Uncertainty laid out

[Selnex]

does the uncertainty principle suggest that activity occurs at a purely undeterministic level or simply that we cannot know both speed and position because of a lack of ability to figure it out

 

[HallsofIvy]

Very good question!

Basically, the idea that "uncertainty" is inherent or that there exist "hidden variables" which, if we knew them, would clear up the uncertaintly are two distinctly different viewpoints about quantum theory.

I wouldn't say that there is a definite answer but the experimental evidence seems to be more on the side of the "inherent uncertainty" people:
an electron, for example, really ISN'T at any specific place (until you measure it!).

 

[chroot]

This is a common question (and indeed a common misconception): is uncertainty inherent in the universe, or is it just a failure of current technology?

The answer is unequivocally that is it impossible, in principle, to know both position and momentum (or energy and time, or...) simultaneously. No technology will ever be able to measure both simultaneously, because the universe forbids it in principle.

As HallsOfIvory said, there were some theory floating around that said that particles have "hidden variables" -- very much as if the particles have some little memory bank built into them that let's them remember where they really are, even though they don't tell the rest of the universe.

The Bell inequalities theoretically doomed hidden variable theories, and the Aspect experiments settled the question. There is no way that a hidden variable theory (any hidden variable theory) can be compatible with what we observe. Uncertainty really is a fundamental quality of the microscopic universe.

- Warren

 

[r637h]

Is the "measure of uncertainty Planck's constant?

 

[maximus]

Originally posted by r637h
Is the "measure of uncertainty Planck's constant?

Planck's constant is a measurment (closly related to the energy content of one quantum of light) that cannot be exceeded in Heisenberg's uncertainty equation which is: (the uncertainty of the position of a paricle) x (the uncertain of the velocity of the particle) x (the mass of the particle) is greater than or equal to Planck's constant. but basically yes, it is a constant.

 

[chroot]

The uncertainty principle is not an equation. The equation you gave is the uncertainty relation between momentum and position, and should not be expressed as (velocity * mass). In quantum mechanics, the momentum is an operator, and velocity itself is not considered.

- Warren

 

[jeff]

Here's something relevant to broaden perspectives on the uncertainty principle.

You know how high school kids who've just learned about quantum theory say things like "electrons are both wave and particle", invoking "wave-particle duality"? Well if QT said that, it would be wrong because something cannot be both wave and particle. But still, there is this idea of wave-particle duality, but what it actually says is that depending on the experiment performed, a system will display a wave aspect or a corpuscular aspect. There is thus no logical contradiction in wave-particle duality. From this point of view, the uncertainty principle is simply the mathematical condition correspondng to wave-particle duality that enforces QT's logical consistency. For example, in the postion-momentum uncertainty principle, position is a corpuscular aspect while momentum - via debroglie - is a wave aspect. So the greater the accuracy with which you know an aspect that is corpuscular, the less you know about it's dual wave-like aspect, thus avoiding logical contradiction.

 

[Claude Bile]

The uncertainty principle can be explained mathematically purely in terms of the principles of Fourier series analysis.

Instead of referring to a 'wave-particle duality', I like to think of particle behaviour as an aspect of wave behaviour. 'Particle' behaviour is still wave behaviour, it just follows particular laws we like to associate with the idea of a 'particle'.

Thinking of it (and explaining) in this manner is less confusing than using the idea of duality, as it does not have any intuitive contradictions associated with it (In my belief, others may have different viewpoints).

 

[jeff]

Originally posted by Claude Bile The uncertainty principle can be explained mathematically purely in terms of the principles of Fourier series analysis.

Not explained, formulated.

Originally posted by Claude Bile Instead of referring to a 'wave-particle duality', I like to think of particle behaviour as an aspect of wave behaviour. 'Particle' behaviour is still wave behaviour, it just follows particular laws we like to associate with the idea of a 'particle'.

This expression of wave-particle duality in the ontological terms warned against above leads to the kind of logical inconsistency that is avoided by thinking purely in terms of experimentally observed behaviour, which is thus the correct way to think about wave-particle duality, as I explained above.

Originally posted by Claude Bile Thinking of it (and explaining) in this manner is less confusing than using the idea of duality, as it does not have any intuitive contradictions associated with it...

And this is less confusing how?

 

[pmb]

Originally posted by Selnex
does the uncertainty principle suggest that activity occurs at a purely undeterministic level or simply that we cannot know both speed and position because of a lack of ability to figure it out

It's a fundamental fact that nature is undeterministic at the quantum level - not that we can't just measure things precisely.

However there is a tendency to misinterpret what this means. It doesn't mean that we can't measure things exactly. What it means is that things don't *have* an exactness. For example: Think of the double slit experiment - there is an interference pattern on the screen. The places of high intensity light represent a high probability that a quantum of light hitting the screen there and low intensity light represent a low probability of a quantum of light hitting there. The distances between these high spots being rlated to the wavelength. But what that does *not* mean is that when we measure the position of the light that we don't know what the momentum is. That's not true at all. The probability comes in with the statistical nature of the experiments. In each measurement I can know both the position and the momentum exactly. But when I do this experiment a huge number of times what happens is that we get a spectrum of different values and we use the table of measurements that we get and we calculate the quantities dx and dp = which are calculated statistically. We then find that

dx*dp >hbar (or something like that - I forget the exact lower bound)

Now this will hold for any two conjugate variables - not just position and momenta.

Also the Momentum 'P' is *not* mechanical momentum p = mv as you'd think of in classical mechanics. It's the canonical momentum which is defined by the Lagrangian which defines the system.

For example - If the particle is charged particle and is moving in a magnetic field then the mechanical momentum "p" is related to the canonical momentum P by

P = p + (q/c)A

where

P = canonical momentum vector
p = mechanical momentum vector
A = Magnetic vector potential.

So I guess you can say that you alter the position/momentum HUP relation by applying a magnetic field - Hmmm. Sounds like a "Heisenberg Compensator" from Star Trek huh? :-D

Well one never knows. I've been meaning to investigate that idea but have yet to get around to it.

Pete

 

[r637h]

"Well, one never knows."

An excellent observation; a profound pun, if you will.

In Classical Physics, one can both fix the position of an "object" and determine its velocity at the same time. In Quantum Physics: One or the other, but not both.

In QP, probability is our salvation. The slit-lamp is a good way to demonstrate this: It is the probability of peak vs. trough that is being dealt with, and that is sufficient to explain the observation.

But is the measure "absolute?"; Of course not.

Does QP work entirely for radioactive decay? Not really: The rate of decay occurs with a probability of ~1, but the decay of an individual nucleus is totally unpredictable. There are surely laws that govern this, but they cannot be measured for now.

"Chances are" they will become measurable some day. "One never knows."

Rudi

 

[Tyger]

The uncertainty principle forbids us

from constructing an experiment which measures the wave-number (classicaly, the momentum) and the position of a particle. We can construct an experiment to measure one or the other, but not both at the same time, to an arbitrary degree of accuracy.

As such it places a limit on what we as internal observers of the world can know. I'm not yet convinced that it means the World is indeterministic, but it definitely says that our knowledge on a working level is.

 

[AndersHermansson]

Don't understand why people mess things up.
Uncertainty is not the same thing as indeterminism.

 

[Tyger]

You're right!

Originally posted by AndersHermansson
Don't understand why people mess things up.
Uncertainty is not the same thing as indeterminism.

But they do confuse things. How many papers, letters and articles have you seen, some by very credentialed people, where the issue was confused.

 

[Sacroiliac]

Originally posted by pmb
But what that does *not* mean is that when we measure the position of the light that we don't know what the momentum is. That's not true at all.

pmb, I believe what you say is true but when I explained this to my friend he told me I was full of it. Would you have cite that explained this?

 

[r637h]

I agree with the last few messages (I think):

Uncertainty has nothing to do with indeterminism.

Uncertainty can have a value (or at least a degree).
Determinism is of course a philosophical concept.
But there is an analogy, which, I'm not sure whether can be applied to physical, philosophical, or mathematical principles: Feynman's "Sum of All Histories (sum-over-paths)" might have application to any or all. I don't want to mis-state the concept, but it would seem that all possibilities, no matter what their probabilities, lead to the same conclusion., i.e., the process is indeterminate but the outcome is determined.

It is meant, of course, to refer to quantum mechanics., but is it possibly a way to look at the Universe, and all of the phenomena therein?

Rudi

 

[pmb]

First off "uncertainy" is a description of indeterminism. It's postulated that nature is indeterministic. That's what quantum mechanics is all about. The Copenhagen interpretation interprets the meaning of the wave function in terms of probability dentsity.

However from what I've read here there seems to be some confusion on the meaning of "uncertainty."

I've written a description on the meaning of "uncertainty." It uses an every day example using dice to describe the meaning. See


http://www.geocities.com/physics_world/probability.htm

Pete

 

[r637h]

"The Quantum Geometry of Spin and Statistics
Authors: Robert Oeckl
Comments: 23 pages, LaTeX with AMS and XY-Pic macros, minor corrections and references added
Report-no: DAMTP-2000-81
Journal-ref: J.Geom.Phys. 39 (2001) 233-252

Both, spin and statistics of a quantum system can be seen to arise from underlying (quantum) group symmetries. We show that the spin-statistics theorem is equivalent to a unification of these symmetries. Besides covering the Bose-Fermi case we classify the corresponding possibilities for anyonic spin and statistics. We incorporate the underlying extended concept of symmetry into quantum field theory in a generalised path integral formulation capable of handling general braid statistics. For bosons and fermions the different path integrals and Feynman rules naturally emerge without introducing Grassmann variables. We also consider the anyonic example of quons and obtain the path integral counterpart to the usual canonical approach."

Enclosed is an abstract with which you are probably familiar.

Your statistical description is of course flawless, but I wonder if there's a rigorous application of Gaussian methods to these phenomena (or are such methods to be considered canonical?).

Just for the record: My comments are never intended to be adverse; they may be ill-informed, but I hope, never rude.

Thanks, Rudi

 

[r637h]

Did the Strong, Weak and Electromagnetic Forces exist before Planck Time? I'm assuming that they didn't.

 

[jeff]

Originally posted by r637h
Did the Strong, Weak and Electromagnetic Forces exist before Planck Time?

No.

Originally posted by pmb
It's a fundamental fact that nature is undeterministic at the quantum level

Deterministic means initial conditions determine evolution. In particular, the shrodinger equation governs the evolution of wave functions in a completely deterministic way, and although the uncertainty principle raises a host of epistemological issues, it doesn't necessarily represent a breakdown of determinism.

Originally posted by pmb
...probability comes in with the statistical nature of the experiments. In each measurement I can know both the position and the momentum exactly. But when I do this experiment a huge number of times what happens is that we get a spectrum of different values and we use the table of measurements that we get and we calculate the quantities dx and dp which are calculated statistically.

That's classical statistical mechanics.