Three Roads To Quantum Gravity

ACCELERATION AND HEAT
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that will not. It is made up of photons which, in spite of their
moving at the speed of light, never come any closer to her. Of
course, this horizon is due entirely to the acceleration. As
soon as the observer turns off her engines and moves
inertially, the light from the horizon and beyond will catch
her up.
Her worldline if she
stops accelerating
Worldline of an
accelerating observer
time
space
A light ray that never
catches up with her as
long as she accelerates
Her horizon
FIGURE 16
We see in bold the worldline of an observer who is constantly accelerating.
She approaches but never passes the path of a light ray, which is her horizon
since she can see nothing beyond it provided she continues to accelerate.
Behind the horizon we see the path of a light ray that never catches up with
her. We also see what her trajectory will be if she stops accelerating: she will
then pass through her horizon and be able to see what lies on the other side.
This may seem confusing. How can an observer continually
accelerate if it is not possible to travel faster than light? Rest
assured that what I am saying in no way contradicts relativity.
The reason is that while the continually accelerating observer
never goes faster than light, she approaches ever closer to that
limit. In each interval of time the same acceleration results in
smaller and smaller increases in velocity. She comes ever
closer to the speed of light, but never reaches it. This is
because her mass increases as she approaches the speed of
light. Were her speed to match that of light, her mass would
become in®nite. But one cannot accelerate an object that has
in®nite mass, hence one cannot accelerate an object to the
speed of light or beyond. At the same time, relative to our