Highly Advanced General Relativity for the Layman 101


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Seeing as how this is an Objectivist forum and Objectivism is mostly about reality, I thought that it might be a good idea for people to know what reality really is. Modern physics gives us the best description of reality that we've ever had, but the math required to understand modern physics makes that totally inaccessible to most people. Worse yet, popular science presentations of modern physics are extremely vague and often leave people with more questions than answers.

Here, I take a "no bullshit" approach. I don't tell you that spacetime is made of wibbly-wobbly-timey-wimey stuff. I tell you that spacetime is a pseudo-Riemannian 4-manifold equipped with a metric that has (3,1) signature. Better yet, I go into great detail describing exactly what that means without using any math at all.

If you have any questions, feel free to ask. The biggest challenge in writing this is figuring out what to leave out since there are so many technical details that one can remain blissfully ignorant of, but I can fill in the gaps if you need them. There also might be a few things I don't fully understand yet, but I'll do my best to try to figure them out should anyone ask.

Anyhoo, here's the first part:

http://www.mediafire.com/view/9ao3bs8xg94nqv0/Part_1_Topological_Spaces.pdf

Part 2 is up also, since its so short:

http://www.mediafire.com/view/9r4kqex2b3tmeax/Part_2_Topological_Manifolds.pdf

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Mediafire?!!

Are you black hat?

:smile:

Michael

.... what?

Is your hat of the charcoal variety? If so, please see a tailor.

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Take your pick

  • Black hat (film), a film's villain or bad guy, especially one literally wearing a black hat in a western, in contrast to the hero's white hat
  • Black-Hat Hacker, Internet term for someone violating computer or Internet security maliciously or for illegal personal gain
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Seeing as how this is an Objectivist forum and Objectivism is mostly about reality, I thought that it might be a good idea for people to know what reality really is. Modern physics gives us the best description of reality that we've ever had, but the math required to understand modern physics makes that totally inaccessible to most people. Worse yet, popular science presentations of modern physics are extremely vague and often leave people with more questions than answers.

Here, I take a "no bullshit" approach. I don't tell you that spacetime is made of wibbly-wobbly-timey-wimey stuff. I tell you that spacetime is a pseudo-Riemannian 4-manifold equipped with a metric that has (3,1) signature. Better yet, I go into great detail describing exactly what that means without using any math at all.

If you have any questions, feel free to ask. The biggest challenge in writing this is figuring out what to leave out since there are so many technical details that one can remain blissfully ignorant of, but I can fill in the gaps if you need them. There also might be a few things I don't fully understand yet, but I'll do my best to try to figure them out should anyone ask.

Anyhoo, here's the first part:

http://www.mediafire.com/view/9ao3bs8xg94nqv0/Part_1_Topological_Spaces.pdf

Someone tell me if you can access it. This is my first time using mediafire.

You cannot really describe a differentiable manifold using just words. Math is necessary because a manifold IS a mathematical object.

I see you have attempted to deal with topological spaces with "no math". Now with what you have prove

the Tychonoff Compactness Theorem. Or prove the Jordan Curve Theorem with a no-math approach. I would really like to see that done.

Ba'al Chatzaf

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You cannot really describe a differentiable manifold using just words. Math is necessary because a manifold IS a mathematical object.

Challenge accepted.

I see you have attempted to deal with topological spaces with "no math". Now with what you have prove

the Tychonoff Compactness Theorem. Or prove the Jordan Curve Theorem with a no-math approach. I would really like to see that done.

This is about physics, not topology.

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Take your pick

  • Black hat (film), a film's villain or bad guy, especially one literally wearing a black hat in a western, in contrast to the hero's white hat
  • Black-Hat Hacker, Internet term for someone violating computer or Internet security maliciously or for illegal personal gain

Which one gets me the handlebar mustache?

Depends on how hirsute you are...

230px-Nuremberg_chronicles_-_Strange_Peo

A woman with hirsutism, as depicted in

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Take your pick

  • Black hat (film), a film's villain or bad guy, especially one literally wearing a black hat in a western, in contrast to the hero's white hat
  • Black-Hat Hacker, Internet term for someone violating computer or Internet security maliciously or for illegal personal gain

Adam,

A black hatter is not necessarily a hacker. Oh... I know there is an ongoing Internet security conference called Black Hat, but they kind of co-opted the term. Another example of that kind of conference is called Defcon. Go to the archives of those sites and you can learn some mean-ass shit. Besides, you find more industry and government people at those places than you do the underground.

Black hat in my sense means gaming search engines and things like that to get advantages on the Internet the owners of sites and resources did not intend. It is similar to hacking because there are a lot of crossover disciplines, but the intent is not destructive. It is more about gaming systems.

A typical black hat activity is to spam forums and blogs to get backlinks so the results of a "money site" will get more visibility in search engine results (although Google has made this a crapload more complicated than earlier years). Another is to find download pages of material for sale and "share" it on black hat sites. Mediafire has been a traditional host for this kind of material. It was weird seeing a Mediafire link on OL. :)

When I first started studying Internet marketing, I haunted black hat sites because I wanted to know how to protect myself. And they are open about teaching one and all: proxies, special hacks for gaming Google, Facebook, Twitter, YouTube, etc., spam bots, link wheels, autoblogs, content scraping, and on and on. It was quite an education. I even started learning persuasion stuff at those places, but I later took that in a more scholarly direction.

Interestingly enough, most of the major Internet marketing gurus, the big dogs, belong to black hat sites. (Smaller ones, too, of course.) I know several of their pseudonyms. :)

Michael

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When I first started studying Internet marketing, I haunted black hat sites because I wanted to know how to protect myself. And they are open about teaching one and all: proxies, special hacks for gaming Google, Facebook, Twitter, YouTube, etc., spam bots, link wheels, autoblogs, content scraping, and on and on. It was quite an education. I even started learning persuasion stuff at those places, but I later took that in a more scholarly direction.

Interesting.

As usual thanks Michael.

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I would love David Harriman to do a book or course on everything after classical physics, starting with Einstein and moving on to quantum physics and showing what can actually be proved, the experiments, and where they went wrong in their theory. It would be illuminating!

I study science at uni and it can be frustrating at times the rationalistic approach to teaching us.

You are given information wholesale presented to you devoid of its tie to nature. It is given without any context. You don't know how the information is important, you don't know any of the concretes that led to the concept, you don't know how the concept was induced, you don't know which questions led to the discoveries, you don't know which questions are important. As a result, the information is a rationalistic system that seems to magically work in nature. The tie to reality is severed, and real understanding rendered impossible. You don't know how to think about it, because you have no context in which to think about it, terms are floating abstractions, and principles are religious commandments. But trust us, it's science.

Even if the material is true, the student has no reason to believe it. The student cannot see why it's true. They have nothing but floating abstractions in their mind, rules to follow and memorized facts.

Plus, they tell us that you can't prove anything. That's real inspiring.

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Peter,

Learn the physics principles and how they are used to solve the problems your texts and instructors present to you. And, as you know, you need to have gotten the math prerequisites for that. You don’t need to know the history or applications of classical mechanics or electrostatics or electrodynamics or thermodynamics or of relativity or quantum mechanics to master the principles and problems. The presentations of the texts and courses are not “rationalistic” in the philosophic sense, but they demand a lot of intense difficult hours of reason from us to learn.

I did have one physics course designed to ease one into relativity and quantum mechanics by contact with critical points in their history, especially experimental evidence in that history. It was great, but it did not make learning the actual subject matter any easier when it came to the first straight course on QM. (Straight SR was part of a semester on intermediate-level classical mechanics, and was no more difficult than the Lagrangian and Hamiltonian mechanics that preceded it in the course.) Without what I’m calling the “straight” courses and texts and what you are calling the “rationalistic,” we would never get to any mastering of the actual subject matter.

I do love the history of science, and I find my understanding of the modern physical concepts is further enriched by seeing that history. One beautiful book, which you may enjoy later on, beyond learning your university physics, is The Conceptual Development of Quantum Mechanics by Max Jammer. But it needs to be the original version of the book, which was in the ’60’s, not the later edition which took out too much of the math and became of less informative.

I later earned a second degree, which was in mechanical engineering, to make money. That is further material to learn about the physical world, and the problems to learn how to solve in those courses are quite practical problems.

Stephen

~~~~~~~~~~~~~~~~

Eva, “caught red-handed,” you said. “Bingo,” I thought. And indeed, now this. You just can’t resist exposing yourself, against all your efforts in your puny game.

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You cannot really describe a differentiable manifold using just words. Math is necessary because a manifold IS a mathematical object.

Challenge accepted.

I see you have attempted to deal with topological spaces with "no math". Now with what you have prove

the Tychonoff Compactness Theorem. Or prove the Jordan Curve Theorem with a no-math approach. I would really like to see that done.

This is about physics, not topology.

Look in any modern physics book. Fiber Bundles and Topology from port to starboard.

Ba'al Chatzaf

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~~~~~~~~~~~~~~~~

Eva, “caught red-handed,” you said. “Bingo,” I thought. And indeed, now this. You just can’t resist exposing yourself, against all your efforts in your puny game.

We poor saps don't have a clue what reality is, eh?

~~~~~~~~~~~~~~~~~

It really is quite easy to spoof an IP address, isn't it Stephen?

149-homer-facepalm.jpg

Look in any modern physics book. Fiber Bundles and Topology from port to starboard.

Ba'al Chatzaf

You have to understand the target audience. I'm not writing a textbook for physics or math majors, so like I said there's gonna be a lot of really technical stuff that gets left out.

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You have to understand the target audience. I'm not writing a textbook for physics or math majors, so like I said there's gonna be a lot of really technical stuff that gets left out.

About 90 percent. At least.

Ba'al Chatzaf

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Naomi,

I can't read what you posted for more than 5 minutes without logging in to mediafire, which I don't really want to do. Is there some other place that you could post your pdf so that it could be downloaded and read? Please, don't post it to facebook either. I don't do facebook at work.

As for your approach, I'm not sure what you save by introducing "big boxes" and "little boxes." You totally eschewed the issue of open and closed sets in the early description, but then introduced it later when posing a question about how to construct a set that contains everything but one point. That didn't bother me since I know the concepts that you're describing, but if you're going to assume a certain level of mathematical literacy, why not just use terms like union and intersection? In short, the little that I read appeared to be sort of sloppy. It would be better if you were to carefully considered which concepts you really need and which ones you don't and then introduce them in a logical order.

Darrell

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Naomi,

I can't read what you posted for more than 5 minutes without logging in to mediafire, which I don't really want to do. Is there some other place that you could post your pdf so that it could be downloaded and read? Please, don't post it to facebook either. I don't do facebook at work.

When you open up the link, do you see the big download button in the upper-right corner and does it work for you?

As for your approach, I'm not sure what you save by introducing "big boxes" and "little boxes." You totally eschewed the issue of open and closed sets in the early description, but then introduced it later when posing a question about how to construct a set that contains everything but one point. That didn't bother me since I know the concepts that you're describing, but if you're going to assume a certain level of mathematical literacy, why not just use terms like union and intersection? In short, the little that I read appeared to be sort of sloppy. It would be better if you were to carefully considered which concepts you really need and which ones you don't and then introduce them in a logical order.

Yeah, my original approach was to delve into a little set theory, but I ended up throwing that out because I thought it was all extremely abstract and dry. I decided instead that I wanted to start things off by giving people a simple idea they could just pick up and play with immediately.

I think I will re-write these when I get some more feedback from people who read this. Actually, deciding what can safely be excluded was the hardest part of writing this, so I am taking that into consideration already. Is there any specific part that you would say needs more work?

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Part 5: From Newtonian Space and Time to Special Relativity.

http://www.mediafire.com/view/89xkq785010t92f/Part_5_Newtonian_Spacetime.pdf

No, No, No .... Newtonian Physics is not Lorentz invariant nor is the space of Newton the right shape.

Newtonian Mechanics assumes space is flat, infinite and independent of time. In short, it is Wrong. But it is close enough to be of use.

Ba'al Chatzaf

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Part 5: From Newtonian Space and Time to Special Relativity.

http://www.mediafire.com/view/89xkq785010t92f/Part_5_Newtonian_Spacetime.pdf

No, No, No .... Newtonian Physics is not Lorentz invariant nor is the space of Newton the right shape.

Newtonian Mechanics assumes space is flat, infinite and independent of time. In short, it is Wrong. But it is close enough to be of use.

Ba'al Chatzaf

Where does it say that Newtonian Physics is Lorentz invariant? It is only invariant under Galilean transformations.

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Part 5: From Newtonian Space and Time to Special Relativity.

http://www.mediafire.com/view/89xkq785010t92f/Part_5_Newtonian_Spacetime.pdf

No, No, No .... Newtonian Physics is not Lorentz invariant nor is the space of Newton the right shape.

Newtonian Mechanics assumes space is flat, infinite and independent of time. In short, it is Wrong. But it is close enough to be of use.

Ba'al Chatzaf

Where does it say that Newtonian Physics is Lorentz invariant? It is only invariant under Galilean transformations.

Which makes it wrong. The world is NOT Galilean Invariant. Nor is space flat (at least locally). Newtonian Mechanics assumes space is infinite and flat and that time is absolute. Neither is the case.

Einstein's genius move was to make mechanics consistent with Maxwell's electrodynamics which is Lorentzian out of the box.

It is amazing that the Lorentz Transform leaves much of Newtonian mechanics intact.

Ba'al Chatzaf

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