Dono
2009-04-06 15:35:29 UTC
On Apr 6, 8:19 am, "Dirk Van de moortel"
h = 100
g = 10
c = 3*10^8
g h/c^2 = 1.1 10^(-14)
1/2 (g h/c^2)^2 = 6.2 10^(-29)
Dirk Vdm
Actually, the second order effect has been measured:
B. Linet , P. Teyssandier, “Time transfer and frequency shift to the
order (1/c)^4 in the field of an axisymmetric rotating body”, Phys.
Rev. D, 66, 024045 (2002)
Einstein elevator and the EEP
Seehttp://www.bartleby.com/173/20.html
After a light pulse is emitted from the top of the
accelerating elevator, the floor of elevator
moves upward, hence the pulse will hit the floor
after a time t < h/c, where h is the distance
between the emitter and the receiver.
After such time t, the light pulse will be at
a distance d1 = ct from the top, and the floor
will have travelled upward a distance
d2= 1/2 gt^2.
From d1 + d2 = h, or ct + 1/2 gt^2 = h, one
gets t = [-c + sqrt(c^2 + 2gh)] / g
= [(c/g) * (sqrt(1 + 2gh/c^2) - 1)],
which is the time at which the pulse meets the
floor. The corresponding upwards velocity of the
floor is then
v = gt = c * (sqrt(1 + 2gh/c^2) -1)
As sqrt(c^2 + 2gh) is approximately equal to
1 + gh/c^2 + (gh/c^2)^2/2,
v =~ c * (gh/c^2 + (gh/c^2)^2/2)
From the formula v/c-1, one gets a blue shift of
gh/c^2 + (gh/c^2)^2/2,
against gh/c^2 for an identical elevator a rest
on the ground.
Even when gh is very small relative to c^2, the
existence of the quadratic term (gh/c^2)^2/2
falsifies the Einstein equivalence principle (EEP),
one of the basis of GRT.
Of course, GRists will claim that such term
is so small that it can safely be dropped!
Of course, people will say that Luttgens in an imbecile.Seehttp://www.bartleby.com/173/20.html
After a light pulse is emitted from the top of the
accelerating elevator, the floor of elevator
moves upward, hence the pulse will hit the floor
after a time t < h/c, where h is the distance
between the emitter and the receiver.
After such time t, the light pulse will be at
a distance d1 = ct from the top, and the floor
will have travelled upward a distance
d2= 1/2 gt^2.
From d1 + d2 = h, or ct + 1/2 gt^2 = h, one
gets t = [-c + sqrt(c^2 + 2gh)] / g
= [(c/g) * (sqrt(1 + 2gh/c^2) - 1)],
which is the time at which the pulse meets the
floor. The corresponding upwards velocity of the
floor is then
v = gt = c * (sqrt(1 + 2gh/c^2) -1)
As sqrt(c^2 + 2gh) is approximately equal to
1 + gh/c^2 + (gh/c^2)^2/2,
v =~ c * (gh/c^2 + (gh/c^2)^2/2)
From the formula v/c-1, one gets a blue shift of
gh/c^2 + (gh/c^2)^2/2,
against gh/c^2 for an identical elevator a rest
on the ground.
Even when gh is very small relative to c^2, the
existence of the quadratic term (gh/c^2)^2/2
falsifies the Einstein equivalence principle (EEP),
one of the basis of GRT.
Of course, GRists will claim that such term
is so small that it can safely be dropped!
h = 100
g = 10
c = 3*10^8
g h/c^2 = 1.1 10^(-14)
1/2 (g h/c^2)^2 = 6.2 10^(-29)
Dirk Vdm
B. Linet , P. Teyssandier, “Time transfer and frequency shift to the
order (1/c)^4 in the field of an axisymmetric rotating body”, Phys.
Rev. D, 66, 024045 (2002)