Does the future affect the present?

By Marcus Wilson 25/05/2010

Well, my comment on Naked Short Selling has certainly sparked a bit of discussion (for readers on you’ll need to look at the sciblogs hosting of the blog, ).  There’s the reasonable question asked as to whether letting people trade in things they don’t yet possess (basically anticipating the future – letting the future, or your interpretation of it, control the present) causes too much instability in the markets.

It’s a matter of common sense that the past influences the present  (like lingering animosity between two countries over something that happened hundreds of years ago, or a piece of baguette being dropped by a bird causes the Large Hadron Collider to be shut down briefly). In theoretical physics, we can describe this sort of effect in some systems with ‘Green’s Functions’.  Basically, if we ‘hit’ a system at a time T, what will the system be doing at a time T+t  (i.e. t seconds in the future). In realistic, common-experience systems, all Green’s functions share a couple of common properties:

First, as t gets large (we get to a time where the ‘hit’ was a long time in the past) the Green’s Function has decayed to zero.  In other words, if you leave it long enough, all past events are forgotten. Some systems have their Green’s functions decay much faster than others – ones describing the way your car suspension behaves when it hits a bump might be a few seconds, ones describing the movement of a tsunami following an earthquake might be a few hours.

Secondly, when t is negative (meaning at a time before the ‘hit’), the Green’s function is zero. This means that the car suspension doesn’t respond BEFORE you hit the pothole. In other words, the future does not influence the past.

All this is logical. BUT, there is a system in physics that has Green’s functions that are not zero for negative t.  The Klein Gordon equation is used to describe relativistic (spin zero) quantum mechanical particles. Let’s not worry about what it is for now.  But its Green’s function can be found without too much difficulty, if you’re a good maths undergraduate, and it has a surprising and worrying property. It isn’t zero at negative t. The implication is that the future can influence the past.

Ouch. An  interpretation of these backwards-moving-in-time solutions is that they represent antiparticles.  That is, an antiparticle (and antiparticles are very very real – ask anyone who’s had a PET scan) can be thought of as a particle moving backwards in time.

Sometimes mathematics overtakes common sense.

Is there any analogy to anti-particles in the financial markets? Maybe there are anti-traders lurking out there waiting to annihilate unsuspecting traders on their lunch breaks (over a baguette, of course).

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