### Re: Equivalance principle

Date: Mon Oct 9 06:58:35 2006
Posted By: Jim Guinn, Staff, Science, Georgia Perimeter College
Area of science: Physics
ID: 1159046841.Ph
Message:
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Dear Ray,

It seems that this question is a follow-up to a previous question and
response.  Unfortunately, I didn’t write that response, and I’m afraid I
couldn’t find it in the MadSci Archives, so I’ll just have to do my best
to answer what I think you’re asking.  I apologize if I repeat some of the
things stated in your first response, but I think for completeness sake,
I’ll start from the beginning.

In formulating his Theory of Special Relativity, Einstein developed two
postulates…

1.  The Relativity Postulate – The laws of physics are the same in every
inertial reference frame.

2.  The Speed of Light Postulate – The speed of light in a vacuum,
measured in any inertial reference frame, always has the same value of c
(3.00E8m/s), no matter how fast the source of light and the observer are
moving relative to each other.*

You can think of a reference frame as what is moving along with you, that
is, what is at rest in your perspective.  So if you are in a rocket ship,
what is at rest with respect to that rocket is part of your reference
frame.  Anything moving with respect to you is in another reference
frame.  In Special Relativity, an inertial reference frame is one that is
not accelerating, that is one that is moving at a constant velocity.

The first postulate states that all the laws of physics are the same in
all inertial reference frames.  What is implied is that it doesn’t matter
how the frames are moving relative to each other, no matter how fast, as
long as they are not accelerating.  This means that there is no way to
determine how fast you are moving without looking outside your frame.
Nothing you can do inside your frame is affected by your motion.  Or,
another way of putting it is that there is nothing wrong with thinking
that you are at rest and the rest of the universe is moving.  (Nothing
wrong in the physics, that is, psychologically is another matter.)

One issue that these postulates do not address is acceleration.  This is
dealt with in Einstein’s Equivalency Principle.  Einstein made the
assumption that gravity and acceleration were equivalent because of
would happen in an accelerating frame away from gravity.

First, Einstein knew that according to all experiments, in a uniform
gravitational field, all objects seem to fall with the same acceleration,
regardless of their mass or chemical composition.  (This was noticed by
Galileo Galilei and demonstrated in his experiment, which might be
apocryphal, of dropping two different masses off the Leaning Tower of
Pisa.)  This is different from the affects of every other force that we
know of.  Gravity seems to affect every object of matter in exactly the
same way.  Near the Earth’s surface, this acceleration is 9.8m/s/s.

Second, Einstein wondered what would happen to objects in an accelerating
reference frame if that frame was not within a gravitational field.
Imagine that you are in a rocket and the rocket is accelerating upwards
with an acceleration of 9.8m/s/s.  In order for you to accelerate along
with the rocket, the floor would have to push on you upwards with a force
equal to your weight.  You would stand on the floor and feel like you were
pushing back on the floor with a force equal to your weight.  If you were
holding an apple, you would have to push upwards on it with a force equal
to its weight to keep it accelerating along with you and the rocket.  The
instant you let it go, it would stop accelerating along with you and it
would start drifting to the bottom of the rocket.  The rocket would keep
accelerating upwards at 9.8m/s/s and so you would think that the apple was
falling downward at 9.8m/s/s, and this is totally independent of the mass
of the apple, since it is really the acceleration of the rocket which is
producing the apparent acceleration of the apple.  Any object released
within the rocket would appear to accelerate downward with the same
acceleration of 9.8m/s/s.

It is the similarity of these two situations, a frame in a uniform
gravitational field and an accelerating frame outside of any gravitational
field, that lead Einstein to the Equivalence Principle, that is, to
consider them equivalent.  So what would be an inertial reference frame in
a gravitational field?  If a stationary frame in a gravitational field is
like an accelerating one outside of a gravitational field, then perhaps
one in freefall in gravity would be like a non-accelerating field away
from gravity.  A frame in freefall is accelerating “downward” completely
under the influence of the gravitational field.  Near the Earth’s surface,
that would be a frame that was accelerating downward at 9.8m/s/s.  In such
a frame, since all objects are accelerating downward with the same
acceleration, there would be no relative acceleration between objects
within the frame, and so it would appear exactly like an inertial frame in
special relativity, non-accelerating and away from any gravitational
field.  Einstein then extended his first Special Relativity postulate to
include inertial reference frames within gravitational fields, and that
what happens in a frame which is stationary within a gravitational field
would be the same as what happens in an accelerating frame without any
gravity.

Now I think I’m in a position to respond to your question.  (Phew!)  Light
in a uniformly moving rocket is not bent.  An observer within the rocket
will say that the light moves along a straight line, that’s simple
enough.  An observer will say that the light also follows a straight line,
although that line will include the motion of the rocket.

(Please take a look at this website

where I have made a diagram to help with this explanation.)

Imagine that the rocket moves from Point 1 to Point 2, an observer within
the rocket would say that the light went straight across the rocket.  An
observer outside the rocket would also say that the light moved in a
straight line, but that it moved a longer distance since it moved not
only “vertically” but “horizontally” in our diagram.  (This is a diagram
that is commonly used to explain the time dilation within moving frames.

If the rocket was accelerating, the light would still appear to move in a
straight line for the external observer, but the internal observer would
see the path deviate from a straight line.  This is completely consistent
with what we have stated above about inertial frames.  An accelerating
rocket is not an inertial frame in special relativity, and so the laws of
physics, as stated for inertial frames, do not hold.  According to the
Equivalence Principle, this must be the same thing that happens when light
moves in a gravitational field.  This was experimentally verified first by
observing how star light was bent as it passed near the surface of the sun
during a solar eclipse.  The eclipse was not necessary for the bending,
just for it to be observed.  Since the sun is so bright, stars are usually
not visible when apparently near the sun’s surface.

Well, Ray, I hope somewhere in there I answered the question you wanted
again.

Sincerely,

Jim Guinn
Georgia Perimeter College

* J. D. Cutnell and K. W. Johnson, “Physics,” 6th Ed., John Wiley & Sons,
Inc., 2004.

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