Quantum Mechanics Explained

Yesterday was Erwin Schrödinger’s birthday, as those of you who actually visit the Google home page would have noticed.


This auspicious event nudged me (a day late, admittedly) to do something I’ve been contemplating for a while now — explain the basic ideas of quantum mechanics the best way I know how, at an accessible level (no equations) but without any frustrating length limitations. Sure, you can do pretty well in just five words, but sometimes you need to be a little more expansive.

Fortunately, very little work was required, since I’ve already done it! This is what happens when you write popular books on physics. Depending on the subject, one of the early chapters is guaranteed to be an overview of either quantum mechanics or general relativity. When I wrote From Eternity to Here, I fooled everybody with an unprecedented step: I put my intro to QM late in the book, in Chapter 11. (The intro to GR was, admittedly, Chapter 5.)

I tried hard in that chapter to do justice to the important ideas of quantum mechanics — superpositions, entanglement, measurement, decoherence, probabilities — without getting bogged down in technical details. I glossed over the fact that amplitudes are complex numbers, although I certainly emphasized that they can be negative as well as positive. It laid some groundwork for the rest of the book, but that chapter itself didn’t really talk about (or rely on previous discussion of) entropy, cosmology, or the arrow of time.

So I’ve simply made it into its own web page, here freely available to all:

It’s about 13,000 words — there’s a lot to explain. But now I have somewhere to point to if someone wants to know the basics.

Of course, physicists famously don’t quite agree about what quantum mechanics actually says. Naturally, I’m giving the version I think is right. At the end I try to distinguish what everyone agrees on from what is still conjectural, but this is certainly not the place to go for an overview of all the different interpretations. It’s just the particular view of one cheerful psi-ontologist.

  1. If one was explaining special relativity one would mention the speed of light c as the key constant in the theory and that objects moving at considerably less than the speed of light can be treated classically. Yet many of the quick or not so quick introductions and explanations of quantum mechanics fail to mention Planck’s constant h, and that quantum mechanics comes into play when the action (units of energy multiplied by time) is of order h. I don’t expect the whole Feynman path integral equation and the classical limit that can easily be demonstrated from it, but I think Planck’s constant should be mentioned. Also the idea that classically we can keep back reactions of measurements as small as we want but in the quantum world there is a minimum action given by h_bar.

  2. I think it was you who said, “If someone says they [completely] understand quantum mechanics, they don’t.”

    Yet, this article brings me a long way towards having the concept of what might be going on.

    May we live in interesting times.

  3. Since I am an experimentalist, I am interested in experimental tests of the interpretations of quantum mechanics. I think we will soon be able to, or are already able to, experimentally rule out some of the interpretations. Dik Bouwmeester has been pushing towards experimental tests of objective collapse theories and is reporting his progress in arXiv. Objective reduction of the wavefunction would provide a solution without the ontological baggage of Many-Worlds or Copenhagen.
    The possibility of retrocausal information transfer is what I myself am currently focused on. Prof. John Cramer, who developed the Transactional Interpretation, is building a retrocausal signalling system to test his ideas. He believes he has found a loophole which allows retrocausal information transfer. Read his work and see if you agree. On that note, there is already published physiological evidence from many independent experiments of physiological retrocausal information transfer at the 6.9 sigma level which definitely looks pretty convincing (I was skeptical originally so I personally replicated one such experiment [published after the time frame of the meta-analysis, so not included in the 6.9, but showing a very strong signal] with some modifications to further rule out mundane explanations. My data taken together appear to show a retrocausal effect at the 5.6 sigma level; it’s not yet published, though, so take my own report with a big grain of salt. But now I’m convinced there’s no significant file drawer effect. Now what if somebody hooks up such a system to the stock market… hmm…?). It would seem to me that any sort of retrocausal information transfer falsifies the Many-Worlds Interpretation. But in these experiments, there is still the issue of the random number generator used to select stimuli being entangled with the rest of the system.

  4. Thank you for demystifying the Many Worlds interpretation (yes, that is a terrible name!) and explaining the relationship to decoherence. One question: in a couple of places you draw an analogy between the irreversibility of decoherence and the irreversibility of thermodynamics. Is it worth taking seriously the idea that they are not merely analogous, but actually the same thing? i.e. that a quantum system decoheres precisely to the extent that it becomes entangled with a thermodynamically irreversible system?

    On a completely separate note, regarding the low entropy state of the early universe: might negative temperatures provide a clue? Imagine a very young universe that would have been extremely hot, potentially “saturated” with entropy such that additional energy in fact lowers the entropy by filling the high energy states. If such a universe suddenly inflates, with space expanding faster than thermal equilibrium could be achieved, would the result be a state of low entropy?

  5. This sounds interesting. I’ll check it out. For now, Mark: action is also momentum multiplied by distance. See In praise of weakness and think of the photon as something like a seismic wave in space. IMHO you can envisage that a seismic wave moving from A to B doesn’t just shake the ground on some thin narrow line between those two points. It displaces the ground back and forth by some distance, even away from the AB line. It therefore takes “many paths”.

  6. Funny: My kitten, Shrodinger had his vet visit on August 12th. (He’d like to mention to this comment spread he’s very much alive and needs boosters.) He was also very sleepy when seeing himself on the homepage of google. At least the vet gave him a heat bath. 😀

  7. I think it is more intuitive that the wave function never actually collapses; you just end up with an amplitude probability so ridiculously high that it is classically considered 100%.

    I don’t understand the conceptual question “why are conscious observers identified with discrete branches of the wave function, rather than superpositions?”. I can’t imagine how we could be discrete branches and NOT be superpositions. My answer to that question would be that someone is having trouble understanding the concept. Though that someone could be me.

    I think it’s like you’ve said before, the classical world doesn’t really exist. It is simply a very good approximation of how we experience reality at our level of existence; given all the details you go over in this part of your book. Despite the fact that it 99.9999% describes reality, it is never 100% effective. However small that difference is, it still makes a massive difference when you are (trying to) calculating the universal (principle maybe? initial?) wave function and are attempting to fully describe what is happening in nature.

  8. Stephen you wrote:
    “It would seem to me that any sort of retrocausal information transfer falsifies the Many-Worlds”.

    The Two State Vector Formalism is retrocausal. Vaidman, who developed this with Aharonov, wrote:

    “The TSVF is compatible with almost all interpretations of quantum mechanics but it fits particularly well the many-worlds interpretation.” http://arxiv.org/abs/0706.1347

  9. Sean, thank you very much for writing this, and for making it freely available
    on your blog. Do you know of any similarly clear account at a higher mathematical level? I can diagonalize Hamiltonians just fine, but I don’t think I really grok what
    QM “means”. 🙁

  10. Jonathan– You might try David Albert’s Quantum Mechanics and Experience, if you like his writing style (many don’t, I do). If you know the basic math of QM, there’s a great book called Quantum Paradoxes by Aharonov and Rohrlich.

  11. A bit late, but I wonder if you can clarify the following:

    In particular, due to details in Miss Kitty’s initial condition and certain aspects of quantum feline dynamics, the final wave function assigns equal positive amplitudes to the sofa possibility and the table possibility. Now let’s consider the other intermediate step, that we see her stop by the food bowl. In that case, the final wave function assigns a negative amplitude to the table, and a positive one to the sofa…

    As I try to chase down the mystery, it keeps finding new places to hide. Currently hiding here as I see no explanation of why (how) the function assigns positive values in one case and a negative one in the other. What breaks the symmetry? Would the sofa get the negative if Kitty visited the objects in reverse order? It must be those details and aspects you refer to that determine the negative. Suddenly they become too important to gloss over…

  12. Jamie– At the level of this explanation, the actual values (including positive and negative signs) given to the amplitudes are simply assertions. In a real calculation, they would come from starting with some initial wave function, and evolving it according to the Schrodinger equation. Wave functions tend to oscillate in time between positive and negative, so it depends on the details of how the object evolves. (Note there is no “symmetry” to be broken; in one case the cat evolved by stopping at the scratching post, and in the other by stopping at the food bowl, so the two cases are different.)

  13. Oh, so you are saying that this is just an instructional example in which we assume the negative, but a case where the table becomes positive is also possible? But some real world cases do evolve just like the example, so the assumption is justified?

  14. It’s a simple exercise to prove that the expectation value of the momentum for a system described by a real wavefunction is zero. So, a cat on the move would have to be described by a wavefunction that takes on complex values (which you can’t get rid of by factoring out a phase factor). So, if the wavefunction of the cat takes on a value of r exp(i alpha) somewhere, it will take on some value s exp(i beta) with beta not equal to alpha somewhere else.

  15. A more complete, long, and extremely enlightening series of posts on QM insterpretation is found at the Less Wrong website. This is the link for the complete series, divided into parts. The main sequence starts at “Basic Quantum Mechanics”:

    This is the link for a smaller set of articles derived from the total set, but it includes the introductory ones too:

    I whish popular book writters like Sean would take a look at that series of articles. They contain some math but it’s very basic, and it presents what I think is BY FAR the best exposition of quantum mechanics I’ve ever came across (and at a perfectly understandable level by the layman; no small feat!)

    I whish a book would be published collecting all that material. Seans’ books are great, but so far I’ve never seen anything comming close to this series of articles.

    Do yourself a favor and read them.

  16. Fascinating stuff but quite incomprehensible – sorry, very late but just a thought : maybe the reason we do not seem to be able to unite the quantum and the macro world is because they are not the same – in the sense of the multiverse, maybe the world we perceive is not one but a conglomerate of two or more universes consisting of a large “space-time” universe which is inter-dispersed by tiny pockets of a “quantum” universe – the first is governed by long ranging forces and the latter by short raging ones, only confined to the small area around fermions – they do not mix but interact via the electroweak interaction which is felt by both. Disturbances in the spacetime universe appear as waves, disturbances in the quantum world appear as particles. The waves move freely according to the wave function in spacetime until they interact with a quantum pocket which would account as a measurement resulting in wave collapse – as all our detectors consist of atoms we can only detect these as particles at a specific location but they get there as a wave .
    Therefore if the cat-wave interacts with the atoms of the bowl or post it collapses into a cat and has then the further options of sofa or table, which it can reach again as a new wave – if it does not interact with these it then has to interact with the sofa as the table seems out of bounds for the initial wave.

  17. Let me make this short and sweet. The parallel universes created in a quantum system is utter nonsense, BS. Just as when you approach speeds close to the speed of light Newtonian physics breaks down. When you get to a size smaller than whole atoms, the reality of discreet particles cease to exist. You simply have energy clouds. You do not have a situations of a near infinite numbers of merely probabilities. An electron is not a probability. A photon is not a probability. At that size they are also no longer discreet particles. They are energy clouds and they are sensitive to thought, which is also a form of energy. The differential energy between a human brain and a subatomic particle is so great that thoughts actually effect subatomic particles. Now let’s take on the double slit experiment. We all know if you observer individual electrons or photons being shot one at a time at the double slit, you get two lines on the photographic plates corresponding to the two slits. If you don’t observe it you get an interference pattern. So what happens if someone does the experiment and in the first instance the experimenter does not observe; but unknown to him a second experimenter has surreptitiously set up unseen observational equipment and is observing the individual particles being shot through the slits. The first experimenter would expect there to be an interference pattern, while the second experimenter would expect the classical result of two lines. So what would there be? It depends on which energy acting on the subatomic particles was stronger. There is still quantum entanglement because everything in the universe is connected. But electrons and photons are not “probabilities”, they are clouds of energy. The two goal posts are the speed of light, and things smaller than individual atoms. For both of these situations there are special rules, but the universe does not become irrational. For heaven’s sake there are new age people trying to manifest millions of dollars, while others are trying to manifest tables in front of their eyes because they think the universe is merely a human thought construction. Let’s get real people.