacetime is quantized so that there are bits of spacetime arranged randomly next to each other. The surface area of each bit of spacetime restricts the entropy inside to that required to describe the properties of that bit. But when we consider that larger regions of space have a smaller entropy per volume, then I suppose that these bits of random spacetime may have to organize themselves in such a way as to reduce the entropy per volume in which they are contained. These re-organizations of spacetime bits would then be the particles of nature. They would not have to be permanent particles, but there might be different kinds of particles popping into and out of existence as long as the same entropy per volume was maintained. This would resemble the virtual particles of the zero point energy. Perhaps there is even a calculation that can be made to show that the zero point energy maintains a constant entropy/volume.

 

[Symbreak]

Curious.

The ZPE does indeed maintain a constant entropy relative to the Universes expansion. (see work by Rueda and Haish) but whether this could be linked with the holographic principle is questionable.
If entropy can be measured by the area of spacetime and the ZPF has an energy decreasing with the area, a definative entropy/energy constant is established.

You may also want to look at Shu Yuan Chu's derivation of time-symmetric version of quantum gravity

 

[emil2k]

I found a very good explanation of the holographic principle a couple of days ago, I know it does not answer the question in the thread but it does very well explain the holographic principle...

URL: http://unano.org/2007/01/27/holographic-principle-explained/

Robert

 

[Mike2]

I found a very good explanation of the holographic principle a couple of days ago, I know it does not answer the question in the thread but it does very well explain the holographic principle...

URL: http://unano.org/2007/01/27/holographic-principle-explained/

Robert

Thanks for the interest. I'm beginning to think I know why the holographic principle might work. Though I haven't worked out the details yet. I'm thinking that connections between the parts of reality within a region (sphere) determine the entropy (or information?) within that region.

A given region contains a conjunction of its various parts (planck units of spacetime perhaps), and a conjunction implies that each part implies every other part. The physical interpretation of this might be entanglement between the various parts. But as one considers larger regions, then there are more connections (entanglements?) between the parts. I'm thinking that the increase in connections within larger volumes works to lower the entropy per unit volume in that region so that it appears that the entropy of a region is determined by its surface area and not its volume.

Now if one part implied a second with absolute certainty, there would be no information or entropy involved with increased regions of absolutely connected parts. So it seems there must be some probability involved when one part implies the next. This might works as a distance function since nearer things generally have more of an effect (with certainty) then farther things. So I'm taking a look at point set topology again from this perspective.

 

[hellfire]

I'm thinking that connections between the parts of reality within a region (sphere) determine the entropy (or information?) within that region.

A similar idea has been already formulated by Mark Srednicki is his paper Entropy and Area, where he proved that for a quantum field, the von Neumann entropy related to the reduced density matrix within a sphere scales with the area of the sphere but not with its volume.