I’ve been re reading brief history of time because the first time I read it I was a vain child who wanted to get to the end of the book and be able to say “hey, i read that” So ive decided to go over it again and attempt to understand every point fully. I have reached the chapter entitled “the origin and fate of the universe” in which there is a large piece on imaginary numbers. I keep re-reading this and the way Stephen hawking explains them simply makes no sense to me. From what I read imaginary numbers work differently from real numbers the imaginary number i multiplied by itself gives -1. with real numbers anything multiplied becomes a positive for example -2x-2 = 4. He further says that understanding imaginary numbers is like seeing numbers at a right angle to real numbers. If you had a chart with 0 in the middle and positive numbers on the right negative numbers on the left, then imaginary numbers would run from up to down with positve on the top and negative on the bottom. By now i was seriously lost, but thought that it might make sense if I read on.
He went on to say that imaginary numbers when applied to space time means that space and time apply by the same rules. Called Euclidean space times. In Euclidean space times he says that space time can be both finite and have no boundaries like the surface of the earth but with 2 more dimensions, there would be no need for a singularity at the beginning of time. Of course this is all well and good, though I cannot think of the alterative, but I don’t understand 2 things about this part either firstly, if there is no singularity the laws of physics don’t break down, so there still must be a cause to the big bang right? secondly we don’t live in imaginary time we live in real time, and the laws don’t apply to this mathematics.
I’m not saying Stephen Hawking wrong, I’m saying I need someone who understands the concept of imaginary time to explain it to me.
Anyone?
Well, think about it this way, the number system which we use isn’t the ‘real’ number system. We are limited by our human view-point. Right? But given the mathematical system which we’ve constructed, saying that the square root of negative 1 has no answer makes no sense.
Of course there is an answer to that equation. It just doesn’t make sense given the way we conceive numbers. The way this was solved back-in-the-day when people thought that the numbers we knew were ‘real’, was by inventing an ‘imaginary number’ i. i is the answer to the question of ‘what is the square root of negative 1’. Once you have an answer to that question, you can do things with it and see where it goes. For example, trigonometry. Sinusoidal curves are imaginary functions. If we just map the ‘real’ numbers the equation gives us, we get sin, cosin, and tan. Quite elegantly as well! So that solves another problem, the problem of ‘what-the-fuck-is-going-on-with-trig-functions.’ From there, the sky is the limit.
What if there were 4 dimensions though what would we call the axis that was at 90° to x and y and z? We’d call it i and them some smart arse, probably Jewish and German would call it equal to time(t). And then we’d be able to denote time and space as a single co-ordinate system. Then some really smart person probably German would produce the wave function or the evolution of a wave in x,y,z,t. And then someone else would produce a probability density (probably also German) by squaring it so removing the negative probabilities and win a prize and then some smart English man would produce a general non time dependant form. Then Stephen Hawking would probably write a book about time and reference it. And then some not very maths capable people would probably ask what i= and then I’d just say 0=x^2+1 or i^2=-1.
And then some very stupid person would point out that Schrödinger was Austrian. And then I’d say so was Hitler.