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Nick Weiner
Attends University of California, Davis
Lives in Davis, CA
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Damn cool stuff.
 
A planet in the fourth dimension

I bet you know that planets go around the sun in elliptical orbits. But do you know why?

In fact, they’re moving in circles in 4 dimensions. But when these circles are projected down to 3-dimensional space, they become ellipses!  This animation by Greg Egan shows the idea.

The plane here represents 2 of the 3 space dimensions we live in. The vertical direction is the mysterious fourth dimension. The planet goes around in a circle in 4-dimensional space. But down here in 3 dimensions, its ‘shadow’ moves in an ellipse!

What’s this fourth dimension I’m talking about here? It’s a lot like time. But it’s not exactly time. It’s the difference between ordinary time and another sort of time, which flows at a rate inversely proportional to the distance between the planet and the sun.

Egan's animation uses this other sort of time. Relative to this other time, the planet is moving at constant speed around a circle in 4 dimensions. But in ordinary time, its shadow in 3 dimensions moves faster when it’s closer to the sun.

All this sounds crazy, but it’s not some new physics theory. It’s just a different way of thinking about Newtonian physics!  Of course you can see that planets move in elliptical orbits without resorting to the 4th dimension.  But it becomes a lot more obvious if you do!

Physicists have known about this viewpoint at least since 1980, thanks to a paper by the mathematical physicist Jürgen Moser. Some parts of the story are much older. A lot of papers have been written about it.

But I only realized how simple it is when I got a paper in my email from someone I didn't know: an amateur mathematician  named Jesper Göransson.  I get a lot of papers by crackpots, but the occasional gem like this makes up for all those.

The best thing about Göransson’s 4-dimensional description of planetary motion is that it gives a clean explanation of an amazing fact. You can take any elliptical orbit, apply a rotation of 4-dimensional space, and get another valid orbit!

Of course we can rotate an elliptical orbit about the sun in the usual 3-dimensional way and get another elliptical orbit. The interesting part is that we can also do 4-dimensional rotations. This can make a round ellipse look skinny: when we tilt a circle into the fourth dimension, its ‘shadow’ in 3-dimensional space becomes thinner!

In fact, you can turn any elliptical orbit into any other elliptical orbit with the same energy by a 4-dimensional rotation of this sort. All elliptical orbits with the same energy are really just circular orbits on the same sphere in 4 dimensions!

For the details, see the Azimuth blog:

https://johncarlosbaez.wordpress.com/2015/03/17/planets_in_the_4th_dimension/

I had to go through Göransson’s calculations to convince myself that they were right. 

And here is his paper:

• Jesper Göransson, Symmetries of the Kepler problem, 8 March 2015, http://math.ucr.edu/home/baez/mathematical/Goransson_Kepler.pdf.

#physics  
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Dude that's trippy! 
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I just got into UC Davis! XD #ucdavis  
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I got my family to sit down and marathon watch all 42 segments of +H+ The Digital Series. Then I watched the Google Hangout video which was posted the same day. Too bad I missed joining the discussion as it went one but now I know to watch out for the next one on here. :) Thanks +John Cabrera and +Cosimo de tommaso for writing such an amazing show.
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sharing things you enjoy is the best
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Freaking amazing.
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yes that's the truth. but if it can be at reduced cost and built and designed away from countries that we are not in war with or distrustful relationships, it would be very beneficial. There is some people who spend quite a bit and can run vehicles with water. but at what cost to design these technologies. not to mention water is not a free source either, what about the purity and cleaning treatments
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Have him in circles
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Looks like a good app for this time.
Communities across the U.S. continue to suffer from over-policing, racial p...
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A gecko kills a spaceman!
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This is my gecko named Mellow Yellow. She seems pretty relaxed in my hand, doesn't she?
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Eww..
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These were taken a while back. I've been meaning to show these off. They're pictures of my leopard gecko Mellow Yellow just before her most recent shedding.
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Have him in circles
155 people
Wade Wallenstein's profile photo
Drew Bennett's profile photo
Max Chang's profile photo
James Bizz's profile photo
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Spirituwal “SHH2C” Superhumanhowtoclinic's profile photo
Brian Chin's profile photo
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Education
  • University of California, Davis
    Biomedical Engineering, 2014 - present
  • Mount San Antonio College
    Biological Systems Engineering, 2008 - 2014
  • New Century Technology High School
    2006 - 2008
  • Catholic High School
    2004 - 2006
  • Pasadena City College
    2011 - 2011
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Other names
HomicidusInfirmorum
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Nick Tech-Know, computer ultra-expert; part of Deep Thought's successor.
Introduction
I'm that guy that handed you his card from his hat. I'm also the zombie that interrupted your class on Halloween week.

I have an extensive personality I've yet to fully organize, catalog, and map. The problem isn't that I'm full of myself; I'm just lost in myself. Now where did I put your name?
Bragging rights
Solved a C++ puzzle nobody else in my class could, isn't afraid to eat giant toasted ants, hitchhikes everyday
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IT Consultant and College Student
Employment
  • IT Consultant and College Student, present
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Davis, CA
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West Covina, CA - Huntsville, AL - La Habra, CA
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