Welcome to this week’s installment of the From Eternity to Here book club. Today we look at Chapter Two, “The Heavy Hand of Entropy.”
[By the way: are we going too slowly? If there is overwhelming sentiment to move to two chapters per week, that would be no problem. But if sentiment is non-overwhelming, we’ll stick to the original plan.]
Excerpt:
While it’s true that the presence of the Earth beneath our feet picks out an “arrow of space” by distinguishing up from down, it’s pretty clear that this is a local, parochial phenomenon, rather than a reflection of the underlying laws of nature. We can easily imagine ourselves out in space where there is no preferred direction. But the underlying laws of nature do not pick out a preferred direction of time, any more than they pick out a preferred direction in space. If we confine our attention to very simple systems with just a few moving parts, whose motion reflects the basic laws of physics rather than our messy local conditions, there is no arrow of time—we can’t tell when a movie is being run backward…
The arrow of time, therefore, is not a feature of the underlying laws of physics, at least as far as we know. Rather, like the up/down orientation space picked out by the Earth, the preferred direction of time is also a consequence of features of our environment. In the case of time, it’s not that we live in the spatial vicinity of an influential object, it’s that we live in the temporal vicinity of an influential event: the birth of the universe. The beginning of our observable universe, the hot dense state known as the Big Bang, had a very low entropy. The influence of that event orients us in time, just as the presence of the Earth orients us in space.
This chapter serves an obvious purpose — it explains in basic terms the ideas of irreversibility, entropy, and the arrow of time. It’s a whirlwind overview of concepts that will be developed in greater detail in the rest of the book, especially in Part Three. As a consequence, there are a few statements that may seem like bald assertions that really deserve more careful justification — hopefully that justification will come later.
Here’s where I got to use those “incompatible arrows” stories I blogged about some time back (I, II, III, IV). The fact that the arrow of time is so strongly ingrained in the way we think about the world makes it an interesting target for fiction — what would happen if the arrow of time ran backwards? The straightforward answer, of course, is “absolutely nothing” — there is no prior notion of “backwards” or “forwards.” As long as there is an arrow of time that is consistent for everyone, things would appear normal to us; there is one direction of time we all remember, which we call “the past,” when the entropy was lower. It’s when different interacting subsystems of the universe have different arrows of time that things get interesting. So we look briefly at stories by Lewis Carroll, F. Scott Fitzgerald, and Martin Amis, all of which use that trick. (Does anyone know of a reversed-arrow story that predates Through the Looking Glass?) Of course these are all fantasies, because it can’t happen in the real world, but that’s part of the speculative fun.
Then we go into entropy and the Second Law, from Sadi Carnot and Rudolf Clausius to Ludwig Boltzmann, followed by some discussion of different manifestations of time’s arrow. All at lightning speed, I’m afraid — there’s a tremendous amount of fascinating history here that I don’t cover in anywhere near the detail it deserves. But the real point of the chapter isn’t to tell the historical stories, it’s to emphasize the ubiquity of the arrow of time. It’s not just about stirring eggs to make omelets — it has to do with metabolism and the structure of life, why we remember the past and not the future, and why we think we have free will. Man, someone should write a book about this stuff!
Sean:
One of the three properties of time that you mentioned is that it orders events. At the quantum level, superposition of states implies an absence of ordering until the wave function collapses. Does this imply that time is an emergent phenomena? And, if we wind the universe back to the big bang singularity, could this imply that the low entropy at the beginning is a quantum property?
Rob, I don’t think it’s right to say that quantum mechanics implies that events aren’t ordered. It just becomes the case that the wave function is ordered: at one time it has a certain value, at the next moment it has some other value, and so on. And it certainly doesn’t imply a low-entropy beginning; there would be nothing incompatible about a high-entropy beginning and quantum mechanics.
I vote for 2 chapters a week.
The Past Hypothesis that you mention at the end of chapter two is used to explain the relative order that we observe. But it seems like this raises as many questions as it answers…
So we have our orderly observations and we want to explain them. To do this, we need some context to place our observations in. So we postulate the existence of an orderly external universe that “causes” our observations. But then we want to explain what caused this external universe…and the only option is to postulate the existence of a much larger multiverse. But then what explains the multiverse? A multi-multiverse?
This leads to the need for an infinite series of ever larger contexts against which to explain the previous context that we used to explain the previous context that we used to explain the fact of our initial observations.
It would seem that nothing can be explained in terms of only itself. To explain it, you have to place it in the context of something larger. Otherwise, no explanation is possible, and you just have to say, “this is the way it is because that’s the way it is.”
Basically it seems to me that there’s only two way the process can end. Two possible answers to the question of “Why do I observe the things that I observe?”:
1) Because things just are the way they are, and no further explanation possible.
2) Because EVERYTHING happens, and so your observations were inevitable in this larger context of “everything”.
Do you see some other option? Some flaw in the reasoning?
In either case it seems like science doesn’t so much explain things as just describe (in a compressed and somewhat “lossy” format) what we observe. A subtle but significant difference I think. Do you see any significance in the difference?
Yes, I think there is a flaw. We need to explain the low entropy of the observed universe, because it seems very unnatural to us. But if we can find an explanation, e.g. in terms of a multiverse, it may very well be that there’s nothing at all unnatural about the evolution of that multiverse. Otherwise it wouldn’t be much of an explanation at all.
The thing that needs to be explained is not “the universe exists,” but rather “our observable part of the universe begins in a very finely-tuned state.”
I vote for keeping to 1 chapter a week. Some of you crazy smart people might just be breezing through this book, but I think there were a few time newbies in the group, and as one of them, I need the week to read, re-read, and process what I just read.
But I won’t drop behind if the votes are overwhelmingly for 2.
Would you say that Entropy had a specific moment it started, and what sort of particle density was present at this moment?
Does Entropy have a “constant” speed, is there a varying speed of Entropy?.. if so will it’s speed of conversion be greater in the future?
Is a Particle’s size relative to it’s contribution to Entropy?
Sorry I have not been able to purchase your book just yet, but I am dropping the birthday present hints on a regular basis!
best wishes pv.
Paul– entropy can be defined at any time, so it didn’t really “start.” The speed at which it changes can be highly variable, depending on what’s going on. And no, a particle’s size has no direct connection to its entropy.
The reversibility of our physical laws, you say, means that “if we knew the present state of every particle…we could deduce the future as well as the past.” (top p.43) I’m trying to figure out how we would DEDUCE the future. Suppose we slightly re-define possibilism as the view that the future MAY not exist. A possibilist could then ask, is there anything in our physical laws (+ the current state of the universe) that guarantees the universe will still exist at all in 3 minutes, or still exist with the same physical laws. To deduce the future, don’t we need this kind of guarantee?
Sure. If the laws of nature change in an unanticipated way (which “the universe ceases to exist” would certainly count as), you wouldn’t be able to predict the future. We are assuming that the laws are both known and reliable.
Firstly. Thanks for the book Sean. I am greatly enjoying it.
I have a question related to the first paragraph of page 41 (it actually starts on page 40).
It seems to me that this paragraph is making a probabilistic argument that the low entropy boundary condition at the start of the universe is required to trust our memories and thus the arrow of time. In other words, if “the past” had a high entropy, then it is less probable that a memory of a particular event in the past is accurate, than it is that that memory (and perhaps the person/brain that experiences that memory) exists on it’s own as a statistical fluctuation away from that high entropy state.
Firstly, could you please correct me if I have misunderstood this paragraph.
Secondly, if I have understood this correctly, does this mean that if there were not a low entropy boundary condition in the past, then it would not really be possible for us to be confident that there is an arrow of time? Also, would this leave us trapped in a Boltzmann brain style paradox?
I suppose for a physicist this is a quibble, as you know what you mean when you speak of the ‘laws’ of physics. That it’s an idiom, a quirk of usage, is not important as long as it doesn’t in itself bear the burden of explanation. As a writer and poet who happens to be fascinated by science, but very much an outsider… the usage bothers me. A lot.
As a poet, linguistic and cultural associations do matter, and ‘law’ suggests agency. A most unfortunate overlap there with the Intelligent Design folks (who or what passed these so-called ‘laws?’) More than that, it suggests a fixity which in the popular mind, leads to misunderstanding of how scientific theory develops. What is accepted as constant and unchanging, under different conditions and assuming additional evidence, necessitates modification… (so what is that about? one might ask. Do ‘laws’ change? Are these laws really not laws at all? Is that what ‘relativity’ is all about? That everything is relative and there’s no ‘truth’ and science is just another religion?” )
You see what I mean?
The use of this metaphor, drawn from legal usage, carries with it a whole set of interconnected associations, which, if you are not scientifically trained–or aware of scientific usage–is fraught with misunderstandings.
Out of concern for the tremendous importance of basic understanding of science for the general public, I think this deserves some attention–a clear, philosophically tuned explanation how this word is used and what it does and does not mean. Maybe even a new word.
Thank you for taking the time, and taking seriously the task of making science at the deepest level, accessible to the general public. There is no underestimating the importance of what you are doing here on Cosmic Variance–all of you who contribute to this forum are my personal heroes!
Sean ? really ?
” …we can’t tell when a movie is being run backward…
…”
To your credit, at least you said ” … The arrow of time, therefore, is not a feature of the underlying laws of physics, at least as far as we know …”
Of course the arrow of time is due to underlying physics, as overwhelming casual observations suggest, you just haven’t identified how yet.
When will physics realize that the whole Time Symmetry argument is fallacious ? As i understand it, the time symmetry notion can be argued by noting that the Feynnan diagram say, a pair creation:
photon p- + p+
… is indistinguishably correct when read from left to right (forward in time) or right to left ( ALLEGEDLY, the backward in time direction).
Time symmetry (bi-directionality) is easily shown to be fallacious because if we were to observe either of these half reactions in isolation, we would say that time is always proceeding in its forward direction. A pair annihilation ( right to left in above) when seen in isolation, IS occuring in the forward direction. The naive error here is simply to realize that when reading the above Feynman diagram right to left is abolutely equivalent to reading it upside down, left to right, in a forward time direction.
The unmeasured wavefunction is always in our past, a measurement is always in our ‘now’ and the wavefunction with its increased entropy is in our future. The entropy inexorably increases because the wavefunction ‘remembers’ or ‘incorporates’ the interaction in its interactions history and the new wavefunction is now the set of all allowed states that a new measurement might reveal, consistent with all previous interations the system has been involved in.
So, it is obvious that the arrows of time and entropy are driven and sustained by Conservation of information( interactions history). By the way, since NO system can avoid ALL interactions, immortality is impossible in principle and that is the quantum mechanical basis of ageing. Ageing is simply every system’s tendency to become progressively indistinguishable from those systems it interacts with ( its environment ).
You collect the Nobel, i’ll take the money, lol.
Nick– Everything you said is correct. We’ll cover this ground much more thoroughly in Part Three.
Jacob– What can I say except that it’s too late? “Law” is very deeply ingrained in scientific vocabulary by now. It is certainly not meant to imply any notion of agency; almost the opposite, in fact. It’s also not used very precisely — not because the usage is sloppy, but because there is no precise definition.
inDistinctMicrostate– The microscopic laws of physics, as we currently understand them, are perfectly reversible. We talk about this in great detail in chapter 7. The collapse of the wave function is the one possible exception, as we’ll discuss in chapter 11. Irreversibility comes from the state, not from the laws.
( sorry if any duplication – Saving an edit failed)
Sean ? really ?
” …we can’t tell when a movie is being run backward…
…”
To your credit, at least you said ” … The arrow of time, therefore, is not a feature of the underlying laws of physics, at least as far as we know …”
Of course the arrow of time is due to underlying physics, as overwhelming observations suggest, you just haven’t identified how yet.
When will physics realize that the whole Time Symmetry argument is fallacious ? As i understand it, the time symmetry notion can be argued by noting that the Feynnan diagram of say, a pair creation:
photon e- + e+
… is indistinguishably correct when read from left to right (forward in time) or right to left ( ALLEGEDLY, the backward in time direction).
Time symmetry (bi-directionality) is easily shown to be fallacious because if we were to observe either of these half reactions in isolation, we would say that time is always proceeding in its forward direction. A pair annihilation ( right to left in above) when seen in isolation, IS occuring in the forward direction. The naive error here is simply to realize that when reading the above Feynman diagram right to left is abolutely equivalent to reading it upside down, left to right, in a forward time direction.
The unmeasured wavefunction is ( in a sense) always in our past, a measurement is always in our ‘now’ and the wavefunction with its increased entropy is in our future. The entropy inexorably increases because the wavefunction ‘remembers’ or ‘incorporates’ or ‘records’ the interaction in its interactions history and the new wavefunction is now the set of all allowed states that a new measurement might reveal, consistent with all previous interations the system has been involved in.
An umeasured wavefunction is in a minimum entropysymmetric state ( since all observers agree on the represented set of allowed outcomes of any next measurement) and a measurement is a symmetry breaking event of zero duration(say) and the entropy of the wavefunction is in a new minimum ( but higher than previous) entropy state post interaction (measurement).
So, it is obvious that the arrows of time and entropy are driven and sustained by Conservation of information( interactions history). By the way, since NO system can avoid ALL interactions, immortality is impossible in principle and that is the quantum mechanical basis of ageing. Ageing is simply every system’s tendency to become progressively indistinguishable from those systems it interacts with ( its environment ).
You collect the Nobel, i’ll take the money, lol.
Hello,
Thank you for the great book. Your thoughts keep a mind fresh!
How does entropy affect vacuum energy?
Larry Kuklinski
PS: One Chapter per week is my vote. I have the time!
For your coffee quest consider:
http://www.starbucks.com/flash/sirena/default.htm
Lawrence– As far as I know, entropy doesn’t affect vacuum energy, it’s the other way around. As we’ll discuss later, the amount of vacuum energy determines the amount of entropy you can fit within an observable patch of the universe.
Hi Sean,
First, thanks for the great read. Couldn’t put it down and have plowed all the way through (including all the end notes). I’ve enjoyed your style and impressed by all your historical research.
I am content to re-read a chapter a week to stay with the discussion (and to prolong this enjoyable exercise as long as possible).
I think your proximity model (earth/updown; big bang/futurepast) elucidates your point quite well. The up/down distinction is mediated by GR where the earth curves space-time and we behave as the “law” requires in curved space-time. So the mechanism by which the future/past distinction is enforce is purely statistical in nature? Sounds like the objections Boltzmann encountered.
It seems the Dark side is the flip side of the observable universe.
A rollercoaster up then down to the dark tunnel.
lmk
Great achievement, this book, but I doubt that I’ll be able to keep up with the club, since I have several others open now. But I found my first error in it (gloat): P. 39, line 2, should be “describing a disk about half a degree across.” But I repeat: the book’s terrific.
Sean–this may be a silly question, and I haven’t really thought about it. But you say that the microscopic laws of physics are reversible. But in kaon and b meson decays, CP (and thus T) is violated. What does “reversible” mean in the context of C,P and T? I would guess that it might mean CPT invariance, not T, but what if CPT is violated at some level?
Upon further thought, it seems to me that CPT invariance is sufficient to establish reversibility. But there are lots of models that violate CPT (albeit often Planck-scale suppressed). Would an observation of CPT violation change your basic thesis?
Tom– Yes, the past/future distinction is statistical. But the statistics are really good! Boltzmann did run into this problem, but also much bigger problems. Very impressive that you read all the notes!
Jonathan– Good catch. If that’s the biggest error in the book, it will be miraculous.
Marc– Not silly. “Reversible” really means “unitary” or “information-preserving” — given the state now, we can reliably construct a unique state at any fixed time in the past. Related to time-reversal invariance, as we’ll discuss to death in Chapter 7, but not quite the same. If laws are reversible, you can always construct some sort of souped-up notion of time-reversal (like CPT) that will be conserved. I suspect the converse is true, but don’t know a theorem off the top of my head.
All my basic points rely on reversibility, but not directly on time-reversal invariance, so CPT violation wouldn’t matter too much as long as reversibility were maintained. (And if it isn’t, see Chapter 15 — I still don’t think it helps.)
If the boundary for the observable universe is the Big Bang and the theory of this book is that there was something else “before” it/ there is a multiverse etc., how can we know about what happened “before” if it is not observable? It seems like the answer to that would be that what happened “before” has an effect (dark energy, if my understanding is correct, isn’t observable but we can observe its effect – the accelerating expansion of the universe). If something isn’t observable and has no effect, than its existence doesn’t really matter right? So my question is (and perhaps you reach it later in the book) what are the effects of the multiverse/the other theories presented in the book that lead us to theorizing their existence? Is it maybe that because of what happened “before” or the multiverse etc. makes everything that we DO observe the way it is? I guess the rest of the book might be taking what effects we do observe and trying to prescribe causes to them (i.e. the multiverse etc.) so sorry if this question is what you try to explain in the rest of the book.
Sam– The idea would be that the observable impact is the low-entropy initial configuration of our universe. To gather confidence that this is the right explanation, of course, requires a great deal better understanding of what the underlying theory is and what it predicts. I talk about this issue a bit in the epilogue.
Sean, why do you describe the entropy of the Universe as ‘low’? Most observable (non-dark) matter is gas of some sort, and is thus has much higher entropy than if it had all condensed out into a crystalline solid.