Are Probability Clouds and Fields in Quantum Mechanics Interconnected?

[misogynisticfeminist]

In QM, we have probability clouds, in QFT, its fields. I don't really hear people talking about probability clouds and fields in the same breath. Can the field be seen as something which attaches a certain probability to each quanta for each point in space? or has this already done? making this thread is essentially redundant. Also, is it exactly unphysical to see things in QM as probability clouds?

 

[vanesch]

In QM, we have probability clouds, in QFT, its fields.

As far as you have "probability clouds" in QM (this is not a really correct thing to say because it means you already have chosen a basis), you should know that these "clouds" are not clouds in real space, but in CONFIGURATION SPACE. Only for a single point particle is there an equivalence between real space and configuration space. For 2 particles, the configuration space is 6-dimensional ; for 10 particles, it is 30-dimensional. (minus some exchange degrees of freedom in the case of identical particles).

In quantum field theory, you have (again with the same caveats) "probability clouds" in the configuration space of the field which is infinite-dimensional. So the field doesn't take over the function of the "cloud" ; it takes over the function of the set of particles.
Note that the configuration space of a field by itself is already a big thing, so the space of possible "probability clouds" in that space is mindbogglingly big and complicated.


cheers,
Patrick.

 

[Hans de Vries]

Also, is it exactly unphysical to see things in QM as probability clouds?

Well, it does looks like clouds when viewed with the brandnew highest
resolution electron microscope (resolution $< 0.7 \AA$)

http://www.reed-electronics.com/semiconductor/article/CA528449?pubdate=5/1/2005

It will be very interesting to see this technology progress further.

Regards, Hans