Author Topic: SGU 5x5 #69  (Read 2148 times)

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Offline Steven Novella

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SGU 5x5 #69
« on: June 11, 2009, 08:22:45 PM »
Einstein's Eclipse and General Relativity
Steven Novella
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Re: SGU 5x5 #69
« Reply #1 on: June 12, 2009, 05:59:16 AM »
this has always been one of my favorite stories, for many of the reasons you mentioned, the post war angle, the questions about validity, but mostly because it seems to be the last time proof of a (then) abstract science theory caught the worlds attention. That the world could be captivated by something that only a small number could really understand. Since that time we have dealt with the concrete: atom bombs, moon landings. This was the purest of joys, a scientific theory with at the time no real world applications. The LHC may come close, but it too is more about an enormous hardware than the theory it seeks to prove.
Humankind cannot stand very much reality.   T. S. Eliot

Offline Trinoc

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Re: SGU 5x5 #69
« Reply #2 on: June 12, 2009, 06:06:42 AM »
Good (and sadly rare) to hear a description of the experiment which points out that there is a bending of light under Newton's gravity, and that Einstein's version simply predicts a greater bending (twice as much). Most versions of the story - including the BBC docudrama "Einstein and Eddington" simply state that Eddington found a shift in the star's position, and that confirmed the theory.

This also adds weight to the suggestion that Eddington's observations may not have been accurate enough to distinguish between the Newtonian and Einsteinian predictions, so maybe it was a lucky break. I wonder what would have happened to General Relativity in future decades if the experiment had been done by someone other than Eddington - Sir Oliver Lodge, for instance - who was opposed to the new theory on either scientific or political grounds.
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Offline 666

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Re: SGU 5x5 #69
« Reply #3 on: June 13, 2009, 08:16:42 PM »
Good (and sadly rare) to hear a description of the experiment which points out that there is a bending of light under Newton's gravity,

How is light bending under Newton's gravity?  Photons have no mass.

Offline Trinoc

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Re: SGU 5x5 #69
« Reply #4 on: June 14, 2009, 04:35:39 AM »
Good (and sadly rare) to hear a description of the experiment which points out that there is a bending of light under Newton's gravity,

How is light bending under Newton's gravity?  Photons have no mass.
Well, of course, Newton didn't know that ... but even if he suspected it, he would know that the equation for the path of any body with mass is independent of the mass itself (the mass in the force due to gravity cancels out the mass in f=ma for the acceleration). So, using Newton's own calculus (he called it "fluxions"), take the limit as mass tends to zero.
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Offline 666

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Re: SGU 5x5 #69
« Reply #5 on: June 15, 2009, 12:02:13 AM »
For any non-zero value of m the acceleration is independent of the mass.  But with m=0 the force is zero.  When did Newton say that you need to smooth non-continuous functions by taking the limit?   Did Newton even consider light as a particle?

Offline Trinoc

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Re: SGU 5x5 #69
« Reply #6 on: June 15, 2009, 06:58:29 AM »
For any non-zero value of m the acceleration is independent of the mass.  But with m=0 the force is zero.  When did Newton say that you need to smooth non-continuous functions by taking the limit?   Did Newton even consider light as a particle?
To answer the last question first: Yes, Newton believed that light consisted of "corpuscles". His reasoning was faulty, and so light was then regarded as waves until Einstein proved the existence of photons by the photoelectric effect. Newton had no reason to think that anything could exist with zero mass, so I don't expect the need to take a limit occurred to him in this case.

Back to the previous question: Yes, Newton devised differential calculus in parallel with Leibniz, though Newton called his version "fluxions". A central process in differential calculus is taking limits, particularly the limit of a function as a variable tends to zero. In this case the function (acceleration in a given gravitational field) is a constant, so the limit is trivial.

Newton/Leibniz calculus does not deal with non-continuous functions, but I don't see why you think a non-continuous function is required here. If the undefined nature of the acceleration due to gravity at m=0 bothers you, simply define it as being equal to the limit.

For an example of a function rigorously defined in this way, see ...

http://mathworld.wolfram.com/SincFunction.html
I'm a skeptic. Not a "skepdude". Not a "man skeptic". Just a skeptic.

 

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