5.1 Reasoning for its Existence (General Relativity)
Description
This article is from the Relativity and FTL Travel FAQ, by Jason W. Hinson jason@physicsguy.com with numerous contributions by others.
5.1 Reasoning for its Existence (General Relativity)
To start off our discussion, I want to indicate why one would reason
that gravity and relativity are connected. While I could start with a
somewhat unrealistic thought experiment to explain the first point I want to
make, perhaps it will be better if I just tell you about actual experimental
evidence to support the point. We thus start by considering an experiment in
which a light beam is emitted from Earth and rises in the atmosphere to some
point where the light is detected. When one performs this experiment, one
finds that the energy of the light decreases as it rises.
So, what does this have to do with our view of relativity and gravity?
Well, let's reason through the situation: First, we note that the energy of
light is related to its frequency. (If you think of light as a wave with
crests and troughs, and if you could make note of the crests and troughs as
they passed you, then you could calculate the frequency of the wave as 1/dt,
where dt is the time between the point when one crest passes you and the
point when the next crest passes you.) So, if the energy of the light
decreases (and thus its frequency decreases), then dt (the time between
crests) must increase. Let's then consider a frame of reference sitting
stationary on the Earth. We will look at a space-time diagram in this frame
which shows the paths that two crests would take as the light travels away
from the Earth.
In Diagram 5-1 I have drawn indications of the paths the two crests
might take. The diagram shows distance above the Earth as distance in the
positive x direction, so as time goes on, the two crests rise (move in the
positive x direction) and eventually meet a detector. Now, we don't know
what the gravity of the Earth might do to the light. We thus want to
generalize our diagram by allowing for the possibility that the paths of the
crests might be influenced in some unknown way by gravity. So, I have drawn
a haphazard path for the two crests marked with question marks. The actual
paths don't matter for our argument, but what does matter is this: whatever
gravity does to the light, it must act the same way on both crests.
Therefore, the two haphazard paths are drawn the same way.
Diagram 5-1
t # = detector's path
| #
| ?
| ? #
| second ? # dt-final
| crest ? ?
| ? ? #
| ? ? #
| ? ? #
? ? first #
dt-initial | ? crest #
| ? #
------------?------------------#------> x (distance above surface)
| #
| #
dt-initial = dt-final
As we see in the diagram, because gravity acts the same way on both
crests, the time between them when they leave the surface (dt-initial) is
the same as the time between them when they are detected (dt-final). Thus,
our diagram does not predict that the energy of the light should change, but
experimental evidence shows it does. According to special relativity, this
frame of reference we have drawn is an inertial frame (that is, if we ignore
the Earth's motion, this frame of reference is stationary--it's just inside
a gravitational field). Thus our diagram (drawn for an inertial frame of
reference) should explain the geometry of the situation, but does not. That
indicates that SR must be changed in light of gravity. However, we have yet
to show that SR must be completely thrown out.
What if there were another way to define an inertial frame such that
its geometry would explain the above situation and other situations which
occur in the presence of a gravitational field? That is what we will
consider next.
Continue to:
My Books
