Books about arrow of time

Question

Are there physics books about arrow of time? The concept of time is so vague, at least to me, it seems may not exist. When I think special relativity, time gets as real as other 3 spatial dimensions. However, considering Schrodinger equation or Newton equation of motion, time looks like just a parameter in order to bookkeeping of the events. It is not real but makes life easier.

I have master in physics, so I do not mind about mathematics involved in such a book. I would like also to know if there is any general agreement on the nature of time or if there is an active research effort to explain its nature in scientific community. It seems time is like consciousness, we know or at least feel it exist but cannot explain it yet.

Answer 1

Books about the nature of time fall into two camps - those that argue for or assume the reality of time, and those that argue that time is not part of the fundamental fabric of the universe.

In the former camp are:

Time's Arrow and Archimedes' Point - Huw Price - an accessible explanation of how a direction of time emerges in cosmology and quantum physics, which implicitly assumes the reality of time.

From Eternity to Here - Sean Carroll - argues for a cyclical "multiverse" in which the apparent direction of time is determined by the direction in which entropy is increasing.

The Singular Universe and the Reality of Time - Roberto Mangabeira and Lee Smolin - an argument for the reality of time and its key role in a theory of quantum gravity that also strongly opposes the idea of a "multiverse".

In the latter camp are:

The Order of Time - Carlo Rovelli - short and accessible with little or no mathematics, Rovelli argues that time is an emergent phenomenon that arises from how we perceive the universe.

The End of Time - Julian Barbour - an argument for a timeless block universe in which time and history arise from the second law of thermodynamics.

And finally a book that has a foot in both camps:

About Time - Paul Davies (mentioned in another answer) - a survey of the role of time in relativity, cosmology and quantum physics. In the argument about the reality of time, Davies sits on the fence.

Answer 2

In the Schrodinger equation time is treated like a parameter. But there is no reason to think it has to be treated this way and there are attempts to put clock times on a more physical footing in quantum mechanics, especially in quantum gravity, e.g. http://arxiv.org/abs/gr-qc/9303020.

There are various problems associated with understanding relativity and quantum mechanics that involve time. But it's a bad idea to think of this as figuring out the nature of time. For an explanation of some of the problems see Physical Origins of Time Asymmetry edited by J. J. Halliwell, J. Pérez-Mercader, W. H. Zurek. The papers in the book discuss various problems, like time asymmetry in thermodynamics, time in general relativity, time in quantum gravity etc.

Answer 3

About Time by Paul Davies is a good read.

So far as is known the only thing that establishes the direction of time is the second law of thermodynamics, which is ultimately a consequence of the very low entropy of the universe around the time of the Big Bang.

But there are some accounts in the book of other physical processes that may establish a time direction, as well plenty of other interesting stuff.

Answer 4

I'm giving just some suggestions and thoughts about time and physics, because I don't have an answer to your question. That's a very interesting one, I'm asking myself since a long time too. Has helped to me a lot to think time as a relation effect between things of the world, more than a variable in itself: the fact of considering it a variable or a parameter may be just a zero-th order approximation of a much more complex answer.

I think that a statistical answer, such as that regarding entropy, goes in the right direction, but is potentially dangerours also because the concept of entropy (and statistics in itself, I think to H-theorem) is not actually well-defined. I think also that risks to be tautological; answering that time is related to entropy, but entropy varies with time, pose a new thing to consider, entropy, but nothing really clear about the nature of time.

Assuming the relational nature of time, is clear that we cannot understand it without understanding what is space first; we can say that the world has three or eleven dimensions, or that they are not constant, maybe they depend on location in time and space (mind blowing, isn't it), maybe they are not even integers, but I think that if we insist to try giving an answer of this kind we are just going far and far away from an actual profound understanding and we are still avoiding to answer why the things are the way they are, that is also the reason why physics and phylosophy were born together and in the past there was no distinction between the two. This is a substantial problem of science as it is thought today, that to understand, it rationalizes and conceptualize and detach things from the world, but maybe reality doesn't work that way; you maybe can't actually think about entities, such as time and space and mass and things, because they may not have a substance, they may not have a nature at all.

So, in summary, there is a deep cut between the mathematical/logical description and the nature of time, if the nature of it exists at all. The only thing that helped to me is stopping giving the time a substantiality in itself and thinking it like an interaction process; the analogy is like the old caloric and the heat.

I asked about this stuff to my professor in the past and he talked about relational quantum mechanics of Carlo Rovelli. I don't know anything about it, but you can give it a try. Hope that these suggestions help.

Answer 5

In case you are interested in a mathematical treatment (maybe the followig is not what you are looking for, but I guess my answer doesn't hurt):

• In modern treatments of classical mechanics, time is modeled as a 1-dim. euclidean space $E^1$. The two orientations of the translation space correspond to future- and past-pointing vectors. In addition, absolute time is postulated - a map $M\to E^1$ defined on the spacetime manifold $M$.
• As you certainly know, absolute time is not existent in special relativity: Two events that are simultaneous for a given observer will not necessarely be so for a second observer. If you are interested in more details and a very modern mathematical approach to special relativity (postulating that spacetime is a 4-dim. affine space (not $\mathbb{R}^4$) with a bilinear form on the translation space), then I suggest you have a look at Éric Gourgoulhon's Special Relativity in General Frames. It has nice sections on proper time (chapter 2) and observers (chapter 3).