(I hope this is posted OK, google groups is doing some odd things at
the moment)
[snip]
De Broglie drove a stake into the heart of presentism when he first
described how the new theory of relativity would give rise to de
Broglie waves (the forerunner of the Schrodinger equation).
Err, what has de Broglie's wave proposal to do with relativity?
See Rindler, W.(2001) Relativity, special, general and cosmological.
page 120.
"What de Broglie now proposed was to extend Planck's and Einstein's
relation E=hf to all particles.. Of course, de Broglie knew that this
wave cannot travel at the same speed as the particle (unless that
speed is c), for that would not be a Lorentz-invariant association..."
"According to de Broglie a particle of 4-momentum P has associated
with it a wave of wave vector L determined by what is now called de
Broglie's equation:
P=hL; that is, (p,E/c) = hf(n/w,1/c)
In fact this equation is inevitable once we accept the universal
validity of E=hf; for (E-hf)/c is the fourth component of the 4-vector
P-hL. Setting p=Eu/c^2 and comparing spatial components, we now find
the following relation between the velocity u of the particle and the
velocity w of its wave:
uw = c^2 "(Rindler 2001)
Hence w = c^2/u but the wave velocity, w is also x/t so:
x/t=c^2/u
and t= ux/c^2 which is the relativistic 'phase', the time difference
between points on the x axis of a moving particle and the x axis of an
observer at a position 'x'.
"Thus de Broglie waves can be considered as waves of simultaneity"
[snip]
According to presentism, defined, material things exist and there
should be lengths in three dimensions that are invariant
(constant).
Pythagoras' theorem is all that is needed to describe a length ie:
(1) h^2 = x^2 + y^2 + z^2
According to four dimensionalism things have no defined location
when
they interact with the world and lengths in three dimensions will
not
be constant, instead a separation called the "space-time interval"
will be constant:
(2) s^2 = x^2 + y^2 + z^2 - (ct)^2
where c is a constant which is also the velocity of light in a
vaccuum.
Either equation (1) or equation (2) applies in the world.
Wrong. Both hold.
No, you cut the earlier paragraph that said constant when rotated,
moved etc. They do not both hold during motion, relative to a
stationary observer the length (h) seems to decrease if something is
moved away or towards an observer.
What you probably wanted to say it: "Either (1) is invariant
under all coordinate transformation between inertial systems, or it
sn't, but only (2) is invariant under all such transformations."
Yep, but you snipped that bit, it was put in laymans language.
If equation (1) applies then quantum theory and relativity are both
wrong.
No, that's a non sequitur. Equation (1) is indeed correct for
the distance between two points (provided that one talks about
one fixed coordinate system!).
But I wasn't. You are probably right to pick me up on my imprecision.
School physics would be right after all and would simply need
to be modified with complicated mathematics to account for QM and
relativistic effects that were not, after all, due to (2).
You mean, due to the invariance of (2) under all coordinate
transformations between inertial systems.
yes
Best Wishes
Alex Green
.
