It’s easy to understand time dilation. Imagine yourself as a metronome. Each tick is a thought in your head, a beat in your heart, a second of your time. If you’re motionless with respect to me I see you ticking like this: |||. If you flash by in a spaceship, I see you ticking like this: /\/\/\. If you could reach c and we know why you can’t
, you wouldn’t tick at all. Your time would flatline like this ______ because any transverse motion would cause c to be exceeded. You wouldn’t tick for me, you wouldn’t tick for you, and you wouldn’t tick for anybody else in the universe.
That’s the thing we’re interested in. The universe. That’s the thing that’s out there, the thing we’re a part of, the thing we’re trying to understand. It’s full of motion, and this is what it’s like:
What can you see? What can you measure? You can measure the height. You can measure the width. And if it wasn't just a picture you could measure the depth. That's three Dimensions, with a capital D because we have freedom of movement in those dimensions. What else can you see? What else can you measure? You might imagine
a fourth dimension, a time dimension. But the picture comes from the wikipedia temperature page. It’s a gif, a moving image, and in that image, those red and blue dots are moving. The thing you can measure is temperature.
Temperature is an aspect of heat, an emergent property, a derived effect of atomic and molecular motion. When you measure the temperature, you are measuring an aggregate motion. If you were one of those dots, you would not talk of climbing to a “higher temperature”. There is no real height. You can’t literally climb to a higher temperature. Hence we don’t call temperature a dimension. But people did. Temperature used to be called a dimension
, but the word has gradually changed from its original meaning of “measure”, and is now assumed to be something that offers a degree of freedom, something you can move
We are immersed in time like the dots are immersed in temperature. It’s a different measure, but just as we cannot travel in temperature because there is no real height, we cannot travel in time because there is no real length. Because time is a dimension with a small d. There is no degree of freedom. I can hop backwards a metre but not backwards a second. Because time is a measure of change rather than a measure of place, and it has no absolute units, because you can only measure one change of place against another. It’s a relative measure of motion. The units are relative, and that’s what Special Relativity was telling us all along.
Special Relativity tells us that your relative velocity alters your measurement of space and time compared to everybody else. You increase your relative velocity and space appears to contract while time dilates by a factor of 1/√(1-v²/c²). It’s just Pythagoras’s theorem really. See wikipedia
. The hypotenuse is the light path, and we’re using natural units where c=1. The base of the triangle is your speed as a fraction of c, and the height is the Lorentz factor. You need a reciprocal because time “dilation” is the opposite sense to length “contraction”. So if you travel at .99c, space appears to contract to one seventh of its former size. So your trip to a star seven light years away only takes you a year. But physics is about the universe, and in that universe it took you seven years. The star didn’t become a disc because you flashed by. The space in the universe didn’t really contract because you
travelled through it. But your time did
If you travel through the universe your local motion is reduced by virtue of your macroscopic motion. Hence your clocks run slower. Yes motion is relative, and there’s a symmetry because we can’t always say whether it’s you moving or me. But if you travel out and back we both agree that it was you moving, and we compare grey hairs and agree that you were time dilated, because your local motion occurred at a reduced rate. Then we apply the Principle of Equivalence, and know that the same applies if you’d been orbiting a black hole. When you "spend time" at a lower gravitational potential, local motion occurs at a reduced rate, hence you’re gravitationally time dilated. It’s like plunging a clock into an oil bath. The oil is viscous, and makes the clock run slower. Only you’re like a clockwork man. When you jump in after it, you run slower too. That’s why we have the GPS