Cosmological Hawking radiation

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HAWKING RADIATION

Cosmological Hawking radiation


In an expanding universe we expect our limit of observability to be bounded by a cosmological horizon. A cosmological horizon is an effective horizon, in that its position depends on the viewer's situation. In many respects its behaviour is analogous to that of a planetary horizon.

Planetary analogies

If we assume that the Earth is a perfect sphere, and that an observer's eyes are at a particular height, we can calculate the furthest points of the surface that the observer can see, and draw a boundary on the surface dividing "what can be seen" from "what cannot be seen", as circle marking that observer's horizon. if they try to approach part of the horizon, it recedes from them, as we calculate and draw new circles corresponding to their new positions – the horizon position is observer-dependent.

In real life, the surface is not perfectly smooth, the viewable surface is not a single continuous area, and the horizon is not a simple unbroken straight line. Part of the horizon might consist of the visible faces of two mountainsides, with a third more distant mountain visible between them - the visible surface of this third mountain will not be connected to the rest of the viewable surface.

If we look out at the ocean, the action of waves means that the extent of the viewable surface is constantly fluctuating and changing, and instead of stopping sharply at a given distance, the surface becomes more and more fragmented with distance, until it "peters out". Closer areas of ocean have a fully-visible surface, further areas start to have concealed regions representing the far-sides of waves, and as we look further away, the proportion of "missing" regions increases and of visible regions decreases, until we are looking at a progressively smaller collection of disconnected surface patches that become smaller and more widely separated until they disappear altogether.

In addition, these visible patches are not static - they fluctuate in size, appear from nowhere and disappear again, and join and detach from other adjacent patches. If we try to watch a marker buoy near the horizon limit, it will repeatedly appear and disappear, with some parts of its history being visible and other parts being hidden.

Cosmological horizon behaviour

Cosmological horizons behave similarly - they fluctuate in response to changes in geometry due to local physics both ahead of and behind the horizon, and represent the breakdown of observerspace causality for a distant future observer. They also seem to show quantum behaviour in the sense that visible patches seem to appear and disappear acausally.

Imagine that the horizon intersects some ancient baseball field, and someone on our side of the horizon once threw a baseball away from us to a batter positioned behind the horizon. To us, the ball never seems to reach its (to us unseen) target, but is frozen into the horizon surface. When the baseball bat then hit the ball, behind the horizon, the resulting acceleration caused a gravitoelectromagnetic distortion that made it easier for light to travel in our direction, making the ball visible to us, as the effective horizon surface snapped discontinuously to a position behind it. We might see the ball in two places at once, with the thrown ball apparently frozen into one section of horizon, while the returning ball is already visible in an adjacent region thanks to events occurring behind the horizon, causing it to retract.

We might even see the ball being hit, sightly off to one side, before it is seen to be thrown.

What we are seeing is an apparent acausality similar to what happens under quantum mechanics - cause without effect, effect without cause, and effect sometimes seen before cause – but in this case the underlying physics is completely classical, and this is an artefact of our only being able to access a part of the complete dataset. The worldlines that we see as incomplete are in fact continuous, the surface is actually continuous rather than fragmented, and local causality and local physics are playing out exactly as they ought to.

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