complexPHILOSOPHY said:
Zorn:
When you are discussing aspects of QM such as the 'problem of measurement', are you extrapolating information strictly out of QFT?
Naa, when discussing measurement etc. I've just been using 'ordinary' QM. By that I mean the single-particle, non-relativistic quantum mechanics that most people learn. Now QM is wrong because it doesn't take into account relativity, but of course it works perfectly fine in situations where that's unimportant. QFT is what you get when you combine QM with Einstein's theory of special relativity, and consider fields rather than single particles. It's the more fundamental, more correct theory, though in practice it's
used much less because it's much harder to do things with and for most problems regular QM works fine.
I've thought about this a bit, and I
believe that going to QFT doesn't change anything about the problem of measurement, it just adds unrelated complications. So vis-a-vis the problem of measurement, it's simpler just to stay with ordinary QM; any solution there will work
mutatis mutandis for QFT.
The issues that I am having with grasping the abstractions of QM (aside from the fact that I do not understand the mathematics involved) is deciding which interpretations of QM are the most accurate. I have read several different theories, which all seem to convey that macroscopic systems emerge out of the quantum level. Several indicate that when we reduce some systems to their constituent parts, that the whole is greater then the parts that make it up and that the properties of the particles which make up the systems, simply are not enough to explain the macroscopic system. I have, however, briefly read Bohm's simple version indicating that causal factors are embedded and we simply do not have the techniques to uncover them yet.
The nice thing about the various interpretations of QM is you can pick whichever one suits you best. There's generally no way of distinguishing experimentally amongst them, so they all yield the same predictions and are all equally consistent with the observations. So you can equally well believe a spontaneous-collapse interpretation, a Bohmian 'pilot wave' interpretation, a many-worlds interpretation, whichever you like. These are different philosophically but make the same quantum-mechanical predictions.
I am not sure what you are talking about when you refer to interpretations that imply "the whole is greater than the parts." The behavior of a system is determined by the rules of quantum mechanics applied to its components; you don't need to add anything new. The problem of measurement applies just as well to systems with only one particle as those with many.
I certainly do not invoke any 'metaphysical' connection to the collapse of the wave function and I understand that any macroscopic physical device such as a particle detector, is capable of collapsing the wave function but I am trying to grasp exactly what is going on. I have read about the pragmatic approach (which I think Neil's Bohr first presented) which essentially states that we shouldn't concern ourselves with 'the problem of measurement' and that we should regard it as one of the universe's deep mysteries.
It's true that most physicists subscribe to the "shut up and calculate" interpretation of QM. In practice it's clear what counts as a measurement, and it's hard to even see how one would go about testing these various interpretations. (There are a few experiments that have been done, in particular putting limits on the scale at which collapse theories could kick in.) So most of us think of it as a philosophical issue and don't worry too much about it. Some physicists (and plenty of philosophers) certainly do work & think about issues of interpretation, but I'm not too familiar with that area.
What it boils down to is this: the physical predictions of quantum theory are well-understood and well-tested. You can learn QM and you will understand the concepts of wavefunctions, incompatible observables, superpositions of different states, how they evolve in time, etc, and use this to understand how the world works. It's not easy but it's straightforward. But the philosophical interpretation -- eg, are things really random or is there some deterministic hidden structure? -- is another matter. There's lots of ideas and no way to say what the 'true' interpretation is. And there is a real difficulty that arises from the measurement problem: where exactly does the collapse behavior you get in macroscopic 'measurements' come from? Why don't we just see a weird superposition of readouts when we look at the display on a particle measuring device? (Or do we?) This is a deep and hard issue in which much thought has been poured without definite answers, AFAIK. The least confusing, least bizarre solutions IMO are spontaneous collapse theories -- where "big" quantum superpositions tend to collapse into a single value -- but these are not entirely problem-free and there's no reason to assume they're the right answer.
Does QFT 'ignore' the problem as well, or are the popular interpretations of QM simply erroneous and inaccurate? Also, I was reading about the vacuum states of various quantum fields and they seem to indicate that QFT generates a lot of infinities which arise out of the zero-point energy. Does E=mc² still govern the quantum vacuum of the various quantum fields?
There are other infinities which arise in QFT, of two types. The first are called 'infrared divergences' and show up when you consider particles of arbitrarily low energy (long wavelength). These are not "real" infinities per se, they are just an artifact that comes from assuming we have perfect detectors, which could never exist -- once you include the realities of a finite detector, the infinities go away.
The second type are much more problematic. They are called 'ultraviolet divergences' and come from the same place the infinite vacuum energy did -- from allowing arbitrarily small-wavelength (high-energy & high-frequency) particles. You could say they arise out of the vacuum in a way, because they only show up when you try to calculate
loop diagrams, Feynman diagrams with loops in them, which represent the effect of vacuum polarization. Consider: the simplest process you can imagine is just a particle propagating through space, which has a Feynman diagram of just a single straight line. But because the quantum vacuum is this complicated things, we also have to include possibilities like a particle-antiparticle pair popping out of the vacuum, interacting with the propagating particle, and then annihilating again. Such a process is represented by a Feynman diagram with a loop in it. Now, the problem arises as before because the momenta of the particles in the loop can go arbitrarily high (arbitrarily low wavelength.) When you do the calculation for how much of a 'correction' arises from these vacuum diagrams, you get an infinite answer.
This was originally a huge disaster, until people discovered how to deal with it, through something called renormalization. At first glance this looks like some sort of bogus cheap trick. What you do is break apart the calculation in a particular way into two parts, one of which is infinite, the other finite. Then you say "well, we are going to redefine the mass of this particle so it's infinite, and cancels of the infinite vacuum correction, leaving a finite result." This is called renormalizing the mass of the particle. Now this sounds shady but there are ways to make it more rigorous. And it works, impressively -- you get consistent finite results, and the finite pieces of loop diagrams actually have been verified to incredible precision. Today, we understand this process & it's not viewed as problematic. It comes from the fact that QFT does not work at arbitrarily small distances but must be replaced by something else (eg, perhaps string theory.) At low energies, though, the effect of this small-distance physics is only to modify the parameters of our theory through renormalization.
E=mc^2 still sort of "applies" I guess. If you mean does Einstein's special relativity apply to QFT, yes, it certainly does. But E=mc^2, though famous, is actually a rather odd equation nowadays. In Einstein's time, it meant that the (apparent) mass of a particle increased as the particle moved faster (ie with more kinetic energy.) Mass and energy are the same thing. But today relativity is so much a part of our thought that we don't even talk about what Einstein called "mass" (the apparent mass) anymore, we just call that energy! When we say "mass" today we mean
rest mass, the mass a particle would have sitting still. So ironically the famous equation is "wrong" using today definitions, or at least only applicable to stationary particles. For moving particles it should be instead E = gamma*m*c^2 , where gamma=1/sqrt(1-v^2/c^2) is a factor which is 1 for stationary particles, and keeps increasing the faster something moves.
) from solving problems & doing the physics... but it's one of the last things. At first you will just be using mathematics without really understanding what's going on, but gradually you will start to see the connections and eventually you will be able to turn your physics knowledge into these kind of popularized explanations for laypeople. It will take a while though.
