Uncertainty Principle - nature or human nature?

[SuccessTheory]

Hi, I have taken an introductory undergraduate QM course, solving for different boundary conditions like particle in a box, but the physical interpretations of some of the tenets was not well explained. I was surprised to find this paragraph on Wikipedia:

"Published by Werner Heisenberg in 1927, the principle means that it is impossible to determine simultaneously both the position and momentum of an electron or any other particle with any great degree of accuracy or certainty. Moreover, his principle is not a statement about the limitations of a researcher's ability to measure particular quantities of a system, but it is a statement about the nature of the system itself as described by the equations of quantum mechanics."

Where can I find more information about the uncertainty principle being related to the nature of the system itself? I was always told that human perturbations caused the uncertainty.

Does it mean if we were to go back to the moments after the big bang, the universe could play out differently?

 

[Fredrik]

Where can I find more information about the uncertainty principle being related to the nature of the system itself? I was always told that human perturbations caused the uncertainty.

This post might be a good start. If you're having difficulties seeing what those Delta thingys have to do with "uncertainty", or if you find some other detail difficult to understand, just ask.

 

[arkajad]

[ If you're having difficulties seeing what those Delta thingys have to do with "uncertainty", or if you find some other detail difficult to understand, just ask.

In fact, in order to calculate precisely these Delta thingys one needs to measure both position and momentum, in an infinite series of separate experiments, with an infinite precision. Otherwise lack of precision of measurements will add to quantum uncertainty.

 

[rahuliitkgp]

1.) the comment on researcher's ability signifies that we're not considering observer in the measurement process. that is observing apparatus(instrument or human) is purely classical. So, quantum mechanics unlike its classical counterpart doesn't stand on its own.

2.) & it says that things we can't measure not because of insufficient accuracy but system in fact is as it is measured i.e. there is no objective reality.

these two as main points along with some other are main points of Copenhagen interpretation.
& these are main point of concern in philosophical implication of QM & considered major loop hole in the theory including Einstein.
There is fantastic monograph on this aspect by J S Bell, Speakable & Unspeakable in Quantum Mechanics. http://books.google.com/books?id=FG...&resnum=1&ved=0CC4Q6AEwAA#v=onepage&q&f=false

 

[arkajad]

There is fantastic monograph on this aspect by J S Bell, Speakable & Unspeakable in Quantum Mechanics.

To quote just one sentence from this book:

"For our generation I think we can more profitably seek Bohr's necessary 'classical terms' in ordinary macroscopic objects, rather than in the mind of the observer."

[Bell, p. 194]

 

[rahuliitkgp]

@arkajad
thanks for a good line...
I can remember Feynman told once, "If I were forced to sum up in one sentence what the Copenhagen interpretation says to me, it would be 'Shut up and calculate!'."
but, that's an opportunistic & ignorant view as far as physicists are considered, isn't it??

 

[dx]

@arkajad
thanks for a good line...
I can remember Feynman told once, "If I were forced to sum up in one sentence what the Copenhagen interpretation says to me, it would be 'Shut up and calculate!'."
but, that's an opportunistic & ignorant view as far as physicists are considered, isn't it??

That was actually said by Mermin, not Feynman. Mermin later even admitted that his understanding of the copenhagen interpretation at the time he said that was superficial and has become more nuanced since then.

 

[rahuliitkgp]

but it's mentioned even on wiki as Feynman's quote...any way a good practical way of saying things..:)

 

[SuccessTheory]

Thanks everyone for your replies.
Fredrik: The book page you link to in your earlier post still mentions "measurements" and implies that uncertainty is only relevant to human observation. However, in your post you say that "that actually appears in QM has nothing to do with "nudges" or "knowledge" about the position and momentum. It's much more profound than that." I would like to know what that more profound aspect is.

rahuliitkgp: so if the observer was included in the measurement, would we have certainty? I will hopefully read the monograph soon.

But the simplest way for me to arrive at an understanding would be for someone to clarify my second question: Does it mean if we were to go back to the moments after the big bang, the universe could play out differently?

 

[arkajad]

Does it mean if we were to go back to the moments after the big bang, the universe could play out differently?

The universe is "playing differently" every time some "quantum event" happens. And they happen all the time.

 

[DaveC426913]

Does it mean if we were to go back to the moments after the big bang, the universe could play out differently?

Absolutely.

The classical Newtonian universe is purely deterministic. In principle, if you know the exact position and momentum of every particle in a system, you could know where those particles were at some arbitrary time in the past, as well as predict where they will be some arbitrary time in the future.

Not so in the quantum mechanical universe. As arkajd says, every passing moment is a crapshoot for each particle.

 

[rahuliitkgp]

rahuliitkgp: so if the observer was included in the measurement, would we have certainty? I will hopefully read the monograph soon.

But the simplest way for me to arrive at an understanding would be for someone to clarify my second question: Does it mean if we were to go back to the moments after the big bang, the universe could play out differently?

I wrote observer & you had probably read anywhere observer in measurement process because this is another problem regarding quantum measurement, i.e. what is an observer?
since everything that we infer is based on many processes in between & all those are quantum process too & apparatus itself is quantum system. So this process is never ending. hence Bohr resolved this difficulty by including in Copenhagen Interpretation that the apparatus has to be classical.
& further Newmann added into it that the last link to this process will be us "humans", however this is debatable. You can say, "ok, we're also quantum systems, our retina, senses & all, so how is this measurement." there are many questions like that.
for second question, universe has it's option every moment for choosing its fate, it's not only at big bang provided you discard objective reality as per CI of quantum mechanics.
I know its hard to swallow, but I think it must have been harder for Einstein...:P

 

[piareround]

I apologize if someone has mentioned this before, uncertainty principle comes from more mathematical roots rather than quantum physics. In fact, it can be shown that:

1. The QM Uncertainty Principle is just a specific case of the Fourier Transform's Uncertainty principle in which the is an uncertainty, or standard deviation, between values in two Fourier transform pairs. In quantum mechanics position and momentum are Fourier transform pair, therefor, it can be shown that their standard deviations should have a uncertainty equal to or greater than the uncertainty principle. The same goes for Fourier transform pair of Energy and time. This is why when ever you get the uncertainty principle as your error value, you say the equation or experiment was Fourier transform limited
2. In quantum mechanics, we often use Hamiltonian in our operators. Like David Griffith does in chapter 3 of his book "Introduction to Quantum Mechanics", the uncertainty in the product of any two Hamiltonian operators is the uncertainty principle hbar/2

 

[Fredrik]

Fredrik: The book page you link to in your earlier post still mentions "measurements" and implies that uncertainty is only relevant to human observation. However, in your post you say that "that actually appears in QM has nothing to do with "nudges" or "knowledge" about the position and momentum. It's much more profound than that." I would like to know what that more profound aspect is.

It's that particles don't have well-defined positions. To understand that, you have to study QM, and in particular the probability interpretation of the wavefunction. Based on the type of questions you're asking, I think it would be better for you to study those things, than to study this theorem and its proof.

It looks like you missed one of the main points of my post, which is that the argument that's based on practical difficulties, and the inequality that goes with it, don't have anything to do with QM, or with the inequality that people call the "uncertainty principle" today. It's just a pre-QM argument for why we might need a theory like QM. The idea is to look for theories in which a similar inequality can be proved as a theorem. The theory that was eventually found is of course QM.

The uncertainty theorem of QM has nothing to do with practical difficulties. It tells you how the results of a large number of measurements would be distributed if our measuring devices had been perfectly accurate.

Does it mean if we were to go back to the moments after the big bang, the universe could play out differently?

If you go back to a millisecond before your last measurement was performed, the "universe could play out differently" in the sense that your result could have been different. This doesn't have anything directly to do with the uncertainty theorem. It's just an obvious consequence of the probability rule of QM (which is of course used in the proof of the uncertainty theorem).

You should probably leave the big bang out of the discussion. The wave function/state vector of a physical system that doesn't interact strongly with its environment evolves deterministically, so if the universe doesn't have an "environment", its should have a state vector that evolves deterministically. But this takes us deep into some sort of many-worlds interpretation and into quantum gravity, since there's no way to neglect the effects of gravity when you consider the whole universe.

 

[Fredrik]

I have to ask, why does everyone call it the "uncertainty principle"? I haven't checked all the books to see what terminology they're using, but I know I've seen "uncertainty relation" and "indeterminacy relation" in books. So why doesn't anyone use any of those terms? (In my opinion, "uncertainty principle" is very inappropriate, since a "principle" is just a loosely stated idea, while this is clearly a theorem). Does every book I've never studied myself call this theorem the "uncertainty principle"?

 

[arkajad]

Well, mathematicians sometimes like to call it "Heisenberg's inequality" -which is neutral and adequate - I think.

 

[atyy]

I have to ask, why does everyone call it the "uncertainty principle"? I haven't checked all the books to see what terminology they're using, but I know I've seen "uncertainty relation" and "indeterminacy relation" in books. So why doesn't anyone use any of those terms? (In my opinion, "uncertainty principle" is very inappropriate, since a "principle" is just a loosely stated idea, while this is clearly a theorem). Does every book I've never studied myself call this theorem the "uncertainty principle"?

http://www.theory.caltech.edu/people/preskill/ph229/notes/chap1.pdf
Furthermore, in quantum theory, noncommuting observables cannot simultaneously have precisely defined values (the uncertainty principle), and in fact performing a measurement of one observable A will necessarily influence the outcome of a subsequent measurement of an observable B, if A and B do not commute.

http://arxiv.org/abs/hep-th/9309034
"We show that a deformation of the Heisenberg algebra which depends on a dimensionful parameter $\kappa$ is the algebraic structure which underlies the generalized uncertainty principle in quantum gravity."

I wonder what Dirac wrote?

Interesting history given by http://plato.stanford.edu/entries/qt-uncertainty/: "Indeed, Heisenberg never seems to have endorsed the name ‘principle’ for his relations. His favourite terminology was ‘inaccuracy relations’ (Ungenauigkeitsrelationen) or ‘indeterminacy relations’ (Unbestimmtheitsrelationen). We know only one passage, in Heisenberg's own Gifford lectures, delivered in 1955-56 (Heisenberg, 1958, p. 43), where he mentioned that his relations "are usually called relations of uncertainty or principle of indeterminacy". But this can well be read as his yielding to common practice rather than his own preference."

 

[DrChinese]

I have to ask, why does everyone call it the "uncertainty principle"? I haven't checked all the books to see what terminology they're using, but I know I've seen "uncertainty relation" and "indeterminacy relation" in books. So why doesn't anyone use any of those terms? (In my opinion, "uncertainty principle" is very inappropriate, since a "principle" is just a loosely stated idea, while this is clearly a theorem). Does every book I've never studied myself call this theorem the "uncertainty principle"?

You're probably right. Maybe it should be Heisenberg Non-commuting Observable Measurement Theory. So instead of HUP we'd have HNOMT.

But I don't think that would help much.

 

[dx]

You're probably right. Maybe it should be Heisenberg Non-commuting Observable Measurement Theory. So instead of HUP we'd have HNOMT.

But I don't think that would help much.

Or we could just call the physical principle behind non-commutativity 'the complementarity principle' and the mathematical theorem derived from non-commutativity 'the uncertainty/indeterminacy relation'.