Question

Can u pls make it clear to me how the contradiction between relativity physics and quantum physics on the other has been leading to a crisis in physics?

Answer 1

Ordinary quantum mechanics is not relativistic. For example, there is instantaneous action at a distance. The term in the Hamiltonian of the hydrogen atom that accounts for the attraction between the nucleus and electron implies that the force is a function of the *instantaneous* distance between them -- there is no delay due to the finite speed of light between when either changes its position and when the other feels the change in force. Location in space is treated as an operator, but location in time is treated as a parameter -- so space and time are not treated the same way.

You can fix this by going to a relativistic quantum field theory. Now both space and time are treated as parameters (the field strength and velocity become operators). There is no instantaneous action at a distance: when a particle changes position, which is to say when a local fluctuation in the field moves to a different location, this effect propagates at the speed of light, naturally, and is felt by other fields elsewhere at a later time.

So far so good. However, relativity introduces the possibility of particle creation and annihilation, because inertial mass and energy are no longer separate things. That is, a given concentration of energy in a field can be interpreted (depending on your viewpoint) as either more particles or faster moving particles, roughly speaking.

If particles can be created and annihilated, then any observable particle is necessarily always surrounded by a sea of "virtual" particles that are being created and annihilated all the time. They will generally interact with the observable particle, and change its properties. If you try to calculate how they change its properties: for example, what is the observed charge on an electron, given the screening produced by the cloud of virtual electrons and positrons around it all the time, using ordinary relativistic quantum field theory, you unfortunate find infinities in your calculations that won't go away. It appears the effect on the charge of the electron, for example, is infinite.

This problems was solved, if solved it was, by Feynmann and Schwinger, who independently found a way to sweep it under the rug. More or less, you can show that all the infinities can be contained within the observable properties of the particle. That is, the only thing affected by the infinites in the case of an electron is its charge and mass. So, the reasoning goes, why not just assume the bare charge on the electron is -infinity, then the correction due to the interaction with the virtual electrons and positrons is +infinity, and the two delicately cancel out -- to give you the actual, observable charge on the electron! Sweet! Of course, the actual assumption is that there is something wrong with the theory when it comes to very, very high energy, or equivalently very small distances close to the electron, and a better theory will take care of this without infinites. But the practical point is, you can do calculations, because you can sweep all the infinities into the measureable parameters (charge, mass) and forget about them.

Unfortunately, when it comes to doing this with the graitational field, you can't sweep all the infinities into some measureable parameters. Why, I don't actually know, because I'm insufficiently familiar with the math of general relativity. But that's the problem. The way this is said is that a quantum field theory of gravity is not "renormalizable" the way a quantum field theory of electromagnetism is.

So far as I know, the efforts people have been making to solve the problem are all centered around finding some natural limit on how many of these virtual particles (or fluctuations in the quantum field) there can be. Essentially, you have to find some very tiny length scale below which there can no longer be any fluctuations, some kind of very small distance (and hence very high energy) cutoff. If the universe is made of strings, this does the trick, because the size of the string is a natural cutoff. Same for constructions of the universe that imply some kind of granularity at the smallest length scales, some way in which space itself (or rather spacetime) has an "atomistic" nature -- has some smallest chunk that can't be subdivided. The problem with most of these theories is they are underdetermined. They can explain reality well enough -- but also equally well predict eighty-six bazillion kinds of reality that do NOT exist, and we have no way of knowing why our reality is the one we have, rather than these others. This is unsatisfactory. We want theories that predict reality, and only reality, and do not also predict things that are not true.

So there we sit. No one's really had any breakthrough ideas about this stuff in at least 50 years. Apparently, we await another Einstein, or Newton.