Spacetime

[cloudsweeper]

I've wrestled with this concept for many, many years.  Now, courtesy of Youtube (Brian Greene and others), I feel I've got a better handle on it.

It comes down to the constancy of c (velocity of light), from which space and time are therefore not fixed, and further, are dependent on each other.  It all now seems to finally make sense, helped by the appreciation that time is not the time, but the rate at which it passes.

From my engineering degree, I have even been able to figure out some of the maths of special relativity, but general relativity is on a wholly different plane!  Reckon I'll keep that on a descriptive level, starting from the Equivalence Principle.

Absolutely fascinating, counter-intuitive stuff!

Doug.

[Hans Joakim]

Absolutely fascinating, for sure! 

I was first introduced to GR as part of a course in classical field theory way back when, but for me the physics remained obscured beneath all the index algebra and Christoffel symbols. The astronomy hobby has rekindled my interest in GR in a major way, and I picked up Sean Carrolls introductory book last year (https://www.amazon.co.uk/Spacetime-Geometry-Introduction-General-Relativity/dp/1108488390/ref=sr_1_1?crid=1W91PXBQ3JB0P&keywords=sean+carroll+general+relativity&qid=1691008661&sprefix=Carroll+genera%2Caps%2C114&sr=8-1), which I think is great and an easier read than what we had! I’ve also been following these lecture recordings, based on the same book (the whole lecture series is up on YouTube): 

 

It is a bit unfortunate that the two most successful theories of the universe, GR and quantum mechanics, are largely confined to advanced students… it is the way it has to be, I guess, as it doesn’t make much sense to introduce Lorentz invariance or Heisenbergs uncertainty principle to most 12 year olds.

Edit: By the way, a nice note on the relativistic correction to the perihelion shift of Mercury: https://www.math.toronto.edu/~colliand/426_03/Papers03/C_Pollock.pdf

Edited August 2, 2023 by Hans Joakim

[George Jones]

15 hours ago, Hans Joakim said:

I picked up Sean Carrolls introductory book last year (https://www.amazon.co.uk/Spacetime-Geometry-Introduction-General-Relativity/dp/1108488390/ref=sr_1_1?crid=1W91PXBQ3JB0P&keywords=sean+carroll+general+relativity&qid=1691008661&sprefix=Carroll+genera%2Caps%2C114&sr=8-1), which I think is great and an easier read than what we had! I’ve also been following these lecture recordings, based on the same book (the whole lecture series is up on YouTube):

 

I really love this beautiful book, and I bought my copy shortly after it was published, but I don't think that this is quite what @cloudsweeper wants, given that he wrote

15 hours ago, cloudsweeper said:

From my engineering degree, I have even been able to figure out some of the maths of special relativity, but general relativity is on a wholly different plane!  Reckon I'll keep that on a descriptive level, starting from the Equivalence Principle.

Absolutely fascinating, counter-intuitive stuff!

 

and given that the YouTube lecture course in meant for folks who want a well-motivated but advanced course, i.e., "8.962 is MIT’s graduate course in general relativity, which covers the basic principles of Einstein’s general theory of relativity, differential geometry, experimental tests of general relativity, black holes, and cosmology."

More appropriate might be a recent book by Sean Carroll, "The Biggest Ideas in the Universe: Space, Time, and Motion".  This book has a lot prose, but does use a few equations. Carroll attempts to explain what equations mean without giving the reader facility to calculate with equations. Carroll explains this in more detail in the book's Introduction, which can be read using Amazon's Look Inside feature.

Roger Penrose, who has a Ph.D. in pure maths, and who won a Nobel Prize for applying pure maths to black hole physics, recommends the following technique for dealing with lines of equations