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Featured I Open problems in mathematical physics

  1. Oct 6, 2017 #1

    fresh_42

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    I came across this beautiful pearl
    https://arxiv.org/abs/1710.02105
    https://arxiv.org/pdf/1710.02105.pdf
    which I like to bring to notice.
    Despite of its title it is heavier on theoretical physics than it is on mathematics, so I placed it in this forum. I think it is equally interesting to those who are interested in history of science, as it is to those who ask "What's left?" from time to time here on PF.
     
    Last edited: Oct 6, 2017
  2. jcsd
  3. Oct 6, 2017 #2
    ok everyone, let's hunker down and get to work :)
     
  4. Oct 8, 2017 #3

    anorlunda

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    I agree with @fresh_42 , this list is a pearl. He provided two links. I found a third link to a version that is somewhat more readable in my opinion.

    Life, the universe, and everything – 42 fundamental questions, by Roland E. Allen and Suzy Lidstrom

    http://people.physics.tamu.edu/allen/42.pdf

    But even easier to read, and motivation for PF members to take the trouble to read the whole paper, the following is the author's summary expressed as 42 questions. If you wonder, "What the heck does that mean?", then go read the paper.
    1. Why does conventional physics predict a cosmological constant that is vastly too large?
    2. What is the dark energy?
    3. How can Einstein gravity be reconciled with quantum mechanics?
    4. What is the origin of the entropy and temperature of black holes?
    5. Is information lost in a black hole?
    6. Did the universe pass through a period of inflation, and if so how and why?
    7. Why does matter still exist?
    8. What is the dark matter?
    9. Why are the particles of ordinary matter copied twice at higher energy?
    10. What is the origin of particle masses, and what kind of masses do neutrinos have?
    11. Does supersymmetry exist, and why are the energies of observed particles so small compared to the most fundamental (Planck) energy scale?
    12. What is the fundamental grand unified theory of forces, and why?
    13. Are Einstein relativity and standard field theory always valid?
    14. Is our universe stable?
    15. Are quarks always confined inside the particles that they compose?
    16. What are the complete phase diagrams for systems with nontrivial forces, such as the strong nuclear force?
    17. What new particles remain to be discovered?
    18. What new astrophysical objects are awaiting discovery?
    19. What new forms of superconductivity and superfluidity remain to be discovered?
    20. What new topological phases remain to be discovered?
    21. What further properties remain to be discovered in highly correlated electronic materials?
    22. What other new phases and forms of matter remain to be discovered?
    23. What is the future of quantum computing, quantum information, and other applications of entanglement?
    24. What is the future of quantum optics and photonics?
    25. Are there higher dimensions, and if there is an internal space, what is its geometry?
    26. Is there a multiverse?
    27. Are there exotic features in the geometry of spacetime, perhaps including those which could permit time travel?
    28. How did the universe originate, and what is its fate?
    29. What is the origin of spacetime, why is spacetime four-dimensional, and why is time different from space?
    30. What explains relativity and Einstein gravity?
    31. Why do all forces have the form of gauge theories?
    32. Why is Nature described by quantum fields?
    33. Is physics mathematically consistent?
    34. What is the connection between the formalism of physics and the reality of human experience?
    35. What are the ultimate limits to theoretical, computational, experimental, and observational techniques?
    36. What are the ultimate limits of chemistry, applied physics, and technology?
    37. What is life?
    38. How did life on Earth begin and how did complex life originate?
    39. How abundant is life in the universe, and what is the destiny of life?
    40. How does life solve problems of seemingly impossible complexity?
    41. Can we understand and cure the diseases that afflict life?
    42. What is consciousness?
     
  5. Oct 8, 2017 #4
    Hmmm, there are a lot of why questions which are not supposed to be answered by physics, so these unanswered philosophy questions?
     
  6. Oct 8, 2017 #5

    fresh_42

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    I think "why" is not automatically philosophy or unanswerable. Those questions can probably also be formulated without the why, but not similarly short. E.g.
    Which physical theory can explain the difference between the cosmological constant predicted by conventional physics in comparison to our observation, i.e. a model in which both are included as boundaries, like Planck's law of black-body radiation explains the agreement to conventional physics for long wavelengths and the discrepancy on short wavelengths.

    So no "why" needed.
     
  7. Oct 8, 2017 #6

    anorlunda

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    The questions are the author's wording, not mine.. Here is the author's full statement of #1 leading to the why question #1.
    I'm just an amateur, not on the level of you @fresh_42 or the paper's authors. Are you saying that this is not an unsolved problem? Or do the authors say that "a model in which both are included as boundaries," is anthropic?
     
  8. Oct 8, 2017 #7

    fresh_42

    Staff: Mentor

    Neither am I. I'm not even sure to which extend the authors are. I only wanted to point out that the why isn't per se nonphysical. Physical models are always valid in a certain range and might fail in another range. So the question as what happens at the boundary is a very physical and not a philosophical question. The QM forum is full of why questions, especially when quantum phenomena are described in our macroworld language. Nevertheless, the papers are a nice read and probably should be taken with a grain of salt. I think they are a nice appetizer and explain why physics is interesting, and I appreciated your list very much. And although we don't discuss philosophy here for practical reasons, it is not as if physicists wouldn't discuss it. And like us who have experienced, that it leads nowhere and is rarely on a scientific level, physicists usually debate about philosophical questions at a dinner table and not in their lectures.
     
  9. Oct 8, 2017 #8

    anorlunda

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    I understand that PF has practical reasons for excluding philosophy. Those reasons don't necessarily apply outside PF.

    But isn't there an aspirational way to look at it? The state of the art: Scientific theory supported by observational evidence. That's hard-core science and the scientific method. Things beyond the state of the art are not science -- we can harshly call it philosophy... But to expand the state of the art, someone must aspire to transform some increment philosophy into science. Those aspirations should be encouraged and discussed as long as there is hope that they might succeed. Otherwise every research proposal is non-science by definition. We must look beyond the state of the art to advance it.

    The kinds of philosophy that waste our time to discuss and deserves harsh treatment are the hopeless cases, or things so far in the future that we can't discuss them intelligently. (I think of FTL drives as an example.)
     
  10. Oct 8, 2017 #9

    fresh_42

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    I agree on the basic sentiment of what you wrote. The difficulty is where to draw the line? FTL is as impossible as squaring the circle is. There isn't even an idea to overcome this hurdle. On the other hand, many discussions start with topics as perception, consciousness or reality. I always find it disrespectful towards real philosophy to discuss them on a level, which is basically defined by an open internet forum. I haven't met a single person here, who has seriously studied philosophy and knows what he talks about, namely knows what dozens of philosophers have already written. Not even the basic schools are common knowledge. So the rule to avoid philosophical questions, has always been more of a rule of respect to me, than merely a rule to confine discussions and avoid endless argues.

    Another aspect is, if we opened the door a little for "fantasies", which I agree completely with you are needed in science, we would instantaneously get many tri-sectionists, cube-doublers and circle-squarers and their physical pendants. It's bad enough what Hawking and Kaku already set into the world in their popular science magazines. Me, too, finds it sad sometimes, that we don't have more brain storming and dinner-table-like discussions and I would like to hear personal views from many of our members, but I certainly won't like to read the flood of nonsense from all who would feel invited to take part. The framework simply doesn't allow it to distinguish - and to establish a judge or a jury would even increase the trouble.
     
  11. Oct 8, 2017 #10

    Drakkith

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    I agree. I think we often use the words "philosophy" or "philosophical" to describe questions or discussions which are either outside the realm of being answered in the near-to-moderate future, or which are too vague and ill-defined to permit a serious discussion within the bounds of the forum guidelines and rules. Technically these are probably still part of philosophy in a very broad way (is there a question which isn't?), but they are very rarely of a quality which professional philosophers would find useful. That's my guess at least, as I'm no philosopher myself.
     
  12. Oct 9, 2017 #11
    This list is actually from different authors (R. E. Allen and S. Lidstrom,“Life, the universe, and everything: 42 fundamental questions”, Phys. Scr. 92 012501 (2017) [Focus Issue on 21st Century Frontiers].) and is acknowledged by Coley to have a lot of questions that are more metaphysics than physics. (p 12 of https://arxiv.org/pdf/1710.02105.pdf ).

    One fundamental unsolved problem in mathematical physics I think Coley missed is that of Quantum Chaos: How does the Schrodinger equation give rise to classical chaos? We do not really understand how the Correspondence Principle works in the case of chaotic systems.

    This problem seemed to garner a lot more discussion in the 1980s and 1990s than in the 21st century. It seems to have fallen out of favor, not because it is uninteresting or unimportant, but because it is hard.
     
  13. Oct 9, 2017 #12
    Some questions are ill-defined. Some already have answers (IMO).

    Define "multiverse". I know several different definitions.

    Any sequence of physicals "whys" ends with a set of axioms which by definition have no answer to "why in your theory are these axioms true?". There is no answer; we just assume them to be true and then develop a theory on them.
    The above three "whys" are of that sort.

    Experiments.

    Self-replicating nanomachines of natural origin.

    Some species of "self-replicating nanomachines" have a natural "computer" (created by evolution) which improves survival chances for them. We have empirical evidence that more powerful "consciousness" allows species to be more successful (consider sequence of amoeba > fish > cat > human and how improved capabilities to process information make them more able to survive and reproduce in adverse conditions).
     
  14. Oct 9, 2017 #13

    anorlunda

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    I think if you read the actual article you'll see that the questions are better defined than the terse paraphrasing questions. After reading the full definitions, I would be interested to hear if you still think that some of them have been answered.
     
  15. Oct 9, 2017 #14
    That's a handwaving description or even simply a vague statement/very incomplete definition, not even coming close to an explanation of the mechanism in terms of some mathematical model consistent with physical theory. In other words, no soup for you!
     
  16. Oct 9, 2017 #15

    WWGD

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    Sorry to throw off things a bit. Is this where the 42 in your name comes from?
     
  17. Oct 9, 2017 #16

    fresh_42

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    I assume they both are based on the same origin. 5-25 is our common celebration day, I guess.
     
  18. Oct 10, 2017 #17

    Svein

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    Somebody has read "the Hitchhiker's Guide to the Galaxy"!
     
  19. Oct 10, 2017 #18
    Unfortunately the question is NOT what is 6x7, and the answer of "42", as the answer to the ultimate question of the universe, gets us no closer.
    On a more serious tone, does proving they are unanswerable or circumvented by a deeper understanding count?
     
  20. Oct 11, 2017 #19
    I can't see mention of the "arrow of time" question .
     
  21. Oct 12, 2017 #20

    Thuring

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    Some of these questions might have Zen- type answers. lol
     
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