Which Problems Brand Adept Enquiry Problems?

mini-problem [answer here]

Scientists solve problems; that’s their job. But which problems are promising topics of research? This is the inquiry I laid out to respond inward Lost inward Math at to the lowest degree concerning the foundations of physics.

Influenza A virus subtype H5N1 first, rough, classification of enquiry problems tin forcefulness out endure made using Thomas Kuhn’s wheel of scientific theories. Kuhn’s wheel consists of a stage of “normal science” followed past times “crisis” leading to a image change, after which a novel stage of “normal science” begins. This grossly oversimplifies reality, but it volition endure expert plenty for what follows.

Normal Problems

During the stage of normal science, enquiry questions commonly tin forcefulness out endure phrased every bit “How create nosotros stair out this?” (for the experimentalists) or “How create nosotros calculate this?” (for the theorists).

The Kuhn Cycle.
[Img Src: thwink.org]

In the foundations of physics, nosotros take keep a lot of these “normal problems.” For the experimentalists it’s because the low-hanging fruits take keep been picked in addition to measuring anything novel becomes increasingly challenging. For the theorists it’s because inward physics predictions don’t precisely autumn out of hypotheses. We ofttimes postulate many steps of argumentation in addition to lengthy calculations to derive quantitative consequences from a theory’s premises.

Influenza A virus subtype H5N1 expert instance for a normal work inward the foundations of physics is mutual depression temperature night matter. The hypothesis is slow enough: There’s some cold, dark, stuff inward the cosmos that behaves similar a fluid in addition to interacts weakly both amongst itself in addition to other matter. But that past times itself isn’t a useful prediction. Influenza A virus subtype H5N1 concrete enquiry work would instead be: “What is the effect of mutual depression temperature night thing on the temperature fluctuations of the cosmic microwave background?” And hence the experimental inquiry “How tin forcefulness out nosotros stair out this?”

Other problems of this type inward the foundations of physics are “What is the gravitational contribution to the magnetic minute of the muon?,” or “What is the photon background for proton scattering at the Large Hadron Collider?”

Answering such normal problems expands our understanding of existing theories. These are calculations that tin forcefulness out endure done inside the frameworks nosotros have, but calculations tin forcefulness out endure be challenging.

The examples inward the previous paragraphs are solved problems, or at to the lowest degree problems that nosotros know how to solve, though y'all tin forcefulness out e'er inquire for higher precision. But nosotros also take keep unsolved problems inward this category.

The quantum theory of the strong nuclear force, for example, should largely predict the masses of particles that are composed of several quarks, similar neutrons, protons, in addition to other similar (but unstable) composites. Such calculations, however, are hideously difficult. They are today made past times role of sophisticated figurer code – “lattice calculations” – in addition to fifty-fifty hence the predictions aren’t all that great. Influenza A virus subtype H5N1 related inquiry is how does nuclear thing deportment inward the substance of neutron stars.

These are but some randomly picked examples for the many opened upwards questions inward physics that are “normal problems,” believed to endure answerable amongst the theories nosotros know already, but I recollect they serve to illustrate the case.

Looking beyond the foundations, nosotros take keep normal problems similar predicting the solar wheel in addition to solar weather condition – hard because the arrangement is highly nonlinear in addition to partly turbulent, but goose egg that nosotros human face to endure inward conflict amongst existing theories. Then at that topographic point is high-temperature superconductivity, a well-studied but theoretically non well-understood phenomenon, due to the lack of quasi-particles inward such materials. And hence on.

So these are the problems nosotros written report when concern goes every bit normal. But hence at that topographic point are problems that tin forcefulness out potentially alter paradigms, problems that signal a “crisis” inward the Kuhnian terminology.

Crisis Problems

The obvious crisis problems are observations that cannot endure explained amongst the known theories.

I create non count most of the observations attributed to night thing in addition to night issue energy every bit crisis problems. That’s because most of this information tin forcefulness out endure explained good plenty past times precisely adding 2 novel contributions to the universe’s issue energy budget. You volition undoubtedly complain that this does non give us a microscopic description, but there’s no information for the microscopic construction either, hence no work to pinpoint.

But some night thing observations actually are “crisis problems.” These are unexplained correlations, regularities inward galaxies that are hard to come upwards past times amongst mutual depression temperature night matter, such every bit the Tully-Fisher-relation or the foreign powerfulness of night thing to seemingly rail the distribution of matter. There is every bit yet no satisfactory explanation for these observations using the known theories. Modifying gravity successfully explains some of it but that brings other problems. So hither is a crisis! And it’s a expert crisis, I dare to say, because nosotros take keep information in addition to that information is getting improve past times the day.

This isn’t the only expert observational crisis work nosotros shortly take keep inward the foundations of physics. One of the oldest ones, but silent endure in addition to kicking, is the magnetic minute of the muon. Here nosotros take keep a long-standing mismatch betwixt theoretical prediction in addition to measuring that has silent non been resolved. Many theorists take keep this every bit an indication that this cannot endure explained amongst the measure model in addition to a new, better, theory is needed.

Influenza A virus subtype H5N1 duo to a greater extent than such problems exist, or perchance I should state persist. The DAMA measurements for example. DAMA is an experiment that searches for night matter. They take keep been getting a signal of unknown source amongst an annual modulation, in addition to take keep kept rail of it for to a greater extent than than a decade. The signal is clearly there, but if it was night thing that would conflict amongst other experimental results. So DAMA sees something, but no i knows what it is.

There is also the still-perplexing LSND information on neutrino oscillation that doesn’t desire to handgrip amongst whatever other global parameter fit. Then at that topographic point is the foreign discrepancy inward the measuring results for the proton radius using 2 unlike methods, in addition to a similar floor for the lifetime of the neutron. And at that topographic point are the recent tensions inward the measuring of the Hubble charge per unit of measurement using unlike methods, which may or may non endure something to worry about.

Of course of written report each of these information anomalies powerfulness take keep a “normal” explanation inward the end. It could endure a systematic measuring error or a error inward a calculation or an overlooked additional contribution. But maybe, precisely maybe, there’s to a greater extent than to it.

So that’s i type of “crisis problem” – a conflict betwixt theory in addition to observations. But every bit good these at that topographic point is an utterly unlike type of crisis problem, which is only on the side of theory-development. These are problems of internal consistency.

Influenza A virus subtype H5N1 work of internal consistency occurs if y'all take keep a theory that predicts conflicting, ambiguous, or precisely nonsense observations. Influenza A virus subtype H5N1 typical instance for this would endure probabilities that travel larger than one, which is inconsistent amongst a probabilistic interpretation. Indeed, this work was the argue physicists were rattling for sure the LHC would encounter some novel physics. They couldn’t know it would endure the Higgs, in addition to it could take keep been something else – similar an unexpected alter to the weak nuclear forcefulness – but the Higgs it was. It was restoring internal consistency that led to this successful prediction.

Historically, studying problems of consistency has led to many stunning breakthroughs.

The “UV catastrophe” inward which a thermal source emits an infinite amount of low-cal at minor wavelength is such a problem. Clearly that’s non consistent amongst a meaningful physical theory inward which observable quantities should endure finite. (Note, though, that this is a conflict amongst an assumption. Mathematically at that topographic point is goose egg incorrect amongst infinity.) Planck solved this problem, in addition to the solution eventually led to the evolution of quantum mechanics.

Another famous work of consistency is that Newtonian mechanics was non compatible amongst the space-time symmetries of electrodynamics. Einstein resolved this disagreement, in addition to got particular relativity. Dirac afterward resolved the contradiction betwixt quantum mechanics in addition to particular relativity which, eventually, gave rising to quantum patch theory. Einstein farther removed contradictions betwixt particular relativity in addition to Newtonian gravity, getting full general relativity.

All these take keep been well-defined, concrete, problems.

But most theoretical problems inward the foundations of physics today are non of this sort. Yes, it would endure overnice if the 3 forces of the measure model could endure unified to one. It would endure nice, but it’s non necessary for consistency. Yes, it would endure overnice if the universe was supersymmetric. But it’s non necessary for consistency. Yes, it would endure overnice if nosotros could explicate why the Higgs majority is non technically natural. But it’s non inconsistent if the Higgs majority is precisely what it is.

It is good documented that Einstein in addition to fifty-fifty to a greater extent than hence Dirac were guided past times the beauty of their theories. Dirac inward detail was fond of praising the role of mathematical elegance inward theory-development. Their personal motivation, however, is only of secondary interest. In hindsight, the argue they succeeded was that they were working on expert problems to laid out with.

There are a few existent theory-problems inward the foundations of physics today, but they exist. One is the lacking quantization of gravity. Just lumping the measure model together amongst full general relativity doesn’t travel mathematically, in addition to nosotros don’t know how to create it properly.

Another serious work amongst the measure model lone is the Landau pole inward i of the coupling constants. That way that the strength of i of the forces becomes infinitely large. This is non-physical for the same argue the UV catastrophe was, hence something must travel on there. This work has received petty attending because most theorists shortly believe that the measure model becomes unified long earlier the Landau pole is reached, making the extrapolation redundant.

And hence at that topographic point are some cases inward which it’s non clear what type of work we’re dealing with. The non-convergence of the perturbative expansion is i of these. Maybe it’s precisely a inquiry of developing improve math, or perchance there’s something nosotros instruct actually incorrect virtually quantum patch theory. The instance is similar for Haag’s theorem. Also the measuring work inward quantum mechanics I uncovering hard to classify. Appealing to a macroscopic procedure inward the theory’s axioms isn’t compatible amongst the reductionist ideal, but hence i time to a greater extent than that is non a cardinal problem, but a conceptual worry. So I’m torn virtually this one.

But for what crisis problems inward theory evolution are concerned, the lesson from the history of physics is clear: Problems are promising enquiry topics if they actually are problems, which way y'all must endure able to formulate a mathematical disagreement. If, inward contrast, the supposed work is that y'all merely create non similar a detail aspect of a theory, chances are y'all volition precisely waste materials your time.

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Homework assignment: Convince yourself that the mini-problem shown inward the overstep icon is mathematically ill-posed unless y'all appeal to Occam’s razor.