[danbruc]

Compare it with temperature. If you run next to fast atom and you touch it, it doesn't actually feel hot. So temperature is not really a fundamental thing in nature but a higher level abstraction of the different moments of a large collection of particles. Temperature also becomes meaningless and the whole concept breaks down if you have only one or a few particles. It is of course a useful concept nonetheless.

So I could probably reformulate the question as whether fields are an abstraction of particles or particles are an abstraction of fields.

[toxikitty]

AFAIK the particles vs fields discussion is not the same as temperature vs fields.

At the risk of straying into quantum info territory:

- given all possible information about a collection of particles, you could compute the temperature. However, knowing the temperature doesn't allow you to determine info about particles uniquely (you can write down a density matrix, and not assign a pure state).

- the above doesn't hold for the case of particles and fields. Given a set of field frequencies and amplitudes, you could describe the positions of particles and probabilities of observing them. Given positions and probabilities of observing particles, you could compute the frequencies and amplitudes of the associated field.

We can describe any given set of particles (however big or small, however fast or slow) in terms of fields, and vice versa.

I like this comment :

When I studied quantum mechanics, my professor advised that I avoid the question "which is more fundamental?" and replace it with "which is more useful?".

From this stackoverflow link (http://physics.stackexchange.com/questions/122570/which-is-m...)

My QFT knowledge is rusty, so please correct me if I'm wrong.

[danbruc]

Looking at what is more useful is certainly a really good idea if your goal is to calculate and understand a specific problem. But I think you would miss out on something if you ignored the question of what is fundamental. And I personally am absolutely not interested in specific problems, I want to know what really is out there. Realism? Locality? Space? Time? Particles? Fields? What is really fundamental, what are just emergent phenomena?

[danparsonson]

If you haven't read it already, you might enjoy this:

http://www.amazon.co.uk/Decoding-Reality-Universe-Quantum-In...

The question of whether or not something is 'real' is a slippery one at the scales we're talking about.

[Retra]

There is no need for abstractions to have a strict hierarchy. they're all abstractions -- They employ some measure of indirection -- and thus neither are fundamental or 'real' if you think about it. The words "physical" or "real" won't help you to understand physics at all.

It's like you're asking if numbers are more fundamental than operations on them when you can't possibly have one without the other.

[selimthegrim]

I would be careful making analogies with temperature, it can be important when actually making a judicious choice of how to calculate observables! cf. https://en.wikipedia.org/wiki/Thermal_quantum_field_theory