1. Apr 17, 2006

In order not to further irritate Marcus, let us move this off-topic discussion from the Rovelli thread.

Whether the foliation is bent or not has nothing to do with my argument. By talking about a foliation, you are making a hidden assumption about classical observers. However, since the observer's trajectory is a quantum variable, it can only be specified if we leave the observer's momentum completely undetermined. Or vice versa. This means that the foliation itself is subject to quantum fluctuations, which is the essential physical novelty.

In typical accelerator experiments, the detectors weigh several tonnes, and measurements are related to the detector's rest frame. The assumption that such a detector does not recoil at all is an excellent approximation, which is implicit in the assumption that the detector follows a sharp, classical trajectory. However, it is an approximation, which amounts to replacing several tonnes by infinity. When gravity is turned on, this becomes a problem, because an infinite mass will immediately collapse into a black hole. This is an essential difference between gravity and other interactions.

2. Apr 17, 2006

### Careful

**
Whether the foliation is bent or not has nothing to do with my argument. By talking about a foliation, you are making a hidden assumption about classical observers. However, since the observer's trajectory is a quantum variable, it can only be specified if we leave the observer's momentum completely undetermined. Or vice versa. This means that the foliation itself is subject to quantum fluctuations, which is the essential physical novelty. **

Don't you think I realize that ?? :grumpy: Moreover, I still do not agree that it is some kind of foliation which is subject to fluctuations in your framework (fix the ontology of your t sensibly). By referring to the standard QFT result I merely asserted that you should obtain the latter result for macroscopic´´ observers in your framework. And for that you do not have to take the sick limit M -> infinity which indeed causes trouble for gravity. You might try to establish such correspondence at the statistical level, by considering the deterministic evolution of expectation values of the worldline operators (a la Ehrenfest) exactly like some people try to take the classical limit´´ of quantum mechanics (it came as a surprise to me that you did not realize that). This answers immediatly the rest of your message. Frankly, the idea of fluctuating foliations is not a novetly either, your work at the Hamiltonian level (again fix the ontology of t) however is (to my knowledge). That is why I said that the paper interesting even if it turns out to be entirely wrong.

Last edited: Apr 17, 2006
3. Apr 17, 2006

But you also wrote

"??? There is no problem whatsoever in defining QFT with respect to (non-uniformly) accelerating observers (and bending the foliation according to local eigentime - as long as one does not encounter focal points)."

Thus you seem to be saying that there is no problem whatsoever in defining QFT over a foliation which itself is subject to quantum fluctuations. This statement may raise some eyebrows. At least I disagree.

It is of course widely expected that the foliation is quantized on quantum gravity, but I am only aware of one more suggestion how to implement this technically, namely the histories approach of Isham, Linden and in particular Savvidou, see e.g. http://www.arxiv.org/abs/quant-ph/0110161 . There is some overlap between my approach and theirs, but I am not sure about the exact status of their work. Anyway, a quantum foliation is certainly *not* part of standard canonical QFT.

4. Apr 17, 2006

### Careful

**But you also wrote

"??? There is no problem whatsoever in defining QFT with respect to (non-uniformly) accelerating observers (and bending the foliation according to local eigentime - as long as one does not encounter focal points)."

Thus you seem to be saying that there is no problem whatsoever in defining QFT over a foliation which itself is subject to quantum fluctuations. This statement may raise some eyebrows. At least I disagree.
**

I repeat myself : all I said is that there is no problem in defining QFT over a foliation corresponding to accelerated observers. OBVIOUSLY, I consider the observer classical here, and I alluded already to the unavoidable problem which raises in quantum theory for the foliation - and that are the focal points. Moreover, I implied by this that any theory which treats the foliation as quantum obviously needs to incorporate the possibility for acceleration.

** namely the histories approach of Isham, Linden and in particular Savvidou, see e.g. http://www.arxiv.org/abs/quant-ph/0110161 . There is some overlap between my approach and theirs, but I am not sure about the exact status of their work. **

I know that approach.

**Anyway, a quantum foliation is certainly *not* part of standard canonical QFT. **

right, but in path integrals that all becomes much easier as I said in the beginning. This conversation is finished.

Last edited: Apr 17, 2006
5. Apr 17, 2006

### marcus

a courteous good morning to you gentlemen (pacific time)
fascinating discussion