String theory nonsense makes comeback

[This is a transcript with links to references.]

I got a lot of questions last week about an article in Quanta Magazine about Dark Dimensions. And for a change this is a case where I think Iā€™m actually the right person to ask. Whatā€™s this all about? Letā€™s have a look.

This recent work is based on string theory, an approach to a theory of everything that was invented in the 1970s. It was quite popular in the 80s and 90s. One of its main features is that it requires 9 dimensions of space. Now, as youā€™ve probably noticed, we donā€™t live in 9 dimensions. So string theorists assumed that 6 of these dimensions are not infinitely large, they are rolled up to such small sizes that we wouldnā€™t notice them.

The new paper says that the extra dimensions could explain dark matter, if that exists, which it may not, hence the combination dark dimensions. Dark matter is what astrophysicists think makes up 80 percent of all the matter in the universe, but we canā€™t see it and we have never managed to directly detect it. We only indirectly infer the presence of dark matter from its gravitational pull. This is why thereā€™s an alternative idea, that thereā€™s no dark matter, itā€™s that weā€™ve got the law of gravity wrong. Though Albert doesnā€™t like that at all.

But back to the extra dimensions. In the original idea of string theory, these additional dimensions were so small that we canā€™t measure them at all, about 10 to the minus 35 meters, a size know as the Planck length. Itā€™s named after Max Planck who also made the quip that science progresses one funeral at a time. Though I think that was very optimistic.

Then, in the late 1990s some people had the ingenious idea to just conjecture that one or several of these hypothetical dimensions are much larger than the Planck length, so that they could become measurable with the next generations of experiments. These were called the ā€œLarge Extra Dimensionsā€.

You see, the way this kind of research work is that itā€™s always the next experiment that will test these ideas. And if that next experiment doesnā€™t find the stuff, then itā€™s the next after that, and so on. Physicists usually justify this by a pseudoscientific argument called ā€œnaturalnessā€ according to which some otherwise arbitrary values of model parameters are preferred by nature. These ā€œnaturalnessā€ predictions can be shifted because theyā€™re not scientific to begin with.

20 years ago, there were a number of experiments that looked for these large extra dimensions, particle colliders, astrophysics, tabletop and so on. And would you believe it they didnā€™t find them.

The new paper is now about a revival of this old idea of large extra dimensions. Indeed, these ā€œDark Dimensionsā€ are a new research program that seems to have begun in 2022 around Cumrun Vafa, a string theorist at Harvard who has been doing this stuff for decades.

In their scenario, there is one extra dimension that is particularly large, and they ignore the other 5 as being too small to be measurable. This is not new, it was a rather common setup 20 years ago. The new thing is the justification for why this one dimension has a size of about one micrometer. This is supposedly ā€œnaturalā€ because itā€™s related to the cosmological constant and something to do with the swampland. Doesnā€™t really matter exactly what this means because the swampland isnā€™t real and naturalness arguments have failed over and over again in the past.

In any case, this supposedly ā€œnaturalā€ size of the extra dimension is great because, guess what, it could be tested with one of the next experiments. The current experimental constraints on the size of this dimension is currently about 52 micrometres.

Okay, but what does this have to do with dark matter?

In such large extra dimensions, you must assume that forces which we have measured on very short distances, thatā€™s the nuclear forces and also electromagnetism, donā€™t notice the additional dimensions. And actually, all the matter that we are made of canā€™t travel into these directions either. In string theory speech, this normal matter is ā€œconfined to the braneā€.

Thatā€™s b r a n e not b r a i n, is derived from ā€œmembraneā€ and is our normal three dimensional space. So all the normal stuff needs to stay on that 3 dimensional brane.

The reason is that atomic nuclei are much smaller than this micrometer which is the supposed size of the extra dimension. And if the constituents of nuclei could spread into more than 3 dimensions nuclear physics wouldnā€™t properly work.

But hereā€™s the thing. Thereā€™s no such problem for gravity, so they can assume that gravity does experience the large extra dimensions.

And these extra dimensions then explain dark matter as follows. Whenever you have rolled something up you get standing waves in this rolled up direction. For gravity, these standing waves are quanta of the gravitational field, called gravitons. And if theyā€™re standing waves, they have masses that depend on how many wavelengths fit into the extra dimension. These massive gravitons can make up dark matter. Again this isnā€™t a new idea, this is the same thing people did 25 years ago. They were even looking for this stuff at the LHC and didnā€™t find it. For this new theory they just use some parameter ranges that have not yet been excluded.

The novelty of the Dark Dimensions scenario is that the extra dimension doesnā€™t have the same radius everywhere. This has the effect that the mass of these gravitons isnā€™t the same everywhere and the heavier ones can decay. This basically heats up the gravitons with lower masses and since theyā€™re hotter that changes the behaviour of the dark stuff. They say that this heating effect would affect the large-scale structure of galactic filaments and guess what, that future experiments could soon rule that out.

You know what Iā€™ll go out on a limb and say they wonā€™t find any evidence for the decay of these massive gravitons.