## question about greene's "the fabric of the cosmos"

I have a question regarding the content of chapters 5 and 6 in Brian Greene's "The Fabric of the Cosmos." Although my question results from what I see as an inconsistency in what he has presented, I'm not claiming that my logic is flawless. In fact, I'm assuming that I've misunderstood something in his writing, and I need some help figuring out what it is. So here's my dilemma:

If time is a "frozen river," meaning that past, present, and future can be thought of as the same, what sense does it make to say that the overall entropy in the universe is increasing? If the universe was ordered in the past, and is disordered in the future, then clearly the past and future are not the same. More specifically, suppose I were to hold an egg in my outstretched hand, count to 10, and then drop it and watch it break all over the floor. At the beginning of my count, my "now" is that the egg is ordered. At the end of my count (or very shortly thereafter), my "now" is that the egg is disordered. Suppose further that Chewie (the character in Greene's book who is at the other end of the universe) is at his end of the universe walking toward me at a constant speed (perhaps a few miles per hour). His "now" at the end of my count would also say that the egg is disordered, but so will his "now" from the beginning of my count. In fact, to him, the egg has been disordered for many, many years.

And so, at the beginning of my count, my "now" tells me that the total entropy in the universe is the entropy of everything in the universe minus the egg plus the entropy of the UNBROKEN egg (low entropy), while Chewie's "now" tells him that the total entropy of the universe is the entropy of everything in the universe minus the egg plus the entropy of the BROKEN egg (high entropy). If each vantage point is to be taken as valid, how can the total entropy in the universe be two different numbers at once? It appears to me as though this only makes sense if we treat entropy as a type of information that can be transmitted only at or below light speed. If this is the case, however, then the concept of "entropy of the entire universe" makes no sense.

I would appreciate any and all thoughts on the subject. I'm rather stumped and it's beginning to annoy me! Thanks in advance . . .
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 Recognitions: Science Advisor You can't talk about the entropy of spacetime as a whole, if that's what you mean. When people talk about the "entropy of the universe" they mean looking at the entropy of some 3D spacelike cross-section of 4D spacetime.

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musik284,

 If each vantage point is to be taken as valid, how can the total entropy in the universe be two different numbers at once? It appears to me as though this only makes sense if we treat entropy as a type of information that can be transmitted only at or below light speed. If this is the case, however, then the concept of "entropy of the entire universe" makes no sense.
As far as we know, all information is limited to travel at c or below. I agree with your logic, and as JesseM says, the concept makes no sense.

M

## question about greene's "the fabric of the cosmos"

Just starting Ch.6, so I'll let you know what I think.

Must say Ch.5 absolutely blew my mind though.

Also you might want to read the notes at the end, really helped me understand a few of the things, the graph was really cool, and I'm about to start a topic about it.

Also quote from wikipedia

In chapters five and six, time has been explained only in terms of pre-modern physics. Chapter seven, Time and the Quantum, gives insights into time's nature in the quantum realm.

http://en.wikipedia.org/wiki/The_Fabric_of_the_Cosmos
 i read chp 5..... would like to know the veracity of his arguement

 Quote by JesseM You can't talk about the entropy of spacetime as a whole, if that's what you mean.
Really why not?

Different spacetimes have different entropies.

 Quote by musik284 If time is a "frozen river," meaning that past, present, and future can be thought of as the same, what sense does it make to say that the overall entropy in the universe is increasing?
You're missing the point of the "frozen river". The universe is not "moving" from past to present to future, it is just that the past is at one end of the frozen river, present is at the middle of the frozen river and future is at the other end of the frozen river.

If I draw a circle on the left side of a piece of paper, a bunch of arcs in the middle, and a bunch of scattered dots on the right side of the paper, we don't talk about the drawing "moving" from one state to another (unless we take the paper in slices and sweep across the page - but that is only one way to view the paper.) Taken as a whole, neither the paper nor anything on it is changing. We have order on the left side and chaos on the right. Period.

4D spacetime is the equivalent of the sheet of paper - i.e. no "passage" of time.

 Quote by DaveC426913 The universe is not "moving" from past to present to future, it is just that the past is at one end of the frozen river, present is at the middle of the frozen river and future is at the other end of the frozen river.
Events in spacetimes are not necessarily ordered right?

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 Quote by MeJennifer Really why not? Different spacetimes have different entropies.
I believe Penrose mentions in one of his books that there is no agreed-upon general definition of gravitational entropy in GR. And even if there was (in either GR or quantum gravity), it would likely be similar to the notion of black hole entropy in that it would allow us to discuss entropy changing over time, which would mean we were talking about the entropy of curved 3D space at a particular moment (relative to some foliation) rather than 4D spacetime as a whole. Talking about the entropy of spacetime as a whole would seem to require a phase space of all possible 4D spacetimes with a well-defined and physically motivated measure on this space (assuming entropy was still defined in the usual sense of statistical mechanics)--are you aware of any such mathematical definition? If so can you provide a reference?
 For entropy of particular spacetimes you might for instance want to look at Gibbons and Hawking - "Action integrals and partition functions in quantum gravity" Phys Rev (1977) Different spacetimes have different entropy "signatures".

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 Quote by musik284 I have a question regarding the content of chapters 5 and 6 in Brian Greene's "The Fabric of the Cosmos." Although my question results from what I see as an inconsistency in what he has presented, I'm not claiming that my logic is flawless. In fact, I'm assuming that I've misunderstood something in his writing, and I need some help figuring out what it is. So here's my dilemma: If time is a "frozen river," meaning that past, present, and future can be thought of as the same, what sense does it make to say that the overall entropy in the universe is increasing? If the universe was ordered in the past, and is disordered in the future, then clearly the past and future are not the same. More specifically, suppose I were to hold an egg in my outstretched hand, count to 10, and then drop it and watch it break all over the floor. At the beginning of my count, my "now" is that the egg is ordered. At the end of my count (or very shortly thereafter), my "now" is that the egg is disordered. Suppose further that Chewie (the character in Greene's book who is at the other end of the universe) is at his end of the universe walking toward me at a constant speed (perhaps a few miles per hour). His "now" at the end of my count would also say that the egg is disordered, but so will his "now" from the beginning of my count. In fact, to him, the egg has been disordered for many, many years.
Why would you think it is a dilemma to say that the past and the future are not the same? Saying that "time is a frozen river" does NOT mean that all parts of it are exactly the same. It only means that one can conceive of the "space-time continuum" in the same way one can think of a landscape- with time being one direction in that landscape. It doesn't follow that landscape is exactly the same in all directions!

 And so, at the beginning of my count, my "now" tells me that the total entropy in the universe is the entropy of everything in the universe minus the egg plus the entropy of the UNBROKEN egg (low entropy), while Chewie's "now" tells him that the total entropy of the universe is the entropy of everything in the universe minus the egg plus the entropy of the BROKEN egg (high entropy). If each vantage point is to be taken as valid, how can the total entropy in the universe be two different numbers at once? It appears to me as though this only makes sense if we treat entropy as a type of information that can be transmitted only at or below light speed. If this is the case, however, then the concept of "entropy of the entire universe" makes no sense. I would appreciate any and all thoughts on the subject. I'm rather stumped and it's beginning to annoy me! Thanks in advance . . .

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 Quote by MeJennifer For entropy of particular spacetimes you might for instance want to look at Gibbons and Hawking - "Action integrals and partition functions in quantum gravity" Phys Rev (1977) Different spacetimes have different entropy "signatures".
The first section of that paper is available online here--where do you get the idea that they are talking about the entropy of entire spacetimes, as opposed to the entropy of curved space at different moments? I don't claim to be able to follow the technical details, but nothing in what I read indicates that, and in fact they talk about deriving black hole entropy from their result, yet black hole entropy explicitly is about the entropy of curved space at a particular time (it is proportional to the area of the event horizon at that time), not the entropy of an entire spacetime containing a black hole. Also, the paper is printed in the book "Euclidean Quantum Gravity", and the wikipedia article on Euclidean quantum gravity says this approach involves formulating gravity as a quantum field theory--I'm sure that if you talk about entropy in the context of quantum field theory, you're talking about a time-dependent notion of entropy, not a global entropy on an entire spacetime.

edit: Also note that this page says in the path integral approach makes use of ADM formalism, and ADM formalism involves foliating 4D spacetime into a collection of 3D surfaces so that one can rewrite the equations of GR in terms of the dynamics of space over time using a Hamiltonian.
 The issues that came out for me in these chapters (and I just got out of the bath from reading chapter 5) were more philosophical. It was the DVD metaphor that really got me thinking and made me feel a little uncomfortable. The fact that the actors in the film could be skipping happily through our concept of time and when paused on a particular frame and questioned would be happy enough in their own reality to not understand the irregularity of their movement through my concept of time. This lead me on to to think deeply about the 'frozen river of time' and that every moment that has existed, is existing and will exist all exist outside of my concept of time. Meaning on a more human level that every thing that I have done, am doing and am going to do - each moment - has, does and will always exist. It kind of takes a lot of the concept of me out of the picture and makes me think we are all just on our own DVD; our story already written and out there existing. Which makes me consider why it is that only sentient life as ourselves, forcing frames of time that exist to use in a 'flowing' state (or that we are able to for that matter) if the universe and everything else in it is not subject to this concept. Also for the 'frozen river' idea to work, it implies that our universe's beginning (if it has one) now and end (if it has one) exist all the time. This is slightly puzzling to me when I consider ideas from the big bang and more so (from 'The Elegant Universe') the possibility that the universe could have come into existence (as we know it) by two branes clashing together giving way to a big bang. And that two branes clashing together would not be a one-off experience. Meaning that the brane that our universe is in may have clashed with another over and over again, meaning that our universe may have taken on many, many other forms. Considering that time as we know it may be limited to our experience, every moment all of these other universes (in the brane on which we are situated) would need to always exist too. But I'm sure I've gone to deep into that. It certainly is difficult to think beyond our linear experience of existence. I am just an enthusiastic after all, with little real physics background. But this chapter certainly got me thinking... it's been fairly mind-blowing for me so far. One other idea that popped into my head was the probability waves of particles, the fact that they exist in the first place and the fact that they disintegrate when we study them. I was thinking that if our time concept was exclusive to us and other life like us and that the universe followed the 'frozen river' metaphor, would it not be possible that the probability wave is related to the particle's whole existence, its past, now and future, all being the same, existing always; perhaps a marker to where it is, where it's been and where it's going to be and it disintegrates when examine it, or 'snapshot' it and force it into our time construct momentarily. I'm not sure I've explained that idea so well, it sounded great in my head. Sorry to bore anyone on my first post, I was just at home alone when I read that and needed to discuss and this was the first off google that was related to the subject!

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Hello Musik...

Anyone who can read those chapters and FULLY understand them will garner the more nobel prizes than have been awarded in all of history!!! Nothing is fuzzier than time and entropy.

You posted:
 If time is a "frozen river," meaning that past, present, and future can be thought of as the same...
In Chapter 5, Green does NOT say they are "the same"...he does say that

 Einsteins relativistic reality treats all times equally
but that's different.

He also says
 ...Is science unable to grasp a fundamental quality of time that the human mind embraces...
meaning,past,present,future...he can't answer that question!!! nor can anyone else!

You posted:
 Meaning ....that every thing that I have done, am doing and am going to do - each moment - has, does and will always exist.
While hard to fathom in most respects, this was easier for me. Just as I can never observe the entire universe because my cosmological horizon is limited I can accept that maybe there is an analogous observational limitation with respect to time. If time passes at the speed of light, for example, there would appear to be severe observational limitions on past and future. This is a personal observation, a bit crazy, but no more crazy than the fact that two different observers see each the others time a passing at different rates but their own time passing normally!

You posted:
 Considering that time as we know it may be limited to our experience, every moment all of these other universes (in the brane on which we are situated) would need to always exist too.
I disagree...don't see any logic in that assertion..but it seems irrelevant to your main areas of concern.

 If each vantage point is to be taken as valid, how can the total entropy in the universe be two different numbers at once? It appears to me as though this only makes sense if we treat entropy as a type of information that can be transmitted only at or below light speed. If this is the case, however, then the concept of "entropy of the entire universe" makes no sense.
I think the issue here is that different observers each have their own cosmological horizons which may or may not overlap..So different observers will in general "see" (observe) different things.....your observers included.

Entropy and thermodynamics can be considered as special cases of information theory. But no one knows exactly what entropy really is any more than they know what time is....as you may know black hole horizons reflect information and entropy in ways that apply here....those surfaces are every bit as crazy as this discussion...

As a final comment, think you are annoyed because
 "then ... the concept of "entropy of the entire universe" makes no sense....
just wait until you discover the multiverse...parallel universes!!! Maybe time comes from and passes to parallel universe(s) (again a personal observation) just as in string theory gravity is sometimes posited to leak out.

 Tags entropy, greene, relativity, time

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