Conversation In Thin Air Continues
“Okay, Tony, if you want to jump into the thick of it, than lets do it,” replied Noel. “The space-time interval, what’s it based on?”
“The speed of light, or rather the constancy of the velocity of light,” Tony responded. “You and I share the same space-time, but my space and your space, and my time and your time, are the same only when we are at rest relative to each other. We live in our own private worlds of space and time, but in the new public domain of space-time, space and time are the same for everybody. In fact, the intrinsic structure of that space-time accounts for the constancy of the velocity of light for all observers.”
“Do you know why?” said Noel.
“Sure,” responded Tony, “it has to do with the implications of relativity theory. In the mathematics of space-time, Minkowski, Einstein’s mathematics professor, showed that even though the Pythagorean theorem does not work in space-time, something like the Pythagorean theorem is still at work. In Euclid’s geometry the square of the hypotenuse of a right triangle is equal to the sum of the squares of its two sides. In the geometry of space-time, the distance between two events, like in the Pythagorean theorem, is equal to the time interval squared minus the space interval squared, however, that minus is the reverse of what takes place in the geometry of Euclid. Subtracting, instead of adding the two intervals, produces four-dimensional space-time. In space-time the distance between two events connected by a light ray becomes zero. Light rays coming at us from outer space take time to reach us, but in space-time no distance is traveled. That’s one of the incredible results that follow from Einstein’s theory. And that is also why the speed of light is constant for all observers. In space-time light is just there, everywhere.”
“I’m just a little confused,” said Noel, “If light doesn’t go anywhere, how can we know that the length of a space-time interval between any two events is the same for everybody?”
“Because of the constancy of light’s velocity,” Tony replied.
“So what you’re saying is that time doesn’t change, just space?” said Noel. “Is that the answer? Don’t answer that. There’s ‘no’ time to answer, right? Anyway, Einstein’s field equations dictate the space of space-time, and, as you have all ready pointed out Tony, we can agree upon the measured value of space-time. Is that about right?”
“Well, a stab in time will get you nine,” Tony muttered. “You know damn well what I’m talking about Noel. It’s just that you don’t like it. You won’t accept that in the cosmic scheme of things, you and I, and everybody else, are just world lines. That past, present, and future may, or may not, possess meaning scares the hell out of you. You hate the idea that your private frame of reference might be limited and meaningful only to you. Einstein’s universe attacks your sense of freedom, your dignity. Well I’ve got news for you. Nobody was more concerned about dignity than the old man. He didn’t bemoan the fact that he wasn’t God. It was enough for him to peer into the heart of nature, or the mind of God if you prefer to call it that, and understand what was really going on. It was enough for him to know that all human beings had this gift, but how it was used was a person’s own business. Denying it, however, was not dignified. It was plain stupid.”