The World of Everyday Experience, In One Equation

Longtime readers know I feel strongly that it should be more widely appreciated that the laws underlying the physics of everyday life are completely understood. (If you need more convincing: here, here, here.) For purposes of one of my talks next week in Oxford, I thought it would be useful to actually summarize those laws on a slide. Here’s the most compact way I could think to do it, while retaining some useful information. (As Feynman has pointed out, every equation in the world can be written U=0, for some definition of U — but it might not be useful.) Click to embiggen.

Everyday-Equation

This is the amplitude to undergo a transition from one configuration to another in the path-integral formalism of quantum mechanics, within the framework of quantum field theory, with field content and dynamics described by general relativity (for gravity) and the Standard Model of particle physics (for everything else). The notations in red are just meant to be suggestive, don’t take them too seriously. But we see all the parts of known microscopic physics there — all the particles and forces. (We don’t understand the full theory of quantum gravity, but we understand it perfectly well at the everyday level. An ultraviolet cutoff fixes problems with renormalization.) No experiment ever done here on Earth has contradicted this model.

(Obviously, observations of the rest of the universe, in particular those that imply the existence of dark matter, can’t be accounted for in this model. Equally obviously, there’s plenty we don’t know about physics beyond the everyday, e.g. at the origin of the universe. Most blindingly obvious of all, the fact that we know the underlying microphysics doesn’t say anything at all about our knowledge of all the complex collective phenomena of macroscopic reality, so please don’t be the tiresome person who complains that I’m suggesting otherwise.)

As physics advances forward, we will add to our understanding. This simple equation, however, will continue to be accurate in the everyday realm. It’s not like the Steady State cosmology or the plum-pudding model of the atom or the Ptolemaic solar system, which were simply incorrect and have been replaced. This theory is correct in its domain of applicability. It’s one of the proudest intellectual accomplishments we human beings can boast of.

Many people resist the implication that this theory is good enough to account for the physics underlying phenomena such as life, or consciousness. They could, in principle, be right, of course; but the only way that could happen is if our understanding of quantum field theory is completely wrong. When deciding between “life and the brain are complicated and I don’t understand them yet, but if we work harder I think we can do it” and “I understand consciousness well enough to conclude that it can’t possibly be explained within known physics,” it’s an easy choice for me.

Let me know if I’ve made any typos here, or have gone too far in trying to make things compact. For instance, can I get away without putting a “trace” around the gauge field kinetic term? I don’t want a notational shortcut to undermine my argument and leave the audience believing in God.

  1. Fair enough, MKS. Art is a personal gift that changes the receiver. It’s all coming clear to me now…

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  3. and if I’m correct m_p is the reduced Planck mass not the Planck mass (see Planck mass on Wikipedia).

  4. Doc C,

    oh, you’re a fellow red pill junkie/transcendence addict? :3

    (and Radaghast the Brown/dr Doolittle are really nifty)

  5. Marcel,

    No, there indeed needs to be a h.c., since the fermion kinetic term is *not* real in this case. It is real in the Standard Model, but here you also have gravity coupled. The covariant derivative (D_{\mu}) fails to commute with the Dirac matrices (\gamma^{\mu}) when gravitational connection is present inside D.

    //nerdtalk: The covariant derivative contains a contribution from a localized Poincare symmetry, which has a nontrivial spinorial representation, which doesn’t commute with the \gamma’s. Hence the conjugate term will have D and \gamma in the reverse order, which is not the same as the original term.//

    In the usual Standard Model (without gravity) the fermion kinetic term is indeed real, so there is no problem in that case. The equation on the mug in your reference is off by a factor of two, unless “h.c.” really stands for “hot coffee”. 😉

    Bottomline — since Sean is not writing this equation on a mug :-), and since he dares to include gravity, he should put an additional h.c. for the kinetic term, and a factor of 1/2 in front of both, to get the relative scaling for fermions in the standard form.

    But the whole equation is just a sketch anyway, so we don’t need to make so much noise about it. 😉

    HTH, :-)
    Marko

  6. Some bullshit follows. But it’s the nearest thing I’m capable of to non-bullshit when trying to explain consciousness. I’d say it falls under the heading of aspect dualism.

    Consciousness is the manifestation of the universe’s innate tendency to hallucinate. The fact that the universe hallucinates is not reducable to physics (even in principle) but the content of the universe’s hallucinations is constrained by physics — specifically by patterns in changes of energy distribution in a material object (the brain). These patterns cause the universe to hallucinate a story that makes sense of them. The universe hallucinates many stories simultaneously, each one oblivious to the existence of the others. Different hallucinations can have different physical substrates (i.e. different brains), and it may be that a single substrate also gives rise to a superposition of many hallucinations. The notion that consciousness is located in its substrate is an illusion caused by the fact that the consciousness we know has evolved to model its substrate’s environment.

  7. Dear Marko,

    Thanks for your explanation. I didn’t realize that D now behaves differently than in the Standard Model as it now also contains the gravitational connection term. Still I hope Sean will add the extra h.c. and the factor of 1/2, which will make it more correct and so more cool, also because you don’t find this full Lagrangian path integral expression easily anywhere else on the Internet.

    What about the absence of the bar in the Yukawa term on the mug and John Ellis’s t-shirt? Is that in the definition of one of the psi or V? You would think that it is more conventional to show the bar explicitly as Sean did or am I again missing something :-)

    Thanks in Advance!

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  9. “We don’t understand the full theory of quantum gravity, but we understand it perfectly well at the everyday level. An ultraviolet cutoff fixes problems with renormalization.”

    I’m not completely sure that an explicit UV energy cutoff solves the problems. The cutoff violates Lorentz-invariance at very high energies. But even in low energy calculations, the virtual particles in the loops can see the high energy Lorentz-violation. So I think that the explicit cutoff breaks Lorentz-invariance even at low energies!

  10. Rezso,

    “The cutoff violates Lorentz-invariance at very high energies.”

    No, it doesn’t need to, if you treat gravity as a quantum-mechanical system (which you should, anyway). There have been successful constructions of the cutoff-dependent QG models which do not break Lorentz invariance. For example, the whole Loop Quantum Gravity framework features this kind of stuff all over.

    You can find the detailed explanation in Rovelli’s book “Quantum Gravity”, but the essence is the same mechanism in QM that makes the spin take only “up” and “down” values, while at the same time not breaking full rotational symmetry.

    Classically you’re right, cutoff would violate the symmetry, but QM can come to the rescue, if you build your QG model properly.

    HTH, :-)
    Marko

  11. Marko,

    OK, my comment was about the standard QFT treatment of gravity, with a simple energy cutoff. I don’t know that much about loop quantum gravity, but I have heard that it has it’s own problems with the correct semiclassical limit.

  12. @ Rezso:

    Oh, sure, the standard qft approach doesn’t work well, neither with nor without a cutoff. :-) In the equation, Sean was wise not to specify the details of how the gravitational path integral is defined, since — honestly — noone knows of a definition that works well enough. As I said in previous comments, the QG path integral is in the state of wishful thinking.

    The way I interpret Sean’s equation is in line with what Renate Loll has nicely formulated: “the path integral for gravity is a statement of intent”. 😉 That is, it is a placeholder term that should be substituted with one’s favorite choice of a QG theory. I just noted that there are choices available for which the UV cutoff plays along well with Lorentz symmetry.

    And sure, all models of QG (including LQG) have a problem with the semiclassical limit. Sometimes it is a bit hidden under the carpet, but it’s always there if you look hard enough.

    Best, :-)
    Marko

  13. Personally I don’t see anything wrong and didn’t in the first place. Maybe just seemingly too simple. But I could be a complete moron, too, which isn’t beyond me.

  14. I still prefer Sean’s way of writing the Yukawa term, as it more clearly shows (as seems the purpose) the chirality (through L and R) of the SM than with Weyl spinors. If he would only add the half and add an extra h.c. then we could all copy this equation and pretend we understand it :-)