The series of Oxford lectures I am enjoying in my lunch hours is prompting a few blog ideas. The latest is the business of the collapse of the wavefunction. So much has been written about the measurement problem in quantum mechanics that I surely do not need to write a boring introduction to it all. So I will just assume you can jump in cold and use Wikipedia or whatever to warm up when needed.
By the way, the idea behind my little cartoon there is that making a measurement need not catastrophically collapse a system into a definite eigenstate as most textbooks routinely describe. This (non-total collapse) is depicted as the residual pale pink region which entertains states in phase space that still have finite probability amplitudes. We never really notice them subsequently because the amplitudes for these regions are too darn small to detect in any feasible future measurements. Every measurement has finite precision, so you cannot completely use an actual real messy brains and wheetbix and jelly experiments to form a pure state. Textbooks on QM are like this, they take so many liberties with the reality of an experimental situation that the theoreticians tend to lose touch with reality, especially when indulging in philosophy while calling it physics.
The issue is rife in many lectures I am watching, one is Simon Saunders’ talk on “The Case for Many Worlds“. He poses a sequence of questions for his audience:
- Why does the collapse of the state happen?
- When does it happen?
- To what state does the state collapse?
He presages this by polling his audience on whether they believe the proverbial Schrödinger’s Cat is exclusively either alive or dead before the observer looks inside the diabolical box with the vial of radioactively triggered nerve gas. Some half of the audience believe the Cat was either alive or dead (i.e., not in a superposition). He then asks what about if the box was not an isolated box but a broom cupboard? Not many people change their mind! But the point was that the cupboard is, surely, in no way or form now isolated from the external universe, and surely has enough perturbations to destroy any delicate entangled superposed states. But I guess some lovers of cats are hard to budge.
Then he asks, “well, what about if the experiment is being done up on a branch of a tree in a forest with no observer anywhere around?” (The clear unspoken implication is to think about the proverbial tree falling …). He cites a quantum information theoretic conference audience 80% of whom believed the Cat would then still not be in an exclusive XOR state, i.e., would still be in a superposition. Which is quite remarkable. Maybe they never heard of the phenomenon of environmental decoherence?
It’s at such times I wonder if Murray Gell-Mann has had an unhealthy influence on how physicists take their philosophy? In much of his popular style writing Gell-Mann has argued for environmental decoherence. The idea though is that there is no collapse, not ever. The universe remains mixed in a superposition of a giant cosmic wavefunctional state. Gell-Mann is not the sole culprit of course, but he’s the head honcho by fame if nothing else. And boy! You don’t want to go up head-to-head arguing against Gell-Mann! You’ll get your ears pulverised by pressure waves of unrelenting egg-headedness.
To be fair and balanced here’s a book cover that looks like it would be a juicy read if you really want to tangle with environmental decoherence as the explanation for classical physics appearances.
I just want to warn you, if you ever feel like you are in a superposition of states then there are some medications that can recover classical physics if you find it too nauseous.
You do not have to take wavefunctions literally. They are just computational devices. The mathematical tool used to model quantum mechanics is not the thing itself that we are trying to describe and model. The point is, the idea is, that whatever the universe is, it must be described by a wavefunction or some equivalent modelling that enjoys a superposition of classical states. That’s what makes the world quantum mechanical, there are classical-like states that get all tensored up in a superposition of some form, and whether you choose to describe this mathematically by a wavefunction, or by matrices, or by Dirac bra and ket vectors in a Hilbert space is largely immaterial.
Many Worlds theorists have a fairly similar outlook to the decoherence folks. Although at some root level their interpretations differ, or are even perhaps empirically incompatible in principle (I’m not sure about that?) I think both views have the germ of the idea that there really is no collapse of state space. In environmental decoherence a measurement merely entangles the system with more stuff, and so gazillions of new things are now entangled, and the whole lot only appears to behave more classically as a result. But there is still superposition, only so many of the coefficients in the linear superposition have shrunk to near zero the overall effect is classical-like collapse. Then of course Schrodinger evolution picks up after the measurement is done, and isolation can gradually be reestablished around some experiment, … and so on and so forth.
Here’s my penny take on this. I’ve become a firm proponent of ER=EPR. So I figure entanglement is as near to wormhole formation as you wanna get. You can take this literally or merely computationally convenient. For the time being I’m a literalist on it, which means I’ll change my mind if evidence mounts contrarily, but I think it is fruitful to take ER=EPR at more or less face value to see where it leads us.
ERrrr … who just collapsed me? You fiend!
I am also favouring something like gravitational collapse ideas. These seem to have a lot of promise, including (and this is a big selling point for me) the possibility of a link with ER=EPR. For one: if entanglement is established via ER bridges, then probably collapse of superposition can be effected by break-up of the wormholes. It seems a no-brainer to me. Technical issues aside. There might be some bugger of mathematical devilishness that renders this all nonsense. But I’m in like with the ideas and the connections.
Ergo I do not subscribe to environmental decoherence and the eternal superposition of the cosmos. Ergo again I do not subscribe to Many Worlds interpretations. Not that physics foundations is about popularity contests. But I think, when/if experimental approaches to these questions become possible I would be wanting to put research money into rigorously testing gravitational collapse and (if you deign to be a bit simplistic) also ER=Superposition, and therefore “NoER=Collapse”.
Well, that’s a smidgen of my thoughts for now on record. I think there are so many vast unexplored riches in fundamental theories and ideas of spacetime and particle physics that we do not yet need to reach out to bizarre outlandish interpretations of quantum mechanics. Bohr was the original sinner here. But pretty much every physicist who has dabbled in metaphysics and sought a valid interpretation of quantum mechanics has collapsed to the siren of the absurd ever since. This includes all those who followed Feynman’s dictum of forget about an interpretation. I think such non-interpretations are just as silly as the others.
Actually I’m not sure why I’ve characterised this as Feynman’s dictum. To be fair he did not say anything so extreme. He just marvelled at nature and warned physicists not to get into the mode of trying to tell nature what to do:
“We are not to tell nature what she’s gotta be. … She’s always got better imagination than we have.”
— R.P. Feynman, in the Sir Douglas Robb Lectures, University of Auckland (1979).
Man, I LOVED those lectures. My high school physics teacher John Hannah exposed our class to Feynman. Those were some of the best days of my life. The opening up of the beauty of the universe to my inner eyes. Here’s another favourite passage from those lectures:
“There’s a kind of saying that you don’t understand its meaning, ‘I don’t believe it. It’s too crazy. I’m not going to accept it.’ … You’ll have to accept it. It’s the way nature works. If you want to know how nature works, we looked at it, carefully. Looking at it, that’s the way it looks. You don’t like it? Go somewhere else, to another universe where the rules are simpler, philosophically more pleasing, more psychologically easy. I can’t help it, okay? If I’m going to tell you honestly what the world looks like to the human beings who have struggled as hard as they can to understand it, I can only tell you what it looks like.”
— R.P. Feynman (b.1918–d.1988).
Feynman actually said, “It’s the woy nature woiks.”
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