Re: SR on accelerating frame of reference
- From: "Spoonfed" <jonathan.doolin@xxxxxxxxxxxxxxxxxxxxxx>
- Date: 29 May 2005 10:57:31 -0700
Curious wrote:
> What's the general consensus in this group on the following question:
> Can you apply SR principles from an accelerating frame of reference?
> And if not, since the Earth is accelerating away from the far side of
> the universe, does this pose any problems?
Gravity vs. Acceleration: The Principle and Limits of Equivalence
In short, I think YES you can apply principle of SR to an accelerated
frame. And whether or not you can, I am attempting to demonstrate this
until I can show the principle of equivalence through SR or I see a
clear reason that you cannot apply SR to an accelerated frame.
Secondly, I have little idea where your idea that the earth is
accelerating away from the far side of the universe. Finally, the
links to my demos on accelerated frames are as follows:
http://www.spoonfedrelativity.com/files/myGravity7.swf
http://www.spoonfedrelativity.com/files/myGravity-contractionvelocity.swf
Now for the really long part...
If gravity is equivalent to acceleration and an object on the surface
of the earth is experienceing the same effects as an object as an
object on an accelerated surface, then it follows that an object on the
surface of the earth must be accelerating toward the edge of the
universe...
But there are limits to the Principle of Equivalence. Gravity and
acceleration differ in certain ways, or else there would be no need to
have two words for the same phenomenon.
Off hand, I can think of two main differences between gravity and
acceleration, one very obvious and usually ignored, and the other
somewhat more subtle.
The subtle difference between gravity and acceleration is the fact that
gravitational fields are not uniform around masses, so they cause tidal
effects, stretching falling objects vertically, and smashing them
horizontally. This effect is a true effect on the free-falling object,
and is not due to differences in perception. On the other hand, if an
accelerated platform were to come toward a free-falling object, it
would NOT be distorted by tidal effects at all.
The obvious difference between gravity and acceleration is that objects
far away from the gravitational source are barely affected by it at
all. That is, the change in the relative rapidity (v/sqrt(1-(v/c)^2))
between the two objects is proportional to the 1/distance^2 (distance
in the gravitating body's frame.
On the other hand, if you accelerate toward an object, no matter how
far away it is, the change in relative rapidity is equal to your change
in rapidity.
I realize this directly confronts your statement that we are
accelerating toward the edge of the universe. I have heard your idea
before, but never with evidence sufficient to back it up, nor with any
sort of argument which seems to hold together. My idea that we are NOT
only comes from assuming a simple model.
So gravity differs from acceleration in these two very important ways.
But is there any way to reduce the differences, or eliminate them
altogether?
Yes. If you've taken any courses in electromagnetism, you will be
familiar with the idea of point, line, and plane geometries for fields.
In a point geometry, the field is proportional to 1/r^2, for line,
it's 1/r and for plane geometries, the field never dissipates.
If we had a gravitational field that never dissipated, such as would be
the case in an infinite plane gravitational source, then we would
eliminate both effects mentioned above, which make gravity different
from acceleration.
(There would still be one remaining difference: the fact that an
accelerated plane has things falling away from it's back side, while an
infinite plane gravity source would have objects attracted to both
sides.)
By assuming an infinite plane, we eliminate the tidal effects, and the
reduction over distance normally associated with gravity. Then,
hypothetically, we should be able to derive the non-tidal effects of
general relativity directly from the Special Theory (and a few
differential equations, and possibly some interpolation functions.)
I've been working on this problem off and on for a month or two, and
put together two demonstrations.
The <A HREF="http://www.spoonfedrelativity.com/files/myGravity7.swf";>
First Demo</A> shows what would happen if the speed of light were
constant, but no length contraction or time dilation took place.
The <A
HREF="http://www.spoonfedrelativity.com/files/myGravity-contractionvelocity.swf";>
second demo</A> applies length contraction but not time dilation. It
is inconclusive so far. I employed a terrible programming technique of
successive addition of floating point numbers to determine positions.
This propagates rounding errors horribly. However, finding space-time
position as a function of time has proved difficult.
For math whizzes, my problem is that t'[t]=EllipticE[ArcSin[a*t],2]/a
and I need to get the inverse, t[t'] to render the events properly in
the animation. There's probably no closed form solution, so I'll have
to put together an interpolation function. a is acceleration in
nils/nanosecond^2, where a nil is a light nanosecond.
.
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- SR on accelerating frame of reference
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