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.


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.

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120 Responses to The World of Everyday Experience, In One Equation

  1. Is the cosmological constant hidden in the Higgs potential?

  2. Mike H says:

    “We don’t understand the full theory of quantum gravity, but we understand it perfectly well at the everyday level.”

    You understand gravity? Great, please explain to me what physically pulls the atoms of my body and the Earth together? What object connects the atoms, mediating the force of pull? Please answer.

  3. Ian Durham says:

    I posted this on Facebook as well but figured I’d post it here to. If what you say is true – that we absolutely fully understand the physics of everyday life – then why did we even bother with that conference 18 months ago? I can’t imagine it was just for the purpose of a nice boat ride in the North Sea.

    Quantum field theory obviously makes very accurate predictions, but that doesn’t necessarily mean it matches reality. A large part of my everyday experience involves my mind. I am not aware of any full explanation of the mind in physical terms yet.

    Plus I think it’s a little disingenuous to make the claim that quantum field theory can fully explain everyday life given that we don’t fully understand emergence yet nor to we fully understand complex systems.

  4. Steve Welker says:

    The only typo I see is in the 4th paragraph: …were simply incorrect and have been replace_d_.

    BTW, I’m currently reading “The Particle At The End Of The Universe” and enjoying it as well as this post. Thanks, Sean.

  5. Sean Carroll says:

    Robert– Yes, but most of us go through our everyday lives unaffected by the cosmological constant.

    Mike– Yes, I do understand gravity, I even wrote a whole textbook about it. Check it out!

    Ian– It’s the physics underlying everyday life. All of the words mean something. (See above about tiresomeness.)

  6. Sean — I agree (of course).
    Since it’s an effective theory I just thought that it would be best to include the lowest dimensional operator in the gravity sector.

  7. Ian Durham says:

    OK, I guess I really don’t understand what you’re saying, then. Because I could just as easily say that the equation does not “explain” entanglement (if it did, I’d be out of a job) and you’d likely counter by saying it has nothing to do with everyday experience. But if you’re talking about the physics underlying everyday experience then how do we even know what that is to begin with if we don’t understand emergence and complexity?

  8. Beautiful work, Sean! I’ll need to do some googling to figure out what the individual terms represent but thank you for the map explaining the big pieces of it.

  9. vmarko says:

    Sean, are you trying to be provocative on purpose? :-)

    Leaving aside all the philosophical stuff about consciousness, God, etc., the gravitational sector of that equation is all but understood. Care to give a definition for the path-integral measure [Dg]? Do you sum over all possible spacetime topologies or not? What about the divergent loop-corrections for gravitons? And no, one can’t even get the classical limit (i.e. general relativity) from the above equation.

    So not even everyday life, sorry.

    There are also some missing pieces in the matter sector, like the proton mass prediction, etc. But those are probably just technical points.

    Best, :-)

  10. Holger says:

    The equation predicts any observable phenomenon associated with what we call “entanglement.” That’s all one can ask for: a model that makes accurate predictions.

  11. Lord says:

    If we discover our minds each have access to a pinpoint wormhole, does that mean our understanding of quantum theory is wrong, or our contemplation of what constitutes everyday experience is flawed?

  12. Garrett says:

    That’s nicely succinct. I do think you can get away with writing the trace in the gauge kinetic term as an implied sum over Lie algebra components, as you’ve done, since the Lie algebra basis generators are usually chosen such that the Killing form is +1 down the diagonal. There might be some trickiness for neutrinos, if they’re not purely Dirac fermions or they have Majorana masses. You should also probably include the cosmological constant. And there will probably need to be some kind of inflaton multiplying the scalar curvature, but there’s not consensus on how that works yet. And it is important to emphasize that this description doesn’t work well for quantum gravity; so as marvelous as it is, it’s still not ready to be chiseled into stone yet. But for describing the physics behind everyday life, it’s sufficient, and probably overkill!

  13. Mike H says:

    “Mike– Yes, I do understand gravity, I even wrote a whole textbook about it. Check it out!”

    Excellent, but I was hoping you could just help me to visualize the process right now, in THIS thread, because I am not convinced.
    I read through a couple of your articles and on the one about explaining how Higgs Bosons work I found this:
    “Now of course you should probably try to explain why fog would give mass to something. That’s left as an exercise for the reader.”

    Is this still your position on the Theory? How can a fog mediate the force of PULL between objects? Isn’t that what we are talking about with gravity anyway, the phenomena of tension between all objects?

  14. doc c says:

    I wonder whether it is fair to say that the laws underlying the physics of everyday life are understood if those laws cannot predict the outcome of all given events of everyday life in the same way they can predict the outcome of any given experiment designed to test them. It seems like the word understood is being used in 2 different ways. Is it a hypothesis, or is it a fact, to say that all of the events of everyday life will conform to the same underlying laws that we have tested experimentally thus far? Does “understood” imply empirically tested, or can a hypothesis be enough?

  15. moonside0 says:

    One thing is for sure we are part of a system and the system would be different without us

  16. Meh says:

    I actually try to be both provocative and irrationally simultaneously ignorant and arrogant to try to get under the skin of people I find to be pompous asses.

    There are two, and only two, possibilities when it comes to understanding the physics of everyday life. The first is that we know enough to completely describe the physics of everyday life. The second is that we will never know enough to “completely” understand the physics of everyday life because it is impossible. Just as it would be impossible to know all information about the universe. I could understand both stances on the topic, but agree most with what Sean is saying. I would prefer to spend my time arguing about how FUC**NG AMAZING this is and if anyone understands how truly important it is;

  17. Jack Weber says:

    Neat stuff! And i especially like the last tongue in cheeker: “I don’t want a notational shortcut to undermine my argument and leave the audience believing in God.

    And, since you asked: some typos/edits:

    “For purposes of one of my talks”… Just “for one of my talks…” or “for the purposes of…” are better.

    “embiggen” should probably be “enbiggen?” We don’t say “emlarge,” so, it should probably stay relative to known good semantics. Just like quantum does not replace relativity, so fun words are more appreciated and need to grow from their predecessors and kin.

    “Equally obviously” should be “equally obvious”

    “As physics advances forward”… redundant: “As physics advances” is right.

  18. Tony Rtz says:

    In the infinite universes theory there could be an infinite number of exact Seans, or any of us, with the exact particle make up, why in reality is there only one of us? There is absolutely no possibility of mathematics or physics or any of the sciences proving the possibility of a higher state of existence, sorry, it simply can’t be done, it’s far, far beyond anything in this universe. If physics can prove the existence of a Love that is substantive, like a solid, such as rock, then it could, but it can’t, it simply can’t, no way, no how, never, never, sorry and I know of what I say.

  19. doc c says:

    I like that as a start to how to approach the real question.

  20. AI says:

    To me there is no such thing as a “complete understanding,” we simply know more than we used to but a “complete understanding” is a complete fiction. If you keep asking further questions you run out of answers almost immediately.

    Why anything at all? Why three spatial dimensions and one time dimension? Why curved spacetime? Why Born rule? Why Pauli exclusion principle? Why these symmetries? Why those masses? Why three families? etc, etc…

    In fact I would say the opposite is true – in reality we don’t understand a damn thing about the laws of physics. All these laws amount to is an efficient description – not explanation – of the patterns we’ve found by trial and error.

  21. MarcS says:

    I’m going to take a crack at describing what I think is meant by “the laws underlying the physics of everyday life are completely understood.” This is generally for my own benefit – I’d like to share this post but I want to make sure I can explain it in my own words. Sean, if you read this comment and I’m out in left field please straighten me out.

    Physics of everyday life means we’re talking about ordinary run-of-the-mill matter and fields in ordinary run-of-the-mill quantities and energies. Specifically we’re not talking about black holes, firewalls or exotic particles living brief lives in an LHC experiment. We’re talking about protons, neutrons, electrons, atoms, molecules, EM fields, electric current, yadda, yadda, yadda.

    That the rules are completely understood means exactly that (and not more). The existing theories provide rules describing how this matter and energy interact. Given a state of a system the rules predict how that state will evolve with time. When these rules are tested against physical reality they are always correct. There is no experimental reason to doubt that these rules really do describe how the run-of-the-mill stuff of ordinary life actually behave.

    That’s pretty much it. So what does it really mean? Well one thing it doesn’t mean is that just because we understand the rules we can predict how every system will behave. A system may be composed of so many parts in such a complex arrangement that we simply don’t have the physical capability to work out all the details. But, under the covers, the interactions of all those many parts is governed by the known physical rules and nothing else. Even though a system is too complex for us to model there is nothing happening inside that isn’t described by the known rules of the physics. For example, we may not be able to predict right now exactly how a protein will fold up but when we are able to work it out we won’t need to invent any new rules of physics to explain it.

    Also, there is no room left for magic or the supernatural. A magical event would entail observing something in the ordinary physical world behaving in a way not predicted by the rules of physics. No observation of the physical world has ever encountered such an event. There is nothing we can imagine doing to objects in the everyday world that isn’t covered by the rules of physics and hasn’t been experimentally verified.

    Thus we can legitimately claim to completely understand the physical rules of everyday life.

  22. Tevong says:

    “But if you’re talking about the physics underlying everyday experience then how do we even know what that is to begin with if we don’t understand emergence and complexity?”

    Because we don’t need to understand every move a chess grandmaster makes to convince ourselves we understand the basic underlying rules of chess, to take a well known analogy.

    I share sean’s position that it’s tiresome having to defend a point that shouldn’t be controversial. It’s like saying the rules underlying chemistry are well known and complete, which they are, then someone goes “oh yeah? Well derive the spectrum of all atoms in the periodic table from first principles. Until then you can’t say quantum mechanics explains chemistry”. Yet no chemist would argue against the fact that quantum mechanics provides a complete description of all chemistry.

  23. Sean Carroll says:

    MarcS– I think that’s a fair way of putting it. I’ve elaborated at length on what is meant by the claim in the various links included in the post, but the more ways of saying it the better.

  24. Ahab says:

    Thanks Sean..

    There’s another such equation, by the way, that was displayed by Neil Turok during his lecture (What Banged?) (available on Youtube).

    Are there any basic differences between the two ?

  25. doc c says:

    MarcS and Sean,
    It seems like what you’re saying is that we completely understand the constraints on what the known universe can present to us. Any experience we have in everyday life will not fall outside of those constraints. Within those constraints, things can happen that we cannot predict or fully understand at present, but those events are limited by the above stated constraints that we have discerned. No more surprises.
    Seems fair if that is what you are saying.
    So is it time to focus mainly on the operations that still elude us within those constraints? Seems like that is where our energy and money ought to go.

  26. vmarko says:

    Sean, I can see that you have modified the equation and the text to account for nonrenormalizability of gravity. But there is another problem, which is a tad more serious — one cannot derive classical Einstein equations of general relativity from that path integral.

    The scalar curvature is not bounded from below, so there is no stable vacuum solution around which to calculate the effective action of the classical theory. This is a well-known property of Einstein-Hilbert action, and a big headache for any quantum gravity model. The path integral you wrote down simply cannot predict *anything* related to gravity. Not even the Newtonian gravitational field of the Earth, from the realm of everyday experience.

    If you really want to collect all fundamental equations in one slide, I suggest that you cut gravity out of the path integral, rewrite the SM-part in flat spacetime, and add classical Einstein equations separately. That would be, by far, a much more accurate and fair account of the known physics.

    A gravitational path integral is still in a state of wishful thinking.

    Best, :-)

    P.S. I hope you didn’t give up on reading the comments… 😉

  27. Craig McGillivary says:

    The equation is very comforting, because it doesn’t care.

  28. DaveDave says:

    Mike- this is the problem sometimes with the scientifically misinformed. Do you honestly expect someone to be able to fully explain gravitons and quantum mechanics in an online thread? There is a reason people attend school for years trying to understand these equations and theories.

  29. wolfgang says:

    A few remarks: Why is the whole thing W and not Z ?
    You integrate over A and g but you do not show how F and R depend on them.
    The sum over a for F^a hangs in the air and I dont see neutrino masses …

  30. MarcS says:

    doc c,

    I think that captures the spirit of it. I might use a little different language, though. There’s no room for magic but there are plenty of surprises left!

  31. Ian Durham says:

    “I share sean’s position that it’s tiresome having to defend a point that shouldn’t be controversial.”

    Honestly I find it tiresome that a certain segment of the physics community continually makes statements that are, at best, rhetorical. It not only does a disservice to physics in general, it marginalizes those of us who study foundational problems from a different point of view (e.g. condensed matter, quantum information, etc.) and makes it appear that the particle physics/cosmology/quantum field theory viewpoint has a monopoly on truth which it doesn’t.

  32. Sean Carroll says:

    Marko– I don’t think it’s that bad as long as we remember that we’re both in the weak-field regime and have an ultraviolet cutoff. Write the metric in terms of small fluctuations about flat space. The conformal instability shows up as a wrong-sign gradient term for the scalar potential (depending on how you write things). It doesn’t matter that it’s unbounded below, since the cutoff regularizes it. All that matters is that classical configurations dominate the remaining path integral. I think that will be true, since those classical configurations are still stationary points of the action. But I will admit that I haven’t checked it, so I might be wrong about that.

  33. Lord says:

    This is a circular definition, what we understand is equivalent to what makes up everyday life, and certainly what we don’t understand we have no inkling of what impact it would make upon our conception of everyday life. That we believe it has no impact, is just another way of saying we don’t understand it and we know of no impacts on everyday life in need of explanation. We don’t know what we don’t know however, so we cannot say such impacts won’t be discovered in the future or that everyday life is not dependent on them in some as yet unknown manner. We can only say that within the scope of what we currently consider everyday life, we believe we understand, but what we currently consider everyday life may be seriously flawed. It may not be flawed in the manner our understanding within our domain is mistaken, but that our domain is far from complete an explanation of everyday life.

  34. Sean Carroll says:

    Hamber, in his book on the path-integral formulation of quantum gravity, seems to say that the conformal instability in the linearized action can be removed simply by a choice of gauge:

    Now, I’m not sure I see that, so maybe it’s not trustworthy. And introducing a UV cutoff is different than linearizing the theory, so that might not be fair. But I think it points in the right direction.

    There is also a review by Donoghue on quantum GR as an effective field theory, which seems reasonable:

    Perhaps I should write the equation explicitly as an integral over small fluctuations h, rather than the whole metric g.

  35. Bee says:

    It’s also the one equation in Turok’s book. Though you get extra points for putting in the measures and a cut-off and indices and so on :)

  36. Matt says:

    Hi Sean,

    You claim that “the only way” that “this theory [couldn’t] account for the physics underlying phenomena such as life, or consciousness” is if “our understanding of quantum field theory is completely wrong”.

    You then link to an article critiquing the idea that consciousness survives the death of of the brain (mush of which I wouldn’t argue with – substance dualism is extremely problematic).

    However, the ideas of consciousness not being explicable by our current understanding of physics, and consciousness being immortal are fundamentally different ideas. For sure, belief in the latter implies the former, but taking the former seriously certainly doesn’t require the latter.

    There are various ideas where the mechanisms underlying consciousness (in-whole or or-part) consist in areas of physics that are currently not understood (the sub Planckian scale for example). It would be true to say that there is no evidence supporting these theories. But equally, while that area of physics (which also happens to be its most fundamental underpinning) remains beyond our understanding, there is also simply no evidence to the contrary.

    As far as I can see, the use of the phrase “the only way” is unjustified by the link or any of the arguments provided, and I’m struggling to see how such a claim could be logically sound when its target is necessarily an area of our knowledge that is currently missing.


  37. vmarko says:

    Hi Sean,

    “All that matters is that classical configurations dominate the remaining path integral. I think that will be true, since those classical configurations are still stationary points of the action.”

    Here is the crux of the problem. We just don’t know that the classical configuration will be the dominant one in the path integral. It is stationary point of the action, but that doesn’t mean that quantum corrections are small. The classical configuration needs to be a proper extremum (as opposed to being just a stationary point) in order to esnure the smallness of quantum corrections. In the matter sector this is automatic, since the SM action has a global minimum. But the gravity sector has no global minimum, hence the problem.

    Hamber gives a physical interpretation of this in the paragraph below eq. (2.39) in his book — gravitational radiation carries positive energy, while gravitational potential energy is negative, since gravity is attractive. Hence no global stable equilibrium. He also admits that this is a physical property of gravity, and cannot be gauged away. And the proposals for solving this problem all have their own set of problems… :-)

    “Perhaps I should write the equation explicitly as an integral over small fluctuations h, rather than the whole metric g.”

    You could do that, but you would additionaly need to postulate by hand that the fluctuations are small, because the action doesn’t tell you that they need to be.

    Best, :-)

  38. Bill says:

    That remarkable equation only tells us how things will *move*,
    but not how they *feel*. The emergence of consciousness is
    a problem of a different order.

  39. Foster Boondoggle says:

    Sean & Matt –

    It’s perfectly plausible that the physics of this equation accounts for everything going on in the brain, and also that it doesn’t “explain” consciousness (whatever that might mean). The only way we know about consciousness is through a form of interaction with the world – introspection – that bears no relationship to the way we know about all physical phenomena, namely external observation (plus some theorizing). Read early Thomas Nagel for a really clear discussion of the difficulty with physicalist – “third person” accounts of subjective – “first person” – phenomena. This is what Chalmers calls the “hard problem” of consciousness, and no new physical discovery – unless of an entirely different kind than anything we currently call “physics” – could possibly shed any light on it.

    Update: Bill, I see you succinctly beat me to it.

  40. Tevong says:

    Ian no one is saying studying emergent systems or complexity is any less important or interesting. To say that QED underlies all of chemistry is not to belittle chemistry.

  41. Sean Carroll says:

    Marko– I still don’t understand why saddle points shouldn’t dominate the path integral, by the stationary phase approximation. I understand it in Euclidean quantum gravity, where the true minima of the action dominate. But I don’t see it in the Lorentzian case. You should just get a highly-oscillating contribution from conformal fluctuations, controlled by the UV cutoff. But I may be missing something, certainly.

    Bee– I didn’t know about Neil’s version, but it is remarkably similar. He’s making a different point — “all known physics” vs. “physics of everyday experience” — but the equation is the same, of course:

  42. Kigen says:

    An interesting formula, I wish I knew what it meant! My field of study deals with explaining physical phenomena by starting from the experience of consciousness and projecting “outward” to explain physical phenomena rather than from “physical” observations projected “inwards” to try to formulate a description of conscious experience.
    I would love to begin to “compare notes”. If one had a hypothesis to explain the under laying function of consciousness and its role in such things as EPR, the collapse of the wave function, the arrow of time, and the curvature of space-time, where would be a good place to post it online in order to receive some intelligent feedback?

  43. Kevin C. says:

    Wow, that is impressive. I wonder how much space it would take to define all those terms using simple operators. (i.e. How big would a program to calculate that equation have to be? or What is the Kolmgorov Complexity of that equation?)

  44. Jimbo says:

    That’s neat! But what does “h.c.” mean at the end of the “matter” bit?

  45. Sean Carroll says:

    Jimbo– It means “hermitian conjugate,” which is like complex conjugation for matrices. Just so the action is a real number.

  46. James Goetz says:

    I don’t want a notational shortcut to undermine my argument and leave the audience believing in God.”

    Hi Sean,

    But what if the mathematical chips fall where they may and your equation supports the existence of God? Would you insist that you made a mistake?

  47. Tony Rtz says:

    I haven’t the slightest understanding of your equations Sean, but you also don’t have the slightest understanding of God, that includes all or most of those who have posted on this blog. I would say all. I was never a math wiz in anyone’s estimation, but I have a certain gift whereof I can at times sense something of that higher power, actually know this higher power, much like the Mystics of old. I can understand much of Physics, but without the math that explains such. Fields of which a particle is just a point, without dimension, someone wrote that a black hole should be studied as a dimensionless point like any other particle. Just wondering. Wouldn’t it be best if Physics would be used to understand the world we live in and forget trying to disprove the existence of a God that most Religious believed created it. Atheists can believe as they will and religious also, and still work together to make this world understandable and a better place to live, each in their own way. Neither condemning the other.

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