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.
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, 🙂
Marko
P.S. I hope you didn’t give up on reading the comments… 😉
The equation is very comforting, because it doesn’t care.
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.
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 …
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!
“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.
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.
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.
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:
http://books.google.com/books?id=dAAqly_8rQoC&lpg=PA64&ots=kz_1bRgM2o&dq=weak%20field%20gravity%20path%20integral&pg=PA64#v=onepage&q=weak%20field%20gravity%20path%20integral&f=false
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:
http://arxiv.org/pdf/gr-qc/9405057.pdf
Perhaps I should write the equation explicitly as an integral over small fluctuations h, rather than the whole metric g.
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 🙂
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.
Matt
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, 🙂
Marko
I don’t know Sean, if you have read my post about U=0,
http://thespectrumofriemannium.wordpress.com/2012/04/25/log004-feynmanity-and-unfeynmanity/
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.
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.
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.
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:
http://www.cbc.ca/ideas/masseys/images/All-Known-Physics-large.jpg
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?
Cheers.
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?)
That’s neat! But what does “h.c.” mean at the end of the “matter” bit?
Jimbo– It means “hermitian conjugate,” which is like complex conjugation for matrices. Just so the action is a real number.
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?
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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