Trying to wrap my head around the the speed of light

Factual Questions
1

This question’s been on my idle mind for a little while.

Say I’m sitting in my car* on a flat, featureless plain. The car’s not moving. I turn on the headlights : photons careen out of the lights, zoom forward at the speed of light before crashing into whatever it is the lights are illuminating like so many drunken stuntmen, bouncing off back to my eyes etc… Fine.

Now I start the engine and accelerate. The photons coming out of the headlights are still being emitted, and zoom forward, at the speed of light. Because nothing can go faster than c (without things going very wonky).

Soooo does that mean that the photons coming out of my accelerating car actually *decelerate *somehow ? If we were talking bullets being fired forward a gun mounted on the hood of my car, they would be fired at [whatever speed the gun itself accelerates them to] + [the speed of my car], correct ? What gives ?

  • a deluxe Fiat , obviously
2

They wouldn’t decelerate. But the wavelength would be compressed, ie blueshifted, from the point of view of someone looking at your car coming at them.

3

Imagine you’re in a boat. You put your hand over the side onto the surface and push it up and down making waves which move away at wave speed v. Now give the boat some velocity. The wave speed remains the same.

The weird thing about light isn’t that it stays the same speed, like any other wave, it’s that if you measure the wave speed in water in the direction of the boat’s travel, relative to the boat, it will be reduced, while for light it stays the same.

Going back to the car. If you stand next to the car the light waves do what they are supposed to, the stay the same speed. But you asked about what happens if you’re sitting in the car. And from the reference frame of the car light behaves like the bullets. Instead of having a different speed in the forward and backwards direction it’s still c, so your experience differs from observing from the “stationary” frame of the plain.

That’s the real weirdness of the speed of light. There’s no slowing down or speeding up, there’s constant lightspeed and time has to change between reference frames to make things match up.

4

At velocities close to c, time dilation and space compression conspire to balance everything out. Here’s what I mean:

You’ve shot the photons from your headlights. One second later - or rather, a time that FEELS like one second to YOU - the photons will be 300,000 km in front of you, by YOUR measurement.

But to an outside observer, you’ll be doing that measurement much later than one mere second after turning on those headlights. To him, one second after the head lights went on, those photons will be 300,000 km from where they were when you turned them on. The photons will be less than 300,000 km in front of the car at that point, but thats okay because the critical thing to remember is this: Light moves at 300,000 km per second relative to the observer, NOT relative to the launching device.

5

Consider this: you break an atom in two, and both halves (H1 and H2) get accelerated to 99% the speed of light. One of the halves splits in two again (H1a and H1b), and both halves again get sped up to 99% of the speed of light, coincidentally one of the new halves shoots off in the direction the original half was already traveling.

So to an observer traveling along with H1, H1a and H1b seem to be going at 99% of the speed of light in opposite directions. But that does NOT mean that to a stationary observer, H1a travels at 198% of the speed of light!

6

Nope. This is one of the fundamental things about the universe that seems obviously true, but is actually false.

The actual speed of the bullets fired from a car/gun combo, as seen by someone at rest is:

([muzzle speed] + [car speed])/(1 + [muzzle speed]*[car speed]/c^2)

Even for a really fast car (50m/s) and a really fast bullet (1000m/s), this value comes out to be only the tiniest sliver away from [muzzle speed] + [car speed], but for things moving near the speed of light, the difference between this formula and the “intuitive” one is very significant.

7

In order to understand relativity, you have to let go of the idea that the universe is huge complicated clockwork sitting on a firm foundation. The truth is that there is no foundation. From one point of view, you see one thing, and from another point of view, you see something completely different. Everything’s relative. That’s why we call it RELATIVITY.

More specifically, there’s what’s called an inertial frame of reference (IFR for short). Newton’s Laws of Motion talk about an object moving in a straight line until it’s acted on by an outside force. That’s an IFR. According to Relativity, every IFR is equally valid. There’s no single perfect IFR which is THE standard by which all the others are measured.

Thought experiments about a boat traveling across a pond and watching the waves ripple outwards suffer from this fatal flaw. The water itself is a preferred frame of reference. When we start talking about light waves, you have to remember that THERE IS NO WATER.

See, right there you’ve already messed up. The plain does not exist. For you to say the Fiat isn’t moving is incorrect. All you can say is that the Fiat is not accelerating in any direction. That means the Fiat has it’s own Inertial Frame of Reference. And in that particular IFR, the Fiat is stationary. But there are infinitely many other IFRs where the Fiat is NOT stationary, but it’s drifting along in a straight line at a constant speed, and all of those IFRs are equally valid.

For this to make sense, we need a few more people to represent various IFRs. Let’s say there’s Alice, initially at the Fiat’s rear bumper before it accelerates, and there’s Bob who’s inside the Fiat driving it, and there’s Carol who is waaaayyyy off in the distance, watching the Fiat’s headlights while she’s driving in a Mitsubishi which is traveling towards the Fiat at 40mph.

Bob accelerates the Fiat up to 60mph (relative to Alice, who hasn’t accelerated) and turns on the headlights. If you ask Alice, Bob, and Carol to measure how fast the photons from the Fiat’s headlights are moving relative to the Fiat, you will get three slightly different answers. So which one is right? All of them are right, from their own point of view. Each of them is in an equally valid IFR.

The secret to understand why they get different answers is to remember that you’re measuring speed in miles per hour and each IFR has a different perspective on what constitutes a mile and what constitutes an hour.

8

Actually, there is still a firm foundation, and it’s a lot easier to use that foundation than it is to use the things that vary from one observer to another. It’s just that the firm foundation isn’t made up of the pieces that you think it is. But there are a great many invariant quantities in nature, enough to do all of physics with.

For instance, the distance between two events depends on the frame of reference of the observer, and the time between them also depends on the frame of reference… But if you square both, and subtract them, that’s going to be the same for everyone.

9

Or, if you ask Alice, Bob, and Carol each to measure how fast they see the photons going relative to themselves, they will all the the same answer – c. Is that right?

10

Yes, that’s right.

But, just to be clear, we’re assuming that this all happens in a vacuum hence the speed of light there will be “c”. If there’s air (or water, or whatever) then the photons will slow down to a speed which is slower than c. How much slower depends on the index of refraction. But still, all three observers will get the same answer for the speed of the photons, relative to their own IFRs.

11

Which is the part where people find it hard to understand. How is that even possible? How can something not obey the laws of physics?

12

Here’s an example I just came up with to explain why light always is going the speed of light (in a vacuum), and why the wavelength changes, but not the speed. An example anybody can understand. It’s a thought experiment.

We have an object that is going to produce the light, in all directions, like a flashbulb, one very fast pulse of bright light. Our object will be travelling at almost the speed of light, from the earth to the moon, and halfway there will pop, creating a burst of very bright light. Visible to everyone, including our three observers, one on earth, one on the moon, and one exactly the same distance to the side. All three are exactly the same distance when the pop happens.

All three will see the light at the same moment after it goes off, because they are all the same distance from it, half the distance of the moon to the earth.

Work with me, it’s a thought experiment. We can have an observer on board as well, but that is only to say the light propagates out from our object at the speed of light, to somebody at the source.

So despite the source moving really really fast, all observers see the light acting as light at the speed of light. How can that be?

It’s easy. All the motion is relative, every last bit of it. Each observer thinks they are sitting still, which they certainly are not. Except they are, from their perspective. So the light travels at the speed of light, to them. It doesn’t matter if you are the earth, the moon or the speeding object, to you, the light is travelling at the speed of light.

How can that be true for our observer at the source? He’s really moving.

No, not to the atoms that create the photons. They see the moon racing towards them at almost the speed of light, and the earth receding at almost the speed of light, but that’s not their concern. They are standing still, radiating the light outward, at the speed of light. Since motion is relative, to them everything else is moving. Not them, not the atoms that create the photons. They are, like everybody else in this thought experiment, sitting still. It’s all the other observers that are moving.

Which also explains why the person on the moon is going to see gamma rays, the person on the earth almost impossible to detect radio waves, and our observer off to the side is going to “see” …

13

Indeed.

186,282 miles per second. Because it’s not just a good idea. It’s the law. :smiley:

14

It does obey the laws of physics. The laws of physics are under no obligation to conform to what you think they are.

15

This statement is only true in the (common) rest frame of Earth guy, Moon guy, and halfway guy.

The light-pulse emitting observer will also see the light pulse travelling away in all directions at the speed of light, but he will see it hit moon guy first, since, in light-pulse-emitting-guy’s reference frame, moon guy is rushing towards him. It will hit middle guy next, and Earth guy later, because Earth guy is quickly receding as the light pulse goes towards him.

One of the important facts in SR is that observers don’t agree with each other as to whether events happen “at the same time” (unless they also happen at the same location).

16

Yes, but the point was to explain how fast moving person can see light travelling at the speed of light, but so do people not “moving” fast. They all experience light at the same speed, which we know from experience, isn’t true for “things”. But it is for light.

None of that matters in regards to the original conundrum.

Nope. In fact, the atoms that create the photons (packets, waves, light) don’t know they are moving. Or rather, they don’t care that they, the atoms, are accelerating. No matter how fast, or slow the car is going, compared to the motion relative to the rest of the Universe, it doesn’t matter much at all. Like every other atom in the Universe, when light leaves the atom, it does so at the speed of light. The atom does not care, or rather the electrons, since they are the source of the light. How fast is an electron moving when it causes a photon? There’s a very hard question.

The problem is thinking that something is leaving the headlight. That light depends somehow on motion of the source for it’s speed. It does not. Not like a bullet or a baseball does.

I used a single “pop” of light for a reason. To an observer of our magical object that creates the light, it doesn’t matter if the object was moving or still when the light went off, in regards to the speed. The light sped out from the source at exactly the speed of light.

But since we know it had a huge relative velocity, something has to be different. Which is why we say the moon observer will “see” a very energetic wavelength of light, while our earthbound observer will have trouble even measuring the light. But the amount of time the light will take to reach all three observers will be exactly the same, since they are all the same distance from the source.

This is true if it was a fast moving source, or not moving at all. Which is what is so hard to grasp about it.

17

After this point, it gets way more complicated.

18

Following up on the idea of a light-pulse; here’s something that’s always bothered me.

Let’s say I take my handy mega-watt laser (I got it at Home Depot) and shine it up in the sky for exactly one second. That seems to me we now have a bundle of light about 50 miles long travelling through space. In front of it, dark, behind it, dark, in-between, light. I have a hard time picturing this tube of light energy travelling along as an entity like that.

But that’s what happens, isn’t it? (If I did the math right - 186,000 mph = 50 miles/sec?)

19

No, it’s 186,000 miles per second.

20

What’s a mere factor of 3600 among photons?