jeebs said:
well it's not really a hard, solid, concentrated collection of "stuff", is it?
This response might sound naive because I'm only just getting introduced to quantum field theory, but can't we thinking of particles not as isolated clumps of stuff, but rather that each species of particle is really a localized disturbance in an all-pervading field?
What I mean is, the brief outline I have in my head of what QFT involves is that we have things like lepton fields and quark fields extending throughout spacetime, and what we consider particles are localized places where these fields have non-zero values.
Then we could start thinking of stuff we imagine as solid, tangible "matter" (eg. electrons) as something conceptually no different from light - which is a traveling disturbance of the electric/magnetic fields. We have no problem thinking that light isn't solid "stuff", so surely this extends to all other stuff that we traditionally consider matter if we consider all stuff as fields?
but then what does it really mean to say a "field" has a certain value at a certain position, what the hell is a field really? I'd like it if someone here who really knows their QFT could either elaborate or rubbish what I've just said.
I'm nowhere near an expert in QFT, but AFAIK this is a correct description, with some
caveats.
The first is that the excitations need not be localised at all - they can occupy arbitrary
volumes of space. A second one is the concept of the value of the field. For a classical
field, a single (scalar or not) value is all you need, but a quantum field, like all quantum
quantities, behaves a lot like a stochastic variable, and thus needs (ideally) a full set
of moments <phi^n>, n from 1 to infinity, for a complete characterisation (though in
practice it often suffices with only the two first ones, <phi> and <phi^2>).
For an example of how this works, imagine the simplest scenario possible, that of an
ideal, non-interacting scalar field, and a single-quantum excitation given by the following
pure state: |Psi> = integral f(k) a*(k) |G>, with |G> the ground state of the field, and
f(k) a square normalisable function in momentum space with the correct weight. If you
try to compute the _value_ of the field, you'll get zero everywhere (despite not being
in the vacuum state). However, if you compute the momentum or the energy, which
depend on the squared field and its spatial and temporal derivatives, you'll get an
energy or momentum density that takes values in a support that's basically the Fourier
transform of f(k), and zero everywhere else. Thus, an ideal single-quantum excitation
can be considered as a 'bump' of energy and momentum of the field.
Of course, the above is not physical, as real fields are interacting, and the whole
scenario gets a lot more complicated, but it serves as both an illustration and as
a way to connect with the concepts already learned from non-relativistic QM.
jeebs said:
*actually something just occurred to me about a difference between light and the matter fields - light can only travel at c, as noted from Maxwell's wave equation, but particles with "mass" can have a range of velocities, so there has to be something different there. Maybe I'm spouting a load of nonsense here...
Fields can be massless OR massive ;-)