Natural Science Forum / Physics / Research / November 2007

I think you may have missed the [**] footnote in my post which briefly
raised and answered the very question you make in your second paragraph
above, which is in fact fairly central.  I'm going to start with it,
because the questions in the first paragraph become easier to answer
when the point is grasped.

[This is going to be a long post, I will try to explain the logic of my
argument in a step by step fashion.  If I am making any incorrect
assumptions or improbable hypotheses, I trust someone will point them
out.]

We will first look at the situation from the point of view of a distant
observer.  He drops a probe (containing and consisting of hydrogen
atoms, among other things) into a large black hole.  We will not argue
here that the distant observer has any special privileges, just that
what he sees is not in any way a *wrong* version of events, any more
than what the probe sees is wrong.  

What he sees is the probe stuck almost permanently in a state of stasis
(from his point of view) almost at the Schwarzschild radius.  He will
soon not be able to see it in practice, due to redshift, but from his
point of view it is nominally still there, even after trillions of
years.  [In principle a probe could go close to the Schwarzschild
radius and come out again much later, with little time having passed on
its onboard clocks, but a lot of time having passed for the distant
observer.  The fuel requirements would be ludicrous, but this is just a
thought experiment.  The point is that *for him*, the probe does not
reach the Schwarzschild radius in any finite time.  For him, any
adventures it may have inside the Schwarzschild radius have not yet
started.]  So far, this is only what GR says.

How does our distant observer analyse this based on his graviton-based
effective field theory?  In brief, he finds that interactions between
gravitons and other particles (including for example electrons,
photons, quarks and other gravitons) shift the phases of wave functions
in such a way that physical processes proceed slowly according to a
nominal clock rate that he applies universally (since he is working on
the basis of a flat background spacetime).  Still we are not at odds
with GR, just making a choice of clock and coordinates that suits a
particular model.

Now we add a few simple considerations from particle physics.  We're
assuming (according to our flat spacetime hypothesis) that at a certain
very large energy scale, some more fundamental processes underlie
gravity and the other forces.  These fundamental processes operate
everywhere in the universe, even on Earth, but we never see them in
action because of their gigantic energy scale.  In principle, though,
we might at any time or place see an effect mediated by these
processes.  Simplistically, we could say that due to the uncertainty
principle, a super-massive particle/particle-pair/string/whatever could
be briefly brought into existence at any time or place, and would
proceed to interact with whatever is at that point.  I'll call it a
super-whatever.  

What can such a super-whatever do?  We would (so it seems to me) expect
it to be capable of doing all the kinds of things that in other
hypotheses we would expect a mini-black hole to do.  That is to say, it
could alter anything that usually remains constant in ordinary
interactions but is not associated with any long-range field.  It could
not affect net electric or colour charge or angular momentum, for
example.  However we would expect it to be able to alter baryon number.  
This would be its most noticeable effect by far, on account of the
important matter-antimatter asymmetry of the universe.  If it alters
baryon number it will cause a proton or neutron to decay.  (There may
well be lower-energy processes that can also cause proton decay, but
they are not under consideration here.)  

Now, here is the key point, from which all follows: the probability of
such a super-whatever interaction at any point in spacetime will not
depend, at least in any simple way, on the gravitational field there.  
These particles/strings/whatever underlie the lower-energy phenomena we
model as gravity and the other forces; even if they can be affected in
some way by them, there is no reason to expect that the effects will be
linear.  

Super-whatevers, in short, go by their own clock which runs at the same
rate everywhere in spacetime.  So a super-whatever interaction breaks
GR.  But these interactions are very rare, right?

Let's say super-whatever interactions are rare enough under Earth
conditions to occur just once per century, on average, in the entire
mass of the Earth.  And that for our distant black hole observer, it is
about the same, though it may be that he is near the centre of the
galaxy and his clocks are fractionally slow compared to those on Earth.  
If he waited long enough, and if no other interactions took place,
though, he could watch the Earth decay slowly away due to such super-
whatever interactions.  It would take an awfully long time; countless
trillions of years.

While he is watching the Earth decay, he could take time occasionally
to consider his black hole probe.  He can't see it due to redshift, but
from his point of view it hasn't reached the Schwarzschild radius yet.  
He knows, though, that super-whatever interactions are happening to it
as well, because they are caused by processes above the gravity
unification scale.  By the time the Earth has decayed, the probe should
have decayed also, though it might be that the rate would be slightly
greater or less (we cannot say that the gravitational field will have
no effect at all).  But if it is anything greater than infinitesimal,
we suddenly have a huge contradiction with GR from the probe's point of
view.  Because from the probe's point of view, very little time has
passed, perhaps only a matter of minutes - it has not yet reached the
Schwarzschild radius.

If our hypothesis is right, therefore, the probe must be observing new
physics, in the form of a hugely increased rate of super-whatever
interactions compared to its ordinary onboard clocks, which keep GR
time.  Assuming that these interactions cause protons to decay, the
probe will suddenly observe an exponential increase in proton decay;
decay will be complete before it reaches the Schwarzschild radius.

All the hydrogen atom in the probe has to know is that it has two
clocks, and they are out of sync.  It obeys all the usual laws of
electrodynamics etc. with reference to its low-energy clock.  Its
proton decays according to a half-life measured on its high-energy
clock.  Near the Schwarzschild radius, the ratio of the two clocks
changes drastically, by a factor of [more than] trillions.  And that
means a complete breakdown in GR.

Summary: under the hypothesis in which gravity is best described in
terms of an effective field theory on a flat background spacetime, GR
will not be noticeably inaccurate except under fields so strong as to
be outside the range of ordinary experiment.  The super-whatever clock
runs far too slowly to be measurable under ordinary conditions.  
However, a probe dropped into a large black hole would rapidly (in
terms of ordinary onboard clocks) undergo complete decay into
particles/energy with a net baryon number of approximately zero.  

An objection that might be raised is that the cloud of particles/energy
that the probe will be converted into will be at an exceedingly high
temperature.  This is perfectly correct, from its own point of view.  
But remember, it is also subject to an equally enormous red shift as
seen by observers distant from the black hole, so any radiation they
pick up from it will be at an extremely low temperature instead.  
Remind you of anything?

In fact it seems to me that this hypothesis automatically gives an
extremely natural and straightforward physical model for the generation
of Hawking radiation, in contrast to the rather questionable
explanations relating to pair production near the event horizon that
are given in the more GR-friendly models!  Needless to say it also
avoids numerous other issues/inconsistencies relating to
thermodynamics, information loss, naked singularities etc.  To me, the
hypothesis of a flat background spacetime seems a very small one to
swallow in order to eliminate these problems.

Anyway, I hope the above makes for a clear picture of the sort of model
I am describing.

- Gerry Quinn