# What is the logic behind the Eddington expedition that proved Einstein's general theory of relativity?

The Eddington expedition in 1919 proved Einstein's general theory of relativity.

[Eddington] argued that the deflection, or bending, of light by the Sun’s gravity could be measured... because Einstein’s theory predicted a deflection precisely twice the value obtained using Isaac Newton’s law of universal gravitation... [Crommelin's] measurements were decisive, and were noticeably closer to the Einstein prediction than to the Newtonian.(Coles, 2019)

Suppose p is the statement"the measured deflection of light by the Sun's gravity matches Einstein's prediction", and q is the statement "the general theory of relativity is correct". To explain the reasoning behind the Eddington expedition, the conditional statement that needs to be used as a premise is q → p. The statement q → p is the only true one, and it allows for keeping the inference valid, which will be shown later.

The statement p → q reads as "if the deflection matches the prediction, then the theory is correct". When both component statements are analyzed, this conditional statement becomes problematic. The mere fact of deflection matching prediction does not necessarily lead to a correct theory. The theory can be false for other reasons even as deflection matches prediction. In the truth table for p → q, both the following rows are possible:

p (T), q (T), p → q (T)

p (T), q (F), p → q (F)

Therefore, using p → q as a premise in the inference is not very reliable.

As p → q appears shaky, the statement p cannot be established as a sufficient condition for statement q. However, the inverse of p → q offers some hope in explaining the expedition. The statement ~p → ~q reads as "if the deflection does not match Einstein's prediction, the general theory of relativity is incorrect". This one looks solid, because once the deflection is found not to match the prediction, there is no other ground for the theory to continue to be correct. This idea is embodied in the following truth table row.

~p (T), ~q (T), ~p → ~q (T)

A conditional statement is logically equivalent to its contrapositive. Using this rule, the preceding explanation for the Eddington expedition can be further tested by evaluating the truth or falsity of conditional statement q → p. The statement q → p reads as "if the general theory of relativity is correct, the measured deflection matches Einstein's prediction". For this statement, reasoning appears solid, because any discrepancy between the deflection and the prediction would render the theory incorrect. This reasoning can be shown in the following truth table row.

q (T), p (T), q → p (T)

Up to this point, it has been shown that q → p is a reliable statement. In other words, p is established as a necessary condition for q.

Lastly, processes of inference are used to derive the desired conclusion.

q → p

~p

therefore ~q

Very unintuitively, the inference uses modus tollens. As far as the Eddington expedition went, the second premise never surfaced, which is, the measured deflection was never found to differ from the predictions made by Einstein. Thus, only the first premise q → p stays relevant. Coupled with the analysis above that reveals the truth of q → p, the general theory of relativity is held to be correct.

A side note on this question: if one day the second premise of the inference block is found, the general theory of relativity will be discredited.

Reference: Coles, P. (2019). Relativity Revealed. Nature. 568. 306-307.

• So what is the question? It seems like the only question is in the title and then the body of the question is an answer to the title. – Dale Sep 12 at 17:57

Eddington did not seek to logically prove that general relativity was correct. Instead, the aim of his expedition was to gather experimental evidence that could distinguish between general relativity and Newton's law of universal gravitation.

General relativity made a specific prediction about the bending of light from stars observed close to the sun during a solar eclipse which differed from the prediction made by Newton's law. The evidence gathered by Eddington's expedition was in much closer agreement with Einstein's prediction than Newton's, but the results could have gone the other way - or could have produced a value different from both predictions.

Together with other evidence (such as the precession of Mercury's orbit), the evidence from Eddington's expedition supports an inductive argument for the validity of general relativity. It does not deductively prove that general relativity is correct - the scientific method does not work that way - but it narrows down the alternatives. A single experimental observation (provided it could be successfully replicated) can disprove general relativity (or any other scientific theory) but any competing theory would have to account for existing experimental data as well as the new observation.

The Eddington expedition in 1919 proved Einstein's general theory of relativity.

This appears to be your conclusion (though no doubt you could find similar statements in pop-sci accounts).

The quote from the text you cite does not say this. Scientific theories are disproved; they cannot be proved. Eddington's measurements went some way towards disproving Newtonian gravitational theory, whilst being consistent with the predictions of General Relativity.

Another experiment in the future may disprove General Relativity, but we already know that Newtonian theory is an approximation to the truth.