Uncertainty about Heisenberg Uncertainty Principle

[Steve Brown]

I'm not certain as to the true meaning of the Heisenberg Uncertainty Principle, and wonder if anyone can provide insight. I understand that there is a reciprocal relation between the certainties as to the position and momentum of a particle such as an electron; the more precisely position is known, the less precisely momentum can be known, and vice versa. Does this mean that a particle cannot have definite position and momentum at the same time, or that we simply cannot know one if we know the other? In other words, does the Heisenberg Uncertainty Principle pertain to reality itself or to knowledge of reality?

Given that quantum physics describes reality in terms of probabilities, does this mean that randomness is an inherent property of nature? Or does it simply mean that we cannot know all the variables and unseen forces of nature? For example, take an atom of thorium-232, an isotope known to have a half life of 14 billion years. Is the precise time at which it decays to radium-228 predetermined by unknown forces, or does it depend entirely on random chance?

 

[Simon Bridge]

Wecome to PF;

I'm not certain as to the true meaning of the Heisenberg Uncertainty Principle, and wonder if anyone can provide insight. I understand that there is a reciprocal relation between the certainties as to the position and momentum of a particle such as an electron; the more precisely position is known, the less precisely momentum can be known, and vice versa. Does this mean that a particle cannot have definite position and momentum at the same time,

Yes - that's the one.

or that we simply cannot know one if we know the other? In other words, does the Heisenberg Uncertainty Principle pertain to reality itself or to knowledge of reality?

Oh I see... In the quantum domain - that's not a clear question. It makes no difference to the outcome of experiments. Look up "empiricism".

It may help to think of it in terms of the mechanism - you cannot find a way to measure position without disturbing the momentum a bit. The more precisely you measure the position, the more you disturb the momentum. If you do a lot of such measurements on identically prepared systems, then you try to measure momentum, you will get a distribution of momentum measurements in accordance with Heisenberg's uncertainty. In this sense the uncertainty certainly describes reality.

I think most people take it deeper than that. In a way, while classical statistics describes the experimenter's state of knowledge, quantum statistics describes the Universes state of knowledge.

Given that quantum physics describes reality in terms of probabilities, does this mean that randomness is an inherent property of nature?

That is the usual interpretation - though we are more careful and say that nature is fundamentally "statistical", since "random" is often taken to imply "unpredictable".
I think it is more accurate to say that our current, very good, models of reality are fundamentally statistical. What reality is or does is still an open question.

Or does it simply mean that we cannot know all the variables and unseen forces of nature?

That would be called a "hidden variables" formulation ... classically we use probability to describe our incomplete knowledge of what is going on: it accounts for stuff that would be deterministic if only we knew all the variables that apply. In QM we can show that even knowing all the variables does not help.

This line of inquiry leads you to Bell's Inequality and quantum non-locality and is actually quite deep. You'll find lots of arguments in these forums about this stuff. One of the things I like about QM is that questions thought to be purely philosophical like "what do we mean by 'reality'?" turn out to have physical significance. Quantum Mechanics is where reality meets imagination and gives it a good kicking.

 

[wuliheron]

The latest weak measurement experiments confirm the Ozawa formulation of the HUP. Particularly interesting is that these experiments rule out the observer effect, that is, the influence of the observer on quanta. Since Bell's Inequality the mounting evidence is quanta are contextual, that is, context trumps content. Using the context to define the properties of the individual parts contextual systems can do a complete end run around metaphysics because the context alone suffices to describe everything observable. As a result the same contextual system can have multiple metaphysical interpretations when none is actually needed to explain anything. The drawback for physics is that because indeterminacy can only be elucidated by its context it is a quintessential metaphor with possibly the void as its root metaphor.

 

[Simon Bridge]

Yah - how I described it (above) was how Werner described it. It can be a useful stepping-stone description for students though.

More information:
http://arstechnica.com/science/2012/09/weak-measurements-show-quantum-uncertainty-is-inherent/

 

[Steve Brown]

Thanks for your replies. Indulge me if you will in a hypothetical thought experiment. Say you start out with two identical universes, and let them each evolve for a billion years. After that time, are they still identical, because everything is determined by prior conditions, or are they different, because random fluctuations occur?

 

[Nugatory]

Thanks for your replies. Indulge me if you will in a hypothetical thought experiment. Say you start out with two identical universes, and let them each evolve for a billion years. After that time, are they still identical, because everything is determined by prior conditions, or are they different, because random fluctuations occur?

No one knows.

I'd bet against it though.

 

[edpell]

I take the HUP to be a simple observation on the limits of measurements. I do not see that it provides any information deeper than that. I go with Feynman's all paths (weighted by the appropriate factor and phase) approach. What I do not understand is how a single particle traveling all paths is reduced to a tightly defined location upon a measurement of its position.

 

[Simon Bridge]

Thanks for your replies. Indulge me if you will in a hypothetical thought experiment. Say you start out with two identical universes, and let them each evolve for a billion years. After that time, are they still identical, because everything is determined by prior conditions, or are they different, because random fluctuations occur?

I don't think the question means anything in QM - there are too many implied ideas in there like who is making the observations?

If we start out with two closed QM systems with the same initial conditions, allowed to evolve for a time, would end up with the same distribution of possible quantum states for a particular measurement. However, subsequent measurement on each system need not return the same state (depends on the measurement.)

I take the HUP to be a simple observation on the limits of measurements. I do not see that it provides any information deeper than that. I go with Feynman's all paths (weighted by the appropriate factor and phase) approach. What I do not understand is how a single particle traveling all paths is reduced to a tightly defined location upon a measurement of its position.

That would be a different topic.
Simply put - the particle does not travel every single path. The sum over all paths is just a way of figuring the probability, by stages (called perturbation theory) which works out mathematically to get the same result as whatever it is that may actually happen. It's a shortcut. It is no different, to use Feynman's own example, than working out when to expect the next eclipse by moving nuts between bowls.

See the mirror example from the lecture series (link post #4) ...

 

[tom.stoer]

this mean that a particle cannot have definite position and momentum at the same time, or that we simply cannot know one if we know the other? In other words, does the Heisenberg Uncertainty Principle pertain to reality itself or to knowledge of reality?

That depends on you definition of reality - which is not physics but metaphysics.

Empirically one could say that complete knowledge of reality is encoded in the wave function. And one could say that it does not makes sense to speculate on some "reality" beyond this knowledge. So in that sense the HUP says something about our limited knowledge (but at the same time we must keep in mind that we are no longer allows to speculate about some reality b/c this would contradict empiricism)

Then we could say that the wave function "is" the ultimate model of reality, or as a Platonist would say it "is" reality. In that sense the HUP says something about an "ultimate principle" of reality.

Please not that these two positions contradict each other metaphysically but are in perfect agreement physically.

There are mathematical results ruling out violations of the HUP using a certain mathematical context (Hilbert spaces, self adjoint operators, ...) so in this context the HUP is always correct as a mathematical theorem. The question about the relation of a mathematical model with reality is beyond math and physics, it's metaphics. And the question whether there could be a more fundamental theory than quantum mechanics from which the latter one plus its theorems follow as an approximation (just like Newtonian Mechanics is an approximation to General Relativity) cannot be answered today (but I think the majority does believe in quantum mechanics as some ultimate underlying principle of nature - w/o having a scientific proof or argument except for the fact that works)

 

[Steve Brown]

No one knows.

I'd bet against it though.

You would bet against the two universes being the same, or different? Or is your answer a superposition of two states?

 

[Nugatory]

You would bet against the two universes being the same, or different? Or is your answer a superposition of two states?

I would bet against the two universes turning out the same. I believe that for all practical purposes, that's a bet against superdeterminism.

 

[Steve Brown]

I would bet against the two universes turning out the same. I believe that for all practical purposes, that's a bet against superdeterminism.

I am inclined to agree that the two universes would proceed along different paths of development. That is certainly what I would prefer to be the case. When Einstein insisted "God does not play dice!", I wonder if he understood that implied superdeterminism, and how he would have reacted to the idea that his life and work were all predetermined. Predetermined or not, we still have to make choices and decisions which have consequences, and in my opinion, that makes the question of determinism moot, from a practical perspective.

 

[Nugatory]

When Einstein insisted "God does not play dice!" I wonder if he understood that implied superdeterminism

Einstein did not live to see Bell's theorem and the experiments that it spawned, so he had every reason to believe that there could be an underlying theory that was local and realistic, yet would not suggest superdeterminism or other conspiratorial conjectures.

 

[1977ub]

We're still at a state of knowledge re: measurement problem where there is no way to say where the heck classical reality comes from, right?

 

[1977ub]

Thanks for your replies. Indulge me if you will in a hypothetical thought experiment. Say you start out with two identical universes, and let them each evolve for a billion years. After that time, are they still identical, because everything is determined by prior conditions, or are they different, because random fluctuations occur?

In the "many universes" view, it's the other way around! You start with one universe, let it "evolve", and you end up with more and more different universes. Since every outcome is represented, the same "everything" would happen if you could try it over again.

http://en.wikipedia.org/wiki/Many-worlds_interpretation

 

[wuliheron]

We're still at a state of knowledge re: measurement problem where there is no way to say where the heck classical reality comes from, right?

This is what has screwed everyone up from day one. You need to turn the question on its head and ask if classical reality is a fable we've carefully constructed over eons, then how does quantum mechanics fit into the picture. A recent paper suggests that if a real live cat were in a state of superposition the amount of computing power required to varify the fact would be astronomical. Hence, the naked human eye sees only one cat. Like the discovery of radiation and electromagnetic waves that have been all around us for since the beginning of time quantum effects look to be no different and an entirely new world for physics to discover.

That's the implication which has been building for over a century and, especially, since Bell's theorem.

 

[Maui]

This is what has screwed everyone up from day one. You need to turn the question on its head and ask if classical reality is a fable we've carefully constructed over eons, then how does quantum mechanics fit into the picture. A recent paper suggests that if a real live cat were in a state of superposition the amount of computing power required to varify the fact would be astronomical. Hence, the naked human eye sees only one cat. Like the discovery of radiation and electromagnetic waves that have been all around us for since the beginning of time quantum effects look to be no different and an entirely new world for physics to discover.

That's the implication which has been building for over a century and, especially, since Bell's theorem.

Without presupposing the existence of fundamentally classical objects(which would be ridiculous), the theory that brains somehow choose a single state of reality for computing reasons appears invalid. Is the human brain to be taken as the fundamental object of reality?

We're still at a state of knowledge re: measurement problem where there is no way to say where the heck classical reality comes from, right?

This experiment(the paper is peer-reviewed) suggests very strongly that neither detectors nor interactions cause the so called "wavefunction collapse". By altering the width of one of the slits and monitoring the inelastic scattering, the researchers were able to cancel out the interference pattern suggesting that the availablity of the which way information is the deciding factor for apparent collapse of quantum states.

http://apl.aip.org/resource/1/applab/v97/i26/p263101_s1?isAuthorized=no

The paper has to be bought and i read it for free on another site but it's probably against the rules to post it here so i'll withhold.

 

[1977ub]

This is what has screwed everyone up from day one. You need to turn the question on its head and ask if classical reality is a fable we've carefully constructed over eons, then how does quantum mechanics fit into the picture.

Unless you're going many-worlds, the cat is either alive or dead. is that a "classical reality" "fable" ?

 

[wuliheron]

Without presupposing the existence of fundamentally classical objects(which would be ridiculous), the theory that brains somehow choose a single state of reality for computing reasons appears invalid. Is the human brain to be taken as the fundamental object of reality?

Again, contextual systems can do an end run around metaphysics altogether by defining the properties of the individual parts in terms of their context. It remains possible to apply any number of metaphysical interpretations, but physics is not in the business of speculating about metaphysics. Instead, it can focus solely on the issue of what is apparently useful in any given context.

 

[Maui]

Again, contextual systems can do an end run around metaphysics altogether by defining the properties of the individual parts in terms of their context. It remains possible to apply any number of metaphysical interpretations, but physics is not in the business of speculating about metaphysics. Instead, it can focus solely on the issue of what is apparently useful in any given context.

But a brain is a classical object and also contextual and subject to the same rules that govern the reality of tables and chairs.

 

[wuliheron]

But a brain is a classical object and also contextual and subject to the same rules that govern the reality of tables and chairs.

That's one argument but, again, metaphysics is not the provence of physics. If you cannot provide a clear and useful definition of "reality" it isn't a physical term and isn't a problem for physics.

 

[1977ub]

That's one argument but, again, metaphysics is not the provence of physics. If you cannot provide a clear and useful definition of "reality" it isn't a physical term and isn't a problem for physics.

"Reality is that which, when you stop believing in it, doesn't go away." - Philip K. Dick

Of course this doesn't seem to apply (straightforwardly) to things quantum.

 

[wuliheron]

"Reality is that which, when you stop believing in it, doesn't go away." - Philip K. Dick

Of course this doesn't seem to apply (straightforwardly) to things quantum.

That definition also sounds more like an issue for psychologists to deal with than physics.