Saturday, March 1, 2014

What is the cause of the Arrow of Time?

This is a dialogue between a Sophist and a Platonist. The topic of the dialogue is: What is the cause of the arrow of time?

The participants of this dialogue are: Socrates and Sean Carroll

Location:  This dialogue takes place in a coffee shop near the ocean in California

Socrates:  Sean, you seem to be saying that the laws of physics are all time reversible, but that the motion of particles can still be time asymmetric. If I understand your argument, then you are saying that we can tell past from future, at least right now, because the future will have higher entropy than the past. You seem to state that this is due to the fact that it is more probable for a system to be in a state of high entropy rather than low entropy.

Sean Carroll: That's right. You have stated my position correctly. The universe started in a state of low entropy and gradually the entropy is increasing. The most probably state of the universe in the future is for it to be in a high state of entropy than the past. Though, if in the future, the universe reaches complete equilibrium, then we will see small fluctuations about this maximum value of entropy. Well, that is of course if there is such a thing as maximum entropy, and there is also the caveat that there might not be a 'we' to measure the entropy that far in the future.

Socrates: You are saying that time will continue to increase even after we reach equilibrium. I think that I understand your position. Let me rephrase what I think that you're saying:  If the state of the universe were probabilistic, and if you were to look at the state of the universe, then most of the time it should be in a state associated with the highest entropy. Though, if the state of the universe were probabilistic, then it might be possible for the universe to be far-from-this-maximum-entropy state. But tell me, Sean, why is the universe in a state so-very-far-from-this-maximum-entropy state?

Sean Carroll: That's because the universe started with a very-low entropy Big Bang. And the universe is still in the process of increasing its entropy. We are headed to a state of maximum entropy, but that is not for some time in the future, and perhaps, if the universe continues to expand, it might never happen. The entropy might just continue to increase as the universe increases.
Socrates:  Thank you for that clarification. Though, I have a few questions. Let me start with the first. How low of entropy did it start?

Sean Carroll:  I'm not really sure, but it was much smaller than it is today. I guess that depends on the number of particles and the size of the early universe.

Socrates:  Could it have started out with an entropy of zero?

Sean Carroll:  That seems unlikely because there were likely many particles to start the Big Bang.

Socrates: There are some in the physics community that think that the universe started from nothing. It seems to me that if a universe could start from nothing, then there would be no entropy, and then all of a sudden, there would be entropy. But doesn't it seem strange that the universe happened to start in such a low entropy state? If, as you say, entropy is a probabilistic quantity, then shouldn't the universe have started in a high entropy state.

Sean: You make a good point Socrates. I don't argue against this. It does seem strange that entropy of the universe was so low to start. I have no way of explaining the low value during the Big Bang. It might be possible that, in other universes, the Big Bang starts with a much high entropy value than for our universe. What I'm arguing is that, the entropy is now increasing because it's more probable for the universe to be in a state of higher entropy.

Socrates: Well, for simplicity sake, let's imagine that there were 4 high-energy particles to start with.

Sean: Well, I highly doubt that there were only 4 particles to start with.

Socrates: How do you know that? Where you around during the Big Bang? Or are you capable of looking back at the Big Bang?

Sean: You know quite well Socrates that we can't receive information about the state of the universe before the time at which it cooled to a temperature where atoms could form. Before that time, electrons and protons were separate. This plasma could absorb light, and essentially blocks our experimental knowledge of the universe before this time.

Socrates: But we can estimate that there were a lot of electrons and protons in the universe at this point in time. But since the particles were at a higher temperature and more densely packed compared with electrons and protons today, we infer that the entropy was lower then than it is now.

Sean: Correct

Socrates: And before this point in time, we infer that the universe was at a lower entropy state because the trend seems to be for entropy to increase with time.

Sean: You have stated things as we see them tonight in the physics community.

Socrates: Good, I'd hate to be misrepresenting your conclusions. So, let's image a hypothetical world of 4 particles at the beginning of a big bang. What keeps them from spontaneously turning into 8 particles of lower energy. This would increase the entropy of the universe, would it not?

Sean: There's nothing, per se, stopping the particles from turning into particles of lower energy. What I'm arguing is that, if the entropy were to increase, then it'd be more likely to happen.

Socrates: Well, let's say that, these 8 particles in turn were converted into 16 particles...increasing the entropy again. My question is: what law of physics tells us how quickly it takes for the particles to go from 4 to 8 to 16 particles?

Sean: Depending on reaction, this would likely either be the strong or weak nuclear force.

Socrates: What if the particles were photons? Could photons spontaneously turn into lower energy photons? It appears that this would increase the entropy of universe.

Sean: I'm not exactly sure if this is possible. We'd have to check to see if splitting of photons conserves momentum and angular momentum.

Socrates: Right, there are laws about whether certain processes can happen. When we see photons travel through the vacuum of space, we don't see photons spontaneously converting into states with higher entropy. Why is that?

Sean: Photons don't interact with each other. They can pass through each other, and they don't notice each other.

Socrates: So, you seem to be saying that, only particles that interact, can cause an increase in the entropy of a system.

Sean: Yes, that's correct. An interaction of some sort is required.

Socrates: But what type of interaction?

Sean: Any sort of interaction, I guess.

Socrates: But what about superfluid helium or superconductivity? How can superfluid helium flow through pipes with no friction and no entropy production? And for that matter, how can electrons flow in a superconductor with no electrical resistance, and hence no entropy production?

Sean: Ah, that's easy to explain. This happens because the electrons in the system link up and form pairs of electrons. These electron pairs are bosons, and bosons can occupy the same energy state. So, nothing really happens and hence there's no entropy generation when all of the bosons are in the same state.

Socrates: I agree with you that electron pairs could form bosons. The problem I have with what you said is that, in superfluid helium and in superconducting electrons, the particles have large directed velocity. Would you agree that we could increase the entropy of the system by having the electrons lose their directed velocity of motion, and to have that energy and momentum be transferred to phonons in the surrounding materials?

Sean: Yes, but once again, we have to check to see if angular momentum and straight-line momentum are conserved.

Socrates: But surely this happens all of the time for non-super-conducting electrons. These electrons can lose their directed kinetic energy to the surrounding materials, just as what happens to a block sliding on a surface. In non-superconducting liquid helium, the electrons in helium interact with electrons in the wall materials via the gravitational and E&M forces, as well as the weak nuclear force. When all three of these interactions are viable, then it is possible for the electrons to lose their directed motion, i.e. their directed kinetic energy and momentum, to the electrons in the wall materials. However, in superfluid helium, the electrons pair to form bosons, and then they lose their ability interact with other electrons via the weak nuclear force. Once this happens, then the entropy of the system remains fixed. But what has changed? The only thing that has changed is that electrons can no longer interact via the weak nuclear force. Would you agree with that statement.

Sean: It seems so. But I don't see how any of this has to do with the weak nuclear force. It's a force that has an extremely small range. What does the weak nuclear force have to do with superfluid helium and superconductivity? 

Socrates: What I'm arguing is that the weak nuclear force is the only force that is time assymetric, and it seems coincidental that irreversible processes stop as soon as the particles turn into bosons, and stop being able to interact via the weak nuclear force.

Sean: I realize that this does look coincidental, but remember that correlation does not prove causation. You still haven't proven mathematically that the weak nuclear force is the cause of what we call the arrow of time.

Socrates: It is a silly for you to being causation into the argument, but you would agree that there are mathemetical terms in the Lagrangian of the weak nuclear force that are T asymmetric, right?

Sean: Yes, there are a few terms in the Standard Model Lagrangian of the weak nuclear force that violated T symmetry. These terms also violate C, P, CP, CT, and PT symmetry. The terms in the Standard Model Langrangian, though, are CPT symmetric. And this is what is important as far as thermodynamics and the arrow of time.

Socrates: I have a problem with what you're saying. Let me try to explain. When the only forces available are the strong nuclear and the E&M force, then parity is conserved. And when parity is conserved, there is a conserved 'multiplicative' constant that I'll call "X-Parity." Total multiplicative parity of a system remains constant during an interaction, unless the particles are capable of interacting via the weak nuclear force. It seems that there should be another constant called "T-Parity." When only the strong nuclear and E&M forces are available for particles, then the multiplicative "Time" of the system should remain constant. The same should be true for the multiplicative "CPT" constant. In other words, symmetries of the laws of nature have their associated constants. For example, continuous symmetries such as shifting time, space, and gauge lead to conservation of the energy, momentum, and electric charge. Discrete symmetries such as mirror-flips of time, space and charge would lead to three more constants of nature X-Parity,T-Parity, and C-Parity, if it weren't for the weak nuclear force. The same would hold for CP-Parity, PT-Parity, and CT-Parity, if it weren't for the weak nuclear force. But perhaps, CPT is a valid symmetry for all of the laws, and in that case, there should be a CPT-Parity constant of nature. However, it seem that you want to have your cake and eat it too. If CPT-Parity is a constant of nature, then you haven't explained how randomination causes entropy production. Remember that changes in the quantum wavefunction aren't random. They only appear random to observers because we don't know the state of the wavefunction prior to observation. You can't invoke CPT symmetry and at the same time evoke randomination. You have to pick one or the other. 

Sean: Socrates, there's nothing wrong with believing in both CPT symmetry and randomination.

Socrates: Well, I disagree. I don't see how CPT symmetry says anything about entropy production. CPT symmetry implies that there is a multiplicative constant 'CPT-Parity' that is either 1 or -1 for the universe. It doesn't say anything about the rate of entropy production of systems. But for now, I'd like to discuss some other things that are nagging at me when you stated that CPT is what's important for thermodynamics.

Sean: That's understandable. What else is causing your skepticism? I've thought about this quite a bit, so I likely can answer your question.

Socrates: Good. I have a problem with how things are stated, and I hope that, by talking with you, you will be able to clear things up for a lay person like myself. So, let me state a few more of my concerns, and see if I am misrepresenting our current theory for the arrow of time.

Sean:  I'll help out as best as I can.

Socrates: First, let's start over at the beginning. At some point in time, if we run things backwards, then we end up in a state of low entropy. The question is: how low could the entropy be? If entropy is only defined for systems with many particles, then could it be possible that there was a point in time in which the "law of large numbers" wasn't valid?

Sean: Perhaps, but you can define the entropy even for systems with small numbers of particles.

Socrates: Can the entropy be defined if there's only one particle?

Sean: Yes, the entropy would be small, but non-zero. But it's not clear that all of the energy we see now could have been in the form of a single particle.

Socrates: True, that does seem unlikely. My concern is that, if we follow your logic, entropy increases with time, so there must have been a time when entropy was low. However, if there were only a few particles, and if the particles followed time-reversible laws of thermodynamics, it's unclear to me where the arrow of time comes from. When we watch videos of planets in motion about the Sun, it's unclear to me if we are watching the movie in forward or reverse time. 

Sean: The reason that it's hard to tell if the movie is in forward or backwards time is that there are only a small number of particles when we looking the motion of the planets.

Socrates: But you will agree that there would have been a point in time in which there were only a small number of particles. What law of physics allows the entropy to increase when there are only a small number of particles.

Sean: There is no law of physics. It's just more probable for the future state of the universe to have more entropy than the past.

Socrates:  What law of physics states how quickly the entropy of universe can increase? In other words, why doesn't the universe just spontaneously end up in thermal equilibrium. If the state of the universe were truly probabilistic, then why didn't the universe go directly from the Big Bang to the final equilibrium? Why did we go through all of these intermediate states?

Sean: Well, there are some derivative laws of physics that predict how quickly reactions occur. You can't just go from Big Bang to Final Equilibrium.

Socrates: But you believe in quantum mechanics, and believe that there is a no-zero probability that the atoms in my body exist at every position in space. Why can't the universe just jump from non-equilibrium to equilibrium? The state of final equilibrium, that also keeps momentum, energy, and angular momentum constant, is much more probable. 

Sean: Well, there is such a thing as activation energy barriers. There are finite rates for collisions and finite rates for chemical and nuclear reactions. This is the field of non-equilibrium thermodynamics. It's a quite well established field of study. The field of non-equilibrium thermodynamics tells us how quickly a system will go from non-equilibrium to equilibrium. Physicists can explain, for example, how quickly processes like diffusion in gases take place. It depends on collision rates between molecules. This has been well established.

Socrates: Let me get this straight. The rate of entropy production depends on collisions between molecules. Of course, let's ignore for now the fact that there's no entropy generation when there's only bosons, such as photons or electron Cooper pairs. So, what happens in a collision that causes entropy generation?

Sean: The particles collide and their momentum change. There's little change in momentum when the particles are far apart.

Socrates: But you agree that the gravitational and E&M forces extend forever. As far as gravity or the E&M force, nothing special happens during a collision. There's conservation of energy and momentum during the collision. 

Sean: Yes, you seem to have the same reservations as Loschmidt. As he put it, there's no way to get time-irreversible motion from time-reversible laws of physics. But I think that this reservation has dissolved in the physics community after the Fluctuation theorem was proved Denis Evans and Debra Searles. 

Socrates: I think that you fail to really grasp my issue with this probabilistic approach to the arrow of time. It feels that you and others have completely ignored the special and general theory of relativity, and are living in world of Newtonian physics with a magical clock that uniformly ticks off time. My real question is: why is there such a thing as a dimension of time that is different from the dimension of space? Your probabilistic argument doesn't explain why or how the dimension of time became separated from the dimension of space.

Sean: I think that you just have to accept that there is such a thing as time, and then ask the question: will the future be higher or lower in entropy?

Socrates: It seems, once again, coincidental that we have 3 forces of nature that are time-symmetric, 1 force of nature that is time-asymmetric, 3 dimensions of space, and 1 dimension of time. I'm much more inclined to believe that there is something about the weak nuclear force that causes the dimension of time to be different from the dimensions of space, then I am inclined to believe that there's some magical ticking clock that causes time to increase.

Sean: You keep talking about some magical ticking clock. The special theory of relativity disproved the Newtonian concept of absolute time. I recognize this, but I don't see what this has to do with entropy or the arrow time. Two observers could disagree about the exact time of an event, but they both will see, on average, an increase in entropy. Entropy is a relativistically invariant concept because it involves counting the number of microstates, and the number of microstates remain the same when viewed at different speeds or from different gravitational heights. This means that different observers might disagree on the absolute time, but they can agree that the universe of a system is increasing. And this has nothing to do with the weak nuclear force.

Socrates: But you have already stated that it is only when there are collisions between Fermions that this can be an increase in entropy. This is precisely when weak nuclear force would be occurring between particles, and the weak nuclear force is the only force that is both Time asymmetric and localized. I guess what I'm arguing is that the reason why the universe has more matter than anti-matter is the same reason why the universe has a time dimension that is different than spatial dimension, and is the same reason why the universe is expanding. The weak nuclear force is the only discrete law of physics, and the only force those exchange particles have mass. The force only acts in a certain direction because without it we couldn't tell left from right, and this directionality is what causes time to be different from space, and what causes electrons & protons to be in abundance compared with anti-electrons and anti-protons.

Sean: Let me interrupt for a second. I agree that the weak nuclear is the reason why we can tell left from right, but that's very different from telling past from future.

Socrates: But both are dimensions, correct?

Sean: Yes, but knowing left from right is different from watching a movie in forward or backwards.

Socrates:  Thank you for making my argument complete.

Sean: What? What are you talking about? I'm arguing that the only way to tell forward from backwards time is to watch a movie in which entropy is changing. But you can tell left from right when you have Beta decay occurring in ultra-cold atoms.

Socrates: Precisely. You can tell left from right by watching the weak nuclear force in action. The same is true for forward and backwards time. The only way to tell if time is going forward or backwards in the movie is if there are interactions between colliding Fermions. If there are no Fermions or if there are no collisions, then there's no way to tell forward time from backwards time. As such, it is the weak nuclear force that is the cause of the directionality of time, just as the weak nuclear force is the reason why left is different than right, and matter is different than anti-matter.

Sean: Socrates, you don't seem to be listening to me. The weak nuclear force has nothing to do with molecules diffusing in a box. The second law of thermodynamics has nothing to do with the weak nuclear force. The entropy of universe would increase even if we didn't have the weak nuclear force.

Socrates: Well, then, this is where we will have to agree to disagree. What you are arguing is that entropy can increase in system that don't have the weak nuclear force. However, you and others haven't demonstrated entropy generation in a system without the weak nuclear force. So, if you'd like to prove that my theory is incorrect, I challenge you to create a system where the weak nuclear force is not available, and then demonstrate that entropy generation can occur.

Sean: That seems to be hard to prove. But it might be possible to prove if we could design an experiment in which photons are trapped in a box made only of Bosons.

Socrates: Well, I look forward to the results of such an experiment. I thank you for sharing your thoughts with me, and thank you for allowing me to voice my reservations with the ideas you present in public about the cause of the Arrow of Time.

Sean: It's too bad that I've been unable to persuade you that the arrow of time is but a fascade and only probabilistic in nature.

Socrates: I have learned a lot from this discussion, but as we have spoken, the entropy of universe has increased. I don't believe that this is just a probability. The change in entropy had to have an underlying cause, and that cause must be time asymmetric. 

Sean: Yes, I understand your fear in accepting modern physics, and its lack of causation. But you had no fear when you gave up believing in Zeus, Apollo, and the other gods. I unfortunately think that you have replaced these gods with the god of causation. There's no way to prove that gods exist, and there's no way to prove causation. So, I think it's best to just throw the whole concept of causation out the window.

Socrates: Fair enough. We'll agree to disagree. I'm not yet ready to give up belief in causation, self, and purpose. Just be careful that you don't flush the baby down the drain with the bathwater.

Sean: You should be careful not impose your beliefs on others, and I'll try my best to not impose my scientific beliefs on you, unless you ask.

Socrates: I do enjoy talking with you Sean, so I look forward to talking in the future to see if there is something obvious we missed and left out of discussion. It does seem odd that we would never disagree about how many peas are in a pod or disagree about how many microstates are in a given macrostate, but for some reason, we can't put the problem in terms that are countable. Until we do so, we might be doomed to disagree.

Sean: Fair enough. I'll look into whether there is some other way of explaining my argument. Until then, have a good weekend.


  1. What do you mean "Photons don't interact with each other", its more likely in a dense energy environment.

    1. Interactions between low-energy photons does not generate an increase in entropy. Most of the time, photons can pass through each other without any interaction. Yes, at high even energy, you can get scattering because there is the generation of virtual fermions. But any irreversibly here is likely due to the weak nuclear force, not E&M.


  3. I find this discussion interesting. However, I was confused by the following exposition by Socrates, I quote: "So, if you'd like to prove that my theory is incorrect, I challenge you to create a system where the weak nuclear force is not available". Is Socrates idea a theory or a hypothesis? There's a huge difference between both terms in science. We should be careful to make a distinction between Philosophy and Science. Science debates are not settled by philosophical arguments, but by the outcome of experiments.

    1. The theory I propose here (via the arguments of Socrates) is that the only cause of the arrow of time is the weak nuclear force. This is a testable theory/hypothesis. What I have the character of Socrates argue here is that this theory/hypothesis can be disproven by showing that there is an arrow of time in a system in which the particles can't interact via the weak nuclear force. So far, all cases of time irreversibility occur in systems in which the particles can interact via the weak nuclear force.

  4. Time, as we know it, from this terrestrial temporal prism, is geocentric. Space is not. EG if you could potentially reverse the earth's rotational spin, and the other ancillary orbital factors that aeffect our perception of TIME, you might have a chance of reversing time's arrow