B Philosophical Perspective: Need for Properties in a Relativistic Field?

[bambambambambam]

Philosophically speaking is there a need for a relativistic field to have no properties without an object on it? It seems like all throughout the history of mathematics there have been fields designed to describe the dynamics of specific particles, but isn't that necessarily a limit to their functionality?

Am I just imagining things or wouldn't it be possible to create a field with only properties relative to the objects it describes?

 

[ohwilleke]

For better or for worse, in general, classical formulations of general relativity have vacuums that have non-trivial properties. This is also generally true of space-time based quantum gravity theories like loop quantum gravity.

 

[bambambambambam]

I'm referring to the mathematical formulation of a relativistic field. Isn't it necessary for the field to have no properties without an object on it? Traditionally it seems like they all have some sort of mathematical properties that are their limits to describe things found on them.

 

[ohwilleke]

I'm referring to the mathematical formulation of a relativistic field. Isn't it necessary for the field to have no properties without an object on it?

No. It is not necessary. It is a very plausible thing to think, but it is not, in general, true.

 

[strangerep]

I'm referring to the mathematical formulation of a relativistic field.

Which formulation? (I have no idea of your background.)

When I see those words, I think: "Wignerian classification of elementary quantum fields as unitary irreducible representations of the Poincare group." But I'm guessing that's perhaps not what you had in mind?

Isn't it necessary for the field to have no properties without an object on it?

At the most fundamental level that we know of, quantum fields are the "objects".

 

[bambambambambam]

Well for example hilbert space exhibits orthogonality. Basically I am just thinking it seems like the formulation of any mathematical space inherently exhibits quantum mechanical problems of measurement. We make a space to fit a rule we find for some naturally occurring phenomena and suddenly it's no longer fit to describe others. It's sort of a moot point from the perspective of usefulness but my perspective is more philosophical/historical and I'm just curious what anyone might know about the process of formulating the properties of a space or the struggles that come from attempting to create a new one to fit some purpose, etc.

 

[newjerseyrunner]

Spacetime certainly has properties without anything in it.

If I remember correctly, completely empty space has an enourmous pressure and will expand rapidly?

In quantum physics it's also simply not possible to have space with nothing in it. You can be sure you start with no particles and you can be sure you ended with no particles. You can say nothing definitive about the in between.