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location United Kingdom
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visits member for 3 years, 2 months
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Manual worker. Live in England. Formal scientific education "peaked" many years ago when I failed maths and chemistry A-level and scraped a bare pass in physics. Still enjoy pottering about in maths and physics.


Dec
21
comment Proper distance and embedding diagrams?
I actually found a useful reference to this at physics.ucsd.edu/students/courses/winter2011/physics161/…. I managed to input the integral equation into Excel and come up with the same results as the author. I then calculated the difference between coordinate height and proper height of Mount Everest, due to the Earth's gravitational field, is 0.0000062m. You'd hardly notice. Another productive day spent!
Dec
21
accepted Proper distance and embedding diagrams?
Dec
21
comment Proper distance and embedding diagrams?
Thanks. I quite like that picture of the two concentric circles because I can then easily see how it builds into the kind of upside down witch's hat shape of an embedding diagram. But how does he calculate the circumference of the inner circle to be 0.99999999x2pi miles less than the outer circle? Does it involve some nasty integral of the proper distance equation I gave in my question? My definition of "nasty integral" is pretty all encompassing.
Dec
21
comment Proper distance and embedding diagrams?
thought I should point out that at my level nothing is trivial.
Dec
21
comment Proper distance and embedding diagrams?
Thank you. The context of the question was trying to understand a really simple embedding diagram in the form of a picture of a couple of 1 mile apart concentric circles around the Sun at pitt.edu/~jdnorton/teaching/HPS_0410/chapters/…. He says, "for each mile that we come closer to the sun, the circle does not lose 2π miles in circumference; it loses only (0.99999999)x2π miles". How does he work that out from the equation?
Dec
21
comment Proper distance and embedding diagrams?
Thank you. The context of the question was trying to understand a really simple picture of a couple of concentric circles around the Sun at pitt.edu/~jdnorton/teaching/HPS_0410/chapters/…
Dec
20
asked Proper distance and embedding diagrams?
Dec
19
comment Difference between coordinate and proper distance in Schwarzschild geometry
@genneth - thanks for that. I'm assuming there's no problem in measuring r with my ruler in the "flat space" circles at the bottom of the diagram?
Dec
19
comment Difference between coordinate and proper distance in Schwarzschild geometry
Well, if r was Euclidean I'd use a ruler.
Dec
19
asked Difference between coordinate and proper distance in Schwarzschild geometry
Nov
13
comment Inertial frames of reference
@Ben Crowell - sorry, I can't see your last point. If I jump off a cliff, I see the sun accelerating at g. OK. But how does that violate Newton's first law?
Nov
13
comment Laws of physics and general relativity
Luboš Motl - many thanks. You must admit it takes some talent to draw not only the wrong conclusion but the totally opposite wrong conclusion! I can see how the experiments would proceed identically in a freely falling frame, but surely the observer would make very different measurements in frames in different gravitational fields (eg a ball thrown on the Moon will travel further than one thrown with the same force on the Earth). I can see that the laws of physics are the same on the Earth and Moon, but how does GTR allow us to derive those laws from different sets of measurements?
Nov
13
asked Laws of physics and general relativity
Nov
12
revised Inertial frames of reference
Had a rethink about what I was trying to ask.
Nov
12
comment Inertial frames of reference
sb1 - if the only definition of an inertial frame is that Newton's laws of motion are valid, why isn't my ice sheet an inertial frame in GTR. For both GTR and STR doesn't there also need to be a notion that the frame is "full" of synchronized clocks, which isn't possible in a gravitational field? Thank you.
Nov
12
comment Inertial frames of reference
Ben Crowell - Does your final paragraph mean that you are saying my two examples (train and ice sheet) are (1) not good approximations in GR, and (2) SR cannot discuss trains and ice sheets because of the presence of a gravitational field? Thank you.
Nov
12
asked Inertial frames of reference
Oct
24
accepted Defining a Riemannian manifold - made easy?
Oct
23
comment Defining a Riemannian manifold - made easy?
Thanks all. I seem to have opened some sort of multidimensional (Riemannian? Hausdroffian?) Pandora's Box. I wish I could speak fluent maths - learning GTR would be so much easier. Trouble is, there's such a steep learning curve and to the uninitiated a page of symbols is incomprehensible and scary. I like a nice real-world mental picture myself - a sheet of paper resting on a ball for a tangent space, that kind of thing. Probably my ideal textbook would contain rigorous maths and pretty cartoons!
Oct
21
comment Defining a Riemannian manifold - made easy?
Thanks, but that's (a) a counsel of perfection and (b) pitched way over my head ("second countable Hausdroff topological space M equipped with a maximal atlas"!). I was hoping for more of a dumbed down answer to my dumbed down, "naive" question, which actually (he say's plaintively) took me ages to formulate. I'm not a physics or mathematics graduate. I'm a manual worker trying, for the fun of it, to learn the basics of GTR. Schutz ("A first course in general relativity") defines a manifold as "essentially a continuous space which looks locally like a Euclidean space". That's about my level!