Physics below the Planck scale: Part II

The integral satellite

In the first part of this post, I presented the context in which the study of very high energy cosmic rays can lead to an understanding of spacetime at the smallest scales allowed by our best current physical theories. It is a widely spread expectation among physicists that the structure of spacetime as we know it (which is three dimensions of space, and one dimension of time in which you can position yourself as precisely as you want) is breaking down when you try to look at things as small as 1.6−35 meters.

Let me tell you a little bit more about the structure of spacetime. It sounds very straightforward, but there are a few subtleties associated with it of great consequences which are generally called special relativity. It is very easy to get your mind blown away when you contemplate special relativity. The best known consequence of it is that objects appear shorter and shorter as you travel faster and faster. Also, time seems to pass more and more slowly as you go faster. We don’t see any of this in our daily lives because we don’t move at any speed close to the speed of light.

An even more mind-blowing way of looking at it is that if you go fast enough, you start converting time into space. Actually, this is not so weird when you look at the equation defining speed:

Rearrange and you get:

The speed is the conversion factor from time to distance. The really weird thing is that this relation is incorrect when the speed gets close to the speed of light. Not only do the speed cannot exceed the speed of light, but the relation start getting skewed in weird ways as you approach the speed of light. Actually, it starts looking suspiciously like a rotation

Let’s take a completely different perspective for a moment. Another thing that we know about spacetime is that it doesn’t matter where you are, or when you are, the laws of physics are the same. This why your computer mouse keeps working as you make it slide across your desk. This is also why it doesn’t transform into an actual mouse after 5 minutes of utilization. Technically, we say that the laws of physics are invariant with respect to translations in space and displacements in time. These are the symmetries of space-time. Of these symmetries, the most fundamental principles of physics follow, such as conservation of energy and momentum.

It doesn’t matter at what speed a box with a cat inside is moving. The cat will feel like she is standing still, as long as the box is not accelerating. You can sympathize for having been in a car before, on a long, straight and boring highway. The laws of physics are independent of the speed, in much the same way as they are independent of the specific position or of the specific instant. This independence also tells us exactly how to modify the speed equation above to get the correct one.

Lorentz contraction, in the direction of motion. c is the speed of light.

The property of being invariant to changes in position, time and speed is usually called Lorentz invariance. Lorentz invariance is everything we know about the structure of spacetime. Then, if the structure of spacetime breaks down at the Planck scale, we should see violations of Lorentz invariance.

Violations of Lorentz invariance are exactly what the team working with the IBIS detector on the Integral satellite have been searching for. However, there are many, many ways in which Lorentz invariance might be broken. It is very difficult to look for a general deviation from Lorentz invariance. What you can do is assume that Lorentz invariance breaks in a certain way, and predict how it will affect the high energy cosmic rays. You can’t predict how they will be affected if you don’t presuppose a way to break Lorentz invariance.

In the last post, I pointed you to this citation from the paper:

Unfortunately, the dimension-5 operator of (3) is not compatible with supersymmetry. We therefore have to resort in this case to dimension-6 operators.

Don’t let the 5 and 6 dimensions things numb your mind. I don’t understand either what these actually are or why they have that many dimensions, but I do understand what they do, and so can you. The 5-dimensional operator represents one way of breaking Lorentz invariance. The 6-dimensional operator represents another. The cosmic ray data lead the researchers to conclude that the 5-dimensional operator cannot possibly break down spacetime at the Planck scale. However, the 6-dimensional operator still can. So to correct the good folks at science daily, we now know that spacetime, if it breaks down at the Planck scale, cannot be broken by a 5-dimensional operator.

There is however a truly fascinating consequence of this investigation into the cosmic rays. I will not explain in detail what supersymmetry actually is, suffice to say that it is a prediction of many physical theories that are attempting to go beyond our current understanding of Nature. The motivations for supersymmetry are good, but not quite enough to convince me that it is real. At least, until I read this paper.

As it turns out, the 5-dimensional operator is not allowed in a supersymmetric theory. However, the 6-dimensional operator is. Just to be clear, this does not prove anything. But in essence, this 5-dimensional operator that got excluded is the simplest way we can think of to break Lorentz invariance. If Lorentz invariance had been found to be violated at the Planck scale by this operator, that would have been very bad for supersymmetry. The IBIS scientists could have excluded supersymmetry, but Nature decided otherwise. Supersymmetry survived a scientific test without having to be adjusted. This is a tremendous achievement for a scientific hypothesis. I still have my doubts about supersymmetry, but I never looked at it so seriously.

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