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- Thread starter Chronos
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In summary: In particular, we have shown that the entropy of the universe at the apparent horizon is a universal constant that can be set to zero. ….This result strongly supports the holographic principle…..The paper is discussing the entropy of the universe and how it is constant at the apparent horizon. It also supports the holographic principle.

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marcus

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Dearly Missed

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http://inspirehep.net/author/profile/S.Viaggiu.1

and citation record

http://inspirehep.net/search?ln=en&p=author:S.Viaggiu.1&of=hcs2

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Jimster41

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On pg 11, temperature is going down. But heat flow is positive. I assume that is because of the previous statement just after eq16 that the internal energy is conserved at the Hubble radius, so that for temperature to go down but internal energy to stay constant, entropy has to go up. But why is U conserved?

Also, I have a very unsatisfying intuition about just what the horizon of the universe is, "dynamical apparent" or otherwise. I can picture one I think is mine (probably safe to say "ours"): the plank scale foam defining the now, sampling the superposition of all the "nexts". But GR makes me doubt that has any kindof cosmologically relevant meaning.

Do we just just have to hold our breath and say, "that's the one, every observer has it, and they are all equally valid definitions of it", or something similar... Simultaneity, non-locality, entanglement, decoherence... Interpretation thereof?

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Jimster, you might be overthinking this, the paper is based on bound surfaces. You are right the cosmological horizon is observer dependent. But, bear in mind the cosmological horizon for any observer is equidistant at any instant in time. Keep in mind an observer in M51 would be a couple million years younger than us, and perceive a horizon a couple million years younger [and closer] than we do 'here and now'. In that sense it is a bound surface..

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Jimster41

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The bound surface with a specific horizon clarifies it for me. I had got that part of the setup, but only had a vague hope it shelved the relativity problem for the purpose at hand. GR burns intuition so easily.

I'm enamored with the temperature-expansion-information nexus, but the signs are confusing. To which, dumb question, I thought entropy went down with a decrease in temperature, up with increase. So the temperature inside (our side) the horizon goes down, but the entropy goes up? I keep wanting (despite my best efforts) to see the SLOT as information coming in, which fits with temperature going down, and the emergence of structure. I see he refs Prygogine. I associate negentropy and such ideas with Prygogine and Chaisson. However negentropy must also be a positive temperature at some point. It can't be information if it isn't right. Confusing, but it feels pretty much like his "non-local contribution*Egrav* due to the gravitational expansion of the universe". If the aDS/CFT holographic boundary is a big image (a superselection mandala!), one the horizon is non-locally perceiving as expansion continues. Well that seems to fit in my simplistic cartoon. And maybe what this paper is saying is that the image is a reflection. But then he's not talking about aDS but rather just DS universes? Again confusing. Though a Desitter universe has positive curvature, and a reflection might be somehow expected?

He also refs Verlinde and Jacobsen. But I didn't catch any mention of Unruh temperature, which is confusing, since it seems so closely related. But then I ran out of steam after pg 12.

I'm enamored with the temperature-expansion-information nexus, but the signs are confusing. To which, dumb question, I thought entropy went down with a decrease in temperature, up with increase. So the temperature inside (our side) the horizon goes down, but the entropy goes up? I keep wanting (despite my best efforts) to see the SLOT as information coming in, which fits with temperature going down, and the emergence of structure. I see he refs Prygogine. I associate negentropy and such ideas with Prygogine and Chaisson. However negentropy must also be a positive temperature at some point. It can't be information if it isn't right. Confusing, but it feels pretty much like his "non-local contribution

He also refs Verlinde and Jacobsen. But I didn't catch any mention of Unruh temperature, which is confusing, since it seems so closely related. But then I ran out of steam after pg 12.

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Finny

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So far I can't get past the idea that I expect Unruh/Hawking radiation at the apparent [Hubble distance] horizon...have to think about that some more...

Meantime, here is a synopsis of quotes from the referenced paper for those interested...

**Abstract**

"...Recently, we have generalized the Bekenstein-Hawking entropy formula for black holes embedded in expanding Friedmann universes. ….Remarkable, when the expression for U is applied to the apparent horizon of the universe, we found that this internal energy is a constant of motion. Our calculations thus show that the total energy of our spatially flat universe including the gravitational contribution, when calculated at the apparent horizon, is an universal constant that can be set to zero from simple dimensional considerations. This strongly support the holographic principle…..

**Conclusions**

"…we can apply our generalized entropy formula to the apparent horizon (Hubble radius for spatially flat Friedmann solutions) of the universe. This permit us to investigate, in a simple manner, the thermodynamic properties of our universe..

…we have investigated some interesting thermodynamics relations due to the new proposal [15] for a generalized Bekenstein-Hawking entropy suitable for expanding universes, with particular evidence to the spatially flat, the universes where we probably live (at least in in a statistical sense). In this regard, we use a close analogy with ordinary thermodynamics…..

….that the total energy of the universe including the gravitational contribution could be zero, our calculations show that this is certainly the case for spatially flat Friedmann universes, but only at the apparent horizon of the universe. This further supports the idea that the apparent horizon is the right place to study the thermodynamics of the whole universe, i.e. the universe is thermodynamically equivalent to a system with internal energy U (U = 0 for the flat case) enclosed in a sphere of radius given by the apparent horizon…

…Only in the flat case k = 0 (zero curvature energy) we have a perfect balance between the positive energy of matter, i.e. the Misner-Sharp energy, and the gravitational expansion energy, according to the results of [42]. This can have interesting cosmological consequences. In fact, as firstly suggested in [41], a universe with zero total energy can be emerged from quantum fluctuations of a Minkowskian spacetime. From this point of view, it is not a surprise that we live in a spatially flat universe (at least in a statistical sense), since a universe born from a Minkowskian spacetime must have zero total energy…"

Meantime, here is a synopsis of quotes from the referenced paper for those interested...

"...Recently, we have generalized the Bekenstein-Hawking entropy formula for black holes embedded in expanding Friedmann universes. ….Remarkable, when the expression for U is applied to the apparent horizon of the universe, we found that this internal energy is a constant of motion. Our calculations thus show that the total energy of our spatially flat universe including the gravitational contribution, when calculated at the apparent horizon, is an universal constant that can be set to zero from simple dimensional considerations. This strongly support the holographic principle…..

"…we can apply our generalized entropy formula to the apparent horizon (Hubble radius for spatially flat Friedmann solutions) of the universe. This permit us to investigate, in a simple manner, the thermodynamic properties of our universe..

…we have investigated some interesting thermodynamics relations due to the new proposal [15] for a generalized Bekenstein-Hawking entropy suitable for expanding universes, with particular evidence to the spatially flat, the universes where we probably live (at least in in a statistical sense). In this regard, we use a close analogy with ordinary thermodynamics…..

….that the total energy of the universe including the gravitational contribution could be zero, our calculations show that this is certainly the case for spatially flat Friedmann universes, but only at the apparent horizon of the universe. This further supports the idea that the apparent horizon is the right place to study the thermodynamics of the whole universe, i.e. the universe is thermodynamically equivalent to a system with internal energy U (U = 0 for the flat case) enclosed in a sphere of radius given by the apparent horizon…

…Only in the flat case k = 0 (zero curvature energy) we have a perfect balance between the positive energy of matter, i.e. the Misner-Sharp energy, and the gravitational expansion energy, according to the results of [42]. This can have interesting cosmological consequences. In fact, as firstly suggested in [41], a universe with zero total energy can be emerged from quantum fluctuations of a Minkowskian spacetime. From this point of view, it is not a surprise that we live in a spatially flat universe (at least in a statistical sense), since a universe born from a Minkowskian spacetime must have zero total energy…"

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Jimster41

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I would love to know how wrong my cartoon is of the horizon as a foam of plank scale black holes, which I take to be a meaningful dual of a bunch of observers around one big black hole. He refs Susskind, and I saw a lecture by him, where he drew something like a picture of building a big BH from a bunch of tiny ones.

Where is the Hubble horizon relative to me sitting here right now? I want to say it is "down inside", (scale) not just me but everything around me. The arrival of incoming quantum information from my past light cone and my causal interaction with it.

Where is the Hubble horizon relative to me sitting here right now? I want to say it is "down inside", (scale) not just me but everything around me. The arrival of incoming quantum information from my past light cone and my causal interaction with it.

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Finny

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Chronos said:under the premises of the paper it does not escape to infinity, rather it is redirected back into the universe,

Ah, Maybe that's the Unruh radiation with which I am trying to reconcile??

The apparent horizon of the universe in thermodynamics is the boundary at which the expansion of the universe causes the escape velocity to exceed the speed of light. This is a theoretical concept and not a physical boundary that can be observed.

Thermodynamics is the study of energy and its transformations. At the apparent horizon of the universe, thermodynamics helps us understand the energy flow and heat transfer in the expanding universe.

The thermodynamic equilibrium at the apparent horizon of the universe refers to the state in which the energy and temperature are evenly distributed throughout the universe. This equilibrium is constantly changing due to the expansion of the universe.

The second law of thermodynamics states that the total entropy of a closed system will always increase over time. At the apparent horizon of the universe, the expansion of the universe causes an increase in entropy, leading to a decrease in available energy for work.

The apparent horizon of the universe shares similarities with the event horizon of a black hole. Both are boundaries at which the escape velocity exceeds the speed of light. Additionally, the thermodynamics of black holes can be applied to the apparent horizon of the universe, such as the concepts of Hawking radiation and black hole entropy.

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