Distinguishing Copenhagen and Many Worlds via experiment

Peter McCluskey pointed me to a nice explanation by Brian Greene of an experiment that could theoretically distinguish the Copenhagen and Many Worlds interpretations of quantum mechanics. This is from The Hidden Reality, ch. 8, endnote 12:

Here is a concrete in-principle experiment for distinguishing the Copenhagen and Many Worlds approaches. An electron, like all other elementary particles, has a property known as spin. Somewhat as a top can spin about an axis, an electron can too, with one significant difference being that the rate of this spin—regardless of the direction of the axis—is always the same. It is an intrinsic property of the electron, like its mass or its electrical charge. The only variable is whether the spin is clockwise or counterclockwise about a given axis. If it is counterclockwise, we say the electron’s spin about that axis is up; if it is clockwise, we say the electron’s spin is down. Because of quantum mechanical uncertainty, if the electron’s spin about a given axis is definite—say, with 100 percent certainty its spin is up about the z-axis—then its spin about the x- or y-axis is uncertain: about the x-axis the spin would be 50 percent up and 50 percent down; and similarly for the y-axis.

Imagine, then, starting with an electron whose spin about the z-axis is 100 percent up and then measuring its spin about the x-axis. According to the Copenhagen approach, if you find spin-down, that means the probability wave for the electron’s spin has collapsed: the spin-up possibility has been erased from reality, leaving the sole spike at spin-down. In the Many Worlds approach, by contrast, both the spin-up and spin-down outcomes occur, so, in particular, the spin-up possibility survives fully intact.

To adjudicate between these two pictures, imagine the following. After you measure the electron’s spin about the x-axis, have someone fully reverse the physical evolution. (The fundamental equations of physics, including that of Schrödinger, are time-reversal invariant, which means, in particular, that, at least in principle, any evolution can be undone. See The Fabric of the Cosmos for an in-depth discussion of this point.) Such reversal would be applied to everything: the electron, the equipment, and anything else that’s part of the experiment. Now, if the Many Worlds approach is correct, a subsequent measurement of the electron’s spin about the z-axis should yield, with 100 percent certainty, the value with which we began: spin-up. However, if the Copenhagen approach is correct (by which I mean a mathematically coherent version of it, such as the Ghirardi-Rimini-Weber formulation), we would find a different answer. Copenhagen says that upon measurement of the electron’s spin about the x-axis, in which we found spin-down, the spin-up possibility was annihilated. It was wiped off reality’s ledger. And so, upon reversing the measurement we don’t get back to our starting point because we’ve permanently lost part of the probability wave. Upon subsequent measurement of the electron’s spin about the z-axis, then, there is not 100 percent certainty that we will get the same answer we started with. Instead, it turns out that there’s a 50 percent chance that we will and a 50 percent chance that we won’t. If you were to undertake this experiment repeatedly, and if the Copenhagen approach is correct, on average, half the time you would not recover the same answer you initially did for the electron’s spin about the z-axis. The challenge, of course, is in carrying out the full reversal of a physical evolution. But, in principle, this is an experiment that would provide insight into which of the two theories is correct.

I’m not a physicist, and I don’t know whether this account is correct. Does anyone dispute it?

Further references on the subject are at Wikipedia.

In any case, such an experiment seems far beyond our reach. But since I’m Bayesian rather than Popperian, I put substantially more probability mass on MWI than Copenhagen even in the absence of definitive experiment. 😉

Comments

  1. Daniel says

    I am a physics student who has an upcoming paper on this topic, and this account is correct to the best of my knowledge.

  2. Rolf Andreassen says

    I see one flaw, possibly repairable: The assumption of time-invariance. It is true that the Schrodinger equation is time-symmetric. The full laws of physics, however, are not time-symmetric. They have, instead, CPT symmetry: That is, they are invariant under reversal of time, parity, and charge. Since we have measured CP violation – that is, the symmetry is slightly broken under reversal of charge and parity – it follows that there must be a slight time-asymmetry as well.

    Two possible repairs: One, we are working with electrons and spin, which is an area of physics that doesn’t have (known) CP violation, so it is presumably time-symmetric as well. (Although note that the experiment calls for reversing the whole experimental setup including the lab, so you’re going to sweep up a lot of quarks as well, which is where CP violation comes in – but perhaps this can be avoided with more careful design.) Two, replace the T reversal (admittedly, already quite difficult to do) with a full CPT reversal, and restore the symmetry.

    NB, I don’t think anyone has any idea of how to do a CPT reversal in practice. Or T reversal.

  3. says

    As far as I can tell, this is not really a threat to Copenhagen.

    The theory that such an experiment refutes is a plain, naive, physical collapse quantum theory (GRW is not plain collapse and is empirically refutable in and of itself as it proposes new physics. I think this experiment too would refute GRW — I’m not sure). I don’t think anyone who’s thought about these things, for even a short while, really believes in naive collapse.

    This experiment doesn’t refute the more sophisticated Copenhagen interpretation: where the quantum theory is simply a calculus of experiences (this is sometimes called neo-Copenhagenism, but it seems to be the position held by Bohr).

    The Copenhagenist says that whenever you come into contact with a quantum system (that is, you’re gaining knowledge about a quantum system), you use the Born rule, with its attendant collapse postulate; otherwise, you use the Schrödinger equation. So in the above experiment, you’d be totally fine using the Schrödinger equation until *you* look at the measurement instrument. But now if you have to reverse the whole interaction, then you’d have to include the human as well. And if you do *that* reversal, including the human, then no one remembers what anyone saw — and therefore there was no collapse because no one acquired any information about the quantum system.

  4. Marko says

    This is essentially correct. The main problem with the experiment is not mentioned however: It is not possible even in principle to perform it and also record the results. The reason for this is that performing a full time reversal of the experiment together with the apparatus entails erasing all records of any measurements made. Thus one cannot possibly tell whether the measurement of the z-spin has changed.

    • says

      No initial measurement is made; the electron is prepared with spin up, but this is not the same as measuring its state. So, there’s no measurement information to be wiped out by the time-reversal; only preparation information – and the time reversal goes only to a point just after the preparation is complete.

  5. AlphaCeph says

    “(by which I mean a mathematically coherent version of it, such as the Ghirardi-Rimini-Weber formulation)”

    – it is well known and accepted that GRW is experimentally distinguishable from many worlds. However, GRW isn’t what most people mean when they say “copenhagen interpretation”.

  6. AlphaCeph says

    … which is because the Copenhagen Interpretation is kind of nonsensical, but it is a very convenient and useful piece of nonsense for actually getting things done. But I digress.

    Anyway, this isn’t really news.

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