The whole "t" thing was bothering me in John's explanation, so I showed it to my son the physicist. He tells me that John's explanation comes from Brian Greene's book, "The Elegant Universe"... A very popular coffee table book, aimed at the same market as those by Stephen Hawking.
Greene's explanation breaks the 4 known dimensions of space into X,Y,Z, and C*T.... That arbitrary multiplication of time by the constant C forces all four dimensions be in terms of distance. In the internet traffic where people seem to spend a lot of time discussing this model, it is common to forget that t is really C*t, and say silly things like the velocity of t in meters/second... Additionally, the dt/dt =0 thing needs the "t"'s to be different, say "t" and Tao. where Tao is the time on the moving frame, and t is the same time as viewed from the stationary frame... There are lots of reasons why one might want to simplify a set of equations by multiplying by an arbitrary constant, and then factoring it out later... It might make the math easier, but it also can completely change the model you are working on. According to my son, that "simple" explanation confuses things more than it helps if you are actually doing physics, but does tend to make an intuitive feeling for special and general relativity available to the unwashed masses. -Chuck Harris Didier Juges wrote:
Wow. So elegantly simple explanation, thanks John! On November 27, 2015 2:54:51 PM CST, John Miles <j...@miles.io> wrote:So, here's how I finally grokked this stuff. c, the speed of light in a vacuum, is often spoken of as a "speed limit" that nothing can ever exceed. That's a bad way to put it, and people who have expressed it that way in popular science writing for 100 years should feel bad. Instead, the way to visualize relativity is to realize that c is the *only* speed at which anything can travel. You are always moving at 300,000,000 meters per second, whether you want to or not. But you're doing it through all four dimensions including time. If you choose to remain stationary in (x,y,z), then all of your velocity is in the t direction. If you move through space at 100,000,000 meters per second in space, then your velocity in the t direction is 283,000,000 meters per second (because sqrt(100E6^2 + 283E6^2) = 300E6.) It doesn't make sense to speak of moving a certain number of "meters" through time, so your location in time itself is what has to change. You won't perceive any drift in your personal timebase when you move in space, any more than you will perceive a change in your location relative to yourself. ("No matter where you go, there you are.") But an independent observer will see a person who's moving at 100,000,000 meters per second in x,y,z and 283,000,000 meters per second in t. They see you moving in space, in the form of a location change, and they also see you moving in time, in the form of a disagreement between their perception of elapsed time and your own. Likewise, if you spend all of your velocity allowance in (x,y,z), your t component is necessarily zero. Among other inconvenient effects that occur at dt/dt=0, you won't get any closer to your destination, even though your own watch is still ticking normally. Particles moving near c experience this effect from their point of view, even while we watch them smash into their targets at unimaginable speeds. This is special relativity in action. The insight behind general relativity is twofold: 1) movement caused by the acceleration of gravity is indistinguishable from movement caused by anything else; and 2) you don't even have to move, just feel the acceleration. That second part was what really baked peoples' noodles. It is what's responsible for the disagreement between the two 5071As. -- john, KE5FX Miles Design LLC
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