Does String Theory Have A Heartbeat Still ?

I've just read Peter Woit's take on the latest String Theory conference. Mr Woit wrote one of my favorite books on non-physics :  Not Even Wrong. It seems that even ardent string theorists are doing something else now. Thus I think ends an almost 50 year hiatus in theoretical physics, plus to me it seems possible that physical observations and measurements may come back into vogue to guide these theorists !! They seem to have gotten over the whole 'truth must be beautiful mathematics' thing. If you are young it might even be a good time to get into theoretical physics.

For example One problem that certainly needs attacking is in quantum mechanics, and is generically called the 'collapse of the wave function' or 'the measurement problem'. This aspect of quantum theory is assumed to occur but there is no known agreed mechanism as to how. If one has a general state |psi>, written in the energy representation thus :

|psi> = Sum_over_n_of{ a_n * e^{( - iE_nt/h)}  * |E_n> }

where the a_n are complex numbers, E_n is the energy value of the eigenstate |E_n>, h is the reduced Planck's constant and n is however many constants you need to completely describe the system that |psi> represents. The entire complex exponential acts like an endless clock, spinning around at an angular frequency^* of E_n/h. This equation describes the state |psi> as being a linear weighted product of terms, where for each a_n when the modulus is taken and squared is proportional to the probability of being in the given energy eigenstate |E_n> upon measurement. So it's a mixture of ( typically very many ) 'pure'/exact energy states and when a system evolves ( via Schrodinger's time dependent equation ) the a_n's will change and so will those probabilities. OK. So now you perform an energy measurement to yield for one value of n, call it k:

|psi> = e^{( - iE_kt/h)}  * |E_k>

In other words, out of all the possible energy values that one could have measured E_k was the one that actually happened ( so a_k is now equal to one^** and all other a_n's are zero ). The state is now one of the 100% pure eigenstates. Now the conundrum : how did the system transition from the multifactorial one ( 1st equation ) to the singular one ( 2nd equation ) ? That this transition exists at all is a non-negotiable part of quantum mechanics. A probabilistic aspect is also required. Complex numbers are mandatory. Some think that the lack of knowledge about the state of the measuring device prior to the act of measurement is what generates the uncertainty in the outcome of the measurement. But the question still stands.

BTW if the system was absolutely & positively left alone in that state of exact energy, it would be eternally so. In reality these exact energy states are never seen. After or during a measurement to yield a given energy value, there will be a disturbance from something to kick it into a new mixture of states. Here you need to blur the lines between the part of the world that is 'the system' and the part that is the 'measuring device', that is arbitrary ( a matter of descriptive choice ) and not intrinsic. Also bear in mind that quantum mechanics is absolutely stunning in it's predictive value, despite the probabilistic aspect, as ever so many phenomena attest.

Now over the years there have been a number of proposed ways to address the question, some quite challenging, and many attacking underlying assumptions eg. is the wave function a 'real' thing. I mention this measurement issue because if one is going for a unified field theory ( 'of everything' ) then you need gravity and quantum mechanics to have some common ground, and sitting in that common ground, like a landmine, is this problem. Or put another way : how can spacetime curvature be made probabilistic ? Should it be made so ? Etc ... etc .....

Cheers, Mike.

* Here the value of h is the key to understanding how quantum theory approximates classical physics for high values of n. Take a Mars bar for instance and call it a 100g lump/mass, with energy mc², and let it sit there on a table just existing. If it was in a state of definite energy, E_n, equal to it's mass/energy equivalent then it's angular frequency E_n/h is of the order of 10⁵⁰. That's a 1 followed by fifty zeroes and that's in Hertz or cycles per second : it's an insane number to oscillate at and guarantees that you won't be seeing interference effects between Mars bars any time soon. :-)

** When 'proper normalisation' has been done all probabilities must add to one. This is just mathematical housekeeping done in order that quantum theory respects our intuition(s) about probability.