Heisenberg uncertainty principal and a Bose-Einstein condensate
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From the wikipedia article:Knotted said:
It also generates a problem that's termed the observer effect. If you measure one of the values then the other, you can't infer anything about the state of the particle during the first observation from anything you observe in the second observation.
MikeMcc said:
Well we have to be a bit careful about what values we are talking about. I don't think HUP applies to the energy of a wave/particle.
I've been reading up a bit and there is a very fundamental assumption being made in quantum mechanics and its the assumption of the principle of the conservation of energy. The mathematical description of quantum particles/waves in the Schrodinger equation is based on 'unitary operators' whose use is derived from the conservation of energy. So we cannot have uncertainty in the total energy of a closed system in any shape or form.
Here's a bit by Dirac:
"Some time before the discovery of quantum mechanics people realized that the connection between light waves and photons must be of a statistical character. What they did not clearly realize, however, was that the wave function gives information about the probability of one photon being in a particular place and not the probable number of photons in that place. The importance of the distinction can be made clear in the following way. Suppose we have a beam of light consisting of a large number of photons split up into two components of equal intensity. On the assumption that the beam is connected with the probable number of photons in it, we should have half the total number going into each component. If the two components are now made to interfere, we should require a photon in one component to be able to interfere with one in the other. Sometimes these two photons would have to annihilate one another and other times they would have to produce four photons. This would contradict the conservation of energy. The new theory, which connects the wave function with probabilities for one photon gets over the difficulty by making each photon go partly into each of the two components. Each photon then interferes only with itself. Interference between two different photons never occurs."
http://en.wikipedia.org/wiki/Theoretical_and_experimental_justification_for_the_Schrödinger_equation
So to answer story's question, the HUP does not apply to energy states and therefore does not apply to temperatures. Furthermore a lot of the weirdness seems to stem from this lack of uncertainty - the single photon going through both slits at the same time and interfering with itself and all that.
The (generalized) unceratinty principle applies to any set of two 'observables'. Postion and momentum are two examples of observables, not only that as a pair they are examples of conjugate observables which means there is a minimum uncertaintiy between the two.
In quantum mechanics energy is an observable too so it is subject to the uncertainty princple, it's conjugate observable would be time, but unfortunately time isn't an observable in 'vanilla' quantum mechanics*.
So uncertaintiy and energy aren't quite as straightfoward as the basic HUP involving momentum and postion, but that's no say the unceratinty principle does not apply to energy or that there cannot be unceratinty related to the measurement of energy.
*that's not say that time doesn't exist in vanilla QM or that it can't be quanitifed, it's just that observables must be associated with a self-adjoint operator and there is no such self-adjoint opertaor than be asscoiated with time.
In quantum mechanics energy is an observable too so it is subject to the uncertainty princple, it's conjugate observable would be time, but unfortunately time isn't an observable in 'vanilla' quantum mechanics*.
So uncertaintiy and energy aren't quite as straightfoward as the basic HUP involving momentum and postion, but that's no say the unceratinty principle does not apply to energy or that there cannot be unceratinty related to the measurement of energy.
*that's not say that time doesn't exist in vanilla QM or that it can't be quanitifed, it's just that observables must be associated with a self-adjoint operator and there is no such self-adjoint opertaor than be asscoiated with time.
camouflage
gaslit at scale.
story said:
Let's get working!
So am I to assume that part of the point of achieving the B-E condensate, is to explore this very question?
It seemed to me like such an obvious question, but it was not mentioned in the documentary.
I was astonished at the notion of being able to actually observe with the naked eye, the dual state of the atoms.
I love quantum wierdness.
But this is already possible, they've done it in labs, observed two-instances of the same atom at once. Must have seemed rather ordinary once achieved. Quatum-simultanious communications here we come eh.
Knotted said:
Not my phrase. If I'd written it, it'd have been QM in the "shut up and calculate mode" as opposed to anything that tries to interpret it, to *cough* "unconventional" QM such as that of David Bohm, to loop quantum gravity, to etc...
But I didn't.
kyser_soze
Hawking's Angry Eyebrow
Incidentally, my bday falls on the same day as the first BEC was created...was WELL chuffed to find that out...
kyser_soze
Hawking's Angry Eyebrow
FWIW, if you see 'vanilla' used as a suffix adjective, it means 'basic' or 'ordinary'..comes from vanilla sex...
story said:oooh
I'm listening....
I think only jcsd really knows what s/he is talking about.
My thinking is that laws of physics basically state things along the lines of:
"When stuff changes, then this feature nevertheless stays the same."
So ultimately its all about symmetries. The most obvious examples of these are the various conservation laws - conservation of momentum, conservation of energy/matter, conservation of charge etc. The one thing that's ordinary about quantum mechanics is that it follows conservation laws.
I've got a background in maths not physics but I can see immediately from the fact that QM uses unitary and symplectic operators that there's a hell of a lot of symmetry in this. Furthermore it all works like clockwork until, that is, something's measured and then things jump to particular (eigen)states. So all in all I expect quantum things to be quite well behaved, and intuitively I would expect BEC to behave in a well understood and predictable manner. I could be wrong though.
Anyway learning quantum field theory is too much of a headache for me at the minute, so there's not much more I can say.
Knotted said:
I don't think I really know what I'm talk about! Quantum physics is extremely hard and extremely easy to misinterpret.
Conservation laws tend to be stated in different ways, e.g. the conservation of energy is stated as part of the conseravtion of four momentum in special relativity. In quantum mechanics the conservation of energy becomes the time-independence of the Hamiltonian (the operator which describes energy in QM and which forr historical reasons has it's own special name)
jcsd said:
Its impossible to tell whether someone is casually explaining what they understand or is having to read up old lecture notes again. You probably don't want a reputation of being the urban75 authority on theoretical physics - people asking, "we need help, where's jcsd? Someone PM jcsd!"
But think of the smiles on their little faces.
jcsd said:
Now here I have a difficult point to make (that I'm unsure of) and a difficult question to ask. Though I should say that at this point we are very probably loosing our audience.
The point: The Hamiltonian comes originally from classical physics and describes the total energy of the (classical) system. Surely the form that the conservation laws are expressed in is something of a matter of convenience rather than anything deep. Can we not use Hamiltonians in special relativity?
This leads onto my question: In relativistic quantum mechanics, time is no longer independent, so what does this mean for the conservation of energy?
Now I realise that's a bugger of a question, so feel free to leave it.
ymu
Niall Ferguson's deep-cover sock-puppet
I'm loving this - don't understand enough to add anything much, but have the desire to dig out my pop science books and reread them.
So, that's the disclaimer to the following random note on HUP and energy: I remember reading summat about particles "borrowing" energy from the HUP to leap into new states that by rights they shouldn't have had enough energy to reach, but once there they can happily exist without the extra energy? (The analogy was a series of concentric hills - a ball settles in the valleys, but if you give it enough energy to get up the hill and over the top, it'll happily settle in the next valley).
It might only be a principle, but you can borrow energy from it. How cool is that?
So, that's the disclaimer to the following random note on HUP and energy: I remember reading summat about particles "borrowing" energy from the HUP to leap into new states that by rights they shouldn't have had enough energy to reach, but once there they can happily exist without the extra energy? (The analogy was a series of concentric hills - a ball settles in the valleys, but if you give it enough energy to get up the hill and over the top, it'll happily settle in the next valley).
It might only be a principle, but you can borrow energy from it. How cool is that?
spiralx
dirty techno junky
And extract energy from that - see the Casimir effect
http://physicsworld.com/cws/article/print/9747
http://physicsworld.com/cws/article/print/9747
.
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