Is Quantum Geometry the Zero Point Energy?

[Careful]

** You are beginning to sound like a detractor. "accelerate and decelerate to an inertial reference frame again" - that's not what I was talking about, and you know it. **

You said that acceleration is equivalent to the existence of an horizon, you never added that the acceleration had to be constant for an infinite amount of time! Such situation is highly idealized and never occurs in practice.

** I was talking about acceleration only, and you know it. Show me any instance where one is accelerating and where there is no horizon involve. **
Very simple (if the acceleration is not necessarily constant) : take a sheet of paper and draw a global congruence of curved timelike curves.

** True, for small accelerations the horizon may be far away indeed, such as the cosmological event horizon. But still where there is one there is always the other. **

Nope, what I wanted to learn you is that the Unruh effect is a *global* result and has nothing to do with the local acceleration of a rocket. Therefore, I do not believe it is a meaningful *physical* result - at least not in its present form.

** And I don't understand your objection to Torsten, either. Didn't we already know that singularities were solutions to Einsteins equation, which also gave curved spacetime around them? **

Yes, but the question is whether Torsten's construction gives rise to that kind of singularities. If you would take his definition of the mixed connection and do the math, then you easily see that there is no curvature effect outside the body, so an observer from outside wouldn't notice anything. Therefore, there is no physical matter source involved - and actually it is no so difficult to understand why but for the moment I leave the matter up to Torsten.

Look, mike2, I am always trying to stay polite but I just cannot understand why certain people do not *listen* to what I say such as R (if he actually reads my previous answers carefully, he will see that many of his ``objections´´ are flawed) and constantly argue using quotes they have read in some magazines. On the other hand, you cannot expect me to type out entire courses with all definitions included: if R wants to know the details I mentioned about CDT, he should in the first place look them up in the papers of Loll and Ambjorn instead of bothering me with that.

You, on the other hand, might also benifit from the references I gave you : otherwise I do not understand the purpose of your questioning in the first place.

Cheers,

Careful

 

[Mike2]

** You are beginning to sound like a detractor. "accelerate and decelerate to an inertial reference frame again" - that's not what I was talking about, and you know it. **
You said that acceleration is equivalent to the existence of an horizon, you never added that the acceleration had to be constant for an infinite amount of time! Such situation is highly idealized and never occurs in practice.

Infinity has nothing to do with it, and I think you know this too. Only where there is acceleration there is a horizon. True or false.

** I was talking about acceleration only, and you know it. Show me any instance where one is accelerating and where there is no horizon involved. **
Very simple (if the acceleration is not necessarily constant) : take a sheet of paper and draw a global congruence of curved timelike curves.

I would assume that if the acceleration changed, then so does the horizon. For example the point at which the universe went from deceleration to acceleration, the horizon's distance began to shrink.

** True, for small accelerations the horizon may be far away indeed, such as the cosmological event horizon. But still where there is one there is always the other. **
Nope, what I wanted to learn you is that the Unruh effect is a *global* result and has nothing to do with the local acceleration of a rocket. Therefore, I do not believe it is a meaningful *physical* result - at least not in its present form.

Where did you get "global" from the equations? The equation gives temperature for a given acceleration, that's all. The equation does not ask for the accelerating particle's mass or charge or spin or distance from any other particles, etc. It applies to acceleration, period. I simply assume that the equivalence principle gives an acceleration that can be entered into that equation. This seems straightforward to me.

** And I don't understand your objection to Torsten, either. Didn't we already know that singularities were solutions to Einsteins equation, which also gave curved spacetime around them? **
Yes, but the question is whether Torsten's construction gives rise to that kind of singularities. If you would take his definition of the mixed connection and do the math, then you easily see that there is no curvature effect outside the body, so an observer from outside wouldn't notice anything. Therefore, there is no physical matter source involved - and actually it is no so difficult to understand why but for the moment I leave the matter up to Torsten.

This sounds similar to how they calculate the gravitational field at the surface of a sphere by using the mass inside that surface. It seems just as strange that all the mass outside the surface does not enter the equation (and seems to have no effect) on the gravitational field at a point on the sphere.
Also, it seems you are worried about things outside the support within which quantities are defined. I'm not so sure that it is valid to question results because of undefined quantities. If Torsten leaves undefined quantities outside the support, then nothing right or wrong can be based on undefined things. If a field is defined on a curve and results obtained from the field, then it is not valid to denouce those results because the field in not defined elsewhere.

 

[Careful]

**Infinity has nothing to do with it, and I think you know this too. Only where there is acceleration there is a horizon. **

No, there is not, you clearly did not take your sheet of paper. Do you know the derivation or not?

**
I would assume that if the acceleration changed, then so does the horizon. **

You simply do *not* seem to get that a vacuum state and the associated Fock particle notion are *global* concepts and in the Uruh effect, there is no point in throwing the low frequences away by making a cutoff on lab scale (since the very long wavelengths are all we get). Did you read the paper of Rovelli which I suggested to you ?? I guess not, since you would have understood my comments otherwise.

**
Where did you get "global" from the equations? The equation gives temperature for a given acceleration, that's all. **

Question : what does temperature mean and how is it related to the ergodic hypothesis ?

**The equation does not ask for the accelerating particle's mass or charge or spin or distance from any other particles, etc. It applies to acceleration, period. I simply assume that the equivalence principle gives an acceleration that can be entered into that equation. This seems straightforward to me. **

Again, this is the THIRD time that I urge you to see HOW the equation is DERIVED which requires a proper understanding of QFT. Please, have some respect for people who refer you to this work in good faith.


** Also, it seems you are worried about things outside the support within which quantities are defined. I'm not so sure that it is valid to question results because of undefined quantities. If Torsten leaves undefined quantities outside the support, then nothing right or wrong can be based on undefined things. If a field is defined on a curve and results obtained from the field, then it is not valid to denouce those results because the field in not defined elsewhere. **


I beg you pardon ! The gravitational field is stilll well defined by the metric outside the body (and as I said before, this remains invariant under Torsten's construction). Please give the honor to Torsten for a reply, I remember having said something similar (to you ?) previously : it seems I was right from the very beginning (and I might be just right again, imagine yourself ).

Cheers,

Careful

 

[Mike2]

**Infinity has nothing to do with it, and I think you know this too. Only where there is acceleration there is a horizon. **

No, there is not, you clearly did not take your sheet of paper. Do you know the derivation or not?

The question was: in what physical situation is there an acceleration without a horizon?

The Black Hole event horizon is inside a gravity well that is an accelerated reference frame with respect to far away. With the Cosmological Event Horizon there is faster speed of expansion with distance (an acceleration). And with the acceleration of a particle there is a distance behind the particle at which light cannot reach the particle (assuming it continues to accelerate at that rate).

**
Where did you get "global" from the equations? The equation gives temperature for a given acceleration, that's all. **

Question : what does temperature mean and how is it related to the ergodic hypothesis ?

AFAIK you can get a temperature from the speed of one particle, and this is a local effect.

 

[Careful]

** The question was: in what physical situation is there an acceleration without a horizon? **

An inertial observer which puts on his rocket engine for a while and then switches it off again is a nice example (which I gave you already). But, to avoid any cunfusion : what definition of horizon do you use ?

** The Black Hole event horizon is inside a gravity well that is an accelerated reference frame with respect to far away. **

That does not make any sense, where did you get that from (I guess I know what you want to say but you state it miserably) ?

**
AFAIK you can get a temperature from the speed of one particle, and this is a local effect. **

? This is entirely false and moreover, you did not seem to grasp that the notion of a particle *itself* is a global one which effectively extends over a great distance in this case since the Unruh temperature is terribly close to the absolute zero point.

Again, you might want to study this paper of Rovelli. There, you will see that some extra physical *assumption* (that of thermal time) is needed to even make (remotely) sense of the Unruh effect in terms of ``localized´´ acceleration. I do not remember the exact details anymore but I definately was far from happy about it.

Cheers,

Careful

 

[Mike2]

** The question was: in what physical situation is there an acceleration without a horizon? **

An inertial observer which puts on his rocket engine for a while and then switches it off again is a nice example (which I gave you already). But, to avoid any cunfusion : what definition of horizon do you use ?

I don't even think this is in good faith anymore. Of course, if he turns off his rocked engine there will be no horizon because there will be no acceleration. But my question is when there IS acceleration when is there not a horizon?

** The Black Hole event horizon is inside a gravity well that is an accelerated reference frame with respect to far away. **

That does not make any sense, where did you get that from (I guess I know what you want to say but you state it miserably) ?

Would you kindly stop playing games? doesn't curved spacetime exacly mean that inertial reference frame is changing, or in other words, there is an acceleration?

**
AFAIK you can get a temperature from the speed of one particle, and this is a local effect. **
? This is entirely false and moreover, you did not seem to grasp that the notion of a particle *itself* is a global one which effectively extends over a great distance in this case since the Unruh temperature is terribly close to the absolute zero point.

Again, you might want to study this paper of Rovelli. There, you will see that some extra physical *assumption* (that of thermal time) is needed to even make (remotely) sense of the Unruh effect in terms of ``localized´´ acceleration. I do not remember the exact details anymore but I definately was far from happy about it.

Dont' they assign a temperature to a particle accelerated to a give velocity in a particle acceleration chamber?

 

[Careful]

** I don't even think this is in good faith anymore. Of course, if he turns off his rocked engine there will be no horizon because there will be no acceleration. But my question is when there IS acceleration when is there not a horizon? **

I will stay polite one last time:
(a) You do not seem to appreciate my point that local acceleration has nothing to do with radiation; at least nothing in the Unruh derivation suggests that (and check out Rovelli's work where a modest attempt is made to improve upon this)
(b) It is entirely possible to construct accelerating observers which are asymptotically free falling such that there is no event horizon (just imagine bending the worldines while holding the endpoints at infinity fixed).

** Would you kindly stop playing games? **

I am not playing games, you are :
(a) I try to teach you an insight which you don't find in textbooks and you just refuse to listen even
(b) I see no goodwill from your side concerning my suggestions to go deeply through the derivations (and preferably do them yourself) - it occurs to me that you merely cite things you have heard somewhere...

** doesn't curved spacetime exacly mean that inertial reference frame is changing, or in other words, there is an acceleration? **

No, an intertial frame in curved spacetime does not accelerate by DEFINITION (of course it accelerates with respect to the Minkowski *background* metric). Inertial means : freely falling. You seem to think that observers are necessarily freely falling in the *physical* spacetime (which is of course not the case at all : for example we earthly inhabitants are not).

** Dont' they assign a temperature to a particle accelerated to a give velocity in a particle acceleration chamber? **

Not at all (and those who do are crackpots). Temperature is associated to statistics and considerations like the thermodynamical limit (that is an infinite number of degrees of freedom).

Cheers,

Careful

 

[rtharbaugh1]

Mike2
takes one to know one, eh?
R

 

[Careful]

Mike2
takes one to know one, eh?
R

I will go to third order here : it takes one to know one who knows Let's refrain from making silly comments, shall we? I hope that in the mean time you started reading a paper on CDT which is actually much more useful than not listing to answers people give on your questions and repeating the same mistakes over and over again.

 

[Mike2]

I will go to third order here : it takes one to know one who knows Let's refrain from making silly comments, shall we? I hope that in the mean time you started reading a paper on CDT which is actually much more useful than not listing to answers people give on your questions and repeating the same mistakes over and over again.

The trouble is that CDT at this point is speculative. And it doesn't even give us matter yet. At least that's what I've been told... in these forums, by people as educated as yourself. (No, I don't remember who).

I'm afraid I am only on the verge of understanding the mathematics involved. I work full time and have lots of things to do. It would be nice if someone other than yourself would confirm your statements. For it seems your answer is to refer me to speculative references such a CDT or QFT in curved space, etc. I was hoping to keep it at the level of concrete examples. When does acceleration not imply an horizon of some kind?

You mentioned, "(b) It is entirely possible to construct accelerating observers which are asymptotically free falling such that there is no event horizon (just imagine bending the worldines while holding the endpoints at infinity fixed)." Can you describe a physical scenario (with a rocket ship, etc) that would exemplify this claim.

Thanks you.

 

[rtharbaugh1]

Hi Mike2

Your question seems reasonable to me. Acceleration and free-fall seem to me to be mutually exclusive concepts. I will go look for more information.

R

 

[Careful]

**doesn't even give us matter yet. At least that's what I've been told... in these forums, by people as educated as yourself. (No, I don't remember who). **

Ah, it seems you are now eating from both sides : on one hand showing interest and on the other declining it when you have to make an effort. But it is true that CDT is highly speculative (and I am rather pessimistic about it), but despite this it is a very useful approach to understand better the problems at hand in trying to nonperturbatively quantize gravity.


** I'm afraid I am only on the verge of understanding the mathematics involved. **

Ok, no problem take your time. Look on the webpage of 't Hooft, there is a useful reference to a good QFT course which is very complementary to the strict mathematical language Wald uses. Gaining a proper understanding of QFT is a serious effort which can take a few years, even of the very best students (and still then people do not agree upon what it means )

**
I work full time and have lots of things to do. It would be nice if someone other than yourself would confirm your statements. For it seems your answer is to refer me to speculative references such a CDT or QFT in curved space, etc. **

Well FREE QFT in curved spacetime is rather well understood (lots of rigorous results have been obtained here), it is just that interacting QFT's are so troublesome.

**I was hoping to keep it at the level of concrete examples. When does acceleration not imply an horizon of some kind?
You mentioned, "(b) It is entirely possible to construct accelerating observers which are asymptotically free falling such that there is no event horizon (just imagine bending the worldines while holding the endpoints at infinity fixed)." Can you describe a physical scenario (with a rocket ship, etc) that would exemplify this claim. **

First of all, really just imagine a bunch of straight treads pinned to a sheet of paper which you push in the middle and hold fixed at the boundaries (imagine the time axis to be oriented along the origal straight lines) - this shows such thing exists. A physical interpretation would be a bunch of rockets which pull off and accelerate for a long time and then lower the acceleration to zero at infinity.

But all this is not the main issue : I just wanted to point that there are some non local features in both the Hawking and Unruh effect which might (and definately do IMO) jeopardize a *physical* interpretation. My objections which I have tried to convey to you relate to the problems associated to the vacuum state and vacuum fluctuations in QFT (and as such are very fundamental). Moreover, you must realize that these temperatures are ridiculously low, I think it was of the order of 10^{-11} Kelvin for realistic accelerations (I think I took 5 G when I once calculated this).

If you have not too much time, but still want to get a good understanding of physics (and you seem to have a fairly good background education) then I advise you to take it step by step. In this respect the program of 't Hooft : ``How to become a good theoretical physicist ?´´ is definately a good way to achieve this.

Cheers,

Careful

 

[rtharbaugh1]

Mike2

Seems that freefall and acceleration are not considered mutually exclusive. An object in free fall is in fact being accelerated by the force of gravity.

However, there is another way to look at this which I have been trying out. The force of gravity may not be a real force at all.

The universe is known to be expanding. The usual interpretation of data is that local objects, planets stars and galaxies, are not expanding. But what if they were? Two expanding solid objects would push each other apart. Two expanding solid objects in free fall would seem to approach each other. Can this push explain the force of gravity, and solve the heirarchy problem? I don't know.

But if this line of thought holds, objects in free fall are not accelerating.

R.

 

[rtharbaugh1]

I had a look at the t'Hooft page,

http://www.phys.uu.nl/~thooft/theorist.html

It looks promising.

R.

 

[Careful]

**Mike2
Seems that freefall and acceleration are not considered mutually exclusive. An object in free fall is in fact being accelerated by the force of gravity. **

Your ``acceleration´´ in not an intrinsic quantity (and therefore not physical - it is a property with respect to some Newtonian frame of reference). Now, you might open a book on GR and study how this
lead Einstein to the equivalence principle.

** However, there is another way to look at this which I have been trying out. The force of gravity may not be a real force at all. **

Well, here of course we fundamentally disagree.

 

[rtharbaugh1]

Ok, I have dipped into the t'Hooft page and it looks like it will be worth study. In fact, Careful, I am grateful to you for this link, and would like to retract my decision not to talk to you, even though your tendency toward insult gives me a headache.

We cannot fundamentally disagree about the expansive explanation of gravity, because I have not taken it as a committed stand. I am just trying to find out where it fails.

I have studied Einstein's equivalence principle including reading the original texts. I have taken and passed a course in modern physics at a state university, as well as the three prerequisite classical physics courses that they offered. I will review this material, but first as an exercise, try to recall it here.

Einstein used an elevator as a model IIRC. A person inside an elevator cannot look outside to find out what state of motion they are in. So, if they feel weight, they cannot know if it is due to a linear acceleration in the vertical direction, or alternatively if it is due to being suspended, motionless, in a gravitational field.

Is this what you meant?


Also, there is one way a person in an enclosed space might be able to differentiate between linear acceleration and gravity. If close enough to the gravitational object, the observer should be able to measure an angle between the direction normal to the horizon at opposite sides of the enclosure. This angle would not appear if they were experiencing linear acceleration.

If I am not mistaken, this measurement is part of the Gravity Probe B experiment which is now under data analysis.

R

 

[Careful]

**
Einstein used an elevator as a model IIRC. A person inside an elevator cannot look outside to find out what state of motion they are in. So, if they feel weight, they cannot know if it is due to a linear acceleration in the vertical direction, or alternatively if it is due to being suspended, motionless, in a gravitational field.
Is this what you meant? **

Unless I misunderstand you, I think you got it wrong. Einstein's beautiful observation was that a lab experiment performed in free fall in a uniform gravitational field, is not influenced at all by the gravitational force. In either, the outcome is the same as for an inertial observer in free space.

 

[rtharbaugh1]

OK fine I got it wrong. No surprises there. Probably another source. Ideas and images stick in my memory, but unfortunately names and references do not.

But the idea does not seem to me now to be in conflict with your summation. The measurement of weight is a lab experiment, right?

Perhaps you missed my edit. Wish I could quote a source for that. I came across it in a discussion on the boards. The idea is that a suspended observer should be able to detect an angle in a uniform gravitational field, since the field is a curvature around a point source. An observer under forced acceleration, say by a rocket for example, would not detect any such angle.

R.

I find a description of the elevator experiment in t'Hooft,

http://www.phys.uu.nl/~thooft/lectures/genrel.pdf

on page nine, under the heading "The constantly accelerated elevator. Rindler space"

 

[Careful]

Hi guys,

I have taken my time now to type out all the details, hope it is clear now why I say that the derivations of the Unruh effect do not tell us too much.

**But the idea does not seem to me now to be in conflict with your summation. The measurement of weight is a lab experiment, right? **

Upon closer inspection your example is also fine

** The idea is that a suspended observer should be able to detect an angle in a uniform gravitational field, since the field is a curvature around a point source. An observer under forced acceleration, say by a rocket for example, would not detect any such angle. **

Sure, you simply want to say that geodesics will converge for testparticles in the gravitational field generated by a pointlike source.

But we are distracting from the issue here : in the Unruh effect both observers are living in the *same* spacetime while the considerations behind the equivalence principle (free falling observer in gravitational field or inertial observer in free space) deal with observers in *different* spacetimes. As you know, these considerations lead to the rejection of the concept of inertial observer and to the question how gravitational effects could be detected (by measuring the deviation vector of free falling test particles). Therefore, gravitation is a *second* order effect with respect to the gravitational potential (which expresses itself through the appearance of the curvature tensor in the geodesic deviation equation).

However, the covariance principle in GR tells you that the physics behind the gravitational field is objective as are the observations of properties which require no extra background structure, such as a foliation. GR has a *local* theory of measurement (no global foliation needed - actually QFT has also), but does need however a *dynamically* generated notion of time in order to make sense (such notion can however be introduced in solutions providing a special physical starting point, such as a big bang - but in all generality it is lacking). QFT however introduces the FOCK vacuum state as a *kinematical* background object (
related to an *a priori* notion of time) which is not invariant under general coordinate transformations (which indeed leads to the notion of non-equivalent vacua through performing SINGULAR coordinate transformations - such as happens in the Unruh effect) but is invariant under a representation of the Lorentz group in Minkowski - good coordinate transformations do of course lead to equivalent theories. Since this is a delicate point, let me state this in full clarity :
(a) What I meant is that there does *not* exist a covariant algorithm which singles out a natural vacuum state in a background spacetime (for QFT) - it is like asking for a covariant algorithm which singles out a smooth physical time function.
In Minkowski of course, one can figure out a fully covariant principle which singles out the Minkowski vacuum state and in (not necessarily symmetric) spacetimes with a big bang one can construct canonical timefunctions which are however non smooth (and do not produce Killing fields) at a set of measure zero which causes radiation there.
(b) What is on the other hand clear however is that once a vacuum state has been chosen, the physical predictions remain invariant under coordinate transformations (when suitably applied).
The problem of quantum covariance which LQG has to solve (but does not mange to) is of course still much more complicated, since the gravitational degrees of freedom have to be incoorporated in the state description as well.

However, let us return to the Unruh effect. In QFT, we have to pick out some natural vacuum state for the detector *besides* the Minkowski vacuum state for inertial observers. If one wants a localized, natural candidate for the detector vacuum state (and actually avoid all the horizon nonsense), then one has to proceed by proposing a coupling between the background Klein Gordon field and a quantum field associated to the dector, which *depends* on the (relative) acceleration of the observer. Such local coupling however will put a restriction to the accuracy up to which long wavelengts can be distinguished depending on the sensitivity of the receptor cells. Therefore, the thermal state, as obtained by the standard derivation is merely an intermediate stage of the calculation, what really counts is the statistics of detector ticks (and this should not depend at all on whether an horizon has formed or not). So, I perhaps should have explicitely stated it like this before : the thermal state representation of the Minkowski vacuum with respect to the Rindler observers has no physical value (just as I said because it depends on global aspects like particle definitions and a global horizon and so on). What does have physical value however is the statistics of detector clicks which depend on local couplings of detectorfields to the Klein Gordon field (conveniently written out in the Rindler frame). To my knowledge, only simple detectormodels have been worked out and are thus by far insufficient to confirm whether measurements will reveal a thermal spectrum or not.
This, to my knowledge, is still an open problem. However, we know it will not exactly be what we usually call thermal (for comments on that see the book of Wald).

Cheers,

Careful

 

[rtharbaugh1]

"Sure, you simply want to say that geodesics will converge for testparticles in the gravitational field generated by a pointlike source. " (Careful)

Yes, I think that part is clear. However, the interesting idea is that this provides a way to determine by experiment a difference between gravitational and inertial acceleration, seemingly in contradiction to the equivalence principle, at least in some special circumstances. I note here that all gravitational fields, so far as I know, are taken as from a point...hence the idea of center of gravity. For example, the gravitational field due to a hollow sphere (or a smooth distribution of pointlike particles) measured from within the sphere (or the dust cloud) is zero.

"in the Unruh effect both observers are living in the *same* spacetime while the considerations behind the equivalence principle (free falling observer in gravitational field or inertial observer in free space) deal with observers in *different* spacetimes. As you know, these considerations lead to the rejection of the concept of inertial observer ...(quote continued after my insertion, rth)" (Careful)

Would you confirm my interpretation of the idea of inertial observer as an unmoving observer, that is, an observer in a preferred reference frame? I am aquainted with the idea that there is no preferred reference frame, no unmoving observer, but I would like to verify that this is what is implied by inertial observer, and your assertion that the concept of inertial obseerver is rejected.

"(quote continued)...and to the question how gravitational effects could be detected (by measuring the deviation vector of free falling test particles). Therefore, gravitation is a *second* order effect with respect to the gravitational potential (which expresses itself through the appearance of the curvature tensor in the geodesic deviation equation). " (Careful)

I think this may be the same idea or similar to what I have restated as local expansion from every point. Gravity is an acceleration, which has time squared in the denominator, and so is graphed as a curve, right? Keep in mind that I have only a vague concept of tensor math, and cannot follow the calculations, so must try to reduce the concepts to what I know of spatial geometry.

If there is local expansion from every point, then, contrary to what is commonly taught, planets and stars and galaxies are expanding along with but perhaps slightly slower than free space. Two solid bodies in contact will force their centers of gravity apart. Two solid bodies in close proximity will seem to approach each other, and obey the inverse square law, since the intervening space is also expanding, albeit at a faster rate.

I know this reinterpretation is difficult and requires a paradigm shift which takes some effort, but I think it may have the advantage of eliminating some paradox, and may provide a way to resolve the heirarchy problem. Anyway I would like to know where this model fails, or if it does, since I don't currently see any error.

I suspect the error in my interpretation, if there is one, probably lies somewhere in the following quote from your last post:

"However, the covariance principle in GR tells you that the physics behind the gravitational field is objective as are the observations of properties which require no extra background structure, such as a foliation. GR has a *local* theory of measurement (no global foliation needed - actually QFT has also), but does need however a *dynamically* generated notion of time in order to make sense (such notion can however be introduced in solutions providing a special physical starting point, such as a big bang - but in all generality it is lacking). QFT however introduces the FOCK vacuum state as a *kinematical* background object (
related to an *a priori* notion of time) which is not invariant under general coordinate transformations (which indeed leads to the notion of non-equivalent vacua) but is invariant under a representation of the Lorentz group in Minkowski. This, if you want to, is the problem of quantum covariance which LQG has to solve (but does not mange to). From the previous discussion, it is a priori clear that any vacuum state of QG shall look very different from the usual Fock state of QFT (for a discussion of these ``polymer´´ states, check out the LQG literature). "(Careful)

I am not totally comfortable with many of these ideas and will have to make a further study to try to find where or if they contradict the idea of local expansion as a source of the (then) pseudo-force we know as gravity. My first thought is that local expansion does not require, and in fact contradicts, the idea of a big bang, which contradiction I see as one of the advantages in the reinterpretation. I sense that you will agree that the idea of a big bang presents many unresolved paradoxes (singularities) which need to be removed before we can establish a clear idea of quantum gravity. I have tried to learn QFT but the math is still beyond my reach. I will have to look up Fock vacuum. However you seem already to think that it is not sufficient for QG and "it leads to the notion of non-equivalent vacua."

As to Lorentz and Minkowski, I think you will agree that the Lorentz metric is fine locally but breaks down or blows up at extrema, such as horizons. It seems to me now from your earlier comments that you do not like the idea of horizons, but I have found them quite useful, so I would like to explore your objections if we get time and space to do so. For Minkowski, my thoughts lead me to believe that spacetime may have many times as well as many spaces, so the Minkowski metric needs to be changed for a more comprehensive view such as we will need for QG. I want to explore the idea that due to space-time equivalence, there should be no less that three dimensions of time to match the three dimensions of space, and in fact I suspect that there need be four of each. I suspect that this may be related to the E8 symmetry of string theory, but I am only a novice and have but a vague understanding of the maths required.

But back to Unruh,

"Such local coupling however will put a restriction to the accuracy up to which long wavelengts can be distinguished depending on the sensitivity of the receptor cells."(Careful)

Will it not also imply that there is a maximum wavelength detectable by any receptor? And is this not the same as the cosmic event horizon? I know you don't like horizons but I would like to know if it is the same or a similar idea, and where the difference, if any, lies.

"what really counts is the statistics of detector ticks (and this should not depend at all on whether an horizon has formed or not"(Careful)

I am beginning to think that your objection to the horizon idea may be that it seems to be action at a distance. Changes in local conditions cannot instantaneously affect distant horizons, right? But if this is your objection, maybe it can be resolved if you will consider that the horizon is not in fact an object in itself in any sense at all. It is not an object. To see this one must only consider the common sense notion of Earth's horizon.

We find the notion of horizon useful in navigation and find our way about the surface by noting the positions of stars and the sun relitive to the horizon, but where exactly is the horizon? Can you go there and find an object which you can touch or mark and say, "this is it!"? No. In fact, the horizon, or rather, the notion of horizon, moves instantaneously with the observer. There is no contradiction or conflict with the action at a distance paradox, because the horizon is not a thing in itself, but is actally defined by the position of the observer. No matter how fast you go or how long you travel, you can never reach your horizon.

This is the same for the event horizon and for the cosmic horizon. They do not exist as objects in themselves, but only as notions or concepts totally dependent on the local condition of the observer.

Now to relate this to Unruh, only consider the ideal gas law. The horizon is constant, so the volume is constant. But Unruh suggests that acceleration results in local virtual particles becomming "real". As in any thermal system, if you increase the number of particles, while holding the volume constant, you will experience an increase in temperature.

Now there are a lot of particles inside the cosmic horizon and the increase in local particles is bound to be very small, so the increase in thermal clicks will be very small, but in principle should be detectable. As acceleration increases greatly, the number of virtual particles which will be encountered as real clicking particles should become significant. In fact, spacetime then becomes "solid" as a test probe approaches light speed, consistant with the idea that light speed is a constant and cannot be exceeded.

I think I am done for now and will go back to my mundane study of tensors, although frankly I often feel I could get as much out of the book by banging my head against it as by reading it. As it happens my time is of little value to anyone, so I have lots of it to use in head banging. I do appreciate that your time is valuable, and I do thank you for trading some of your valuable time for my worthless but still enduring existence. I wish I could find a university which would tolerate my presence and a sponsor to pay for it, but so far to no avail.

nevertheless, as you say,

cheers.

Richard T. Harbaugh

 

[Careful]

**
Would you confirm my interpretation of the idea of inertial observer as an unmoving observer, that is, an observer in a preferred reference frame? I am aquainted with the idea that there is no preferred reference frame, no unmoving observer, but I would like to verify that this is what is implied by inertial observer, and your assertion that the concept of inertial obseerver is rejected. **

Well what I meant is that Einstein concluded from this is that the laws of physics should be defined irrespective of some special reference frame. Obviously, inertial observers still exist but we earthly inhabitants are definately not inertial.

** Gravity is an acceleration, which has time squared in the denominator, and so is graphed as a curve, right? **

Gravity is an acceleration which cannot be undone by a coordinate transformation. As the rocket thought experiment pointed out, an accelerating (in the Newtonian sense) observer in empty space (with -g) is still in empty space. You really have to understand tensors well in order to appreciate this idea.


** I will have to look up Fock vacuum. However you seem already to think that it is not sufficient for QG and "it leads to the notion of non-equivalent vacua." **

It is known that the Fock vacuum is not suitable, finding a Hilbert space representation of the constraint algebra and getting out semiclassical states is probably the most difficult issue in LQG.

**As to Lorentz and Minkowski, I think you will agree that the Lorentz metric is fine locally but breaks down or blows up at extrema, such as horizons. **

Nope, the accelerating observers are Killing observers and actually leave the Minkowski metric invariant. It is the coordinate transformation (from inertial to accelerating observers) which is singular at the bifurcation horizon.

** But back to Unruh,
"Such local coupling however will put a restriction to the accuracy up to which long wavelengts can be distinguished depending on the sensitivity of the receptor cells."(Careful)
Will it not also imply that there is a maximum wavelength detectable by any receptor? And is this not the same as the cosmic event horizon? **

Well, there is certainly a limit to the wavelenghts which can be detected, but this can be resolved by building bigger and bigger telescopes.
But I have no problems with event horizons, you know. It is just that local physics cannot depend on them, implying that the derivation of the Unruh effect does not necessarily mean at all that a thermal spectrum is to be observed. That's all I said.

**, you will experience an increase in temperature. **

Here I think you misunderstood Unruh, these virtual particles become only ``real´´ when they interact with a detector which will merely thermalize (again, this is not for sure ).

** In fact, spacetime then becomes "solid" as a test probe approaches light speed, consistant with the idea that light speed is a constant and cannot be exceeded. **

Well, you seem to say that a large mass density could be created from the vacuum through some inertial effect. First of all the state of the radiation field will also change when energy is withdrawn by the detector (there is a nice paper about this by Wald and Unruh 1984), second it costs also energy to accelerate mass in Minkowski spacetime (think about the rocket fuel) so some form of equilibrium has to settle in eventually and looking at the value of the Unruh temperature, my guess is that the fuel will just burn out, the rockets will stop accelerating and the minkowki vacuum state will have become slightly thermal (due to the heat caused by the fuel), but the Unruh effect will not have been important at all (it is just waaaay to insignificant for all that)

Anyway, gravity is the most important force on the cosmic scale, you cannot replace it in the way you seem to be suggesting.

Cheers,

Careful

 

[rtharbaugh1]

Thanks for the discussion.

R.

 

[Careful]

Thanks for the discussion.
R.

Hi, I updated my second last post since I might have been a bit unclear about the covariance issue. Now, concerning these detectors: it is a funny story. There has been quite some argument about wether a detector would register something or not and people have been busy constructing models in which there would be no response as otherwise (it all depends upon the coupling between the detectorfield and the KG one - and the evolution of the detectorfield) Anyway, I do believe there might be some response in principle but doubt whether it would be thermal.

 

[Mike2]

Hi, I updated my second last post since I might have been a bit unclear about the covariance issue. Now, concerning these detectors: it is a funny story. There has been quite some argument about wether a detector would register something or not and people have been busy constructing models in which there would be no response as otherwise (it all depends upon the coupling between the detectorfield and the KG one - and the evolution of the detectorfield) Anyway, I do believe there might be some response in principle but doubt whether it would be thermal.

Every particle in an accelerating body requires energy from somewhere to accelerate with the rest of the body. Therefore there are at least photons striking each and every accelerating particle (or it wouldn't be getting the energy to keep up with the rest of the particles). The question is where do these photons come from, and is their orientation of a statistical nature. If they are of a statistical nature, then perhaps this is the Unruh radiation, right?

 

[Careful]

Every particle in an accelerating body requires energy from somewhere to accelerate with the rest of the body. Therefore there are at least photons striking each and every accelerating particle (or it wouldn't be getting the energy to keep up with the rest of the particles). The question is where do these photons come from, and is their orientation of a statistical nature. If they are of a statistical nature, then perhaps this is the Unruh radiation, right?

I explained you that the Unruh effect is too small to serve as an ``engine´´. Moreover, what is detected all depends on the dynamics of the detectorfield and the coupling to the KG field. I told you that there are ``silent´´ detector models as well as those which register ``something´´. I cannot tell you anything more since AFAIK, no further results on this topic are known (and I am not going to throw some wild speculation into the air).

Cheers,

Careful

 

[Mike2]

I explained you that the Unruh effect is too small to serve as an ``engine´´. Moreover, what is detected all depends on the dynamics of the detectorfield and the coupling to the KG field. I told you that there are ``silent´´ detector models as well as those which register ``something´´. I cannot tell you anything more since AFAIK, no further results on this topic are known (and I am not going to throw some wild speculation into the air).
Cheers,
Careful

I'm not even sure I was talking about "Unruh radiation". I was merely commenting that when a body is accelerated, there is energy/photons given to each particle throughout the body. Suppose we accelerate a single particle with a laser? Would the particle always get only energy in one direction? Or would the particle begin to heat up because of the statistical nature of the laser light? Each photon cannot always hit the particle dead on, right? But on average it will accelerated in one direction. So the off-center hits would accumulate and effect the particle as if thermal radiation, right? I suppose the uncertainty principle would tell us how likely we could hit the particle dead on. If we did hit it dead on every time, then there would be complete uncertainty about the momentum of the photons, right. And the particle would appear to oscillate/heat in the direction of motion. But if we could control the momentum, then we would lose certainty about direction and the particle would heat up in the direction transverse to acceleration. Is there a relation that tells us what the particle will heat to for a given acceleration? Is this independent of the accuracy of the momentum or direction of the incident photons? Is this the Unruh effect? Thanks.

 

[rtharbaugh1]

"there is another way to look at this which I have been trying out. The force of gravity may not be a real force at all.

The universe is known to be expanding. The usual interpretation of data is that local objects, planets stars and galaxies, are not expanding. But what if they were? Two expanding solid objects would push each other apart. Two expanding solid objects in free fall would seem to approach each other. Can this push explain the force of gravity, and solve the heirarchy problem? I don't know.

But if this line of thought holds, objects in free fall are not accelerating." (Richard T. Harbauagh)

I don't wish to belabor this idea, but I do want to find out where, or if, it fails. It has occurred to me that, if it were stated as a theory, it would be falsifiable, however not in an entirely satisfactory way, since it would, at this point, only be by a lack of evidence.

If gravity waves or gravitons are shown to exist, then the idea is false. The idea that gravity may be regarded as a pseudoforce, due to local expansion of the universe from every defined point, woud not require gravitons or a gravity field (in the sense of a quantum field or EM field).

It would have the advantage of removing the need for a big bang singularity, it would lead to a way to reconcile the heirarchy problem, and it would be, AFAIK, consistant with both GR and QM, so would lead to a geometry that would contain both theories.

I am not asserting this idea as a fact, but only as fully falsifiable. I do have some ideas about attainable (even cheap) apparatus for further testing, but would like to fly the idea for a while in the hope that someone can shoot it down.

Thanks,

Richard