Busting the myth of the observer: the double slit experiment

[stevendaryl]

Why not just repeat the infinite number of trials? We can have an infinite number of trials in one location, and another infinite number of trials in another location.

Hmm. I'm a little uncomfortable with talking about a completed infinite number of experiments, but it's possible that you could make sense of such a thing. You want to assume that any infinite sequence of trials must have all relative frequencies equal to their theoretical probabilities?

One thing about making your probabilities about infinite runs of trials is this: what does it tell you about a finite trial?

 

[atyy]

One thing about making your probabilities about infinite runs of trials is this: what does it tell you about a finite trial?

It says that finite trials can be misleading, but that the more and more trials we make, it is less and less likely to be misleading. So if we are looking for the Higgs, we report "evidence" at 3 sigma, and keep on taking data. Then we report "discovery" at 5 sigma. And we are still not certain it really is the Higgs, but as take more data and the theory is not falsified, we accept it provisionally until it is.

Truth to tell, de Finetti's subjective approach is much prettier here. The only problem is that the his approach cannot be applied perfectly in real life, because it requires the prior be non-zero over all future possibilities (as long as it is non-zero, our beliefs will converge to the truth). But we don't know all future possibilities, so we must be incoherent at some point. Anyway, prettier doesn't mean the ugly method is lacking, it's just ugly.

 

[stevendaryl]

It says that finite trials can be misleading, but that the more and more trials we make, it is less and less likely to be misleading. So if we are looking for the Higgs, we report "evidence" at 3 sigma, and keep on taking data. Then we report "discovery" at 5 sigma. And we are still not certain it really is the Higgs, but as take more data and the theory is not falsified, we accept it provisionally until it is.

To me, using a criterion such as "3 sigma" or "5 sigma" is much MORE subjective than using Bayesian reasoning. The cutoff is completely subjective.

 

[atyy]

To me, using a criterion such as "3 sigma" or "5 sigma" is much MORE subjective than using Bayesian reasoning. The cutoff is completely subjective.

They are just arbitrary subjective criteria. It's like Maxwell's equations - are they true or not? In science, you cannot prove a theory, only falsify it. So we provisionally accept Maxwell's equations because they've passed an arbitary subjective number of tests. Similarly, we provisionally accept the Higgs boson because it's passed an abrbitrary subjective number of tests. Both theories can be falsified in the future.

 

[atyy]

To me, using a criterion such as "3 sigma" or "5 sigma" is much MORE subjective than using Bayesian reasoning. The cutoff is completely subjective.

To add to my reply above. The idea is that if God decided to use frequentist probability and quantum mechanics of the Higgs boson (with appropriate UV completion) were the true theory, there would be no problem. Similarly, if God decided to use Maxwell's equations to make the universe, he'd be ok as long as he didn't make point charges. So these are objective things. The subjectivity lies in our inability to prove that God really used these theories, instead of some other theories that mimicked them.

 

[bhobba]

Hmm. I'm a little uncomfortable with talking about a completed infinite number of experiments, but it's possible that you could make sense of such a thing.

Same here.

I just think of it as simply something so large that from the law of large numbers the probability of something else is so small its negligible.

But then you face the issue of what exactly is small enough to neglect. This isn't confined to probability though - in the intuitive application of calculus you think of dt as a quantity so small you can neglect dt^2. Its wrong of course and exactly what is the amount that can be neglected. But this view will take you a long way without any issues. And if you actually want to be rigorous then how does one actually measure a limit to get say an actual velocity - what you actually do is measure the change in distance over a small time dt such that for all practical purposes dt^2 is neglected.

But it even goes further than that. Think of good old Euclidean geometry. A pont has position and no size, a line no thickness. They don't exist out there so when you apply it you decice what to model with a point, and a line - even though they will not conform to its definition.

Like I said - applying theory is always messy.

Thanks
Bill

 

[steviereal]

Talking about probability...
I also have a problem with that. Again, it suggests that "in any moment, it is impossible to calculate an electron's position, it only has a probability of being in a region".
Isn't it that WE are unable to calculate it? Because as soon as we measure it, we interfere yet again? Sure, it may be a practical problem for all physical creatures but it does not mean that the electron has no good reason to be wherever it is in a given moment. Sure, we may not be able to calculate it and we may not even have all the information to do so, but in theory it is possible to calculate it, right?

We wouldn't say that a given air molecule has a probability of being in a certain position in a room in a given moment, we only say that we are lazy to calculate it because it takes an awful amount of work and data, so let's just say we use probability for convenience.

So I suspect we COULD calculate the next position of an electron if we had all the information of it and its environment (virtual particles and all kinds of yet-undiscovered quantum froth included :-)).

 

[stevendaryl]

Talking about probability...
I also have a problem with that. Again, it suggests that "in any moment, it is impossible to calculate an electron's position, it only has a probability of being in a region".
Isn't it that WE are unable to calculate it? Because as soon as we measure it, we interfere yet again?

That sounds like a "hidden variables" idea, that particles have definite properties, such as position, but we just don't have any way to measure them precisely. But I think that Bell's Theorem suggests that that is not the correct way to think about probabilities in quantum mechanics.

 

[bhobba]

I also have a problem with that. Again, it suggests that "in any moment, it is impossible to calculate an electron's position, it only has a probability of being in a region".

That's not quite what QM says - but you are hardly Robinson Crusoe in not completely getting it.

Its silent about anything, being in a region, having a momentum, whatever, when not measured.

The only thing it's has is this thing called the state which aids in calculating probabilities of the outcome of observations if you were to measure it.

Isn't it that WE are unable to calculate it?

No - it built right into its basic axioms. The theory is about the outcomes of observations - that's it - that's all.

See post 137:
https://www.physicsforums.com/showthread.php?t=763139&page=8

The fundamental axiom from which all else follows is:
An observation/measurement with possible outcomes i = 1, 2, 3 ... is described by a POVM Ei such that the probability of outcome i is determined by Ei, and only by Ei, in particular it does not depend on what POVM it is part of.

Thanks
Bill

 

[atyy]

Talking about probability...
I also have a problem with that. Again, it suggests that "in any moment, it is impossible to calculate an electron's position, it only has a probability of being in a region".
Isn't it that WE are unable to calculate it? Because as soon as we measure it, we interfere yet again? Sure, it may be a practical problem for all physical creatures but it does not mean that the electron has no good reason to be wherever it is in a given moment. Sure, we may not be able to calculate it and we may not even have all the information to do so, but in theory it is possible to calculate it, right?

We wouldn't say that a given air molecule has a probability of being in a certain position in a room in a given moment, we only say that we are lazy to calculate it because it takes an awful amount of work and data, so let's just say we use probability for convenience.

So I suspect we COULD calculate the next position of an electron if we had all the information of it and its environment (virtual particles and all kinds of yet-undiscovered quantum froth included :-)).

Within quantum mechanics, a particle does not have a definite position and momentum at all times. In theory the particle does not have a classical trajectory, so it is not even in theory possible to calculate the electron's definite position at all times. It is only when position is measured, that the electron can be assigned a definite position.

However, there are theories beyond quantum mechanics, in which it is possible to assign the particle a definite position at all times. If such theories are true, we could calculate the position in principle. However, we do not yet have any experimental evidence that such theories are true. Since there are many possible such theories beyond quantum mechanics, we have to wait until quantum mechanics is found to fail to match observation, before knowing which, if any, of these theories beyond quantum mechanics we should use.

 

[microsansfil]

No - it built right into its basic axioms. The theory is about the outcomes of observations - that's it - that's all.

Quantum contextuality seem to be a very useful property/feature for quantum computation ( http://www.nature.com/nature/journal/v510/n7505/full/nature13460.html ).

http://www.cifar.ca/contextuality-puts-the-magic-in-quantum-computing-contextuality-puts-the-magic-in-quantum-computing-contextuality-puts-the-magic-in-quantum-computing-contextuality-puts-the-magic-in-quantum-computing

“One way of thinking about contextuality is that inevitably measurements involve some kind of disturbance. I'm not just learning about some definite property the system had prior to the measurement. I can be learning about some property the system had, but only in a way that depends on how I did the measurement.”

Patrick

 

[Greg Bystroff]

We all remember the animations describing the double slit experiment to the public, laying out the foundations of the mysterious quantum world. Now take the part when we try to determine which slit the electron went through. The narrator will say something like this, in a hushed voice: „And now, the electron, as if it somehow knew we were watching, becomes a particle! It changes just because we observe it!”
If I’m correct, the notion of the intelligent observer is so serious that it gave rise to the anthropic principle where consciousness interferes with quantum objects. I don’t understand something here because I see an error so glaring, it’s as bright as the Sun.
How could anyone call a which-way detector an innocent little observer? For a quantum particle, it is a brutal machine, that interacts with it in a physical way. The detector has no choice by the way but to interact, after all, how else would it get any information out of that photon or electron? It places an electromagnetic field in the path of the particle, or is bombarding the path with particles, I don’t know exactly how it does it but there is no choice but to do something like that. And it is perfectly natural for an electron in its wave form to collapse into a particle after you bump it against some other particle for the purpose of measurement.
Suggesting that all we do is observe gives everyone the false idea that a flying particle in the double slit experiment is bothered by an imaginary line, which we call our line of sight.
I think the word „observe” should only be used if we know what we are talking about:
Step one: Brutal interference
Step two: Drawing conclusions after checking what happened (good luck by the way, after step one)
So what am I missing here? Surely I can’t be smarter than all those scientists who had good reason to pursue the theory of the intelligent observer.

 

[stevendaryl]

The notion of the intelligent observer is so serious that it gave rise to the anthropic principle where consciousness interferes with quantum objects.

The "anthropic principle" was not developed from the notion of consciousness interfering with the wave function. Instead, it's an attempt to explain some seemingly unlikely facts about the universe by saying that if they weren't true, we wouldn't be around to observe them.

Your suggestion that measurement causes wave function collapse through disturbing the particle has been investigated, and there are good reasons to believe that that can't be the full explanation. In the EPR experiment, we have a pair of correlated particles, that travel far apart before a measurement is performed. Then apparently a measurement of one particle causes the wave function of the OTHER particle to collapse. If you assume that physical disturbances can't instantaneously cause effects on far-distant particles, then there is no way for wave function collapse to be an ordinary physical disturbance.