# I Fields as medium for light?

1. Jul 3, 2017

### FallenApple

It is said that light needs no medium. But light is just an excitation of the electromagnetic field in QFT. This excitation presumably propagates within that field at the speed c and once that excitation has left a point in space, the field has settled down to 0 energy again, analogous to pond returning to tranquility after a ripple goes through it.

2. Jul 3, 2017

### Staff: Mentor

No, the excitation is the field. The field is not something different from the excitation.

3. Jul 4, 2017

### FallenApple

so that is what is meant when people say that all electrons are the same? Because each one is the field

4. Jul 4, 2017

### Staff: Mentor

Each one is a particular kind of state (an "excitation" is one common term, the one you used in this thread) of the same field, yes.

5. Jul 4, 2017

### FallenApple

The only thing that might be unintuitive about that is the simultaneous occurrence of multiple states in one entity.

6. Jul 4, 2017

### Staff: Mentor

What does "simultaneous" mean? At any given point in spacetime, the field has only one state. But that state might not be a "one electron" state.

7. Jul 4, 2017

### hilbert2

The electromagnetic field does not have a special rest frame, unlike a material medium that sound waves can travel in.

8. Jul 4, 2017

### kith

I think that the terminology is a bit strange here. In QM, we generally have systems, states and observables/operators. I have seen the term "field" been used for all three of them.

A couple of years ago, I started a thread about some of this terminology.

9. Jul 4, 2017

### hilbert2

That's a good thread. I was thinking about something related to this last week, specifically, whether there's any quantum state of a field that's simultaneously an eigenfunction of the field operator $\hat{\varphi} (x)$ at all points $x$ (either spacetime points or equal-time points in some frame).

10. Jul 4, 2017

### haael

I disagree. Excitation is a particular solution of the field. In a broad sense, it's a solution that has energy. Thus, the energy has to be nonzero and it has to be defined.

There are solutions to fields that have zero energy or no energy at all (undefined). So there are fields that are not excitations.

Analogy: field is the air and excitations are sound waves. But air is not the sound.

11. Jul 4, 2017

Staff Emeritus
FallenApple, a while ago you posted a thread asking if it is possible to understand physics without being quantitative. Your difficulty here stems from trying to do just that. "Field" and "medium" have different properties when you look at the equations, but if you don't look at the equations you might find them hard to differentiate.

12. Jul 4, 2017

### Staff: Mentor

Yes, this is a better way of putting it. However:

This makes it seem like the field is a medium in which the excitations happen. I don't think that's correct. There is a field, which has some set of possible states. Some of the states in that set are called "excitations", others are not.

13. Jul 4, 2017

### haael

OK, field is the pressure and excitations are sound waves.

14. Jul 5, 2017

### vanhees71

This is nonsense written by careless popular-science-book writers. In quantum theory the system is in some state (pure or mixed) due to a preparation procedure. It's never simultaneously in several states.

15. Jul 14, 2017

### FallenApple

So the state of field is not considered as a whole across all points, just at a particular point in spacetime?

16. Jul 14, 2017

### Staff: Mentor

There is a state of the field at each particular point in spacetime. There is no such thing as a single state of the field "as a whole across all points".

Note that this is equally true of classical fields--any kind of field has a state at each point, not a single state across all points.

17. Jul 14, 2017

### FallenApple

Fields are rather abstract, so it seems that equations are a must here. I've also heard of the infinite array of harmonic oscillators analogy. Not sure it that is sufficient picture, but an array of oscillators seems highly different from a medium.

18. Jul 14, 2017

### FallenApple

Ah ok. So a medium can be analyzed as a whole, i.e finding momentum of the chunk that contains the propagation , finding the mass density of medium etc. But for a field, it's only the value at (x,y,z,t) that matters, which makes sense since a field point in and of itself cannot interact with another field point, unlike a medium which are molecularly chained though out the entire substance.

19. Jul 14, 2017

### Staff: Mentor

"Medium" is much too vague a term. If all it really means is "something that can produce waves", then an array of oscillators is a medium. But that's not going to help you much in actually solving problems.

Where did I say that? As noted above, "medium" is much too vague a term to be useful. Even in cases like sound waves in air, you don't analyze the medium (the air in this case) "as a whole". The medium is still a collection of points, and its properties (like the sound speed) can vary from point to point.

I don't understand what this means.

Not if you want to understand the dynamics. For that you need to understand the variation in the field from point to point, and how that is connected to the presence of a source. In the "array of oscillators" analogy, the oscillators at neighboring points are coupled, and you have to understand the coupling.

20. Jul 14, 2017

### FallenApple

But while you don't analyze the medium as a whole, you can still make statements about the whole. For example, if I want to find the average density of a medium, I'd just integrate, which technically is only analyzing each point, but is also summing them all up so that I can get a one number summary of the substance.

I was giving the momentum example as an instance of where I can make meaningful statements about the aggregate of the parts that make the whole.

Does coupling with the neighboring points roughly imply that only the immediate surrounding oscillators has an influence on the oscillation but points far away does not have an influence? Similar to a first order Markov Chain?

21. Jul 14, 2017

### Staff: Mentor

It implies causality--causal influences can only travel at a finite speed. That does not rule out influences that travel a long way, as long as they don't travel faster than that finite speed.

22. Jul 16, 2017

### Staff: Mentor

Exactly.

In fact you can by mathematical manipulation transform it into the so called 'second quantisation' formulation of QM:
https://pdfs.semanticscholar.org/2fb0/4475228ff385a44a16e3ba42b432d3bf5b17.pdf

All the above are equivalent formulations. Its just miraculous how QFT fields lead immediately to particles and is how fields and particles are unified.

But it must always be remembered in QFT what the fields are - they are fields of quantum operators operating on whats called a Fock Space - not fields in the classical sense.

Thanks
Bill