Understanding the Uncertainty Principle

[ZapperZ]

Actually, I would first recommend this paper to reilly.

Maybe, but I thought it fits in roughly with what vanesh had described. So this would be the "experimental verification".

Zz.

 

[reilly]

Originally Posted by reilly View Post

The "thing", as you put it, cannot, under any circumstances, be in two places at the same time.That's why we use probability -- maybe it's here, maybe it's there. But we don't know until we measure. And by the nature of the measurement, we'll always find one electron in one place at one time; never in two or more places.
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nanobug
Well, for this type of thinking you wouldn't need quantum theory, classical probabilities would be fine. What happens, however, is that things such as interference and superposition, which don't have a classical interpretation, manifest themselves both theoretical and practically. They are a property of quantum mechanics and states in which 'cats' are both alive and dead at the same time are very much a possibility. What you described above are 'mixed states'. But 'pure states' also exist.
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As I'm sure you know, standard probability theory says the only difference between classical and quantum probability structures is in the determination thereof. And, by the way, in classical probability systems involving waves you can find interference phenomena. Think about dealing with weak reflected radar signals -- noise can result in much interference;and you measure the incoming energy, power if you will, , hence amplitudes squared, hence interference; hence interference playing a role in probabilities, including those related to decoding, dependent on the received signal, the state of the system, and ...

Note that cats are quite familiar to all of us. And, like all living creatures, cats are either dead or alive, at least that's the conclusion of thousands of years of human experience. Let's assume you are right about being alive and dead at the same time. So, first, how would I determine such a state? Then what are the circumstances in which we might see such a cat, and why haven't any of us never experienced such a curiosity?



Originally Posted by reilly View Post

And, how in the world can a dead cat observe? Please tell us how.

nanobug
The dead cat 'observes' the same way that a lump of coal does, by being a macroscopic system.
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And exactly how does a macroscopic system observe? What is it that a lump of coal observes -- are you suggesting that a lump of coal has a brain, albeit a very primitive one?
Regards,
Reilly Atkinson

 

[nanobug]

standard probability theory says the only difference between classical and quantum probability structures is in the determination thereof.

Could you please explain the result of the double-slit experiment using classical probabilities and particles with precise but unknown positions and momenta?

 

[reilly]

Could you please explain the result of the double-slit experiment using classical probabilities and particles with precise but unknown positions and momenta?

Can't be done. I said a bit ago that to get the right probabilities for a quantum experiment, you need to follow the prescriptions of QM to find the probabilities. After that, the prescriptions for applying the probabilities in any probabilistic situation are identical -- true for market research, signal detection, horse race and short term stock market betting schemes, line broadening, transmission of light through an absorbing non-equilibrium gas, economic forecasting, ..

How you ever thought that I considered "classical-like" objects for QM in my post above is totally beyond me -- I said no such thing, nor do I subscribe to any such view.

I've answered your question. So how about at least one answer -- cat state or lump of coal, take your pick.

Regards,
Reilly

 

[nanobug]

And exactly how does a macroscopic system observe? What is it that a lump of coal observes -- are you suggesting that a lump of coal has a brain, albeit a very primitive one?

'Observation', within the context of QM is simply a synonym of decoherence. As decoherence relies on the entangling of quantum systems with a macroscopic environment, a cat is as good as a lump of coal. No brains are necessary, just lots and lots of entanglements with the corresponding tracing-out of the density matrix.

By the way, the situation is somewhat similar to the use of 'observer' in special relativity, in which one is really talking about a specific setup of rods and clocks and not about awareness.

 

[vanesch]

Can't be done. I said a bit ago that to get the right probabilities for a quantum experiment, you need to follow the prescriptions of QM to find the probabilities. After that, the prescriptions for applying the probabilities in any probabilistic situation are identical

This is true! But only when using it for observations. The probabilities you obtain for a set of outcomes (in a definite observation basis) are 'normal' probabilities, which can be dealt with in the usual way, as you describe.

The error is to assume that we can use this rule also for non-observed quantum states. Indeed, how do you link the 50% chance of going to the left slit and 50% chance of going to the right slit to the interference pattern ?

As I said, it CAN be done, in Bohmian mechanics, where you can have a modification of the dynamics instantaneously, at a distance. This is maybe what you mean with "a setup with 1 slit is not the same as with 2 slits" (implicitly implying that the dynamics of the 50% of the particles that came through the left slit is now modified by the closing of the right slit - as in Bohmian mechanics).

But if you stick to "local" explanations, it is not clear what the 50% through the left slit means, given that these 50% are going to behave differently, than a particle that goes for sure through the left slit. If 50% was just our *ignorance*, then a particle which went through the left slit (but we weren't sure) should do the same thing as a particle that went through the left slit (but we knew it for sure).

 

[reilly]

vanesh: you might want to read this paper:

T.L. Dimitrova and A. Weis, Am. J. Phys. v.76, p.137 (2008).

especially in the last section of it where they did something interesting with their Mach-zehnder interferometer:



Zz.

How can I get to the paper; AJP won't let me do a download\
Thanks, Reilly

 

[reilly]

'Observation', within the context of QM is simply a synonym of decoherence. As decoherence relies on the entangling of quantum systems with a macroscopic environment, a cat is as good as a lump of coal. No brains are necessary, just lots and lots of entanglements with the corresponding tracing-out of the density matrix.

By the way, the situation is somewhat similar to the use of 'observer' in special relativity, in which one is really talking about a specific setup of rods and clocks and not about awareness.

Really? So, what exactly does a lump of coal observe? How do we know the coal actually observes? Could we decode coal to describe an experiment's results?

Consider a double slit experiment, one that is fully automated so that the experimenter can be thousands of miles away. Let's suppose that the photon pattern is transmitted to the experimenter over a noisy line. Does decoherence get rid of the noise? Would there be any difference between communicating with lasers(quantum), vs. AM radio(Classical)?

Re observers and relativity. Perhaps, you have forgotten, but Einstein was quite anthropormorphic with respect to observers in his more popular writings. In his classic book, Relativity, Einstein always refers to human observers. If there is a specific setup at issue, Einstein's observers will construct it. And, not infrequently, Einstein suggests how the setup is to be done.

I would suggest, with all due respect, that your take on relativistic observers is somewhat at variance with the common practice of the last 100 years.

Regards,
Reilly Atkinson

 

[jsc314159]

The rabbit hole gets deeper.

Besides x and p, t and E also have an associated uncertainty in QM.

\Delta t * \Delta E \geq \hbar/2.

From what I understand about this, it means that there is a finite limit on how well we can know the energy of a particle that has existed for a finite time \Delta t .

In addition, when we use dynamical variables like position and momentum, we are applying classical concepts to the quantum world. One of the postulates of QM is that independent dynamical variables are represented by Hermitian operators. These operators are the observables and they act on wavefunctions when we measure a dynamical variable. The wavefunctions themselves represent the state of a particle and can be thought of as vectors (in the broader sense than lines in a Cartesian coordinate system) in Hilbert space.

Therefore, the way I interpret this is that until we measure position or momentum of a particle, the particle does not have a specific position or momentum. When we take a measurement, the values that we measure are limited to being the eigenvalues of the observable we are measuring. The wavefunction helps us to determine the probability of measuring one of these eigenvalues. Once measure, the state of the particle is known and will now be the eigenvector of the observable that corresponds to the measured eigenvalue (ignoring degeneracies).

jsc

 

[Fra]

Philosophical reflections

I partly share a generalized view of the observer, although perhaps not identical to nanobug. To be an observer is something that makes observations by interactions. I think this connect to the other thread.

How do we know the coal actually observes?

IMHO we don't - at least I don't (that way I have not said too much). But by the same reason I don't know of anyone but me observes anything. How do we KNOW anything at all?

It still seems highly *plausible* that other systems around me are similarly constructed, because the opposite seems less plausible.

So if we ask, if it's plausible that a lump of coal observes? I think it is.

Can I prove it? No. But if my rating systems which suggest it's plausible, serves me well, that alone is indirect support.

Could we decode coal to describe an experiment's results?

Possibly to a certain extent at least - isn't that what we do, when we analyse the state ad composition of matter? But certainly the information encoded in a piece of coal would not come anywhere near the information stored in the human brain if we talk about complex human level things.

But decoding a lump of coal would mean not just chemistry, it would mean decoding the matter in the coal. Which takes us right down to quark level. So maybe a piece of coal can even tell us a few things about nature? But decoding it is a process of learning.

/Fredrik

 

[kenewbie]

I just wanted to jump in with a simple question about the double slit experiment:

Has this ever been done in an environment where care has been taken to remove everything (including things which are not considered to act on a particle) else? By everything I mean doing the experiment in a vacuum at 0 kelvin in a led box blocking out gamma rays, removing magnetic fields, preferably at 0 g, and so on.

If this has been done, did it affect the result at all?

I can't stop looking the unknown variable in this experiment, because I don't understand the math / underlying physics of it (yet).

k

 

[ZapperZ]

I just wanted to jump in with a simple question about the double slit experiment:

Has this ever been done in an environment where care has been taken to remove everything (including things which are not considered to act on a particle) else? By everything I mean doing the experiment in a vacuum at 0 kelvin in a led box blocking out gamma rays, removing magnetic fields, preferably at 0 g, and so on.

Can you show an argument or derivation on why this would matter?

Please also note that the double-slit experiment is testing a more general principle of QM, which is the principle of superposition of orthogonal states. The experiments that tests this principle come in many different types, not just the double slit. I've mentioned the Delft/Stony Brook experiments many times on here which illustrates this principle even MORE dramatically than the double-slit. Those are done on a "robust" system at very low temperature (0 Kelvin is unrealistic especially when no one has achieve it) that was "immune" to such external factors that you described (superconductivity is a "quantum protectorate" state).

So doing what you wanted would not change anything.

Zz.

 

[kenewbie]

I certainly cannot show or make it logically follow that any of the criteria I mentioned has any impact. My only argument would be that historically there has been cases where "obvious" non-relevant factors turned out to have an impact after all, once they were removed.

So, if I where to do a follow-up to the original experiment (which had a result which seemed counter-intuitive at least at that point) I would go the extra mile and remove as much as possible.

I will take a look at the Delft/Stony Brook experiments, thanks a lot for the pointer.

k