Quote by Lawrence M. Krauss

“When I am carrying an object such as a ruler, and moving fast compared to you, my ruler will be measured by you to be smaller than it is for me. I might measure it to be 10 cm, say: [Image] But to you, it might appear to be merely 6 cm: [Image] Surely, this is an illusion, you might say, because how could the same object have two different lengths? The atoms can’t be compressed together for you, but not for me. Once again, we return to the question of what is “real.” If every measurement you can perform on my ruler tells you it is 6 cm long, then it is 6 cm long. “Length” is not an abstract quantity but requires a measurement. Since measurement is observer dependent, so is length. To see this is possible while illuminating another of relativity’s slippery catch-22s, consider one of my favorite examples. Say I have a car that is twelve feet long, and you have a garage that is eight feet deep. My car will clearly not fit in your garage: [Image] But, relativity implies that if I am driving fast, you will measure my car to be only, say, six feet long, and so it should fit in your garage, at least while the car is moving: [Image] However, let’s view this from my vantage point. For me, my car is twelve feet long, and your garage is moving toward me fast, and it now is measured by me to be not eight feet deep, but rather four feet deep: [Image] Thus, my car clearly cannot fit in your garage. So which is true? Clearly my car cannot both be inside the garage and not inside the garage. Or can it? Let’s first consider your vantage point, and imagine that you have fixed big doors on the front of your garage and the back of your garage. So that I don’t get killed while driving into it, you perform the following. You have the back door closed but open the front door so my car can drive in. When it is inside, you close the front door: [Image] However, you then quickly open the back door before the front of my car crashes, letting me safely drive out the back: [Image] Thus, you have demonstrated that my car was inside your garage, which of course it was, because it is small enough to fit in it. However, remember that, for me, the time ordering of distant events can be different. Here is what I will observe. I will see your tiny garage heading toward me, and I will see you open the front door of the garage in time for the front of my car to pass through. I will then see you kindly open the back door before I crash: [Image] After that, and after the back of my car is inside the garage, I will see you close the front door of your garage: [Image] As will be clear to me, my car was never inside your garage with both doors closed at the same time because that is impossible. Your garage is too small. “Reality” for each of us is simply based on what we can measure. In my frame the car is bigger than the garage. In your frame the garage is bigger than my car. Period. The point is that we can only be in one place at one time, and reality where we are is unambiguous. But what we infer about the real world in other places is based on remote measurements, which are observer dependent.”

Quote by Lawrence M. Krauss