Author Topic: Episode 157 Gravity and Stupid Dreams  (Read 5645 times)

Offline bobmath

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Episode 157 Gravity and Stupid Dreams
« on: November 20, 2012, 09:41:36 AM »
So, does Fermat's principle apply in a bubble of blasphemously curved spacetime?

Offline bn

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Re: Episode 157 Gravity and Stupid Dreams
« Reply #1 on: November 20, 2012, 06:44:21 PM »
yes
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Offline Daneel

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Re: Episode 157 Gravity and Stupid Dreams
« Reply #2 on: November 20, 2012, 07:05:24 PM »
Ryan!!! I cannot forgive you for not using Hell March (the badass song Jacob talked about) as transition music to the last segment.

http://www.youtube.com/watch?v=9WqwFhX6Cqg

The awesome Red Alert 2 intro:

<a href="http://www.youtube.com/v/fnd0qg4I_MM" target="_blank" class="new_win">http://www.youtube.com/v/fnd0qg4I_MM</a>

Abridged version:
<a href="http://www.youtube.com/v/GuwtNDkHch0" target="_blank" class="new_win">http://www.youtube.com/v/GuwtNDkHch0</a>
« Last Edit: November 20, 2012, 07:11:52 PM by Daneel »

Offline bn

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Re: Episode 157 Gravity and Stupid Dreams
« Reply #3 on: November 21, 2012, 01:27:49 PM »
So, does Fermat's principle apply in a bubble of blasphemously curved spacetime?

maybe i should explain better.
Fermat's principle is lovely. it says that "light rays will always travel on the shortest path between two points". which is crazy because "how do they know?".

the short answer is that light rays are really good at variational calculus (the calculus of finding the extremal path or shape... it's why bubbles are spherical. )

anyway, in general relativity, all non-accelerating trajectories are determined using variational calculus, and they are all extremal paths.

so in short "yes".

in long "yes i had to write a  numerical code which found the shortest paths across the spacetime in order to graph how light behaves in the bubble of spacetime curvature"
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Offline bobmath

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Re: Episode 157 Gravity and Stupid Dreams
« Reply #4 on: November 25, 2012, 02:19:27 AM »
it's why bubbles are spherical.
... neglecting gravity and atmospheric disturbances. </pedantry>

Quote
in long "yes i had to write a  numerical code which found the shortest paths across the spacetime in order to graph how light behaves in the bubble of spacetime curvature"
I guess I shouldn't be surprised that there wasn't already code out there to do that.

Here's another application of variational calculus: if you take a lumpy ball of mostly iron floating in space and spin it, it will flatten out a bit so that gravity plus centrifugal force is perpendicular to the surface everywhere.

Latitude is measured as the angle of the normal vector, not the angle from the center of the Earth. Where I work, we have homegrown software to convert between latitude/longitude coordinates and x-y-z spatial coordinates. The code that goes one way is written in Fortran. The code that goes the other way is written in C. They use different reference ellipsoids, so if you round-trip your coordinates they will come back a little different. It drives me mad. In order to use them both in the same program, they used a Fortran-to-C converter, and the output of f2c is downright Lovecraftian. (This has been a bit of a tangent... I'm really a software guy, but I majored in Physics.)

Offline bn

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Re: Episode 157 Gravity and Stupid Dreams
« Reply #5 on: November 25, 2012, 06:33:24 PM »
i believe you.

man, when i wrote on my resume/CV that i can code in fortran
people are like "what's fortran?"
and i'm like "FORTRAN IS VERY IMPORTANT A LONG TIME AGO AND THINGS LIKE THIS STICK AROUND"
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Offline bobmath

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Re: Episode 157 Gravity and Stupid Dreams
« Reply #6 on: November 26, 2012, 01:36:30 AM »
"FORTRAN IS VERY IMPORTANT A LONG TIME AGO AND THINGS LIKE THIS STICK AROUND"
It's totally true. Some of our fortran is older than I am.

Offline stephako

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Re: Episode 157 Gravity and Stupid Dreams
« Reply #7 on: January 14, 2013, 04:06:29 AM »
So, does Fermat's principle apply in a bubble of blasphemously curved spacetime?

maybe i should explain better.
Fermat's principle is lovely. it says that "light rays will always travel on the shortest path between two points". which is crazy because "how do they know?".

the short answer is that light rays are really good at variational calculus (the calculus of finding the extremal path or shape... it's why bubbles are spherical. )

anyway, in general relativity, all non-accelerating trajectories are determined using variational calculus, and they are all extremal paths.

so in short "yes".

in long "yes i had to write a  numerical code which found the shortest paths across the spacetime in order to graph how light behaves in the bubble of spacetime curvature"

I briefly had a look at a paper recently, something about gravastars and de-sitter bla. I didn't really understand half of the words in the title. Anyway they talked about optical geometries and had the following line (Emphasis mine):

Quote
Conformal invariance of the wave equation for massless particles (photons) is particularly useful because it allows to introduce a specific conformally related metric, known as an optical metric in which geometric optics can be derived from an analog of the Fermat principle.

I took that to mean that Fermats principle and our idea how light travels work only sometimes in general relativity.
Null results, open questions and a bit of my writing: JUnQ

Offline bn

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Re: Episode 157 Gravity and Stupid Dreams
« Reply #8 on: January 14, 2013, 06:48:56 AM »
no.
actually, it's a fun shortcut.

the deal is that spacetime geometry is hard to chew and digest.
it is helpful to take the geometry and simplify it.
but most times when you simplify it, it changes the geometry.

BUT
there is a family of transformations you can make, where the trajectories that photons travel along stay the same.

so what you can do, as a result, is get a simplified spacetime geometry, which retains some of the optical properties of the original spacetime.
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Offline stephako

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Re: Episode 157 Gravity and Stupid Dreams
« Reply #9 on: January 14, 2013, 08:49:27 AM »
I see.

Good that we could clear that up so quickly :)
Null results, open questions and a bit of my writing: JUnQ

Offline bn

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Re: Episode 157 Gravity and Stupid Dreams
« Reply #10 on: January 14, 2013, 12:39:32 PM »
@_@ quickly. yes.
Titanium Physicists has a pro-bee-analogy agenda. That's certainly no secret.