Fifteen Eighty Four

Academic perspectives from Cambridge University Press


History, Economics, and Time Reversal

Shahn Majid


First off, congratulations America! Electing the first black US president has to be significant and already puts Obama into the history books, whatever economic and other problems may loom worryingly in the future. Certainly his work will be cut out for him given the falls in the stock market and some of the dire predictions going forward.

Maybe in such times of history, change and future uncertainty, it is appropriate to reflect, then, what exactly do we mean by past, present and future? What is the cutting edge of modern physics telling us about these important concepts?

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.

Please, just pick a side.

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.

So, you could view physics with a reversed arrow of time relative to everyone else (looking backwards so what you call time increasing corresponds to everyone else’s time decreasing) and this would be OK with subatomic physics as long as you also flip particles with antiparticles and left with right. The equations would not know, it would be a matter of convention and your conventions would be related to usual ones by these flips.

What is controversial is extending this to macroscopic physics. Let’s try, and you will see why. I am saying that there is a symmetry between, say, being a historian and being an economist (by which I mean broadly predicting the future in similar terms to modern historians, not just the stock market but governments, social trends etc.). Both take the world as it is today and extrapolate — backwards or forwards according to models of how the world works, to the past or future respectively. So if there was some other part of the Universe (another ‘region’ in the driving analogy) where people used the reversed convention on the arrow of time, their historians would be our economists in the sense above. Let’s call this, for the sake of discussion, time-reversed world, or TR world. It need not be an actual other world but just a reversed world-view.

This is not a problem with reversible classical mechanical models of evolution of the world. It is also not a problem for (unitary) evolution of the quantum state in quantum theory but there might be problems when you make quantum measurements. In quantum theory when you measure something the quantum state ‘collapses’ to the result of the measurement; information about the range of possibilities and their probabilities prior to measurement is lost. I think this is a red herring. Historians make use of probabilistic models just as well as economists, i.e. saying:

‘Given what we know now, its 99% certain that Caesar visited Gaul in the year 56 BCE.’

Vercingetorix surrenders to Caesar

Vercingetorix surrenders to Caesar

That sort of thing. Notice that the ‘arrow of time’ in the use of the probability here is past-pointing.

From a physicists point of view the main objection is the second law of thermodynamics, that entropy always increases. My view, however, is that this is ultimately not actually a fundamental law of nature. Rather, I think of it as a tautology about the way that we define and use probability. Thus, if you view probability as quantifying what will happen given what you know now, then you already built in an arrow of time into the very notion of probability and into probabilisitic concepts such as entropy. If, as just discussed, you reverse your usage then you will also be using these terms differently. A historian’s state of knowledge gets more and more uncertain as you go further back in time.

The real problem is that the arrow of time is so built into everything we do the moment that we communicate and share information — into the very concepts that we use — that tracing through all of the details of the reversed interpretation, fleshing out the dictionary between our usual way of speaking and the reversed way, is an immense and almost unimaginable task. It would be akin to creating a new and unfamilar langauge and way of looking at the world, but would be harder because every bit of science and not just every day life has to go into the dictionary. It is certainly much harder than converting your driving mentality from left to right as you go from the UK to the US.

The deepest part of the problem here is, well, how we speak about the notion of reality itself. Clearly, the past is somehow real, fixed, while the future is not yet written. Isn’t this where the historians-economists symmetry surely fails? Just because historians don’t know the past for certain does not mean that the past does not absolutely exist. I agree with that statement. But the thing is that the equations of physics are generally a-temporal, i.e. one looks down on the whole spacetime continuum past and future so from that perspective the future is also ‘real’. Free will and such matters are not really understood in physics, although some would say that they should be one day (one can point at the ‘measurement problem’ in quantum theory as providing a hint). This is a point that John Polkinghorne makes in his section of On Space and Time, that we do not yet have but do need a ‘theory of time unfolding’. Until then, the best we can say is that what for us is the actual past would for the people of TR world be the uncertain future, while what for us is uncertain would be fixed for them even if their knowledge of it to their historians was as murky as to our economists. It is ultimately a philosophical point as to what ‘exists’ really means.

To see some of the problems for scientists to define this ‘present’ where the solid past becomes the uncertain future, consider that someone zooming past you at high velocity experiences a different ‘now’ than you do. A standard illustration of this is the ‘pole in the barn’ paradox. Perhaps the reader will know that fast moving objects also shrink (this is called Lorentz contraction). So imagine a runner with a 20 foot pole going so fast that it appears to us as 10ft. Imagine is passes through a barn that is 19ft long and has doors at each end, and when the pole is inside we briefly shut both the doors. So the pole is momentarily enclosed in the barn. But from the point of view of the person running with the pole, the pole is not moving, so it is 20ft long and the barn is zooming towards them and is shrunk to 9.5ft. Clearly, the pole can at no instant fit entirely in the barn! The only way out is that what appears to us on the ground as closing the doors simultaneously appears from the point of view of the person moving with the pole as first one door closing for an instant and then the other door closing for another instant. The notion of ‘now’ is therefore ill defined. This is an instance of Einstein’s Special Relativity in action and one of the surprises is that it does not matter that much to physics; one can still have a notion of cause and effect without a universally agreed ‘now.’

So, can we have time travel? Over the years, there have been several fictional works about meeting someone traveling backwards relative to us. The Time Traveler’s Wife by Audrey Niffenegger is a recent one, while earlier efforts included stories by John Wyndham and by Brian Aldiss. I have not read any of these myself but I suppose that the traveler or the traveler’s consciousness travels back in jumps but is then aligned with our own arrow of time moving forward before the next jump. This is obviously wrong. What would it be like to truly meet someone from TR world? In view of what we have said above it would be much more serious even than recording what they said and playing it backwards. Our very notions of what it was for them or us to be would be different and need to be part of the dictionary.

But I can show you how it might work at the subatomic level.

Reading the figure from the bottom with time going ‘up’, we have at A a very high energy photon (a gamma ray) turning into an electron-positron pair (the paths marked e_- and e_+ respectively). These propagate and, perhaps in an electromagnetic field depicted by interacting with more photons, bend round and happen to recombine back into a gamma ray. It could happen, with low probability. In TR world the same series of events would be read backwards from the top of the page and I’ve done the diagram in such a way that they would see the same thing, just with the roles of electron and positron swapped. But a third way, remembering what Feynman said, would be to say that an electron appeared out of no-where at A, absorbing a photon of light, travelled to the upper part of the diagram and then disappeared in a flash of light at B, to travel back in time to the bottom of the diagram where it appeared at A as the electron we started with.

How to extend such subatomic ideas to macroscopic physics remains a mystery. We got a glimpse of how it might work thinking about history v economics, but fundamental gaps remain. But what I find fascinating is that some of it could be viable scientific research, i.e. proceeding in an incremental manner from the subatomic end up through the different layers of science, if only to see exactly where the symmetry goes wrong. I have a hunch that we would learn a lot about ourselves in the process.

About The Author

Shahn Majid

Shahn Majid is co-author of On Space and Time (2008) and author of A Quantum Groups Primer (2002) and Foundations of Quantum Group Theory (2000). He is Professor of Mathematics at ...

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