10 ms·

Are We Wrong About Black Holes?

93 points by theafh 7y ago

kovrik 7y ago
> Stephen Hawking proved that the area of a black hole’s event horizon — the surface that marks its boundary — cannot decrease. I thought he proved the opposite: that black holes (slowly) evaporate through Hawking radiation, lose mass, hence their event horizon shrinks. Could anyone please elaborate? Also, do scientists actually say that thermodynamics and black holes are the same thing? Never heard of that. I think they only mean that laws of thermodynamics are universal and should be applicable to black holes as well.
- knzhou 7y ago
  He proved this in the context of classical general relativity. Hawking radiation is a (semiclassical) quantum gravity effect which is remarkable for being able to break this classical result. The identification of area with entropy doesn't mean that entropy decreases as a black hole evaporates, because the emitted particles carry the entropy.
  - kovrik 7y ago
    But mass decreases which implies that event horizon shrinks, right? Also, I thought never-increasing entropy was only applicable to closed systems. In that sense, when particles leave black hole through Hawking radiation, total entropy of the Universe remains the same. Am I missing something?
    - pdonis 7y ago
      > mass decreases which implies that event horizon shrinks, right? Yes. So the entropy of the hole by itself decreases. But the entropy of the whole system, including the hole and the Hawking radiation it emits, increases. > when particles leave black hole through Hawking radiation, total entropy of the Universe remains the same We have no way of evaluating the total entropy of the universe. The concept itself might not make any sense, since we have no way of making measurements or running experiments on the universe from the outside.
- pdonis 7y ago
  He proved both. He and Penrose proved theorems that showed that, under certain assumptions, the area of a black hole's event horizon can never decrease. But he later showed that quantum fields near the horizon can violate some of the assumptions that are required for the area theorem, so when those quantum effects are taken into account, black holes can radiate and this can cause the area of their event horizons to decrease.
  - deleted 7y ago
    [deleted]
  - kibibu 7y ago
    So he proved "if x then y", then later proved "!x"
    - knzhou 7y ago
      Well, perhaps, but in physics we like to think of our field as containing many separate, logically independent models of reality. Yes, "x" probably isn't true in our universe, but it is true in an exceptionally good model for our universe, and that's what makes it an important result. It's like how the round Earth is wrong, but way less wrong than the flat Earth.
    - nightcracker 7y ago
      No. x -> y && !x does not give !y, it just gives nothing. He proved y under some set of assumptions, and then later !y under another set of assumptions. So he proved a -> y && b -> !y.
      - xamuel 7y ago
        But, given x->y, if you prove !y, you can conclude !x, so in a sense kibibu is right (possibly requiring "proved" to be read as "indirectly proved"), and we should give them the benefit of the doubt.
        pdonis 7y ago
- pdonis 7y ago
  > I think they only mean that laws of thermodynamics are universal and should be applicable to black holes as well. That's correct; that's all they mean.
- platz 7y ago
  Use the word proof carefully. We've never observed Hawking radiation, we just think it's likely to exist.
  - antonvs 7y ago
    The proof is theoretical. It doesn't mean that Hawking radiation must exist, but it means that if the theories that the proofs are based on are sufficiently correct, then Hawking radiation must exist.
Causality1 7y ago
The featured professor implies credentials he doesn't have by describing himself as a "philosopher of science" when his actual degree is in philosophy, not any hard science. In fact he has no scientific or mathematic background whatsoever. Read his opinions with the same amount of skepticism you would apply to a post on 4chan, because he's exactly as credible.
- dang 7y ago
  This breaks the site guideline against shallow dismissals. Please don't do that here.
  - Causality1 7y ago
    Pointing out that someone is misrepresenting themselves as an authority is not a shallow dismissal. In fact I didn't even say he was wrong; I said take his claims with a large degree of skepticism.
    - dang 7y ago
      Snarkily putting someone down because of his credentials is certainly a shallow dismissal, and just the sort of thing that guideline asks you not to do here.
- deleted 7y ago
  [deleted]
kgin 7y ago
> Craig Callender worries that the analogy between black holes and thermodynamics has been stretched too far. Spaghettification
gus_massa 7y ago
> If a black hole is obeying thermodynamic laws, we can presume that a statistical description of all its fundamental, indivisible parts can be made. No. It is posible to define the entropy of an object that has no internal indivisible parts, for example a black hole. > Here’s another way in which the analogy falls flat. Black hole entropy is given by the black hole area. Well, area is length squared, volume is length cubed. So what do we make of all those thermodynamic relations that include volume, like Boyle’s law? Is volume, which is length times area, really length times entropy? That would ruin the analogy. So we have to say that volume is not the counterpart of volume, which is surprising. This paragraph makes no sense at all. No sense at all! First, Boyle's law is a law for ideal gases (that can be applied somewhat correctly to real gases). It can't be applied to solids, it can't be applied to liquids, it can't be applied to a photon gas, it can't be applied to black holes. Trying to apply it to black holes shows a completely lack of understanding of the subject. In particular: > Is volume, which is length times area, really length times entropy? What? First the entropy of a black hole is not equal to the area, it's only proportional to the area, there are some constants. (I had to look up S = A * c^3 / 4Għ.) Second, you can't pick any three length [1] and multiply them and expect that the result that has the units of a volume can be used in any formula you want. [1] For example, the height of the Eiffel tower, the atomic radio of an iron atom in the Eiffel tower and the width of the door of the elevator of the Eiffel tower. You can multiply them and get a volume, but this volume doesn't follow the Boyle's law when the atmospheric pressure changes in Paris.
- reallydude 7y ago
  > No. It is posible to define the entropy of an object that has no internal indivisible parts, for example a black hole How? If there is no system of parts, there is no entropy. I'm not sure why you have a "black hole" as an example, when you talk about the entropy of a black hole afterward and it's has not been concluded that black holes violate the second law. You have failed to give an example and I think it's important to at least clarify your statement. > First, Boyle's law is a law for ideal gases (that can be applied somewhat correctly to real gases). It can't be applied to solids, it can't be applied to liquids, it can't be applied to a photon gas, it can't be applied to black holes. He didn't say that Boyle's law applied to black holes. He was expounding on the initial point you objected on. If you have a system of parts, it has a volume. > Trying to apply it to black holes shows a completely lack of understanding of the subject. You're being disingenuous by not even attempting to understand the assertion and then attacking every logical conclusion as if that means something. He has an understanding, even if you think it's wrong. > Is volume, which is length times area, really length times entropy? To your first point, it's semantics when you drop the constants. This isn't some obscure way of speaking and he uses it generously. To your second point, he didn't. This was a generalization of the concept expanded to how you calculate the event horizon of a black hole. A sphere's surface area can be calculated from the length of the radius (ie A=4πr2). (from google) S/V = 3/R 4πr2/Volume = 3/r or Area/3/radius = Volume So the interpretation is volume = Area x 1/length or Area x Length (ie radius) when dealing with the variants. A x c^3 / 4Għ = Entropy (Bekenstein–Hawking formula) and dropping all the invariants (A = E) we get Area = Entropy So the volume of a black hole (given it has entropy) could be the volume of the black hole (Area x Length) = Entropy and since we can get area from Length, we can drop the invariants and we get Length = Entropy with constants and invariant proportions.
sidcool 7y ago
Black holes are the most astonishing of stellar objects. They were mathematically predicted first and then discovered, which is fascinating.
- jsweojtj 7y ago
  Just like Neptune! https://en.wikipedia.org/wiki/Urbain_Le_Verrier https://en.wikipedia.org/wiki/Urbain_Le_Verrier
  - fhars 7y ago
    And Vulcan! https://en.m.wikipedia.org/wiki/Vulcan_(hypothetical_planet) https://en.m.wikipedia.org/wiki/Vulcan_(hypothetical_planet) ... oops.
- thunderbong 7y ago
  This is true for many scientific discoveries, including the General Theory of Relativity
- newsgremlin 7y ago
  And they (well one of them) will probably be one of the last things in the existence of our universe. It feels like they hold the key to the answers we seek, even if the answer turns out to be nothing.
saagarjha 7y ago
I really hate to do this (especially since I am not an expert in this field), but this really seems like a philosophical argument against scientific theory rather than one actually backed by evidence. No offense to the author, he just goes into some sort of superficial argument that thermodynamics doesn't apply to black holes because the analogy doesn't really make sense for what looks to be personal issues with how certain things are defined. Honestly, it's great and all that there are people willing to exercise caution about our current models, but I'm not seeing anything to back Callender's views here and his viewpoint comes across as pseudoscientific.
- normalhuman 7y ago
  The very idea of a "scientific theory" is a philosophical concept, and your implicit assertion that empiricism trumps abstract reasoning (which I am here neither agreeing with nor opposing) is in itself a philosophical position. Pseudoscience refers to activities that superficially have the aesthetics of science but do not follow its constraints. For example, homeopathy is pseudoscience. They dress in white coats and use chemistry lab equipment, but they do not test their ideas with experiments that could falsify them. This has nothing to do with reasoning with the current scientific theories. What do you think theoretical physicists do? I say this because more and more I notice people using "pseudoscience" in a sense similar to "heresy", and treating philosophy as some sort of inferior system of knowledge that is bound to be replaced by science. These people misunderstand both science and philosophy, and would benefit from a bit more of reading and thinking outside of their comfort zone.
  - naringas 7y ago
    > I say this because more and more I notice people using "pseudoscience" in a sense similar to "heresy" I think that for some people science has replaced religion as a belief and social control system For these people science defines what is possible within reality and how the world works in a fundamental way; but they don't really understand how these scientific theories work, they just accept them. I am not saying that science is a religion (they do work under different constraints), I am just saying that science has started to serve a similar role within our civilization, like religion did back in the "dark ages"
imvetri 7y ago
Human sees ant - Be busy as an ant. Ant is incredible, We have to colonise world just like they are doing. Ant has more strength when compared to its body. only queen ants talk to small ants. Queen controls the ants. Ants are disciplined. Some ants attack. Some ants build bridges. What if Human are the ant?. Proving it being right / wrong is not the point.
deleted 7y ago
[deleted]
sleepysysadmin 7y ago
The problem with black holes is that all of our science is observationally weak. You can't use any science that's based on the speed of electromagnetism or for that matter light. If your observational weakness prevents you from making any observations. Then you know nothing at all about it.
giardini 7y ago
Arieh Ben-Naim is a well-respected thermodynamicist who believes that application of the laws of thermodynamics to the whole universe and to black holes is not valid. He's written books about it: https://en.wikipedia.org/wiki/Arieh_Ben-Naim https://en.wikipedia.org/wiki/Arieh_Ben-Naim https://www.amazon.com/Arieh-Ben-Naim/e/B001HD1O86/ref=dp_byline_cont_book_1 https://www.amazon.com/Arieh-Ben-Naim/e/B001HD1O86/ref=dp_by... I enjoyed Ben-Naim's "Briefest History of Time, The: The History of Histories of Time and the Misconstrued Association Between Entropy and Time " https://www.amazon.com/s?k=briefest+history+of+time https://www.amazon.com/s?k=briefest+history+of+time Ben-Naim takes credit for Hawking later cutting most of his "Brief History of Tme" in later editions.
danbruc 7y ago
There’s a long debate in the foundations of statistical mechanics about whether entropy is a subjective notion or an objective notion. I’m firmly on the side of thinking it’s an objective notion. I spread out two decks of cards on the table in front of you. One is thoroughly mixed up, the other one is neatly ordered by suit from spades to diamonds and each suit is ordered from ace to king, except for 7 and 8 of clubs, they are in the wrong order. »Which deck has the higher entropy?« I ask. »The mixed up one of course.« you answer. Out of my pocket I pull a flashlight and turn it on, under the shine of its blacklight you can read the numbers 1 to 52 written onto the mixed up deck in perfect order, the numbers written onto the neatly ordered deck are in no discernible order.
- mgsouth 7y ago
  My question is "why does the symbol '1', followed by '2', ... '52' define an ordered state?" It would seem that the "cheat sheet" which defines the progression is part of the system. Not sure where I'm going with that... This brought up another set of questions: is it possible to define entropy without a definition of simultaneity, or some other global ordering of events? Is it possible for two different observers to have differing views of entropy? What does rotation of the time-like axis do? Googling didn't find much, but it did find a discussion on physicsforums [0]. The answer seemed to be... it's complicated. Good discussion, though. [0] https://www.physicsforums.com/threads/time-dilation-and-entropy.837480/ https://www.physicsforums.com/threads/time-dilation-and-entr...
  - platz 7y ago
    You can't calculate entropy without defining the macroscopic variables you are interested in. Once you have done that, you can start counting the microstates that satisfy those macroscopic variables.
    - deleted 7y ago
      [deleted]
    - mgsouth 7y ago
      So, in other words, yes, entropy is subjective, and depends upon your definition of variables (and ordering). What's the other argument, leading to debate?

93 points by theafh 7y ago

> Stephen Hawking proved that the area of a black hole’s event horizon — the surface that marks its boundary — cannot decrease. I thought he proved the opposite: that black holes (slowly) evaporate through Hawking radiation, lose mass, hence their event horizon shrinks. Could anyone please elaborate? Also, do scientists actually say that thermodynamics and black holes are the same thing? Never heard of that. I think they only mean that laws of thermodynamics are universal and should be applicable to black holes as well.

knzhou 7y ago
He proved this in the context of classical general relativity. Hawking radiation is a (semiclassical) quantum gravity effect which is remarkable for being able to break this classical result. The identification of area with entropy doesn't mean that entropy decreases as a black hole evaporates, because the emitted particles carry the entropy.
- kovrik 7y ago
  But mass decreases which implies that event horizon shrinks, right? Also, I thought never-increasing entropy was only applicable to closed systems. In that sense, when particles leave black hole through Hawking radiation, total entropy of the Universe remains the same. Am I missing something?
  - pdonis 7y ago
    > mass decreases which implies that event horizon shrinks, right? Yes. So the entropy of the hole by itself decreases. But the entropy of the whole system, including the hole and the Hawking radiation it emits, increases. > when particles leave black hole through Hawking radiation, total entropy of the Universe remains the same We have no way of evaluating the total entropy of the universe. The concept itself might not make any sense, since we have no way of making measurements or running experiments on the universe from the outside.
pdonis 7y ago
He proved both. He and Penrose proved theorems that showed that, under certain assumptions, the area of a black hole's event horizon can never decrease. But he later showed that quantum fields near the horizon can violate some of the assumptions that are required for the area theorem, so when those quantum effects are taken into account, black holes can radiate and this can cause the area of their event horizons to decrease.
- deleted 7y ago
  [deleted]
- kibibu 7y ago
  So he proved "if x then y", then later proved "!x"
  - knzhou 7y ago
    Well, perhaps, but in physics we like to think of our field as containing many separate, logically independent models of reality. Yes, "x" probably isn't true in our universe, but it is true in an exceptionally good model for our universe, and that's what makes it an important result. It's like how the round Earth is wrong, but way less wrong than the flat Earth.
  - nightcracker 7y ago
    No. x -> y && !x does not give !y, it just gives nothing. He proved y under some set of assumptions, and then later !y under another set of assumptions. So he proved a -> y && b -> !y.
    - xamuel 7y ago
      But, given x->y, if you prove !y, you can conclude !x, so in a sense kibibu is right (possibly requiring "proved" to be read as "indirectly proved"), and we should give them the benefit of the doubt.
      - pdonis 7y ago
pdonis 7y ago
> I think they only mean that laws of thermodynamics are universal and should be applicable to black holes as well. That's correct; that's all they mean.
platz 7y ago
Use the word proof carefully. We've never observed Hawking radiation, we just think it's likely to exist.
- antonvs 7y ago
  The proof is theoretical. It doesn't mean that Hawking radiation must exist, but it means that if the theories that the proofs are based on are sufficiently correct, then Hawking radiation must exist.

Causality1 7y ago

The featured professor implies credentials he doesn't have by describing himself as a "philosopher of science" when his actual degree is in philosophy, not any hard science. In fact he has no scientific or mathematic background whatsoever. Read his opinions with the same amount of skepticism you would apply to a post on 4chan, because he's exactly as credible.

dang 7y ago
This breaks the site guideline against shallow dismissals. Please don't do that here.
- Causality1 7y ago
  Pointing out that someone is misrepresenting themselves as an authority is not a shallow dismissal. In fact I didn't even say he was wrong; I said take his claims with a large degree of skepticism.
  - dang 7y ago
    Snarkily putting someone down because of his credentials is certainly a shallow dismissal, and just the sort of thing that guideline asks you not to do here.
deleted 7y ago
[deleted]

kgin 7y ago

> Craig Callender worries that the analogy between black holes and thermodynamics has been stretched too far. Spaghettification

gus_massa 7y ago

> If a black hole is obeying thermodynamic laws, we can presume that a statistical description of all its fundamental, indivisible parts can be made. No. It is posible to define the entropy of an object that has no internal indivisible parts, for example a black hole. > Here’s another way in which the analogy falls flat. Black hole entropy is given by the black hole area. Well, area is length squared, volume is length cubed. So what do we make of all those thermodynamic relations that include volume, like Boyle’s law? Is volume, which is length times area, really length times entropy? That would ruin the analogy. So we have to say that volume is not the counterpart of volume, which is surprising. This paragraph makes no sense at all. No sense at all! First, Boyle's law is a law for ideal gases (that can be applied somewhat correctly to real gases). It can't be applied to solids, it can't be applied to liquids, it can't be applied to a photon gas, it can't be applied to black holes. Trying to apply it to black holes shows a completely lack of understanding of the subject. In particular: > Is volume, which is length times area, really length times entropy? What? First the entropy of a black hole is not equal to the area, it's only proportional to the area, there are some constants. (I had to look up S = A * c^3 / 4Għ.) Second, you can't pick any three length [1] and multiply them and expect that the result that has the units of a volume can be used in any formula you want. [1] For example, the height of the Eiffel tower, the atomic radio of an iron atom in the Eiffel tower and the width of the door of the elevator of the Eiffel tower. You can multiply them and get a volume, but this volume doesn't follow the Boyle's law when the atmospheric pressure changes in Paris.

reallydude 7y ago
> No. It is posible to define the entropy of an object that has no internal indivisible parts, for example a black hole How? If there is no system of parts, there is no entropy. I'm not sure why you have a "black hole" as an example, when you talk about the entropy of a black hole afterward and it's has not been concluded that black holes violate the second law. You have failed to give an example and I think it's important to at least clarify your statement. > First, Boyle's law is a law for ideal gases (that can be applied somewhat correctly to real gases). It can't be applied to solids, it can't be applied to liquids, it can't be applied to a photon gas, it can't be applied to black holes. He didn't say that Boyle's law applied to black holes. He was expounding on the initial point you objected on. If you have a system of parts, it has a volume. > Trying to apply it to black holes shows a completely lack of understanding of the subject. You're being disingenuous by not even attempting to understand the assertion and then attacking every logical conclusion as if that means something. He has an understanding, even if you think it's wrong. > Is volume, which is length times area, really length times entropy? To your first point, it's semantics when you drop the constants. This isn't some obscure way of speaking and he uses it generously. To your second point, he didn't. This was a generalization of the concept expanded to how you calculate the event horizon of a black hole. A sphere's surface area can be calculated from the length of the radius (ie A=4πr2). (from google) S/V = 3/R 4πr2/Volume = 3/r or Area/3/radius = Volume So the interpretation is volume = Area x 1/length or Area x Length (ie radius) when dealing with the variants. A x c^3 / 4Għ = Entropy (Bekenstein–Hawking formula) and dropping all the invariants (A = E) we get Area = Entropy So the volume of a black hole (given it has entropy) could be the volume of the black hole (Area x Length) = Entropy and since we can get area from Length, we can drop the invariants and we get Length = Entropy with constants and invariant proportions.

sidcool 7y ago

Black holes are the most astonishing of stellar objects. They were mathematically predicted first and then discovered, which is fascinating.

jsweojtj 7y ago
Just like Neptune! https://en.wikipedia.org/wiki/Urbain_Le_Verrier https://en.wikipedia.org/wiki/Urbain_Le_Verrier
- fhars 7y ago
  And Vulcan! https://en.m.wikipedia.org/wiki/Vulcan_(hypothetical_planet) https://en.m.wikipedia.org/wiki/Vulcan_(hypothetical_planet) ... oops.
thunderbong 7y ago
This is true for many scientific discoveries, including the General Theory of Relativity
newsgremlin 7y ago
And they (well one of them) will probably be one of the last things in the existence of our universe. It feels like they hold the key to the answers we seek, even if the answer turns out to be nothing.

saagarjha 7y ago

I really hate to do this (especially since I am not an expert in this field), but this really seems like a philosophical argument against scientific theory rather than one actually backed by evidence. No offense to the author, he just goes into some sort of superficial argument that thermodynamics doesn't apply to black holes because the analogy doesn't really make sense for what looks to be personal issues with how certain things are defined. Honestly, it's great and all that there are people willing to exercise caution about our current models, but I'm not seeing anything to back Callender's views here and his viewpoint comes across as pseudoscientific.

normalhuman 7y ago
The very idea of a "scientific theory" is a philosophical concept, and your implicit assertion that empiricism trumps abstract reasoning (which I am here neither agreeing with nor opposing) is in itself a philosophical position. Pseudoscience refers to activities that superficially have the aesthetics of science but do not follow its constraints. For example, homeopathy is pseudoscience. They dress in white coats and use chemistry lab equipment, but they do not test their ideas with experiments that could falsify them. This has nothing to do with reasoning with the current scientific theories. What do you think theoretical physicists do? I say this because more and more I notice people using "pseudoscience" in a sense similar to "heresy", and treating philosophy as some sort of inferior system of knowledge that is bound to be replaced by science. These people misunderstand both science and philosophy, and would benefit from a bit more of reading and thinking outside of their comfort zone.
- naringas 7y ago
  > I say this because more and more I notice people using "pseudoscience" in a sense similar to "heresy" I think that for some people science has replaced religion as a belief and social control system For these people science defines what is possible within reality and how the world works in a fundamental way; but they don't really understand how these scientific theories work, they just accept them. I am not saying that science is a religion (they do work under different constraints), I am just saying that science has started to serve a similar role within our civilization, like religion did back in the "dark ages"

imvetri 7y ago

Human sees ant - Be busy as an ant. Ant is incredible, We have to colonise world just like they are doing. Ant has more strength when compared to its body. only queen ants talk to small ants. Queen controls the ants. Ants are disciplined. Some ants attack. Some ants build bridges. What if Human are the ant?. Proving it being right / wrong is not the point.

deleted 7y ago

[deleted]

sleepysysadmin 7y ago

The problem with black holes is that all of our science is observationally weak. You can't use any science that's based on the speed of electromagnetism or for that matter light. If your observational weakness prevents you from making any observations. Then you know nothing at all about it.

giardini 7y ago

Arieh Ben-Naim is a well-respected thermodynamicist who believes that application of the laws of thermodynamics to the whole universe and to black holes is not valid. He's written books about it: https://en.wikipedia.org/wiki/Arieh_Ben-Naim https://en.wikipedia.org/wiki/Arieh_Ben-Naim https://www.amazon.com/Arieh-Ben-Naim/e/B001HD1O86/ref=dp_byline_cont_book_1 https://www.amazon.com/Arieh-Ben-Naim/e/B001HD1O86/ref=dp_by... I enjoyed Ben-Naim's "Briefest History of Time, The: The History of Histories of Time and the Misconstrued Association Between Entropy and Time " https://www.amazon.com/s?k=briefest+history+of+time https://www.amazon.com/s?k=briefest+history+of+time Ben-Naim takes credit for Hawking later cutting most of his "Brief History of Tme" in later editions.

danbruc 7y ago

There’s a long debate in the foundations of statistical mechanics about whether entropy is a subjective notion or an objective notion. I’m firmly on the side of thinking it’s an objective notion. I spread out two decks of cards on the table in front of you. One is thoroughly mixed up, the other one is neatly ordered by suit from spades to diamonds and each suit is ordered from ace to king, except for 7 and 8 of clubs, they are in the wrong order. »Which deck has the higher entropy?« I ask. »The mixed up one of course.« you answer. Out of my pocket I pull a flashlight and turn it on, under the shine of its blacklight you can read the numbers 1 to 52 written onto the mixed up deck in perfect order, the numbers written onto the neatly ordered deck are in no discernible order.

mgsouth 7y ago
My question is "why does the symbol '1', followed by '2', ... '52' define an ordered state?" It would seem that the "cheat sheet" which defines the progression is part of the system. Not sure where I'm going with that... This brought up another set of questions: is it possible to define entropy without a definition of simultaneity, or some other global ordering of events? Is it possible for two different observers to have differing views of entropy? What does rotation of the time-like axis do? Googling didn't find much, but it did find a discussion on physicsforums [0]. The answer seemed to be... it's complicated. Good discussion, though. [0] https://www.physicsforums.com/threads/time-dilation-and-entropy.837480/ https://www.physicsforums.com/threads/time-dilation-and-entr...
- platz 7y ago
  You can't calculate entropy without defining the macroscopic variables you are interested in. Once you have done that, you can start counting the microstates that satisfy those macroscopic variables.
  - deleted 7y ago
    [deleted]
  - mgsouth 7y ago
    So, in other words, yes, entropy is subjective, and depends upon your definition of variables (and ordering). What's the other argument, leading to debate?