PDA

View Full Version : Quantum Theory and the Uncertainty Principle.

Artemis Fowl
2006-May-10, 10:15 AM
I have just read a brief description about the Quantum Theory and The Uncertainty Principle of Werner Heisenberg. I would like to know more about them. Is is theory really applicable in the universe?

Ken G
2006-May-10, 10:25 AM
Yes, the theory is the most fundamental truth about the universe at the smallest scales that we have ever encountered. It explains, for example, the size of atoms. Newton's laws applied to electic forces allow for any size at all, it is the uncertainty principle, along with those forces, that specify the size we observe.

Artemis Fowl
2006-May-11, 09:47 AM
But what does the uncertainty principle actually clarify? I have read about a book on Quantum Physic and Reality named "In Search Of Schrodinger's Cat". If you see the cover it shows a cat alive and dead at the same time. After further inquiry into this strange phenomenon I found out that this is something related about the uncertainty principle. Could you please elaborate on the principle?

gwiz
2006-May-11, 10:53 AM
The Uncertainty Principle is the fact then if you try to measure exactly where something is and where it's going, there is a minimum level of uncertainty that you cannot better. Basically, this is because any measurement method disturbs what it is trying to measure.

The dead/alive cat is something else. Quantum theory is a theory about probability. You can predict the probability of what something is going to do very accurately, which is fine when what you're interested in is made up of a lot of particles and the average of what they do is good enough, but vague for a single particle. One interpretation is that it's behaviour only becomes certain when it is observed. The cat is a thought experiment where the fate of a cat in a box depends on what a single particle does. The theory is that you only know if the cat is alive or dead - "the probability wave collapses" - if you open the box to observe it.

My opinion is that the cat is also an observer and knows if it is alive.

swansont
2006-May-11, 12:01 PM
The Uncertainty Principle falls out of a the porobablistic nature of QM. Momentum and position, for example, are conjugate variables (as are energy and time). They are described by a wave function and are Fourier transforms of each other, so there is a limit to how well you can determine each value. If you know one exactly, it means you have a delta function; the FT of that function is a constant, meaning that all values are possible.

Cougar
2006-May-11, 02:52 PM
The Uncertainty Principle is the fact then if you try to measure exactly where something is and where it's going, there is a minimum level of uncertainty that you cannot better. Basically, this is because any measurement method disturbs what it is trying to measure.
I believe most physicists (at least many) will tell you that the uncertainty is NOT because your measurement method disturbs what you are measuring. Rather, it is an intrinsic characteristic in the quantum realm.

As an aside....

While walking with Heisenberg, the physicist Felix Bloch, who had just read Weyl's Space, Time and Matter, felt moved to declare that space is simply the field of linear equations. Heisenberg replied, 'Nonsense. Space is blue and birds fly through it.'"

Cougar
2006-May-11, 02:59 PM
The Uncertainty Principle is the fact then if you try to measure exactly where something is and where it's going, there is a minimum level of uncertainty that you cannot better.
To clarify this a bit, the more you know about a particle's location, the less you can know about its momentum... and vice versa. Location and momentum are the two commonly referred-to conjugate variables that Swansont mentioned.

gwiz
2006-May-11, 03:19 PM
I believe most physicists (at least many) will tell you that the uncertainty is NOT because your measurement method disturbs what you are measuring. Rather, it is an intrinsic characteristic in the quantum realm.

Don't claim to be an expert, but don't you get the same answer whichever way you look at it? I was just trying to keep things as simple as possible for someone who's never encountered the ideas before.

Spaceman Spiff
2006-May-11, 03:35 PM
As Cougar says, experiments have verified that only the creation of an *opportunity* to measure/observer a certain event is enough to see the whacky world of the Heisenberg Uncertainty Principle in action. i.e., the idea that an observer is needed to "collapse the wave function" has been demonstrated to be bunk. Weirdness happens whether or not we are actually in the act of illuminating our sample with other electrons or photons. And even when we are, the magnitude of the effects is usually many times larger than those imposed by the energy/momentum transfer from the "illuminating" particles.

And "Schroedinger's Cat" was put forward as a poke in the eye at some of the early interpretations of quantum mechanics - it was never intended to be taken literally and it does not apply at all to the real world. Cats are macroscopic objects composed of zillions of quantum particles, far more than is necessary to produce completely incoherent "noise" that totally swamps the weirdness effects of individual quanta (such as the HUP). Unfortunately, the punchline was lost amongst some popularizers of science.

Nereid
2006-May-12, 01:16 PM
Somewhat off-topic, what is the largest 'cat' (of the Schr&#246;dinger kind) that has been made/observed to date? What sorts of such 'macroscopic cats' are there?

Cougar
2006-May-12, 02:13 PM
Somewhat off-topic, what is the largest 'cat' (of the Schrödinger kind) that has been made/observed to date? What sorts of such 'macroscopic cats' are there?

Maine Coon? :D

http://www.xmission.com/~dcc/coon1.jpg

Spaceman Spiff
2006-May-12, 02:59 PM
Somewhat off-topic, what is the largest 'cat' (of the Schr&#246;dinger kind) that has been made/observed to date? What sorts of such 'macroscopic cats' are there?

That's a good question. I am vaguely aware that there are experiments being done at the "meso level" that lie between that of systems containing small numbers of quanta and the "macroscopic". Not my field. Maybe someone else knows.

Ken G
2006-May-12, 05:20 PM
Before we get too deeply into the realm of macroscopic quantum mechanics, perhaps we should be sure the OP has been satisfied. I think the key idea in the uncertainty principle is one of limits on information-- we tend to think that reality encodes infinitely precise information about everything at all times, but quantum mechanics shows that this is not the case. Reality does not need infinitely precise information about everything, and indeed appears to be unable to handle such precise information. There is a limit to what we can know about reality, and what we need to know in order to understand what is going to happen. To choose a concrete example, the size of atoms is determined by this lack of complete information. In Newtonian physics with two bound charges, the square of the momentum of the electron is inversely proportional to the separation. But the uncertainty principle essentially says that in order to know that you have a smaller and smaller separation, what you know about the momentum must become increasingly unclear, and this uncertainty is inversely proportional to the separation. So Newton is telling us that the momentum can only rise inversely with the square root of the separation, but Heisenberg says that the very uncertainty in the momentum must rise inversely with the separation itself, so the uncertainty would eventually have to dwarf the momentum itself. That's impossible, so atoms may not be arbitrarily small. They can be no smaller than when the uncertainty in the electron momentum, from Heisenberg, is of the same order as the momentum itself, from Newton. That comes when p^2/m ~ e^2/r, where r ~ h/p, so substituting yields p ~ me^2/h, or r ~ h^2/me^2, and that's the Bohr radius of an atom in a nutshell.