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Chalnoth
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Here's one:Mordred said:I've never heard of that, could you provide a reference. I' d definitely interested in reading it
http://arxiv.org/abs/1007.4044
Here's one:Mordred said:I've never heard of that, could you provide a reference. I' d definitely interested in reading it
What does that have to do with particle production in the early universe ?
..uniquely-defined particle states do not exist in general, in QFT on a curved spacetime. ... in general, particle states are difficult to define in a background-independent quantum theory of gravity...
Quantum fluctuations in the inflationary vacuum become quanta [particles]...these are vacuum fluctuations -- virtual particles. How do you suppose they become real? Now, particle production via changing gravitational fields and expansion is a real phenomenon, and might be relevant to the origin of matter.
expansion and can be imprinted in the spectrum of primordial inhomogeneities.Inflation provides a natural mechanism to account for the origin of cosmic structures. The generation of primordial inhomogeneities during inflation can be understood via the spontaneous creation of quanta from the vacuum. We show that when the corresponding stimulated creation of quanta is considered, the characteristics of the state of the universe at the onset of inflation are not diluted by the inflationary
Naty1 said:... An idea along these lines is if the proper separation distance between virtual particles expands faster than the proper path distance between them, the particle pair will not annihilate. ...
Because the cosmological horizon for an accelerated expanding universe is an event horizon, it produces Hawking radiation.phinds said:Yes, THAT I can see but I cannot see how that has anything to do with our cosmological horizon, and in fact I cannot see how the above could occur at all except in the final stages of a "big rip" scenario.
...that ALL virtual particles are at SOMEBODY'S cosmological horizon,
Naty1 said:Anyway, the first paradigm you'll likely have to forgo is that everybody observes the same particles...they don't according the Unruh effect, for example. Just like time and space are relative: different observers make different observations.
This is the exact same issue as that with the Unruh effect.phinds said:Yes, but I don't get what that has to do with what has now become my fundamental question based on responses so far.
I appreciate the effort being put into helping me out with this but I still am left feeling that I have not gotten ANY answer to my fundamental statement/question:
EVERY particle pair is at SOMEBODY'S cosmological horizon ... etc (as previously stated)
Rather it's saying that the existence of a particle is, in some cases, a matter of perspective. Also, my understanding is that the virtual particle/anti-particle pair description of Hawking radiation is more a heuristic device to get the idea across rather than an accurate description of what's going on.phinds said:OK, that to me comes across as one of those things that translate very badly from math to English and I don't get the math so it just sounds like nonsense to me.
Sounds like you, and/or the Unruh effect, are saying that every vitrual paritcle-pair both does and does not annihilate.
Also, my understanding is that the virtual particle/anti-particle pair description of Hawking radiation is more a heuristic device to get the idea across rather than an accurate description of what's going on.
...you are saying every vitrual paritcle-pair both does and does not annihilate.
or if like me, you like illustrations better than math, try the ones here:In the context of the quantum harmonic oscillator, we reinterpret the ladder operators as creation and annihilation operators, adding or subtracting fixed quanta of energy to the oscillator system.
... Because of the zero-point energy, the position and momentum of the oscillator in the ground state are not fixed (as they would be in a classical oscillator), but have a small range of variance, in accordance with the Heisenberg uncertainty principle. The zero-point energy also has important implications in quantum field theory and quantum gravity.
so the energy for particles, 'quanta', is all around us globally in the 'vacuum'...what does it take to localize it...turn it to detectable quanta??There is not a definite line differentiating virtual particles from real particles — the equations of physics just describe particles (which includes both equally). The amplitude that a virtual particle exists interferes with the amplitude for its non-existence; whereas for a real particle the cases of existence and non-existence cease to be coherent with each other and do not interfere any more. In the quantum field theory view, "real particles" are viewed as being detectable excitations of underlying quantum fields
phinds said:AGAIN, I say, and would like to see a response to, that ALL virtual particles are at SOMEBODY'S cosmological horizon, so if they fail to annihilate at a cosomological horizon, they ALL fail to annihalate (I am not conflating this with your sentence above, which is a different situation).
lukesfn said:Perhaps you are in error to assume that all virtual particles must not be able to annihilate to cause the observed radiation, may be it is only a small fraction.
Mordred said:I agree with you Phinds. I can find no reason why the cosmological horizon would have any of the following, Hawking radiation, blackbody radiation or Unruh effect. The cosmological horizon is an observational limit of what we can see and measure. The only possibility of how it would have any of the previous is that we would never be able to measure beyond that point. In that case I can see one particle going beyond that limit, the other staying where we can measure. In that case the models could describe it as one of the aforementioned. However that is the only possibility I can see. In the case of a BH event horizon, that event horizon exists for a different reason in that outside the event horizon particles and light can still escape. I've looked for papers that described any of the mentioned radiations and have yet to find one that justified the cosmological horizon portion of the articles.
Perhaps a very small number of pairs become real, and one escapes the horizon, but in this case the particles would not recombine in any reference frame.
Sounds like you, and/or the Unruh effect, are saying that every vitrual paritcle-pair both does and does not annihilate.
...One important lesson, discovered first by Fischler and Susskind[3] and developed by Bousso[4], is that in a cosmological spacetime the holographic principle must be formulated in a way that employs the lightcones of the spacetime. .. we need a framework for a cosmological quantum theory which incorporates causal structure. .. As each observer receives information from a distinct past, the algebra of observables they can measure, and hence the (finite-dimensional) Hilbert spaces on which what they observe can be represented, vary over the history. Consequently, the algebra of observables of the theory is represented on a collection of Hilbert spaces. These replace the single wavefunction and single Hilbert space of other approaches to quantum cosmology… Quantum causal histories were originally motivated by the need to provide a general framework to understand what observables are in background independent approaches to quantum gravity, such as those proposed in [16, 18, 19, 20]. In these theories a causal quantum spacetime is constructed from local changes in a spin network or a network of abstract surfaces...
...A key feature of the weak holographic principle# is that a complete description of the universe requires more than one screen [horizon]. This is simply because in a generic cosmological history there is no single screen whose past is the entire universe. Thus, a cosmological holographic theory must be a many-screens theory, each screen recording information about its causal past...we expect that no cosmological form of the holographic principle, even one that holds in the semiclassical limit, can escape the fact that many screens are necessary to give a complete description of a cosmological spacetime.,,,
phinds said:So what you are saying is that a small fraction of all virtual particle pairs fail to annihilate only because there happens to be a frame of reference from which they are at the cosmological horizon! Why would that be? It still makes absolutely no sense to me.
Chronos said:The 'location' of a black hole's event horizon is a frame dependent measurement [i.e., relative]. What a remote observer perceives is not the same as that of an infalling observer, and reconciling the two perceptions is no trivial matter. On this basis it could be argued the event horizon is purely subjective, lacking any objective sense of 'physicality'. For discussion, see http://www-e.uni-magdeburg.de/mertens/teaching/seminar/themen/touching_ghosts.pdf
The 'location' of a black hole's event horizon is a frame dependent measurement [i.e., relative].
The technical definition of true event horizon makes it a feature of global geometry, completely independent of coordinates: the boundary separating null geodesics that reach null infinity from those that don't. Apparent horizons (local trapping surfaces) are coordinate dependent.
Chronos said:The 'location' of a black hole's event horizon is a frame dependent measurement [i.e., relative]. What a remote observer perceives is not the same as that of an infalling observer, and reconciling the two perceptions is no trivial matter. On this basis it could be argued the event horizon is purely subjective, lacking any objective sense of 'physicality'. For discussion, see http://www-e.uni-magdeburg.de/mertens/teaching/seminar/themen/touching_ghosts.pdf
...unless there is a firewall at the horizon that fries all of the infalling observers upon horizon crossing...PAllen said:The 'mystery' occurs only by forgetting that the horizon is just an outgoing null surface from the point of view of infallers. If you actually set this up, assuming B could not see radio waves, they would not disinguish their crossing the horizon from any other moment; the way prior infallers look would be indistinguishable from just before to just after B crossed the horizon.
jambaugh said:… [The event horizon of a BH is not a physical object, it is a mathematically defined boundary (corresponding to physical phenomena).]..
We can recover the analogy however if we look more closely at what happens when a physical clock (or other real object) falls into a BH rather than just the behavior of the future geodesic path of the object.
Remember that an infalling physical object will have some mass or at least momentum-energy. So the full description of the space-time geometry along the future geodesic will no longer be static. The "infalling object never reaches the event horizon" derivation reflects an idealized limit as the object has zero effect on space-time. This zero effect and infinite time to infall should cancel to a finite outcome.
What should happen (and I'm working heuristically here as I've not seen or done the hard calculations) is that as the infalling object nears the event horizon, the horizon itself should move outward, reflecting the additional curvature of space-time due to the object's mass. Then in a finite time (of the external observer's clock) the event horizon will envelope the object, you'll have a no-longer-spherical BH and its EH will "ring" emitting gravity waves as it settles down to a new ever so slightly larger spherical configuration
How does the De Sitter model define cosmological horizon ?
The exponential expansion of the scale factor means that the physical distance between any two non-accelerating observers will eventually be growing faster than the speed of light. At this point those two observers will no longer be able to make contact. Therefore any observer in a de Sitter universe would see event horizons beyond which that observer can never see nor learn any information. If our universe is approaching a de Sitter universe then eventually we will not be able to observe any galaxies other than our own Milky Way (and any others in the gravitationally bound Local Group, assuming they were to somehow survive to that time without merging).
..The event horizon of a black hole is actually lightlike. This follows from it being a null surface, and you can even think of the event horizon as being "trapped light". “the EH is a null surface--more precisely, it has two spacelike and one null dimension.”
PAllen & PeterDonis…… the event horizon is a 3-surface whose tangent space at each point can be given a basis that has two spacelike basis vectors and one null basis vector…the EH is not a "thing". It's just a boundary between two regions of the spacetime.,,,,
Let me describe a Rindler horizon scenario. Two ships are accelerating together at 1 g for a long time approaching near c. One of them runs out of fuel and stops accelerating. The accelerating ship will see the out of fuel ship fall a little behind, but then become red shifted, clocks on it appear to slow down and asymptotically stop; red shift grows to infinity. The empty ship becomes invisible. The empty ship is never seen to be farther than a short distance away from accelerating ship, as long as it can be seen at all. It is 'trapped' on the Rindler horizon. Of course, for the empty ship, nothing strange has happened. The other ship accelerates away from it, getting ever further away. The empty ship can receive signals from the accelerating one, but any signals it sends can never reach the accelerating ship (because the accelerating ship stays ahead of the light; no contradiction because it had a head start and keeps accelerating.