This was a great read! But I wish the article would have mentioned how tiny the microscopic time-reversal effects are, compared to macroscopic time reversal. The microscopic effects are too small to explain why we have such a clear direction of time.
Our direction of time is defined by the observation that entropy (or "chaoticness") always increases with time. If you mix orange juice with water, you will not see the result unmix itself again, even though the interactions between the individual molecules are perfectly reversible.
In fact, you can build a toy-universe in your head, where all interactions are time-reversible, and you would still observe that the chaotic-ness increases with time, unless you start with a completely random initial state (in which the chaoticness stays roughly constant). This increase in chaoticness is comletely unsurprising: It's a simple consequence of the fact that there are much, much more "states" in which a system looks chaotic, than states in which it looks ordered. Therefore, a system transitioning from state to state is much more likely to be in one that looks chaotic, and very, very unlikely to ever go back to a state that is non-chaotic.
The real mystery, for me, is: Why was the initial state of our universe so completely non-chaotic? Why did the universe not start out in a state that is essentially equal to the heat-death [1]? The microscopic processes that are not time-reversible might have something to do with this, but it's not clear at all how they can solve this mystery.
Those questions are very old. You may think the anthropic principle is sufficient here: complex systems seem to rely on an entropy gradient (no life exists in an uniformly chaotic or static state). Ludwig Boltzmann made this argument in the 19th century [1].
However, the argument can apparently be extended to the conclusion that, in a probabilistic sense, your consciousness is just a sliver of a random fluctuation of a near-maximal entropy state. Feynman argued[2] that this shows we do not arise from a random fluctuation, because (even though we're conscious), when we look far away the universe looks highly organized.
Note that those arguments make a bunch of assumptions that may not be valid in our universe, and may not make cosmological sense (entropy is not well defined cosmologically).
>Feynman argued[2] that this shows we do not arise from a random fluctuation, because (even though we're conscious), when we look far away the universe looks highly organized.
Oh that is an interesting and compelling argument I have not heard! Thank you for sharing.
Both Boltzmann's idea of fluctuation and Feynman's argument against it are unfortunately devoid of meaning, because we do not know how highly organized and thermal death universe look like. We never saw and probably never will see another state of the universe and there is no way to experiment with it.
His argument is sound. If there is infinite #s of universes, or the universe keeps reforming infinitely (implication being it will have varying degrees of uniformity), then it's mathematically probable that we would be boltzman brain's in a less coherent universe. We don't observe that.
We don't know whether what we observe is more coherent than the majority of universes, because we have never observed other kind of universe. The very fluctuation hypothesis and the argument against it have no solid basis in science.
The context of those arguments is almost metaphysical. When you ask 'Is it more likely my consciousness is a local random fluctuation of some large system or the result of a one-off process?' you have to imagine you may be part of some abstract system that satisfies our notion of time and has rich enough dynamics to comport entropy and intelligence, but this universe could look nothing like ours, and you have to notice you are abusing probability, which is nothing more than a model of uncertainty and not an Oracle of reality.
But if you're willing to make some assumptions, Feynman's evidence for the latter seems valid.
> Our direction of time is defined by the observation that entropy (or "chaoticness") always increases with time. If you mix orange juice with water, you will not see the result unmix itself again, even though the interactions between the individual molecules are perfectly reversible.
Entropy does not always increase in time, because entropy is rarely a function of time. The most common meaning of the word is a thermodynamic quantity that is not, in general, defined in non-equilibrium states. It is a function of state variables rather than time.
What people are talking about when they say "entropy increases in time" is actually some variant of minus Boltzmann H-function. This kind of resembles thermodynamic entropy, but is a distinct and less general concept. There are processes where entropy gets higher but "entropy" (minus Boltzmann H-function) get lower.
If you mix oil and water, you will see the result does unmix itself again. Does this mean entropy decreased and time direction got reversed? Nah. It is not even clear how to define entropy of the system in between, since it is in highly non-equilibrium state.
>If you mix oil and water, you will see the result does unmix itself again. Does this mean entropy decreased and time direction got reversed? Nah.
Moving an object to higher gravitational potential decreases the entropy of the system (and thus requires work, unsurprisingly).
Mixing oil into water means you displace some volume of water which were closer to Earth with oil bubbles (which are lighter than equivalent volume of water) while you force the displaced water volume higher/further from Earth. Thus by mixing lighter oil with heavier water you decrease the entropy of the gravitational system consisting of the oil, water and Earth. Left to its own devices, the system evolves along the entropy increasing gradient - heavy water goes down displacing lighter oil up, thus decreasing the gravitational potential of the system (the friction during that "unmixing" is the work of the gravitational force that ultimately results in the heat that is lost away into the environment).
When the fluids are mixed by a spoon, surely work has been done by the stirring spoon on the system and energy of the system increased. But this does not by itself imply entropy of the system increased. The reason is the system got to a non-equilibrium state which has no macroscopic thermodynamic description and no unique way to assign entropy and detect its changes.
Entropy always increases over time within a closed system, except in idealized interactions that leave entropy unchanged, which are not practically possible. From what we know, the only thing that might actually be a true closed system is the universe. If you've identified some system that has decreased in entropy, then you've failed to notice something outside of it that has increased in entropy by a greater amount.
Is it possible that our understanding of entropy is flawed? Yes. But unless you have some novel physics experiment or mathematical model to share with us, I'll stick with the second law of thermodynamics.
>But this does not by itself imply entropy of the system increased. The reason is the system got to a non-equilibrium state which has no macroscopic thermodynamic description and no unique way to assign entropy and detect its changes.
Entropy is the tendency to equilibrium. Your earlier statement, that entropy is only a measure of systems that are in equilibrium, is false. If you were right, entropy would be a totally meaningless notion because there are no closed systems and true equilibrium (as opposed to the near-equilibriums that we work with in practical terms) can only exist in one.
My response here is actually overly-simplistic and somewhat wrong. effie is right about classical thermodynamics only defining a measure of entropy (and various other properties of a system) for idealized states of equilibrium. There's been some attempts to define entropy for non-equilibrium systems, but our understanding is incomplete. It's partially a philosophical debate too.
Admittedly, the concept of entropy density has been used somewhat successfully for description of continuum close to equilibrium. But there are problems with extending this to general non-equilibrium case. I think a mix of oil with water is rather awkward to describe thermodynamically, because it is unstable and it is hard to introduce thermodynamic description for a fluid consisting of many drops of oil of different sizes scattered in water.
Second law of thermodynamics can be phrased in terms of entropy, but it does not really involve time at all. All it says is after process involving no heat transfer is finished, entropy of final equilibrium state is not lower than entropy of initial equilibrium state.
>But this does not by itself imply entropy of the system increased.
doesn't matter what way it got there, entropy of the gravitational system oil-water-Earth is lower and the gravitational potential is higher when oil bubbles are inside the water when compared with the same system in the state when all oil is on top of the water. Thus system naturally moves from the former state to the latter, from lower entropy to the higher, from higher gravitational potential to the lower.
Of course, gravitational potential energy of the system is higher when the oil is scattered temporarily in the water, because the water is higher than it would be in equilibrium state. However, I do not see how this has anything to do with the concept of entropy. The non-equilibrium state cannot be easily assigned thermodynamic entropy, because there is no obvious thermodynamic state variable that could describe the state of mixed water and oil. If you know how to introduce such a variable and corresponding entropy, then please explain it.
>However, I do not see how this has anything to do with the concept of entropy.
in short - entropy of the system with lower gravitational potential is higher (https://en.wikipedia.org/wiki/Entropic_gravity). When oil is mixed into water, the thermodynamic entropy "St,mix" of oil/water system is higher than "St,unmixed" while the entropy "Sg,mix" of the gravitational system of oil/water/Earth is lower when mixed than the "Sg,unmixed" of the unmixed case. In case of bad solubility, like oil in water, we have ["St,mix" - "St,unmixed" < "Sg,unmixed" - "Sg,mix"] and thus system on its own will evolve toward unmixed state.
Entropic explanation of gravity force is not an accepted physics theory. Regardless of whether it is right or not, the concept of entropy in common thermodynamics I was referring to above is different from that in entropic gravity. In thermodynamics, in contrast with theories of entropic forces, entropy is assigned only to states of thermodynamic equilibrium that can be achieved by exchanging heat reversibly. State that is not a state of mechanical equilibrium (such as state of accelerating bodies, unmixing water+oil) is not such a state.
the thermodynamics (and specifically the notion of "heat") is just statistical/aggregate description of the interaction between the forces which are subject to the same entropic description like the entropic gravity and obey the same 2nd law. It is not surprising once you see that "minimal action principle" is just the 2nd law ("entropy evolves along the gradient") expressed using the language of Lagrangian in mechanics. Thus all the known forces are subject to it, ie. in addition to gravity electromagnetic forces is subject to the same, and the Schrodinger too. That allows to calculate and use entropy for the whole system along its whole evolution path.
Your statements are incompatible with classical physics developed for centuries and enjoying high level of acceptance. The concept of thermodynamic entropy brings nothing to understanding of mechanics. There is no time in thermodynamic theory, thermodynamic entropy is not a function of time so there is no possibility of deriving equations of motion of mechanics from the laws of thermodynamics. You may need to study mechanics and thermodynamics and their history from several books before you realize that.
well, i have MS in Math with ~3.85 GPA (all A except for ROTC program and English) from one of the best math school in Russia which also included graduate level courses in mechanics, mathematical physics, etc.
What about you?
>there is no possibility of deriving equations of motion of mechanics from the laws of thermodynamics
i didn't say that. It actually works the other way - thermodynamics is derivable as an aggregation from the laws of motion. And thermodynamical entropy is just a facet of the entropy (which in general can be defined using relative volume in the space of states of possible configurations of the system for a given values of generic coordinates)
I have a hard time to understand what you mean by "aggregation" and "facet of the entropy which in general can be defined using relative volume in the space of states of possible configurations of the system for a given values of generic coordinates". Please post a link to some exposition of your theory, I'd like to take a look.
As I understand it, the universe actually started in a heat-death state (very small temperature differences, homogeneous and isotropic), it's just that it is a very hot heat death state, not the usual cold one where everything freezes.
Then it is the universe expansion that made the entropy per volume decrease, actually allowing complex systems to evolve. The expansion still has to occur faster than the entropy increase rate but I read somewhere that the universe total entropy did not increase that much since the Big Bang.
>The real mystery, for me, is: Why was the initial state of our universe so completely non-chaotic? Why did the universe not start out in a state that is essentially equal to the heat-death [1]?
taken as a closed system, our Universe's initial state was a heat-death and it would stay here, nothing would happen. Fortunately or unfortunately our Universe is embedded into previous very old and cool Universe, and this gradient is what drives the expansion of our Universe and thus provides for all the things we see happening to happen, including life (which is just entropy maximizing process in some conditions).
100-200+B year later our Universe will too be very cool and expanded very "thin". The matter will be collected into several hyper-super-black holes with Schwarzschild radii of tens or even hundreds o billions of light years - some probably bigger than our visible Universe (which has 10B light years Schwartzild radius). The matter inside a regular black hole is neutrons being driven into higher and higher states as result of mass being added into the black hole. At some point the neutrons get to split into gluons/quarks and those would continue to be driven into more energetic states as more mass is added, and may be split as a result into something else too. At the same time the space around becomes "thinner" and cooler. At some point, when even more mass is added, and thus this "soup" becomes even more energetic, beyond currently known physics unfortunately, something happens to the gravitational force what has been keeping it together and it explodes and start expanding (as there is extremely high gradient between the "soup" and the space of the old Universe - thus that will be a birth of new Universe inside our old Universe, inside the parent Universe of our Universe ... ad infinitum ... with non-zero gradient, though smaller and smaller as parent-child Universe pair is getting older...
> Therefore, a system transitioning from state to state is much more likely to be in one that looks chaotic, and very, very unlikely to ever go back to a state that is non-chaotic.
This one thing I don't understand about the 2nd law of thermodynamics: given enough time won't the system go back to a more organized state simply by chance? And in that case, wouldn't the total entropy be reduced?
As entropy is usually a probabilistic concept, a "more organized" future is very very unlikely, but not impossible. Numberphile has a video[1] that discusses the Poincaré recurrence[2] time for the universe. So while it may be possible, you probably have top wait about 10^10^10^10^2.8 "Plank times, millenia, or whatever"[3] for a state to occur.
Yes, that can happen, but with overwhelmingly small probability. Say if you consider the probability that all the gas atoms in a box spontaneously are in one half of the box, the chance is approximately (1/2)^N, where N is on the order of Avogadro's number.
You understand it just fine. What may be nonintuitive is the incredibly low change of that happening even in microscopic scale. Difference between macroscopic 'organized states' vs 'unorganized states' just mind mindbogglingly huge.
If the model is Hamiltonian and the phase space finite, then any state will get eventually reapproached. For systems with infinite phase space (infinite volume suffices) or non-Hamiltonian systems, such conclusion may not be true.
As others said, your understanding is fine - you just need to gain the appreciation to how much more unordered states are there for a system to be in than the ordered ones. My physics professor used to underscore it by drawing diagrams that show a line that suddenly goes from almost 0 to "the tip of this line is somewhere in the next galaxy".
Or to give you a somewhat similar problem - consider a 32x32px 8bit image (a standard Windows icon since version 3.0). The image consists of 1024 pixels, each capable of representing a different color from the set of 256 colors. How many possible pictures like this are there? Or, as you'd ask in thermodynamics, in how many states such a system can be? It's 256 states per pixel raised to 1024th power (just like 6-digit binary number has 2^6 possible values). It's 256^1024. You know how much is it?
Now ask yourself, how many of those pictures represent a letter "A". Quite a lot probably, but nowhere near that much. In all those 256^1024 pictures, you have every possible representable letter A, as well as any other possible Unicode character. In those images are all your most cherished private photos (or at least their thumbnails), and also the photos of all things that you'd wish happened but didn't. A thumbnail of every possible photo of the universe is there as well.
There's also something else. Something much more frequent than all other image I've just mentioned taken together. It's the noise. The things we don't recognize, the things we consider uninteresting. I ask you, use your intuition - if you were to create a random Windows icon every second, how soon would you expect to get one depicting a letter "A"?
And now realize we were talking about silly icons that are probably barely visible on your screen.
There are 6.02 x 10²³ atoms in 12 grams of carbon. I.e. in a tip of your pencil. 602000000000000000000000 atoms. Those are your pixels. And if you want to compute the number of states this pile of atoms can be in, that is the number that goes in your exponent. The base is some combination of possible positions, orientations and velocities, and then probably something else I'm forgetting right now. And almost all of those states are noise. That's how the Second Rule works.
The Digital Library of Babel (https://libraryofbabel.info/) was posted here a while ago, which is a tangible way to search through this space. The library comes from a book by Jorge Luis Borges, which has all possible books, meaningful and not. The people in the book are searching for books with meaning, but the chance of finding one is really small. The digital library lets you do the search electronically. Kind of fun to play around with.
It also has a link to the Universal Slideshow. Which let's one browse every image (of a given size) that represents what TeMPOral was talking about.
Ever since I discovered that site I've been slightly obsessed with it. In the "This is really interesting" sort of way. It makes one think how everything is noise. We just happen to find meaning in some of it.
It's funny though as I had a very similar idea some years ago sticking much with virtual machines. I thought that if VM's disk image is just a file represented by sequence of zeroes and ones and what if someone would generate a final number of those images starting from 0...0 to 1...1 and then probe them all on a given emulated hardware what would be a chance to discover some viable/useful software? How would we detect it? How would we know or reverse engineer it to understand what it could be used for and how to use it, interact with it etc.?
So I ended up thinking that it would be a project similar to SETI but on a smaller scale (let's say if the image size would be limited to just 1Gb).
>Our direction of time is defined by the observation that entropy (or "chaoticness") always increases with time. If you mix orange juice with water, you will not see the result unmix itself again, even though the interactions between the individual molecules are perfectly reversible.
Perhaps in zero-g, under the effect of no acceleration and/or gravity. But I've seen all (most of) the non-water bits settle in the bottom of a bottle left alone for a long time.
That doesn't detract from your overall point about entropy, but it's probably to use an example based on the quality of energy (try to generate electricity from the heat that leeches from the walls of your cabin in winter).
> The real mystery, for me, is: Why was the initial state of our universe so completely non-chaotic?
Here's a possibility: if you "start" at a random state, after enough exploration of the state space, there would be a local minima that was arbitrarily well-ordered. Both directions of time would then view that as the "past", and the other direction as "future".
These perceptions as to the arrow of time would last until a state equivalent to heat death is reached, at which point the "arrow" of time would flip around again.
The modern history of T invariance begins in 1956.
Or 1781, when Critique of Pure Reason was published. Kant proposed that time was an empirical fact based on experiencing events in time being a precondition of all human experience. The tradeoff for a well reasoned non-skeptical position was that we give up claims to "really really" know how things really are independent of human experience...i.e we give up claims to potential omniscience.
That we normally take "knowledge" to mean human knowledge, doesn't change that this is what we mean. Or to put it another way, what would time be for a computer with knowledge or as the article mentions for creatures that experience time backward?
Great read on some of the history and current efforts in particle physics by a leader of the field (Frank Wilczek).
I was surprised to read such a well written article on quanta magazine (I've often been disappointed there) but it made sense when I saw who the author was. It read more like what might be published in a general audience Nature or Science article.
This is an honest question, how are we so certain time exists? Does anyone have a few quick references to books or articles that would explain it to the layman?
I always found the concept of time completely artificial, created by observation of cyclical systems.
"created by observation of cyclical systems". Can you elaborate on that? I'm not sure what you mean, but it sounds interesting. It seems to me we believe time "exists" because of causality; things that happen at "this moment" affect things that happen "in the future" but not things that happen "in the past". We've also predicted and measured certain weird things about time, such as how it can go faster or slower.
So, you could condense my knowledge of physics to an index card, but here we go...time seems like it's always based on the measurement of a regular thing. Say the oscillation of a quartz crystal. So we have no proof there of time, just that certain phenomena can be very regular in intervals/cycles.
I've heard things like, "if you go the speed of light, or at least really fast, time will move differently." But that seems like it would be a side effect of that local system moving at a rate that interferes with its physical interaction relative to what we consider normal.
There are probably tons of holes in that. But my point is that we tend to think of time almost as an invisible "thing", and I really have trouble wrapping my brain around that. It just feels like things happen and we call it time, but really its ordered intervals of effects.
Consider what it would look like if you ran the solar system in reverse - all the planets and moons would go backwards in their orbits, but gravity still works exactly the same. The equations of mechanics don't care about time.
And yes, information being lost in black holes would be an issue, if true - that's why that problem has been studied so much recently.
You'd see radiation hitting the planet warming the mantel, complex chemicals breaking down & releasing heat, all warming the planet significantly to the point where it was a molten ball, and finally lots of instability where large explosions were throwing pieces of it into space.
That is what is so unsettling about T-symmetry. What you describe is merely improbable, not impossible. With appropriate starting conditions, it is certain. Basically we'd require all the particles in the comet to bounce into each other in such a way that their heat motion cancels and organizes into momentum in one direction, away from the planet. This is physically permitted in either time-direction, but we only see it in one.
Yes, but the reason you do is that it's merely (and extremely) unlikely, not impossible. The third law of thermodynamics has its own arrow of time (the one in which entropy increases), but the basic interactions of the universe don't need to change to make that happen. They work symmetrically (mostly, with some tiny exceptions as detailed in the linked article).
Gravity gets double-negated when you reverse time. Its units are over seconds squared instead of just seconds.
A simple way to see this is to imagine taking a movie of a heavy back arcing upward through the air then back down. What do you see when you run the movie backwards? A ball arcing upward them downward. The acceleration still points in the same direction: down.
Lets consider only the moment before the collision of the small planet pieces: these are all accelerating to the center of mass.
If you revert time, you still have a lot of pieces, with high speed, but these are going away from the center (and getting slowed by the gravity).
After collision, it gets more tricky, because the kinetic energy of a body will be lost (mostly transformed in thermal energy) and it will be less intuitive to imagine how to revert that.
Interstellar gas/dust forming a planet increases its temperature, and it radiates thermal photons out into space. For the planets to fly apart, you would have reverse the photons as well, and aim them super precisely, and define the initial state of the planet super precisely, and...
It's essentially a problem of entropy. All weirdness of macroscopic time-reversal can be reduced to the weirdly low entropy of the big bang.
So if I understand correctly, time reversal means that all the object speeds get inverted, but the fields remain the same. If you change the sign of the field (gravity becomes repulsive) then things will explode very quickly :)
If you go to the 'overview' section, there is a nice snippet explaining all this. It points out that gravity works fine in a universe that is running backwards, however entropy is decreasing instead of increasing.
The equations that govern quantum mechanics are time reversible, and describes a system of consisting of superimposed states.
The Copenhagen (traditional) interpenetration of quantum mechanics posits that when a system gets large enough [0] these superimposed states collapse down to a single state. This interpenetration does pose a problem with time reversibility, as if you run time backwards, then forwards again, it is not guaranteed that you will arrive in the same state after collapse.
A more modern interpenetration is Many Worlds. In this interpenetration, there is no collapse. So when we observe the cat, the universe is in a superposition of us having observed a dead cat, and us having observed a living cat. When we run time backwards, we end up at the point where we put the cat into the box, as you would expect. If we run time forwards again, we arrive at the same superposition of observing a living cat, and observing a dead cat.
Without looking at the math, the ability to go from a superimposed state to a pure state may seem like it presents an asymmetry, but the equations allow (and we have experimentally done) this in forward time already. As it turns out, the mechanism that allows for this to happen (interference) is the essence of quantum computation.
[0] The standard phrasing is is "gets measured". I read this as "gets large enough" because we could, in principle, consider the measurement device to be part of the system.
Are you proposing a "hidden state" which is unobservable? Such a formulation is not consistent with quantum mechanics, as proven by Bell's theorem, unless you permit instantaneous influence from arbitrarily distant parts of the universe.
Put another way, aside from the possible "instantaneous influence" exception above, there are no "hidden variables" or mechanisms under the surface that we just haven't figured out yet. At that level it is truly probabilistic.
I'm saying that the construction "indeterminate" is only a statement about the knowledge of the person making the statement. Are you proposing that the universe doesn't act unless you are considering it?
Certain observations are probabilistic, and the correlations in them predicted by quantum mechanics cannot be reproduced by ascribing them to the traits of particles.
It means that at the lowest level, the universe is (barring faster-than-light communication, generally regarded to be false) "truly random". (No concept of an "observer" needs to be devised in order to arrive at this conclusion).
How do you know it's truly random though? Couldn't it be the result of a pseudo random process? Or universe splitting, where two universes are created, one where a coin lands head, and one where it lands tails. To the people inside, it seems random, but it's actually deterministic.
Pseudorandom means the choice is deterministically chosen by according to the state of hidden variables. Bell's theorem says there are no hidden variables that completely explain the predictions of quantum mechanics.
A many-worlds interpretation (which is consistent with QM) is basically the same as saying the result is random, because you can't predict exactly which branch any particular interaction will follow.
There is a hypothesis that universes with reversible time can't exist. Or time travel of any kind. Such universes, the hypothesis goes, can't have any meaningful cause and effect, like we know it. Causality is an extremely important property of our universe. And it's really weird that our universe has it, if the hypothesis isn't true. The space of possible universes without causality is much larger than restricted subset that obeys that rule. This is difficult to explain, so see here: http://lesswrong.com/lw/fok/causal_universes/
Our direction of time is defined by the observation that entropy (or "chaoticness") always increases with time. If you mix orange juice with water, you will not see the result unmix itself again, even though the interactions between the individual molecules are perfectly reversible.
In fact, you can build a toy-universe in your head, where all interactions are time-reversible, and you would still observe that the chaotic-ness increases with time, unless you start with a completely random initial state (in which the chaoticness stays roughly constant). This increase in chaoticness is comletely unsurprising: It's a simple consequence of the fact that there are much, much more "states" in which a system looks chaotic, than states in which it looks ordered. Therefore, a system transitioning from state to state is much more likely to be in one that looks chaotic, and very, very unlikely to ever go back to a state that is non-chaotic.
The real mystery, for me, is: Why was the initial state of our universe so completely non-chaotic? Why did the universe not start out in a state that is essentially equal to the heat-death [1]? The microscopic processes that are not time-reversible might have something to do with this, but it's not clear at all how they can solve this mystery.
[1] https://en.wikipedia.org/wiki/Heat_death_of_the_universe