[ExI] QT and SR

[The Avantguardian]

--- Jeff Davis <jrd1415 at gmail.com> wrote:

> Everything I've googled up suggests that the string breaks.

Everything you Googled probably referenced Bell. People love to hide behind
authority. Personally I am rather certain you are right. So much so I will bet
$100 USD on the results of any experiment using two real masses under equal
accelerating forces and a real string. 

Case 1- No string:
Two 100 meter long spaceships that weigh in at 100 metric tons each start at
relative rest, one 100 meters behind the other stern to bow without a string
and accelerate to .7071 c in 24 hours (86,400 seconds). This is a huge amount
of acceleration, a little more than 250 g's worth. Enough to squash any would
be astronaut flat against the back of the ship with about 25 tons of force. But
lets say the astronauts have really soft cushions on their back rests or the
ships are unmanned.

At the point the ships reach .7071 light speed, the rear ship bounces a radar
signal off of the stern of the front ship. The radar would read the distance
between the ships at 100 meters*(1+ sqrt(1-(.7071c)^2)) or about 129.29 meters.
In other words, the length of the spaceships themselves contracted from 100
meters long each to 70.71 meters long each but their centers of mass remained
the same 100 meters distance apart.

Case 2- a string connects the spaceships:
To asses what happens when you join the two spaceships stem to stern with a 100
meter string, one must realize that as John Clark said, both the space ships
and the string have to skrink. So lets say that as in the first example they
start out at rest and accelerate at 250.53 g. Now in the 24 hours that the
ships accelerated to .7071 lightspeed, the string would have to shrink by by
100 meters*(1- sqrt(1-(.7071c)^2))=29.29 meters due to its own relativistic
contraction winding up a mere 70.71 meters long just like either of the two
space ships. This means that the centers of mass of the two ships will be
closer together with the string than without.

The only way this is possible is if the string in the process of contracting
generates a force on the space ships that accelerate their center of masses
closer together by exactly 58.58 meters (29.29 meters for the string and 14.645
meters for each of the two ships) in 24 hours. How big of a force will be
needed for this? Well as an approximation, acceleration =2*distance/time^2. So
the shrinkage acceleration will be about 2*58.58 meters/(86,400 seconds)^2 or
1.57E-8 meters/second^2. Since the two 100 ton space ships weigh a total
200,000 kilograms, the force on the poor string is a truly underwhelming .00314
newtons.

This is the equivalent of a string able to support 320 milligrams or an aspirin
tablet in earths gravity. I imagine belly button lint woven together into a 100
meter string would have enough tensile strength to pull the ships together
under fitzgerald contactile forces alone. The real challenge for the string
would be surviving its own 250 g acceleration. But I assure you that any string
that is capable of being accelerated to relativistic speeds will not snap
because of Bell's Paradox.


Stuart LaForge

"A portion of mankind take pride in their vices and pursue their purpose; many more waver between doing what is right and complying with what is wrong." - Horace