Hard Problems

Among those who study the human mind and consciousness, there is what is termed “The Hard Problem.” It is in contrast to, and qualitatively different from, problems that are merely hard. (Simply put, The Hard Problem is the question of how subjective experience arises from the physical mechanism of the brain.)

This post isn’t about that at all. It’s not even about the human mind (or about politics). This post is about good old fundamental physics. That is to say, basic reality. Some time ago, a friend asked me what was missing from our picture of physics. This is, in part, my answer.

There is quite a bit, as it turns out, and it’s something I like to remind myself of from time to time, so I made a list.

These aren’t in any particular order, but I group them as best as I can by their sector of physics. There’s a lot of overlap, so in some cases it’s dealer’s choice (and I’m the dealer). This list is by no means exhaustive.

These are all questions we haven’t answered so far, because they’re hard to figure out (for a variety of reasons). Some of them, in fact, may be unanswerable (for a variety of reasons), but I think all have answers in principle.

Note that I am not here including the various limits we’ve found, such as Gödel’s, Heisenberg’s, Turing’s, Einstein’s, or Cantor’s. I don’t see these as unanswered questions.

I’ll start big with…

The Universe (Cosmology)

What caused the Big Bang? What physical context and set of laws provided a setting for it to happen? What, if anything, came before? Was there a universe (or many) similar to ours before?

What is time? Is it fundamental or does it emerge from something? Is it smooth (a continuum) or lumpy (quantized)?

What is space? Is it fundamental or does it emerge from something? Is it smooth or lumpy? Is time unified in 4D spacetime? What about ideas such as Loop Quantum Gravity?

Is reality determined? Is the future fixed by the past or random?

Is reality a continuum? (Is reality real or just rational?) If the continuum doesn’t apply to reality, then reality isn’t fully determined. (Nor could the block universe exist.) “God made the integers, all else is the work of man.” ~Leopold Kronecker

Is Inflation a correct story? Does an especially uniform initial creation reduce or eliminate the need for it? Is it necessary or is there another explanation for the homogeneity we see?

Is the universe flat? Do extremely large triangles always have angles that sum to 180°, and do two parallel lines always remain the same distance apart? It seems so, but we’re not absolutely positive.

What is Dark Energy? Is is real? Are our observations about increasing expansion correct? Is Dark Energy the cosmological constant?

How to explain the vacuum problem? (Off by a factor of 10120!) Theory puts vacuum energy far too high; something seems to cancel it out very precisely. What’s going on there?

Is the universe infinite or bounded? Can you potentially return to the same spot by going in a “straight” line (that is, by following a geodesic)?

Where did the anti-matter go? Theory says equal amounts should have been created, but everything we see now appears to be “normal” matter. Why was anything left after matter and anti-matter combined?

What is the ultimate fate of the universe? What are its ages, and how long does each last? How long will the universe last in total?

Gravity (Theory of General Relativity)

What happens at small scales (high energies)? Specifically, what happens inside a black hole? Is there really a singularity? What can GR say about the Big Bang?

Is space and/or time quantized or smooth? This repeats the questions above, but they have special application here since Einstein’s math assumes the continuum and defines spacetime as a 4D unified whole. Was he right about that?

Is some form of MOND correct? Does GR need to be extended or modified? Is GR just an approximation, just as Newton is an approximation?

How can the GR be reconciled with quantum physics? One of the great conundrums of physics (and a very hard problem). Our two most thoroughly tested theories, and they absolutely refuse to get along. It’s very upsetting. Like siblings who always fight.

Quantum Physics (The Standard Model)

How can quantum physics be reconciled with GR? (Just the mirror side of the GR question, but worth repeating. Both theories work so well, and yet…)

How does time fit into physics? GR defines it as part of the background fabric, but physics often insists it doesn’t exist or, to the extent it does, is emergent or an illusion. In QM, time isn’t an observable (like charge, spin, momentum, or position).

What is Dark Matter? Does it really exist (or is MOND right)? We’re having a hard time finding candidate particles. WIMPS turn out to be either extremely shy… or nonexistent?

Is gravity a force (is there a graviton)? Or is it really just the bending of space as in GR?

Why are there (only) three families of fermions? Why are there two (and only two) extra families we only see in high-energy colliders? As Nobel laureate I.I. Rabi once famously said about the muon, “Who ordered that?”

Why do neutrinos oscillate? In fact, there are many unanswered questions about neutrinos. We don’t know their masses, for one thing. Whether there are sterile neutrinos for another. They’re the SM’s elusive ghosts.

Can the particle masses (et al) be explained by theory? The SM has about 18 parameters (masses, coupling constants, etc) that seem to be “dial settings” on reality whose values we cannot account for theoretically. We have no idea why these things have the values they have.

Questions about the Higgs mass and Higgs interactions. (And hence part of the desire for a bigger collider to study the Higgs.)

Are there super-symmetric particles? Or is SUSY just plain wrong? No shred of it has been found, and the window is closing. At what point do we give up?

Is the Standard Model somehow wrong? Is string theory or Loop Quantum Gravity or some other theory a better model?

Quantum Physics (The Standard Interpretation)

What divides the quantum world from the classical world? How real is that division? How does decoherence fit into this picture? What creates the Heisenberg Cut?

What exactly is superposition? What’s going on there? It’s not as simple as its physical analogues, for instance, of superposed sound waves.

What causes quantum interference? What’s going on there? In two-slit and interferometer experiments, what actually is interfering?

What is entanglement? What’s going on there? What’s really happening when two (or more) subsystems are described by the same wave-function?

What happens during a measurement? How do we explain the discontinuity that measurement produces in the Schrödinger equation?

Is reality really random? Does measurement necessarily produce only probable results (per the Born rule)?

Is reality really non-local at the quantum level? (Demonstrated explicitly in Bell’s experiments and implicit in the notion of wave-function entanglement and collapse.)

§ §

For completeness, here are some ideas requiring some imagination and greater metaphysical commitment. (FTR, I file these under FBS. I would bet they will someday be shown to be false.)

Quantum Physics (The MWI)

What is the ontology of the 3N-dimensional complex-valued wave-function? (Given the Tegmarkian view is denied.)

How does decoherence allow matter physically to coincide? Is superposition possible without knowing it? We’re apparently all in superposition all the time.

What happens with energy? Is it really “thinned out” in branches? How does gravity remain constant given energy and mass are equivalent and mass generates gravity?

What exactly determines whether a branch exists? If Alex and Blair can potentially perform myriad different experiments, do they perform them all? Do all possible failure modes (even really weird ones) occur? (This is called the preferred basis problem.)

Is the MWI non-local or local? The QM math (and our experiments) suggest quantum non-locality is real, but some use the MWI to try to recover local realism. There’s nothing that seems to require that the MWI provide local realism.

What does the MWI say about probability? If an experiment has 1% chance of reflecting a photon and a 99% chance of transmitting it, the MWI insists both always happen, so what does that mean about that 1:99 odds?

Doesn’t what appears as measurement, and thus an abrupt change to the wave-function, still occur in MWI? How does the MWI account for this change? How do we perceive anything?

[see: Many Worlds Insanity]

§

In the same way I take computationalism a bit more seriously than, say SUSY or string theory, I take the MWI a bit more seriously than what follows. I don’t find enough value in these to really have questions.

I just have objections:

The Virtual Reality Hypothesis

• The argument for it raises the turtles all the way down problem. The same arguments insisting we’re a simulation apply to those supposedly simulating us. (As with colonizing the galaxy, someone has to be first.)

• It implies information patternism (which is currently another FBS idea and the actual “hard problem” to boot).

• It assumes such simulations are physically reasonably possible. If they’re possible at all, they may be so resource intensive as to be extremely rare (which destroys the argument).

• I’m not generally sympathetic towards arguments such as the Anthropic “Principle” (but is it really?) or the Doomsday Argument.

• There are interesting implications regarding teleology. Presumably a VR universe would have a teleology its inhabitants might note. The presumption is that raw reality would appear less teleological, but a well-designed simulation should emulate the less teleological reality and be indistinguishable. Still, the idea would be to consider the apparent teleology as well as look for possible “mistakes” in the coding.

The point is, something constructed by an intelligence might shows signs of that. A big problem is determining how actual apparent teleology is.

[see: Reality IS Virtual (probably)!]

The Mathematical Universe Hypothesis

• What is the exact ontology of the MU? Of all the mathematical structures, why are only certain ones reality? (Or are all math structures realities?)

• How does change occur?

• How does the generally shared subjective “now” occur? (Actually a refinement of the change question.)

[see: Tegmark: MUH? Meh!]

The Block Universe Hypothesis

• What accounts for all the structure? What generated it (and when and how)?

• How does the shared “now” occur in a static block? What causes time to seem to pass for us?

• Are “simultaneous” space-separated points in the distant future as “real” as the present?

[see: Blocking the Universe]

§ §

As you see, there are many unanswered questions! Some answers may be forever out of reach, but many no doubt we’ll solve eventually (one way or another).

If you know of probative factual evidence that helps resolve any of them, please do speak up.

Also speak up if there’s a Big Physics Question I should add. The list isn’t exhaustive. I left off some esoteric stuff about the weak force, for instance, but still might have missed some interesting Big Ones.

Stay questioning, my friends!

About Wyrd Smythe

The canonical fool on the hill watching the sunset and the rotation of the planet and thinking what he imagines are large thoughts. View all posts by Wyrd Smythe

23 responses to “Hard Problems

  • Wyrd Smythe

    So how do I get my post to show up in the WP Reader? It’s not, and WP chat seems offline (so I sent an email). 😦 😦 😦 Oh, how I hate the WordPress Reader! So buggy!

  • Wyrd Smythe

    One less old draft post! A few things I missed (it always seems to take reading the already published work to spot all the errors and ommissions):

    Under MOND and Dark Matter questions, should also be a question about observations of galaxy spin rates, which is where the idea of Dark Matter began. I’m just not quite sure how to word that question. The observational data seems less debatable than that for Dark Energy, and it seems we’re clear it has to be due to either Dark Matter or some kind of MOND. It is, I gather, determined that it’s not due to any “viscosity” or “dragging” of the galactic mass. (I’ve wondered if galaxies are more rigid — wheel-like — than we suspect and, if so, if that would explain observations.

    I should add a question under the GR heading about black holes and information loss. The deeper question is whether information can, in fact, be created and destroyed. QM says no. GR says [shrug]. Intuition seems (to me, anyway) to suggest sure. We certainly routinely create and destroy information at the classical level. Maybe “conservation of information” isn’t a thing. (Another question: Is there a symmetry associated with conservation of information such as their is for other conservation laws?)

    There could be an entire blog post about unanswered mathematical questions. That’s a whole other field. In fact, of the five limits I mentioned at the top of the post, only Heisenberg’s and Einstein’s are really in the realm of physics. Gödel’s and Cantor’s were directly mathematical, and Turing’s is the same thing applied to computing.

    I wanted to give equal time to the hypothetical ideas, but in retrospect they stand out to me and probably don’t belong on the list. For one thing, there are so many other hypotheses — why not Roger Penrose’s CCC idea or even the Flat Earth Hypothesis? Next time they get left off.

  • SelfAwarePatterns

    To make the post show up in the reader, un-publish another post still in the feed, and then republish it. (I usually chose the oldest one still in the list since it’s the one people were least likely to notice disappear and reappear.) That usually triggers the reader to pull again from your feed.

    Just fyi, since I switched to the block editor, I haven’t seen the issue.

    Pretty comprehensive list. The only addition that immediately springs to mind is, what the heck is energy? (At least beyond the banal definition we normally get.)

    “If the continuum doesn’t apply to reality, then reality isn’t fully determined.”

    I remember this from the Quanta article on intuitionist math. But I’m not sure I understand why it follows that reality wouldn’t be determined. A digital computer isn’t continuous, yet its operations are fully deterministic.

    Some of these issues may turn out to be related to each other. For example, apparently some physicists, coming from very different directions, are playing with the idea that space may emerge from entanglement.

    • Wyrd Smythe

      The post now shows up (six hours later), although I didn’t do anything. WP replied to my email to basically say they see it now, too. (I was very surprised by their advice to keep Tags and Categories to 15 or less to insure a post shows up in the Reader. Long ago the editor would complain about too many Tags, but that hasn’t been true in years, and I assumed there was no limit. Apparently the Reader may not show a post with more than 15. Sheeze.)

      I edited both this post (multiple times) and an older post, to no avail, but didn’t try the unpublish trick. I’ll keep that in mind.

      Energy! Huh, never thought of it. (Like ever. I’ve never asked that question. Why is that?) Maybe it should be under Cosmology right after Space and Time.

      “A digital computer isn’t continuous, yet its operations are fully deterministic.”

      The short answer is: chaos.

      A digital computer can calculate as many digits of pi as we want, but it’s an iterative computational process we don’t see naturally in reality. Reality is more like an analog computer, which is limited by the precision of its components.

      In a deterministic view, assuming a set of conditions in the past necessarily leads to the exact conditions today (and none other) seems to require extraordinary precision in those conditions. That Quanta article suggests if one goes all the way back to the Big Bang, the precision of information required exceeds the information content of the universe. There wasn’t room for enough data.

      Reading about keeping an eye on dangerous asteroids, I read something interesting. Our best efforts can only predict, with precision, the Solar System about 100 years into the future. This is as much about observational limits as computational ones (perhaps more so), but it illustrates how tracking a model into the future diverges from reality due to precision.

      In 50 years, the data extends the forecast 50 more years because we update the model. But any numerically fixed model can’t be specified with enough precision to run accurately forever. Chaos will always blow it up eventually.

      “Some of these issues may turn out to be related to each other.”

      Indeed. I’d go so far as saying many of them possibly connect. In the end there may only be a handful of real questions. (Although doesn’t it seem as if the more answers we get the more questions we have? So many not.)

      • SelfAwarePatterns

        On the post showing up, yeah, updating the post did sometimes shake it loose, but it was rare. The only thing I found reliable was to generate a publish event. (The support people, after numerous cases, finally revealed that as the secret.) You could also do it by publishing and then deleting a quick small post, but I was concerned that would spam email subscribers. Unpublishing and re-publishing worked pretty consistently.

        I can definitely understand how chaos prevents us from predicting outcomes, but not how it prevents determinism in general. I know the Quanta article asserted that infinite precision was needed at the big bang, but it seems like the state of any particular system today is the cumulative result of interactions from a light cone 93 billion light years in diameter with 10^80 particles. Even in a precision limited universe, that still seems to leave an enormous capacity for encoding future states. Anyway, thanks for taking a shot!

      • Wyrd Smythe

        It’s not a given; more of an argument. You’re right, a precise “chunky” universe would be determined in the sense of tracing a set of casual events backwards. The implication is that uncertainty would cause “bobble” in some of those steps — at times the universe would have to “choose” a discrete value randomly, whereas with a continuum it would just take the precise value previous steps imply.

        That means reality can be traced backwards but not forwards based on the assumption reality has to randomly choose values. It has to decide between two discrete rational values.

        It’s a seriously weird thing that, given any two rational values, a and b, there is always a rational value, c, between them. So it seems rational numbers can be as precise as one desires.

        But (in a rather mind-blowing proof) it can be shown that the rationals can be covered by the reals, and that coverage is shown to be strictly less than the continuum. The countable infinity of the rationals can’t hold a candle to the uncountable infinity of the reals. Infinity is bad enough, but the continuum, once we really start looking at it, almost has too many issues to be real (making the term “real number” hugely ironic).

      • Wyrd Smythe

        As an example, think of all the places our physical laws include pi or e. A rational reality can never take on those values, only approximations of them. What does such a reality do when the math says it should take on a real value? It has to round up or down, and the presumption is this wouldn’t be deterministic.

      • SelfAwarePatterns

        Just thought of another addition (assuming you don’t have it and I just missed it): the discrepancy in the Hubble constant, the expansion rate of the universe, between measurements taken using the cosmic distance ladder and those derived from the CMB. It’s actually considered a major crisis in cosmology. (A “crisis” everyone hopes reveals new physics rather than being resolved by some mundane correction somewhere.)

      • Wyrd Smythe

        Yeah,… maybe. I have mixed feelings about that one. So much of it depends on observations of extremely distant objects and a lot of assumptions. I do tend to lean towards it be an assumption error of some kind.

        I think I have some bias against cosmological questions that don’t affect us directly. Space, Time, Matter, Energy, Mass, those are all very real issues for us. The actual size or expansion rate of the universe, not so much. You’ll notice I didn’t give Dark Energy much mention. This might be filed under that (or close by as related).

        I think the real problem was trying to keep the list within a reasonable word count. The hypotheticals really need to go or be separate, and even cosmology might deserve its own list.

  • Michael

    Great list, Wyrd!

    What do you think about the question of what happens to physical laws as you approach the center of a Tootsie Pop…err… an electron? I was thinking that conundrum was the basis for renormalization–which I understand is a mathematical procedure moreso than a physical theory–and also a motivation for string theory.

    Michael

    • Wyrd Smythe

      Thanks, Michael!

      I would hope the laws are the same inside an electron (whatever “inside” means), but I think you’re asking the deeper question about what an electron (or any particle) actually is.

      I think between you and Mike, there are two missing questions:

      ⋅ What exactly is Energy?

      ⋅ What exactly is Matter? Is quantum field theory (QFT) a correct view?

      To go with the Time and Space questions. (Weird how neither occurred to me. I’m not even sure what sub-questions go with the Energy one.)

      String theory I’d have to consign to the Hypotheticals list, but electrons (assuming realism) have to be something.

      OTOH, the answer to some of these questions may be: X is axiomatic and fundamental. It just is what it is. Which is how we currently kinda view the QFT fields and spacetime under GR. (I suspect time turns out that way.)

  • Michael

    I may have worded my comment poorly Wyrd. I was under the impression the math related to the electromagnetic force ‘blew up’ too close to theoretical center of an electron, and that this dilemma is what led to renormalization and string theory. But yes, it’s related to the question of what an electron is.

    These other two questions–mass and energy–are good too!

    • Wyrd Smythe

      Oh, okay, sorry, I jumped the track a bit there. I think what you’re talking about is, at least in part, due to treating the electron as a point source. As you say, string theory, in making particles actual physical things with size, got around that problem. (It was one of the things that attracted me to ST at first.)

      This isn’t something I’ve explored in any detail, but it rang a bell I’d read something. I did find this in the John Baez post. (I’m copying text with LaTeX images and I’m won’t know if it works until I submit this reply.)

      First, the electromagnetic field energy approaches +\infty as we let R \to 0, so we will be hard pressed to take this limit and get a well-behaved physical theory. One approach is to give a charged particle its own ‘bare mass’ m_\mathrm{bare} in addition to the mass m_\mathrm{elec} arising from electromagnetic field energy, in a way that depends on R. Then as we take the R \to 0 limit we can let m_\mathrm{bare} \to -\infty in such a way that m_\mathrm{bare} + m_\mathrm{elec} approaches a chosen limit m, the physical mass of the point particle. This is an example of ‘renormalization’.

      ⋅ What is Mass? Would be yet another good question!

      • Michael

        Just FYI, no equations showed up in the WordPress app on my phone. But I followed the link you gave and skimmed most of it. I cannot follow all the math, but it’s well written and the descriptions all seem to point to challenges as R –> 0… Agreed.

      • Wyrd Smythe

        Yeah, the WP app has some issues with rendering, too. I checked my iOS version, and it shows the images, but hilariously hugely oversized so only a small bit can be seen on screen. Makes the text impossible to read. OTOH, in the app’s admin section, under comments, all HTML is stripped out and the images are gone (so is the paragraphing).

        But, yeah, R –> 0 is an issue in all sorts of places. That John Baez paper (reproduced as a series of posts on his website) is all about that. Even Newtonian mechanics has problems when considering point sources. Since masses are usually represented as points, two objects can never actually collide! It’s Zeno’s Paradoxes all over again. 🙂

    • Wyrd Smythe

      Okay, that cut-n-paste seems to have worked. “R” is radius, and as it approaches zero, things get insane. (The same thing that happens regarding spacetime curvature as we approach the singularity of a black hole.) So they do a little math dance to renormalize the numbers.

      That in itself is probably another question:

      ⋅ What, if anything, does the need to renormalize say about quantum theory? Is it an indication of a wrong path?

  • Anonymole

    Nice to know what we don’t know. I wonder about what we don’t know we don’t know…

  • Brian

    That should have been a further hard question: “Why does it always seem to take reading the already published work to spot all the errors and omissions?” If I could answer any of your other questions with “God” I could answer this one also with God… he has a sense of humour.

    • Wyrd Smythe

      Ha, indeed! I’ve always thought knees were a good proof of that.

      More seriously, our gift of humor is pretty special. (I’ve long ranked laughter as the most important aspect of life.) In one of my favorite books, two beyond powerful alien brothers are stranded on a primitive Earth. One gives the local unevolved primates the gift of self-awareness, the power of which overwhelms and paralyzes the species experiencing it far before they’re ready for it. So the other brother gives them the gift of humor so they can see the absurdity of life, and that balances the sheer terror of self-awareness. Very clever idea, I thought.

      There is a truism about proofreading: The number of proofreads necessary to catch all errors is N+1, where N is the actual number performed. This is true regardless of how high N is.

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