h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Can anybody tell me why a Bose-Einstien condensate does not violate heisenberg's uncertainty principle?
I am assuming the position is known and the velocity is known.I am assuming the velocity is zero.

I am a bit unclear about this, but I believe it comes from the wave properties of matter. It has been shown that light can behave as both a wave AND a particle (see the guide entry on wave-particle duality). In a similar way, matter can behave as both a particle and a wave. At ordinary temperatures and masses then the wave-like nature of matter has a very small wavelength. As the temperature is lowered then the wave-like properties become more prominent. As bosons can exist in the same quantum state as each other then they tend to all sit in the ground state at these low temperatures. The wave-functions of the bosons start to overlap each other and the bosons begin to loose their individual identities. This is a Bose-Einstein condensate. It doesn't violate the HUP because the position and velocity cannot be exactly known (the wave-function is like a probability of finding the thing and it spreads out in space, therefore the condensate can be 'moving around' in the space occupied by the wavefunction).
For more information try doing a search on Altavista or similar for Bose-Einstein. The results are a lot of university groups working on the subject.

Wick

The uncertainty principle applies to all objects not simply subatomic objects. It is related to the de Broglie wavelength of the object and for anything larger than the simplest of objects it is too small in relation to the object itself to be measurable. For a Bose Einstein condensate this also applies. The velocity of the condensate is not zero as it it is not at absolute zero and therefore has an element of thermal motion.

Does this help?

Isn't the answer in the title article?

It would appear to me that HUP is a limitation of measurement and observation when establishing data relating to sub-atomic particles. It is not a governing law which describes the basis of reality.

In the case of a ground state boson or any other particle, it will have a definite velocity (in this instance when T = 0K, v = 0) and position however; when we attempt to measure the properties using photons that bounce off the target they inevitably disrupt the target to the extent that it will move thus although we have a reading it is instantly inaccurate and therefore useless in further calculations. HUP is not compromised.

Perhaps I am over simplifying? ...Or maybe I am just "Uncertain"?

I think we are discussing something deeper than our ability to carry out a measurement. The uncertainty about the position and momentum of a particle is 'built in' to quantum mechanics. It's not a question of our measurement altering the position or momentum because that assumes they were there as absolute, precise values to begin with. QM seems to say that the values are inherently uncertain and the more you try to pin down one value, the more uncertain you must be about the other.

It seems to me that QM is saying that there is an interval of space, time and mass that you cannot enter, squeezing down the space interval to measure position leads to an inflation in the time and mass interval thus destroying any precise data you had about momentum. Squeezing any of the values to realise more precise measurements will inflate the intervals of the other elements.

This does seem to be a fundamental reality rather than a description of imperfect technology. There is a thread running in the wave/particle duality topic where these issues are also starting to be discussed. Other views would be greatly appreciated.

Yes, it would appear that in my own unique and blunderous way I have given the impression that HUP is a failing of technology. This is wholly inaccurate and I offer my apologies.

What I should have made clear is that the effect I described whereby a photon is bounced off a target, such as an electron, that in turn causes a randomised recoil in the target is referred to as the Compton Effect. However; as has quite rightly been pointed out this is only part of the story.

Elementary particles, such as electrons, appear to randomly phase shift thus even in the ground state an electron would be said to have a lifetime in any one phase. I seem to remember that Schrõdinger posited equations that seem to suggest a ground state electron can be observed accurately are still subject to HUP as electrons pop in and out of phases over different lifetimes.

HUP, as already explained in this discussion, does indeed also apply to all objects regardless of size. In the case of a macroscopic object photons do still bounce off the target and change the momentum but the change in relation to the initial momentum of the object is insignificant.

This thread is associated with the Wave/Particle Duality thread and is fascinating for me in terms of organising thoughts and ideas in my own mind with others that have a much wider insight into this subject.

I am slightly daft, and this whole HUP is still slightly ellusive to me ... My primary confusion boils down to this: Does the Heisenberg Uncertainty Principle imply that a given particle's future is by nature indeterminate, or does it imply only that *we* are unable to figure out where it's headed because of the delicacy recquired for such a measurement?

Mr. Googoplex has alluded to the random phase shifts of electrons ... but still, is there any way of knowing if they are indeed random? The idea of a particle really moving about randomly just strikes me as specious ...