- #1
rjbeery
- 346
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I wanted to discuss Lorentzian length contraction (and time dilation, for that matter). Books on the subject do a fine job describing it but I've generally found that they lack an adequate explanation of it. What follows is my personal explanation.
Special Relativity, in my opinion, is best explained in the following way: there is but one speed in the universe, c, at which all objects travel for a given (inertial) observer. In SR, though, "travel" occurs through spacetime, rather than space only, and one must consider the space- and time-vector component of such travel when making measurements.
Time Dilation. In the picture below, the car is sitting in your driveway. It's spatial travel component, relative to you, is null; in other words, it's "travelling" through time along with you at a speed of c and there is no time dilation.
Now your wife takes the car out to go shopping, and tears off down the road at a speed of .5c. Since we postulate that her "spacetime" speed is constant at c, and we know her "space-component" speed is .5c, we calculate that her "time-component" speed to be .86c because
(.5c)^2+(.86c)^2=c^2
...and indeed, SR calculates that your wife's watch would be ticking at 86% of yours as she speeds away.
Length Contraction. In this description we're only concerned with treating dimensions as temporal or spatial but Lorentzian length contraction has a purely spatial analogy: Hold a the blue face of a Rubik's Cube squarely in front of your face and measure it with the ruler also squarely facing you. Now, turn the Rubik's Cube face partially away from you without moving the ruler and...it's length will APPEAR to contract.
Turn it such that the blue face is completely to the side and its width appears to be zero. In fact, if we consider in this analogy the blue face to be the c invariant, the width dimension to be temporal, and the depth dimension to be spatial, SR makes the same predictions as shown below...
Considering SR in this light, one could make the case that objects DO have an absolute length, that being their maximally-measured inertial length, and that any Lorentzian contraction is in fact an illusion.
Thanks for your time and feedback. *8^)
Special Relativity, in my opinion, is best explained in the following way: there is but one speed in the universe, c, at which all objects travel for a given (inertial) observer. In SR, though, "travel" occurs through spacetime, rather than space only, and one must consider the space- and time-vector component of such travel when making measurements.
Time Dilation. In the picture below, the car is sitting in your driveway. It's spatial travel component, relative to you, is null; in other words, it's "travelling" through time along with you at a speed of c and there is no time dilation.
Now your wife takes the car out to go shopping, and tears off down the road at a speed of .5c. Since we postulate that her "spacetime" speed is constant at c, and we know her "space-component" speed is .5c, we calculate that her "time-component" speed to be .86c because
(.5c)^2+(.86c)^2=c^2
...and indeed, SR calculates that your wife's watch would be ticking at 86% of yours as she speeds away.
Length Contraction. In this description we're only concerned with treating dimensions as temporal or spatial but Lorentzian length contraction has a purely spatial analogy: Hold a the blue face of a Rubik's Cube squarely in front of your face and measure it with the ruler also squarely facing you. Now, turn the Rubik's Cube face partially away from you without moving the ruler and...it's length will APPEAR to contract.
Turn it such that the blue face is completely to the side and its width appears to be zero. In fact, if we consider in this analogy the blue face to be the c invariant, the width dimension to be temporal, and the depth dimension to be spatial, SR makes the same predictions as shown below...
Considering SR in this light, one could make the case that objects DO have an absolute length, that being their maximally-measured inertial length, and that any Lorentzian contraction is in fact an illusion.
Thanks for your time and feedback. *8^)