# The transactional interpretation of quantum mechanics

An entry in Ars Mathematica has alerted me to John Cramer’s Transactional Interpretation of Quantum Mechanics [see also Wikipedia]. It feels exactly right.

The trouble with quantum mechanics has always been that it makes accurate predictions but doesn’t make sense. People make a virtue of this. It shows how far above our heads the whole theory is. “My thoughts are not your thoughts, my ways are not your ways, says the Lord”.

This is self-indulgent obscurantism and it leads to such New Age loopiness as The Dancing Wu Li Masters (in which, among other delights, every chapter is called Chapter One).

The transactional interpretation is solidly and sensibly based on mathematics – specifically, on a bit of mathematics that has mostly been ignored because it’s embarrassing.

The equations that describe the propagation of an electromagnetic wave (such as light) have two solutions. One describes a wave that is carrying energy into the future; the other describes a wave that carries negative energy into the past. It is this second solution that people don’t like much and consequently ignore.

It turns out that if you don’t just look at the particle that’s sending out the radiation but also look at the one that’s absorbing it, the second particle’s backward wave reinforces the first particle’s forward wave between the particles, but the second particle’s backward wave cancels out the first particle’s backward wave, which is why you don’t see a backward wave before the first particle; and the second particle’s forward wave cancels out the first particle’s forward wave, which is why you don’t see a forward wave after the second particle has absorbed it.

That was rather an involved sentence, but it amounts to this: if you embrace all the solutions of your equation instead of cowering away from the one you don’t like, the result you get makes perfect sense.

More than sense, in fact: because we have both a wave going from the transmitter T to the receiver R and a wave going backwards in time from R to T, the two particles can interact in the way called for by quantum physics – the “collapse of the wave packet” and so on – without requiring an act of measurement by an external observer. There really can be a world “out there” independent of us. We have got our real universe back.

This is all really nice but what makes it smell right to me is something about the mathematics of quantum measurements. When you make a measurement, the famous “collapse” yields an eigenvalue of the measurement operator and puts the system into a state represented by the corresponding eigenvector. This reminds me of what happens when you multiply a vector repeatedly by a matrix: gradually, as you multiply more and more times, you end up with the results growing like powers of the largest eigenvalue of the matrix, and the vector itself turns more and more into a multiple of the corresponding eigenvector.

So the eigenvalue behaviour of quantum measurement makes me think “an operator is being repeated infinitely often”. The way I always thought this would work was if time were circular on a sufficiently small scale; but the advanced-and-retarded-wave scenario does the same thing more economically.

An additional advantage of the transactional interpretation seems to be that time is relegated from being some grand causal factor to being just another co-ordinate. This parallels what happens in classical dynamics – where, since everything is determined by everything else, the entire behaviour of the universe can be portrayed as a static unchanging configuration in 3-plus-1-dimensional space and the entire notion of “cause” disappears. This precedent seems to say that a physical theory that requires concepts of causality is in some way flawed. If the transactional interpretation of quantum mechanics really does remove that flaw then it is something we have been waiting for for a long time.