Pentcho, Eckard et al.
First I am surprised that Pentcho can call the interchangeable use of +/- sign, the interchangeable use of proper time and coordinate time, sometimes in the same papers and sometimes substituting these with "time measured by a remote observer and "time measured where the gravitational potential is С„". This is not sloppiness but sometimes the sleight of hand which Pentcho knows quite well is rampant in Einsteiniana. An observer can only measure the time where he is, at other places he can only infer what the time is. Anyway, let me leave that issue for now and post what I had earlier intended before seeing Pentcho's suggestion that we should overlook the way +/- is used which has prompted this preamble.
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*My original post.
I have a few references demonstrating the ambiguous interpretation of the influence of gravity on light frequency in Einsteiniana. These I can post later. But as this will not resolve the issue as they may be deemed selective since there are counter references in Einsteiniana, I decided to post this first so that we can reason in Steps 1-3 together and make sure 2+2 does not equal to 5 as Pentcho frequently says, taking one step at a time.
Step 1). Let's have a switch we can move left or right to reduce or increase the Earth's gravity respectively
- в†ђ O в†' +
If gravity is increased, what happens to light frequency on Earth? That is, does it increase (blueshift) or is it reduced (redshift)?
Step 2). On a mountain, is gravity higher or lower than in the valley?
Step 3). From 1) and 2), if light is beamed from the mountain top to the valley, what will happen to its initial frequency at the top as it descends?
Divine Albert himself did not help matters mathematically although he was clear in other places on what he had in mind. For instance in Eq.(1a),:
which can be written E1 = E2 (1+С„/C2)
since С„ is -GM/r
with E2 the energy from a source, S2 at a higher gravitational potential arriving at S1, it follows from his own equation that given С„ is -GM/r (which MINUS sign IS what actually makes the gravitational potential at S2 HIGHER than at S1), that E2 > E1. The minus sign is not negotiable or interchangeable with a Plus sign.
But 'Divine Albert' says the energy E1 arriving at S1 is greater than the energy E2, measured by the same means, which was emitted from S2. From that Eq.1a, can this be mathematically correct?
As another example, see "For measuring time at a location which, relative to the origin of the co-ordinates, has the gravitation potential С„, we must employ a clock which - when transferred to the co-ordinate origin - goes (1 + С„ /c2) times more slowly than the clock used for measuring time at the origin of co-ordinates". What is the difference between 'origin of coordinates' and 'origin of coordinates''?
The following references may however help us decipher what Einstein was pondering over despite the confusion:
[link:www.gutenberg.org/files/36276/36276-pdf.pdf]"the rate of a clock is accordingly slower the greater is the mass of the ponderable matter in its neighbourhood", p.97 and "We therefore conclude that spectral lines which are produced on the Sun's surface will be displaced towards the red, compared to the corresponding lines produced on the earth, by about 2•10^-6 of their wavelengths..."[/link], both on p.97.
Best regards and happy weekend.
Akinbo
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