Why Does Equivalence Principle Imply Non-Existence of Higher Spin Fields?

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Discussion Overview

The discussion revolves around the implications of the equivalence principle in general relativity (GR) on the existence of higher spin fields, particularly those with spin greater than 2. Participants explore the theoretical foundations, including references to the Weinberg-Witten theorem, and question the validity of claims regarding the nonexistence of such fields.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant questions the assertion that the equivalence principle forbids higher spin fields, expressing confusion over the reasoning behind this claim.
  • Another participant uses the analogy of a bicycle wheel to challenge the applicability of the equivalence principle to the concept of spin in fields.
  • A reference to the Weinberg-Witten theorem is made, suggesting that it provides a framework for understanding the limitations on massless particles with spin greater than 1 in renormalizable quantum field theories.
  • Some participants argue that there are arguments against the existence of spin greater than 2, while others assert that such arguments cannot be absolute, citing the construction of free fields of arbitrary spin by Weinberg.
  • Questions are raised about the mechanisms behind the arguments for prohibiting spins greater than 1 and 2, as well as how supersymmetry (SUSY) might provide a loophole in these arguments.

Areas of Agreement / Disagreement

Participants express disagreement regarding the implications of the equivalence principle and the validity of claims about the nonexistence of higher spin fields. Multiple competing views remain on the interpretation of the Weinberg-Witten theorem and its consequences.

Contextual Notes

There are unresolved questions about the definitions and assumptions underlying the equivalence principle, the nature of fields, and the implications of the Weinberg-Witten theorem. The discussion reflects a range of interpretations and theoretical positions without reaching consensus.

ismaili
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I was told that the existence of higher spin fields whose spin is higher than 2 is forbidden by "equivalence principle" of GR(general relativity).

But after considering about it, I can't understand why equivalence principle could imply the nonexistence of higher spin fields (>2).

Could anyone explain this?
Thanks
 
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I cannot understand such a statement.
A wheel from my bicycle has very often a spin incredibly much larger than 2.

If you don't have first-hand information, better forget it completely.
But if you can have an explanation of this statement, tell me, I would like to know.

Maybe the whole point lies in the word "field" and a wheel has no relation to a field!
First of all, why was it that photons have spin 1?
And why should quantum gravity be a spin 2 field?
I think in both cases this can be traced back to the form of the classical Lagragian.
I can only remember how that goes for electrodynamics.
 
Last edited:
It's called the Weinberg Witten theorem, that's all I can say to u.
 
ismaili said:
I was told that the existence of higher spin fields whose spin is higher than 2 is forbidden by "equivalence principle" of GR(general relativity).

This is a very inaccurate statement. A more accurate version from http://en.wikipedia.org/wiki/Weinberg–Witten_theorem says:
''no massless (composite or elementary) particles with spin j greater than one are consistent with any renormalizable Lorentz-invariant quantum field theory excluding only (nonrenormalizable) theories of gravity and supergravity.''

References to the original papers (where you can find more details about the precise meaning of this statement) are given there, too.
 
Nevertheless there is an argument that spin greater than 2 is forbidden completely.

questions:
- how does the argument for spin > 1 work?
- how does the argument for spin > 2 work?
- how does SUSY bypass the first argument? what is the loophole?
 
tom.stoer said:
Nevertheless there is an argument that spin greater than 2 is forbidden completely.

It cannot be completely, since Weinberg constructs free fields of arbitrary spin.
 

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