The Best and Worst Prediction in Science

How much energy is there in empty space? We believe there is 10 to the minus 8th ergs in every cubic centimeter of empty space. How much is an "erg"? It's a very small amount. You know, if a mosquito flaps its wings, or a fly I guess flaps its wings, it's about 1 erg's worth of energy. So, an erg is not very much.

Uhh, we're talking about a hundred millionth of an erg in every cubic centimeter of space. Now, it might seem strange that completely empty space contains energy, but there are 2 good reasons why scientists think this is the case. One is because the expansion of the universe is speeding up, and that's thought to be caused by dark energy, which fills all space and makes gravity repulsive.

We always think that gravity always pulls, but according to Einstein, the way gravity works really depends on the material itself and energy tied to space; gravity pushes, it doesn't pull. If that number is 10 to the minus 8th ergs per cubic centimeter, then you fit the data; then that's the dark energy that makes the universe accelerate. It's constant; does everything you want.

The second reason why empty space contains energy is because it isn't really "empty". There is the idea that, thanks to quantum mechanics, we do expect particles to come in and out of existence, and so space is full of energy. Yeah, there was nothing there when we first looked, and nothing there when we later looked. Could we say for sure, if we had looked in the middle, that there weren't particles there? No, there might have been.

Evidence for these so-called "virtual particles" came from studying the light emitted by energized hydrogen atoms. Niels Bohr first used the particular colors of light to devive his quantum model of the atom, where the electron orbits the nucleus in certain allowed orbits, each with its own specific energy. When the electron jumps from a higher-energy orbit to a lower one, it gives off light, and the energy-enhanced color of that light is determined by the energy difference between the two levels.

As quantum theory developed, Bohr's orbits were superseded by probabilistic electron clouds, but the energy levels remained mostly unchanged. Then, in 1947, Willis Lamb and his grad student Robert Retherford attempted to test the best version of quantum theory at the time, which was the Dirac equation. And they did this by measuring the energy levels in hydrogen more precisely than ever before.

Now, what they found did not match up with the theory. One of the energy levels was actually not one, but rather two, very closely spaced energy levels. And this is known as the Lamb shift. They used microwaves to excite the electron between these two levels. So, why were there two energy levels where there was supposed to be just one? Well, the answer is virtual particles.

For example, around the proton, virtual electron-positron pairs pop in and out of existence. This is permitted by the laws of Quantum Mechanics so long as they don't stick around for too long. During their brief lives, the negative electron is attracted to the positive proton, while the positron is repelled away from it. This means the charge of the proton is shielded by the virtual electrons surrounding it.

This affects the energy of the 2s orbital - in which the electron is closer to the nucleus - differently from the 2p orbital, and that's what causes the energy levels to split. And this is just one contribution to the energy difference. The full calculation involves drawing a series of Feynman diagrams that show all the possible interactions between real and virtual particles and adding up the contribution from each one. And there's an infinite chain of these different diagrams.

So you might worry that you can predict nothing at all because you'd need to add up an infinite number of numbers to get the right answer. But the point is that every time you have these two vertices, these two places where the photon hits the electron, that's associated with a number alpha, the fine-structure constant, which is 1/137, which is a small number.

So, this leading term, this classical contribution is already small, and these more complicated ones, you notice there are more vertices up here, and as the diagrams get more and more complicated, there are more and more of these terms. So you get alpha squared; alpha cubed; alpha to the fourth, and the numbers become smaller and smaller and smaller. So the more complicated diagrams, the more intricate effects of the virtual particles become less and less important.

Using the Dirac equation, but adding in the effects of virtual electrons, positrons, and photons, we can actually calculate the values of atomic parameters with better accuracy than 1 part in a billion. That is incredible. In fact, physicists Lawrence Krauss calls it: "The best and most accurate prediction in all of science."

So with the spectacular usefulness of virtual particles, you think it would be pretty hard for anyone to doubt their existence. But then again, they have never been directly observed. In fact, theoretically, that's impossible. Explaining virtual particles is always tricky because it's very hard to think of them in any sort of real way. They can go in the opposite direction of their momenta and... and... and do these things which are not consistent with... with a real particle. So virtual particles have a strange sort of existence.

Where they're indispensable for calculations, obviously, but you can never directly observe them. But maybe this is not actually a real problem; it's just the result of thinking about reality in the wrong way. Maybe as the fundamental building blocks of our universe, we shouldn't be talking about particles at all; but rather, "fields." The truth is that Quantum Field Theory is, according to our best current modern understanding, the right way to talk about nature at a fundamental level.

Uh... when we talk about particle physics, when we talk about electrons and gluons and quarks... to the modern physicist, these are vibrations in fields. In exactly the same way the photon is a vibration in the electromagnetic field. Just like there is an electromagnetic field, there is also an electron field, there's a neutrino field, there's an up-quark field, and a top-quark field, et cetera. And these fields fill space, and usually, they're just sitting there, fairly quietly, but when they vibrate, and you look at it, you see that in terms of individual particles.

In this picture, virtual particles are quantum fluctuations. Little disturbances in the field. They play a role in interactions, but they aren't measurable as 'real particles' themselves. And since they exist everywhere, they should imbue the vacuum with energy.

If you were to try to estimate the amount of energy due to the virtual particles in empty space, what kind of number do you get for the energy of empty space? Yeah, this is a huge problem because the 'back-of-the-envelope' estimate says there should be about 10^112 erg for every cubic centimeter, compared to the 10^-8 that we actually get.

In other words, you predict 10^120 times the energy density of empty space that you actually observe. So obviously, your 'back-of-the-envelope' calculation is wildly, wildly incorrect and no one is really quite sure why. The way we said the universe responding to the cosmological constant, the way we expect the vacuum to behave are the most discrepant things we have in physics, if they are the same things.

How is it possible that both the best and the worst prediction in science are both based on the same underlying physics of virtual particles? I mean, one experiment seems to show that the theory is perfectly correct, while another shows that we could not be more wrong. You know, there are a lot of areas of human endeavor where we fear being so wildly incorrect, but in science, this discrepancy is actually really exciting.

Because it shows us a piece of the puzzle that we haven't figured out just yet. That we have to solve this problem if we are to fully understand the universe. And in that way, this is the best clue we have at the work that still needs to be done. So... yeah. We don't know. But that's always good! It's always good to say you don't know, right? I think so!

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