Can Multiple Infinite Quantum Fields Coexist in Spacetime?

[sci-guy]

The following must be false, since if it were true we'd have proof of a unified field, but can someone tell me why:

Why doesn't the fact that a quantum field, which by definition is infinite (correct me if I'm wrong), prove that there is essentially only one underlying quantum field? How can we have multiple infinite fields?

 

[betel]

I think you missed to post the important point after "fact that".
I don't get much sense out of your sentence this way.

 

[sci-guy]

I'm not sure exactly what you mean by that, but I'll try re-phrasing:

How is it possible to have multiple infinite quantum fields?

 

[betel]

Why should it not be possible?

 

[sci-guy]

At the risk of quoting from Wikipedia:

"In physics, a field is a physical quantity associated to each point of spacetime...Defining the field as 'numbers in space' shouldn't detract from the idea that it has physical reality. 'It occupies space..."

Maybe I'm wrong (if so, tell me), but wouldn't an infinite field then occupy all of space?

If so, in order for multiple fields to exist, they would need to occupy the same point in space. Is that possible, or am I missing something?

 

[betel]

I see.
Well, a field usually will not "occupy" space. They only assign a physical quantity to point of spacetime.
As a classical example at each point you could have a value for the temperature, humidity, wind, etc. each being a different field.
Now a quantum field will describe a certain kind of particle. Each specific particle will be an excitation of the field. If you want a classical analogue, take a violin string. A quiet string will be no particle. The first harmonic will be one particle etc.
Usually it will not be possible two excite to particles in the exact same point of spacetime.

 

[sci-guy]

I see what you're saying about temperature, humidity, wind, etc. But isn't that analogous to measuring electricity and magnetism, which are ultimately part of the same electromagnetic field?

You say that it's not possible to excite two particles at the same point in spacetime. Isn't that because there is ultimately only one field there? If there were innumerable distinct fields at every point, you could excite innumerable particles at every point.

 

[betel]

No. Each field has a certain value at each point of space time. For simplicity take the value one to indicate that there is a particle and 0 no particle.
Then the idea that at any point only one particle is possible does not exclude the existence of many different fields. And a field by definition has to have a value at every point.

There are however attempts to describe all particles using one field, so called superfields in supersymmetry. It is however just a description and not neccessary.

 

[sci-guy]

I see your point and thank you for the explanation; that's what I was looking for.

But it still raises the question: if a value of 1 in one field precludes a value of 1 in another field at the same point in spacetime, doesn't that imply a connection between the two fields (a value in one field affects possible outcomes in others), and hence an underlying unity?

 

[HallsofIvy]

I see your point and thank you for the explanation; that's what I was looking for.

But it still raises the question: if a value of 1 in one field precludes a value of 1 in another field at the same point in spacetime, doesn't that imply a connection between the two fields (a value in one field affects possible outcomes in others), and hence an underlying unity?

If that were true, yes, but "a value of 1 in one field precludes a value of 1 in another field" is simply not true. The values of one field are completely independent of the values of any other field.

 

[sci-guy]

Then you're saying, in our hypothetical example where a value of 1 means there's a particle at that point in spacetime, that it's possible to have another particle from another field at that same point in spacetime. Is it true that that's possible?

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P.S. I realize now that I posted this thread in the wrong forum; if moderators want to move it to "quantum physics," it's okay by me.