## Relativity Challenge – part 2## Dealing with acceleration and gravity
## The Situation
In the first preliminary step we take Earth and relocate it far into
intergalactic space. It will be far enough out such that
gravity from the nearest galaxy is a trillion times less than Earth’s
surface gravity. The reason for doing this is firstly so that
we don’t need to consider the gravity of surrounding stellar bodies,
and secondly to remove the motion of the Earth around the Sun and Milky
Way from consideration.
## Discussion
Now that the story has been told, it’s worth anticipating with what
objections might arise. Several things can be predicted about
how relativity supporters will handle this:
- Start discussing other aspects of SR such as length contraction, simultaneity, and additive velocities.
- Claim that both are running slower
than each other, and/or that the calculated amounts of time dilation
refer only to
*perceived*rates of slow down, not actual slow down. - Claim that the brief turnarounds are all that is needed to break symmetry and cause one twin to be several months older than the other.
- Claim that the small amount of acceleration at lift-off is all that is needed to break symmetry and cause one twin to be several months older than the other.
- Ignore the thought experiment and discuss various real-world experiments.
- Claim that only the rocket slows down because the Earth is somehow a special/universal reference frame that all velocities need to be compared to.
- Claim that SR only applies to the rocket because it experiences acceleration.
These are popular claims, and it’s worth addressing each of them before
covering the final point (7) in detail:
## The Principle of Equivalence
This brings us to the focal point of the story. Namely that
the gravity/acceleration was the same for both clocks/twins, and
therefore according the to the Equivalence Principle, there should be
no way of selecting one clock over the other.
“Experiments performed in a uniformly accelerating reference frame with
acceleration
Einstein used a number of similar statements before settling on: “Whenever an observer detects the local presence of a force that acts on all objects in direct proportion to the inertial mass of each object, that observer is in an accelerated frame of reference.”
## Time dilation due to gravity
Let’s now look at GR theory and see what it says about gravity, in
terms of predicting time dilation. Since time dilation is
often attributed to gravity, one might assume there must be an equation
that can tell you how much dilation will be caused by a given amount of
gravity. But that’s not the case. GR describes time
dilation not according to gravitational ---- (1)
Where (phi) is the potential.ΦGravitational potential refers to the amount of energy required to lift a unit mass (i.e. 1kg in SI units) from its present height, all the way to an infinite height. We know that gravitational acceleration can be measured by dropping an object and observing how it falls. We can also measure it in terms of a static force, e.g. by placing a unit mass on some scales. But gravitational potential is impossible to detect, let alone measure. The only way to determine it is to measure the acceleration function of gravity all the way to a height of infinity, which obviously can’t be done. In theory you could also determine it by multiplying the surface gravity by the radius of the planet you are on. But this would only work if the planet was: (a) spherical, (b) non-rotating, (c) of uniform density, or the density was ‘radially symmetric’ i.e. identical at any given radius. So how is it possible for clocks to time-dilate according to something that can never be detected? Not just detect from where they are located, but not detect no matter how they move about, assuming they were allowed to. Or are GR proponents saying that clocks are somehow aware of the shape of the planet they are on, their density distribution, and their distance from the mid-point? Do clocks have ‘remote viewing’ abilities? If so you’d think some relativity expert would have bought that exciting fact to our attention! Either of these claims should be seen as impossible. And this alone is sufficient to demolish the GR gravitational time dilation equation as a possibility. It also demolishes the Equivalence Principle because it admits the time dilation ‘equivalence’ is not due to acceleration but potential. At this stage, there doesn’t seem much point in going further because all the claims relating to SR and GR have been shown as unworkable. Unless that is, you are a geocentrist and believe clocks have psychic powers. Still, there is another aspect that should be addressed: acceleration.
## Time dilation due to acceleration
A final aspect to consider is the amount of time dilation due to
acceleration. ---- (2)
But doing this with acceleration is a problem. Acceleration ( ---- (3)
Two important points about this. First, it’s not an
expression for a
[1]
http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/grel.html g*R. When calculating the time dilation at the centre of a
planet, you need to use = (3/2)ΦG*M/R[3] http://en.wikipedia.org/wiki/Time_dilation#Time_dilation_at_constant_acceleration |

Copyright © 2013
Bernard Burchell, all rights reserved.