Einstein’s Relativity Used to Weigh a Star(scientificamerican.com)
scientificamerican.com
Einstein’s Relativity Used to Weigh a Star
https://www.scientificamerican.com/article/for-first-time-einsteins-relativity-used-to-weigh-a-star/
16 comments
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
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):
Now Snell's law says
So it turns out this principal works even in the case of gravitational spacetime distortion, and can be applied there as well.
Suppose you have the following situation
x1 | n2
|
|
n1 | x2
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
Now Snell's law says
n1 sin θ_input = n2 sin θ_output
So it turns out this principal works even in the case of gravitational spacetime distortion, and can be applied there as well.
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.
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.
wow! Very cool explanation! I wonder what happens at the point that it changes direction - is the change instant or is there a curve? I suppose that because photons/waves don't have mass it can be instant, but that still sounds weird.
Heh, I just saw this in Chiang's Stories of Your Life and Others.
The mechanism is completely different, but gravitational lensing also involves changing the angle of a ray of light.
Do we know that the mechanism is different? Do we know what causes light to slow down when passing through material and that it's unrelated to gravity? I know that refraction effects is documented through experiments - but I don't believe I've seen any real explanation of the cause of the effect? (Not that I've looked - I only have very basic knowledge of physics)
Light bends and travels slower in matter because it has (QM) interactions with the particles of the matter. Gravity is not involved.
Light bends due to gravity because gravity is the bending of spacetime so that light's straight line path is curved. QM is not involved.
Light bends due to gravity because gravity is the bending of spacetime so that light's straight line path is curved. QM is not involved.
I still think that's nuts. Isn't the "space" "straight" as seen by light, but the light/space is curved so it does bend... man... so maybe the "alcubere drive" we wouldn't feel the compression of our bodies/expansion.
When you're being stretched or compressed by GR, you don't feel it at all in your frame of reference.
Physically we are not sure. Mathematically the equations could be taught in the same class. (Exaggeration a little as they in very complicated but hopefully you see my point) they come from similar places.
The point is to remind the reader that light doesn't always "travel in straight lines". Obviously refraction and gravity aren't the same thing, but nonetheless you can measure the index of refraction of a material by looking at the deflection of light through it in (sort of) the same way you can measure the gravity well of a star by looking at similar deflections.
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Probably, if you think of refraction variationally in terms of Fermat's principle.
This is actually what inspires me as a physicist. So back in the day people were looking for an encapsulated theory of why the hell things happened. The Principle of Least Time was the original theory, but that didn't make sense (look at a spring) so then there was The Principle of Least Energy, but that also wasn't good enough. Until Hamilton came along and gave us the Principle of Least Action. This is the basis for all physics. All of our laws incorporate this theory. Einstein took it one direction and Maxwell took it another and Planck another. So all of these phenomena are basically the same. Just different manifestations.
Physics isn't 10,000 problems it's 10,000 manifestations of like 5.
Physics isn't 10,000 problems it's 10,000 manifestations of like 5.
The original Science paper is here: 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.
The section "Relativistic deflections by foreground stars" walks through the math which enables this, which I found really interesting.
Does that comparison make sense to bending space time? I thought that was an angle of light thing.