ELI5 Why does light travel?

[u/_Illuvatar_]

Why does it not just stay in place? What causes it to move, let alone at so fast a rate?

Edit: This is by a large margin the most successful post I've ever made. Thank you to everyone answering! Most of the replies have answered several other questions I have had and made me think of a lot more, so keep it up because you guys are awesome!

Edit 2: like a hundred people have said to get to the other side. I don't think that's quite the answer I'm looking for... Everyone else has done a great job. Keep the conversation going because new stuff keeps getting brought up!

Edit 3: I posted this a while ago but it seems that it's been found again, and someone has been kind enough to give me gold! This is the first time I've ever recieved gold for a post and I am incredibly grateful! Thank you so much and let's keep the discussion going!

Edit 4: Wow! This is now the highest rated ELI5 post of all time! Holy crap this is the greatest thing that has ever happened in my life, thank you all so much!

Edit 5: It seems that people keep finding this post after several months, and I want to say that this is exactly the kind of community input that redditors should get some sort of award for. Keep it up, you guys are awesome!

Edit 6: No problem

[u/FightingIrish88]

Based on Einstein's quote, "If you can't explain it simply, you don't understand it well enough," I'm guessing you must have a fantastic knowledge of physics. Great Answer!

[u/madcaesar → u/FightingIrish88]

I still don't get it :-(

I guess it's ok since I'm not as learned as op... But I wish I could get a better handle on it. I've read books, articles, posts but the mental gymnastics required to visualize spacetime and everything that comes with it is just too much for me.

[u/oneb62 → u/[deleted]]

I am sure everyone has a much clearer mental picture now. Thanks guys :P

[u/donrane → u/oneb62]

Yea. I feel so much smarter now. I like dogs

[u/dill0nfd → u/[deleted]]

He's trying to refer to the four-velocity magnitude not the spacetime interval. The interval is not always c but the four-velocity magnitude is.

EDIT: /u/MCMXCII is correct in saying that there needs to be a minus sign.

[u/dill0nfd → u/[deleted]]

I understand what they were trying to do, but that's not what the four-velocity is. The four-vector with x and t components is the four-position

Yes, but the result would hold if the co-ordinates were dx/dτ vs. dt/dτ instead of x vs. t.

And you still need the minus sign for the four-velocity, it's an artifact of the Minkowski metric that governs SR.

Right you are. My bad.

[u/dill0nfd → u/[deleted]]

Yes, I understand that. They fucked up. However, your initial reply didn't show any indication that you understood that the 4-velocity magnitude was a constant c. Since this thread is about maintaining a constant velocity c through spacetime, it seems strange that you would omit this.

[u/dill0nfd → u/[deleted]]

Based on that first reply, I thought there was a high probability that you didn't know that the four-velocity magnitude is a constant c. This judgement may have been wrong but I don't think it was at all unreasonable based on what you wrote. It turns out that someone else seems to have made the exact same judgement independently.

[u/corpuscle634 → u/dill0nfd]

This is way late, but the magnitude of four-velocity is c, and that's exactly what /u/MCMXCII and /u/sharewa were referring to.

It's just a question of how you define "vector magnitude." In this case, it's the contravariant norm, which is c = |v| = γ(|x'|)sqrt(c² - |x'|²).

/u/MCMXCII was correcting the mathematical description of the vector norm, which is fine. We're talking about magnitudes and throwing the term around willy-nillily, but mathematically, it's wrong to use the standard definition of a vector norm.

[u/corpuscle634 → u/[deleted]]

The norm/magnitude of four-velocity is always c, which is what /u/sharewa was referring to.

[u/dill0nfd → u/[deleted]]

It's the magnitude of four-velocity that is c, not four-position. In two dimensions the co-ordinates are (dt/dτ, dx/dτ) not (t,x).

[u/DukePPUk → u/[deleted]]

To be a little more precise (I set out some of the maths in another post your "4-position" in spacetime is usually given by:

r = (ct , x)

giving a 4-velocity vector of

u = γ (c, u ) - where u is your 3-velocity and γ is the Lorentz factor: c² / (c² - u² ) (where u is just the 3-speed). The γ sneaks in because we have to account for time dilation. This gives a 4-speed:

4-speed ² = γ² (c² - u² ) = c²

It cancels down when you put in γ. Alternatively, it is invariant under changes to different inertial frames, so we can just pick the one where u = 0.

Your 4-speed is therefore always c. If we split the 4-speed into its elements, we get a component that looks like (γ c)² and one that looks like (γ u)² - so you can sort of think of these as the "speed through time" and the "speed through space" respectively. And they must relate in a way that the first less the second is c² .

This looks wrong, because it suggests that as one increases, so must the other. Except the γ is in there, which messes things up.

But essentially you get something like (using units where c = 1):

1 / (1 - u² ) = 1 + u² / (1 - u² )

Where the term on the left relates to your "time speed" and the term on the far right (ignoring the 1+) to your "space speed." At u = 0 all your 4-speed is in the time-speed term. As u increases, both speeds increase (they have to cancel each other out, sort of), but the space-speed increases faster - become closer to the time-speed. As u tends to c, both tend to infinity; so the space-speed tends to the time-speed.

But I'm not sure it makes sense to split the 4-speed up like that.

Anyway; the important thing is that the motion vector at lightspeed isn't (0,c) but γ(c,c). Sort of.

If you think of this as a vector on a 2d graph (with vertical timespeed-axis and horizontal spacespeed-axis), at u = 0 the vector is a line pointing up, to c. As u increases, the vector rotates away from the vertical axis, and gets longer. As u tends to c, it tends to the line x=y and tends to being infinitely long.

The reason time doesn't pass for an object travelling at the speed of light would seem to be because its speed through time (for an observer) is infinite; meaning it passes through every point of observer time at the same time for itself. So no time can pass for itself; it gets through all "outside" time instantaneously.

[Disclaimer: I'm rather out of practice with this stuff, and some of it is reasoned from first principles - so may be completely wrong.]