This is great, and captures a pretty common state of affairs for me :)



This is great, and captures a pretty common state of affairs for me :)

Originally shared by Calvin and Hobbes

Comments

  1. Michael GrantJuly 1, 2014 at 12:52 PM

    What's a record?

    ReplyDelete
  2. Melinda GreenJuly 1, 2014 at 4:59 PM

    It gets worse when you take relativity into account. The outer parts should appear to be foreshortened more than the inner parts, and the radius should remain the same! So what should a spinning disk look like at relativistic speeds?

    ReplyDelete
  3. Dan PiponiJuly 1, 2014 at 8:24 PM

    Back in the day, PC floppies used to spin at a constant rate, but Mac floppies would spin slower as the head moved towards the edge of the disk so as to store date at a constant density and not waste disk.

    ReplyDelete
  4. Roice NelsonJuly 2, 2014 at 7:59 AM

    Melinda Green, true to the spirit of this comic, I thought about your comment while trying to fall asleep last night :)  The logic that foreshortening is a function of distance seems sounds, so how to resolve the paradox?

    I think the resolution involves the following...  All the points are undergoing a central acceleration, and different points along the radius are undergoing different accelerations.  Since accelerations are involved, general relativity will be relevant.  That means spacetime measurements won't be flat.  Our intuitive expectation for arclength at some radius, s = r * theta, doesn't hold, and circle circumferences will deviate from their Euclidean value of 2 * pi * r.

    That's as far as I got though.  I can't offer specific details about what it would actually look like.

    ReplyDelete
  5. Dan PiponiJuly 2, 2014 at 8:42 AM

    > Since accelerations are involved, general relativity will be relevant.

    There is no difficulty in using accelerations within special relativity. Any time you draw a curved worldline in a spacetime diagram you've drawn the path of an accelerating object. Nothing breaks as a consequence. Unless the disk has a very high mass, and hence a significant gravitational field, its entire story can be told in the context of special relativity.

    ReplyDelete
  6. Roice NelsonJuly 2, 2014 at 9:44 AM

    ah, ok.  Guess I'll be wide-eyed again tonight :)  I will need to think on it more, but I just did a quick search for "spinning disk relativity" and this surfaced:

    http://math.ucr.edu/home/baez/physics/Relativity/SR/rigid_disk.html

    A few quotes from that page:

    "Einstein's 1916 paper on GR [5] makes no mention of elevators; instead, the Equivalence Principle is introduced via the rotating disk.  Einstein reproduces Ehrenfest's argument, but with a different conclusion: since we are no longer assuming flat Minkowski space, Einstein asserts that geometry for the rigid rotating disk is noneuclidean.  The Equivalence Principle now implies that geometry in a gravitational field will also be noneuclidean.  (By "geometry", I mean spatial geometry, i.e., we're not concerned with the temporal components of the spacetime metric.)"

    "This really has nothing to do with general relativity, which is a theory of gravity.  If one draws planes of simultaneity at various events in a rotating system such as a disk, then one can form a coherent picture of those events.  Much care must be taken with the mathematical details, but these are an expected part of applying the machinery of special relativity." (as Dan Piponi is pointing out)

    Having not read Einstein's paper, I hadn't known he discussed a rotating disk.  In any case, the link makes it sound like the "fate of the rigid disk" is a subtle problem that has been given much attention!

    ReplyDelete
  7. Richard GreenJuly 2, 2014 at 10:48 AM

    I'd never thought about this before. Now it's going to keep me awake.

    ReplyDelete

Post a Comment

Popular posts from this blog

Hyperbolic Hopf Fibrations

Image
Hyperbolic Hopf Fibrations The Hopf Fibration of S^3 is amazing and beautiful.  Rather than describe it here, I'll point you to a lovely online reference with pictures and videos by Niles Johnson. nilesjohnson.net/hopf.html To understand it better (and fibrations in general), I recommend this talk by Niles too. www.youtube.com/watch?v=QXDQsmL-8Us It turns out there is an analogue of the Hopf fibration for H^3.  In fact, there is not just one "fiberwise homogenous" fibration in the hyperbolic case.  There is a 2-parameter family of them, plus one additional fibration that does not fit the family.  As with S^3, fibers in the H^3 cases are geodesics.  They are ultraparallel in fibrations from the family, and parallel in the exceptional fibration.  I found the following dissertation by Haggai Nuchi a good intro and resource to help think about all this. www.math.upenn.edu/grad/dissertations/NuchiThesis.pdf I'm posting three early pictures of H^3 fibrations belo...
Read more

76 Unique Honeycombs

76 Unique Honeycombs Last weekend, Tom Ruen and I hit the milestone of uploading to wikipedia at least one image for 9 families of compact, Wythoffian, uniform H3 honeycombs, a total of 76 unique honeycombs. http://en.wikipedia.org/wiki/Uniform_honeycombs_in_hyperbolic_space You can easily browse all the images on my wiki user page: http://commons.wikimedia.org/wiki/User:Roice3 - Compact means the cells are finite in extent.  - Wythoffian means we can generate them using a kaleidoscopic construction, that is by reflecting in mirrors.    - Uniform means they are vertex transitive and have uniform polyhedral cells. There may even be more honeycombs that meet all these criteria, I don't know. ( update: see Tom's comment below! )  I do know there are hundreds more which don't meet one or more of these criteria, many undiscovered.  In fact, there are infinitely more because there are some infinite families of honeycombs.  wendy krieger continues to discover and enumerate more...
Read more