- #1

lindberg

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- TL;DR Summary
- The Reeh-Schlieder theorem, the Unruh effect and Haag's theorem don't seem to leave much room for particles in QFT. Or do they?

In a paper by Bain (2011), particles are left with little ontological value because of the Reeh-Schlieder theorem, the Unruh effect and Haag's theorem. The author claims (and here I am copying his conclusion):

First, the existence of local number operators requires the absolute temporal metric of a classical spacetime. This structure allows NQFTs (non-relativistic QFTs) to avoid the consequences of the

Second, the existence of a unique total number operator requires the absolute temporal metric of a classical spacetime. An absolute temporal metric guarantees the existence of a unique global time function for non-interacting NQFTs, and hence a unique way to define an inner-product (or its equivalent) on the space of single particle states. This ultimately leads to a uniquely defined total number operator via a Fock space construction, thus avoiding the implications of the

Finally, an absolute temporal metric allows interacting NQFTs to avoid polarizing the vacuum, and this immunizes such theories against the consequences of

My questions:

1. So what are we to conclude? There are no particles? Or that we need absolute time (a heresy in much of the Physics community)?

2. If we accept an absolute time, thought, will we be able to integrate and explain the observation of the Unruh effect? Does the accelerated detector click

(I already have some hints to answers to the second question, coming from the two papers below by Dundar and Nikolic, but I would like to cast the question wide-open for now in order to gather several opinions)

Link to Bain (2011):

https://www.sciencedirect.com/science/article/abs/pii/S1355219810000493?via%3Dihub

Link to Unruh in a Shape Dynamics context, Dundar 2017:

https://arxiv.org/abs/1706.05890

Link to Nikolic 2022 on defining objective particles in Unruh-like effects:

https://arxiv.org/abs/0904.3412

First, the existence of local number operators requires the absolute temporal metric of a classical spacetime. This structure allows NQFTs (non-relativistic QFTs) to avoid the consequences of the

**Reeh-Schlieder****theorem**. In particular, it prevents the non-relativistic vacuum state from being separating for any local algebra of operators, and this allows for the possibility of local number operators.Second, the existence of a unique total number operator requires the absolute temporal metric of a classical spacetime. An absolute temporal metric guarantees the existence of a unique global time function for non-interacting NQFTs, and hence a unique way to define an inner-product (or its equivalent) on the space of single particle states. This ultimately leads to a uniquely defined total number operator via a Fock space construction, thus avoiding the implications of the

**Unruh****Effect**.Finally, an absolute temporal metric allows interacting NQFTs to avoid polarizing the vacuum, and this immunizes such theories against the consequences of

**Haag’s theorem**. In particular, interacting NQFTs exist that are unitarily equivalent to non-interacting NQFTs, and hence the former can appropriate the Fock space structure of the latter, and, in particular, the total number operators defined in the latter.My questions:

1. So what are we to conclude? There are no particles? Or that we need absolute time (a heresy in much of the Physics community)?

2. If we accept an absolute time, thought, will we be able to integrate and explain the observation of the Unruh effect? Does the accelerated detector click

*at all*in a background with absolute time? Or may the observation of the Unruh effect be used to falsify the notion of absolute time?(I already have some hints to answers to the second question, coming from the two papers below by Dundar and Nikolic, but I would like to cast the question wide-open for now in order to gather several opinions)

Link to Bain (2011):

https://www.sciencedirect.com/science/article/abs/pii/S1355219810000493?via%3Dihub

Link to Unruh in a Shape Dynamics context, Dundar 2017:

https://arxiv.org/abs/1706.05890

Link to Nikolic 2022 on defining objective particles in Unruh-like effects:

https://arxiv.org/abs/0904.3412