I’m currently reading Max Tegmark’s book Our Mathematical Universe. In talking about the number of space and time dimensions we live in, he briefly mentions tachyons existing in one space dimension and three time dimensions.
I guess my questions are as follows:
What exactly are tachyons and how can they have imaginary mass?
How widely accepted are they in the science world?
What would reality with 3 time dimensions and one space dimension even be? Is it something the human mind can even imagine?
In: Physics
If you look at the equations for energy of a moving particle in special relativity, you find that there is no solution for a particle with mass moving at the speed of light. The mass of the particle (and so the energy) goes to infinity as you approach it. However you can solve the equations for particles moving faster than the speed of light. Those hypothetical particles are called tachyons. They have never been observed, nor has there been any experiment that would require one to explain an observation. But if you plug a number for velocity > c into the relativistic kinetic energy equation you have to take the square root of a negative number, so the kinetic energy is a multiple of i which means is is imaginary. The only way for that to be possible is if the rest mass is imaginary.
As for the dimensions, they don’t exactly have 3 time dimensions and 1 space dimension. By solving other relativistic equations for them you find 3 of their dimensions have properties similar to the dimension we call time and 1 dimension has properties similar to the ones we call space. I don’t recall what those properties are, it was a long time ago that I studied this. But I can’t imagine what that would be like.
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