Reading and article in today’s Guardian about Arthur Eddington’s confirmation of General Relativity I came across this passage:
Could someone explain the mechanism by which Newton’s gravity would cause such a shift?
For small objects affected by the gravity of very much larger bodies you will see that the objects’ own masses are cancelled out in the calculation of their trajectories (that’s how Galilei had the marble and cannon ball hit the ground simultaneously when dropped from a tower). Now, cancelling out two zeroes is admittedly a bit risky; but if light were a stream of nearly massless corpuscles with a fixed speed c you would expect it to behave in the same way, i.e. to be slightly deflected by a gravity source.
Someone asking the same question in the comments that follow that article was offered this.
I know of no situation in physics where something that’s exactly zero behaves significantly differently from something that’s merely almost zero. In other words, if you can take the limit, take the limit.
I don’t see any mechanism in Newtonian physics for a massless light particle to be effected by gravity. The link provided by Weirofhermiston did not provide any explanation, simply a rather simple animated gif of various paths.
Is there any Newtonian mechanism for light to be effected by gravity?
The force on an object due to the Sun’s gravity is F=GmMs/r[sup]2[/sup] (where m is the mass of the object and Ms is the mass of the Sun).
The acceleration due to a force is a=F/m. Notice that m cancels out, leaving the acceleration/deflection proportional to the mass of the Sun and the distance - and nothing else. As Chronos suggested, it is possible therefore to take the limit and conclude that the same deflection occurs for zero mass as would occur for an incredibly tiny mass.
As far as I’m aware, though, no one thought of this approach until Einstein came up with a different way of thinking about the effect of gravity on massless objects.
ETA: Nope - in 1804, this paper makes just the prediction I’m talking about On the Deflection of a Light Ray from its Rectilinear Motion - Wikisource, the free online library
Thanks Andy L that was a lucid summary.
Thanks.
The cite helped.
My first thought had been that given a=F/m Newtonian mechanics didn’t apply when m=0 since the equation makes no sense. Writing the equation as F=ma gives a force of 0, while writing the equation as a=F/M gives an acceleration of infinity. But that is not the case.
IIUC, the actual (Einsteinian) deflection is almost exactly twice the predicted Newtonian deflection. Is there an easyish intuitive explanation for the doubling?
Thank you.
This article gives a little information on that subject (and a lot of very interesting stuff about the Eddington expedition)
https://physicstoday.scitation.org/doi/full/10.1063/1.3099578#
"Eddington and Dyson labeled the value Einstein calculated in 1911 as the “Newtonian” value, a label justified by the subsequent discovery that a similar value based only on Newtonian physics had been published in 1804 by the German astronomer Johann Georg von Soldner. 4 In 1916, after he had developed the final version of his theory of general relativity, Einstein realized that there was an additional component to the light-deflection effect caused by the way that the Sun’s mass curves spacetime around itself. Thus a straight path, or geodesic, near the Sun is curved, compared with a path through flat space. The extra deflection caused by that curvature is comparable to the deflection due solely to falling, so that the general relativistic prediction calls for twice as great a shift in stellar positions—about 1.75″ at the limb of the Sun—as does the Newtonian theory. "
Don’t know for sure but if the masses of the three neutrinos were exactly zero, there would be no oscillations between types, correct?
Yes, but the oscillation experiments tell the difference in the mass splittings. If they all had a mass of a few pico-eV (or femto-eV or yotto-eV or whatever), it still wouldn’t work.
Sorry, you’re right. Your statement sounded like a theoretical one to me not empirical.
While never mainstream until Einstein’s prediction, there had been plenty of Newtonian predictors of a deflection. The thing to realise is that Newton’s own theory of light involved particles. I’ve never gone through the details, but it wouldn’t surprise me if his followers in the period between him and Einstein assumed that those particles had to have some (small) mass. Otherwise, wasn’t the notion of a massless particle a contradiction in terms?
Soldner’s only significant amongst this horde because he was German. Literally so. He gets picked up and promoted as the forerunner by the anti-Einstein crowd in Germany during the Twenties as part of their silly “Einstein is just a plagiarist” argument. Milena Wazeck’s (horribly dry) Einstein’s Opponents (2009; CUP, 2014) goes through this in detail.
On the factor of 2 in the final result, the usual claim is that Einstein had previously failed to realise that time bending had to be considered along with space doing so. (Another issue I’ve never actually sat down and checked.)
Aside: The big one I know of is the fact that the zero-mass limit of a massive linear gravity theory is not equivalent to a massless linear gravity theory. But that’s somewhat obscure.