The dominant paradigm for dark matter has long been the weakly interacting massive particle (WIMP). WIMPs are hypothetical particles motivated by supersymmetry. This is well-posed scientific hypothesis insofar as it makes a testable prediction: the cold dark matter thought to dominate the cosmic mass budget should be composed of a particle with a mass in the neighborhood of 100 GeV that interacts via the weak nuclear force – hence the name.
That WIMPs couple to the weak nuclear force as well as to gravity is what gives us a window to detect them in the laboratory. They should scatter off of nuclei of comparable mass, albeit only on the rare occasions dictated by the weak force. If we build big enough detectors, we should see it happen. This is what a whole host of massive, underground experiments have been looking for. So far, these experiments have succeeded in failing to detect WIMPs: if WIMPs existed with the properties we predicted them to have, they would have been detected by now.
The failure to find WIMPs has led to the consideration of a myriad of other possibilities. Few of these are as well motivated as the original WIMP. Some have nifty properties that might help with the phenomenology of galaxies. Most are woefully uninformed by such astrophysical considerations, as it is hard enough to do the particle physics without violating some basic constraint.
One possibility that most of us have been reluctant to contemplate is a particle that doesn’t interact at all via strong, weak, or electromagnetic forces. We already know that dark matter cannot interact via electromagnetism, as it wouldn’t be dark. It is similarly difficult to hide a particle that responds to the strong force (though people have of course tried, with strange nuggets in the ’80s and their modern reincarnation, the macro). But why should a particle have to interact at least through the weak force, as WIMPs do? No reason. So what if there is a particle that has zero interaction with standard model particles? It has mass and therefore gravity, but otherwise interacts with the rest of the universe not at all. Let’s call this the Angel Particle, because it will never reveal itself, no matter how much we pray for divine intervention.
I first heard this idea mooted in a talk by Tom Shutt in the early teens. He is a leader in the search for WIMPs, and has been since the outset. So to suggest that the dark matter is something that simply cannot be detected in the laboratory was anathema. A logical possibility to be noted, but only in passing with a shudder of existential dread: the legions of experimentalists looking for dark matter are wasting their time if there is no conceivable signal to detect.
Flash forward a decade, and what was anathema then seems reasonable now that WIMPs remain AWOL. I hear some theorists saying “why not?” with a straight face. “Why shouldn’t there be a particle that doesn’t interact with anything else?”
One the one hand, it’s true. As long as we’re making up particles outside the boundaries of known physics, I know of nothing that precludes us from inventing one that has zero interactions. On the other hand, how would we ever know? We would just give up on laboratory searches, and accept on faith that “gravitational detection” from astronomical evidence is adequate – and indeed, the only possible evidence for invisible mass.
Experimentalists go home! Your services are not required.
To me, this is not physics. There is no way to falsify this hypothesis, or even test it. I was already concerned that WIMPs are not strictly falsifiable. They can be confirmed if found in the laboratory, but if they are not found, we can always tweak the prediction – all the way to this limit of zero interaction, a situation I’ve previously described as the express elevator to hell.
If there is no way to test a hypothesis to destruction, it is metaphysics, not physics. Entertaining the existence of a particle with zero interaction cross-section is a logical possibility, but it is also a form of magical thinking. It provides a way to avoid confronting the many problems with the current paradigm. Indeed, it provides an excuse to never have to deal with them. This way lies madness, and the end of scientific rationalism. We might just as well imagine that angels are responsible for moving objects about.
Indeed, the only virtue of this hypothesis that springs to mind is to address the age-old question: how many angels can dance on the head of a pin? We know from astronomical data that the local density of angel particles must be about 1/4 GeV cm-3. Let’s say the typical pin head is a cylinder with a diameter of 2.5 mm and a thickness of 1 mm, giving it a volume of 10 mm3. Doing a few unit conversions, this means a dark mass of 1 MeV* per pin head, so exactly one angel can occupy the head of a pin if the mass of the Angel particle is 1 MeV.
Of course, we have no idea what the mass of the Angel particle is, so we’ve really only established a limit: 1 MeV is the upper limit for the mass of an angel that can fit on the head of a pin. If it weighs more than 1 MeV, the answer is zero: an angel is too fat to fit on the head of a pin. If angels weighs less than 1 MeV, then they can fit numbers in inverse proportion to their mass. If it is as small as 1 eV, then a million angels can party on the vast dance floor that is the head of a pin.
So I guess we still haven’t answered the age old question, and it looks like we never will.
*An electron is about half an MeV, so it is tempting to imagine dark matter composed of positronium. This does not work for many reasons, not least of which is that a mass of 1 MeV is a coincidence of the volume of the head of a pin that I made up for ease of calculation without bothering to measure the size of an actual pin – not to mention that the size of pins has nothing whatever to do with the dark matter problem. Another reason is that, being composed of an electron and its antiparticle the positron, positronium is unstable and self-annihilates into gamma rays in less than a nanosecond – rather less than the Hubble time that we require for dark matter to still be around at this juncture. Consequently, this hypothesis is immediately off by a factor of 1028, which is the sort of thing that tends to happen when you try to construct dark matter from known particles – hence the need to make up entirely new stuff.
God forbid we contemplate that maybe the force law might be broken. How crazy would that be?