🚀 go-pugleaf

Koobee Wublee schrieb:

> On Jan 18, 1:03 pm, Dieter Heidorn wrote:
> 
>>Pentcho Valev schrieb:
> 
>>>Roberts Roberts, Einstein's 1911 equation c'=c(1+V/c^2) is consistent
>>>with the gravitational redshift factor 1+V/c^2 confirmed
>>>experimentally by Pound and Rebka.
>>
>>In his 1911 work "�ber den Einfluss der Schwerkraft auf die Ausbreitung
>>des Lichtes", Annalen der Physik 35 (1911); translated: "On the
>>Influence of Gravitation on the Propagation of Light" Einstein uses the
>>equivalence principle to derive the relation for gravitational red-shift
>>
>>nu_1 = nu_2 (1 + V/c^2)
>>
>> From this he concluded that the speed of light must vary according to
>>
>>c = c_0 (1 + V/c^2)
>>
>>Using this equation Einstein derives a relation for the deflection angle
>>for light passing the sun (1911):
>>
>>alpha = 2 GM / (c^2 R)
>>
>>This is wrong by a factor 2. Experimentally is found
>>
>>alpha = 2 GM / (c^2 R)
> 

Sorry, here I meant to write

alpha = 4 GM / (c^2 R).

>>>In other words Roberts Roberts, the
>>>equation c'=c(1+V/c^2) is CORRECT, NOT APPROXIMATE:
>>
>>This equation is not correct, because it leads to a wrong prediction for
>>the deflection of light.  The reason for the error was: In 1911 Einstein
>>used "curved time" and "flat space", not curved space-time.
> 
> The equation is correct for gravitational redshift.  <shrug>
> 

Of course, because Einstein derived the c-equation in his 1911 work from
the correct equation for gravitational red-shift. The sequence of his
steps was:

     equivalence principle

--> red-shift: nu_1 = nu_2 (1 + V/c^2)

--> varying speed of light: c = c_0 (1 + V/c^2)

--> deflection angle for bending of light: alpha = 2 GM / (c^2 R)

>>>any different
>>>equation (that may seem correct to you) would be inconsistent with the
>>>redshift factor.
>>
>>The gravitational red-shift is not caused by a variable speed of light.
>>
>>In his 1916 work "Die Grundlage der allgemeinen Relativit�tstheorie",
>>Annalen der Physik 49 (1916) Einstein shows:
>>
>>* Space-time is described with the metric
>>
>>   ds^2 = g_mu,nu dx^mu dx^nu
>>
>>* The gravitiational red-shift depends on the metric:
>>
>>   nu_B / nu_A = sqrt(g_00(r_A)/g_00(r_B))
>>
>>* In weak fields the following approximation holds:
>>
>>   nu_B / nu_A = 1 + Delta V/c^2
>>
>>* Speed of light:
>>   - In a local inertial frame of reference the speed of light
>>     is constant c
>>   - In general, global coordinates the speed of light varies
>>     (in weak fields) according to
>>
>>     c_A = c ( 1 + 2 V/c^2)
> 
> This equation will lead to a wrong value of the gravitational
> redshift.  This is another example where GR is contradictory of itself
> because it does not agree with the metric derivation as you have shown
> above.

You can take this as contradiction only, if gravitational red-shift
would depend on a variable speed of light. In fact this is not correct
in GR. Gravitational red-shift depends on the metric, so I wrote a few
lines above:

The gravitiational red-shift depends on the metric:

    nu_B / nu_A = sqrt(g_00(r_A)/g_00(r_B))

In weak fields the following approximation holds:

    nu_B / nu_A = 1 + Delta V/c^2

You can find this in Einsteins 1916 work:

Die Grundlage der allgemeinen Relativit�tstheorie.
AdP 49, 769 (1916)
(�22, pp 818 - 820)
http://www.physik.uni-augsburg.de/annalen/history/papers/1916_49_769-822.pdf

(Sorry, but I don't know where to find an english translation of this work.)

Dieter Heidorn