User talk:Geometer

From Wikipedia, the free encyclopedia

You have new messages (last change).

[edit] Image tagging for Image:Relothertwin.gif

Thanks for uploading Image:Relothertwin.gif. The image has been identified as not specifying the source and creator of the image, which is required by Wikipedia's policy on images. If you don't indicate the source and creator of the image on the image's description page, it may be deleted some time in the next seven days. If you have uploaded other images, please verify that you have provided source information for them as well.

For more information on using images, see the following pages:

This is an automated notice by OrphanBot. For assistance on the image use policy, see Wikipedia:Media copyright questions. 18:07, 27 September 2006 (UTC)

[edit] Special relativity

Hi Geometer,

I read some of your comments on the twin paradox talk page

Pythagoras' theorem is the metric of a 3 dimensional space with signature +++ or a 2d space with signature ++, [...] The point is that SR is also a mathematical theory. It is the mathematics of the following metric:
{ds^2}_{ }^{ } = g_{\mu \nu}dx^{\mu}dx^{\nu} = g_{\nu \mu}dx^{\mu}dx^{\nu}
with 4 dimensions and where the metric tensor has the signature ---+ (or +++-). Notice that this is an identical formulation to Pythagoras' theorem with different parameters. Once you have this metric the whole of the descriptive and predictive properties of SR fall into place. [...]
Geometer 08:44, 16 October 2006 (UTC)

I wrote a article that is located on a subpage of my user page that is devoted to showing (with animations) just what you are describing. User subpage article about special relativity
I agree with you that the shift from newtonian dynamics to relativistic dynamics is a shift from the euclidean metric to the Minkowski metric. That is: throughout history, up until the shift to relativistic physics, the Euclidean metric was both a formula in abstract mathematics and a physics theory of space.

More precisely: Newton codified the practice of using the euclidean metric as a theory of motion in space. Newton asserted (implicitly) that position, velocity and accceleration can be represented as spatial vectors, and that addition of these vectors proceeds according to the mathematical rules of vector addition in Euclidean space. In newtonian dynamics theory of space and theory of motion coincide.

Newtons laws of motion also codify a specific relation between time and space. Newton showed that Kepler's law of areas could be derived from his fundamental assumtions. Kepler's law of areas enabled Newton to represent time geometrically. Seizing the opportunity to geometrize passage of time was key to Newton's success.

I also have created a website of my own, with physics articles. Here is My article opening with a discussion of Newton's wonderful derivation of Kepler's law of areas --Cleonis | Talk 15:57, 18 October 2006 (UTC)

Nice gifs! I will take a look at the website. Geometer 16:19, 18 October 2006 (UTC)
Retrieved from "http://en.wikipedia.org../../../g/e/o/User_talk%7EGeometer_e673.html"