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    (Original post by AlphaNumeric)
    ^ Short of doing a terrorist attack on the Nobel Awards Ceremony I don't think anyone will ever has as much of an impact as he did again. Since his day physics and maths have gone from being the playground of a dozen or so giants to being such enormously diverse fields that even people who do problems like Fermats Last Theorem don't alter the landscape much anymore.

    Ed Witten, a living physics god (despite being a pure mathematician!), has contributed enormous amounts to String and M Theory, but few outside the research area know his name. His maths ability outstrips that of Hawking certainly.

    IMO in high energy physics too many people work too much for it to be conceivable that someone could come along with such a vastly revolutionising completed idea. The material now is too vast for one person to do it alone. String Theory is 20~30 years old now, and its nowhere near a finished form.
    Have you read "The Elegant Universe"?
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    Yes. Its a good book, though when I read it 4 years ago I found it somewhat heavy going towards the end. Since then though I've done a lot more maths and physics and its much more accessible now. I plan on doing a PhD in it (well, Branes) next year, hence my comments about it being impossible for one person to come from nowhere now, I'm seeing the material from the point of view of someone about to do research in it and can see how enormously vast the field is.

    The PBS documentary of the same name is quite good too, though seems to rely a bit too much on using computer graphics. Worth a download from your local friendly Bittorrent site.
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    how do you sit on light? and how do you travel at the speed of light, isn't that theoretically impossible?
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    (Original post by h_espin)
    how do you sit on light? and how do you travel at the speed of light, isn't that theoretically impossible?
    You don't its a thought experiment. You can't Actually perform it. And yes for an object with mass you can't travel at the speed of light.
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    (Original post by AlphaNumeric)
    The PBS documentary of the same name is quite good too, though seems to rely a bit too much on using computer graphics. Worth a download from your local friendly Bittorrent site.
    Or if you don't have Bittorrent access you can watch it on the PBS website
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    I may as well join. I do have a liking for Einsteins works.

    I think that special relativity is just amazingly, particularly the way you can start from any one of the concepts being taken as fact (the exchange of energy and mass, the invariance of the speed of light, the lorenz contractions) and work from that to get virtualy all the other ideas in no time. If you are willing to do the legwork.

    Just a little something I put together a few weeks back, taking things from the ideas around pre-Einstein, and working to get to a point virtualy level with special relativity.
    To start with, there are two simple rules you need to accept.

    1) Photons, the carriers of light and electromagntic force, always travel at c, the speed of light.
    2) All systems traveling at constant speed of light are justified in claiming to be stationary (Principle of relativity).

    From these we can deduce that light seems to travel at the same speed for everyone moving at a constant speed, regardless of their relative speed, otherwise the principle of relativity would be violated. This holds true in experiment, and is the only major leap of faith I ask you to make today. That over a century of experiments and observations are right doesn't seem like a big leap to me.

    Now, I need to introduce you to the first player in this explanation. The light clock.

    This diagram is very simple, and mostly just knocked up to avoid copyright risks. The idea is that you have two, perfect mirrors held parrelel and opposite each other, with a single photon bouncing between the two. This forms the worlds simplest clock possible.

    The idea here is that one bounce, up and down, represents a simple time unit. This unit is defined as the distance traveled divided by the speed of light. To keep things simple, I am going to use some very rough numbers to aproximate this.

    Speed of light = 3 x 10^8 (300,000,000) meters per second (m/s).
    Distance between the two mirrors = 1.5 meters (5 feet)
    Total distance traveled by the photon in each cycle (down and up) = 3m
    Time taken for one cycle = 3/3 x 10^8 = 10^-8

    This means that the photon bounces about 10^8 times each second. A very fast, and therefore accurate, clock. If only it was physicaly possible... still, handy for this thought experiment.

    Now, this system obays the principle of relativity. It works perfectly if you have it sitting in a room, or if you decide to take it for a train ride. Let us, for arguments sake, put it in a spaceship and take it into deep space, where we can really play with the thing.

    In this experiment, we have two spaceships. One is an observer, with fantastic cameras and sensors to watch the other. The other is a superfast one, which can travel at speeds up to the speed of light. It happens to be made of glass, so the other can see all that is going on inside.

    The two set up in space. The observer is watching as the other starts up and makes a run, so as it travels at a constant speed.

    Assuming they are tracking the photon in the light clock aboard, here is what they will see.

    Remember, the view from inside the traveling spaceship would be the same as the first image.

    As you can see, the photon is traveling a longer path for each cycle. It has to travel 1.5 meters up, and 1.5 meters down, but is also traveling an extra 2 meters across for each of these, giving a horizontal component of motion of 4 meters.

    The total distance traveled can be found simply with some basic pythagoras theory. The triangle is actualy a special case, a 3,4,5 triange.

    So the photon has to travel a total of 5 meters in each cycle, rather than the normal 3. Put this into the earlier calculations.

    Speed of light = 3 x 10^8 (300,000,000) meters per second (m/s).
    Total distance traveled by the photon in each cycle (down and up) = 5m
    Time taken for one cycle = 5/3 x 10^8 = 1.666666666666666666666666666666 7 x 10^-8

    In other words, each cycle takes two thirds of a second longer than it should. At least, from the outer ships point of view. Definatly a noticable change.

    This is strange. What happens if you take the other ship faster though?

    Increasing the speed increases the distance traveled horizontaly, so increases the total distance traveled by the photon. This slows the cycles further and further, the closer you get to light speed. If you increased the speed so that the ship was traveling at, ever closer to light speed, the path would increse more and more, slowing the time measured by the internal clock.

    However, no-one in the traveling spaceship would notice this. They would be goverened by the principle of relativity, and still think that the clock was working perfectly. For them, nothing is going wrong. How is this possible?

    Well, one very simple answer lies in the work photons do in the real world. They don't just carry light. They carry all electromagnetic force.

    The electromagnetic force is the most important one in most matter, as it governs the communications between all charged objects, such as electrons and protons in atoms. Infact, you can model every atom, every interaction between atoms or between charged particles as a version of the basic light clock, with photons exchanged between two objects.

    Obviously, the same effects would slow the interactions between matter. This would mean that any person observing such a phenomion would also be subject to it, as the atoms in their body slow down with the clock. This is true of all objects and anything you care to put in such a situation.

    See, simple Einstein, and no major equations.
    Excuse the crap diagrams. Paint jobs. And this needs smartening up sooner or later. And expanding a bit. If you play with the concept a bit, you soon come to a simple equation;

    t(relative) = T(absolute)/(1 - u²/c²)

    As you can see, that gives the same result as the common sense look at a pythagorean triangle did in the above explanation. I like equations where you can do that. And if you can see wherethe above equation came from (other than this), you will see what I was getting at at the start.
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    your gamma is missing a square root!

    I like : t' = (gamma)t0 because you know t' is the time in the frame with relative velocity... there is no absolutre frame from the first postulate so t(absolute) is a little confusing!
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    technically the equation should be E_0 , not e or E
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    MEEE, einstein is the most "wwoaa-thing" ever!! and E=mc2 too
 
 
 

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