[brueggert]

Originally Posted by TinyTree I'd like to see the reference to Hawking calculating Entropy of a black hole, and what the partition function he is using is defined to be.

http://en.wikipedia.org/wiki/Black_hole_entropy
This is a link to black hole entropy, of course. Hawking used thermodynamical arguments to arrive at his formula. The counting of the microstates, or partition funcion (statistical mechanics), is touched upon briefly later in the entry, with links provided (entropy of a supersymmetric black hole in string theory), by A. Strominger and C. Vafa. I am trying to learn about D-brane mechanics and must admit that I do not fully understand this yet...

[TinyTree]

Originally Posted by AntonioLao A simple concept does not need complicated equation for its description.

Sure, unless there are ill defined terms, which seem to be rampant in the domain of considering randomness, entropy, and energy. If we define terms using equations, then we can not get confused as to what the equations are, only how they are interpreted.

Claude Shannon defined a information theoretic term of "Entropy" which has been confused with "Entropy" of physical systems as defined by Boltzmann, even though the two have nothing to do with each other except that they sum probabilities.

Originally Posted by AntonioLao What is really going on with the energy that is everywhere? Its density? Entropy is just describing the variability of this energy density.

I will agree with this- entropy describes the variability of the energy density. It has nothing to do with randomness, or the probability of the system EXCEPT as considering the probability of the system among a number of systems which are within the partition.

Originally Posted by AntonioLao Energy can only become useful when a potential difference exists like potable water at the top of the hill supplying downhill communities.

I agree. Is this the part where I fall? I hope so I look forwards to hearing what it sounds like when I land.

I look forward to any further disagreements you can raise, because then I can get you on the same page I am and then you can fall off of wherever you are to land on a consistent interpretation along with me

[TinyTree]

Originally Posted by brueggert http://en.wikipedia.org/wiki/Black_hole_entropy This is a link to black hole entropy, of course. Hawking used thermodynamical arguments to arrive at his formula. The counting of the microstates, or partition funcion (statistical mechanics), is touched upon briefly later in the entry, with links provided (entropy of a supersymmetric black hole in string theory), by A. Strominger and C. Vafa. I am trying to learn about D-brane mechanics and must admit that I do not fully understand this yet...

Thanks for the link, I will have to investigate it more fully. Right off the top though, there is the claim "in order not to violate the second law of thermodynamics".

I will claim that reality is what it is- and backwards deriving the entropy of the black hole in order to preserve what we measure here far away from a black hole seems "realistic" but also "a stretch".

Similarly when we see "information can not travel faster than light" I agree with this statement- but if they figure a way to do this within physical law I am not going to cry about it. Reality is what it is, and making up mathematics to conform to our expectations of what it should be is moving towards belief and away from reality.

But thanks for the link I will try to check it out later.

[brueggert]

Originally Posted by TinyTree Thanks for the link, I will have to investigate it more fully. Right off the top though, there is the claim "in order not to violate the second law of thermodynamics". I will claim that reality is what it is- and backwards deriving the entropy of the black hole in order to preserve what we measure here far away from a black hole seems "realistic" but also "a stretch". .

This is not exactly the case- they did not derive the entropy equation to meet what we see here (as in measurable quantities). Rather, they said that if the second law of thermodynamics is not to be violated.... Hawking radiation... formula for entropy of a black hole. It continues to hold. A subsequent statistical mechanics based computation using D-brane mechanics aslo provides this result. As far as I'm concerned, if the formula was seen by Hawking in his tea leaves, and then is shown to be correct time and time again yet never shown to be incorrect, then it is good. This theory gives predictions which can be tested, and until they are shown to be incorrect I think that it is reality, no matter how one might perceive that reality should be.

[AntonioLao]

Originally Posted by TinyTree As for the energy spectrum becoming continuous- actually as I understand it light is made of photons that occur at specific spectral intensities. How do you understand it differently?

Photons of the same blackbody distribution, for example, the cosmic background radiation photons of ~3 kelvins.

Originally Posted by TinyTree I look forward to any further disagreements you can raise, because then I can get you on the same page I am and then you can fall off of wherever you are to land on a consistent interpretation along with me

It's Ok by me, as long as it's falling into a bottomless pit (I don't mean the other connotation of falling into hell but more like free falling without the feeling of gravity).

[TinyTree]

Originally Posted by AntonioLao It's Ok by me, as long as it's falling into a bottomless pit (I don't mean the other connotation of falling into hell but more like free falling without the feeling of gravity).

Antonio, I am confident you can see my point of view- and either point out where I am wrong, or else see where I am right.

Here is a decent explanation, which you may have read but I encourage you to peruse it again:

http://www.toequest.com/forum/showthread.php?t=1020

Now here is an explanation of the derivation of the partition function:

http://en.wikipedia.org/wiki/Derivation_of_the_partition_function

Read these two things back to back if you please.

Let me highlight a few things from the derivation of the partition function:

In order to proceed we assume the ergodic hypothesis. This means that we assume that all states corresponding to a given energy are equally probable. (If there are other conserved quantities like particle number, this assumption becomes all states corresponding to a given energy and particle number/charge, and a similar derivation would lead to chemical potentials, electric potentials and the like) For example, vibrational states of a given energy are just as likely to be populated as rotational or electronic states of the same energy.

In reality, the state vector of the universe actually is not equally probable across the spectrum. However, this is a useful mathematical tool for a first approximation to derive statistical mechanics. Now quantum statistical mechanics allows for probabilities of microstates to be different than unity and the approximation of equally probable states is close enough that it will give us measurable results that conform to statistical laws.. but let us proceed..

Of these two configurations, the second is much more likely, since any of the N molecules could be in the excited state resulting in a total of N possible arrangements of molecules

Note- in the derivation they say "since any of the N molecules could be in the excited state"- all of these microstates are linked into one partition. The probability of the system is given as the sum across these individual probabilities. This is not the same thing as ascertaining the exact probability of a specific microstate.

Why does this matter?

Because it determines our interpretation of reality! And as you have been pointing out- entropy is related to probability. It is related in the nature of how partitions are divided across microstates. Now I am claiming to you that individual microstates have their own unique, specific, and different probabilities from each other which is different than the "grouped probability" of statistical mechanics.

It is this particular probability which is of interest, and which is "a theory of everything". It is of interest because it describes both on a microscopic and macroscopic level how the universe functions- it functions as a propagation of a wave form from the past into the future- similar to a wave passing through water or air, but where the medium itself is modifying the waveform.

[AntonioLao]

Originally Posted by TinyTree I encourage you to peruse it again:

Still perusing your idea but I have a question. What is the probability that energy will always transfer along a 1 dimensional string with various modes of vibration?