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Most of the major unsolved problems in physics today tend to arise either at very small scales that quantum mechanics deals with or at very large scales, involving cosmological like dark matter and dark energy.

But I am curious: are there still phenomena that are purely classical in nature (i.e., not involving quantum mechanics or relativity) that we do not understand? I don’t mean problems where the physics is known but the equations are too hard to solve (like the Navier-Stokes equations in turbulence) — in such cases, we at least understand the governing principles even if the math is intractable.

Rather, I’m asking about classical-scale physical phenomena for which we lack a complete or even qualitative understanding of the mechanisms involved, despite being in regimes where classical physics should be applicable.

To clarify: I am most interested in problems that have "no explanation at all", rather than those that have explanations, but their mathematical models differ from reality by some amount (meaning the explanation is "incomplete").

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    $\begingroup$ I'm not quite sure what you are asking. There are plenty phenomena in the classical physics regime that don't have a complete explanation, like understanding the dynamics of dust. But I don't think there are any phenomena that people believe can't ultimately be explained with classical physics in the regime where classical physics applies. Which is pretty much "we at least understand the governing principles even if the math is intractable," which you said is not what you're interested in. $\endgroup$ Commented Jun 19, 2025 at 22:07
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    $\begingroup$ -1 This question is a good example of why list questions are unsuitable. $\endgroup$ Commented Jun 20, 2025 at 13:27
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    $\begingroup$ Sidney Nagel of the University of Chicago has made a career of investigating everyday phenomena which are not readily explainable by classroom physics. Link: quantamagazine.org/… $\endgroup$ Commented Jun 24, 2025 at 14:23
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    $\begingroup$ A question with THIRTY UPVOTES in a week gets closed! Why am I not surprised! $\endgroup$ Commented Jun 26, 2025 at 8:30
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    $\begingroup$ @Qmechanic is there anything that can be done to improve this question? $\endgroup$ Commented Jun 27, 2025 at 14:30

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The form of the optical force density remains unresolved in classical electromagnetism. That is, when an EM wave exerts radiation pressure on an object, where within the object is the force? How is the force distributed? There are several competing forms of the force density which all conserve momentum globally (i.e. if you integrate the force density over the whole object, they all agree with the simple momentum conservation formula for radiation pressure); however, they disagree regarding the distribution of the force.

The most prominent examples are the “Lorentz” force density (unit = force/volume): $$F= -(\nabla \cdot P)E + J\times B $$ and the “Einstein-Laub” force density: $$F=(P\cdot\nabla)E + J\times B $$ (these are simplified for non-magnetic materials and are sometimes referred to by different names). You can use these to (relatively easily!) calculate the force density distribution within a material given the fields and the material’s optical properties. But which to use??

As one example of the difference, the Lorentz version in some cases results in surface forces, while the other does not. So they give differing predictions of a ubiquitous classical phenomenon: EM waves exerting pressure on a charge-neutral object (though they agree when integrated over the whole object).

There are theory papers about this conundrum from the current century (e.g. this) and at least one experimental paper (and it’s vaguely related to the famous Abraham-Minkowski debate). But there remains no conclusive experimental evidence to rule in favor of one or another because radiation pressure is famously weak, and it’s insufficient to look at the recoil of a whole rigid object because, again, all the candidate optical force densities conserve momentum globally.

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  • $\begingroup$ I spent a fair amount of my PhD research time deforming biological cells with radiation pressure. My collaborator held the optics expertise, though; my interest was in the deformability of soft and compliant materials. Can you comment on whether this tool would be useful in resolving the uncertainty? $\endgroup$ Commented Jun 20, 2025 at 11:52
  • $\begingroup$ @Chemomechanics I have not read your paper in detail, but I can say that deformability of small objects in radiation pressure could potentially resolve this. I encourage you to look into this further. But it can be a complex and subtle thing: pubs.aip.org/aip/pof/article/35/4/042008/2883017 $\endgroup$ Commented Jun 20, 2025 at 14:36
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    $\begingroup$ @Chemomechanics I should also note that while optical tweezers are a well-established technique, most practitioners are unaware of this fundamental gap in EM theory and blithely use the E-L force density simply because that's what everyone else does. $\endgroup$ Commented Jun 20, 2025 at 14:41
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    $\begingroup$ This has been resolved for quite some time (circa 1970). For some reason people keep on ignoring the resolution to this issue and persist in claiming that it is unresolved. arxiv.org/abs/0710.0461 $\endgroup$ Commented Jun 21, 2025 at 14:02
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    $\begingroup$ @Dale the Abraham-Minkowski debate is not the same thing. Whatever your opinion on that, and I agree there has been some degree of resolution there, this is a different problem. $\endgroup$ Commented Jun 21, 2025 at 19:21
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  • Mpemba_effect: hot water sometimes freezes faster than cold water, when frozen under identical conditions.
  • A proper understanding of turbulence. Especially a precise, predictive mathematical model, but also more general understanding. Numerical simulation is also insanely hard because of all the lengths scales involved. So I would argue that this still counts as lack of understanding.
  • Stick-slip motion in dry friction. Amonton's laws, which were not discovered by Amonton, are given by
    • The force of friction is directly proportional to the applied load. (Amontons' 1st law)
    • The force of friction is independent of the apparent area of contact. (Amontons' 2nd law)
    • Kinetic friction is independent of the sliding velocity. (Coulomb's law)

There is no derivation yet of this laws from microscopic dynamics alone. Also there are plenty exceptions to these rules.

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    $\begingroup$ The Mpemba effect is not in fact a thing. $\endgroup$ Commented Jun 20, 2025 at 19:44
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    $\begingroup$ Whether the Mpemba effect is a thing is one of the questions about the Mpemba effect. There was a nice literature review in Am.J.Phys. about ten years ago which pointed out that people who saw the effect were generally not doing quite the same experiment as people who didn't. Also people who saw the effect were not all doing quite same experiment as each other, and people who didn't see the effect weren't all doing quite the same experiment as each other, either. Stating what the problem is is part of the problem. $\endgroup$ Commented Jun 21, 2025 at 14:10
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    $\begingroup$ Oh, the review I remembered is from 2006. That was only ten years ago, right? $\endgroup$ Commented Jun 21, 2025 at 14:17
  • $\begingroup$ Amonton's 2nd law of friction: You don't regard Rabinowicz's analysis of the coefficient of friction as explaining $\mu$ being independent of $A$ ? $\endgroup$ Commented Jun 21, 2025 at 16:13
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    $\begingroup$ @rob The Mandela-Mpemba effect: when you believe that it's been conclusively proven that a liquid freezes faster when it's hot than when it's cold. ;) $\endgroup$ Commented Jun 22, 2025 at 13:35
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How cresting (modeled only by multivalued functions) water waves behave.enter image description here

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    $\begingroup$ This must be an area of intense (though never overly determined) research in Southern California . . . $\endgroup$ Commented Jun 21, 2025 at 13:51
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    $\begingroup$ There are people who constantly circle the earth searching for a solution to this problem. $\endgroup$ Commented Jun 22, 2025 at 22:43
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"Known" equations and physics?

But I am curious: are there still phenomena that are purely classical in nature (i.e., not involving quantum mechanics or relativity) that we fundamentally do not understand? I don’t mean problems where the physics is known but the equations are too hard to solve (like the Navier-Stokes equations in turbulence) — in such cases, we at least understand the governing principles even if the math is intractable.

(emphasis is mine)

Nigel Goldenfeld claims that turbulence is the last great unsolved problem of classical physics. However, the same Goldenfeld also claims that the idea that turbulence can be explained within Navier-Stokes equations is misguided, and the person who solves the problem of turbulence likely would not qualify according to the criteria of the prize award for solving this problem.

Classical vs. quantum/relativistic
Another point regarding unsolved problems is that distinction between classical and quantum/relativistic is somewhat artificial. Firstly, the distinction is somewhat historical - we now know that the world is not classical, and that none of the phenomena is classical. Apart from this obvious historical value, classical can be viewed as a limit, which is applicable in certain cases... but it is hard to say whether it is applicable to a problem that is not solved yet.

Thus, as the book by already mentioned Nigel Goldenfeld explains, many strongly correlated systems, although inherently quantum in nature, can be described by the same models as classical systems. At least, in the normalization group perspective. There are plenty of research (and hence the unresolved problems) in this direction.

Many-body systems and non-equilibrium statistical physics
Finally, other answers have already mentioned many problems related to behavior of many-body systems (like entropy/arrow of time.) These are specially numerous when it comes to non-equilibrium situations (like explaining life, evolution, etc.)

Related:
Is limited computational capacity a fundamental obstacle?
Life and Death, and Energy Conservation
Does physics explain why the laws and behaviors observed in biology are as they are?

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Two things that come to mind are:

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    $\begingroup$ I thought both are pretty much solved? (or disproven in the case of Mpemba effect) $\endgroup$ Commented Jun 20, 2025 at 10:05
  • $\begingroup$ @Michael They are? (See sources) $\endgroup$ Commented Jun 20, 2025 at 10:17
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    $\begingroup$ The Wikipedia links this article: Questioning the Mpemba effect: hot water does not cool more quickly than cold $\endgroup$ Commented Jun 20, 2025 at 11:36
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    $\begingroup$ @Michael Doesn't that show it's not conclusively understood? $\endgroup$ Commented Jun 21, 2025 at 1:47
  • $\begingroup$ I think the OP wants problems that are 5% understood, not 95% understood. $\endgroup$ Commented Jun 21, 2025 at 17:27
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The "shower-curtain" effect is not fully understood$^*$. (A shower curtain blows inward while a shower is running.) There is a lot of unexplored terrain in chaos theory. And the study of PDEs is a rich mathematical field with a lot of unanswered questions. To the extent that you model a physical system with PDEs there may be "unexplained" phenomena depending on what you mean by unexplained. (This includes Navier-Stokes.)

$^*$The shower curtain effect may be closer to being "solved" than I thought, but sources are mixed.

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  • $\begingroup$ Wouldn't this generally be an extension of the Venturi effect? All that water in the shower is moving the air along with it, creating lower pressure within the shower. shower curtains also rarely form airtight seals at the bottom of the shower, which is where the air would be assumed to escape. $\endgroup$ Commented Jun 22, 2025 at 0:03
  • $\begingroup$ @EdwinBuck I don't really personally know, I have just read that it is still as yet unexplained en.wikipedia.org/wiki/Shower-curtain_effect $\endgroup$ Commented Jun 22, 2025 at 21:38
  • $\begingroup$ That Wikipedia page has six answers to the problem. That's not unexplained. Like all physical items, odds are all the answers apply partially. $\endgroup$ Commented Jun 24, 2025 at 22:32
  • $\begingroup$ @EdwinBuck I quote, "The problem of identifying the cause of this effect has been featured in Scientific American magazine, with several theories given to explain the phenomenon but no definite conclusion." $\endgroup$ Commented Jun 24, 2025 at 23:26
  • $\begingroup$ Reading the first reference in the Wikipedia article says differently. scientificamerican.com/article/why-does-the-shower-curta which indicates that the computer simulations indicated the water drops elongate though the shower head to drag the air more effectively than some imagined, creating a vortex of wind, causing a temporary low pressure center, so if not the Venturi effect directly (or Bernulli, which is realted) at least incredibly similar. Wikipedia is wrong, again, and that's why you don't use Wikipedia as a reference. $\endgroup$ Commented Jun 25, 2025 at 1:38
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Surface tension phenomena, especially involving a solid phase. Young's equation for contact angle is not really well understood. Whether it is really classical, I shall leave for readers to decide. The only quantum effects which seem to be involved are the nature of intermolecular potentials. If these are taken for granted, then surface phenomena can be treated as classical physics, I think.

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  1. I would say that we still lack a good model for cuprate high temperature superconductivity. Just hand waving and saying "d mixing" is...not enough.

E.g. to predict which cuprates will superconduct and which will not. It seems like you have to get things just right--many cuprate perovskites DON'T superconduct--and right now, the exploration is still sort of led from the synthetic solid state chemical side, using intuitions about structure and ion size and the like.

How come they surprised everyone in 1986, when BCS had been around for 30 years and experimental observation of conventional superconductors since 1911 and sort of become a boring field, before Bednorz and Muller?

I guess you could debate if this is a macro phenomenon, but it certainly presents and is researched with ~cm sized pellets that you put into a SQUID or cut into bars for doing pretty tractable lab scale electrical tests on.

  1. Fractional quantum hall effect was also an example of a (semi-recent) "discovery in the field" that sort of surprised people, rather than just being predicted and later shown.
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    $\begingroup$ Are you implying that those phenomena are in the realm of classical physics? $\endgroup$ Commented Jun 21, 2025 at 23:11
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    $\begingroup$ I’m not sure if either of those would be considered classical physics, commonly they’re described as “macroscopic quantum phenomena” $\endgroup$ Commented Jun 22, 2025 at 2:45
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How about the arrow of time and its relationship with the rate of change of entropy? Why does time only go forward, but in space you can go backwards?

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    $\begingroup$ physics.stackexchange.com/q/451979 I think this is already answered. $\endgroup$ Commented Jun 20, 2025 at 3:55
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    $\begingroup$ I think this really is an open question but the common view AFAIK is that an answer will come from more than just classical mechanics, which OP limited the question to $\endgroup$ Commented Jun 21, 2025 at 16:59
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Many of these are listed among the unsolved problems in physics on Wikipedia (usually under condensed matter or fluid dynamics) https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_physics. Here's some :

  • Granular Convection (Brazil Nut Effect): Why do large particles rise in a shaken mixture?

  • Fracture and Material Failure: How do cracks initiate, propagate, and lead to material failure?

  • Glass Transition: Why do liquids become incredibly viscous and form amorphous solids (glasses) without a distinct phase transition?

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    $\begingroup$ please explain in detail and don't just give a link $\endgroup$ Commented Jun 21, 2025 at 7:26
  • $\begingroup$ #2: Crack initiation and general propagation are well studied. In regard to Al alloys, there is a wide range of early stage propagation behaviors that are not conclusively known but maybe this is being overhauled by atomistics and high-speed computation. #3: It's just certain compositions in liquid form, for practical purposes. For polymers, free volume theory is a commonly used model/explanation for glass transition at some temperature $T_g$. Metallic glasses are only possible to specific compositions and at cooling rates > $100,000^\circ$ K/sec. Ceramic glass formation is understood. $\endgroup$ Commented Jun 21, 2025 at 14:04
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Intelligence and consciousness.

Can we create these or can they exist outside an animal's brain?

We have recently made great progress in answering the question, but we still have a long way to go.

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  • $\begingroup$ What does a mirror see when it looks in the mirror? : ) $\endgroup$ Commented Jun 25, 2025 at 10:05
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Surely there is no phenomenon whose behavior can be definitively said to be wholly within the realm of classical physics - especially phenomena whose behavior cannot be explained via classical physics analysis alone.

Surely the failure of a classical physics approach will only spur scientists to explore the matter from the point of view of relativity and quantum physics.

So I think your designation of (strictly) classical physics phenomena is simply invalid.

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