Precession of Mercury: Adaptation for Observers

[Mickey1]

TL;DR Summary

I ask simply whether an observation from e.g. Jupiter of Mercury´s precession wouöd yield a diffrent value as opposed to the one we see from the Earth.

For the observation of the gravitational redshift one needs an adaptation of the GTR of the object (related to the Sun´s gravity) and the observer (related to the Earth’s gravity). I assume that the situation is similar for the observation of the precession of Mercury, another experiment suggested by Einstein. Is that also the case?

(That might suggest that the precession would be seem slightly different as viewed from e.g. Jupiter and it is perhaps more counterintuitive.)

 

[Dale]

The measured anomalous precession of Mercury is about 43 arcseconds/century. So to clarify your question, are you asking whether an observer on Earth and an observer on Jupiter would measure the same 43 arcseconds/century of anomalous precession for Mercury?

 

[Mickey1]

The answer is YES! that is what I wonder.

Let me give you the background:

The Nobel Prize physics committee was influenced by the physicists in Uppsala in the beginning of the 20th century, and the discipline was dominated by the so called Ångström dynasty of instrumentalists. Physics in Uppsala was a sleeping beauty strongly disturbed by the new currents represented by quantum physics and relativity. Quantum physics eventually developed into a tool which the physicists understood might actually help them to explain the lines the spectroscopy experts were studying, but the theory of relativity, be it the special or the general version was considered complete bogus.

Of the three effects Einstein suggested, i) Mercury perihelion’s precession, ii) light bending around the Sun and iii) gravitational redshift, the only solid effect was the precession of Mercury’s perihelion above what Newtonian mechanics predicted.

This problem was solved by Gullstrand, a self-taught optical expert, looking into the theory. He found that the theoretical derivation for Mercury’s perihelion precession contained a constant of arbitrary value and that it therefore couldn’t claim anything in particular regarding Mercury.

Later he was criticized by Oseen, a new committee member, and Kretschmann, a German physicist.

The Swedish professor Lars Gårding describes the situation in “Mathematics and Mathematicians, Mathematics in Sweden before 1950”, American Mathematical Soc., 1998 :

“Gullstrand examines Einstein's equations for the movements of bodies and his explanation of the movement of the perihelion of the planet Mercury. His criticism was that Einstein’s equations for this phenomenon permit several solutions. As remarked by Oseen in a subsequent paper, Gullstrand did not observe that the choice of coordinates must be adjusted to the observer and that this gives the correct result.”

 

[Ibix]

It depends how the observer on Jupiter defines a century. If they use their own local clocks they will not agree that Earth orbits the sun exactly 100 times in a century, and will measure a different perihelion shift because they consider a different period. On the other hand, if they define a century to be the time it takes the Earth to orbit the Sun 100 times then they will measure the same perihelion shift.

The complication that Gullstrand refers to is, I suspect, due to using a different definition of coordinate time (Gullstrand-Painleve coordinates, I would guess). I'm not sure that they were initially recognised as a transformation of Schwarzschild's coordinates. As always, there's some ambiguity in how you interpret remote observations in GR. There's no ambiguity in actual measurements, though.

 

[Dale]

The answer is YES! that is what I wonder.

So the 43 arcseconds is a geometrical quantity that would be the same for both Earth and Jupiter. It is only the per century that would potentially be problematic.

If you define a century in terms of the time that it takes for Earth to go around the sun then that becomes the same sort of geometric quantity as the 43 arcseconds. So both Earth and Jupiter would agree.

If you define a century in terms of a certain number of seconds as measured by a local atomic clock, then the Earth would go around the sun a slightly different number of times in a century for Earth and Jupiter. So with that definition there would be a very slight discrepancy between the two.

Of the three effects Einstein suggested, i) Mercury perihelion’s precession, ii) light bending around the Sun and iii) gravitational redshift, the only solid effect was the precession of Mercury’s perihelion above what Newtonian mechanics predicted.

I completely disagree with this. Gravitational redshift can be measured on the scale of 1 m now, and the gravitational lensing is verified to exquisite precision. All three are unambiguously solid, and further there is weak experimental evidence for frame dragging and solid observational evidence for gravitational waves.

Edit: @Ibix for the win!

 

[Mickey1]

I am referring to the situation 1915-1921 when the Nobel Prize physics committee was discussing relativity.
St. John from Mount Wilson could not confirm the gravitational redshift.

The Physics Committee report for 1918 notes that: “A most careful experimental test carried out at the Mount Wilson Observatory (by the astronomer Charles St John) has shown that this shift does not exist, even though it should have been quite measurable with the method used."

The Physics Committee in its reasoning comes close to giving a mathematical proof of the non-existence of gravitational red-shift. This is in contrast to St. John (from the Wilson observatory): “For the lines of highest weight there is no displacement to the red either at the center or at the limb. The measurements are inherently difficult, and results may he more or less influenced by the choice of lines and by the resolving power, definition, and dispersion of the spectrographs used."(C. St. John, The Principle of Generalized Relativity and the Displacement of Fraunhofer Lines toward the Red, Contributions from the Mount Wilson Solar observatory, No 138, reprinted from 109 the Astrophysical Journal, Vol. XLVI, pp 249-265, 1917.

***
Let me direct you to the original issue " Gullstrand did not observe that the choice of coordinates must be adjusted to the observer and that this gives the correct result.” The idea is that Einsteins theory had a constant in connection with the the precession and that this had to be adjusted to the observer. According to Gullstrand the theory was "an issue of faith" and that the theory had no predictive power at all which he proved in relation to the precession issue."

I assume thus that the situation is similar to the calculation of the redshift from the Sun which – for an observer on Earth - must take into account the Sun’s gravity at its surface, and the Sun’s residual gravity in the Earth’s orbit, plus the gravity of the Earth.

Of cource we don't know what particular angle Gullstrand had at the time in his approach. Therefore perhaps my question is difficult to answer. However, I assume perhaps generously, that he had a correct initial approach and received an answer which must be adjusted to bothe object and observer's gravity field, such as the case for for the redshift.

This is to help me in finalize may essay on physicalism below in a draft form.

<Deleted>

 

[Dale]

I am referring to the situation 1915-1921 when the Nobel Prize physics committee was discussing relativity.

Ah, I misunderstood. I have no knowledge of the deliberations of the Nobel committee, and little knowledge of the historical twists and turns of those days.

Anyway, @Ibix and I both gave the same answer for the technical question. You will have to decide how that fits into the history.

The idea is that Einsteins theory had a constant in connection with the the precession and that this had to be adjusted to the observer.

Since the observers in question are all on Earth it is hard to see how this could possibly matter. All of the relevant observers will agree on the definition of a century whether they are using the one based on revolutions around the sun or one based on atomic clocks. Either definition would result in the same invariant prediction and the only free parameter in the theory (the cosmological constant) is negligible on this scale. Nothing else is adjustable, or rather no other adjustable parameter affects the measured outcome.

This is to help me in finalize may essay on physicalism below in a draft form.

We do not give pre publication support. I have deleted the attachment

 

[PeterDonis]

This problem was solved by Gullstrand, a self-taught optical expert, looking into the theory. He found that the theoretical derivation for Mercury’s perihelion precession contained a constant of arbitrary value and that it therefore couldn’t claim anything in particular regarding Mercury.

Do you have a reference for this?

As far as our current understanding goes, there is definitely an invariant (i.e., a quantity that is independent of any choice of coordinates) associated with perihelion precession: roughly speaking, it is the number of orbits it takes for the precession to amount to one complete orbit. Values like "43 seconds of arc per century" are basically translations of this invariant into particular coordinate systems that are useful for us on Earth (that particular value is in barycentric solar system coordinates, i.e., coordinates in which the origin is the barycenter of the solar system and which are not rotating with respect to infinity, and in which a "century" means "the coordinate time required for the Earth to complete 100 orbits around the Sun").

I suspect that Gullstrand did not fully understand the above, but that would have been quite likely at the time since nobody at that time really had the modern understanding of GR, that the actual physics is contained in invariants, not coordinate-dependent quantities.

I assume thus that the situation is similar to the calculation of the redshift from the Sun which – for an observer on Earth - must take into account the Sun’s gravity at its surface, and the Sun’s residual gravity in the Earth’s orbit, plus the gravity of the Earth.

Here, again, there is definitely an invariant associated with the redshift observed by a particular observer: in this case it is the inner product of the 4-momentum of incoming photons from the Sun with the 4-velocity of the observer on Earth that observes them.

We could also define another invariant, namely, the same inner product but with the 4-velocity this time being that of an idealized observer at rest at infinity. The latter is the value that is usually quoted when "the gravitational redshift of light from the Sun" is discussed. This invariant will be slightly different from the first one above because, first, the Earth is a finite distance from the Sun, not at infinity, so photons coming from the Sun don't have to "climb" as far out of the Sun's gravity well, and second, incoming photons from the Sun observed at the Earth's surface are very slightly blueshifted by falling in the Earth's own gravity. Both of these effects reduce the second redshift as compared with the first.

 

[Mickey1]

First, regarding references. it is Aant Elzinga Einstein's Nobel Prize, A Glimpse Behind Closed Doors, Science History Publications, USA, 2006. He was granted access to the Nobel archives and I believe this is the most important study of Einstein's document in the NObel Archive..
(I was not allowed to forward my essay by the moderator, since that wopuld count as a publication. I assume I can tell you that it is called "The principle of physicalism applied to a few example areas" and can be found on ResearchGate under my name Mikael Jensen.)

The issue here, framed in a more general way is; did Einstein's theory of relativity around 1920 allow for a correct calculation of Mecury's precession, and consequently was Gullstrand therefore wrong in claiming the opposite?

I assume the calculation could be performed simply since the right numerical value was mentioned historically.

 

[PeterDonis]

did Einstein's theory of relativity around 1920 allow for a correct calculation of Mecury's precession

Einstein's theory allowed for it in 1915; the calculation of Mercury's precession was the first one Einstein himself did to check his theory. The same calculation Einstein did then is routinely assigned to physics students today as a homework problem. There is no doubt about its correctness.

was Gullstrand therefore wrong in claiming the opposite?

AFAIK the quote you gave at the end of post #3, which says that Gullstrand was mistaken and explains why, is correct.

 

[Mickey1]

Thanks
That is really all I need.
I don't think I would go into more finer details. That would require looking at the original article by Kretchmann , (Kretchmann, Das statische Einkörperproblem in der Einstein'schen Theorie. Antwort an Hrn. A. Gullstrand. Ark. för Mat., Astron, och Fys. 17, Nr. 25, 4 S. 1923).

 

[vanhees71]

So the 43 arcseconds is a geometrical quantity that would be the same for both Earth and Jupiter. It is only the per century that would potentially be problematic.

It's not so problematic since 2019, because the "new SI" makes it very easy to communicate the meaning of units to our Jovian physicist colleagues. It's all based on universal constants of Nature and thus we can communicate what we mean by "century" by telling them the relation to the SI second which is determined by the Cs-137 finestructure transition frequency.