Nature Unsolved

[written July 2022, last revised Aug 2022]

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The effort to understand the universe is one of the very few things that lifts human life a little above the level of farce, and gives it some of the grace of tragedy. - Steven Weinberg

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I. Questions that bother me greatly, happening to be the most unanswerable ones.

Good scientific methodology is not an abstract set of rules dictated by philosophers. It is conditioned by, and determined by, the science itself… Let's not put the cart before the horse. Science is the horse that pulls the cart of philosophy. - Leonard Susskind

The primordial question.

How did the universe begin?¹

Was there even a beginning?²

The problem of gravity.

What is gravity? On large scales, it shows itself as a two-way street between spacetime curvature and energy (the central concept of general relativity), but what is it at the fundamental/quantum level?³

The trouble with quantum mechanics.

The trouble is not that Nature is probabilistic as opposed to deterministic; probabilities in themselves are not too terrible, for one at least gets precise predictions for those.⁴
The trouble is, as Steven Weinberg put it, why do probabilities get into quantum mechanics at all? That is the very bridge between the microscopic deterministic world of the quantum and the macroscopic world of observations. It is hence the heart of all the unease about quantum physics.⁵

Another way to state the problem: how do you prove the Born rule? Standing independent of the Schrodinger equation,⁶ it is the rule that states that the absolute square of a particle's wavefunction must be interpreted as the probability density of its presence at a given point. Nobody knows why.⁷

The problem of time.

What is time?

In quantum mechanics time is an absolute background quantity — unlike position, it is not an operator⁸ — and observer-independent. Whereas in relativity (both special and general), it's an observer-dependent malleable on the same footing as space. How are these two pictures compatible?

Why is there a directionality to time? The "arrow of time" seems to appear on two different levels. As a macroscopic phenomenon, it is equivalent to the continual increase of entropy as per the Second Law of Thermodynamics. At a fundamental level, it shows up as the violation of charge-parity symmetry in the weak interactions. Are these arrows related?

Why is there just one dimension of time?⁹

The cosmological constant problem: "the worst prediction in physics".

Why is the universe big? as Nima Arkani-Hamed elegantly states it. More precisely stated, why is the minimum gravitating energy density of spacetime, sourced by fluctuations of quantum fields, 122 orders of magnitude smaller than standard expectation (or 56 orders if the Standard Model is somehow the ultimate theory of quantum fields)?¹⁰ The observed value of the energy density of the vacuum is the caloric content of one little crystal of sugar per cubic kilometre — still enough to contribute to three-fourths the energy budget of the current universe. Yet the expectation is that just a cubic zeptometre (10^-63 m³) should contain enough energy to unbind the Milky Way.

Spooky observation: had the measured cosmological constant been slightly larger while remaining positive, not only would the cosmological horizon be smaller than observed, but galaxies would not have formed, as the first over-densities would have been ripped apart, preventing their role as seeds for amassing neighbouring matter; had it been slightly larger and negative, the universe would have by now shrunk to a psychotically tiny volume via a Big Crunch. Both scenarios prompt Arkani-Hamed's question. The exceptionally tiny cosmological constant appears to be exceptionally fine-tuned for life, and hence observers.¹¹

The electroweak hierarchy problem.

(a.k.a. the gauge hierarchy problem.)

Why is the weak force detectable? That is, why isn't the electroweak energy scale (100 GeV, corresponding to length scales of 10^-18 metres) at its natural value of the Planck energy scale (10¹⁷ times greater) or something similarly large?¹²

Spooky observation: had the electroweak scale been slightly smaller or larger, per Donoghue et al. cosmologically long-lived nuclei and/or atoms would not have formed. The unspeakably tiny value of the electroweak scale appears to be unspeakably fine-tuned for life, and hence observers.¹³

Another statement of the problem,¹⁴ via reversal: why is gravity so much weaker than the other forces?¹⁵

The Fermi paradox/Drake equation.

Are we alone?

I do not get the Fermi paradox, not in my bones. It is not (yet) clear to me why intelligent life must be commonplace in the universe, i.e. whether the mediocrity principle can be applied to the emergence of a species like ours. This is to say that, on the basis of my reading and grasp, it seems to me that we have very little idea of the odds that inanimate molecules turn into microscopic life forms, and the odds that such forms turn into sapient, self-aware life.

Thus I understand Where is everybody? far less than the much more basic Are we alone? — any answer to which is, as Arthur C. Clarke wrote, terrifying.

The fundamental question.

Why is reality the way it is? Even if all the questions here get answered at some point by humanity with some "theory of everything", why is that the answer and not something else?¹⁶

A specific interest. Quantum mechanics is the underlying grammar with which all the literature of the natural world ("laws of physics") is written.¹⁷ But why quantum mechanics? Is this somehow related to the "The trouble with quantum mechanics" above?

Sean Carroll: "Do advances in modern physics and cosmology help us address these underlying questions, of why there is something called the universe at all, and why there are things called 'the laws of physics,' and why those laws seem to take the form of quantum mechanics, and why some particular wave function and Hamiltonian? In a word: no. I don't see how they could."

The mystery of mysteries.

Why is mathematics so unreasonably effective in describing the natural sciences?¹⁸

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II. Questions of interest the answers to which are highly desirable.

Nature uses only the longest threads to weave her patterns, so each small piece of her fabric reveals the organization of the entire tapestry. - Richard Feynman

The chirality of life.

Why are live molecules left-handed? Has it do with the left-chirality of the weak interactions (whose provenance is in itself a mystery; see below) — cosmic muons selecting left-handed amino acids over lengthy times?
If so, does this lend more credence to the anthropic solution to the electroweak hierarchy problem?

The matter-antimatter imbalance.

Why do we see only matter in the visible macroscopic universe, and not antimatter? What (mechanism of baryogenesis) set off this asymmetry, which started out as one lone extra baryon for every billion baryon-antibaryon pairs? How come the universe didn't just begin with a symmetric population of matter and antimatter, which would all have annihilated away into radiation by now?¹⁹

The flavour problem: basic.

Who ordered that? - I. I. Rabi.

Why are there three near-identical copies of matter? Why didn't Nature stop at 1? If going for more, why did she stop at 3?²⁰

The mystery of charge quantization.

Why does electric charge seem to come in units of the absolute charge of down-type quarks (1/3 e)?²¹

Is spacetime supersymmetric?

Is the symmetry that unites fermions and bosons realized in Nature?²²

Supersymmetry is the only loophole to the Coleman-Mandula no-go theorem, which states that spacetime and internal symmetries of any theory must factorize.²³ A supersymmetric extension to the Standard Model will certainly mitigate the electroweak hierarchy problem, if not provide a candidate for dark matter (in versions with "matter parity" or "R-parity") and facilitate a precise unification of the gauge forces.²⁴

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III. Questions of interest to which the want of an answer wouldn't kill me.

We live on an island surrounded by a sea of ignorance. As our island of knowledge grows, so does the shore of our ignorance. - John Wheeler

The dark matter problem.

What is the microscopic identity of dark matter,²⁵ the invisible substance that makes up five-sixths of the mass of the matter content of the universe, and which via gravitational condensation gave the cosmos its current looks on the largest scales?

The parity problem.

Why do weak interactions act only on left-handed matter (those with left helicity, roughly)? In other words, if the universe were seen in a point mirror, the weak force vanishes like a vampire.²⁶ Why?

The flavour problem: advanced.

Why is there a peculiar pattern of masses and mixings among fermions? And why is there a vast hierarchy of masses in each family? The {tauon, top quark, bottom quark} outweigh the {electron, up quark, down quark} by {3600, 34800, 4200}. What sets the CP-violating phase among the quarks?
And then there are neutrinos. Why are their masses ridiculously tiny? The sum of the three neutrino masses is at best a million times smaller than the electron mass.²⁷ Are neutrinos their own anti-particles? And what sets the CP-violating phase among them?

The strong CP problem.

Why does the strong interaction seem symmetric under time-reversal (equivalent to a charge-parity transformation if Lorentz symmetry holds) while nothing prevents the violation of said symmetry?²⁸

The character of high density matter.

What is the phase — and equation of state — of matter at densities above nuclear saturation, for instance in the inner core of neutron stars? Is it merely nucleons, or do you have matter with strange content such as hyperons and kaons, or do you have free quarks, or something a touch more exotic like a colour-flavour-locked phase?

Experimental anomalies.

Here are some deviations from the Standard Model observed in experiments, presented roughly in the order of my belief in their reality. Their possible solutions are too numerous to list here. Explanations have fallen broadly under three categories or somewhere in between: (i) there is an unknown bug in the experiment, (ii) the Standard Model prediction was not calculated right, (iii) some exotic new physics is causing the anomaly.

The muon magnetic moment.

What explains the long-standing discrepancy with the Standard Model in measurements of the anomalous magnetic moment of the muon, first observed at Brookhaven and recently again at Fermilab?

The Galactic Center excess.

Why is the central 10 degrees of the Milky Way shining excessively in gamma rays?²⁹

The Hubble tension.

Why is the Hubble constant measured significantly smaller —at a 4.4 $\sigma$ level — in the cosmic microwave background (the early universe) than in the expansion rate from standard candles, e.g. Type Ia supernovae (the late universe)?³⁰

The neutron lifetime puzzle.

Why do neutrons seem to disappear faster from traps than the rate at which their decay products appear from neutron beams?

The cosmological lithium problem.

Why does the abundance of lithium-7 alone fall short of the prediction of Big Bang Nucleosynthesis, when all the lighter nuclides are in spectacular agreement with BBN+CMB?

The DAMA/LIBRA anomaly.

What is causing the DAMA/LIBRA experiment to see a highly significant annually modulating signal over two decades even while other experiments with similar set-ups fail to replicate it?

The mass of the W boson.

What made CDF at Tevatron measure the W boson's mass significantly higher than everyone else?

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There is a theory which states that if ever anyone discovers exactly what the Universe is for and why it is here, it will instantly disappear and be replaced by something even more bizarre and inexplicable. There is another theory which states that this has already happened. - Douglas Adams

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Footnotes

1. That is, what came before the inflationary phase of exponential-rate expansion that came before our universe was filled with hot radiation and matter? Whatever that is, how did that come about? Perhaps related question, coming up next: what is the quantum picture of gravity? This question must arise because the Beginning occurs within a Planck time and at energies that could presumably exceed the Planck mass.

2. Eternal inflation leading to a grand multiverse of self-reproducing bubbles of spacetime (shown by Vilenkin to be generic to inflation) accommodates the case of no boundary conditions required: universes can be born purely from the quantum laws of physics. And indeed, the laws of physics would exist even if the universe(s) did not. This is phrased evocatively as "a universe from nothing". But caution: the "nothing" is the existence of a scalar potential with a metastable minimum from which the inflaton field tunnels to a deeper vacuum and initiates spatial inflation, so one may ask where did that (quantum fluctuation) come from? It has been shown (e.g. here and here) that inflation is not only eternal in the future, but could also be made eternal in the past, avoiding the need for an origin. Stephen Hawking and James Hartle have an altogether different way of avoiding boundary conditions via the proposal of a "wavefunction of the universe", a quantum ground state defined on a 3-dimensional manifold. Time as a 4th dimension simply emerges from this state, neatly circumventing any "beginning". Here is a verbatim transcript of an exchange in the middle of a heated discussion on the merits of cosmic inflation at a conference on quantum gravity I attended in August 2022. Viatcheslav Mukhanov: You can create a universe from nothing, as you say. Alexander Vilenkin: Yes, but that's a beginning. Mukhanov: OK, so what's wrong with a beginning?

3. It is very likely string theory due to mathematical consistency: the "only game in town" that can cure the loss of renormalizability that arises when matter is coupled to gravitons in a field theory, and can furnish a consistent description of black holes, viz., objects that starkly unite the seemingly contradictory principles of classical relativity and quantum mechanics, in particular by giving a count of microstates that accurately reproduces the Bekenstein-Hawking entropy. The theory identifies elementary particles with quantum excitations of Planck length-sized open or closed one-dimensional entities: strings. In particular, the lowest excitation of a closed string is a massless species of spin-2: the graviton. For consistency — to keep, say, the photon non-tachyonic and massless — numerous extra spatial dimensions must be introduced. As we only observe three dimensions around us, the rest are perhaps "compactified" to imperceptible tininess. All in all, this spacetime structure allows for the existence of multi-dimensional massive objects called D-branes and several interesting dualities, which have enabled various string theories to be unified into a single M-theory operating on 10+1 dimensions. Dualities between strings and D-branes imply that one cannot talk of strings as fundamental entities any more than talk of the electric charge as more fundamental than the magnetic monopole in a theory with variable coupling. The avenues for compactification down to 3+1 dimensions are many, in fact, very many: about 10⁵⁰⁰ by a popular counting. These correspond to an ensemble of vacua, and perhaps our universe has picked one for residence — a notion called the "string landscape". It is perhaps not surprising that we find ourselves in a 3+1-dimensional world: other dimensionalities of spacetime seem unfriendly for observers to emerge.

4. With apologies to Einstein, who cares whether God plays dice? At least we know the precise construction of the dice.

5. For instance, the unease shows up as the infamous "interpretations of quantum mechanics" such as Niels Bohr's concept of the wavefunction collapsing inexplicably at the moment of measurement (providing a sharp "Heisenberg cut"). The interpretations also side-step the issue. The modern Copenhagen interpretation attributes all reality to measurement/observation and none to the wavefunction, thought merely to be behind-the-scenes machinery of the true physical realm ("Shut up and calculate!" - David Mermin). Hugh Everett's many-worlds interpretation goes in the other direction, attributing all reality to the wavefunction and its deterministic evolution, the Schrodinger equation, implying that observation preserves the superposition of quantum states. The implication is that every act of measurement splits history into independent timelines that are undetectable to each other, by and by amounting to an uncountable multitude of parallel universes.

6. (and therein lies the ultimate logical drawback of the many-worlds interpretation — it can neither account for nor quantify the world-splitting probabilities, and the Born rule must still be input separately)

7. Not for want of trying.

8. (which is why there is no operator form for the time-energy uncertainty relation, which must be written down in a special way)

9. It may have been selected in the anthropic sense. Multiple time dimensions result in particles decaying to heavier final states. In particular, there can be no stable particles with which a habitable universe can be built; see here for details.

10. Stated yet differently, how do you explain the cancellation to colossal precision of a bare cosmological constant in Einstein's equations against quantum field contributions to the zero-point/vacuum energy? The problem is further exacerbated when seen in the light of cosmological phase transitions: the bare CC appears fine-tuned today against the sum of several terms representing the zero-point energies of past epochs. In any case, perhaps there is no fine-tuning if you consider the UV/IR mixing of Andrew Cohen, David Kaplan & Ann Nelson: ultra-violet cutoffs are generically bounded from above by an infrared scale if you want the Schwarzschild radius of a box of quantum fields to be smaller than the box: one must avoid over-counting unphysical quantum states. For a box the size of the cosmic horizon, the bound satisfies the measured value of the vacuum energy density, (meV)⁴.

11. An observation used by Steven Weinberg to predict the value of the vacuum energy density or effective CC — before astronomers measured it — by positing that the CC must not lie far below the anthropic bound. Such an anthropic solution is natural in the multitude of vacua available in the string landscape: much like the environmental selection of our solar system, we find ourselves in a habitable patch of inflated spacetime in the multiverse. A refinement by Weinberg and co-workers accounting for primordial density fluctuations stood the test of measurement. A caveat due to Tegmark and Rees is that the density fluctuation $\delta$, 10^-5 in our universe, may itself scan over the multiverse: 10x smaller, and galactic gas may be too dilute and cold to trigger radiative cooling and form stars; 10x larger, and galaxies that are too packed may destabilize solar systems (and 10x yet larger would birth a hostile profusion of supermassive black holes), this latter direction of increase seemingly accommodating larger values of the CC. However, it is the ratio CC/$\delta$³ that is anthropically fixed (separately from $\delta$), as Garriga and Vilenkin have clarified (and Reese & Livio have plotted). At least one elegant variation of this paradigm exists: Bousso-Harnik-Kribs' "causal entropic principle", to wit, complex sub-structures such as human beings find themselves in a universe in which total entropy production is maximized within our "causal diamond", the largest volume of spacetime that could be causally connected, with the entropy sourced chiefly by cosmic dust reprocessing starlight into soft radiation. The much greater entropy sourced by horizons — of black holes or the cosmic boundary — is neglected in this prescription as it is unclear how they are useful for making observers. The idea has two attractions: one, in general the causal diamond and in particular using entropy production within it to weight the probabilities of sub-universes avoid the ills of infinity in the "measure problem" of trying to determine if our sub-universe is mediocre/typical; two, it explains away the "cosmological coincidence problem" of why we happen to live at just the right moment to witness near-equal contributions of vacuum energy and matter to the energy of the universe over the course of its long (future) evolution: producing entropy is maximized exactly when the universe contains near-equal parts of the two. (This latter problem has an answer in Weinberg's anthropic bound as well, for it is just in the epoch following nucleation of galaxies that we expect both observers to emerge and the vacuum energy to dominate the universe.) Moving on, there is also Stephen Hawking's notion of the "wavefunction of the universe" peaking near a trivial CC; see Weinberg's review for caveats. Finally, selection need not be anthropic, but dynamic, for instance via a slow-rolling scalar first settling into a small negative CC spot, triggering reheating via contraction of the universe, which then bounces if some new fluid prevents the classical singularity (as explored by Paul Steinhardt & Neil Turok in their cyclic cosmology solution to the CC problem) — letting the scalar phase-transition to a spot giving the observed positive CC.

12. Stated differently, what explains the cancellation to enormous precision a bare squared mass term in the potential of the Higgs field against quantum corrections to it? These corrections are quadratic in the ultraviolet cutoff owing to the apparent lack of a symmetry protecting the Higgs. One satisfying explanation: there is some hidden symmetry conspiring to afford protection, likely supersymmetry between fermions & bosons, or a mirror symmetry in the guise of a "twin parity". Another (not independent) explanation could be that the Higgs is not an elementary field, but a composite pseudo-Nambu Goldstone boson of some confining dynamics in the ultraviolet, so that its lightness need not be wondered at. One other way to invoke naturalness is to imagine a great many fraternal copies of the Standard Model, each taking on a different Higgs vacuum expectation value; to then find some copies with the electroweak scale at 1/$\sqrt{N}$ times the Planck scale would be unsurprising as a statistical fluctuation (though care must be taken to reheat only the lightest sectors). In this category of dynamic selection is a model with a QCD axion that, by coupling to the Higgs field, scans the latter's mass as it slow-rolls during inflation. Shortly after crossing zero the rolling stops due to tall barriers in the periodic potential of the axion, and one ends up with a Higgs mass much smaller than the cutoff of the potential — satisfying technical naturalness as the Higgs-axion dimensionful coupling is a spurion softly breaking shift symmetry.

13. There is at least one counter to this anthropic reasoning: the weakless universe of Harnik, Kribs & Perez may support life, if you retain the masses of the up, down and strange quarks by tuning technical natural Yukawa couplings whilst sending the electroweak scale up to the Planck scale, and if you specify the baryons-per-photon as a hundredth of that in our universe, and if you have a similar amount of dark matter — perhaps axions or primordial black holes — to trigger linear growth of density perturbations and hence galactic structures. Then cosmological nucleosynthesis will leave comparable-to-hydrogen levels of deuterium in star-forming gas clouds, such that instead of the weak-mediated proton-proton fusion the stellar burning cycle may now be initiated by the strong-mediated proton-deuteron fusion. (These arguments are still inapplicable to the cosmological constant, suggesting that its fine-tuning problem has a physical origin different from that of the electroweak scale.) Gedalia, Jenkins & Perez follow this up by including Yukawa couplings as parameters that scan on the (weakless) multiverse landscape, due presumably to a dynamical origin such as the Froggatt-Nielsen mechanism. More habitable universes are located, seemingly further weakening the anthropic precept of Donoghue et al. To me, however, the conclusion of these studies appears quite the opposite. The facts that special relations between the Yukawa couplings and the weak scale are required to make a universe habitable seems to me to strengthen the case for an anthropic selection of the observed values: we may be somewhere on a family of solutions as opposed to a single-point solution. While on the topic of weak force versus anthropics, how about Strumia et al.'s position that life-giving supernovae are powered by fine-tuned neutrinos?

14. A mild mystery that comes attached: why is the scale of the strong force so close to that of the weak force? Though Donoghue et al.'s anthropic solution to the electroweak hierarchy problem addresses this on the side, Weinberg cautions: "There is always the possibility that the electroweak symmetry breaking scale is determined by the energy at which some gauge coupling constant becomes strong, and if that coupling happens to grow with decreasing energy a little faster than the QCD coupling then the electroweak breaking scale will naturally be a few orders of magnitude larger than the QCD scale."

15. When asked in this form, the answer may be that there are extra spatial dimensions, with us living on a 3-dimensional (mem)brane. If the extra dimension is macro-sized courtesy Arkani-Hamed, Dimopoulos & Dvali, the propagation of gravity through it may appear to us as its feebleness. If the extra dimension is warped thanks to Lisa Randall & Raman Sundrum, it could be pretty small and bridge branes housing the electroweak and gravity sectors; then Newton's constant may seem to us exponentially smaller. Even without invoking extra spatial dimensions one may obtain such illusion of an exponentially large scale: if a chain of fields under a large symmetry group reside on a mundane scale of symmetry breaking, and neighbours are linked by soft symmetry-breaking off-diagonal masses that leave a residual symmetry, the true Goldstone boson would then be well-sequestered and appear to have an effective decay constant sequentially cranked up by the pseudo-Goldstones, the "gears" of the "clockwork". Then again there is a solution in the Weak Gravity Conjecture: if gravity is ordained to be the weakest force (when the states are charged under a local abelian group), the electroweak cutoff must be small if, say, the baryon minus lepton number is gauged.

16. One response may be in Max Tegmark's suggestion that all mathematical structures would get realized, not just the ones that resulted in our uni/multiverse.

17. (which is partly why it is so hard to experimentally test quantum mechanics by itself)

18. Tegmark weighs in unsatisfactorily: "the physical world is mathematics".

19. Andrew Long, and before him Nelson-Kaplan-Cohen, bring this problem, somewhat crudely in my opinion, under the venerable question Why is there something rather than nothing? I am warmer to Sidney Coleman's reversal of this question to describe the cosmological constant problem.

20. Is this somehow related to there being 3 perceptible spatial dimensions? The 3 colours of strong nuclear interactions? Is the Koide formula a numerical coincidence or something deeper that answers this question? Is the solution in the string theory landscape? How about Lee Smolin's fecund universes via cosmolgical natural selection, in which he posits that the heavier generations are relics of the multiverse's early evolution during its trials to form fermions light enough for producing a pathway to black holes, serving as the cradles of future universes?

21. Possible answer 1: magnetic monopoles must exist. As Poincare showed with mathematics and Dirac with wizardry, the product of electric and magnetic charges is the radial component of angular momentum, and since the latter is quantized, so too must be the two charges. (Then where are the magnetic monopoles? Probably diluted away by cosmic inflation.) Possible answer 2: if the electromagnetic, weak and strong forces are unified into a single force at a more fundamental scale, embedding their symmetry groups into a larger one often spits out charge quantization for free. (Then why don't we see this "grand unification" in Nature? Observing its effects is very hard.)

22. Graham Kribs' way of putting it: is chiral symmetry extended to bosons?

23. The loophole comes from using generators that are spinorial, so that one gets anti-commutation relations of a "super-Lie algebra" instead of commutation ones of a Lie algebra.

24. However, Nathaniel Craig cautions: "Pick two."

25. Although I can live without the answer, this is funnily the question on which I spend the greatest fraction of my research time. Broadly speaking, it appears that dark matter must be comprised of either particles (including those so light their Compton wavelength exceeds their inter-particle distance, at which point they are better treated as waves), macroscopic structures of such particles (e.g., stars or mini-clusters), primordial black holes, or topological defects in spacetime.

26. (parity is "maximally violated")

27. This is perhaps due to some "seesaw mechanism" in mass generation.

28. The most likely answer lies in the existence of the Peccei-Quinn axion, a field that dynamically relaxes to a real number in the CP-odd term of QCD; extensive searches for the axion particle are underway.

29. Is it from something spectacular like self-annihilating dark matter (the "Hooperon") or something pedestrian like millisecond pulsars?

30. Could it be that some novel energy injection over a narrow redshift-window near recombination shrinks the measured sound horizon of plasma oscillations, which is sensitive to early expansion? Interestingly, measurements of S₈, the fluctuation in the matter power spectrum at 8 Mpc h^-1 scales, are 2—3 $\sigma$ smaller than $\Lambda$CDM prediction, suggesting a common primordial origin of the two tensions.