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Thread: Group Study: Special Relativity

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    Mens bona regnum possidet ferrus's Avatar
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    Group Study: Special Relativity

    Here.

    A MOOC by Brian Greene on special relativity. Anyone else interested in studying it/forming a study group with me here?
    Die Logik ist keine Lehre, sondern ein Spiegelbild der Welt. Die Logik ist transcendental. - Wittgenstein

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    just dont think about it mhc's Avatar
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    i would love to, sadly i have never studied physics nor algebra, so would not be very useful and probably more of a hindrance
    Just look at the blue sky

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    yeah I signed up.

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    Aporia Dysphoria Dirac's Avatar
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    I might join in if I get some time.

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    Mens bona regnum possidet ferrus's Avatar
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    Well I've gone through the first module. It is purely conceptual with only tiny, trivial forumlae. Still, my experiences with this subject before is that you need to have a very clear understanding of precise definitions of many of the concepts when you get into the meat of the subject for it to make sense. So, if you're unfamiliar with the subject I'd suggest you pay attention. There are two 'streams' in this course, the non-maths and the maths parts, with the latter forming an extension to the first as a full 'university' track course akin to a class in it at an American university.

    He kind of skips the Michelson-Morley experiment, except as a brief discussion. The historian/skeptic in me kind of wants a bit more information on this important piece of experimental evidence and the maths behind it, and you can find it here with a good analogy of swimmers and rivers.
    Die Logik ist keine Lehre, sondern ein Spiegelbild der Welt. Die Logik ist transcendental. - Wittgenstein

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    I plan to. Haven't done it yet.

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    Mens bona regnum possidet ferrus's Avatar
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    I carried on last night somewhat more. There was (finally) a non-trivial algebra problem to solve regarding the angular velocity needed by a binary star if the aether theory were correct to ensure that two emitted light waves arrived at the same time on Earth. This is a pretty cool calculation because it ties a theoretical idea to an actual experimental prediction, which is proven to be false with astronomical data. (I mean, we see no strange effects with the images produced here by these visual binaries say.)

    Some light discussion of dimensional analysis. I wonder if in the university level material he will go into it somewhat more. I also wonder how his pedagogical techniques will transfer to that level of discussion also.

    Also, the 'particles' he refers to intrigued me. I never realise that they were the last nail in the coffin of the emitter theory and the particles in question were actually mesons, more specifically neutral pions. Alvager's experiment is discussed here.
    Die Logik ist keine Lehre, sondern ein Spiegelbild der Welt. Die Logik ist transcendental. - Wittgenstein

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    Mens bona regnum possidet ferrus's Avatar
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    Playing around with the graph for . This is kind of going to be a blog for my attempt to conceptually understand or problem solve something, and I guess it would be interesting to see other people's thought processes.

    It sounds weird and almost infantile, but I like just playing with the equation. Getting a 'feel' for it as Greene says. Sometimes thinking about it in new ways.

    I've sort of thought about it for 5 minutes or so and rationalised it such. Obviously it forces a limit w.r.t the speed of light. But actually what it is doing really can be summarised thus:

    The denominator is kind of like scaling factor for the gradient of the combined velocity. If we consider c = 1, the essentially it scales between a normal flat graph and a tangent that approaches c as flat. I actually calculated the derivative for this behaviour using the quotient rule and it is surprisingly complex. There is an inverse quadratic term in the gradient which explains the rapidly different gradients along the way.

    Being the sort of 'tard I am, I also kind of pondered over why numerically it ensures it can never be more than c. Obviously if both objects ARE C it is 2/2, thus one. So next I did a quick calculation in my head for two objects at 0.9c. I get 1.8/1.81. Aha! The pattern here is obvious but I kind of want to see why the algebra forces it so. I quickly realise that the key inequality is if both v and w are positive. With the equality holding at 1. So I sort of set out to prove this. Which was simple enough. I just applied the following reasoning. . When does this NOT hold? When either v or w or both are 1 or in the open range 0.5-2. And how much is it off when it is 1? 1. So the addition of 1 on the right corrects this inequality for the entire positive range.

    I also managed to derive the equation for the addition of three velocities. . This may not seem much to many here but - at school I struggled with Physics because it was never taught by first principles, and I could never accept using the equations from authority as a logic game as in maths (where it made sense to do so). So actually the experience of independently deriving a mathematical relationship from the laws of nature is kind of a novel experience for me, and increases my confidence in my capacity for algebraic manipulation.

    There is also the question - is the relativity of simultaneity 'mind blowing' as a discussion. It is a startling fact about time, sure. But I object to such words because as I explain:

    I kind of find though that any of these non-intuitive concepts are only 'mind-blowing' if you take a stance not dissimilar to Ptolemian astronomy. We as these fleshy collections of cells have an evolved sense of the world - and a neurological mechanism to reconstruct it in consciousness that predisposes us towards certain philosophies of sufficient reasons behind everything and Newtonian mechanism. But surely one of the most important aspects of the grand process that is science is the profound conclusion that the human perspective in everyday life, when we tease the phenomena of reality enough to produce them, in no way should have any correlation with our intuition at such scales. It is what it is, and a predisposition for not letting reality speak to us as it is instead of trying to foist anthropocentric concepts of how reality works on it is a major intellectual stumbling block for its true understanding.
    Last edited by ferrus; 07-11-2014 at 11:39 PM.
    Die Logik ist keine Lehre, sondern ein Spiegelbild der Welt. Die Logik ist transcendental. - Wittgenstein

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    Mens bona regnum possidet ferrus's Avatar
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    I've worked on through about half of it now. It's well presented, and I've learnt a lot.

    A couple of minor grumbles. The actually mathy part of the relativity simultaneity is presented well in so far of the base derivation and visualisation, but the relative importance of the variables in terms of differing positions is ignored, or covered partially in the Q&A session. This makes some of the questions extremely difficult as it is hard enough to get a grasp of what is happening in each perspective. The simple use of subscripts and a discussion of the different possible permutations of perspective would be much appreciated. I mean it is a subtle difference between which is what an stationary observer thinks another inertial frame must synchronise its clocks to based on the speed of the clocks in that frame and what it thinks the clocks should be synchronised to based on its own time. When to use each is often confusing. And then there is a third permutation which is basically the same think with BOTH gamma factors removed.

    Another question that threw me off was one which asked to solve a system of three equations, which you find yourself and then solve a quartic equation as part of this. I mean this by itself is fine, but you jump from pretty simple algebra to this without any warning. Which is a trifle confusing.

    The live discussion feature with Office Hours is pretty poor also.

    But I believe he is taking suggestions on what to do. The core of the video content is great. It just needs some rough edges taken off. I'm looking forward to finishing it though. I have a deeper conceptual understanding of SR now than in my previous dilettantish forays into the subject.

    Looking to get to the real meat of the subject which will lead (I hope) a facility with Minkowski diagrams.
    Die Logik ist keine Lehre, sondern ein Spiegelbild der Welt. Die Logik ist transcendental. - Wittgenstein

  10. #10
    I'm at about module 13 or 14 I think right now. I agree that it's overall very well done. I've had to leave off temporarily as I've been ignoring other things that are piling up because it's so interesting.

    mostly I get the overall ideas but I have a few things that aren't quite clicking for me. for instance the set of problems where a ship leaves for alpha centauri and 10 years later earth time a commemorative peace sign laser is beamed at the ship. I got all of the questions correct except for the last one where it asks how much the ship occupants would have clocked passing when earth beams the laser at the ship (at 10 years earth time).

    I recall him stressing that the earth should always be regarded as the reference frame at rest wrt time dilation and thus a ship accelerating away from the earth will be where time slows. he mentions that perhaps the ship crew may have knowledge that earth is sending the laser signal in 10 years of their time. so since time is passing slower on the ship traveling at 3/5c I'm thinking the crew would account for that and calculate that at 8 years of elapsed time on the ship it would be 10 years on earth, but the answer he got was 12.5. he said from the perspective of the ship they could regard it as the earth accelerating away from the ship and earth's clocks would run slower. that seems to contradict what he stressed in the preceding lesson.

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