[SEQ RERUN] The Born Probabilities
Today’s post, The Born Probabilities was originally published on 01 May 2008. A summary (taken from the LW wiki):
The last serious mysterious question left in quantum physics: When a quantum world splits in two, why do we seem to have a greater probability of ending up in the larger blob, exactly proportional to the integral of the squared modulus? It’s an open problem, but non-mysterious answers have been proposed. Try not to go funny in the head about it.
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This post is part of the Rerunning the Sequences series, where we’ll be going through Eliezer Yudkowsky’s old posts in order so that people who are interested can (re-)read and discuss them. The previous post was Decoherent Essences, and you can use the sequence_reruns tag or rss feed to follow the rest of the series.
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I think there’s a key reminder missing from this “mangled worlds” hypothesis (and its endorsement). And it’s that humans (Us! Me right now!) are configurations of particles. We are not waveunction-riders who can’t touch down in a world if we it doesn’t have the right kind of landing strip. We are the world. The only way for a state of the world to not have humans (Us!) in it is for it to simply not have that configuration of particles.
I mean, past a certain amount of fluency you can easily see there’s a problem by thinking about a weighted quantum coinflip. But it’s more important to really grok that “the probability that you find yourself in a particular world” does not mean there’s anything to call “you” before you’re a configuration of particles.
Here is yet another question to help me reveal my misunderstandings:
So, according to decoherence, a human believing that a quantum event with probability 50% occurs is equivalent to a “version” of a human brain becoming coupled with the amplitude blob corresponding to that 50%. The seeming complication that yet another “version” of a human brain is coupled with the other 50% of the amplitude distribution is all in our heads; the quantum physics giving rise to this “complication” is quite simple.
How about this experiment then? I set up an event that I know has two blobs A and B, each corresponding to 50% probabilities. I also set up, on the side, a two-slit experiment. I agree to myself beforehand that no matter the outcome of the event, I will cover one of the slits in my side experiment. As expected, no interference pattern occurs on the film.
Next, I do a similar experiment. This time, I only cover a slit on outcome A. If I find myself the version that observes outcome A, will I find 50% of an interference pattern caused by the amplitude distribution in the version of the world caused by outcome B, and importantly, the version of myself in outcome B that fails to over the slit?
If there is something wrong with this setup, might there not be another similar way to prove that other worlds exist?
Its this, and “where experience confuses physicists” that make me think that this sequence doesn’t succeed in its stated goal. As readers, we start by trying to come to grips with the idea that quantum mechanics shouldn’t be confusing, it should be normal and we should try and update our beliefs to make that happen. Confusion is in the mind, and all that.
Then we get to the end of the sequence, and we find the born probabilities are still somewhat confusing! Thats unfortunate- the evidence for quantum mechanics is entirely the born probabilities. How can gathering evidence cause us to update to a belief that leaves the evidence confusing? Whether collapse or many worlds, isn’t that the confusing thing about quantum mechanics?
The main evidence for quantum mechanics actually came from spectroscopy—that is, it correctly predicts how atoms will interact with light. This, along with interference, pretty much wraps up the Schroedinger equation.
Is there any scenario in which many-worlds would be testable by placing humans in a simulation and restricting the information they receive?
Yes. See the citations in this SEP article. If I recall correctly, you upload a human into a quantum computer, and then that uploaded human observes a system that is in a superposition of states x y. The human can be decomposed into two factors, aotimesb, where the second factor is capable of remembering the result of the observation and the first factor is only capable of remembering the fact that an observation has been made. Before the observation, the system is
and afterwards, it’s
a′otimesb_xotimesx a′otimesb_yotimesy
Now the evolution
Now we communicate with the human, who tells us that they remember observing the mixed state, but they cannot remember what they observed. Then we verify that indeed, the mixed state is still mixed, despite having been observed by a human. That’s what MWI predicts, anyways.
This is one of those models fighting a “straw collapse”. The orthodox approach is “this is the math, shut up and calculate”. Until the MWI math is different from “unitary evolution+Born rule”, it’s indistinguishable from collapse.
Those computations wouldn’t really be humans doing their regular human thing… you’d have to suspend the ‘human’ program for parts of that experiment.
I think a better way of phrasing it is, ‘Is there any scenario in which a collapse postulate would be testable...’
We have done tests far more sensitive than this one and not found any collapse behaviors separate from decoherence. The sort of experiment proposed would not be as sensitive because we would not expect coherence in the first place—you can’t get any sort of quantum effect out of a person just because of its size and inhomogeneity.
Feel free to elaborate on what you mean by this.
What if you have an automated setup perform the double slit experiment with and without detectors at each slit and observe the interference pattern.
After the experiments, the humans/ems in the simulation are only told whether the interference patterns are different, they are given no other information about the outside world and are especially not told what the detectors read.
What would you expect to happen differently depending on whether the MWI is more than an interpretation?
I was hoping to ask a really vague question so I displayed less of my total ignorance of QM.
Well wouldn’t it determine whether wave function collapse happens because of scale or because a human observed it or because you yourself observed it?
If neither having other humans outside the simulation nor having detectors changes the interference pattern, then the wave function collapse happens only if you yourself are effected by the information from the detectors.
If having other humans outside the simulation changes the interference pattern, then wave function collapse happens because any human is effected by the information from the detectors.
If having detectors changes the interference pattern even when no humans were effected by the information from the detectors, then wave function collapse happens at certain scales.
Having detectors present is already known to destroy the interference pattern, even if the detected information is silently and automatically erased right after (though I have trouble locating a relevant reference right now). A similar example is the experiment by Anton Zeilinger with hot bucky balls. The hotter they are, the less self-interference is observed, because the black-body radiation they emit gives away their position to some degree, even if this radiation is not specifically measured by anyone. Not sure what it says about your models.
Doesn’t this contradict it though? If the detected information is silently and automatically destroyed, the interference pattern is recovered ..
Not sure where you see a contradiction.
Indeed, but it would take a lot more than a single polarizer to destroy all traces of thermal radiation from a fullerene molecule. Once those thermal photons are out, you cannot really destroy all traces of their interaction with the rest of the Universe. Well, maybe you can, somehow, but that was not attempted in the experiment. My original point was that entanglement with the environment (=possibility of detection) is enough to destroy the interference pattern. Hence my puzzlement by Incorrect’s statement that “wave function collapse happens at certain scales”.
Yes but it can still effect the humans through butterfly effects. If we put the humans in a digital simulation, nothing short of data corruption will effect them.