What Happens Inside the Quantum Wave Function?

Many things can “happen” inside a quantum wave function, of course, including everything that actually does happen — formation of galaxies, origin of life, Lady Gaga concerts, you name it. But given a certain quantum wave function, what actual is happening inside it?

A surprisingly hard problem! Basically because, unlike in classical mechanics, in quantum mechanics the wave function describes superpositions of different possible measurement outcomes. And you can easily cook up situations where a single wave function can be written in many different ways as superpositions of different things. Indeed, it’s inevitable; a humble quantum spin can be written as a superposition of “spinning clockwise” or “spinning counterclockwise” with respect to the z-axis, but it can equally well be written as a superposition of similar behavior with respect to the z-axis, or indeed any axis at all. Which one is “really happening”?

Answer: none of them is “really happening” as opposed to any of the others. The possible measurement outcomes (in this case, spinning clockwise or counterclockwise with respect to some chosen axis) only become “real” when you actually measure the thing. Put more objectively: when the quantum system interacts with a large number of degrees of freedom, becomes entangled with them, and decoherence occurs. But the perfectly general and rigorous picture of all that process is still not completely developed.

So to get some intuition, let’s start with the simplest possible version of the problem: what happens inside a wave function (describing “system” but also “measurement device” and really, the whole universe) that is completely stationary? I.e., what dynamically processes are occurring while the wave function isn’t changing at all?

You’re first guess here — nothing at all “happens” inside a wave function that doesn’t evolve with time — is completely correct. That’s what I explain in the video above, of a talk I gave at the Philosophy of Cosmology workshop in Tenerife. The talk is based on my recent paper with Kim Boddy and Jason Pollack.

Surprisingly, this claim — “nothing is happening if the quantum state isn’t changing with time” — manages to be controversial! People have this idea that a time-independent quantum state has a rich inner life, with civilizations rising and falling within even though the state is literally exactly the same at every moment in time. I’m not precisely sure why. It would be more understandable if that belief got you something good, like an answer to some pressing cosmological problem. But it’s the opposite — believing that all sorts of things are happening inside a time-independent state creates cosmological problems, in particular the Boltzmann Brain problem, where conscious observers keep popping into existence in empty space. So we’re in the funny situation where believing the correct thing — that nothing is happening when the quantum state isn’t changing — solves a problem, and yet some people prefer to believe the incorrect thing, even though that creates problems for them.

Quantum mechanics is a funny thing.

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60 Responses to What Happens Inside the Quantum Wave Function?

  1. Matt McIrvin says:

    Perhaps because if you assume nothing is happening inside a time-independent wave function, it’s so easy to jump to the paradoxical conclusion that nothing is happening inside a time-dependent wave function either. After all, it’s nothing but a superposition of a bunch of energy eigenstates, and they don’t do anything but spin their phases around.

    So, clearly, nothing worth mentioning ever happens at all!

  2. jacob stene-jonassen says:

    Just curious, does anything interesting happen to the metric or scale when the universe is essentially empty? Penrose seem to think so. He also hypothezises something might happen when the temperature is nearing absolute zero. Any opinions?

  3. Sean Carroll says:

    Matt– That’s a possible perspective, but only if you convince yourself that “spinning phases around” is essentially uninteresting. I think it includes quite a bit of going-on! Of course there is work to be done picking out how semiclassical worlds arise from eigenstates with changing relative phases.

    Jacob– The universe can certainly be “expanding” in the traditional sense even when it’s nearly empty. But in that case it’s probably better to use some more robust way of characterizing what the metric is doing, since there’s no matter around with respect to which to do measurements.

  4. Blake Horton says:

    Firstly I’d like to mention that I consumed you’re greatcourses.com lecture on the Higgs and was truly blown away. The only other lecture that has struck me so hard was Schumacher’s lecture on gravity.

    My question is this: so many of our theories and understandings (particularly those involving time) seem to be explainable through the use of thought experiments. Often times these thought experiments hash out the finer details using a symmetric or transitive approach to consider things from an improbable or impossible perspective. I often wonder if it is necessarily constructive to consider something such as “what is happening given an unchanging quantum state”. Are there times when a mathematical representation of a system might fail to predict the actual nature of a system? Are there systems in nature that defy their mathematical representations when we apply the properties of equality to rearrange their variables?

  5. Larry says:


    I sure hope there’s no mention of MWI in this talk. You might as well talk about angels.

  6. Bob Zannelli says:

    I have struggled to understand why Sean ( and Colleagues) are making the argument, as I understand it, that there are no quantum fluctuations in a De Sitter space or more accurately a near De Sitter space. ( the Inflaton potential is slow rolling) Sean says there is no matter to create environmental degrees of freedom , hence the state is unitary. We can agree that unitary evolution doesn’t involve measurement fluctuations of course , but given that the Inflaton potential is slow rolling how can there be no measurement process? There are Horizons and Gibbons Hawking radiation during inflation, how is this possibly unitary? Sean is a very smart guy, so I may just not be getting the argument being made, but I don’t see it. Also I found your Teaching Company course on the Higgs awesome as have been every course you have done for the Teaching Company.

  7. trivialknot says:

    I haven’t watched the talk yet, but it occurs to me that you may be clashing with certain popular explanations of quantum field theory. It’s often said that even in a vacuum, many virtual particles are constantly jumping into and out of existence.

    When I actually took a QFT class, I was disappointed to learn that what they really mean is that the ground state of a vacuum is not the same as the state with no particles in it. The ground state is nonetheless stationary.

  8. Bob Zannelli says:

    rivialknot says:
    March 11, 2015 at 10:43 am
    I haven’t watched the talk yet, but it occurs to me that you may be clashing with certain popular explanations of quantum field theory. It’s often said that even in a vacuum, many virtual particles are constantly jumping into and out of existence.

    When I actually took a QFT class, I was disappointed to learn that what they really mean is that the ground state of a vacuum is not the same as the state with no particles in it. The ground state is nonetheless stationary.


    But if there is an horizon the quantum state of the vacuum IS being measured. That’s the basis of Davies Unruh Hawking Radiation.

  9. Sean Carroll says:

    Bob– This isn’t directly tied to inflation. We’re talking about true de Sitter space, with no rolling inflaton. And the horizon doesn’t “measure” the quantum state of the vacuum; it’s stationary itself.

  10. Jim Manning says:

    Would you say “consciously” measure the thing? I have a running debate with one of your fans and the outcome depends on your answer.

  11. trivialknot says:

    I see that “quantum fluctuations” were addressed at length in the talk.

    I think it’s really neat to leverage the preferred basis problem of Everettian Quantum Mechanics into the preferred basis *solution* to Boltzmann Brains. Good talk.

  12. Tom Murphy says:

    It seems to me that time is a correlate of change. If there is no change, there is no time, and vice versa. This discussion refers to change within the wave function as well as to time exogenous to the wave function. Given that the wave function enfolds the entire universe, the latter notion seems self-contradictory.

  13. Sean Carroll says:

    Jim– No. Consciousness has nothing to do with how quantum mechanics works.

  14. Richard says:

    Does MWI have anything to do with empirical science? Just curious. How about the multiverse?

  15. eigenman says:

    Sean love your work. Keep talking 🙂

    In case anyone wants a really down to Earth video of Sean just talking about anything then try this one:

  16. Ichigo says:

    Don’t we already know that T is not a symmetry, but that CPT is?

  17. David Park says:

    Sorry Sean but none of your videos play. However the one posted above by eigenman does play.

  18. eigenman says:

    David, Sean is using an HTML 5 player. All the latest browsers support this natively now. I posted a youtube embed which still uses Flash. Make sure you have the latest update to your browser.

  19. Michael Sommers says:

    Possible typo near end of first paragraph after video: one of the axes mentioned should probably be x or y.

    Feel free to delete this.

  20. Richard says:

    According to Boltzmann’s Brains, the videos are playing in another part of the multiverse on the new 12″ MacBook. The videos are also playing on this planet but in another parallel universe.

  21. Ben Bevan says:

    … stays inside the quantum wavefunction.

  22. I’ve been having issues with embedded Youtube videos a lot lately, this one included. When I press Play, it says, “An error occured, please try again later”, but trying later never helps. When I click the logo to watch the video directly on Youtube, it takes me to a URL at youtube-nocookie.com instead of youtube.com (in this case https://www.youtube-nocookie.com/watch?v=5TFy6Ben0Ho), and gives me a “404 Not Found”. When I manually remove the “-nocookie” from the URL, the video plays correctly.

    I’m using the latest version of Firefox, and my cookie settings are to accept them for session on most sites, and permanently on whitelisted sites (youtube.com is whitelisted). The issue has only started recently (perhaps since the latest Firefox upgrade).

  23. Jim Manning says:

    I should have watched some of your videos first. It was a trap! Thanks for responding Sean.

  24. Pingback: A Beginner’s Guide to Cosmological Speculation | Letters to Nature

  25. Luke Barnes says:

    I asked this at the conference, but I’m still not clear on the answer. Consider the distant future of our universe. Accelerating expansion has thinned out the matter, black holes have evaporated, and there is either one or zero particles in each Hubble radius / event horizon / whatever. If there are no particles, then your argument states that, being a complete vacuum with only vacuum energy, no fluctuations happen and so no Boltzmann brains arise.

    Question: would Boltzmann brains still arise in those very rare regions of the universe which happen to still have a stray particle? Or two stray particles? After all, the photon remnants of our universe end up somewhere, right?