Sunday, July 3, 2011

What is the source of the directionality of time?

I've been thinking a lot recently about why time only seems to go in one direction. There's still an on-going debate in the scientific community about why (or if) there is a directionality to time. So, I'd like to highlight a few of the opinions in this area. (Other thoughts on this subject can also be found here. And be sure to check out the very end of this post where I discuss research from March 2011 that possible supports the theory that the weak nuclear force is the reason for the directionality of time.)

The directionality of time is an illusion.  As stated by Albert Einstein: "People like us, who believe in physics, know that the distinction between past, present, and future is only a stubbornly persistent illusion."  Einstein stated this in part because all of the laws of physics (at that point in time) had time reversal symmetry and in part because special relativity tells us that the lifetime of a unstable particle in our reference frame is a function of how fast it is moving with respect to our reference frame. You can't talk about absolute time if different reference frames can't agree on which event came before another event. (see the barn-door thought experiment.)
The idea of time as an illusion has come under attack from multiple scientific directions; here are a few of the major arguments against time as an illusion.

Prigogine:  The directionality of time is due to the fact that there are many particles, which form resonances and singularities such that the future is not longer predictable from the initial conditions. The generation of entropy in chemical and biological process, according to Prigogine, shows that there is a directionality to time. Even more, Prigogine argues that systems far-from-equilibrium exhibit a 'history.' Examples are system with hysteresis or biological evolution. So, for Prigogine, the directionality of time and the meaning of time stems from systems far-from-equilibrium. The concept of time disappears once the system reaches equilibrium. And interestingly, the entropy of a system (either in equilibrium or far-from-equilibrium) is not a function of position, velocity, or angle at which one views the system. So, entropy and special relativity are not at odds with each other, even though absolute time and special relativity are at odds with each other.

The classical argument against Prigogine's argument is that entropy is only a probabilistic concept; and how can the concept of time be defined by probability because there is always a small chance that the system could return close to its initial conditions. But this argument against Prigogine is not a real argument because it fails to understand that there is such things as irreversible processes. Without the addition of work from outside the system, information about the exact microstate of a system disappears with time. However, a valid argument against Prigogine's argument is that there are systems with plenty of interactions but with near-zero generation of entropy that are far-from-equilibrium: superfluids and superconductors. Why entropy generation goes nearly to zero for superfluids and superconductors is still largely an open question? What is it about bosons that allow for minimal generation of entropy? (This question leads to the next concept.)

The Weak-Nuclear Force is not time reversal symmetric: This line of reasoning argues that the directionality of time is due to the fact that the weak nuclear force does not have the symmetry operator of time inversion. This idea stems from the fact that the weak-nuclear force does not conserve parity, and hence this force is not symmetry with respect to reflections of spatial direction, i.e. there is a preferred direction for particle interactions involving the weak-nuclear force. Using relativity to equate spatial and time dimensions, the lack of spatial reflection symmetry implies the lack of a time reflection symmetry operator.
(In technical terms: "this means that the parity operator and the electroweak Hamiltonian do not commute" ) There's also an open question of why we haven't detected any parity violations in the strong nuclear force. As discussed earlier in my post on symmetry and forces of nature, the strong nuclear force is associated with a division algrebra (the octonions) with is even more complicated than the weak-nuclear force (the quaternions.) Parity and hence time reversal symmetry will exist for all interactions that only involve gravity and the electromagnetic force because these forces are associated with division algebras in which all operators commute with each other. (i.e. A*B=B*A) [Perhaps, the reason for time/parity irreversibility has something to do with the fact that the weak nuclear force is the only force that exchanges boson with non-zero rest mass.]

What one could argue here is that since there is no time reversal symmetry for particle interactions involving the weak-nuclear force, then the future can not be predicted given initial conditions. This implies that pure determinism is dead. (Even though, practical determinism really died decades ago when we realized that the Uncertainty Principle implies that we can never really know both the position and velocity of a particle.) The following questions remain: how does the lack of time reversal symmetry imply that the entropy of the universe can only increase or stay the same? Does the increase in entropy in the world have anything to do with the weak force? (i.e. does entropy production in chemical reactions or in molecular diffusion/viscosity have anything to do with the weak nuclear force? Do particles go in random directions after a collision because of the weak nuclear force? This seem a little bit of a stretch at first because the weak nuclear force is really, really weak compared with the E&M force. However, it might not be as crazy as it sounds at first. There are two unknown variables whenever two particles collide in 3-D space. (Due to six variables and four equations) This means that there are many ways in which particles can collide in 3-D space while conserving momentum and energy. If the weak nuclear force violated time reversal symmetry, then there are an infinite number of ways that the particles could go after a collision without violating conservation of energy and momentum, and it wouldn't require a strong force. Hence, we lose information about the starting conditions and entropy has been produced if the system is far-from-equilibrium. But once again, we are left with the problem of bosons vs. fermions. As mentioned above, there appears to be situations in which entropy generation goes nearly to zero (superconductors and superfluids). Why would the weak nuclear force cause entropy production for individual electrons in solid (fermions) but not for pairs of electrons in solid (bosons)? It appears that the weak nuclear force only acts on left-handed particles or righted-anti-particles. So, if electrons could couple together to form zero-spin couplets, then the weak nuclear force might not apply. The same might hold for boson states of superfluid helium. But it's not clear that the formation of bosons is enough to prevent the generation of entropy (i.e. the loss of information about the initial microstate of a system.)

The directionality of time is due to the fact that the universe is expanding. This argument tries to conclude that entropy always increases because the universe is expanding, and hence entropy would always decrease if the universe were contracting. This argument is most likely incorrect because if the equations of motion are deterministic, then they are time reversible, even if it's expanding or contracting. It seems that there could still be irreversible processes that lead to loss of information in a contracting universe. It seems hard to believe that the Rosen-Curie Symmetry principle (i.e. that the symmetry of the future is greater than the symmetry of the past) could ever be violated. Why would a contracting universe imply that the symmetry of the future is less than the symmetry of the past?

The directionality of time is due to the fact that the quantum wave function must collapse when the wave is measured. This argument suggestions that there is a directionality to time because a particle must either be spin up or spin down, but before it was measured it could have been either spin up or spin down. The act of measurement is irreversible. Once measured to be spin up, it can't be in the spin down state until a future interaction with another particle. But this argument isn't very convincing because the real question is:  how is information about the state of the particle lost in future interactions? The loss of information is what we mean when we state that the entropy of the universe is always increasing. It's not clear what the wave function collapse has to do with increase in entropy of the universe. In fact, it's the opposite that is more important. Once the state of the particle is known, how does the wave function of the particle uncollapse and go back into a probability? This appears to be the real source of irreversibility, and this seems to require that at least one of the forces of nature to be time irreversible.

So, these are the four main reasons given for a directionality for time: 1) entropy production for multi-particle interactions; 2) time irreversibility of the weak nuclear force; 3) the expansion of the universe; and 4) the wave function collapse.

I personally think that the reason for the directionality of time is a combination of 1) and 2). This means that, in order to have a directionality to time and to talk about the 'history' of a system, you need: 1) a system far-from-equilibrium and 2) a force, such as the weak nuclear force, that does not have a time reversal symmetry operator that commutes with the Hamiltonian of the system. I think that 3) and 4) are not the reason why there is a directionality to time, and I think that Einstein is wrong when he stated that time is an illusion. But I understand where Einstein was coming from because it wasn't until after his death that we realized that the weak nuclear force could be time irreversible. Without the irreversibility of this force of nature, I find it difficult for us to talk about a directionality to time.

Since writing this post, I found the following quote on superconductivity in a neutron star:
"They say that shortly after the creation of the neutron star, protons would combine to form Cooper pairs, so creating a superconducting state by virtue of their charge. Bound up in this way, the protons would not be able to take part in various neutrino-emitting reactions that occur in non-superfluid matter, reducing cooling early on in the life of the star and leading to a sharper drop in temperature later on."

I think that this quote pretty much explains why I think that the weak nuclear force is actually the reason for the directionality of time.  Check out the article above.  Two independent research groups suggest that there are still some protons inside of the neutron star, and that the reason that they have not yet converted to being neutrons is that they are in a superconducting state, and hence "would not able to part in various neutrino-emitting reactions."   i.e. the protons are in a boson-like state and hence aren't able to interact using the left-handed weak nuclear force. I see this as strong, but speculative, evidence that the weak nuclear force (along with non-equilibrium starting conditions) is the reason why there is a directionality to time. The bosons don't interact using the weak nuclear force, so this appears to be why superconductivity and superfluid flow don't generate entropy.


  1. bravo to you sir. i think you are right on.

    tell us what you can make of a notion of 2 species of time ;weak force time; absolute time.

    seems unlikely but its been nagging me for a long "time"

    k thomas

  2. K Thomas,
    Thanks for the comment.
    While two observers moving at different speeds will often not agree on the 'timing' of certain actions, and hence will often not agree on 'cause' and 'effect,' observers moving at different speeds will measure the same entropy within a closed system. Regardless of the speed of the observer, the entropy of a closed system will remain the same, but since they will disagree about timing, this means that the observers could potentially disagree about the rate of entropy production.

    So, while I think that the arrow of time is due to the time irreversibility of the weak nuclear force, I do not think that this arrow of time allows us to define absolute time. The laws of physics appear to be independent of absolute time (which leads to energy conservation according to Noether's theorem.)

    In other words, time is relative regardless of whether there is an arrow of time.

    Let me know if this response answers the question from your comment.