Month: November 2022

The Angel Particle

The Angel Particle

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?

Tooth Fairies & Auxiliary Hypotheses

Tooth Fairies & Auxiliary Hypotheses

I’ve reached the point in the semester teaching cosmology where we I’ve gone through the details of what we call the three empirical pillars of the hot big bang:

  • Hubble Expansion
  • Primordial [Big Bang] Nucleosynthesis (BBN)
  • Relic Radiation (aka the Cosmic Microwave Background; CMB)

These form an interlocking set of evidence and consistency checks that leave little room for doubt that we live in an expanding universe that passed through an early, hot phase that bequeathed us with the isotopes of the light elements (mostly hydrogen and helium with a dash of lithium) and left us bathing in the relic radiation that we perceive all across the sky as the CMB, the redshifted epoch of last scattering. While I worry about everything, as any good scientist does, I do not seriously doubt that this basic picture is essentially correct.

This basic picture is rather general. Many people seem to conflate it with one specific realization, namely Lambda Cold Dark Matter (LCDM). That’s understandable, because LCDM is the only model that remains viable within the framework of General Relativity (GR). However, that does not inevitably mean it must be so; one can imagine more general theories than GR that contain all the usual early universe results. Indeed, it is hard to imagine otherwise, since such a theory – should it exist – has to reproduce all the successes of GR just as GR had to reproduce all the successes of Newton.

Writing a theory that generalizes GR is a very tall order, so how would we know if we should even attempt such a daunting enterprise? This is not an easy question to answer. I’ve been posing it to myself an others for a quarter century. Answers received range from Why would you even ask that, you fool? to Obviously GR needs to be supplanted by a quantum theory of gravity.

One red flag that a theory might be in trouble is when one has to invoke tooth fairies to preserve it. These are what the philosophers of science more properly call auxiliary hypotheses: unexpected elements that are not part of the original theory that we have been obliged to add in order to preserve it. Modern cosmology requires two:

  • Non-baryonic cold dark matter
  • Lambda (or its generalization, dark energy)

LCDM. The tooth fairies are right there in the name.

Lambda and CDM are in no way required by the original big bang hypothesis, and indeed, both came as a tremendous surprise. They are auxiliary hypotheses forced on us by interpreting the data strictly within the framework of GR. If we restrict ourselves to this framework, they are absolute requirements. That doesn’t guarantee they exist; hence the need to conduct laboratory experiments to detect them. If we permit ourselves to question the framework, then we say, gee, who ordered this?

Let me be clear that the data are absolutely clear that something is wrong. There is no doubt of the need for dark matter in the conventional framework of GR. I teach an entire semester course on the many and various empirical manifestations of mass discrepancies in the universe. There is no doubt that the acceleration discrepancy (as Bekenstein called it) is a real set of observed phenomena. At issue is the interpretation: does this indicate literal invisible mass, or is it an indication of the failings of current theory?

Similarly for Lambda. Here is a nice plot of the expansion history of the universe by Saul Perlmutter. The colors delineate the region of possible models in which the expansion either decelerates or accelerates. There is no doubt that the data fall on the accelerating side.

I’m old enough to remember when the blue (accelerating) region of this diagram was forbidden. Couldn’t happen. Data falling in that portion of the diagram would falsify cosmology. The only reason it didn’t is because we could invoke Einstein’s greatest blunder as an auxiliary hypothesis to patch up our hypothesis. That we had to do so is why the whole dark energy thing is such a big deal. Ironically, one can find many theoretical physicists eagerly pursuing modified theories of gravity to explain the need for Lambda without for a moment considering whether this might also apply to the dark matter problem.

When and where one enters the field matters. At the turn of the century, dark energy was the hot, new, interesting problem, and many people chose to work on it. Dark matter was already well established. So much so that students of that era (who are now faculty and science commentators) understandably confuse the empirical dark matter problem with its widely accepted if still hypothetical solution in the form of some as-yet undiscovered particle. Indeed, overcoming this mindset in myself was the hardest challenge I have faced in an entire career full of enormous challenges.

Another issue with dark matter, as commonly conceptualized, is that it cannot be normal matter that happens not to shine as stars. It is very reasonable to image that there are dark baryons, and it is pretty clear that there are. Early on (circa 1980), it seemed like this might suffice. It does not. However, it helped the notion of dark matter transition from an obvious affront to the scientific method to a plausible if somewhat outlandish hypothesis to an inevitable requirement for some entirely new form of particle. That last part is key: we don’t just need ordinary mass that is hard to see, we need some form of non-baryonic entity that is completely invisible and resides entirely outside the well-established boundaries of the standard model of particle physics and that has persistently evaded laboratory signals where predicted.

One becomes concerned about a theory when it becomes too complicated. In the case of cosmology, it isn’t just the Lambda and the cold dark matter. These are just a part of a much larger balancing act. The Hubble tension is a late comer to a long list of tensions among independent observations that have been mounting for so long that I reproduce here a transparency I made to illustrate the situation. That’s right, a transparency, because this was already an issue before end of the twentieth century.

The details have changed, but the situation remains the same. The chief thing that has changed is the advent of precision cosmology. Fits to CMB data are now so accurate that we’ve lost our historical perspective on the slop traditionally associated with cosmological observables. CMB fits are of course made under the assumption of GR+Lambda+CDM. Rather than question these assumptions when some independent line of evidence disagrees, we assume that the independent line of evidence is wrong. The opportunities for confirmation bias are rife.

I hope that it is obvious to everyone that Lambda and CDM are auxiliary hypotheses. I took the time to spell it out because most scientists have subsumed them so deeply into their belief systems that they forget that’s what they are. It is easy to find examples of people criticizing MOND as a tooth fairy as if dark matter is not itself the biggest, most flexible, literally invisible tooth fairy you can imagine. We expected none of this!

I wish to highlight here one other tooth fairy: feedback. It is less obvious that this is a tooth fairy, since it is a very real physical effect. Indeed, it is a whole suite of distinct physical effects, each with very different mechanisms and modes of operation. There are, for example, stellar winds, UV radiation from massive stars, supernova when those stars explode, X-rays from compact sources like neutron stars, and relativistic jets from supermassive black holes at the centers of galactic nuclei. The mechanisms that drive these effects occur on scales that are impossibly tiny from the perspective of cosmology, as they cannot be modeled directly in cosmological simulations. The only computer that has both the size and the resolution to do this calculation is the universe itself.

To account for effects below their resolution limit, simulators have come up with a number of schemes to account for this “sub-grid physics.” Therein lies the rub. There are many different approaches to this, and they do not all produce the same results. We do not understand feedback well enough to model it accurately as subgrid physics. Simulators usually invoke supernova feedback as the primary effect in dwarf galaxies, while observers tell us that stellar winds do most of the damage on the scale of star forming regions – a scale that is much smaller than the scale simulators are concerned with, that of entire galaxies. What the two communities mean by the word feedback is not the same.

On the one hand, it is normal in the course of the progress of science to need to keep working on something like how best to model feedback. On the other hand, feedback has become the go-to explanation for any observation that does not conform to the predictions of LCDM. In that application, it becomes an auxiliary hypothesis. Many plausible implementations of feedback have been rejected for doing the wrong thing in simulations. Only maybe one of those was the right implementation, and the underlying theory is wrong? How can we tell when we keep iterating the implementation to get the right answer?

Bear in mind that there are many forms of feedback. That one word upon which our entire cosmology has become dependent is not a single auxiliary hypothesis. It is more like a Russian nesting doll of multiple tooth fairies, one inside another. Imagining that these different, complicated effects must necessarily add up to just the right outcome is dangerous: anything we get wrong we can just blame on some unknown imperfection in the feedback prescription. Indeed, most of the papers on this topic that I see aren’t even addressing the right problem. Often they claim to fix the cusp-core problem without addressing the fact that this is merely one symptom of the observed MOND phenomenology in galaxies. This is like putting a bandage on an amputation and pretending like the treatment is complete.

The universe is weirder than we know, and perhaps weirder than we can know. This provides boundless opportunity for self-delusion.