"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