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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  50. Torbjörn Larsson, OM says:

    I really wish I understood the discussion of the equation. Since it should describe everyday life, I assume it has no need to predict the flat space that comes out of Lambda-CDM alone I take it. I would think that means it should describe small fluctuations in flat space, and not the full GR.

    [And I seem to remember flat space in itself is awfully problematic, so Lambda-CDM is perhaps a savior and everyday physics can be thankful for it.]

    On to the other side of the coin, the observed and now predicted absence of magic.

    @Tony Rtz:

    “proving the possibility of a higher state of existence”, “don’t have the slightest understanding of God”.

    Any idea of gods so far is based on magic, that energy conservation is broken locally or cosmologically, so that non-physical entities exist and/or do non-physical magic. That is all the understanding necessary, and all what is needed to test magic.

  51. Torbjörn Larsson, OM says:

    @AI: What is the difference between a predictive efficient description and an “explanation”?

    Computer scientist Scott Aaronson has put up an interesting seminar on his blog, on how math have gone from examples to zero-knowledge proofs, modern proofs and their testing (validation) is mapped to manipulation of string symbols.

    At the end he asks if mathematics will now go on to understand “explanation”.

    [Maybe “explanation” needs knowledge, maybe not. But validation (testing) doesn’t seem to, in principle. It produces knowledge when findings are put in context, of what works.]

    @Lord: “Circular definition” is an empirical method, a hypothesis is circular based and tested on its constraints and observations. As long as observation can break theory and move the area, there is no static circularity to get caught up in.

    Philosophy, where the notion comes from, is not empirically cognizant, it is about making up conflicting just-so stories from the same basis. All can have their own opinion, which is nice but not empiric.

    And I think Carroll explicitly claims that we do know what we don’t know of the basis for the physics of everyday life.

    @Foster Boondoggle:

    Define “consciousness” testably. If not, why would it be a problem re physics (or magic)? Neuroscience seems to be concerned with awareness and other biological traits.

    Chalmers’ make-belief qualia and zombies has to prove themselves, and I don’t see how magic can ever do that.

  52. Richard M says:

    Jack: “embiggen” is perfectly cromulent. It has always been spelled that way, from its very first use:

  53. Richard M says:

    Also for Jack: “Equally obviously” seems correct to me, since the context calls for an adverb, not an adjective. Or it could be changed to “It is equally obvious that…”

  54. AI says:

    Description states what is, explanation states why it is that way. Being able to describe something amounts to knowing, being able to explain something amounts to understanding.

    To explain something you have to show how it follows from something else, something already known. An explanation always builds on some other knowledge. For example the structure of the periodic table of elements can be explained in terms of the Pauli exclusion principle (wave function anti-symmetric with respect to exchange) , but the principle itself cannot currently be explained in terms of anything more fundamental and is therefore not understood it is simply known.

    So the original statement that “the laws underlying the physics of everyday life are completely understood” is invalid. The correct version would be:

    Most aspects of everyday life can be explained in terms of the known laws of natural sciences.

    Most instead of all because there are crucial aspects that cannot be explained in terms of anything, the number of dimensions and their properties are one example. Natural sciences in place of physics because explanations of great many aspects of everyday life like evolution or love require more information then is contained in just the laws of physics.

  55. MarcS says:

    Richard M — Thank you for sharing that article. I am chastened to admit that I didn’t know half of that.

    AI — Your restatement of “the laws underlying the physics of everyday life are completely understood” with “Most aspects of everyday life can be explained in terms of the known laws of natural sciences” shows that you really don’t understand what Sean was saying in the first place. Try reading those posts again a little slower.

  56. Richard M says:

    I don’t know, AI. Google says:

    Perceive the intended meaning of (words, a language, or speaker): “he could usually make himself understood”.
    Perceive the significance, explanation, or cause of (something): “she didn’t really understand the situation”.
    comprehend – realize – see – apprehend – grasp – perceive”

    You seem to be insisting that only the second definition is correct.

  57. vmarko says:

    Hi Sean, :-)

    “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.”

    Ok, the difference between Euclidean and Lorentzian cases can be tricky, and implementation-dependent. I know some QG models where the Lorentzian version is defined by analytic continuation from the Eucliden case (i.e. “Wick-rotated”), and also other QG models where Lorentzian and Euclidean versions are defined quite differently and have little in common.

    I agree that a Lorentzian model could be made to work, given an appropriate definition of the path integral, but I think we are still far from a straightforward computation of the effective action. There is always a lot of handwaving involved before one can say that the classical solutions dominate the path integral.

    But I guess we’ve beaten this topic enough. ;-)

    Best, :-)

  58. Neil says:

    One will need an XXL t-shirt for that equation. Or real fine print.

  59. AI says:

    @MarkS: Your thinking that I am trying to restate, as opposed to correct, Sean’s statement shows that you really don’t understand what I wrote. Try reading those posts again a little slower.

    @Richard M: In this context it is indeed the second definition that applies. If you interpreted the statement according to the first definition it would have Sean arguing that physicists know what they mean by their own laws.

  60. Imperius says:

    Most impressive. I wonder, how far is physics from becoming a monastic discipline, wherein monks study in isolation from mundane society for many years to understand the arcane truths of theoretical physics as discovered by the great minds of previous centuries, and the rest of their lives passing on this received wisdom to the next generation? Is there any future in fundamental physics as an experimental science? Is this the beginning of the new scientistic religion?

  61. Richard M says:

    No AI, it means Sean is saying that physicists understand what the *Universe’s* laws are (up to the limit where the weird stuff comes in, hence the “everyday” qualfication).

    Neil, I like the idea of getting this on a t-shirt.

    Imperius, I have no idea why this would make things any different from the way they are now.

  62. Gizelle Janine says:

    What a great post, Sean. I enjoyed this one in a serious way.

    Richard: I thought a tattoo on my behind would be more sufficient. I was told by the significant other that it might be a bit too hard to remember written on my own butt.

  63. AI says:

    No Richard, the original statement (“the laws underlying the physics of everyday life are completely understood”) uses the second definition of the term “understand” from your dictionary. The first definition – “to perceive the intended meaning of” something – in the case of the laws of physics means knowing that “a” in “F = m a” stands for acceleration and that it means the change of velocity with time and so on. Clearly not the intended meaning. If you still don’t see it it’s your loss.

  64. Ian Durham says:

    Tevong – that’s not the point. This is the point.

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  66. Richard M says:

    AI, your argument is getting tiresome, so this is the last I will post on the subject. You are taking a very reductionist approach to interpreting the verb, by claiming that the first sense of “understood” means simply that the meaning of each of the symbols in an equation is known. That’s absurd.

    If you ask a physicist whether our understanding of gravity changed during Newton’s time, and again with Einstein, I do not think you will get the answer you are hoping for. And the answer they give you will not be because we now know the meanings of symbols we didn’t know the meaning of before (as if the equations had been written out long before Newton but we didn’t know how to interpret them). It will be because we have grasped certain fundamental facts about nature.

  67. Richard M says:

    Gizelle Janine: Sadly, I guess the world will never see the tattooed rendition.

  68. Gizelle Janine says:

    Richard: I hope you’re right. I’d hate to see the therapist bills I’d be responsible for…

  69. Toby says:

    Hi Sean,

    I’m interested in why you don’t think that even just classical mechanics (including classical electrodynamics) isn’t enough to describe the world of everyday experience? I grasp your point about a table really being empty space with a smattering of atoms that relies on a quantum mechanical explanation–but it seems to me as though the table’s really being empty space is not really everyday experience (as I recall, it was rather a surprise to turn-of-the-20th-century physicists to find that tables are mostly empty space).


  70. Sean Carroll says:

    Classical mechanics can’t explain many important things, like chemistry.

  71. Steve says:

    Imperius: I think you have a point, and I think we’re not too far from having further advances in many fields depend on medical advances in delaying senescence. Of course, most fields have more severe problems than that; but physics has avoided other problem areas well enough that hours-to-mastery vs. productive-hours-remaining is a standout bottleneck.

  72. Robert Allan says:

    You have Empiricle and theoretical Scientists working on the understanding of “The Physics of Everyday Experience”. I believe that mathematics is a beautiful language and can explain a multitude of physical processes.But to imply that mathematics can explain everything is not a valid statement. Mathematics requires information and information is infinite.

  73. Toby says:

    Good point. Embarrassed that it didn’t occur to me, actually. I suppose explaining why things are different colours, too.

  74. mk says:

    “every equation in the world can be written U=0″

    Yes, obviously, but not every true proposition about the world is an equation. Some are inequalities and some are logical forms such as conjunctions, disjunctions, and material implications, for instance.

  75. mk says:

    Also, the laws underlying the physics of everyday life are not nearly enough to understand all of everyday life; those laws have numerous complex implications that aren’t understood, and aren’t even theoretically understandable from the laws alone because the implications are contingent on historical events … the entire history of the Earth, in some cases. An obvious example is that there is much we don’t understand about physiological processes, especially of the brain … how does spider cognition work, let alone human cognition? What’s the difference between the brains of a smart person, a stupid person, a person in a coma? What’s the difference between the brain of someone who knows the stated law and someone who doesn’t? How is the knowledge stored and how is it made available to behavior? Merely being familiar with the law is not nearly enough to answer these questions.

    And the attribute of “understanding” is not a simple one. Properly understood (heh), understanding is about *competence*. That’s why we determine whether students understand something by *testing* them. One might be familiar with the law but have no idea how to apply it … that’s a low level of understanding. Some can apply it only in limited circumstances. Consider understanding a computer language, or understanding how to program … there is a wide range of varying competence.

    I could go on and on about the naive reductionism that seems implied here. I’m a physicalist, but I recognize that, while everything is a manifestation of physical law, not all concepts reduce to the physical. You cannot derive the rules of chess from the laws of physics , let alone how to play well.

  76. mk says:

    ” 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.”

    Oops, I didn’t read that. Well, call me tiresome but that’s what your title *implies*, whether you mean it to or not … making it *false*. “The World of Everyday Experience, In One Equation” — this is just wrong; the world of everyday experience is not in that equation and is not entailed by that equation; that the equation is accurate and that the world of everyday experience is *consistent* with it is a different matter entirely. But in fact the world of everyday experience is largely determined by historical facts … such as the K-T event that allowed mammals to occupy niches formerly held by other organisms that were extinguished … our everyday experience would be very different otherwise, if it’s even meaningful to talk about “us” in such a counterfactual. Or consider the everyday experience of humans 50,000 years ago … very different from our own. So your statement about everyday experience is only true in a very narrow sense … through the parochial view of a physicist.

  77. mk says:

    I think it would be a lot better to say that the laws underlying the physics of everyday life are completely *known*. That would avoid the suggestion that all of the *implications* of the laws are also known, as well as why the laws are what they are.

  78. Daniel says:

    This equation is not an argument against God. The equation simply says that anything is possible and that people will interpret QM as they please.

  79. mk says:

    “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.”

    Actually there’s a great deal of evidence to the contrary, as you would know if you studied neuroscience. There is overwhelming evidence that the entire content of consciousness maps to brain processes — the mind is what the brain does.

    Talk about David Chalmers and “the hard problem” is really embarrassing in this day and age, like talking about vitalism and suggesting that explaining “life” is some sort of especially hard problem. No competent philosopher of mind takes Chalmers’ zombie arguments and his notions of panprotopsychism seriously anymore.

  80. Marcel van Velzen says:

    Hello Sean,

    Great formula and nice to look at.

    The only thing you seem to ignore (and everyone who is responding) or at least don’t emphasize, is that it only gives you probabilities of things happening, so, for example, it can’t even tell you the future. Stronger even, it says that it is impossible to predict the future! It’s the same as saying that you have a beautiful theory of a person randomly throwing a dice because you know that it has a 1/6 probability for 1, 1/6 probability for 2 etc. This is exactly the same thing your formula is doing. Feynman, being the brilliant and honest physicist he was, clearly saw this and said “Has physics has given up? Yes, physics has given up!”. Also Einstein saw it, couldn’t stand it and even refused to except it. So although “it’s one of the proudest intellectual accomplishments we human beings can boast of” is always inherently very limited.

  81. mk says:

    “This equation is not an argument against God.”

    The argument against God is a simple application of Ockham’s Razor … there is nothing that God is necessary to explain (and Goddidit isn’t really an explanation of anything).

    “The equation simply says that anything is possible ”

    No, it doesn’t say anything like that.

  82. mk says:

    “it can’t even tell you the future”

    It constrains the future.

    “It’s the same as saying that you have a beautiful theory of a person randomly throwing a dice because you know that it has a 1/6 probability for 1, 1/6 probability for 2 etc. ”

    That’s very useful information.

  83. Daniel says:

    The equation doesn’t constrain the future anywhere close to what we mean by “everyday experience”. Let’s say someone walk water. It’s in the equation.

  84. MP says:

    I think most scientifically literate people would agree with you, Sean. One might consider though that it is not very useful to summarize the current knowledge by a single equation such as the one above. And this is especially the case when presenting it to lay people, since it adds not one iota to their understanding: it’s just hieroglyphs to them.

    Furthermore, since it is impossible to derive most of current day phenomena from that single equation alone (in the sense of the chess analogy), it might be/will probably be seriously misleading to the vast majority of lay people — at least without serious qualifications –, as they are not knowledgeable enough to capture the subtilities and you might easily be misinterpreted as implying that one is able to derive everything from such equation. They will most probably not be able to make the distinction.

    It might be better to just say things in simple words: we know the basic constituents of matter and of the laws that determine their behavior. After many years of work by many many people, we have come to think that they provide a satisfactory explanation (often spectacularly so!) of everyday phenomena. But physics (and science in general) is most successful in dealing with simple systems and in Nature complex systems abound. These are hard to analyse and to predict, in the end to understand. Even so, we cannot identify any phenomena, no matter how complex, which we can recognize as being in blatant contradiction with these laws. In some cases, this may be just because we haven’t a clue about the mechanisms involved — such as in the case of consciousness.

  85. mk says:

    “The equation doesn’t constrain the future anywhere close to what we mean by “everyday experience”.”

    I didn’t say it did. (Actually, I don’t think that statement is coherent.)

    “Let’s say someone walk water. It’s in the equation.”

    Try reading the article, especially the bit about being tiresome.

  86. Daniel says:

    You’re tiresome.. I think QM is a weak argument against God and now you want me to shut up. That’s normal.

  87. G says:

    Any chance of getting a nomenclature section on this for the more armchair variety of us who don’t necessarily know what all of those variables are? Also, where are your differentials for those integrals?

  88. OMF says:

    Question: Does it have to be One?

    I know Physicists do like unification laws, but sometimes individual laws are beautiful in their own right. So, my question is: Can the laws of physics be written as a series of individual equations dealing with specific forces in a way that is equivalent to the unified law, or does theoretical physics discovery operate by Highlander rules(“There can be only one”)?

  89. mk says:

    “You’re tiresome.. ”

    Nice personal attack.

    “I think QM is a weak argument against God”

    Strawman … no one proposed it as such.

    “and now you want me to shut up.”

    I didn’t say or imply any such thing. Funny though that, despite my never having expressed anything like that, you ceased. I actually would be interested in your explaining what “Let’s say someone walk water. It’s in the equation.” was supposed to mean — it’s rather incoherent on several levels.

    “That’s normal.”

    For what?

  90. mk says:

    Ah, I think I understand … if someone walks on water, that is consistent with the equation. Well, it depends on the microdetails. As Sean said, ” 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”. The equation simply isn’t about things at the level of walking on water … which goes to my complaint that the title is false, more like a provocative newspaper headline that misrepresents the content of the article than like physics.

  91. vmarko says:


    “Any chance of getting a nomenclature section on this for the more armchair variety of us who don’t necessarily know what all of those variables are? Also, where are your differentials for those integrals?”

    The differentials for the path integral (the first one) are inside the [D…] terms, which represent the path integral measure. The differential for the spacetime integral (the second one) is written explicitly, d^4x.

    As for the rest (going from left to right): W is the state-sum amplitude, g is the determinant of the metric tensor, m_p is the Planck mass, R is the curvature scalar, F^{a\mu\nu} are the field strengths for the gauge potentials A, \psi^i are the Dirac bispinors, D_{\mu} is the covariant derivative, \gamma^{\mu} are the Dirac matrices, \Phi is the Higgs doublet of scalar fields, V_{ij} are the Yukawa coupling constants for fermions, and V(\Phi) is the symmetry-breaking potential for the Higgs. The boundary condition for the path integral features the generic momentum variable k and the cutoff scale \Lambda. As previously explained, “h.c.” stands for “Hermitean conjugate” of the Yukawa coupling term. The letter “i” which is not an index is the imaginary unit (square root of -1).

    You can find definitions (and more) for most of this stuff on Wikipedia. :-)

    Speaking of the “h.c.” term, it would be more correct to put the kinetic term for the fermions inside the parentheses, since it also needs the h.c. contribution if you want to get the fremion-gravity coupling correct. ;-)

    HTH, :-)

  92. vmarko says:

    Oh, and I forgot — repeated indices are to be summed over (the Einstein convention is assumed).


  93. MKS says:

    that equation is sheer poetry

    humanity akhbar!

  94. BG says:

    I think you have forgotten the second law of thermodynamics…

  95. doc c says:

    When naturalists fully comprehend the beautiful and poignant irony of that post, it will be a huge step for the cause. “The heart has its reasons that reason can never know”. Google the full “pensee”, and you will see why Naturalism has a huge gap in helping many people to navigate the universe that presents itself to us.

  96. G says:


    Thanks, I’ll be sure to look that stuff up on Wikipedia. Also, thanks for the help on those integrals, the change between upper and lower case was throwing me there.

  97. Gizelle Janine says:

    Yeah. This is one sexy equation alright. That hermitian conjugate is staring at me from across the room…

  98. MKS says:

    doc c,

    science is a way of knowing where we discover/uncover facts. art is a way of knowing where we create meaning. religion is an art.

    Einstein grokked with fullness the role of religion & art

    (plus, not every BS — belief system — covers and accounts for everything equally well)

    variety is the life of spice ;3

  99. MKS says:


    totally would love to have that equation on a t-shirt :3 I can hear Feynman banging his drums…

  100. doc c says:

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

  101. MKS says:

    doc c,

    some programs you might be interested in lissening to (esp the “Genius born of anguish” episode):

  102. Doc C says:

    Thank you. However, I had in mind the kind of wonder from which total commitment springs.

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  104. Marcel van Velzen says:

    I agree with vmarco in that there should be an extra h.c. or the parentheses should include both matter terms so h.c. can pertain to both. The way it is written now, I think, is otherwise actually wrong. See John Ellis’s t-shirt

  105. Marcel van Velzen says:

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

  106. Gizelle Janine says:

    Yeah, I shouldn’t of said anything… :/

  107. MKS says:

    Doc C,

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

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

  108. Marcel van Velzen says:

    Sorry, maybe there shouldn’t be a second h.c. as the term is already real, but what about the bar on the second matter term? See:

  109. vmarko says:


    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, :-)

  110. 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.

  111. Marcel van Velzen says:

    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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  113. Rezso says:

    “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!

  114. vmarko says:


    “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, :-)

  115. Rezso says:


    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.

  116. vmarko says:

    @ 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, :-)

  117. Gizelle Janine says:

    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.

  118. Marcel van Velzen says:

    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 :-)