Philosophical Perspective: Need for Properties in a Relativistic Field?

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Discussion Overview

The discussion explores the philosophical implications of relativistic fields and their properties, particularly whether a field can exist without properties in the absence of objects. Participants examine the historical and mathematical context of fields in physics, questioning the necessity of properties in relation to the objects they describe.

Discussion Character

  • Philosophical perspective
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants question whether a relativistic field can exist without properties when no objects are present, suggesting this might limit the field's functionality.
  • Others argue that classical formulations of general relativity and quantum gravity theories typically involve vacuums with non-trivial properties.
  • A participant emphasizes that it is not necessary for a field to lack properties without objects, proposing that this is a plausible but not universally true assertion.
  • There is a discussion about the mathematical formulation of relativistic fields, with one participant referencing the Wignerian classification of quantum fields.
  • Another participant reflects on the inherent issues in mathematical spaces, particularly regarding quantum mechanical measurement problems and the historical context of formulating properties of spaces.
  • One participant asserts that spacetime possesses properties even when devoid of matter, mentioning concepts like pressure in empty space and the nature of quantum physics regarding the existence of particles.

Areas of Agreement / Disagreement

Participants express a range of views, with no clear consensus on whether a relativistic field can exist without properties in the absence of objects. The discussion remains unresolved, with competing perspectives on the nature of fields and their properties.

Contextual Notes

Participants highlight limitations in understanding the properties of fields, including dependence on definitions and the historical context of mathematical formulations. There are unresolved questions about the implications of quantum mechanics on the nature of fields.

bambambambambam
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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?
 
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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.
 
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.
 
bambambambambam said:
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.
 
bambambambambam said:
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".
 
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.
 
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.
 

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