Re: Equivalance principle

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 
gravitational experiments that had been done, and his thoughts about what 
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
 http://www.gpc.edu/~jguinn/MadSci/EquivPrinc.pdf


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 
answered.  If not, please ask again and perhaps I’ll get a chance to try 
again.

Thank you for your interest.

Sincerely,

Jim Guinn
Georgia Perimeter College



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