Quantum Field Theory and the Limits of Knowledge

Last week I had the pleasure of giving a seminar to the philosophy department at the University of North Carolina. Ordinarily I would have talked about the only really philosophical work I’ve done recently (or arguably ever), deriving the Born Rule in the Everett approach to quantum mechanics. But in this case I had just talked about that stuff the day before, at a gathering of local philosophers of science.

So instead I decided to use the opportunity to get some feedback on another idea I had been thinking about — our old friend, the claim that The Laws of Physics Underlying Everyday Life Are Completely Understood (also here, here). In particular, given that I was looking for feedback from a group of people that had expertise in philosophical matters, I homed in on the idea that quantum field theory has a unique property among physical theories: any successful QFT tells us very specifically what its domain of applicability is, allowing us to distinguish the regime where it should be accurate from the regime where we can’t make predictions.

The talk wasn’t recorded, but here are the slides. I recycled a couple of ones from previous talks, but mostly these were constructed from scratch.

The punchline of the talk was summarized in this diagram, showing different regimes of phenomena and the arrows indicating what they depend on:

layers

There are really two arguments going on here, indicated by the red arrows with crosses through them. These two arrows, I claim, don’t exist. The physics of everyday life is not affected by dark matter or any new particles or forces, and its only dependence on the deeper level of fundamental physics (whether it be string theory or whatever) is through the intermediary of what Frank Wilczek has dubbed “The Core Theory” — the Standard Model plus general relativity. The first argument (no new important particles or forces) relies on basic features of quantum field theory, like crossing symmetry and the small number of species that go into making up ordinary matter. The second argument is more subtle, relying on the idea of effective field theory.

So how did it go over? I think people were properly skeptical and challenging, but for the most part they got the point, and thought it was interesting. (Anyone who was in the audience is welcome to chime in and correct me if that’s a misimpression.) Mostly, since this was a talk to philosophers rather than physicists, I spent my time doing a pedagogical introduction to quantum field theory, rather than diving directly into any contentious claims about it — and learning something new is always a good thing.

59 Comments

59 thoughts on “Quantum Field Theory and the Limits of Knowledge”

  1. Sean, I think the main issue which arises whenever you make this claim is that your statement has a Weak Form and a Strong Form.

    Weak Form: There are no phenomena in everyday life which are known to be inconsistent with known physics.

    Strong Form: It has been shown that all everyday phenomena occur only due to known physics.

    I find that whenever you write on this topic, you are essentially arguing for the Weak Form. As you say, 100 years ago, the Weak Form statement would be false. Now its not.

    But the title makes it seem like you are claiming the Strong Form which is, of course, unproven.

  2. Liked your post. Brought to mind what Oscar Wilde wrote: “Society exists only as a mental concept; in the real world there are only individuals.” Which, in turn, reminded me of the “knowledge” problem in science (i.e., what does scientific knowledge mean; what is the object of scientific theories?). Does science uncover the Truth (with a capital “T”) behind experience, or does it provide a construal of experience whose success is judged by how satisfactory the explanation is in matching observations, in providing testable predictions and in bringing about technological applications, without actually giving a True picture of reality (the TRUTH or MENTAL CONCEPTS THAT WORK). Hopefully both objectives will be met but that does not seem be the case historically.

  3. Wow. I read this post and the three others linked to it and I am really surprised. I understood it. I thought it was all very clear. I appreciate the clarity of writing (vs overly pedantic physics legalese). Yet the comments seem to argue a point that was explicitly pointed out as not the point being made. Studying black holes does not mean the physics of a black hole is something one experiences in everyday life (hopefully.)

    Maybe it might have been better to say the laws of physics predict everyday life experiences rather than say they are understood . Regardless, I got it. Maybe the people that commented are not representative of those that read the post.

    Its almost like saying it’s a beautiful day and then be chastised for not defining beautiful or recognizing that it’s night at other places and cold on other continents.

    To me the more interesting part of the claim is not that we understand the physics, but that we ( or at least Dr. Carroll ) claim that there is reason to believe that there are no more everyday physics to be expected. ( as pointed out in the last few slides. ) It’s also a good point to start off with when someone wants to talk astrology or homeopathic medicine.

  4. As a layman, it seems to me that the animal digestive system is well-understood. For example, we know that one end result is:

    C6H12O6 (simple sugar) + 6O2 –> 6H2O + 6CO2 + energy

    Every step of this process is explained by QM and the Standard Model, as are the chemical reactions that break down proteins and carbohydrates to sugar. There is no need for some unknown, mysterious, never-seen-in-millions of experiments mechanism.

    In welding there is a problem known as hydrogen embrittlement which causes welds to crack unless the weldments and weld materials are kept very dry. It turns out this is predicted by quantum mechanical analysis of hydrogen bonds. QM has turned metallurgy from an art to a predictive science. Material properties of alloys can now be predicted in advance, and new materials are designed by computer.

    One can always postulate some mechanism which hides itself from our experiments, whether it exists or not. This postulate is unfalsifiable. Similarly, every accused criminal could be the victim of a frame perpetrated by unknown space aliens with far superior technology, for unknown reasons. One can (and I think should) only go by the most plausible explanation based on what one knows.

    As for consciousness, so far there is no super-computer with the processing capability of our 70-odd billion neurons and trillions of connected synapses – by more than one order of magnitude. Nor of a rat’s neurons, for that matter. However, we know that flatworms can memorize mazes, and (at least according to my observations) that dogs and cats have personalities, emotions, and memories. We can simulate the flatworms, but should not expect to simulate more complex nervous systems without the necessary processing power. Although at specialized tasks, such as playing chess and Jeopardy, computer simulations can already beat us. In principle, therefore, enough computer systems with enough specialized simulations could simulate our nanotech brains.

    I expect that there will always be things that humans don’t know and/or are too difficult for us to understand. This doesn’t mean that there aren’t things we do know and understand. Of course, philosophers tell me that the Induction Principle is not logically valid, but as an engineer I depend on it every day. (So far it has worked.)

  5. cosmonut said hypothetically “Strong Form: It has been shown that all everyday phenomena occur only due to known physics.”

    Supposing Sean’s hypothesis about the ‘core model’ is correct, and I am far from sure, I agree that it is not so much that bulk matter physics and other everyday phenomena are consistent with it within reasonable margins. Rather it is whether the equation actually predicts them given some likely starting state.

  6. I guess my last comment comes under Sean’s category of ‘annoying’ as defined in one of the associated posts. But it is indeed interesting to look, as Sean has begun to, at what an equation like this, if definitive of everyday reality, would rule out.

    But isn’t QFT as final reality highly questionable? It seem to me to be full of pragmatic fixes. So it may not be an exclusive blocking pass through point between ToE and Bulk/Everyday. Just a suggestion for the far better qualified.

  7. Doesn’t just the knowledge of ‘underlying phenomena’ and the fact we can observe them in accelerators imply explaining ‘everyday life’ requires an inclusive explanation of them?

  8. JimV,

    Photosynthesis can similarly be characterized by a simple equation:

    n CO2 + 2n H2O + photons → (CH2O)n + n O2 + n H2O

    But this equation is *extremely* lacking from a physics point of view.
    I’m sure there are a number of completely different physical processes that result in this same chemical description of the reaction, each with a different efficiency, robustness, etc.

    The role of entanglement in photosynthesis is (as far as I know) unclear as of yet, but the suggestion is that it makes for better efficiency, robustness, etc.

    As for the digestive system – that was a random example for a complex biological process.
    However we do NOT yet know for certain that every step of this process is explained by QM and the Standard Model, for the simple reason that we barely understand the process from a physics point of view.
    (That’s not to say we don’t understand the chemistry, as I hope was evident from the photosynthesis example).

    Of course we are not completely clueless about the world and QM has proved incredibly successful in every realm to which it has been applied thus far.
    But comparing hydrogen bonds in metallurgy to biological processes is like comparing throwing a rock to flight of an airplane (if that). You can understand the one very well while being clueless about the other.

    I’d even go as far as agreeing with Sean’s argument when it comes to system much more complex than those in metallurgy, such as modern transistors.
    My argument is that biology is FAR too complex to make Sean’s argument about it, as of yet.

    This argument is absolutely falsifiable. All one needs to falsify it is to show that every observed phenomenon is derivable from physics. It may be hard to do so, but I’d argue that it’s not so hard as to even be impractical over the next century or two.

    To reiterate and summarize:
    We KNOW that there is more physics to discover. The only question we are debating is whether or not this new physics would apply to everyday life. I argue that this new physics might be necessary to explain standard biological processes. In which case our current physics is not enough to explain everyday life.

  9. “Gap”arguments which require that physicists explain how every molecule of the universe was formed are unfalsifiable. If you are saying that all it will take to convince you is for someone to investigate and confirm that photosynthesis, complex as it may be, is fully consistent with the currently-known laws of physics, that might be reasonable, but I expect there would be some other biological process which has not yet been thoroughly investigated which you would then cite.

    For me it is convincing that in now trillions of data points from accelerators at energies at and well above those of everyday life, we have identified no anomalies, and when we apply our current physics knowledge to long-standing problems such as hydrogen embrittlement we are successful. (No physicist actually cared enough to do the QM calculations for that, but some metallurgists have Phd’s also.) At some point the Principle of Induction convinces us that, as the engineer said who knocked over a vase, “Dang, Frank! F times L equals M!” (True story.)

    Similarly, at some point we have enough data that the claim “photosynthesis cannot be explained by current physics” becomes an extreme claim and the burden of proof shifts to the claimer.

  10. Yes, modern physics in principle has an explanation for all everyday phenomena. However, that is not to say that discoveries in particle physics and cosmology won’t dramatically improve/modify that everyday understanding, make it more calculable, or change the way we think about it.

    For example, in principle we know how to calculate the energy levels of atoms, molecules, viruses, or stars … it’s just the Schrodinger equation (or QFT). However, even numerically it can’t be done exactly much beyond a Li atom with its 9 position variables for its 3 electrons.

    Similarly for the scattering or time evolution problem for complex states. Whereas the scattering of electrons on electrons can be calculated to beyond the limits of experimental accuracy; we give up on calculating the scattering of a virus on a cell because it is too “complex” …. though we know in principle how to do it .., it’s just the Schrodinger equation in ~10^20 variables.

    Even in classical mechanics there are only a few idealized problems that are solvable in closed form. Many more are solvable numerically, but if propagated too far in time (or space) become chaotic.

    Past success (and Nobel Prizes) in elementary particle physics have come from describing how smaller things build the particle we are studying. We understand water because molecules build it, molecules because atoms build them, atoms because protons/neutrons/electrons build them, and protons/neutrons because quarks build them. But perhaps we are at the bottom of the ladder, at the least complex objects (leptons,quarks) that nothing builds. Apparently, the next theory will have to calculate an object’s properties without having to take it apart.

    Following this thought, perhaps the great future gift of fundamental physics to everyday life will be the making of all “complex body” problems calculable. Presumably, there will be a mass formula that you put the N numeric labels of an electron into to get the mass of an electron, different values of the N numeric labels to get the mass of a muon, and yet different values of the N numeric labels to get the exact mass of that particular virus. Similarly, the formula for the scattering amplitudes will only require the N numeric labels of each of the input and output objects …even if these are “complex” objects like viruses and cells.

    The calculation of Clebsch-Gordan coefficients for the rotation group provide an example of this idea. Higher spin particles may be viewed as “complex” because they are built of the product of many fundamental spin ½ states. Calculating a CG coefficient by first expressing all the higher spin input/output particles as combinations of spin ½ particles is a very tedious (if not impossible) way of solving the problem. However, there exists a simple formula you can plug the 2 input and 2 output spins into which gives the GG coefficient …even if the 4 spins are really big like 10^20. Here, the calculational wall of complexity has gone away.

  11. Quote from Frank Close: “What is reality? Answering this superficially simple question is like trying to eat porridge with your fingers.”

  12. I agree that humans should celebrate the fact that the world (on our scale) we live in can be fully explained by natural theory. I don’t get why the assertion is controversial.

    All that is claimed is that in the limited scale of our lives (say from atoms to the solar system), no phenomenon has been found which is not explained by theory to experimental accuracy (which is extraordinarily fine in many cases). That doesn’t mean that we can explain every detail (e.g. all details of conciousness), just that there is no objective evidence of anything but natural phenomena at our scale.

    This is not true at larger and smaller scales and there is no claim to it. Still lots to learn at cosmological scales and subatomic scales.

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  14. Tried to come up with at least one exception but failed. However the exercise took me on a tangent. So excuse me for this somewhat off-topic question …

    Given that all of space is expanding EXCEPT not within gravitationally bound systems such as a galaxy cluster or smaller … Then can the tiny temperature fluxuations in the cosmic microwave background be considered a function of the percentage of the travel path of this radiation across gravitationally bound regions of space where the expansion has been less? (Never heard it described in this manner.)

    [Sorry but this is what happens at night when I fail to take my sleeping pill.]

  15. When the everyday life is that of a cosmologist …

    1. Can’t explain the rotational velocity of stars within a galaxy or the degree of gravitational lensing by a foreground galaxy or galaxy cluster without resorting to dark matter.

    2. Can’t explain the mass of the neutrino or have predicted neutrino oscillation from the Standard Theory.

    3. Can’t explain fluxuations in the CMB from General Relativity.

    4. Can’t explain with the current laws of physics what will happen to a basketball (an ordinary everyday object) tossed into a black hole. (Yes it will be spaghettified but that’s not the whole story.)

    5. Can’t explain what is time?

  16. Of course we’re making a mockery of your real points here that (1) everything that occurs in the everyday world can be explained by the natural known laws of science without resorting to pseudo-science or the supernatural, and (2) there is no need to resort to unknown laws of physics to explain silly stuff like astrology / faith healing / perpetual motion or anti-gravity machines / superstitions / ESP / UFOs or alien abductions / miracles / life after death or reincarnation / a soul / heaven or hell / demons or angels / ghosts because there is no reasonable evidence that any of these exist.

  17. If I write a software program to draw fractals on a computer monitor, I can run the program on my machine. I can also email the program to another and they can run the program on their machine.

    Are the images that appear on the monitor “explained” by the underlying hardware of the CPU, RAM, and the monitor or do we need to include the software program as part of the explanation?

    If computer program is analogous to mental activity, can the mental be causative?

  18. We depend upon mathematics to run our everyday lives, yet the known laws of physics (which themselves are based on mathematical equations and relationships) can’t explain whether math is a fundamental property of the universe or why certain numbers such as pi have such fundamental importance.

  19. It seems like most people are not aware of the frequency or density of random particle pair production. I had read somewhere that they only spawn about once every cubic meter. That really seems like it would play an interesting role in Hawking Radiation. Then Hawking Radiation doesn’t even account for random particle pair production densities or systems, and his equations just say that the radiation would increase dramatically on smaller scales. It would seem like, if a black hole was smaller than a cubic meter in diameter, it would begin to start having a hard time finding a random particle pair, especially if it was microscopic. It would seem to be something like hitting a hole in one at the golf course. Then if we ever relied on that to get rid of a microscopic black hole, then it would seem like the physics of everyday life could really become a complete mystery…

  20. Bostontola echoes one of the implications of Carroll’s post by asserting:

    “In the limited scale of our lives (say from atoms to the solar system), no phenomenon has been found which is not explained by theory to experimental accuracy.”

    Bostontola asserts that this state of “full explanation” is something “humans should celebrate.”

    Unfortunately, with regard to gravity, the assertion is less well supported than is commonly supposed. For it to be supported well enough to warrant a “celebration,” we would need to provide evidence that our theories of gravity have been thoroughly tested not only on the indicated range of size, but from the inside to the outside (i.e., from r = 0 to r —> R_solarsystem) over that whole range.

    Unfortunately, with regard to gravity-induced motion, only the domain of General Relativity’s (Schwarzschild) exterior solution (within the solar system) may arguably be regarded as well tested. This is the domain from the surface of a gravitating body upward. From the surface downward is still an empirical mystery. The Schwarzschild interior solution predicts that a clock at the center of a massive body is a minimum. This prediction has never been tested. Maybe the rate of a clock at the center is not a minimum, but a maximum. We don’t really know.

    Of course it is customary to guess that we know how clock rates vary and what kind of motion would ensue for objects falling inside a massive body—say, within a hole drilled through a body’s center. These guesses have the authority of Newton, Einstein, and various principles such as energy conservation to recommend them. Yet it must be admitted that inside massive bodies is exactly where these authorities and principles have not yet been tested. This is exactly where we have not yet looked.

    Further reasons for filling the huge gap in our empirical knowledge of gravity may be found here:

    http://www.gravitationlab.com/Grav%20Lab%20Links/Galileo's-Belated-Experiment.pdf

    It is important to realize that there is no good reason NOT to do the experiment. It is not only well within the feasibility of modern technology, the cost of performing it would be quite cheap compared to many physics experiments that are underway or have been proposed.

    It is relevant also to point out that Galileo proposed essentially the same experiment nearly 400 years ago. The apparatus needed to carry it out (e.g., a modified Cavendish balance) may be called a Small Low-Energy Non-Collider. I’d guess that the Father of Modern Science would prefer to let Nature speak on the matter before breaking out the champagne.

  21. Richard,
    There is plenty to celebrate. I said nothing has been found, I.e. No experiment has conflicted with the theories at the fundamental level. It has never been claimed (or required) that every prediction of a theory has been tested. GR predicts what happens inside the event horizon of a BH. We can’t test that specific prediction, but since every other test has proven correct, we regard the theory as valid within its range of application. That’s all any theory is good for at this point. Plenty of reason to be awed and celebrate.

  22. Bostontola,

    It’s true that things like black hole interiors cannot be explored, and that the domain of the Schwarzschild exterior solution appears, within the solar system, to support GR. Insofar as this support establishes a more accurate theory than Newton’s, we should be happy. Something about Einstein’s theory is closer to the truth than Newtonian gravity.

    Two things suggest to me that it is nevertheless not yet time to celebrate. First, note an important distinction between the two physical domains under discussion: Black hole interiors can never become “everyday physics.” We cannot go there and come back, so we have no choice but to guess.

    Second, the low energy regime inside ordinary bodies of matter could conceivably become “everyday physics.” We need only imagine a civilization that plans to build a through-the-center transit system on their world. Before attempting the full scale “gravity train,” they would test the principle first with a small scale model.

    With a modified Cavendish balance or in an orbiting satellite, they would build a Small Low-Energy Non-Collider, just to make sure it works as planned. Caution is in order because, though Einstein gravity supercedes Newtonian gravity, we still don’t know exactly why: We still don’t know the mechanism of gravity; we don’t know what matter does to make spacetime curve.

    On the basis of an analogy that Einstein used to build GR, it is possible that the scaled down Non-Collider would provide a clue in this regard. As John Stachel has emphasized, the need for non-Euclidean geometry became clear to Einstein only after he considered the ways gravity appears to be analogous to uniform rotation.

    The analogy served to justify, to Einstein, regarding the rotating body as being “at rest.” But perhaps it’s more logical to turn the analogy around. Perhaps non-Euclidean geometry is best suited to describe the spacetime in and around gravitating matter for the same reason it is best suited in the case of rotation. Spacetime curvature may, in both cases be caused by motion. This argument is developed in more detail here:

    http://www.gravitationlab.com/Grav%20Lab%20Links/Rethinking-Rotation-Sep-5-2012.pdf

    Whatever successes may be claimed for the prevailing ideas of gravity, it remains a profound enigma. Failure to understand gravity has sometimes evoked comments of despair (Okon, 2014):

    “It is the opinion of at least a sector of the fundamental theoretical physics community that such field is going through a period of profound confusion. The claim is that we are living in an era characterized by disagreement about the meaning and nature of basic concepts like time, space, matter and causality, resulting in the absence of a general coherent picture of the physical world.”

    We can celebrate because some fraction of our glass is “full.” Or we can more humbly keep exploring; we can insist on testing our theories of gravity inside matter because that represents one of the largest fractions of the glass that is still empty.

    What would Galileo do?

  23. Richard,
    I don’t know what Galileo would do. I also never said we are done with natural theory. I’m sure we will find more general theories, maybe even one theory that covers QM and gravity. The key point is, when we do, this new theory may describe more of the universe, but it will agree with the current theories in the range of every day life defined above.

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