On 17 mar, 17:44, "Dirk Van de moortel"
<dirkvandemoor...@nospAm.hotmail.com> wrote:
> mluttg...@orange.fr <mluttg...@orange.fr> wrote in message
> cef4a580-a789-44db-9370-96623b399...@p20g2000yqi.googlegroups.com
>> On 16 mar, 18:07, "Dirk Van de moortel"
>> <dirkvandemoor...@nospAm.hotmail.com> wrote:
>>> mluttg...@orange.fr <mluttg...@orange.fr> wrote in message
> 
>>> c63207a3-1336-4764-8629-27723fce3...@z9g2000yqi.googlegroups.com
> 
>>>> Is the equivalence principle considered as the foundation of GR?
> 
>>>> Einstein imagined a thought experiment to illustrate the principle:
>>>> One elevator is at rest on Earth and another one, far away from
>>>> any gravitational field, is accelerationg upwards at g = 9.81 m/s^2.
>>>> According to him,"no experiment made inside the elevators would
>>>> distinguish between the Earth's gravitational field and the
>>>> equivalent
>>>> uniform acceleration".
> 
>>>> This is plainly wrong:
> 
>>>> Let's imagine that a light of known frequency f(top)is emitted at
>>>> the top of the elevator. A receiver situated at the bottom will
>>>> observe a freqency f(bottom) <> f(top).
>>>> In the elevator at rest on the ground, the observed frequency shift is
>>>> very close to gh/c^2, whereas in the second elevator, the
>>>> corresponding shift is gh/2c^2 (h is the distance separating
>>>> the emitter from the receiver).
> 
>>> In the second elevator, when the signal is emitted, in the
>>> comoving inertial frame of the top, the signal takes an
>>> approximate time
>>> T = h/c
>>> to reach the receiver at the bottom. By that time the receiver
>>> has the (small) speed
>>> v = g T = g h/c.
>>> The classical Dopper tells you that the received speed at the
>>> bottom is
>>> f' = (1+v/c) f
>>> = (1+g h/c^2) f
>>> So in the second elevator, the corresponding shift is
>>> g h/c^2.
> 
>> You are falsely using the Doppler formula.
>> In the case of the second elevator, the emitter and the receiver
>> are comoving!
> 
> Marcel, shouldn't you try to crawl before you try a marathon?
> 
> Here is chapter 13 of something that was written for 1st year
> students:
> http://student.fizika.org/~jsisko/Knjige/Klasicna%20Mehanika/David%20...
> Intro to general relativity for kids, so to speak.
> 
> Before you try to understand it, make sure you understand the
> 12 preceeding chapters and all the exercises.
> http://student.fizika.org/~jsisko/Knjige/Klasicna%20Mehanika/David%20...
> 
> Dirk Vdm

Exerpt from
http://student.fizika.org/~jsisko/Knjige/Klasicna Mehanika/David Morin/CH13.PDF

	"However, the light takes a finite time to reach the receiver,
	and by then the receiver will be moving. We therefore cannot
	ignore the motion of the rocket when dealing with the receiver.
	The time it takes the light to reach the receiver is h/c,
	at which point the receiver has a speed of v = g(h/c).
	Therefore, by the usual classical Doppler effect, the time
	between the received pulses is tr = ts/(1 + (v/c).
	Therefore, the frequencies, fr=1/tr and fs=1/ts, are related by
	fr = (1+v/c)fs = (1+gh/c^2)fs."

According to this derivation, the corresponding frequency shift is
fr/fs-1 = v/c = gh/c^2

But such derivation is false, because the classical Doppler formula
can only be used when the velocity v of the receiver relative
to that of the emitter is constant during the trip of the light.