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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?
What is "imaginary time constriction"?imaginary time constriction
Have you tried to work this out mathematically? What does the math tell you?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.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.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...
A multiple of i is not the "opposite" of a real number in any useful sense, so I don't think this is a valid line of reasoning.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).
No. I'm saying that you can't just wave your hands and say a complex number for the ##\gamma## factor means what you are saying it means.Are you saying complex numbers have no use in physics?
Your hesitation is warranted.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.
A prerequisite so to speak for the Lorenz transform is that v<c... therefore that restriction must be assumed if you want to even consider the factor itselfAre 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.
They don't. They lie in a plane. Points in a plane do not have a linear order.I understand they can't be compared to reals, but would've thought they lay on a number line in some order.
I don't think you're saying anything meaningful at all.I'm not sure what I'm saying by "imaginary time contraction." What do you imagine I'm saying?