
Einstein’s Relativity Used to Weigh a Star - Mz
https://www.scientificamerican.com/article/for-first-time-einsteins-relativity-used-to-weigh-a-star/
======
ge96
>Water can also create this kind of displacement illusion; try placing a
pencil in a glass of water, and note that the submerged half of the pencil
appears disconnected from the dry half.

Does that comparison make sense to bending space time? I thought that was an
angle of light thing.

~~~
archgoon
There is a way of looking at this phenomenon in terms of an optimal path
problem, Fermat's Principal of Least Time.

Suppose you have the following situation

    
    
        x1  |  n2
            |
            |
        n1  |  x2
    

We have two different materials, with index of refraction n1 and n2. Now
suppose that light has traveled between points x1 and x2, we can ask the
question, what path did it take? (Note here, we are asking about classical
rays of light, so we're thinking in terms of geometrical optics, not quantum
:) )

When light travels through the left hand side, it's traveling at a velocity,
c/n1, but in the right, it will travel at c/n2.

It turns out that we can answer the question of which path the light takes by
asking "Which path takes the shortest amount of time?". From that assumption
you can actually re-derive Snell's Law.

An example when n2 is very large (and thus moves slower on the right hand
side):

    
    
        x1  |  n2
          \ |
           \|
        n1  |--x2
    

the light will travel more distance on the left hand side because it can move
faster there, and thus get close as possible to the destination. It will then
make the last bit of distance in the right hand side.

Now Snell's law says

    
    
      n1 sin θ_input = n2 sin θ_output
    

Since n2 is very large, the only way to make this work is to make sin θ_output
very small. So we see in this case at least, both approaches agree as to what
will happen.

So it turns out this principal works even in the case of gravitational
spacetime distortion, and can be applied there as well.

~~~
ge96
This somewhat reminds me of the swimmer swimming across the river vs. up/down
(disproving ether interferometer). I was a physics student (did not end well
ha no focus). 4-5 years ago I was in school. Lucite and calculating the speed
of light, some cool labs. The bending of an electron beam into a circle due to
an orthogonal magnetic field was a good one.

Thanks for explaining. Funny making images with ASCII (is that right?)

I might be misconnecting dots.

Damn... I can't read/pay attention right now at this time (just woke up trying
to read this). I appreciate your time writing this out though/accompanied with
diagrams.

------
natekupp
The original Science paper is here:
[http://science.sciencemag.org/content/356/6342/1046.full](http://science.sciencemag.org/content/356/6342/1046.full)

The section "Relativistic deflections by foreground stars" walks through the
math which enables this, which I found really interesting.

