What is the biggest problem in physics?

I like to be reasonably forthcoming both here and in my “Ask a Physicist” columns at io9 about what we do and don’t know about the world. As successful as physics (and in particular, the idea of symmetry) has been in unifying various phenomena, there are at least two classes of questions that we don’t seem to be particularly close to answering at all:

  1. Why these symmetries and not others?

    It seems very strange that the laws of the universe are symmetric under CPT transformations (simultaneously flipping the arrow of time, looking at the universe in a mirror, and trading every particle for its antiparticle) or the continuous “U(1) symmetry,” while other symmetries, like “SU(5),” (which was thought to be a prime candidate for a Grand Unified Theory), turn out to be wrong, experimentally.

    All we can do is check with the universe and see whether certain symmetries hold, and if they don’t, check other symmetries instead.

  2. What about all of the free parameters?

    Some of my colleagues are experimental neutrino physicists. They spend their efforts trying to figure out the masses and mixing angles between the various neutrino species — numbers that tell us, essentially how likely it is that one type of neutrino turns into another. But these angles and the masses, and the mixing angles in quarks and the strength of the various forces and so forth… all of these numbers have to be put into our theories more or less by hand.

    Even “obvious” numbers like the number of spatial dimensions in the universe or the fact that there are three generations of quarks and leptons (e^-, mu^-,tau^-, for instance) are put in in a completely ad hoc way.

    Many, perhaps all of these numbers may not ultimately have a deeper explanation. They may, in fact, vary significantly over the multiverse. This is the origin, as you may know, the so-called “weak anthropic principle.” It’s only in our region of space that the parameters and symmetries are just right to produce complicated life.

But to my mind, these aren’t anywhere near the worst problems in physics. The biggest problem in physics comes from the vacuum all around us. I don’t want to make this an overly mathematical discussion, but I do want to give you a feel of why the vacuum poses such a big problem in physics. But first, let me give you a simple result that comes from the Uncertainty Principle of quantum mechanics.

Suppose you had a little mass on a spring.


This is a good model for lots of physical systems. The most obvious is molecules, which are in a continuous state of oscillation, but as we’ll see, if we take a lot of these, it turns out to be a great model for the universe as a whole. No matter how much you cool down your oscillator, it turns out that you can’t extract all of the energy. There’s a lowest possible energy, which is:

 displaystyle  E_0=frac{1}{2}hbar omega

where hbar is the reduced Planck constant (which basically says that we’re doing quantum mechanics) and omega is the angular frequency of the oscillator.

One way of thinking of this is that if it were possible to stop the oscillations exactly, you’d be able to know the exact position of the mass (the equilibrium position) and the exact momentum (zero) simultaneously. That is expressly forbidden by the Uncertainty Principle.

Now here’s the big twist: There are fields surrounding us, even in empty space, and the way a physicist might imagine it, the field behaves a lot like a rubber sheet or a mattress:

What you see here is a cartoon version of a field (like the electromagnetic field) in a two dimensional universe. The height of each of the points is something like the amplitude of the field. In this picture, we basically have two particles flying around, hence two peaks.

(Notes to experts: a) I realize that this really only describes a spin-zero field, and even so, we could have troughs or imaginary numbers as well as positive amplitudes. b) Nobody likes a showoff.)

But then quantum mechanics intervenes. I described our field as behaving exactly like little masses on springs. As a result of that, every single spring contributes some minimum amount of energy to the universe. Given that there are an infinite number of them, this is an infinite contribution — an infinite vacuum energy density.

In practice, we expect that you wouldn’t get any oscillations smaller than the Planck Length, about 10^{-35} m. This is the scale where quantum mechanics and gravity combine to make all of our knowledge of physics completely useless. Saying anything smaller than the Planck scale just makes us look silly.

So the good news is that the vacuum energy isn’t infinite. The bad news comes in two parts:

  1. Even if the vacuum energy density isn’t infinite, it still ends up being about 10^{96} kg/m^3, or about 120 orders of magnitude denser than the universe itself.
  2. Experimentally, there really is a non-zero vacuum density out there. I’m not going to get into the Casimir effect, but the basic idea is that you can use metal plates to measure a force from the vacuum directly. The diagram up top or the wikipedia link may be of some help, but in either case, it’s a discussion for another day.

If the vacuum energy is so huge (and real), why don’t we see it gravitationally?

Ah, but we do see a gravitational source in the universe that has the exact properties of the vacuum energy (including a bizarre “negative pressure.”) It’s called “Dark Energy” or “Cosmological Constant,” and as you may recall, it’s the mysterious substance that drives the acceleration of the universe. Unfortunately, the cosmological constant is about 10^{120} times smaller than reasonable estimates of the vacuum energy.

This, in my opinion, is the worst problem in physics.

Without getting into even further anthropic arguments, the question remains as to why we should have any cosmological constant at all?

And yet, as the Nobel committee recently confirmed, we do seem to have just that.

Curious universe.

-Dave

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