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### Author Topic: Is the entropy of a singularity system equal to its volume ?  (Read 1842 times)

#### Thebox

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##### Is the entropy of a singularity system equal to its volume ?
« on: 21/06/2016 12:21:17 »
Does S=V?

It seems to me that the entropy (S) of a system is equal to its volume.  A volume can surely only hold as much energy (hf)  as the amount of energy ''space'' available of a system.

Like a glass overflows if we keep pouring the water into it, the volume of the glass ''empty'' space being equal to the amount of ''something'' that fill's it. Obviously at this stage I have not objectively looked at densities of ''matter'' or have any related thoughts to this.

My question is related to an equilibrium state, I have not considered two or more photons occupying the same ''space'' at the same ''time'' in an ''enclosure'' .

''singularity
sɪŋgjʊˈlarɪti/Submit
noun
1.
the state, fact, quality, or condition of being singular.''

#### Bill S

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##### Re: Is the entropy of a singularity system equal to its volume ?
« Reply #1 on: 23/06/2016 22:23:38 »
A lot must depend on what you mean by a "singularity system".  It is not unanimously accepted in scientific circles that a singularity is a physical reality.

If you are referring to a black hole, my understanding is that the entropy is proportional to the surface area of the event horizon.

#### jeffreyH

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##### Re: Is the entropy of a singularity system equal to its volume ?
« Reply #2 on: 23/06/2016 22:34:35 »
Thebox you are in real danger of approaching scientific sense. Sometimes I really do get what you mean when others don't. I don't know why that should be. Your aim should be to make it understandable to everyone. You never know what you might accomplish.

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#### Bill S

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##### Re: Is the entropy of a singularity system equal to its volume ?
« Reply #3 on: 23/06/2016 22:58:43 »
Have a care, Jeffrey, or people might suspect "folie a deux".

Seriously, I think The Box often has reasonable scientific thoughts, but has a mode of expression that leaves most of us thinking, "What?".

#### Thebox

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##### Re: Is the entropy of a singularity system equal to its volume ?
« Reply #4 on: 24/06/2016 10:13:50 »
A lot must depend on what you mean by a "singularity system".  It is not unanimously accepted in scientific circles that a singularity is a physical reality.

If you are referring to a black hole, my understanding is that the entropy is proportional to the surface area of the event horizon.

I did put the definition Bill, singularity=single, not plural, one of,

A single particle for example.

#### Thebox

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##### Re: Is the entropy of a singularity system equal to its volume ?
« Reply #5 on: 24/06/2016 10:15:42 »
Thebox you are in real danger of approaching scientific sense. Sometimes I really do get what you mean when others don't. I don't know why that should be. Your aim should be to make it understandable to everyone. You never know what you might accomplish.

I keep trying Jeff, thanks for understanding me sometimes.

#### evan_au

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##### Re: Is the entropy of a singularity system equal to its volume ?
« Reply #6 on: 24/06/2016 12:38:17 »
Quote from: BillS
If you are referring to a black hole, my understanding is that the entropy is proportional to the surface area of the event horizon.
As Bill said, the entropy of a black hole is proportional to its area, not its volume.
And some cosmologists believe that this applies to the whole universe - the entropy is proportional to its area.

https://en.wikipedia.org/wiki/Black_hole_thermodynamics#Black_hole

One interesting detail in that article is that the entropy of a black hole was first accurately calculated using string theory. This is presumably a result that could not be obtained confidently from general relativity.

#### jeffreyH

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##### Re: Is the entropy of a singularity system equal to its volume ?
« Reply #7 on: 24/06/2016 14:12:17 »
Quote from: BillS
If you are referring to a black hole, my understanding is that the entropy is proportional to the surface area of the event horizon.
As Bill said, the entropy of a black hole is proportional to its area, not its volume.
And some cosmologists believe that this applies to the whole universe - the entropy is proportional to its area.

https://en.wikipedia.org/wiki/Black_hole_thermodynamics#Black_hole

One interesting detail in that article is that the entropy of a black hole was first accurately calculated using string theory. This is presumably a result that could not be obtained confidently from general relativity.

That makes string theory marginally more interesting.

#### Thebox

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##### Re: Is the entropy of a singularity system equal to its volume ?
« Reply #8 on: 24/06/2016 15:40:17 »

As Bill said, the entropy of a black hole is proportional to its area, not its volume.

Huh?  I thought entropy was basically the ways a system can change and the randomness of change of that system ?

I am quite sure that any point of space or ''matter'' can change in an instant in it's ''entropy'', so I do not understand why you are are mentioning area which would only be XY and not XYZ and volume.

Any ''o'' point of a volume can change anytime by thermodynamics if more than 1hf occupies that space?

And I would of thought the entropy of a black hole is equal to its volume density of ''something''?

#### jeffreyH

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##### Re: Is the entropy of a singularity system equal to its volume ?
« Reply #9 on: 24/06/2016 18:29:09 »
It has been found that if you were to consider a volume of space say bounded within an imaginary sphere then the surface area of that sphere would represent the maximum entropy that can be contained within the volume of that sphere. This is the relation between boundary area and interior volume.

#### jeffreyH

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##### Re: Is the entropy of a singularity system equal to its volume ?
« Reply #10 on: 24/06/2016 18:37:27 »
Since volume is V = (4/3)*pi*r^3 and area is A = 4*pi*r^2 then entropy S could be stated S = V/A. This is then purely dependent upon the scale set via r.

#### Alan McDougall

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##### Re: Is the entropy of a singularity system equal to its volume ?
« Reply #11 on: 24/06/2016 18:56:22 »
Since volume is V = (4/3)*pi*r^3 and area is A = 4*pi*r^2 then entropy S could be stated S = V/A. This is then purely dependent upon the scale set via r.

At the zero entropic state of the Big Bang singularly I am baffled as to why volume had anything to do with it,  because volume did not exist.  For entropy to exist or begin to happen there must be a difference between a higher energy state and a "heat sink"

An infinite volume at absolute zero or ultimate heat sink could have resulted in the universe emerging out of the Big Bang singularity and instantly dissipating itself into nothingness .This scenario would have meant that the universe might have existed for a brief moment, reached equilibrium with all its useful dissipated into the nothingness of the infinite void. Thus creation would never had happened. Alan Guth's theory of inflation saved the day?

#### jeffreyH

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##### Re: Is the entropy of a singularity system equal to its volume ?
« Reply #12 on: 24/06/2016 19:39:16 »
You cannot make any assumptions about volumes before the big bang. Neither can there be certainty about a value for density. Neither can be equated with being infinite with any degree of certainty. If infinite is even meaningful in this or any other sense. I believe not.

#### Thebox

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##### Re: Is the entropy of a singularity system equal to its volume ?
« Reply #13 on: 24/06/2016 19:58:57 »
A = 4*pi*r^2

It has been found that if you were to consider a volume of space say bounded within an imaginary sphere then the surface area of that sphere would represent the maximum entropy that can be contained within the volume of that sphere. This is the relation between boundary area and interior volume.

Firstly to consider a volume of space, I would ask myself how big of a volume of space?  Then to consider this space to be bounded by an imaginary sphere, I ask myself why the imaginary part?  If it is imaginary it hardly seems relevant!  However I could ''imagine'' an ''imaginary'' sphere that has physicality , we could not visually ''see'' this sphere because it is ''invisible'' to the eye like light is in the subjective ''gin-clear'' space  we observe, so I could certainly imagine an ''invisible'' sphere that was made of ''invisible'' matter.
However regardless of the surfaces contained entropy volume, I imagine the sphere shares its energy with the outer volume of space I imagine the sphere to be in.
But ok, I ''see'' why a spheres surface is mentioned.

#### puppypower

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##### Re: Is the entropy of a singularity system equal to its volume ?
« Reply #14 on: 25/06/2016 00:36:43 »
In chemistry, entropy is considered a state variable meaning it has a specific value for a given state of matter. For example, the entropy of water at 25C is 6.6177 J ˣ mol-1 ˣ K-1. This does not change and will be measured the same by all labs. Randomness might be how we model this state, but the entropy of this state is a constant.

Volume alone can't tell the entire picture, because entropy depend on the state more than the volume. For example, if we freeze water the water will expand by about 9%, yet the entropy goes down; ice Ih: -21.99 J ˣ mol-1 ˣ K-1 (0 °C).

With a singularity, I would guess it depends on state of the singularity. One would need to know the particle type and the temperature in degrees K. Are black holes hot or cold? A hot black hole has a higher entropy than a cold one, even if both are compressed to singularities.

If the second law applies to black holes, once it reaches a singularity, for the entropy to increase via the second law, it has to change state. It may not be able to remain in one state, unless time is slowing. The result will be that the state changes so slow from our reference, it seems to be in one state.
« Last Edit: 25/06/2016 00:38:44 by puppypower »

#### Thebox

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##### Re: Is the entropy of a singularity system equal to its volume ?
« Reply #15 on: 25/06/2016 01:12:04 »
In chemistry, entropy is considered a state variable meaning it has a specific value for a given state of matter. For example, the entropy of water at 25C is 6.6177 J ˣ mol-1 ˣ K-1. This does not change and will be measured the same by all labs. Randomness might be how we model this state, but the entropy of this state is a constant.

Volume alone can't tell the entire picture, because entropy depend on the state more than the volume. For example, if we freeze water the water will expand by about 9%, yet the entropy goes down; ice Ih: -21.99 J ˣ mol-1 ˣ K-1 (0 °C).

With a singularity, I would guess it depends on state of the singularity. One would need to know the particle type and the temperature in degrees K. Are black holes hot or cold? A hot black hole has a higher entropy than a cold one, even if both are compressed to singularities.

If the second law applies to black holes, once it reaches a singularity, for the entropy to increase via the second law, it has to change state. It may not be able to remain in one state, unless time is slowing. The result will be that the state changes so slow from our reference, it seems to be in one state.

Just a quick question puppy and sorry mods not really related to topic but an answer I need.

You mention freezing water and the expansion of frozen water(ice) ,  now does the water expand like a ''balloon'' which seems contradictory to boiling water and expansion, or does the water expand by gain of ''water'' turning to ice from the surrounding atmosphere/humidity, which seems more plausible?

The snow fall gets ''deeper''.

« Last Edit: 25/06/2016 01:14:15 by Thebox »

#### evan_au

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##### Re: Is the entropy of a singularity system equal to its volume ?
« Reply #16 on: 25/06/2016 12:46:18 »
Quote from: puppypower
With a singularity, I would guess it depends on state of the singularity.  One would need to know the particle type and the temperature in degrees K.
With our current technology, there is precious little that an outside observer can observe about a singularity that formed before she got there: only its Mass, Angular Momentum and Electric Charge.

The state of the interior is unknowable (with our current knowledge).

But the theory of black holes suggests that the information about what went into the black hole is somehow preserved on its event horizon (...you may just have to wait for the age of the universe to collect it). Information and Entropy are closely related.

Quote
Are black holes hot or cold?
Hawking radiation defines an effective temperature for a black hole. For a solar mass black hole, it is almost absolute zero (about 100 nano Kelvins). Visible light goes in, and what comes out is the occasional radio photon.
See: https://en.wikipedia.org/wiki/Black_hole#Evaporation

Quote
A hot black hole has a higher entropy than a cold one, even if both are compressed to singularities.
Hypothetically, "Micro Black Holes" could have been created in the Big Bang - perhaps with the mass of an asteroid or a large meteorite. The Hawking radiation of these would be quite hot (thousands or millions of degrees).

But because the surface area of the micro black hole is so small (maybe the size of a proton), its entropy is also lower than a stellar-mass black hole. So the intuition from chemistry fails you here: cold black holes have more entropy than hot black holes.

Quote
If the second law applies to black holes
Yes, there are equivalents to the laws of thermodynamics for black holes, but the equivalence to entropy in chemistry is not immediately obvious.
https://en.wikipedia.org/wiki/Black_hole_thermodynamics#The_laws_of_black_hole_mechanics

And it seems that Hawking radiation (if it exists) appears to break one of these rules (that a black hole's entropy can only increase).

#### Thebox

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##### Re: Is the entropy of a singularity system equal to its volume ?
« Reply #17 on: 25/06/2016 16:03:32 »

micro black hole

You mention a micro black hole being the size of a Proton, at the moment there is an hypothesis ''floating'' around that all galaxies are in a black hole and the recent detection of gravitational waves is the ''contortion' of the milky way black hole. (something like that).

Why is it no thought of that any particle is a black hole because all particles have mass and entropy and can absorb ''energy'' and have the ability to attract, but not all particles can be seen unless ''magnified'' by often ''telescope'' means.
In simple terms if out in space there was a black rock ''floating'' around, you would not observe this unless it passed a star or highlighted planets line of sight, but the rock would affect anything around it, now if we imagined this rock is as big as the moon but very far away beyond the visual angle of sight, the rock still affects the space and may look like a black hole?

#### evan_au

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##### Re: Is the entropy of a singularity system equal to its volume ?
« Reply #18 on: 26/06/2016 12:43:10 »
Quote from: TheBox
an hypothesis ''floating'' around that all galaxies are in a black hole
It is thought that most galaxies have a black hole inside them, with a mass perhaps 0.1% of the central bulge.
If the galaxy were in a black hole, we would not be able to see the galaxy (it would be black).
Perhaps you have your cosmology inside-out?

Quote
Why is it no thought of that any particle is a black hole?
Large objects like the Sun, Moon and asteroids are not black holes, because we can see them.

Black holes can collide with each other, but they always form a larger black hole.
• Radioactive atomic nuclei can emit gamma rays. This means the nucleus of an atom is not a black hole.
• Atoms can emit light. This means that atoms are not black holes..
• Protons colliding in the LHC emit a spray of particles, so protons are not black holes.
• These particles produced in the LHC break down into other subatomic particles, so none of them are black holes.
• The LHC is explicitly searching for black holes; some speculative theories about higher dimensions suggest that the LHC might produce an occasional black hole... but they haven't found any yet. (

Quote
now if we imagined this rock is as big as the moon but very far away beyond the visual angle of sight, the rock still affects the space and may look like a black hole?
There have been a number of searches for "gravitational microlensing", as a way of detecting free-floating planets or black holes.

These objects are far beyond the distance at which any current telescope could detect a visible disk. (And quiescent black holes don't have a visible disk anyway.)

These microlensing events are very rare, but when the alignment is exactly right, and the event can be observed by different telescopes at the same time, it is often possible to determine the mass of the object coming between us and the distant star. This allows us to distinguish between Planet-sized objects and black holes.
See: https://en.wikipedia.org/wiki/Gravitational_microlensing

One of these microlensing surveys was looking for evidence that dark matter could be black holes or brown dwarf stars. They didn't find nearly enough of these microlensing events to account for the observed effects of dark matter.

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#### jeffreyH

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##### Re: Is the entropy of a singularity system equal to its volume ?
« Reply #19 on: 26/06/2016 13:15:54 »
If in order to calculate proton entropy we define a sphere that encloses the proton we have an immediate problem. The proton itself is highly unlikely to be a well defined object and uncertainty will play a part in that. So that we would have to set an arbitrary radius for the enclosing sphere. This leads, inevitably, to the conclusion that the entropy of a single particle is uncertain. So scale matters. If we increase the radius to the electron orbital then we may assure ourselves that we have the proton contained within our sphere and yet its electromagnetic field will never be contained. This leads to another conclusion. Confinement within a black hole must include the electromagnetic field entirely and it has to play a part in its entropy. What that part is I haven't contemplated.
« Last Edit: 26/06/2016 13:18:44 by jeffreyH »

#### Alan McDougall

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##### Re: Is the entropy of a singularity system equal to its volume ?
« Reply #20 on: 26/06/2016 16:59:00 »

micro black hole

You mention a micro black hole being the size of a Proton, at the moment there is an hypothesis ''floating'' around that all galaxies are in a black hole and the recent detection of gravitational waves is the ''contortion' of the milky way black hole. (something like that).

Why is it no thought of that any particle is a black hole because all particles have mass and entropy and can absorb ''energy'' and have the ability to attract, but not all particles can be seen unless ''magnified'' by often ''telescope'' means.
In simple terms if out in space there was a black rock ''floating'' around, you would not observe this unless it passed a star or highlighted planets line of sight, but the rock would affect anything around it, now if we imagined this rock is as big as the moon but very far away beyond the visual angle of sight, the rock still affects the space and may look like a black hole?

Again as clear as mud, thank you for nothing!

#### Alan McDougall

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##### Re: Is the entropy of a singularity system equal to its volume ?
« Reply #21 on: 26/06/2016 17:04:13 »
Quote from: TheBox
an hypothesis ''floating'' around that all galaxies are in a black hole
It is thought that most galaxies have a black hole inside them, with a mass perhaps 0.1% of the central bulge.
If the galaxy were in a black hole, we would not be able to see the galaxy (it would be black).
Perhaps you have your cosmology inside-out?

Quote
Why is it no thought of that any particle is a black hole?
Large objects like the Sun, Moon and asteroids are not black holes, because we can see them.

Black holes can collide with each other, but they always form a larger black hole.
• Radioactive atomic nuclei can emit gamma rays. This means the nucleus of an atom is not a black hole.
• Atoms can emit light. This means that atoms are not black holes..
• Protons colliding in the LHC emit a spray of particles, so protons are not black holes.
• These particles produced in the LHC break down into other subatomic particles, so none of them are black holes.
• The LHC is explicitly searching for black holes; some speculative theories about higher dimensions suggest that the LHC might produce an occasional black hole... but they haven't found any yet. (

Quote
now if we imagined this rock is as big as the moon but very far away beyond the visual angle of sight, the rock still affects the space and may look like a black hole?
There have been a number of searches for "gravitational microlensing", as a way of detecting free-floating planets or black holes.

These objects are far beyond the distance at which any current telescope could detect a visible disk. (And quiescent black holes don't have a visible disk anyway.)

These microlensing events are very rare, but when the alignment is exactly right, and the event can be observed by different telescopes at the same time, it is often possible to determine the mass of the object coming between us and the distant star. This allows us to distinguish between Planet-sized objects and black holes.
See: https://en.wikipedia.org/wiki/Gravitational_microlensing

One of these microlensing surveys was looking for evidence that dark matter could be black holes or brown dwarf stars. They didn't find nearly enough of these microlensing events to account for the observed effects of dark matter.

Your posts are always, informative, accurate and put over in a concise manner from which all of us can only advance our knowledge of physics.

Thank you

Alan

#### The Naked Scientists Forum

##### Re: Is the entropy of a singularity system equal to its volume ?
« Reply #21 on: 26/06/2016 17:04:13 »