- #1
- 371
- 35
As v approaches c, the Lorentz factor approaches infinity. The math and physics is well understood and observed. Is it true that, just mathematically, as v exceeds c the Lorentz factor approaches 0i for imaginary time constriction?
Chris Miller said:imaginary time constriction
Chris Miller said:Is it true that, just mathematically, as v exceeds c the Lorentz factor approaches 0i
The Lorentz transforms are derived starting from assumptions that are equivalent to assuming that ##v## must be less than ##c##. Thus, the complex numbers that appear when you try plugging in a speed greater than ##c## tell you nothing except that you're using the formula in a situation where it doesn't apply.Chris Miller said:As v approaches c, the Lorentz factor approaches infinity. The math and physics is well understood and observed. Is it true that, just mathematically, as v exceeds c the Lorentz factor approaches 0i for imaginary time constriction?
I think @Nugatory's answer is best. It doesn't make sense to do this. When you insert ##v>c## you may be defining some kind of coordinate system, but it doesn't have the naive interpretation you are trying to put on it.Chris Miller said:Thanks for your answers. By "imaginary" I just meant the square root of a negative. By "constriction" I meant the opposite of dilation. I assumed that if time dilates as the Lorentz factor approaches infinity, then it must constrict as it approaches 0 (times i). The math is simple: 1/(n*i) as n approaches infinity. When you assume...
Chris Miller said:By "constriction" I meant the opposite of dilation. I assumed that if time dilates as the Lorentz factor approaches infinity, then it must constrict as it approaches 0 (times i).
Chris Miller said:Are you saying complex numbers have no use in physics?
Chris Miller said:I'll admit to having a very weak grasp of complex numbers. Like even a simple statement like 2i < 3i I'm not sure is true, or if the < operator's use in it is valid.
Chris Miller said:Are you saying complex numbers have no use in physics? I wrote "imaginary time constriction." Not being understood, or applicable, might not make it meaningless. I'll admit to having a very weak grasp of complex numbers. Like even a simple statement like 2i < 3i I'm not sure is true, or if the < operator's use in it is valid.
Chris Miller said:I understand they can't be compared to reals, but would've thought they lay on a number line in some order.
Chris Miller said:I'm not sure what I'm saying by "imaginary time contraction." What do you imagine I'm saying?