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from the I-can-really-learn-my-maths-and-sciences-now dept.
If you ever wanted to learn General Relativity, now here's your chance. The caveat is that first you must learn differential geometry. But it's not difficult, really. Only lots of hard work, but not difficult. I was attending this February such a course. This course is fully documented: there are recordings of all lectures, and of tutorials with solutions (also the .pdf files with practice questions). For easier access you can also visit the The WE-Heraeus International Winter School on Gravity and Light YouTube channel.
You should know though that this material on the internet is not everything we were doing there, the biggest omission are the advanced tutorials, which were done in groups and couldn't be filmed. Also their solutions were too difficult to be "quickly" filmed like the tutorials that have videos. However there's hope that advanced tutorials will also be put online some time later this year (as promised by the organizers). In that case I'll submit a follow up story.
I must tell you that attending this course was really a great experience, and Prof. F. P. Schuller is in fact on of the best lecturers I have ever met.
(Score: 3, Interesting) by maxwell demon on Tuesday April 07 2015, @07:02PM
Your problem is the word "bending". The spacetime is not bent, it is just curved.
Maybe the following example helps:
Imagine you're measuring a plane with rods. Now the plane is hotter at some area, and therefore the length of the rods increases due to thermal expansion. And this causes you to measure consistently shorter distances across that area than you would expect from measuring around that area and applying Euclidean geometry. Thus you are measuring a curved space; indeed, you can apply the complete machinery of differential geometry to your measurement results. However it doesn't bend into the third dimension; after all, all what physically happens in that scenario is that your rods expand when entering that region, which means that, when measured with those rods (and those rods are all you have to measure it), there's less space there.
The Tao of math: The numbers you can count are not the real numbers.
(Score: 3, Informative) by FatPhil on Tuesday April 07 2015, @07:27PM
Great minds discuss ideas; average minds discuss events; small minds discuss people; the smallest discuss themselves
(Score: 2) by maxwell demon on Tuesday April 07 2015, @07:45PM
Yes, that's indeed another problem; the rubber sheet is probably the most misleading "illustration" of GR in existence.
The Tao of math: The numbers you can count are not the real numbers.
(Score: 2) by hendrikboom on Thursday April 09 2015, @08:41PM
The rubber sheet sure misled me for a while way back in the sixties.
(Score: 2) by HiThere on Wednesday April 08 2015, @06:19PM
Actually the word used may have been curved. It doesn't make things any easier for me.
And, WRT those who previously replied to you, this was a class in Differential Geometry in the Math department, not Physics. This class was dissociated from any contact with General Relativity.
I still feel the need for a dimension for things to be curved into. (Now perhaps if they'd talked about compression and expansion of the metric it would have been easier. I *now* think that was what they were trying to get at. But it took me *years* after taking the class to decide that.
Javascript is what you use to allow unknown third parties to run software you have no idea about on your computer.