The Heisenberg Uncertainty Principle (HUP)

Here are the original posts that led to this one. Non-italicized posts are nemesio, italicized ones are not nemesio.

Originally posted by AThousandYoung
That's the thing though. The HUP states that it is not predictable, period, by the very nature of matter. It's very confusing and counterintuitive, but that's how it is. There is no "hidden" information that we just can't detect that determines how things come out. You misunderstand the HUP.

I don't know if this discussion is relevant to this thread; maybe you
could start another (copy my post as a point of departure):

It was my understanding that the process of measuring one of the
variables made the other unknowable. I have done some reading
and have learned that, while this is true, the imperfection of the
manner of measurement (in that measuring adds energy to the
system) is not the sole affecting factor.

I learned that, with theoretical perfect instruments, knowing one
would still make the other mathematically unknowable. I can
(barely) follow the forumla that demonstrates this, and can plug
in numbers and so forth. I understand its application, but I don't
understand it from a theoretical level. Could you explain this further?

The reason I ask is because it would seem that the information is
there but unattainable. It makes it practically unavailable, but
theoretically present.

(Again, this seems a departure from the tack of this thread, so if
you want to start another one, that's fine.)

Originally posted by AThousandYoung
No particle simultaneously has both a perfectly defined location and momentum. If you measure one, the result you get will be truly random, guided by certain probabilities but otherwise random. If we could know both these things, then maybe you'd be right. However we would no longer be in our universe, because in our universe, both things do not exist with perfect definition at the same time.

Yeah. This. Can you explain it to someone with a less proficient
understanding of physics/high mathematics?

Theoretically, if we could trace all of these variables, we would
be able to predict every action of every person

Originally posted by AThousandYoung
We would to a great extent, but not absolutely, 100.0000000...% perfectly.

Hmm. It would seem that, as the number of variables that could be
traced approaches infinity, the prediction would approach 100% accuracy.
No?

I know that I am out of my league mathematically and philosophically here,
so I am happy to sit on your knee and learn a bit.

Nemesio

Originally posted by Acolyte
The conventional one (the Copenhagen interpretation) is that the information simply isn't there until you obtain it by measurement, and that the values of the parameters are randomly distributed until you fix them by whatever process you use to measure things. The reason most scientists assume this, it seems, is that they'd like to carry certain concepts over from statistics and probability, not because they've shown it's actually what goes on.

Is this the bit about Schrödinger's Cat Paradox? That the cat is
both simultaneously dead and alive at the same time?

If so, it's another example of something I understand conceptually
and can understand in the context of a mathematical equation, but
isn't something I understand intellectually/intuitively.

Perhaps you could give a lesson in another thread?

Please?

Nemesio

OK. To start with, here's a good website:

http://c2.com/cgi/wiki?HeisenbergUncertaintyPrinciple

This is good that we're discussing this. I am procrastinating from studying for my QM final tomorrow morning. This might get me in the spirit.

There are six postulates of QM according to

http://vergil.chemistry.gatech.edu/notes/quantrev/node20.html

Part of one of these postulates according to that website is:

"The state of a quantum mechanical system is completely specified by a function that depends on the coordinates of the particle(s) and on time. This function [is] called the wave function or state function"

What does this mean? Well, take out a piece of paper (or imagine it). On the paper, make a graph like you did in algebra class in high school. On the horizontal axis position in one dimension (say, x) will be the variable. On the vertical axis "wave intensity" (WI) will be the variable. What is "wave intensity"?

Well, if one were to make another graph similar to this one but with the square of WI as the vertical axis, one would have a position vs probability graph. That is, on this second graph, if you were to take a very small part of the x axis - very tiny (dx it's called in calculus) then the area between the x axis itself (where WI = 0) and the graph of WI^2, and between the two edges of the very small area dx represents the probability that if one were to measure the position of the particle then you'd get the answer that it's within dx.

Confusing, I know.

Now, in classical physics, the wave function for the center of mass of an object would be a spike on this graph. Absolute certainty that the object lies within that spike. If you measure the object's position in QM, the wave function changes to look like that spike, so every measurement you make afterwards will give the same answer.

However, if you took a particle in exactly the same state that the first one was in - exactly the same - and made the same measurement, you might get a different answer, and that wave function would collapse around this answer instead.

How does velocity (or momentum, which is velocity times mass) get involved?

Here's another website: http://216.239.63.104/search?q=cache:2QVxtOaCJkgJ:www.phys.ufl.edu/~pjh/teaching/phy4605/notes/measurement.pdf+momentum+%22collapse+wave+function%22&hl=en

Disclaimer - I don't understand that well what part of the graph velocity is. However, I think because of how my textbook describes it (David J. Griffiths Introduction to QM 2nd ed), in which wavelength and position are shown to be incompatible and then the Debroglie formula is used to convert wavelength to momentum:

Velocity is measured by the regularity of this graph. If you've taken trigonometry then you know what the sine graph looks like. If not, here are a couple pictures:

http://www.krellinst.org/UCES/archive/resources/trig/plot8.gif

http://www.krellinst.org/UCES/archive/resources/trig/plot11.gif

You can see that sine graphs have a regular, repeating pattern. I think that the sharper the bumps in the pattern (the more frequent the graph hits zero as it goes along x), the higher the momentum. I'm not sure. The more perfectly regular the pattern, the more sharply defined the momentum is. Now contrast this with a well defined position (focus on the tallest, sharpest spike):

http://www.maths.soton.ac.uk/staff/Andersson/MA361/img17.png

That spike is the only spot that has any significant height. Period. For any x not near that spike, the wave function is about zero. Think of an infinitely long line with one spike in it. There's no regularly repeating sine function pattern there. The momentum is not well defined. When the momentum is well defined, which of the infinite bumps of the sine function is the particle in? It has an equal probability of being in any of them, over the entire infinite range of position, as x goes from negative infinite to positive infinity.

Well defined momentum requires a regularity of pattern of the wave function. Well defines position requires a spike like shape with no overall repeating pattern. The two are incompatible.

Here's an interesting thought experiment:

Take a particle in any state. Now measure it's position. You get some result P1. The wave function has now collapsed to a spike. Now measure the momentum (without altering the particle in any way - this can be done, there were some experiments done somehow recently that prove this if I remember correctly). You get a momentum. Call it M1. The wave function collapses to a sine wave. Now measure the position, without affecting the particle. The wave function collapses to a spike, and you get a result P2. Even though you did not in any way modify the particle except by switching measurements from position to momentum and back, P2 does not necessarily equal P1. You keep changing the particle from something with well defined position to one with well defined momentum and back, which alters the state the particle is in, simply by trying to define them.

This is a subject of much debate and has been ever since QM appeared, and from what I understand Hidden Variable theories are generally considered unlikely. Einstein was a believer in the Hidden Variable idea and John Bell proved that Einsteins proof of it was flawed. Here's a website about the Hidden Variable interpretation of QM:

http://en.wikipedia.org/wiki/Hidden_variable_theory

Hmm. It would seem that, as the number of variables that could be
traced approaches infinity, the prediction would approach 100% accuracy.
No?

Yeah, that makes sense. I'd imagine that there would be a greater weight given to those variables within the brain of the person making decisions however, which might limit this effect somewhat. Or maybe not? I don't know.

Interesting thing to think about.

Is this the bit about Schrödinger's Cat Paradox?

I haven't really studied that paradox enough to understand it.

You seem to be falling into the standard trap of Physics. Physics as a subject attempts to model the natural world as observed. All the equations, laws and so on are models: they are not descriptions of what the universe is. The attempt to understand the model is interesting as it often shows weakeness in that model, or leads to further refinement of the model, but it does not lead to understanding of the universe itself, only to better understanding of the model.

When people start with the cat or the demon, it shows a problem with the approach, particularly in the field of quantum mechanics. The model is not extendable beyond its application to quantum events: phrase it using a macroscopic thing like a cat and it doesn't make sense. So what. It isn't meant to. It is only meant to give you the mathematical tools to evaluate and predict ensemble quantum behaviour, not to explain it.

All the equations, laws and so on are models: they are not descriptions of what the universe is.

Models are descriptions. I think you are mistaken.

The attempt to understand the model is interesting as it often shows weakeness in that model, or leads to further refinement of the model

This is true.

but it does not lead to understanding of the universe itself, only to better understanding of the model.

That depends on how you define "understanding of the universe." If you can't use your interpretations of your perceptions to "understand the universe" then there's no way to do so, unless you define it in some weird way.

The model is not extendable beyond its application to quantum events: phrase it using a macroscopic thing like a cat and it doesn't make sense.

Yes it does. The reason why they talk about momentum instead of velocity most of the time is because mass figures into the uncertainty equations. Large masses make uncertainties insignificant. And/or when you have large numbers of particles (such as in macroscopic objects) they are each uncertain but the probabilities average out to something you can measure with a certain amount of reliability.

I just took a quick glance at the SC Paradox in my text. It seems that the paradox is resolved by defining "measurement" properly, and the "measurement" that causes the collapse of a wave function is when the Geiger counter in the box is triggered, which occurs before the cat is killed. So the cat is alive or dead regardless of whether someone looks in the box. It's not a paradox.

Alas it seems the trap is truly sprung.

Models is as models does. Momentum, velocity and such are used because they are based on the particle model of quantum behaviour. Switch to the equivalent wave model and they vanish. Just because Green's theorm can be used to get from quantum state models to macroscopic models doesn't make it right. After all, Green's theorm, while used heavily, is easily disproved. Not that I can remember the disproof offhand.

Originally posted by Toe
Alas it seems the trap is truly sprung.

Models is as models does. Momentum, velocity and such are used because they are based on the particle model of quantum behaviour. Switch to the equivalent wave model and they vanish. Just because Green's theorm can be used to get from quantum state models to macroscopic models doesn't make it right. After all, Green' ...[text shortened]... , while used heavily, is easily disproved. Not that I can remember the disproof offhand.

"Particle model of quantum behaviour"? "Equivalent wave model"?

I have no idea what you are talking about. There's only one model incorporating both particle and wave characteristics as far as I understand it. They are related by the de Broglie formula. The more particle like something is, the less wavelike it is. The more wavelike it is, the more precisely can it's momentum be defined, and the less precisely can it's position be defined. The particle/wave duality is another way of looking at the uncertainty principle.

Green's Theorem has to do with taking integrals over a planar region.

What the hell are you talking about? Can you explain please?

You must be trolling me.

Originally posted by squaccerman
I once understood the HUP completely, but then I didn't know how fast I was moving and walked into a wall, suffreing concussion and causing me to forget...

Originally posted by Toe
Alas it seems the trap is truly sprung.

Models is as models does. Momentum, velocity and such are used because they are based on the particle model of quantum behaviour. Switch to the equivalent wave model and they vanish. Just because Green ...[text shortened]... y disproved. Not that I can remember the disproof offhand.

Originally posted by AThousandYoung
If so, it's another example of something I understand conceptually
and can understand in the context of a mathematical equation, but
isn't something I understand intellectually/intuitively.

Originally posted by DoctorScribbles
Nobody understands quantum physics intuitively, not even quantum physicists. They themselves only understand it as a descriptive and predictive model of certain physical events. Much like there is no definite quantum state before an observation is made, there simply is no intuitive meaning to quantum mechanics.

If you think about it, th ...[text shortened]... en really, it's your lack of familiarity with interacting with quantum events that is to blame.

Originally posted by nemesio
Actually I said this. He was quoting me from another thread.

Can you please (try to) explain to me what it means to say that
'there is no definite quantum state before an observation is made?'

Nemesio

Originally posted by bbarr
He mispoke. There is a definite quantum state before an observation is made, and that state is exhaustively described (supposedly) by S's wave equation. It is at measurement that the system resolves into a determinate classical stat ...[text shortened]... inciple predict the result if we knew all the relevant variables).