8 ms·

Entropy in the Universe

115 points by chmaynard 7y ago

gab007 7y ago
That zoom-able image is amazing. Sometimes we forget how big the universe is. And that's just an image of the Milky Way.
- monkeydust 7y ago
  Yea that also amazed me, aside from the science a great way to put things into perspective when you are struggling with something.
  - K0SM0S 7y ago
    I honestly think this is what I love in sci-fi, some space opera most notably: whereas most stories are usually told in terms of space and time, sci-fi sometimes speaks in terms of scale, of orders of magnitudes — because space (I mean the cosmos, not the dimensions) is a natural playground for that. Sometimes, when I ponder the discrepancy between quantum, or whatever's smallest, perhaps strings 'below' (in scale) or 'within' (physically), and the largest relativistic objects like "dark attractors" and meta-galactic structures (streams of 'dark matter', light nodes, etc)... It almost seems like scale is but another kind of dimension in and of itself. Like you've got spacetime at our human-ish scale (roughly 10 orders of magnitude smaller to larger around our size), and that spacetime behaves in a certain way, that probably Einstein describes accurately. Then you've got spacetime at smaller scales, below "quantum uncertainty" if we must place a limit, and there spacetime behaves in a much different way, the picture is very, very different. And so there could be yet another spacetime at a higher threshold of scale, and intuition tells me it may be at the galacatic level already, because dark matter, rotation discrepancy, and those weird supermassive blackholes; the flow of galaxies, the meta-structure we see. Dark energy, if it's real, also begins at that scale (doesn't break galaxies apart, but makes holes bigger between them, the non-correlated enough sets). Going from this idea to postulating disjointed (1+3) spacetimes forming, in effect in this example, 3x4=12 dimensions to explore mathematically, let alone physically, is a stretch which I'm certainly not willing to make (although I think that's what some string theories must reduce to, somehow, maybe reduced to a single unified dimension of time maybe?); no really this doesn't make sense in my head. It's pretty but nonsensical, like art I guess. Worth the sci-fi, not the studies. But the feeling, the intuition really is that, and conveyed by these extreme zooming animations: a different scale means totally different phenomena, and no macro-system can be reduced to its parts in that view, nor can it be deduced from its parts (I mean, we can't even solve the 3-body problem, that's harsh on "scaling continuity" or smoothness, on the "linearity" of scales so to speak). A "basic" intuition I guess is that the 4 fundamental interactions have ranges, and kick in or out depending on a particular scale of the system. Scales are obsessing me.
- daxfohl 7y ago
  What struck me was the link to Hoag's Object which came up a couple days ago. And that even though it's a bazillion miles away there's another much more distant ring galaxy that you can make out way in the distance beyond it in the picture. https://en.wikipedia.org/wiki/Hoag%27s_Object https://en.wikipedia.org/wiki/Hoag%27s_Object
_Microft 7y ago
Since this is interesting and nobody has commented yet, let me say as a side note that I like how Mr. Baez emphasized the difference in orders of magnitudes here: The neutrinos from the Big Bang also carry about 10^90 bits — a bit less than the photons. The gravitons carry much less, about 10^88 bits. A difference in exponents of 2 might not look like a lot but one can almost ignore any of the earlier numbers once a larger exponent appears.
sq_ 7y ago
I find it interesting that he mentions gravitons as a definite piece of particle physics, on the same order as photons, etc. I was under the impression that gravitons were simply one part of one possible conception of quantum gravity, and that we were definitely unsure about whether or not they exist.
- K0SM0S 7y ago
  Since this is coming from a physicist / mathematician, I immediately assumed it meant the placeholder for those — i.e. whatever conveys gravity, all of it must hold that many bits to describe the observable universe.
- ahuth 7y ago
  The same thing stuck out to me, and definitely seemed presumptuous. However, I'm not a physicist, so what do I know? Maybe one way of looking at it is that despite the fact that gravitons are hypothetical, we can still do the math and calculate the amount of entropy or information that they would/could contain.
- auntienomen 7y ago
  Gravitons are speculative in that they haven't been observed, but they're almost certainly the correct language for describing mild quantum corrections to general relativity. Simple scaling arguments show that _any_ theory of quantum gravity that reduces to general relativity at low energies passes through a regime where it can be described by gravitons. Whether gravitons are fundamental objects in quantum gravity is irrelevant for the kind of state counting Baez is talking about.
  - sq_ 7y ago
    Thanks for the explanation!
drskaugen 7y ago
The image is awesome!
badrabbit 7y ago
I thought you 0 kelvin was the lowest possible value on the kelvin scale. How come this post mention negative kelvin values? Is it not temperature?
- Sharlin 7y ago
  There are no negative kelvin values in the article. 10^-30 is a positive number.
- transitorykris 7y ago
  If you're referring to "there will be a cosmological event horizon surrounding each observer, which will radiate Hawking radiation at a temperature of roughly 10-30 kelvin" this is a very tiny fraction: https://www.wolframalpha.com/input/?i=10%5E-30 https://www.wolframalpha.com/input/?i=10%5E-30
  - badrabbit 7y ago
    I was referring to that, my mistake, and thank you very much!
- jandrewrogers 7y ago
  I don't see negative Kelvin in the article. I do see Kelvins with a negative exponent, which is just a positive value that asymptotically approaches zero.
  - badrabbit 7y ago
    My mistake, I thought that notation implied negative numbers. Thank you.
    - johncarlosbaez 7y ago
      I was saying that the temperature of the Universe in the far future will be about 0.000000000000000000000000000001 kelvin, if our current theories are correct. This is 10^(-30) kelvin.
acqq 7y ago
From the comments of the author: "You can puzzle your group by asking whether entropy increases as clouds of gas and dust in the early Universe collapse and form stars and planets. If it doesn’t increase, this process violates the Second Law. So it must increase. But why is it increasing? It seems that order is increasing… so doesn’t that mean entropy is decreasing? If someone can’t answer this puzzle correctly, they don’t understand how thermodynamics works in our Universe." So, who knows the right answer to the puzzle: where and how the increase of the entropy happens? (I also suggest that those who really know should wait for some hours... I'd first actually like to see some wrong answers which try to be right but don't manage to be -- just to get some better picture of the readers here -- I don't know if this will work).
- t156654 7y ago
  The question is based on a false premise. What the Second Law of Thermodynamics states is that the entropy of an isolated system is never decreasing. Is the Universe an isolated system (meaning it cannot exchange matter or energy with its environment across its boundary)? We don't know anything about the boundaries of the Universe, or if it has any at all, therefore the 2nd law doesn't apply. QED.
  - acqq 7y ago
    Based on our observations we can see a lot of galaxies as in practice isolated systems, and for each separate galaxy second law still holds. So this attempt for explanation fails to answer the question.
    - lostmsu 7y ago
      No galaxies are particle isolated, as all of them emit radiation.
- Ono-Sendai 7y ago
  Entropy increases because its much more likely than for it to decrease. And the reason higher entropy states are more likely than low entropy states are that there's more of them.
foxes 7y ago
Entropy is not disorder. It is S ~ log #{microstates} For hn readers, microstates you can think of as a configuration of a system, so its counting number of configurations. Disorder is not well defined. Stop using the word disorder with entropy. A bunch of more complicated elements have more configurations than just pure H.
- BLKNSLVR 7y ago
  My interpretation is that "order" and "disorder" are subjective. One person's order is another's disorder. For example, my wife and I have differing tolerances of "order" as it pertains to the tidiness of a room. That may seem far separated from the topic at hand, but if a thing is able to be somewhere, then it's purely subjective as to whether it's the right place, ie. ordered. There's a time component to it as well, I might have a bunch of in-progress things laying around, but that's the correct place for those things for the current moment, for me. In parallel, however, it's most definitely the incorrect place, at all times, according to my better half. Potential Configurations = n Configurations considered "order" by me: x Configurations considered "order" by milady: 1 Configurations considered "order" by the universe: 0 Configurations considered "order" by the universe at this point in space and time: 1 That which is, is order. That which isn't, is not. Reminds me of this scene from Hi Fidelity: Dick: It guess it looks as if you're reorganizing your records. What is this though? Chronological? Rob: No... Dick: Not alphabetical... Rob: Nope. Dick: What? Rob: Autobiographical. Dick: No way.
- spectramax 7y ago
  This may be correct but its useless to make any engineering sense out of it. For engineering and practical intuition, use the following definition that we used at an Ivy-league college in US: https://en.wikipedia.org/wiki/Entropy_(energy_dispersal) https://en.wikipedia.org/wiki/Entropy_(energy_dispersal) Quoting the article: > Even though courses emphasised microstates and energy levels, most students could not get beyond simplistic notions of randomness or disorder. Many of those who learned by practising calculations did not understand well the intrinsic meanings of equations, and there was a need for qualitative explanations of thermodynamic relationships.
ShamelessC 7y ago
The article got me thinking about the universe's mass distribution. Is the number of galaxies at any edge of our observable universe similar to the number of galaxies in our observable universe? tl;dr does the (entire) universe have a uniform distribution of mass? Now, I'm aware that the universe has always been expanding from every point in all directions since the singularity before the big bang. This means that effectively 1.) every point in the universe can make the claim of being "at the center" 2.) none of them can 3.) the question is meaningless Which of those answers you find satisfying is more of a philosophical question which I'm not concerned with for this question. My question is this - if we were to somehow reach the edge of our universe instantaneously, simply to observe what things looked like from that point of view, would we find that there's roughly the same distribution of stars/galaxies/matter in all directions? I'm aware that questions with the premise that FTL/instantaneous travel is possible tend to be "unknowable" to a degree. Perhaps another way of wording it would be - do we expect the amount of matter to be of a uniform distribution in every spot in the universe? Is it impossible to know? Or can we use models of the big bang theory to predict that the distribution is roughly equal everywhere? Some philosophical implications that are curious but are probably scientifically meaningless: If there's reason to believe that there is a uniform distribution of mass in all observable universe, and the universe is infinite, does that imply there are an infinite number of galaxies, all of which are inaccessible if they're outside our observable universe? If so, is out ever appropriate to consider these infinite observable universes as essentially a multi-verse, containing many combinations of observable universes, one of which is statistically likely to be similar to our own observable universe? As always with questions regarding the size of the universe, it's center, etc. I suspect the answer will be "it's a meaningless question because we can never know", but I'm hoping that research into the big bang itself could provide some evidence. Please let me know if I haven't used proper terms or am making a critical mistake in my current understanding of astronomy.
- aeternum 7y ago
  The way I understand it is that there is not really an edge. Spacetime itself is expanding, the best analogy I've heard is consider a spherical balloon that is being inflated. We exist as two dimensional beings on that balloon. No matter where you put two dots on that balloon, they will move further apart. You could also draw a circle on the surface of that balloon which represents the furthest points that we can reach if we traveled at the speed of light. Nothing outside that circle would be observable to us, so it could be argued that it doesn't exist.
Zamicol 7y ago
The total entropy of all the stars, 10^82, is 2^270 I love this, because the useful 256 bit string (2^256) is only 43 characters long in base64, and to get to 2^270, it is only 45 base64 characters. I was just playing with this on Thursday, January 9th 2020 because I wanted to predict how many bits I needed to address every atom in the observable universe, which also just so happens to be 10^82. I use this example to depict the power of cryptography.

115 points by chmaynard 7y ago

That zoom-able image is amazing. Sometimes we forget how big the universe is. And that's just an image of the Milky Way.

monkeydust 7y ago
Yea that also amazed me, aside from the science a great way to put things into perspective when you are struggling with something.
- K0SM0S 7y ago
  I honestly think this is what I love in sci-fi, some space opera most notably: whereas most stories are usually told in terms of space and time, sci-fi sometimes speaks in terms of scale, of orders of magnitudes — because space (I mean the cosmos, not the dimensions) is a natural playground for that. Sometimes, when I ponder the discrepancy between quantum, or whatever's smallest, perhaps strings 'below' (in scale) or 'within' (physically), and the largest relativistic objects like "dark attractors" and meta-galactic structures (streams of 'dark matter', light nodes, etc)... It almost seems like scale is but another kind of dimension in and of itself. Like you've got spacetime at our human-ish scale (roughly 10 orders of magnitude smaller to larger around our size), and that spacetime behaves in a certain way, that probably Einstein describes accurately. Then you've got spacetime at smaller scales, below "quantum uncertainty" if we must place a limit, and there spacetime behaves in a much different way, the picture is very, very different. And so there could be yet another spacetime at a higher threshold of scale, and intuition tells me it may be at the galacatic level already, because dark matter, rotation discrepancy, and those weird supermassive blackholes; the flow of galaxies, the meta-structure we see. Dark energy, if it's real, also begins at that scale (doesn't break galaxies apart, but makes holes bigger between them, the non-correlated enough sets). Going from this idea to postulating disjointed (1+3) spacetimes forming, in effect in this example, 3x4=12 dimensions to explore mathematically, let alone physically, is a stretch which I'm certainly not willing to make (although I think that's what some string theories must reduce to, somehow, maybe reduced to a single unified dimension of time maybe?); no really this doesn't make sense in my head. It's pretty but nonsensical, like art I guess. Worth the sci-fi, not the studies. But the feeling, the intuition really is that, and conveyed by these extreme zooming animations: a different scale means totally different phenomena, and no macro-system can be reduced to its parts in that view, nor can it be deduced from its parts (I mean, we can't even solve the 3-body problem, that's harsh on "scaling continuity" or smoothness, on the "linearity" of scales so to speak). A "basic" intuition I guess is that the 4 fundamental interactions have ranges, and kick in or out depending on a particular scale of the system. Scales are obsessing me.
daxfohl 7y ago
What struck me was the link to Hoag's Object which came up a couple days ago. And that even though it's a bazillion miles away there's another much more distant ring galaxy that you can make out way in the distance beyond it in the picture. https://en.wikipedia.org/wiki/Hoag%27s_Object https://en.wikipedia.org/wiki/Hoag%27s_Object

_Microft 7y ago

Since this is interesting and nobody has commented yet, let me say as a side note that I like how Mr. Baez emphasized the difference in orders of magnitudes here: The neutrinos from the Big Bang also carry about 10^90 bits — a bit less than the photons. The gravitons carry much less, about 10^88 bits. A difference in exponents of 2 might not look like a lot but one can almost ignore any of the earlier numbers once a larger exponent appears.

sq_ 7y ago

I find it interesting that he mentions gravitons as a definite piece of particle physics, on the same order as photons, etc. I was under the impression that gravitons were simply one part of one possible conception of quantum gravity, and that we were definitely unsure about whether or not they exist.

K0SM0S 7y ago
Since this is coming from a physicist / mathematician, I immediately assumed it meant the placeholder for those — i.e. whatever conveys gravity, all of it must hold that many bits to describe the observable universe.
ahuth 7y ago
The same thing stuck out to me, and definitely seemed presumptuous. However, I'm not a physicist, so what do I know? Maybe one way of looking at it is that despite the fact that gravitons are hypothetical, we can still do the math and calculate the amount of entropy or information that they would/could contain.
auntienomen 7y ago
Gravitons are speculative in that they haven't been observed, but they're almost certainly the correct language for describing mild quantum corrections to general relativity. Simple scaling arguments show that _any_ theory of quantum gravity that reduces to general relativity at low energies passes through a regime where it can be described by gravitons. Whether gravitons are fundamental objects in quantum gravity is irrelevant for the kind of state counting Baez is talking about.
- sq_ 7y ago
  Thanks for the explanation!

drskaugen 7y ago

The image is awesome!

badrabbit 7y ago

I thought you 0 kelvin was the lowest possible value on the kelvin scale. How come this post mention negative kelvin values? Is it not temperature?

Sharlin 7y ago
There are no negative kelvin values in the article. 10^-30 is a positive number.
transitorykris 7y ago
If you're referring to "there will be a cosmological event horizon surrounding each observer, which will radiate Hawking radiation at a temperature of roughly 10-30 kelvin" this is a very tiny fraction: https://www.wolframalpha.com/input/?i=10%5E-30 https://www.wolframalpha.com/input/?i=10%5E-30
- badrabbit 7y ago
  I was referring to that, my mistake, and thank you very much!
jandrewrogers 7y ago
I don't see negative Kelvin in the article. I do see Kelvins with a negative exponent, which is just a positive value that asymptotically approaches zero.
- badrabbit 7y ago
  My mistake, I thought that notation implied negative numbers. Thank you.
  - johncarlosbaez 7y ago
    I was saying that the temperature of the Universe in the far future will be about 0.000000000000000000000000000001 kelvin, if our current theories are correct. This is 10^(-30) kelvin.

acqq 7y ago

From the comments of the author: "You can puzzle your group by asking whether entropy increases as clouds of gas and dust in the early Universe collapse and form stars and planets. If it doesn’t increase, this process violates the Second Law. So it must increase. But why is it increasing? It seems that order is increasing… so doesn’t that mean entropy is decreasing? If someone can’t answer this puzzle correctly, they don’t understand how thermodynamics works in our Universe." So, who knows the right answer to the puzzle: where and how the increase of the entropy happens? (I also suggest that those who really know should wait for some hours... I'd first actually like to see some wrong answers which try to be right but don't manage to be -- just to get some better picture of the readers here -- I don't know if this will work).

t156654 7y ago
The question is based on a false premise. What the Second Law of Thermodynamics states is that the entropy of an isolated system is never decreasing. Is the Universe an isolated system (meaning it cannot exchange matter or energy with its environment across its boundary)? We don't know anything about the boundaries of the Universe, or if it has any at all, therefore the 2nd law doesn't apply. QED.
- acqq 7y ago
  Based on our observations we can see a lot of galaxies as in practice isolated systems, and for each separate galaxy second law still holds. So this attempt for explanation fails to answer the question.
  - lostmsu 7y ago
    No galaxies are particle isolated, as all of them emit radiation.
Ono-Sendai 7y ago
Entropy increases because its much more likely than for it to decrease. And the reason higher entropy states are more likely than low entropy states are that there's more of them.

foxes 7y ago

Entropy is not disorder. It is S ~ log #{microstates} For hn readers, microstates you can think of as a configuration of a system, so its counting number of configurations. Disorder is not well defined. Stop using the word disorder with entropy. A bunch of more complicated elements have more configurations than just pure H.

BLKNSLVR 7y ago
My interpretation is that "order" and "disorder" are subjective. One person's order is another's disorder. For example, my wife and I have differing tolerances of "order" as it pertains to the tidiness of a room. That may seem far separated from the topic at hand, but if a thing is able to be somewhere, then it's purely subjective as to whether it's the right place, ie. ordered. There's a time component to it as well, I might have a bunch of in-progress things laying around, but that's the correct place for those things for the current moment, for me. In parallel, however, it's most definitely the incorrect place, at all times, according to my better half. Potential Configurations = n Configurations considered "order" by me: x Configurations considered "order" by milady: 1 Configurations considered "order" by the universe: 0 Configurations considered "order" by the universe at this point in space and time: 1 That which is, is order. That which isn't, is not. Reminds me of this scene from Hi Fidelity: Dick: It guess it looks as if you're reorganizing your records. What is this though? Chronological? Rob: No... Dick: Not alphabetical... Rob: Nope. Dick: What? Rob: Autobiographical. Dick: No way.
spectramax 7y ago
This may be correct but its useless to make any engineering sense out of it. For engineering and practical intuition, use the following definition that we used at an Ivy-league college in US: https://en.wikipedia.org/wiki/Entropy_(energy_dispersal) https://en.wikipedia.org/wiki/Entropy_(energy_dispersal) Quoting the article: > Even though courses emphasised microstates and energy levels, most students could not get beyond simplistic notions of randomness or disorder. Many of those who learned by practising calculations did not understand well the intrinsic meanings of equations, and there was a need for qualitative explanations of thermodynamic relationships.

ShamelessC 7y ago

The article got me thinking about the universe's mass distribution. Is the number of galaxies at any edge of our observable universe similar to the number of galaxies in our observable universe? tl;dr does the (entire) universe have a uniform distribution of mass? Now, I'm aware that the universe has always been expanding from every point in all directions since the singularity before the big bang. This means that effectively 1.) every point in the universe can make the claim of being "at the center" 2.) none of them can 3.) the question is meaningless Which of those answers you find satisfying is more of a philosophical question which I'm not concerned with for this question. My question is this - if we were to somehow reach the edge of our universe instantaneously, simply to observe what things looked like from that point of view, would we find that there's roughly the same distribution of stars/galaxies/matter in all directions? I'm aware that questions with the premise that FTL/instantaneous travel is possible tend to be "unknowable" to a degree. Perhaps another way of wording it would be - do we expect the amount of matter to be of a uniform distribution in every spot in the universe? Is it impossible to know? Or can we use models of the big bang theory to predict that the distribution is roughly equal everywhere? Some philosophical implications that are curious but are probably scientifically meaningless: If there's reason to believe that there is a uniform distribution of mass in all observable universe, and the universe is infinite, does that imply there are an infinite number of galaxies, all of which are inaccessible if they're outside our observable universe? If so, is out ever appropriate to consider these infinite observable universes as essentially a multi-verse, containing many combinations of observable universes, one of which is statistically likely to be similar to our own observable universe? As always with questions regarding the size of the universe, it's center, etc. I suspect the answer will be "it's a meaningless question because we can never know", but I'm hoping that research into the big bang itself could provide some evidence. Please let me know if I haven't used proper terms or am making a critical mistake in my current understanding of astronomy.

aeternum 7y ago
The way I understand it is that there is not really an edge. Spacetime itself is expanding, the best analogy I've heard is consider a spherical balloon that is being inflated. We exist as two dimensional beings on that balloon. No matter where you put two dots on that balloon, they will move further apart. You could also draw a circle on the surface of that balloon which represents the furthest points that we can reach if we traveled at the speed of light. Nothing outside that circle would be observable to us, so it could be argued that it doesn't exist.

Zamicol 7y ago

The total entropy of all the stars, 10^82, is 2^270 I love this, because the useful 256 bit string (2^256) is only 43 characters long in base64, and to get to 2^270, it is only 45 base64 characters. I was just playing with this on Thursday, January 9th 2020 because I wanted to predict how many bits I needed to address every atom in the observable universe, which also just so happens to be 10^82. I use this example to depict the power of cryptography.