Like any reasonably normal human being, I would very much like to understand General Relativity. Alas, Special Relativity is currently my limit, and I am pretty muddled about that!
The splendid Sean Carroll has made his Lecture notes freely available:
https://www.preposterousuniverse.com/spacetimeandgeometry/
He also has a rather expensive book on the subject:
I attach the condensed version for anyone who is interested.
A brief excerpt on the METRIC of Minkowski space in Special Relativity, which is somethng you see often enough:
General Relativity is a lot deeper. It is within a Pseudo-Riemannian Space. Any normal person might find more easier topics to understand, IMO, But "One must try", as Dirac said. 🤣
I was wowing my friends with pictures of the Comet yesterday on my friend Bernie's Kindle. I had told them I would show them my efforts at the seafront. I try to keep my promises. 😎
I find I got a passable snap of M31, the Andromeda Galaxy too, The smudge here, not far from the W of Cassiopeia. I think I can do better with an ISO of 1600 and a clear night soon:
Oh, the PDF. Sean Carroll's General Relativity for Dummies. It's below. Good luck. 🙁
The splendid Sean Carroll has made his Lecture notes freely available:
https://www.preposterousuniverse.com/spacetimeandgeometry/
He also has a rather expensive book on the subject:
I attach the condensed version for anyone who is interested.
A brief excerpt on the METRIC of Minkowski space in Special Relativity, which is somethng you see often enough:
General Relativity is a lot deeper. It is within a Pseudo-Riemannian Space. Any normal person might find more easier topics to understand, IMO, But "One must try", as Dirac said. 🤣
I was wowing my friends with pictures of the Comet yesterday on my friend Bernie's Kindle. I had told them I would show them my efforts at the seafront. I try to keep my promises. 😎
I find I got a passable snap of M31, the Andromeda Galaxy too, The smudge here, not far from the W of Cassiopeia. I think I can do better with an ISO of 1600 and a clear night soon:
Oh, the PDF. Sean Carroll's General Relativity for Dummies. It's below. Good luck. 🙁
The Lorentzian manifold is a pseudo-Riemannian manifold that is used in general relativity for modelling spacetime.
There, we encounter causality - basically a description of which events in spacetime can influence which other events.
The curvature of a Lorentzian manifold dictates that massive particles follow timelike curves and massless particles follow lightlike curves.
The hard stuff is here: https://en.wikipedia.org/wiki/Causal_structure
The established Lorentzian manifold is the Minkowski spacetime that is familiar to all followers of this thread.
Referring back to post #4,999, I have discovered that the symbol ∇ refers to the covariant derivative operator (whatever that is!).
AFAIK, these are Sean Carroll's lectures from Caltech. And interesting reading, but not for the faint-hearted...
https://ned.ipac.caltech.edu/level5/March01/Carroll3/Carroll_contents.html
I was down Southsea Castle again tonight. Weather looked reasonable, maybe around 20% cloud predicted and the usual damp haze.
Wanted to see if the Comet was fading much. About 15 degrees high following the sunset on the West. Your horizontal fist outstretched is a bout 10 degrees. The full moon is half a degree.
Monday night, and the bright star is Kappa Ophiucus:
And Tonight, Wednesday:
Best viewed in a dark room.
No sign of the Nova. I think we could wait a year for this one! Corona Borealis and the Head of Serpens Caput there.
I got a decent shot of Andromeda Galaxy tonight and the rich star clusters in Perseus at ISO 1600, but too much sky glow really.
Most people want a telescope, but I enjoy my different and cheaper sort of camera and tripod Astronomy. I was explaining to my young friend Lorenzo that the Earth is not flat and Buzz Aldrin really did walk on the Moon.
But he was unconvinced. He also believes he will live forever, a view held by few older people in my experience... 🙂
https://ned.ipac.caltech.edu/level5/March01/Carroll3/Carroll_contents.html
I was down Southsea Castle again tonight. Weather looked reasonable, maybe around 20% cloud predicted and the usual damp haze.
Wanted to see if the Comet was fading much. About 15 degrees high following the sunset on the West. Your horizontal fist outstretched is a bout 10 degrees. The full moon is half a degree.
Monday night, and the bright star is Kappa Ophiucus:
And Tonight, Wednesday:
Best viewed in a dark room.
No sign of the Nova. I think we could wait a year for this one! Corona Borealis and the Head of Serpens Caput there.
I got a decent shot of Andromeda Galaxy tonight and the rich star clusters in Perseus at ISO 1600, but too much sky glow really.
Most people want a telescope, but I enjoy my different and cheaper sort of camera and tripod Astronomy. I was explaining to my young friend Lorenzo that the Earth is not flat and Buzz Aldrin really did walk on the Moon.
But he was unconvinced. He also believes he will live forever, a view held by few older people in my experience... 🙂
I opened up Part 2: Manifolds
Scrolling down I came across one statement that looked familiar: "The spacetimes of interest in general relativity have Lorentzian metrics".
The rest was tantamount to gobbledygook as far as I was concerned, although I can recognise a doughnut when I see one!
Then I opened up Part 3: Curvature
Lo and behold, I immediately saw reference to the covariant derivative operator ∇ that I mentioned in my previous post!
Apparently ∇ performs the functions of the partial derivative, but in a way independent of coordinates. Well blow me down!
Guess what, I am now none the wiser. The mathematics of general relativity is, and will remain, a closed door to me.
Me, I'm giving the comet chasing prize to Steve - I have given up efter a few more attempts, one including a fall in hilly terrain inducing a dent in my 7dii :-/ clumsy.,,,
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Hmm, a Canon EOS 7D Mk II body is £350... I hope it's OK. I didn't know there are hills in Sweden either. But glad you are unscathed.
https://uk.webuy.com/product-detail...=956177CCCA1C58438EFD5CF291CB6FD2&position=40
I always carry a torch on my Comet hunting expeditions. And my camera wrapped in a towel in my backpack.
This is my spot:
The downlighters have only the inward facing LEDs enabled, so it all woks quite well down the steps, although the lamp-posts in the distance glare.
The conditions were terrible on Wednesday as this ISO 1600 shot shows, you really could only see a couple of stars with your eyes:
I could also do with a lens with a manual focus scale like this, but even that is full of complications and expense:
An interesting comparison of the first good photograph of Andromeda and what modern enthusiast equipment can achieve.
https://www.galactic-hunter.com/post/m31-the-andromeda-galaxy
Mostly down to modern image processing.
Best Regards from Steve in Portsmouth, UK. The Comet Coast. 🤣
https://uk.webuy.com/product-detail...=956177CCCA1C58438EFD5CF291CB6FD2&position=40
I always carry a torch on my Comet hunting expeditions. And my camera wrapped in a towel in my backpack.
This is my spot:
The downlighters have only the inward facing LEDs enabled, so it all woks quite well down the steps, although the lamp-posts in the distance glare.
The conditions were terrible on Wednesday as this ISO 1600 shot shows, you really could only see a couple of stars with your eyes:
I could also do with a lens with a manual focus scale like this, but even that is full of complications and expense:
An interesting comparison of the first good photograph of Andromeda and what modern enthusiast equipment can achieve.
https://www.galactic-hunter.com/post/m31-the-andromeda-galaxy
Mostly down to modern image processing.
Best Regards from Steve in Portsmouth, UK. The Comet Coast. 🤣
I always recommend you carry a large plastic bag with you when out with your camera. I’ve been caught in some serious downpours and ended up putting the whole camera bag in the plastic bag. Towel seems like a good idea too to prevent condensation 👍
I went out on the backyard with my reading glasses on the forehead and was on the hunt for the comet. Pitch dark - stumbled on a little rock and fell forward 🙂
Most of my shootings has been as a sailing photographer so I'm used to ruff conditions. This was just silly stupid.
Found my glasses this morning on the ground 😉
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Most of my shootings has been as a sailing photographer so I'm used to ruff conditions. This was just silly stupid.
Found my glasses this morning on the ground 😉
//
Another great article here from Ethan
https://bigthink.com/starts-with-a-...source=flipboard&utm_content=topic/technology
https://bigthink.com/starts-with-a-...source=flipboard&utm_content=topic/technology
Another one here exposing why string theory falls short of explaining the two biggest mysteries of the cosmos: dark energy and dark matter]
https://bigthink.com/starts-with-a-bang/inflation-dark-matter-string-theory/
Ethan makes the point that ‘ST doesn’t solve any of the data driven problems’ we observe in the cosmos.
https://bigthink.com/starts-with-a-bang/inflation-dark-matter-string-theory/
Ethan makes the point that ‘ST doesn’t solve any of the data driven problems’ we observe in the cosmos.
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I am not alone in my lack of mathematical ability as it would appear that Einstein also struggled with differential geometry and tensor calculus!
Simply put, there is indirect evidence for inflation, dark matter and dark energy, while string theory lacks any such evidence.
Of particular note in the article are the three hurdles that a new theory must clear in order to supersede an old theory.
Quote: "One of the greatest examples of this in history is the arrival of Einstein’s general relativity, which superseded and replaced Newton’s law of universal gravitation as humanity’s best theory of gravity."
I’ve been reading Juergen Renn and Hanoch Gutfreund’s ‘The Road to Relativity’ which is an annotated script of Einstein’s GR paper along with lots of history, anecdotes and his interactions with other physicists and mathematicians between c 1905 and 1916. He indeed did lean heavily on others to help him choose the right maths for his theory, and Marcel Grossman was especially important. What I find interesting is he started out with a sort of intuitive idea about what GR as a mathematical expression should look like and then went to the math. Ultimately it took 7 years. He was always magnanimous and mentioned where he had help from.
There is a very nice story about a teenager who wrote him a letter in IIRC the late 1940’s asking for advice because she was struggling with math. Apparently he replied saying ‘don’t worry, my problems with math are certainly worse than yours!’
He was never able unify gravity and EM, which for him personally was the holy grail.
There is a very nice story about a teenager who wrote him a letter in IIRC the late 1940’s asking for advice because she was struggling with math. Apparently he replied saying ‘don’t worry, my problems with math are certainly worse than yours!’
He was never able unify gravity and EM, which for him personally was the holy grail.
In Einstein's own words: "I want to acknowledge gratefully my friend, the mathematician Grossmann, whose help not only saved me the effort of studying the pertinent mathematical literature, but who also helped me in my search for the field equations of gravitation".
Note also his acknowledgement of Minkowski and several others in his writings: https://einsteinpapers.press.princeton.edu/vol6-trans/158
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In the 1920s when Einstein started the quest for a unified theory of gravity and electromagnetism those were the only two forces known to exist.
The later discovery of two additional forces - the strong and weak nuclear forces - contributed to making his goal of a unified field theory based on only gravity and electromagnetism unattainable.
Einstein worked on a unified theory for 30 years, even up to his penultimate day in the Smithsonian hospital.
https://theconversation.com/einstei...ied-theory-stumped-him-to-his-dying-day-49646
What you mean is you and your camera entered a momentary inertial frame of reference when inadvertently free-falling over a rock.
Just like an astronaut in Space! Congratulations. 🤣
As we all know there is no such thing as "The Force of Gravity".
Brian Cox explains all. I found this at The Conversation website which @Galu mentioned.
I have just got the @cummb joke. The punchline is AC/DC. Frankly, I find it does not embody my progressive and inclusive values. I am a modern man.
Not much to add to the search for a Grand Unified Theory. TBH, you only need it to explain the Big Bang, and that was a long time ago, But will let you know if I figure one out. 😎
String Theory proposes that the Big Bang produced a primeval Super Force from which Gravity and the Grand Unified Force emerged as separate entities.
As you seem to imply, Steve, trying to understand this Super Force may be futile!