Rubber Rods? JS Bell on Special Relativity
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
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!
On Feb 12, 2005, at 6:46 PM, email@example.com wrote:
These Lorentz vs. Einstein arguments have already been made many times over. I mistakenly assumed you would be familiar with them.
Jack, you don't seem to have any intuitive appreciation of the difference between a Lorentzian "rubber-rod-and-clock" model and an Einsteinian "moving coordinates" model of the Lorentz transformations.
I am familiar. The argument is completely stupid as Kip Thorne says IF THERE IS NO EMPIRICAL DIFFERENCE. The Cahill difference is not relevant to that distinction.
Didn't you read Feynman's "Lectures on Gravitation"? He explains the difference from the standpoint of a spin-2 quantum field model quite vividly.
NO you completely MISUNDERSTAND Feynman. He is only talking about perturbation theory to finite order from a flat background and there you can maybe make the distinction you want to make implicit in Puthoff's PV "Tables I & II". As Penrose explains YOU CANNOT DO IT for the complete GR, which in Feyman's terms is a INFINITE SUM of flat diagrams! This is like in BCS theory
gap energy ~ (Debye Energy)e^-1/V(binding)(Density of Fermi Sea States Per Unit Energy at Fermi Surface)
You cannot get this SPONTANEOUS BREAKING of the VACUUM SYMMETRY from a FINITE NUMBER of flat back-ground diagrams.
Penrose distinguishes the "linear graviton" of Feynman here, also of Puthoff's Yilmazian PV from the "nonlinear graviton" in the book "Geometric Universe".
So your basic error here Paul is to take a limited approximate idea BEYOND its proper domain of validity.
Feynman's approximation and your distinction above violates what all the Big Boys today like Ashtekar, Smolin et-al call BACKGROUND INDEPENDENCE closely connected to the full meaning of the equivalence principle that your distinction essentially violates. That is NO RIGID BACKGROUNDS that act without direct back-reaction. Everything is a player. No stages. No fixed arenas - not even in quantum theory, hence the signal nonlocality of consciousness!