# Holographic principle and conservation of energy

1. Mar 4, 2012

### Schreiberdk

Hi PF!

I was wondering, if the holographic principle (from string theory) really can be true. I see some physical flaws in the way it works. Here is why:

Suppose that the second law of thermodynamics is true. It states that for any system, the multiplicity of the system must increase, ergo the entropy of the system must increase. As a result of this, the entropy of the universe must increase.

So how does this relate to conservation of energy? Well, first of all Stephen Hawking and Jacob Beckenstein showed a relation between the entropy of a black hole and it's surface area and therefore to the square of its mass $S \propto M^2$ (due to the Schwarzchild radius' direct proportionality to mass). So we can now state, that if the entropy changes, so does the mass of a black hole.

So now, how does the holographic principle work? Well it generalizes the principle of black hole information to the whole universe (see fx http://arxiv.org/abs/hep-th/0203101). So what does this mean physically?
If we change the entropy of the universe, we change the mass of the universe, and by applying special relativity's mass-energy relation, we also increase the energy of the universe by changing it's entropy.

So by the second law of thermodynamics, the energy content of the universe should increase till the entropy is at a maximum, which it is clearly. This has really been puzzling me, so can anyone give a hint or clarification if the above is right or wrong?

Thank you so much for your time.

2. Mar 8, 2012

Anyone?

3. Mar 8, 2012

### Constantin

Holographic principle is correct.
Holographic theories are an interesting area of research.

Your question in this thread is not clearly stated. That might be why you didn't get an answer.

4. Mar 8, 2012

### Schreiberdk

Well, my question is, why does it seem like energy is not conserved?

Because to me, it looks like, that the energy of the universe must increase in time, because of the increasing entropy of the universe due to the second law of thermodynamics. Therefore energy is not conserved, which contradicts experimental data.

5. Mar 8, 2012

### fzero

The holographic principle states that every volume has a surface that encodes the information. However, for a general volume, $S \leq A/4$, where the equality is reached precisely in the case that the area is the event horizon of a black hole. A black hole is a maximal entropy configuration.

The problem with your reasoning is twofold. First, the universe is not a black hole. The entropy of the universe is not precisely equal to its area. Second, trying to treat the whole universe as a closed system has a list of problems. What are you measuring the energy with respect to? It would make more sense to consider subspaces which are "observable universes," that is bounded by the universes that were once in casual contact. For such patches, entropy can increase without violating any conservation laws. Once the maximal entropy configuration is reached we'd essentially have a black hole.

6. Mar 10, 2012

### czes

Our Observable Universe is not a closed system:
http://arxiv.org/abs/astro-ph/0310808
Therefore Holographic Principle is right, Conservation of Energy is right, second law of Thermodynamic is true and increasing Entropy is true.