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Mathematical Intro to Special Relativity with Brian Greene

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Posted (edited)

Go here: http://www.worldscienceu.com

Sign up. It's free.

Go here: http://www.wolfram.com/cdf-player/

You have to download CDF player (~190 mb) in order to play with the interactive demonstrations. They were created in Mathematica.

Go to > university courses > special relativity.

prereqs?

I have clicked through the material, and it is not super in-depth. You should know algebra. Calculus isn't even really required. You should know what a derivative is, and you should be able to understand graphs of derivatives.

Basically... know what calculus is, and understand the equations he is writing.

----

I think this is great stuff if you want to actually understand relativity, but you're not a professional scientist, so you don't want to take a super in-depth 16 week class with extremely involved homework.

I remember watching the movie "A Serious Man"... there was this kid in a quantum mechanics class who was failing. One day he goes to the professor's office and the dialogue was something like...

"Professor, I cannot fail this class. I understand the cat. I understand the box."

"That's great, but ... the math is what's important. If you don't master the math, then you don't really know the material."

I'm pretty stoked.

Please join me on this journey through time and space.

Edited by Michio

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Posted (edited)

comments on module 02 "speed", Q&A

It's important to understand what an "inertial reference frame" is. This confused me when he brought it up.

Throughout this entire module, keep in mind that he is essentially describing what an inertial reference is, intuitively and conceptually. There are much more involved, mathematical ways to define what an "inertial reference frame" is, but that's a lot of non-essential information.

He uses the example of Galileo (the boat with the flies & the dripping water), which is where the idea began, the inertial reference frame can also be called the "Galilean reference frame".

https://www.princeto..._reference.html

In Newtonian physics and special relativity, an inertial frame of reference (or Galilean reference frame) is a frame of reference in which Newton's first law of motion applies: an object moves at a constant velocity unless acted on by an external force. All inertial frames are in a state of constant, rectilinear motion with respect to one another; they are not accelerating (in the sense of proper acceleration that would be detected by an accelerometer). Measurements in one inertial frame can be converted to measurements in another by a simple transformation (the Galilean transformation in Newtonian physics and the Lorentz transformation in special relativity)

Discussion on physics forums about this: http://www.physicsfo...ad.php?t=183267

foucault pendulum:

http://en.wikipedia....ucault_pendulum

Edited by Michio

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Posted

Right, it's not an accelerated frame. The fundamental point is that long before Einstein's relativity, we had Galilean relativity. Galileo showed that in an inertial frame, you can't do any physics test that will show you whether the frame is "really" in motion, or "really" in absolute rest. Einstein generalized this to the speed of light, showing you can't run a test that will distinguish the speed of light in an inertial frame v. an at-rest frame, as they will both read the same, and the rest is history.

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Posted (edited)

I've been powering through the math on khan academy. At the rate I'm going, I think I will have practiced and review everything in about a week.

I was very disappointed with myself when I was unable to derive a proper solution to the first problem in the speed of light module... and it was really basic. :/

Right, it's not an accelerated frame. The fundamental point is that long before Einstein's relativity, we had Galilean relativity. Galileo showed that in an inertial frame, you can't do any physics test that will show you whether the frame is "really" in motion, or "really" in absolute rest. Einstein generalized this to the speed of light, showing you can't run a test that will distinguish the speed of light in an inertial frame v. an at-rest frame, as they will both read the same, and the rest is history.

I dusted off Greene's book The Fabric of the Cosmos today and crammed the first 80 pages. The history of this question is a long one. The fundamental question is what is space? Newton thought about what would happen if you tied two rocks together and spun them around in a completely empty universe. Would the rope between them go taut, or remain slack? What are the rocks spinning with respect to?

There were 4 main ideas.

Newton - Space is an entity, accelerated motion is not relative, absolutist position.

Leibniz - Space is not an entity, all motion is relative, relationist position.

Mach - Space is not an entity, the force of accelerated motion is proportional to the amount of mass in the universe, relationist

Einstein - Spacetime is an entity, accelerated motion and gravity are equivalent forces (principle of equivalence), everything moves through time at the speed of light (in a way), moving through space converts movement through the time dimension into movement through space

People had no idea gravity could be a field (how did gravity exert a force?) until Faraday & Maxwell discovered that magnetism was a field that exerted a force without anything seemingly touching.

According to general relativity, the benchmark for all motion, accelerated motion included, are freely falling observers.

If you are freely falling toward the Earth in a vacuum, you feel nothing, you will feel weightless, and you would be justified in saying the Earth is rushing toward you.

A person on the ground, watching you fall toward the Earth, would not be justified in saying that you are falling toward them, because you are on the ground, feeling the force of gravity. You are the one who is accelerating upward. :p

Edited by Michio

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