Time Reversal? Think History vs. Economics

Shahn Majid

So far in these blogs I have focussed on hard science verifiable by experiment. But it is also part of the background to my multiauthored volume On Space and Time that to proceed further with fundamental science may need revolutionary new ideas for which science is still grasping. So this week we are going to let our hair down and extrapolate from what is understood into what is definitely, well, speculative.

Incidentally, I did run these ideas here past a BBC producer for Horizon a few years ago when he called me asking about the possibility of time travel, and obviously I was not controversial enough as he never called me back.

What I propose, as a motion for debate, is:

The direction of time is a spontaneously broken symmetry, in the same way as which side of the road to drive on is a spontaneously broken symmetry.

Let me explain the analogy first. For the sake of argument, let’s say that either driving on the left or driving on the right is equally good. At some point, with enough drivers crowding the road, you have to break the symmetry and decide somewhat arbitrarily (‘spontaneously’) on one side or the other. But once enough of you have bought right handed cars and started driving them, you are pretty much locked into that choice in your region.

Now for the arrow of time. This is not controversial at a subatomic level and at the level of fundamental equations of physics; there is a symmetry between, say, t and -t in the eqations i.e. between increasing and decreasing time. For example, the relativistic wave equation that governs the simplest particles involves (d/dt)2 which does not change under such a change of variables. In physics the actual symmetry is PCT — it means left-right reversal (“parity”), particle-antiparticle interchange (“charge conjugation”) and time-reversal. This is what led the legendary physicist Richard Feynman once to say that in his view a positron (an anti-electron) is just an electron traveling backwards in time.

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