A Understanding Barandes' microscopic theory of causality

[Rev. Cheeseman]

vacuum = empty = containing absolutely nothing.

Thank you, but what about this statement "The vacuum is a very special state of the field"? The field is something when there are particles, gravity, electromagnetism, etc. but if there is nothing at all the field is just absolute nothing?

 

[A. Neumaier]

Thank you, but what about this statement "The vacuum is a very special state of the field"? The field is something when there are particles, gravity, electromagnetism, etc. but if there is nothing at all the field is just absolute nothing?

... then the field contains absolutely nothing! This is a significant difference.

Don't give too concrete meanings to abstract concepts:

The field can be in many physical states, and one of them is the vacuum state. It describes an empty universe. A field in a 1-particle state describes a universe consisting of a single particle. etc.

It is like the concept of space. Space can be empty or nonempty, but it isn't "there'' - nothing to point to.

 

[Rev. Cheeseman]

... then the field contains absolutely nothing! This is a significant difference.

Don't give too concrete meanings to abstract concepts:

The field can be in many physical states, and one of them is the vacuum state. It describes an empty universe. A field in a 1-particle state describes a universe consisting of a single particle. etc.

It is like the concept of space. Space can be empty or nonempty, but it isn't "there'' - nothing to point to.

Sorry, but it gets confusing to me as someone who is more familiar with classical physics. Is the field itself (not the quantum field but this particular field that we are talking about. Not just inside but the whole field) something or nothing? Is it finite or infinite?

 

[A. Neumaier]

Sorry, but it gets confusing to me as someone who is more familiar with classical physics. Is field (not the quantum field but this particular field that we are talking about) something or nothing? Is it finite or infinite?

I was always talking only about the many-component quantum field that describes everything that exists.

A quantum field is (ignoring technical subtleties that don't matter here) an assignment of N-point function values to each list of N points anywhere in spacetime, for each N. The values <phi(x)> at a single point x (thus N=1) tells what of phi is present at x. If it is identically zero we say that nothing of phi is there.

Just like in shallow water waves, a water field assigns to each point on a ground surface the height of water above that point. If it is identically zero, no water is present.

 

[Rev. Cheeseman]

I was always talking only about the many-component quantum field that describes everything that exists.

A quantum field is (ignoring technical subtleties that don't matter here) an assignment of N-point function values to each list of N points anywhere in spacetime, for each N. The values <phi(x)> at a single point x (thus N=1) tells what of phi is present at x. If it is identically zero we say that nothing of phi is there.

Just like in shallow water waves, a water field assigns to each point on a ground surface the height of water above that point. If it is identically zero, no water is present.

Ok, so in that context, field is finite because we choose to assign some numbers to some particular points in an area.

But this particular field (i.e vacuum) we are talking right now is not quantum field, isn't it? A field without anything else represent absolute nothing while a field with 1-particle state represent a universe with a single object.

So, a field is nothing but just a mathematical abstraction especially representing a particular state or a smaller area in an area. If there is something, then the field is something and if there is nothing, the field is nothing. If we choose to pick only a small area within a particular area, that field is finite. But is it possible to assign numbers if the field is infinite?

I'm not sure if I 100% get what you mean but quantum physics is surely incomprehensible to many people.

 

[A. Neumaier]

Ok, so in that context, field is finite

A shallow water field is finite. A relatvistic quantum field, however, extends over all of spacetime. One can restrict it to finite regions, of course, but the field extends beyond these.

But this particular field (i.e vacuum)

The vacuum is the quantum field attached to an empty infinite universe, in the same way a zero water height field is attached to an empty finite water basin.

we are talking right now is not quantum field, isn't it?

A quantum field phi is always in some state, and if the universe is empty (i.e., does not containy any phi, in the sense that <phi(x)>=0 everywhere) , this state is refered to as the vacuum state of the quantum field. Here phi can be an electron field, a photon field, a graviton field, a neutrino field, depending what you substitute for phi.

So, a field is nothing but just a mathematical abstraction especially representing a particular state or a smaller area in an area.

No, in the entire universe. Just as a water field is just a mathematical abstraction repesenting water heights in the entire water basin, even when most of it is empty.

If there is something, then the field is something and if there is nothing, the field is nothing.

There is something in a region X iff the field values <phi(x)> is nonzero for (almost) all x in X

If we choose to pick only a small area within a particular area, that field is finite. But is it possible to assign numbers if the field is infinite?

The space to which the field refers is infinitely extended but the field value at every point is finite. Think of the temperature anywhere in the universe.