So, I was planning on writing a blog post much earlier than this. But then, I came down with a cold, and as a secondary effect I got behind on my homework. But I'm almost healthy by now—if not entirely caught up on my homework—and a blog post popped up in my RSS feeds that I just can't ignore. Over at Tommaso Dorigo's blog, Rick "Island" Ryals has been given the floor for a very interesting guest post. As far as I can make out, the claim is that taking into account the gravitational effects of pair production solves many open problems in physics, including the inflationary universe, fine-tuning, and even the Higgs mechanism. The clearest statement of how this should be done seems to be the following sentence:

…an increasing anti gravitational *effect* is offset by the local increase in positive gravitational curvature that accompanies the created massive particle pair.

While I'm dubious that this truly has as many interesting consequences as Ryals claims, it does seem likely that he's on to something. I do wonder what the "conventional" solution to this problem is, however: that is, what would most physicists answer when asked Ryals's motivating question, "Does particle creation from vacuum energy change the gravity of the universe?"

Connection to the Dirac Sea?

This may be a flaw in my understanding (or in Ryals's writing, as opposed to his theory), but the post mentioned above makes a pretty abrupt jump into the Dirac sea theory, and as far as I can tell doesn't actually make any kind of even semi-mathematical connection between the two concepts. That is, I'm not seeing anything discussing the implications of gravitational pair-production effects in the Dirac sea paradigm, but instead just an attempt to use the Dirac sea idea to point out that quantum field theory has problems with the vacuum state.

(There's also the puzzling matter of this quote: "Dirac’s theory was flawed though, in-spite its success at predicting the existence of the 'positron', because it can’t fully account for particles of negative energy, since it is restricted to positive energy particle." Um, Dirac's theory works pretty much in the opposite way of what he's describing: it does fully account for particles of negative energy, using them to fill the vacuum state. It does not contain conventional quantum field theory's restriction to positive-energy particles only, but instead allows both to exist and relegates one to filling the vacuum state. Or is he claiming that there are actual negative-energy particles—as opposed to positive-energy antiparticles—and then saying that they shouldn't be confined to filling the vacuum state?)

However, what really caught my eye in this section was his link to one of Dan Solomon's papers. During the summer, while browsing idly through the arXiv, I too ran across Dan Solomon and the many papers he has written on the vacuum state in quantum field theory, with emphasis on how it differs from that of the Dirac sea theory. Curiously, nobody seems to have cited him or picked up on his results. I emailed Dan about his ideas, and received the following summary of them:

As you evidently know quantum field theory (QFT) is suppose to be gauge invariant. However when calculations are done non-gauge invariant terms can appear. These terms must be eliminated in order to achieve a physicaly correct result. There are a number of mathematical techniques that are used to eliminate the problem. The question is why does the problem exist in the first place? As you know from my papers I claim to show that the problem occurs due to the fact that when the vacuum state is defined in the standard way it is the state of minimum energy.

Now this has an interesting implication. It implies that if the vacuum state were defined correctly it would not be the state of minimum energy. This possibilty is a frightening thought to most physicists. If you look in any book on QFT the vacuum state is always assumed to be the state of minimum energy. This is where my work on Dirac Hole theory comes in. Hole theory is not of much interest to current physics because it has been replaced by Quantum field theory. However at a "simple" level Hole theory and QFT should be equivalent. Therefore results from hole theory should carry over to QFT. Now consider the hole theory vacuum, or the dirac sea, as it is sometimes called. This consists of electrons that occupy the negative energy solutions to the Dirac equation. These electrons are like "normal" electrons in that they interact with an electromagnetic field. So the question I asked myself is whether or not the Hole theory vacuum is a state of minimum energy. That is, can you extract energy from the vacuum through interaction with an electric field? In my paper "Some new results concerning the vacuum in Dirac's hole theory" I show that the anwer to this question is yes. You can extract energy from the hole theory vacuum therefore it is not the state of minimum energy. The result of all this is that perhaps some of the assumptions we have made about the vacuum should be re-examined.

He also confirmed that he has received almost no feedback on his ideas, and admits that one of the possible reasons might be that "there is something fundamentally wrong with my work and everbody knows it except me." And that might be a possibility, just as it might be a possibility for Ryals's ideas as well. But for an interested, open-minded amaeuter like me, without any research grants to waste or supervisors to displease, I'm willing to give them the benefit of the doubt.

Is There Something Wrong with QFT?

Back during the summer, shortly after exchanging emails with Dan, I showed his papers to another undergraduate friend of mine with a passion for physics. While he generally knows more than me, neither of us have the background to check over the papers in all their mathematical detail, so I wasn't able to get any conclusive answers. But we both agree that this kind of problem ultimately seems to stem from the shakiness of the mathematical foundations of perturbative quantum field theory. For a funny introduction to these problems, and also an idea of how much I understand of them, check out the section "Life Cycle of a Theoretical Physicist" in these quantum field theory lectures.

In essence, as far as I understand, we've been trying ever since QFT came out to apply quantum mechanical methods and logic to our new theory; this often doesn't work too well. For some reason we're able to get a lot of predictions out of QFT, but we do so by through renormalization and cutoffs and all of these messy, often ad-hoc procedures that, at least to me, say that we're missing the right combination of conceptual and mathematical framework. I mean, virtual particles? What are those supposed to be? Mathematical artifacts, or actual particles that travel from here to the moon and back—faster than the speed of light, no less—before contributing to our path integral? The work of people like Dan Solomon and Rick Ryals, assuming it's at least partially valid, is bringing this kind of thing to light. But it would wbe nice if we were just able to start from some simple axioms (like, say, "the laws of physics are the same for all comoving observers" or "coordinates don't matter") and come up with a way of reproducing the predictive power of quantum field theory, while naturally being able to handle things like gauge invariance, Lorentz covariance (or, better yet, general covariance), etc. without making a big perturbative mess and fixing our gauge and so on.

Going Forward

As we move forward, it seems like there might be a lot to be gained from attempting to reshape quantum field theory into something more elegant, instead of hoping that quantum gravity will solve all of our problems. (Our current major contenders seem to have calculational difficulties of their own that remind me vaguely of QFT's, but here I'm getting way out of my league so I should stop speculating.) If we manage to axiomatize it in a nice way, with general relativity-style axioms (as above) instead of quantum mechanics-style axioms (states are vectors in an abstract space that contains an inner product; upon "measurement" these collapse to eigenstates; etc.), then maybe we'll solve some problems in quantum foundations too! And if we're lucky, once this hypothetical "beautiful-QFT" is worked out, quantizing gravity might become easy in its framework.

Unfortunately, there's another alternative that also seems likely. Namely, that we won't be able to solve QFT's problems without incorporating some features of gravity. This would certainly make things more complicated, and explain why quantum field theory is such a mess right now. And one the one hand, it'd be pretty exciting: everything is connected to such a degree that we can't even separately account for these aspects of nature! On the other hand, it might just reduce to our existing quantum gravity programs (which, while not boring, aren't yielding any "eureka!" moments currently). I don't know, though; has anyone looked at quantum field theory, and said "what do we need to fix, and can gravity help?" It seems more as if people are asking "how can we quantize gravity?" Ryals's work seems to be driven at least somewhat from the former direction, which is part of why it interests me.

Clearly, the only thing for me to do is learn quantum field theory myself so I can start working these questions out to my satisfaction! Curse my silly wave mechanics homework for getting in the way…