Spacetime, and Time Dilation

Posted on Sun 10 November 2019 in Ramblings

I remember reading Stephen Hawking's A Brief History of Time back when I was about 16 years old - a bit over 20 years ago. I didn't even come close to understanding it then. I re-read it on Audible a year ago and I can report that I still didn't understand it at all. Either way, I've been interested in physics and spacetime for a huge chunk of my life, and I wish I'd spent more time on mathematics when I was younger, because I'd have really loved to be a theoretical physicist. I shit you not. The universe just seems to be more predictable than computers.

Einstein published the special theory of relativity in 1905, and it took him another ten years to bring this into the general theory of relativity (which incorporated gravity) in 1915. The special theory is only "special" in the sense that it assumes a flat spacetime; it was the general theory which extended relativity to allow for the curvature of spacetime - for example, the curvature caused by massive objects.

Today I'm going to share my understanding of time dilation, based on what I've learned from Dr Brian Greene, Dr Michio Kaku, and my favourite astrophysicist Marcus Chown. I'll start with a disclaimer: I don't understand any of the calculations behind any of this. I'm familiar with some of the words, and I have a vague grasp of some of the concepts, but I'm mostly limited to regurgitating things I've read and then swearing loudly to distract people from asking questions.

I'm also quite conscious that this is around step three in the age-old progression:

Primary school: "This is how the weather works."
High school: "That wasn't quite right - this is how the weather works."
Undergrad: "That wasn't quite right - this is how the weather works."
Postgrad: "That wasn't quite right - this is how the weather works."
Doctorate: "Nobody knows how the weather works."

... Nevertheless, the actual concept is pretty simply stated, once we get everything laid out. In brief, time dilation is when time appears to slow down for an object, when that object is moving very quickly. There are three important parts to that:

  • the slowing of time;
  • the fact that it looks to you as if time has slowed for the object;
  • the object travelling quickly relative to you.

That means, if your twin travels (around Europe, say) at the speed of light for "ten years" (your time), you will age ten years, but they will hardly age at all.

That's pretty weird - why does that happen? We can understand where time dilation comes from by remembering a few things:

  • We all know that the universe's speed limit is the speed of light, c.
  • We're all familiar with the three dimensions of motion.
  • We've probably heard someone say "time is the fourth dimension" (aka "Minkowski spacetime").

Here's the thing about speed limits: they apply whether you're moving in a straight line, or if you're moving on an angle. Imagine a box, a hundred kilometers square. If you travel a hundred kilometers from left-to-right, you will start at one edge of the box, and finish at the other. But if you start at the top-left corner of the box, and travel towards the bottom-right corner of the box, and still travel a hundred kilometers, you will end up only about 70% of the way to your destination... because some of your motion has been 'used up' travelling in the up/down direction, instead of just the left/right direction.

Now, here's the thing: you're always travelling at c. It's just that mostly you're travelling through time at the speed of light. Any movement in the other three dimensions will 'use up' your speed through the time dimension (because your total speed can't be faster than c). Quick examples:

You, sitting here now reading this:

Speed in x dimension: 0km per second
Speed in t dimension: 299,793km per second

You, 20 years from now, travelling away from Earth at a currently-safe velocity of 3G's (29.42 meters per second):

Speed in x dimension: 0.02942km per second
Speed in t dimension: 299,792.97058km per second

You, 200 years from now, travelling away from Aldeberan at a somehow-safe-by-then velocity of 300G (2942 meters per second):

Speed in x dimension: 29.42km per second
Speed in t dimension: 299,763.58km per second

You, never, travelling away from the milky way at 95% of the speed of light:

Speed in x dimension: 284,803km per second
Speed in t dimension: 14,989km per second

So, as you get faster in one dimension, you necessarily must move more slowly through time! Time dilation comes down to that, plus the hard-to-grasp concept that you're only either accellerating or stationary in your own frame of reference... but that's a story for another day.

That pretty much exhausts everything I know about time dilation... I hope you enjoyed reading it. Huge thanks to Ellie for finding me a friendly physicist to check over this for me!

In case you're looking for some good books on the science of the very fast, the very big, the very heavy, and the very small... Here are some books that I really enjoyed reading:

  • Brian Greene - The Elegant Universe
  • Marcus Chown - Quantum Theory Cannot Hurt You
  • Michio Kaku - Einstein's Cosmos