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Ask HN: Without Einstein, would General Relativity be discovered by now?

46 points by matt-attack ↗ HN
Similar to Calculus where two different people were more or less discovers the same thing around the same time, was anyone else working on something that would have led to its discovery? If not when do scientists thing it would have been discovered?

14 comments

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dsr_
Completely practically: clocks in orbit keep consistently different time from clocks on the surface. The discrepancy requires accounting for relative frames of reference.

" Because an observer on the ground sees the satellites in motion relative to them, Special Relativity predicts that we should see their clocks ticking more slowly (see the Special Relativity lecture). Special Relativity predicts that the on-board atomic clocks on the satellites should fall behind clocks on the ground by about 7 microseconds per day because of the slower ticking rate due to the time dilation effect of their relative motion [2].

Further, the satellites are in orbits high above the Earth, where the curvature of spacetime due to the Earth's mass is less than it is at the Earth's surface. A prediction of General Relativity is that clocks closer to a massive object will seem to tick more slowly than those located further away (see the Black Holes lecture). As such, when viewed from the surface of the Earth, the clocks on the satellites appear to be ticking faster than identical clocks on the ground. A calculation using General Relativity predicts that the clocks in each GPS satellite should get ahead of ground-based clocks by 45 microseconds per day.

The combination of these two relativitic effects means that the clocks on-board each satellite should tick faster than identical clocks on the ground by about 38 microseconds per day (45-7=38)! This sounds small, but the high-precision required of the GPS system requires nanosecond accuracy, and 38 microseconds is 38,000 nanoseconds. If these effects were not properly taken into account, a navigational fix based on the GPS constellation would be false after only 2 minutes, and errors in global positions would continue to accumulate at a rate of about 10 kilometers each day! The whole system would be utterly worthless for navigation in a very short time. "

-- from http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps....

frankish
I'm curious to know if this GPS example has any significant dependencies on prior technologies/physics that was only possible after Einstein discovered general relativity. I don't know enough physics or history to know how much would be different, but can anyone weigh in on if GPS satellites would still be possible?
detaro
You don't need relativity to design something like GPS for a universe where it doesn't exist, so the idea of GPS still makes sense. Presumably we'd have noticed that this clock discrepancy happens at some point when trying to sync clocks in orbit, probably chased a bunch of odd paths trying to figure out why it happens, but in the end found some model to correct the error.
thecabinet
The story I’ve heard was that GPS was invented due to Sputnik. The Doppler shift in its beeps proved its speed and thus its orbit. Somebody (in the Navy?) wondered if the “reverse” could be done: could you listen to various shifting beeps and figure out your location?
DavidSJ
David Hilbert discovered general relativity at practically the same moment as Einstein.
gnramires
I believe there was a race at that time, physicists knew there was a need to generalize SR to non-inertial frames, and that perhaps that it involved metric spaces (following the lorentz transformations). Hilbert was working on it, but apparently did not make much progress at deriving the GR equations (I don't have a source, sorry -- scattered articles on GR). You're right that eventually he or someone else would have made it, but how long would it take is speculation.

Edit: More information here https://en.wikipedia.org/wiki/Relativity_priority_dispute

I think the main takeaway is that Hilbert and Einstein ended in amicable terms, and it seems both contributed greatly to eachother's result.

supernova87a
Whether or not someone would have formulated an explanation for physically observable discrepancies as quickly is maybe what you mean?

Because all those pesky missing factors of 1/2 were already being seen in astronomical phenomena, correct? Orbit of Mercury, aberration of light, etc. A postulate / explanation was what was needed (of course, maybe some more examples too).

But yes, there is also the question of whether the publicizing of the theory (and correct predictions) led to an explosion of interest that caused lots of technological advances due to the excitement around the new field.

dntbnmpls
Yes. It's even disputed whether Hilbert discovered it first. But regardless of einstein or hilbert, technological advancements would have necessitated the discovery of general relativity. Just like the advances of telescopes/observation lead to kepler's planetary laws or the advances of computing technology led to the theory of computation.

Science can lead to new technologies, but new technologies lead to new science as well.

https://undsci.berkeley.edu/article/whathassciencedone_03

The general direction of science and technology in the first half of the 20th century indicates that general relativity, theory of computation, etc would have been discovered.

BenoitP
From the horse's mouth:

"There is no doubt, that the special theory of relativity, if we regard its development in retrospect, was ripe for discovery in 1905. Lorentz had already recognized that the transformations named after him are essential for the analysis of Maxwell's equations, and Poincaré deepened this insight still further. Concerning myself, I knew only Lorentz's important work of 1895 [...] but not Lorentz's later work, nor the consecutive investigations by Poincaré. In this sense my work of 1905 was independent. [..] The new feature of it was the realization of the fact that the bearing of the Lorentz transformation transcended its connection with Maxwell's equations and was concerned with the nature of space and time in general. A further new result was that the "Lorentz invariance" is a general condition for any physical theory."

-- Albert Einstein

----

In "La théorie de Lorentz et le principe de réaction", Poincaré published a paper in which he said that radiation could be considered as a fictitious fluid with an equivalent mass of m = E/ c^2. He derived this interpretation from Lorentz's 'theory of electrons' which incorporated Maxwell's radiation pressure.

Plenty of material here: https://en.wikipedia.org/wiki/Relativity_priority_dispute

----

TL;DR: it definitely did not happen in a vacuum. IMHO his contribution is making science happen 1-2 years earlier (which is still a tremendous feat by itself).

IXxXI
Richard Feynman said he could not conceive of how Einstein came up with Relativity Theory with the level of scientific advancement of the time. So there is that.