Einstein interpretation of gravitational redshift is misleading

Einstein interpretation of gravitational redshift is misleading
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Excerpts from arXiv: physics/ 9907017 v2 27 Jul 1999

ON THE INTERPRETATION OF THE REDSHIFT IN A STATIC GRAVITATIONAL FIELD
L.B. OKUN and K.G. SELIVANOV
ITEP, Moscow, 117218, Russia
e-mail: okun@xxxxxxxxxxxxx, selivano@xxxxxxxxxxxxx
and
V.L. TELEGDI
EP Division, CERN, CH - 1211 Geneva 23
e-mail: valentine.telegdi@xxxxxxx

Excerpt:

"ABSTRACT

The classical phenomenon of the redshift of light in a static
gravitational potential, usually called the gravitational redshift,
is described in the literature essentially in two ways:

on the one hand the phenomenon is explained through the behaviour
of clocks which run the faster the higher they are located in the
potential, whereas the energy and frequency of the propagating photon
do not change with height. The light thus appears to be redshifted
relative to the frequency of the clock.

On the other hand the phenomenon is alternatively discussed
(even in some authoritative texts) in terms of an energy loss of
a photon as it overcomes the gravitational attraction of the massive
body. This second approach operates with notions such as the
"gravitational mass" or the "potential energy" of a photon and
we assert that it is misleading.

We do not claim to present any original ideas or to give a
comprehensive review of the subject, our goal being essentially
a pedagogical one."


Let's consider that photons loose energy as they overcome the
gravitational attraction of the Earth:

A light signal of frequency Nu1 is emitted by an atom at rest on the
surface of the earth. The energy of a photon is thus E1 = hNu1 and
its "mass" m = E1/c^2 = hNu1/c^2.

At a height H, i.e. at a distance d = Rearth + H from the Earth's
center, the frequency of the received signal is Nu2, hence the
photon's energy is E2 = hNu2.
Its potential energy is Ep = m * gm * H, where gm = GMearth/(Rearth*d).
From E2 = E1 - Ep, one gets
hNu2 = hNu1 - hNu1/c^2 * GMearth/(Rearth*d) * (d-Rearth)
Nu2 = Nu1 * (1 - GMearth/c^2 * (1/Rearth - 1/d)
The corresponding shift Nu2/Nu1 - 1 = -GMearth/c^2 * (1/Rearth - 1/d),
which is a redshift.

The same shift would be obtained using GR.

To simplify, one could consider, like the authors of the paper did,
that g is approximately constant when H is small.
Then Ep = m * g * H = hNu1/c^2 * g * H (where g = GMearth/Rearth^2)
hNu2 = hNu1 - hNu1/c^2 * g * H = hNu1 (1 - g*H/c^2)
The shift then reduces to -g*H/c^2.

It is easy to show that the interpretation according to which
"clocks run the faster the higher they are located in the
potential, whereas the energy and frequency of the propagating photon
do not change with height" is wrong.
It suffices to consider the case when the signal receiver is freely
falling.

Excerpt:

"Consider now another situation, when the upper atom (absorber) moves
in the laboratory frame with a velocity v = gH/c downwards. Then in
the elevator frame it will have zero velocity at the moment of
absorption and hence it will be able to absorb the photon resonantly
in complete agreement with experiments [4, 5]. Obviously, in the
elevator frame there is no room for the interpretation of the redshift
in terms of a photon
losing its energy as it climbs out of the gravitational well."

"[4] R.V. Pound and G.A. Rebka, "Apparent weight of photons", Phys.
Rev.
Lett. 4, 337-341 (1960); "Variation with temperature of the energy of
recoil-free gamma rays from solids", Phys. Rev. Lett. 4, 274-275
(1960); "Gravitational red-shift in nuclear resonance", Phys. Rev.
Lett. 3, 439-441 (1959).
[5] R. Pound, Uspekhi Fiz. Nauk 72, 673-683 (1960); "On the weight of
photons", Sov. Phys. Uspekhi 3, 875-883 (1961) (English translation)."

In such situation, for the freely falling absorber, the signal emitted
from the ground would appear *Doppler blue shifted* by gH/c^2 if it
were
not *beforehand* red shifted by gH/c^2 by "the gravitational attraction

of the massive body". Iow, for the absorber, the signal is not shifted
at all. This is a logical proof that the signal is red shifted when
it leaves the emitter.

This proof falsifies Einstein's view:

Excerpt:

"The gravitational redshift is a classical effect of Einstein's
General
Relativity (GR), one predicted by him [1] well before that theory
was created [2] (for the historical background, see e.g., [3]).
Phenomenologically one can simply affirm that the frequency of light
emitted by two identical atoms is smaller for the atom which sits
deeper in the gravitational potential.

[1] A. Einstein, ¨ Ueber das Relativitaetsprinzip und die aus
demselben gezogenen Folgerungen, "Jahrb. d. Radioaktivitaet
u. Elektronik 4, 411-462 (1907); ¨Ueber den Einfluss der
Schwerkraft auf die Ausbreitung des Lichtes, "Ann. Phys. 35, 898-908
(1911).
[2] A. Einstein, "Die Grundlage der allgemeinen Relativitaetstheorie",
Ann. Phys. 49, 769-822 (1916) §22; The Meaning of Relativity
(Princeton
University Press, New York, 1921), Eq.(106).
[3] A. Pais, 'Subtle is the Lord ...', The Science and the Life of
Albert Einstein (Oxford University Press, Oxford, 1982), Chapter 9."


Marcel Luttgens

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