OnlyMe said:
The equivalence principle, is just a bit more limiting than you suggest. Though it is arrived at through acceleration, it is the inertial resistance to the acceleration.., the constantly changing state of motion, which is equivalent to the force experienced as gravity. It really reduces to similarities between inertia and gravitation. Einstein never cracked that nut, though he spent a great deal of time trying.
Getting any deeper into what the implications of the dynamics of space may represent, within what appears to be implied in your above post(s), begins to venture into some shaky ground.
I believe that it ultimately turns toward some attempt to better define the mechanism of inertia. There are at least a few papers available, focused on attempts to address inertia as emergent from QM. I have seen none as yet that presents a compelling argument. Though I find the idea that the dynamical Casimir effect might be somehow involved, intriguing.
I don't know where else to take this discussion. Any which way you turn it becomes a tangled web.
Just say what you think. It doesn't really seem to be a definite answer. Any discussion is better than none.
Since it was mentioned Einstein had some ideas about space, but reading his works on it I would say a modern explanation is probably better.
Relativity
http://www.bartleby.com/173/
It doesn't really seem to be a definite answer.
You're right, it is not a definite answer. The problem is nearing 100 years old now. If we accept that the equivalence principle represents some connection between inertia and gravity, how can we explain that connection? Einstein seemed to favor a Machian view of inertia, where inertia was an artifact, of the influence of the gravitational interaction of all mass in the universe, on any individual body or object. He was unable to incorporate this view into his field equations and GR... And it does not seem that anyone has had any better success.
So the question becomes:
- Does the equivalence principle represent some coincidence? Where inertia and gravity only look the same. or
- Since we know that Einstein's field equations do describe gravity better than all other models (so far), are we missing something when we attempt to incorporate inertia into the same model? or
- Is there some error in the way that Einstein's field equations are projected into the world, as a curvature of space (or spacetime), which limits the incorporation of inertia?
Back to these a bit later...
There have been a number of attempts in the last few decades to develop a model of quantum gravity, that duplicates the predictive success of GR. So far no real success. There have also been a number of attempts to describe inertia as an emergent phenomena, within QM. Though as I mentioned earlier, none that I have seen seem to present a compelling argument, but they come closer than the search for quantum gravity, seems to.
The problem here remains the same as it has for the last 100 years. GR and QM just don't get along well when they are put together.
Again, as mentioned in an earlier post, I find the idea that inertia, is emergent from some interaction between matter and the vacuum energy of empty space, which involves the Dynamical Casimir Effect (DCE), intriguing. Though it does not address inertia, the following paper,
Observation of the Dynamical Casimir Effect in a Superconducting Circuit, does discuss the DCE.
As long as you are looking for speculation, it would seem that, if the DCE is confirmed, it would be applicable to any object moving through empty space. Though the paper linked above does not address inertia, the following excerpt(s), can be viewed as supporting some interaction between, an object moving through the vacuum energy of empty space, where that interaction represents an inertia like relationship.
from, Observation of the Dynamical Casimir Effect in a Superconducting Circuit
One of the most surprising predictions of modern quantum theory is that the vacuum of space is not empty. In fact, quantum theory predicts that it teems with virtual particles flitting in and out of existence... 40 years ago, Moore[3] suggested that a mirror undergoing relativistic motion could convert virtual photons into directly observable real photons. This effect was later named the dynamical Casimir effect (DCE)... That a mirror can be used to measure vacuum fluctuations was first predicted by Casimir in 1948[4]. Casimir predicted that two mirrors, i.e. perfectly conducting metal plates, held parallel to each other in vacuum will experience an attractive force. Essentially, the mirrors reduce the density of electromagnetic modes between them. The vacuum radiation pressure between the plates is then less than the pressure outside, generating the force...
For some perspective on the implications, for inertia in the above paper, consider the following,
from Einstein's 1905 E = mc[sup]2[/sup] paper DOES THE INERTIA OF A BODY DEPEND UPON ITS ENERGY-CONTENT?
If a body gives off the energy L in the form of radiation, its mass diminishes
by L/c2. The fact that the energy withdrawn from the body becomes energy of
radiation evidently makes no difference, so that we are led to the more general
conclusion that
The mass of a body is a measure of its energy-content; if the energy changes
by L, the mass changes in the same sense by L/9 × 1020, the energy being
measured in ergs, and the mass in grammes...
If the theory corresponds to the facts, radiation conveys inertia between the
emitting and absorbing bodies.
Taking these two references together, where it is understood that the radiation Einstein refers to, in the above quote, are photons.., and the virtual particles involved in the DCE are photon's, which should the DCE be conclusively confirmed, are converted to real photons, when exposed to matter moving at relativistic velocities, the interaction of moving bodies through the vacuum energy of empty space, becomes a viable mechanism for inertia... Or at least a mechanism worthy of further exploration.
Where the equivalence principle is considered, there are some difficulties that are not resolved, by this approach. There remains a divide between gravity, as described by GR and inertia, as an emergent phenomena associated with the DCE. However, setting that aside for a time...
Assuming that empty space is filled with the vacuum energy of QM. Any object moving through the vacuum energy would be subjected to the same interaction with virtual particles as would, a mirror. While at classical velocities that interaction would be trivially insignificant, as the velocity approaches relativistic magnitudes, that interaction could no longer be considered trivial.., and as an increase in the rate or magnitude of interaction, between an moving object and the vacuum energy of "empty space" grows, with its increasing velocity, so would the object's inertial resistance to further acceleration, increase. This is consistent with our experience of inertia, but it does not bring us any closer to a unified understanding of the relationship between inertia and gravity, as suggested by the equivalence principle.
Just as a side note; If inertia is emergent, as a function of the DCE, it might explain the OPERA FTL neutrino data. Where, neutrinos being (charge) neutral and interacting only weakly, may not theirselves be subject to the DCE, even at relativistic velocities, such that should inertia be a DCE emergent phenomena, the neutrino would not be subjected to any inertial resistance, to motion. Once in motion at any $$v <= c => v$$, a neutrino would remain at that velocity until such time as it does interact weakly with an atomic nucleus or subatomic particle.
So returning to the three choices listed earlier,
- Does the equivalence principle represent some coincidence? Where inertia and gravity only look the same. or
- Since we know that Einstein's field equations do describe gravity better than all other models (so far), are we missing something when we attempt to incorporate inertia into the same model? or
- Is there some error in the way that Einstein's field equations are projected into the world, as a curvature of space (or spacetime), which limits the incorporation of inertia?
it would seem once again, that if inertia is emergent from either the DCE or some other aspect of QM, the equivalence principle represents either a coincidence or that the physical projection of GR, as a curvature of space is not an accurate description.., and gravity is also an emergent phenomena of QM, in some way similar to inertia.
In the end I believe that gravitation, will be found to be an emergent phenomena of QM, and that the equivalence principle will not represent a mere coincidence, of experience. However, I also believe, that when that time arrives QM and the standard model, will not look completely consistent with the way we project them into the world today.
It seems to me that the odds favor some new hybrid theory and approach and that neither GR or QM as we know them today represent a conclusive description of physics and the universe, as we will come to know them, in the future.
