| Topic: |
Science > Physics |
| User: |
"Jack Sarfatti" |
| Date: |
13 Feb 2005 01:17:57 PM |
| Object: |
JS Bell teaches Special Relativity 1 |
JS Bell in his "Unspeakable" book tells how almost entire Theory
Division at CERN got an elementary SR problem wrong at first. Z made
same error and I did not catch him in it.
Alice and Bob are in two rockets separated by distance L(0) at t = 0 in
space when they fire their rockets equally to make a 1g artifical
gravity field in their ships accelerating along z-axis. A taut string
connects the rockets. What happens to the string? Correct answer is it
will break. Most of the theorists in CERNs theory division guessed it
would not break before they really thought about the problem. The
problem is counter-intuitive because our Galilean relativity "common
sense" assumes falsely that the separation between Alice and Bob L(t) is
not changing when in fact it increases because the measuring rods along
z shrink from the Einstein equivalence principle. See Kip Thorne "Black
Holes and Time Warps" p. 30 picture for analogous spherically symmetric
problem that also explains why the three real on-mass-shell quarks
inside nucleons shrink to points in high magnification Heisenberg
scattering microscopes using electron probes (e.g. SLAC deep inelastic
"parton" data).
The effective artificial gravity metric, from the rockets inertial
fields from Einstein's equivalence principle EEP, is
ds^2 = (1 - 2gz/c^2)(cdt)^2 - dz^2/(1 - 2gz/c^2)
The actually measured time and space intervals dT and dZ are
dT = dt(1 - 2gz/c^2)^1/2
dZ = dz/(1 - 2gz/c^2)^1/2
respectively.
Where dz ~ L(0)
In the weak field limit
x = 2gz/c^2 << 1
1/(1 - x^2)^1/2 ~ 1/(1 - (1/2)x^2) ~ 1 + (1/2)x^2
we can use the Newtonian kinematics of Galilean relativity to good
approximation
z = (1/2)gt^2
1 - 2gz/c^2 = 1 - (gt/c))^2
L(t) ~ L(0)[1 + (1/2)(gt/c^2)] > L(0) if t > 0
That is, the actual physical separation between the two LNIF rockets
each accelerating locally the same way actually increases so that the
string will eventually snap and break!
.
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