Heisenberg's Uncertainty Principle

the real ramon

Hi, this my first post on the physics/Chemistry forum, and I'm afraid I'm going to have to start off with a heavy one:

Heisenberg's Uncertainty Principle: I did this a bit in Physics in Engineering at college but I never really fully grasped it and it's consequences.

Could someone explain the basic reasoning behind it for me as I recently read a piece arguing that it made the existence of a non-material aspect to the mind probable and thus was the best evidence for something approximating a soul or spirit that transcends matter, and I'm afraid to say I couldn't offer much in the way of an opinion on it, as I just don't know.

If someone wouldn't mind enlightening me on this subject I'd be very grateful.

Ta.

Son Goku

The uncertainty principle, or to call it by its correct name, the principle of indeterminacy, doesn't suggest anything spiritual at all, but is largely a mathematical outcome of Quantum Mechanics.

I'll try as best I can to explain tomorrow. It'll probably be a long post.

Civilian_Target

There's nothing religious or mysterious about it.

Basicly, all the uncertainty principle says is that there's a finite distance at which we can no longer determine somethings each location & momentum or it's exact energy or time, and this is a physical reality, a hard limit that cannot be surpassed.

Why is this so? Well, it's all to do with wave-particle duality, the fundemental reason quantum physics exists. All particles mathematically exist as a wave (and also, each wave as a stream of particles) - and where these two overlap we get a very small uncertainty. Its not that the particle doesn't have an exact location or momentum, it does, it is simply a limitation of our current physical models that no-matter how accurate our equipment, we cannot exactly determine something's position and momentum, and the more accurately we can determine one, the less accurately we can determine the other.

dudara

It essentially says that there is a limit of accuracy imposed upon us by nature. No more, no less. Don't read any kind of metaphysics or philosophy into it, other than questions on measurement.

A soul exists if you believe in it, not because of the Heisenberg Uncertainty Principle

nesf

dudara wrote:

A soul exists if you believe in it, not because of the Heisenberg Uncertainty Principle

Them's be fighting words in a science forum.

kippy

I always found this to be a good explaination:
http://zebu.uoregon.edu/~imamura/208/jan27/hup.html

nesf

To elabourate:

dudara wrote:

A dragon exists if you believe in it, not because of the Heisenberg Uncertainty Principle

nesf

nesf wrote:

To elabourate:

elabourate!Whats that?

nesf

Deleted User wrote:

elabourate!Whats that?

It's what happens when you've been drinking since 12 this morning after finishing your last exam.

It's kind of like phishing, but in reverse.

the real ramon

Thanks for the explanations, it's more or less what I remembered it to be. If it's all to do with the limitations of our present technology and nothing to do with the mind or some affect of observation of particles, then that piece was off target - the guy had a degree in physics and an MA in philosophy: makes you wonder!

Civilian_Target

A lot of people mistakenly explain the Uncertainty Principle as "you can't measure either position or momentum without upsetting the system and introducing an uncertainty given by the uncertainty principle" but in fact that's not true. That's a confusing the uncertainty principle with a quantum mechanical effect called "collapse of the wavefunction" - which is actually more likely to have philosophical consequences than the uncertainty principle.

Son Goku

The indeterminacy principle is mainly a statement on how position and momentum, or Energy and Time or a variety of pairs of quantities, are related on the Quantum level.

For ease of explanation I'll only take position and momentum and a single particle in a box.

The position of a particle is described by the spatial wavefunction of the particle. The spatial wavefunction gives the chance of a particle being detected at any given point in the box.
Let's label the spatial wavefunction with this symbol: (Ψ_q).


The momentum of a particle is described by the momentum wavefunction of the particle.
The momentum wavefunction gives the chance of a particle being detected with any given momentum.
Let's label the momentum wavefunction with this symbol: (Ψ_p).

If I write down the spatial wavefunction I can easily find out the momentum wavefunction by performing what is called a Fourier transform:
(Ψ_q) -> Fourier Transform -> (Ψ_p)
And vice-versa:
(Ψ_p) -> Inverse Fourier Transform -> (Ψ_q)

Now let's perform an experiment to find out where the particle is.
If I find the particle at point "A" that means that the spatial wavefunction (Ψ_q) has peaked at that point, because there is now a 100% chance of the particle being there.

So now let's perform a Fourier transform to find out what the momentum wavefunction (Ψ_p) is and see what value it peaked at, so we can figure out the momentum.

It turns out that the momentum wavefunction has now spread out over a huge range of momentum values so the particle could have any momentum.

If I measure the momentum, the momentum wavefunction peaks at single momentum value and the spatial wavefunction spreads out over several position values, so now the particle could be anywhere.

This is because a particle cannot have both a well defined (classically) momentum and a well defined position at the same time.
If the particle has one type of wavefunction peaked at a certain value, the other type of wavefunction has to be spread over several values.

If you have a single position, you have to have several momenta and vice-versa.
Or to put it another way, any process which collapses one wavefunction, uncollapses the other.

As Civilian_Target said, this has nothing to do with disturbing the system.
Position and Momentum are just related like this at the Quantum level.
I could explain how, but it's pretty "involved".

Professor_Fink

People tend to misinterpret the uncertainty principle, and I think this is what is leading to confusion here.

In quantum mechanics a particle can be in a superposition of states, i.e. it can be in more than one state at once. Each state it can be in has an associated amplitude, and the probability of a particle being measured in a given state is the square of the absolute value of its amplitude.

The most common type of measurements in quantum mechanics are projective measurements, and that is what we are effectively talking about when we talk of measuring position or momentum (the following can be easily extended to more general POVMs but that is left as an excercise for the interested reader ;-) ). When we make a projective measurement on a superposition, we collapse the wave function into one of the possible measurement outcomes, such as a position (more specifically an eigenvector of the operator we apply).

Classically, the state of a particle is determined by its position and momentum, and so it's state is described by two independant variables (x,p). In quantum mechanics this is not the case.

After a measurement of the position of a particle determines it is at position X, the particle is then in state |X>. The position completely determines the state of the particle.

A position can be transformed into a momentum, usually by applying a fourier transform. The problem, however is that when we apply a fourier transform to a position, we get a superposition of momentums. If we subsequently measure one of these, and then transform back into a position, we again get a superposition, and so we may measure a different position.

Mathematically we say that the momentum and position operators don't commute.

Heisenberg worked out a rigorous bound on how how close a measurement of momentum and then position is to a measurement of position and then momentum, and this is known as the uncertainty principal.

So, the uncertainty principal is really a measure of how well classical mechanics can describe a quantum system, rather than a measure of how much information is 'hidden' from us.

We know for (almost) certain that there is no hidden information, thanks to John Bell.

Professor_Fink

Sorry for the overlap with your post, Son Goku, but I wanted to point out that the uncertainty principal is a measure of how well classical mechanics can ever describe reality, which is quantum.

There is no hidden or lost information.

People who try to use the uncertainty principal as a) evidence for the existance of some god, b) the evidence for the existance of the soul, c) a mechanism for paranormal phenomena, d) an explanation of how homeopathy works (and there are people who try to use it for each of these) tend not to understand it, and often have a less than tenuous grasp on reality.