## Sunday, October 30, 2011

### Time's Arrow

This post is part of a series, Nonsense and the Second Law of Thermodynamics. The previous post is entitled The Second Law, Microscopic Reversibility, and Small Systems. The previous post is essential to understanding this post.

Why does time move forward instead of backward? In the spatial dimensions, one can move left or right, up or down, backward, or forward.

Time, on the other hand, has a preferred direction. Why is that so? The underlying physics does not seem to have a preferred direction, but time does.

I am not going to answer this question in this post. Rather, the fact that entropy has a preferred direction in time provides an excuse to think about this issue.  The previous post helps to explain why entropy increases with time, but it includes an underlying assumption that time moves forward.

Microscopic Physics and Time

The previous post, The Second Law, Microscopic Reversibility, and Small Systems looked at the fact that the underlying microscopic physics is not dependent on the direction that time flows, but that such microscopic interactions combine to produce a flow of increasing entropy with time because of the statistics involved.

In fact, this description was a bit of an oversimplification because it ignored electrical charge and parity.

CPT Symmetry

In the previous post, I discussed the idea that the basic physical laws of the universe were symmetrical with respect to time.  In fact, this notion is an oversimplification.  The microscopic laws of the universe are not symmetric with time, but under the standard model, they are symmetric under a deeper symmetry called CPT symmetry.

CPT-Symmetry is the invariance with respect to charge, parity, and time simultaneously.

Charge: Particles can have positive charge, negative charge, or no charge.  For example an electron has negative charge, whereas a positron has positive charge. Charge is a conserved quantity (provable from gauge invariance).

Parity: Parity, in three three dimension is simply the inversion of all three Cartesian coordinates (x, y, and z) to their opposites (-x, -y, and -x).

Time:  Trying to define time  could be the subject of a book, several books, or an entire library of books.  The purpose of this post is to wonder about entropy and time.

Consider a particle moving forward in time. Now consider reversing its charge, reversing its parity, and propagating it backward in time. Under CPT symmetry, these two situations are indistinguishable.

A violation of CP-symmetry on the other hand, implies a violation of T-symmetry and vice verse.

The universe is not invariant under CP symmetry; in fact, the standard model predicts very small deviations from such symmetry.  The standard model in invariant under CPT symmetry, but allows violations of CP symmetry. Such CP asymmetries have been observed for interactions involving the weak force. This asymmetry implies a violation of T-symmetry as well.  So in rare cases, time is not actually symmetric for certain interactions.

It is not clear that such small asymmetries can  help with understanding why time moves forward instead of backward, but it is a necessary detour to make our understanding a bit more sophisticated. Even if such interactions were more common than they are, they can still be understood as a consequence of the fact that time moves forward. They are not sufficient to explain why time moves forward.

The universe is also not known to be invariant under CPT symmetry.  String and quantum gravity theories allow the possibility of CPT violation. There are some very recent experiments looking for CPT-violation as well.

Time

John Wheeler famously said that "time is what stops everything from happening at once."  In fact, it is necessary to think a little deeper about what time is.  It turns out that our intuitive sense of simultaneity is not something that we can trust. It turns out that that in relativity simultaneity depends on one's frame of reference. Two events that happen simultaneously but in different places in one frame of reference do not happen at the same time in a different frame of reference.

The definitions of time therefore needs to be operational.  Time is what we measure with a clock.  Of course we want to use a very good clock, but aside from that it is not particularly important what the mechanism of the clock is.

For the purposes of standardization the second has been defined. Time is one of the seven fundamental quantities in International System (SI) units.  The unit of time is the second, and it is defined as the time it takes for a specific number of periods (9,192,631,770) of the radiation corresponding to the transition between the two hyperfine levels of cesium 133 in its ground state.  It's not important to understand all of that; what is important is to understand that we need to be able to measure time to define it.  Because of relativity, we need to be careful how we measure it.

Entropy and Time

Aside from the very  infrequently observed violations of CPT symmetry, entropy appears to be the only physical quantity that is dependent upon the direction in which time flows.

It is tempting to want to draw some grand conclusions from such facts.  Is it possible that entropy itself is responsible for the fact that time moves forward?  Or, is it more reasonable to think that time just does move forward and increasing entropy is a natural consequence?

As scientists, we need to be careful about jumping to conclusions about questions to which we do not know the answer.  If we propose an answer, is there a consequence of that proposal that leads to a result that we can actually measure?

One area of research that is of current interest is the relationship between the inflation of the universe, entropy, and time.  To understand some of these issues it is necessary to understand the proposed heat death of the universe.  These topics are part of the next post.

The next post in this series is entitled, the Second Law, the Universe, and Cosmology.

Sources