Existence of the Unruh effect In the paper Quantum field aspect of Unruh problem (and others with similar approaches) Buchholz and Verch show that applying the rigorous algebraic approach to QFT, the derivation of the Unruh effect usually done by almost everyone is incorrect, and that the Unruh effect doesn't exist.
More than that, as far as I know, the Unruh effect hasn't been observed. So in the end of the day, the Unruh effect has no mathematicaly rigorous theoretical derivation, nor any kind of experimental observation that would point towards its correctness.
Either way, lots of physicists insist the effect exists and claim that the "mathematicaly rigorous approach thing" is nonsense.
Well, if the prediction was actually observed (as many things in QFT which are not mathematicaly rigorous), I could agree that probably the predicition is correct and certainly one day a rigorous mathematical approach will be found. The issue here is that the prediction simply isn't observed.
Why so many physicists believe the Unruh efffect exist then, when it has been established the traditional derivation is simply plain wrong and there is no experimental evidence of the effect?
Edit: Regarding more material on the subject, there are some more recent papers:


*

*Macroscopic aspects of the Unruh effect,

*Life in the Rindler Reference Frame,


The first one is from 2015 and it seems it has been published. The second article is from this year, but I think it hasn't been published yet (although as far as I know it will be). From a mathematical point of view I've found the second paper quite convincing. The might be more that I don't know about yet.
 A: I find that the "derivation" by using a Bogoliubov transformation and then tracing out part of the field is sufficiently dubious that one could not confidently expect the effect based on that derivation alone. However, it is backed up by calculations in Minkowski frame concerning the evolution of internal degrees of freedom of accelerated detector. This makes it a robust result IMO.
The Unruh effect is also sufficiently closely related to Hawking radiation as to say each implies the other, and the Hawking radiation has been calculated by sufficiently many approaches that it seems to me to be well established.
Unruh radiation has not been detected simply because it is a very small effect and therefore hard to detect. I gather, though, that there are now some experimental claims to have detected it indirectly. See for example https://arxiv.org/abs/1903.00043 which was helpfully posted as an "answer" (really a comment) by Hooman Neshat. 
A: I have read only the abstract of the paper you pointed to, but I believe it is enough to answer your question. The key point being (I quote the abstract):

As is explained, this result is not in conflict with the well-known fact that microscopic probes respond non-trivially to acceleration if coupled to the vacuum.

The conclusion of the paper, as stated in the abstract, is not that the Unruh effect does not exist, but rather that the interpretation that macroscopic observers will have a feeling of temperature is incorrect. This conclusion, as far as I know, would not follow from any derivation of the Unruh effect, but would rather be taken as reasonable based on intuition of what we understand as a thermal state.
However, there are mathematically rigorous proofs of the Unruh effect. As mentioned in Wald's Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics, more specifically on pp. 117–118, the standard derivation based on Bogoliubov transformations is mathematically awkward, but the conclusions can be put in rigorous footing through the usage of techniques coming from Axiomatic or Algebraic Quantum Field Theory. More specifically, the Bisognano–Wichmann theorem and the notion of KMS states. If I recall correctly, these rigorous derivations are mentioned, referenced, and illustrated on arXiv: 0710.5373, which is an excellent review on the Unruh effect.
Furthermore, while there is no direct experimental evidence for the Unruh effect, one can show that the Unruh effect should be taken to be as reliable as standard Particle Physics — see arXiv: gr-qc/0205078 — and, in fact, to question the Unruh effect one might also question the validity of Classical Electrodynamics ― see arXiv: 1701.03446.
In summary, while the Unruh effect hasn't been observed experimentally yet due to the extreme subtlety of its predictions, it is an incredibly reliable prediction. Furthermore, the Hawking effect — which is related, but not equal, to the Unruh effect — has been recently observed in analogue condensed matter systems, see doi: 10.1038/s41586-019-1241-0. While this is not an observation of the Unruh effect, it certainly strengthens the belief that the effect is indeed real. Nevertheless, if the paper you mentioned is correct, the usual interpretation that a macroscopic, accelerated observer would feel themself immersed in a thermal bath is incorrect, but, according to the paper's abstract, that is not in contradiction with the usual microscopic conclusions about the existence of the Unruh effect.
