Where are the particles created in BH evaporation?

[marcus]

This thread is about a Bill Unruh article ("Where are the particles created...?") and an article on the same theme by Unruh and Ralf Schützhold ( http://arxiv.org/abs/0804.1686 "Origin of particles in BH evaporation")
and Schützhold's participation in the LQG-BH workshop taking place this month at the University of Valencia.

This page has photos and brief CVs for both Unruh and Schützhold:
http://royalsociety.org/page.asp?id=7185

The Unruh article is here:
http://pos.sissa.it//archive/conferences/043/039/QG-Ph_039.pdf
He didn't post it on arXiv, but it is free for download at PoS (proceedings of science).
It's interesting.

I guess most people know about Unruh discovering the Unruh temperature and Unruh radiation about the same time (1970s) that Hawking came out with the Hawking temperature and Hawking radiation. Unruh has remained active and creative. The PoS article is based on a talk he gave at a QG conference in the summer of 2007. It cites his work with Schützhold.

In this paper Unruh uses a hydrodynamic toy model of a black hole to develop intuition and useful concepts---he thinks in a concrete physical way about BH radiation through this fluid flow model. The speed of sound in the fluid plays the role of the speed of light.

What called my attention to this is the fact that just a day or two ago the organizers of the March 2009 University of Valencia workshop on Black Holes and Loop Quantum Gravity added Schützhold to their speakers list.
http://www.uv.es/bhlqg/
http://www.uv.es/bhlqg/speakers.htm
Abhay Ashtekar
Martin Bojowald
Alejandro Corichi
Bianca Dittrich
Jonathan Engle
Amit Ghosh
Viqar Husain
Jerzy Lewandowski *
Alejandro Perez
Jorge Pullin
Hanno Sahlmann
Ralf Schuetzhold
Madhavan Varadarajan

In the past two years there have been a number of new LQG BH results---Corichi, Engle, Ghosh, Sahlmann have been principals in that. Bianca Dittrich has co-authored with Loll about BH in CDT---I can't say but it's possible she could report on some Triangulations BH research. In any case knowing the recent work of some of the speakers one can make a rough guess about what new stuff will be covered in the workshop. BTW Schützhold is fairly young---PhD Dresden 2001, postdoc at British Columbia where Unruh is, professor 2008 at Duisberg-Essen.

Schützhold's name was unfamiliar and caught my attention. So this goes back to what William Unruh was saying in 2007. Let's look at that paper.

 

[marcus]

The introduction to Unruh's paper reveals what is going on in a highly concise way:

==quote==

...An uncomfortable aspect of Hawking’s derivation is that the radiation emitted at a time t
after the black hole has formed originates, in his calculations, from the zero point fluctuations in the field at frequencies of Me^{t /4M} in the early stages before the black hole has formed.

Thus if we consider the radiation emitted, say, 1 second after a solar mass black hole has formed, this radiation originates from quantum fluctuations in the vacuum before the black hole formed, with an energy of
e¹⁰⁵ times the mass of the whole universe.

For such quantum fluctuations, even if they are vacuum fluctuations, we do not expect a simple quantum field theory in a fixed background spacetime (the arena in which Hawking did his calculation) to be an adequate approximation.

This has been noticed since shortly after the original paper, but since the Hawking’s results are so appealing, it was felt that the calculation, though obviously unphysical in detail, was surely right in principle. In 1981 [2], I noticed that sound waves in a background irrotational flow where the fluid velocities exceeded the velocity of sound were mathematically exact analogs of scalar fields in a black hole background spacetime, at least in the hydrodynamic approximation. Furthermore the quantization of those sound waves (phonons) corresponded exactly to the quantization of a scalar field theory in a background black hole spacetime. Thus one expects and, if one naively carries out the analog of Hawking’s calculation, one gets that the horizon would emit sound quanta with some temperature. In this sonic case, that temperature is given by...
...where c(x) is the (perhaps spatially dependent) velocity of sound, and the expression is evaluated at the point where the velocity of the fluid equals the velocity of sound. This sonic analog of a black hole I called a dumb hole– from the phrase “deaf and dumb”– since such structures were incapable of emitting sound.

And the calculation of this temperature suffers from the same exponential dependence with time of the initial vacuum fluctuations. However, unlike the case for the black hole, we know that hydrodynamics breaks down at short wavelengths. A fluid has a natural high frequency and wave-number cutoff–--at a minimum at the interatomic spacing. I.e., such a system has no ultra-high frequency problem.
==endquote==

Something a bit doubtful about Hawking's derivation---that mass which is
e^100,000 times the mass of the observable universe.

He concludes that quantum field theory on a fixed background spacetime not really applicable. So this might possibly be a suitable application of a background independent QG like LQG, which moreover has UV-finiteness features. The discrete spectra of area and volume operators in LQG could play an analogous role to the minimum interatomic spacing and control the ultra-high frequency problem. One can see how it might possibly be worth discussing at the Valencia workshop.

 

[Haelfix]

Part of the problem I gather is that the background spacetime is chosen to be something like the Schwarzschild metric, which is static. For those early moments you really want a metric with time dependance, so its always been technically challenging to really draw many conclusions from that sort of early time analysis which is why you essentially have to ansatz solutions like Unruh does.

Analytically the best you can really hope for at this time is to look at the long term ringing modes of the BH (which gives the exponential feature so important for the information loss puzzle) and argue on statistical grounds that no amount of semiclassical time dependence is going to be able to cut that off, the only hope is some sort of UV completion not governed by field theory alla AdS/CFT.

 

[Dmitry67]

Interesting. May be offtopic, but as we are talking about the horizons...
I read somewhere that as in the expanding Universe there is also a horizon, there is a radiation from that horizon too. So if our universe expands forever it cools not to an absolute zero, but to 10^-33K because matter is heated by that radiation. Is it true?

 

[marcus]

...
Analytically the best you can really hope for...

from a certain limited perspective. (Say the way a string or QFT practitioner might see it.)
We'll have to see what happens in the LQG context. It's interesting that the organizers thought to invite Schützhold, and that he decided to attend and give a talk. He may get something from them--it might work both ways.

 

[marcus]

Interesting. May be offtopic, but as we are talking about the horizons...
I read somewhere that as in the expanding Universe there is also a horizon, there is a radiation from that horizon too. So if our universe expands forever it cools not to an absolute zero, but to 10^-33K because matter is heated by that radiation. Is it true?

In an ordinary expanding universe with zero cosmo constant there is no cosmological event horizon.
(Cosmology has several different horizons, hard to keep from confusing, only the cosmo event horizon would be associated with a radiation temp.)

Before 1998 there were the open and flat models that had unlimited expansion, they just didn't have "dark energy" or a positive cosmo constant. These did not have an event horizon.

After 1998 there was this dark energy density assumed to be 0.6 nanojoule per cubic meter. Assumed constant throughout space and time, in the standard LCDM model that is mostly used. It is indeed associated with a temperature! I don't happen to know the temp off-hand. Your figure of 10_-33 kelvin could well be right.

This is a good point but it is the wrong place to discuss it.

Please start a thread in Cosmo forum about the cosmo event horizon, to get more information.

The present distance to the cosmo event horizon is about 16 billion lightyears. We can see things that are almost 3 times farther than that---it is not an observation past lightcone horizon. What it says is that if someone in a galaxy which is now more than 16 away from us sends us a message TODAY the message will never get here.

And if you were to leave today and travel at speed of light towards that galaxy you would never get there.

16 billion lightyears is not the distance at which objects are receding at the speed of light, that is something different, called the Hubble radius, and it is about 13.8 billion lightyears. So there is a fair amount of difference in the definitions. So if you want more discussion you would do well to start a thread in the right forum.

 

[marcus]

I see that Renate Loll has scheduled Schützhold to give a talk in her seminar at Utrecht on 23 March, just 3 days before the start of the BH-LQG workshop at Valencia.

Bianca Dittrich is currently postdoc with Loll at Utrecht. Dittrich and Loll have collaborated on some BH work using the Causal Dynamical Triangulations approach. Dittrich is one of the speakers scheduled for the Valencia workshop. I am curious what she will talk about. She is expert in LQG and has made an important contribution to the new spinfoam version.
But there is the CDT and BH thing, maybe someone else knows more about this and can offer a better guess than I can.

 

[Dmitry67]

Sorry for the offtopic.
Returning to the Unruh effect.

I have one question
I accelerate a ball and it melts because of the unruh radiation (unruh radiation is visible it the accelerating frame)
My question is how it is explained in the inertial frame, where observers do not see any radiation?

 

[marcus]

Sorry for the offtopic.
Returning to the Unruh effect.

I have one question
I accelerate a ball and it melts because of the unruh radiation (unruh radiation is visible it the accelerating frame)
My question is how it is explained in the inertial frame, where observers do not see any radiation?

Neat question, hopefully you get several answers. I will only say this: the formula for Unruh temp is LINEAR in the acceleration.

That means that high acceleration is only possible for a very brief time (in the lab frame).

If you double the acceleration, you double the temp. But you also cut in half the time that the ball can be exposed to that temp (before the speed limit curtails acceleration.)
Oooops I have to go, back later

 

[friend]

Interesting! But as I understand it, at the point where the particles of Hawking radiation are created, the event horizon, the particles themselves don't observe a horizon. All the particles feel at that point is a gravitational field. But a gravitational field of any strength can exist at the event horizon of a black hole of the appropriate size. So it must be that it is the gravitational field that is creating the radiation and not the event horizon. Right?

 

[Dmitry67]

QM is weird, but still it is strange that real (not virtual) particles exist only in SOME frames.

 

[marcus]

QM is weird, but still it is strange that real (not virtual) particles exist only in SOME frames.

Particle is not always a good concept in curved spacetime.
Field is the basic idea. Particle concept is most at home in approximately flat space.
Inconsistency is to be expected when you get away from the vanilla situation, so it's not a good idea to always try to think in terms of particles.

This point was made for me by a paper of Rovelli's which as I recall gave some revealing concrete examples.

http://arxiv.org/abs/gr-qc/0409054
What is a particle?
Daniele Colosi, Carlo Rovelli
19 pages
(Submitted on 14 Sep 2004 (v1), last revised 5 Nov 2008 (this version, v2))
"Theoretical developments related to the gravitational interaction have questioned the notion of particle in quantum field theory (QFT). For instance, uniquely-defined particle states do not exist in general, in QFT on a curved spacetime. More in general, particle states are difficult to define in a background-independent quantum theory of gravity. These difficulties have lead some to suggest that in general QFT should not be interpreted in terms of particle states, but rather in terms of eigenstates of local operators. Still, it is not obvious how to reconcile this view with the empirically-observed ubiquitous particle-like behavior of quantum fields, apparent for instance in experimental high-energy physics, or "particle"-physics. Here we offer an element of clarification by observing that already in flat space there exist --strictly speaking-- two distinct notions of particles: globally defined n-particle Fock-states and *local particle states*. The last describe the physical objects detected by finite-size particle detectors and are eigenstates of local field operators. In the limit in which the particle detectors are appropriately large, global and local particle states converge in a weak topology (but not in norm). This observation has little relevance for flat-space theories --it amounts to a reminder that there are boundary effects in realistic detectors--; but is relevant for gravity. It reconciles the two points of view mentioned above. More importantly, it provides a definition of local particle state that remains well-defined even when the conventional global particle states are not defined. This definition plays an important role in quantum gravity."

 

[marcus]

... it must be that it is the gravitational field that is creating the radiation and not the event horizon. Right?

Friend, I think that is right (although I do not speak with authority.)

One reason I feel sure that this is a correct statement is that to define the event horizon requires a knowledge of the infinite future. In other words the event horizon as normally defined is not physical in the usual sense. It is an abstract manmade concept based on non-existent knowledge, not something which exists in nature.

For this reason people doing black hole research have been replacing the event horizon concept by other kinds of horizons, defined differently, so that they have empirical or operational meaning. Ashtekar has a number of papers along that line. And of course others as well.

these variously defined BH horizons are necessarily features of the geometry, that is, the gravitational field. So once one says the particles are created by the gravitational field, that says it all. That includes anything that some sort of human-defined "horizon" can be said to have created. So it seems quite safe to make the statement you did. It could hardly be wrong.

 

[Haelfix]

from a certain limited perspective. (Say the way a string or QFT practitioner might see it.)

I should note in passing that its controversial whether quantum gravity will help matters for the Trans Planckian problem (which incidentally occurs in Inflation also) b/c of the strong interplay between semiclassical and strongly coupled sectors making the calculations extraordinarily difficult on either side. Anyway, Unruh himself showed that regardless of that problem the hawking calculation remains valid over long time frames:

W. Unruh, Phys. Rev. D51, 2827 (1995).

and its just the short term regime where things are dicey (large backscattering, superhorizon fluctuations, etc)

Also the OPs paper linked above is specifically tailored to remove the problem by appealing to the acoustic model and NOT quantum gravity effects; rather, the hope is that whatever the eventual QG model that becomes favorable will reproduce the results of the acoustic models. For instance various stringy early inflation scenarios are eerily analogous in many ways and evaded the problem.

Wiki has a nice bit with some good references:
http://en.wikipedia.org/wiki/Hawking_radiation#Trans-Planckian_problem

 

[friend]

these variously defined BH horizons are necessarily features of the geometry, that is, the gravitational field. So once one says the particles are created by the gravitational field, that says it all. That includes anything that some sort of human-defined "horizon" can be said to have created. So it seems quite safe to make the statement you did. It could hardly be wrong.

Thanks for the encouragement, marcus.

In fact, I see in some books where they replace the mass term in the lagrangian with the metric tensor in order to generalize concepts to curved spacetimes, etc. If you insist, I can quote those sources. But that pretty much states right there that particles are a local manifestation of gravity.

Now, if the Hawking radiation is a manfestation of gravity (and not necessarily of BHs alone), then this radiation density has an energy density and therefore a mass density, all due to the gravitational field. It contributes a very minute amount of mass density, but it would have an effect of accumulating over a very large volume of space wherever the gravitation field exists. I wonder if this could account for the effects of dark matter. But someone more qualified than I will have to do the math on that.

 

[Haelfix]

"it must be that it is the gravitational field that is creating the radiation and not the event horizon. Right?"

Yes that's correct. Theres a number of ways to see this, ranging in sophistication. One handwavey way is to note the following: If you believe in the equivalence principle the event horizon must not be a special place for any infalling observer. You cannot decide if there is an event horizon by any local measurement as its a global property of spacetime. This confused people for a long time (b/c you might naively think you'd see very strong emissions from the thermal bath of Hawking particles as you approached the horizon) until things like black hole complementarity became accepted. But still we know there is hawking radiation on general grounds, ergo it must be the field (actually the far field) that carries the full information about the radiation.

Another related mistake people often make is this statement "the black holes mass is carried away by energy escaping to infinity (or it loses mass by a particle radiating away). Thats not correct! The black hole loses mass b/c it receives a *negative* energy density contribution to its stress energy tensor!

 

[Dmitry67]

Neat question, hopefully you get several answers. I will only say this: the formula for Unruh temp is LINEAR in the acceleration.

That means that high acceleration is only possible for a very brief time (in the lab frame).

If you double the acceleration, you double the temp. But you also cut in half the time that the ball can be exposed to that temp (before the speed limit curtails acceleration.)
Oooops I have to go, back later

Well, so it the labs frame acceleration time is limited because you reach 0.999... of the lightspeed soon

But let's switch to the ref frame L1, initially moving at 0.99c
When our accelerating objects reaches the same speed, it is in rest at this time frame. Continue monitoring in L1 frame. Object is still accelerating in L1, so object is still receiving the heat.

Then swith to L2 which is moving at speed 0.99 in L1 et ad infinitum :)

 

[Dmitry67]

http://arxiv.org/abs/gr-qc/0409054
What is a particle?
Daniele Colosi, Carlo Rovelli
19 pages
(Submitted on 14 Sep 2004 (v1), last revised 5 Nov 2008 (this version, v2))
"Theoretical developments related to the gravitational interaction have questioned the notion of particle in quantum field theory (QFT). For instance, uniquely-defined particle states do not exist in general, in QFT on a curved spacetime. More in general, particle states are difficult to define in a background-independent quantum theory of gravity. These difficulties have lead some to suggest that in general QFT should not be interpreted in terms of particle states, but rather in terms of eigenstates of local operators.

Interesting. And it makes sense.
BTW can it help to finally get rid of at least some interpretations?
For example, MWI is consistent with written above: there are only waves and "particles" are just an experimental effect of a decoherence.
For Bohm for example it would be a real problem to explain how 'particle' can become something different in a curved spacetime.

 

[friend]

"it must be that it is the gravitational field that is creating the radiation and not the event horizon. Right?"

Yes that's correct. Theres a number of ways to see this, ranging in sophistication. One handwavey way is to note the following: If you believe in the equivalence principle the event horizon must not be a special place for any infalling observer. You cannot decide if there is an event horizon by any local measurement as its a global property of spacetime.

But by the equivalence principle, gravitation is the same as acceleration. So acceleration produces particles as well, the Unruh effect. So as the universe expansion increases, this presents another form of acceleration, be it very small on the local scale. I would think that the accelerated expansion of the universe would produce particles (and radiation) as well. I wonder if this is equivalent to dark energy.

 

[friend]

Particle is not always a good concept in curved spacetime.
Field is the basic idea. Particle concept is most at home in approximately flat space.
Inconsistency is to be expected when you get away from the vanilla situation, so it's not a good idea to always try to think in terms of particles.

This point was made for me by a paper of Rovelli's which as I recall gave some revealing concrete examples.

http://arxiv.org/abs/gr-qc/0409054
What is a particle?
Daniele Colosi, Carlo Rovelli
19 pages
(Submitted on 14 Sep 2004 (v1), last revised 5 Nov 2008 (this version, v2))
"Theoretical developments related to the gravitational interaction have questioned the notion of particle in quantum field theory (QFT). For instance, uniquely-defined particle states do not exist in general, in QFT on a curved spacetime. More in general, particle states are difficult to define in a background-independent quantum theory of gravity. These difficulties have lead some to suggest that in general QFT should not be interpreted in terms of particle states, but rather in terms of eigenstates of local operators. Still, it is not obvious how to reconcile this view with the empirically-observed ubiquitous particle-like behavior of quantum fields, apparent for instance in experimental high-energy physics, or "particle"-physics. Here we offer an element of clarification by observing that already in flat space there exist --strictly speaking-- two distinct notions of particles: globally defined n-particle Fock-states and *local particle states*. The last describe the physical objects detected by finite-size particle detectors and are eigenstates of local field operators. In the limit in which the particle detectors are appropriately large, global and local particle states converge in a weak topology (but not in norm). This observation has little relevance for flat-space theories --it amounts to a reminder that there are boundary effects in realistic detectors--; but is relevant for gravity. It reconciles the two points of view mentioned above. More importantly, it provides a definition of local particle state that remains well-defined even when the conventional global particle states are not defined. This definition plays an important role in quantum gravity."

It would seem that any curved spacetime is locally flat. That means for some small region of curved space there should exist particles. They may lose definition if the wavelength of the wavefunction is comparible to the curvature. So it may be that only high energy particles with their short wavelengths exist in highly curved spacetimes. The question then becomes what is the mechanism of exchange between curvature and particles.

 

[Fra]

I wonder if this is equivalent to dark energy.

There is an old cosmo thread regarding that idea discussing this
http://arxiv.org/PS_cache/arxiv/pdf/0803/0803.1987v4.pdf

https://www.physicsforums.com/showthread.php?t=228842

I just skimmed Rovelli and Colosi's what's a particle paper during a bath and the association I made is that due to the ordinary definition of particles via a symmetry (Poincare) the question of the physical basis of this symmetry is to me equivalent to the question of the local basis of definition.

To me the general extended conslusion about is that it is not possible to locally construct a global symmetry in a unique way, and that global symmetries only emerge as "locally" global symmetries as systems interact and where the interaction process seleces the quasi-global symmetries.

This is what I would personally like to think of as the logical continuation of the reasoning in Rovelli's RQM reasoning. Even global symmetries, if existing has to be "communicated", and until that's done, the observer is acting as if it doesn't exist. That's what I think.

The particle question is IMHO a special case of a general question.

/Fredrik

 

[marcus]

The question then becomes what is the mechanism of exchange between curvature and particles.

Yes! probably the ultimate question for quantum gravity.

what is the mechanism that connects matter and geometry?

One hope might be that QG researchers can uncover the more fundamental degrees of freedom underlying both matter and geometry (they will simply be different aspects of the same thing) so it will be clear how one must interact with the other.

 

[Dmitry67]

They may lose definition if the wavelength of the wavefunction is comparible to the curvature. So it may be that only high energy particles with their short wavelengths exist in highly curved spacetimes.

On the contrary
GR vs QM effects should affect mostly low energy particles with their LONG wavelength

 

[Fra]

The question then becomes what is the mechanism of exchange between curvature and particles.

Yes! probably the ultimate question for quantum gravity.

what is the mechanism that connects matter and geometry?

One hope might be that QG researchers can uncover the more fundamental degrees of freedom underlying both matter and geometry (they will simply be different aspects of the same thing) so it will be clear how one must interact with the other.

I agree that these seems to be like one of a handful "epic keys" yet to be found.

I think another point is the whenever we ask question, or picture a measurement/interacting, who is asking, and to what extent does it make sense to just flatly move the abstraction between observers? We are used from curved geometry that to transport abstractions from different observer frames, there are special transformations.

How does the general transformation of a measurement operator between two observers look like? Perhaps this is not even a deterministic transformation? In particular when picturing observers of different complexiy and mass, some operators may even vanish in communication, and some other may rather EMERGE or be created in the communication process? This would mean that this isn't necessariy information preserving unitary transformations. My guess is that in general it can't be.

This is what I personally consider to be one of the other "epic keys".

/Fredrik

 

[friend]

On the contrary
GR vs QM effects should affect mostly low energy particles with their LONG wavelength

I think it would be highly unlikely to observe low energy particles in tightly curved spacetimes because that is inherently a high energy situation.

 

[Ilja]

"it must be that it is the gravitational field that is creating the radiation and not the event horizon. Right?"

Yes that's correct. Theres a number of ways to see this, ranging in sophistication. One handwavey way is to note the following: If you believe in the equivalence principle the event horizon must not be a special place for any infalling observer. You cannot decide if there is an event horizon by any local measurement as its a global property of spacetime. This confused people for a long time (b/c you might naively think you'd see very strong emissions from the thermal bath of Hawking particles as you approached the horizon) until things like black hole complementarity became accepted. But still we know there is hawking radiation on general grounds, ergo it must be the field (actually the far field) that carries the full information about the radiation.

Another related mistake people often make is this statement "the black holes mass is carried away by energy escaping to infinity (or it loses mass by a particle radiating away). Thats not correct! The black hole loses mass b/c it receives a *negative* energy density contribution to its stress energy tensor!

I have a general problem with such energy considerations: How can we make such considerations given that GR does not define a local energy-momentum-stress tensor for the gravitational field?

It seems to me that such considerations can be made only if we fix some coordinates or something similar, thus, violate basic GR principles.

As well, I see no reason to expect that the renormalization of energy-momentum of quantum fields can be made in a covariant way. The back-reaction would also violate
GR principles. Not?

Ilja

 

[Haelfix]

"I have a general problem with such energy considerations: How can we make such considerations given that GR does not define a local energy-momentum-stress tensor for the gravitational field?"

The *pseudo* tensor Tuv in these calculations is very much a local object and not defined globally. In the Hawking radiation case, its actually even worse. Tuv is meaningless for *quantum* fields, instead you have to look at an admittedly formal object <Tuv>, the expectation value of the stress energy tensor. In so far as that sort of thing makes sense, the rest holds (and you don't really have to even use that, the hawking process has been derived using purely thermodynamic considerations).

"As well, I see no reason to expect that the renormalization of energy-momentum of quantum fields can be made in a covariant way."

The renormalization of Tuv typically done in these sort of semiclassical analysis does indeed mantain covariance. So something like <Tuv> ;v = 0. Note the tensor arises from an effective action so that more or less has to happen. In the 70s, when people were worrying about that sort of thing, they actually used covariance as one requirement utilized to actually create the object <Tuv>, so a sort of bootstrap.

 

[Demystifier]

For Bohm for example it would be a real problem to explain how 'particle' can become something different in a curved spacetime.

Good observation!
Still, it does not imply that the Bohmian interpretation is wrong. There are at least 3 ways how can a version of the Bohmian interpretation be made consistent in curved spacetime:
1. The Bohmian interpretation is to be formulated for fields, not for particles. (Personally, I don't prefer this variant because it leads to even more serious problems, even in flat spacetime.)
2. There is a preferred foliation of spacetime, with respect to which particles should be defined. This seems very natural because even in flat spacetime most versions of the Bohmian interpretation seem to require a preferred foliation of spacetime. Nevertheless, I am not completely happy with that either. First, it looks too cheap. Second, it seems very artificial to have a theory that is fully relativistic-covariant only at the classical level.
3. At low energies, the fundamental entity is particle, not field. On the other hand, the usual theory of QFT in curved spacetime assumes the opposite, that the fundamental entity is field, not particle, which implies that some results of this usual theory may be physically wrong. The main problem with such an approach (which I prefer) is that it is not yet sufficiently developed. For some results in that direction see
http://xxx.lanl.gov/abs/hep-th/0702060