Does the Holographic Principle Suggest a Schwartzchild Radius for the Universe?

[johne1618]

I understand that the holographic principle applies to black holes and states that they are objects of maximum information/entropy. It states further that this information/entropy is bounded by the black hole's area rather than its volume.

Apparently the holographic principle might apply to the Universe as a whole. Maybe the Universe is a maximum information/entropy object.

Would this imply that, like black holes, the Universe obeys the equation:

G M / R = c^2 / 2

where M and R is the mass and radius of the Universe?

In other words does the holographic principle imply that the Universe has a Schwartzchild radius?

 

[bcrowell]

In other words does the holographic principle imply that the Universe has a Schwartzchild radius?

No. You might want to take a look at this entry in the cosmology FAQ: "In the early universe, matter was gathered together at very high density, so why wasn't it a black hole?" It's intended for a different context, but I think some of the points in it are still relevant: the universe doesn't have a black-hole event horizon (which is what defines the Schwarzschild radius of a black hole), and it doesn't have a center (so that there is no preferred point from which to measure a radius).

Maybe the Universe is a maximum information/entropy object.

I don't think so. The following may be helpful.

FAQ: Was the early universe in a disordered state?

No. The second law of thermodynamics says that entropy can only increase, so if the early universe had been in a state of maximum entropy, then the cosmos would have experienced its heat death immediately after being born. This contradicts the observation that the present universe contains burning stars, heat engines, and life. These observations imply that the early universe was in a very low-entropy state, which shows that its initial conditions were extremely finely tuned. The reasons for this fine-tuning are not explained by general relativity or the standard model. I'm not an expert on inflation, but apparently adding inflation to the model does not cure this fine-tuning problem.[Penrose 2005]

These ideas are strongly counterintuitive to most people, since we picture the early universe as an undifferentiated soup of hot gas, very much like what we might imagine a heat-dead universe to be like. In what way is the early universe *not* equilibrated?

We observe that the cosmic microwave background radiation's spectrum is a blackbody curve, which would normally be interpreted as evidence of thermal equilibrium. However, this observation only really tells us that the *matter* degrees of freedom were in thermal equilibrium. The gravitational degrees of freedom were not. In standard cosmological models, which are constructed to be as simple as possible, there are no gravitational waves. Although the real universe presumably does have gravitational waves in it, they are apparently very weak. In a maximum-entropy universe, the gravitational modes would be equilibrated with the matter degrees of freedom, and they would be very strong, as in Misner's mixmaster universe.[Misner 1969]

Even in Newtonian mechanics, gravitating systems violate most people's intuition about entropy. If we psssssht a bunch of helium atoms into a box through an inlet valve, they will quickly reach a maximum-entropy state in which their density is nearly constant everywhere. But in an imaginary Newtonian "box" full of gravitating particles, the maximum-entropy state is one in which the particles have all glommed onto each other in a single blob. This is because of the attractive nature of the gravitational force.

Charles W. Misner, "Mixmaster Universe", Physical Review Letters 22(1969)1071. http://astrophysics.fic.uni.lodz.pl/100yrs/pdf/07/036.pdf

Roger Penrose, 2005 talk at the Isaac Newton Institute, http://www.Newton.ac.uk/webseminars/pg+ws/2005/gmr/gmrw04/1107/penrose/

 

[Imax]

Another way of looking at it is that the Big Bang (BB) is a bit of a misnomer. Don’t look at the BB as an explosion within an infinite space-time metric, something you could get from exploding dynamite. Distribution of matter defines space-time. Just before the BB, matter was highly concentrated, and space-time was concentrated around that matter. When the BB happened, space-time itself began to grow, and continues to grow today. Technically, the Universe doesn’t have a Schwartzchild radius, but there are limits on observables.