The Universal Speed Limit

Ok, it's come up in a couple of threads before, so I figured I'd post a thread about why we can't travel faster than the speed of light. I'll do this like I did the quantum mechanics one back on scam.com, so it will take place in a couple of posts over an as yet unspecified amount of time.

Feel free to ask questions, make comments, call me names etc...

Here we go.



First things first.

Speed.

It sounds like an easy concept, right? How fast something is moving. But our everyday concept of speed is pretty firmly rooted in the motion of the Earth. Someone driving in a car at 60mph is moving quickly, while someone standing still is not moving at all. Right?

The first thing we need to do is scrap this concept of speed. It's perfectly ok to say that the person in the car is not moving, while the person standing still is travelling at 60mph. The only thing that matters is relative speed.

If I'm sitting next to the driver of the car, and someone asks me how fast he's moving, I'd say he's stationary. If someone asked how fast the street sign we just passed is moving, I'd say it's moving at 60mph.

On the other hand, if I'm standing on the side of the road and someone asks me how fast the street sign and car driver are moving, I'd say the street sign is stationary, but the car driver is moving at 60mph.

These are all perfectly valid ways of describing things. Also valid would be someone standing on Mars saying that the person standing still is moving at 100,000mph as the Earth spins around the Sun, and the car driver is moving at 100,060mph.

We call each of these opinions, "frames". So if I'm in the "frame" of the person on the side of the road, then the car is moving at 60mph and the street sign is stationary. If I'm in the "frame" of the person in the car, then the car is stationary, but the street sign is moving at 60mph.

Adding together speeds

Ok, take a look at the picture below:



We have person A, holding a gun inside a train, heading to the right of screen. We have person B standing on the side of the railroad track.

Lets say the train is moving at 100mph, and the gun can shoot a bullet at 100mph. If I'm in the frame of person A, then person B is moving towards me at 100mph, and the bullet is moving away from me at 100mph.

If I'm in the frame of person B, then person A is moving towards me at 100mph, and the bullet is moving towards me at 200mph.

All pretty straightforward so far, I hope.

Now let's mix it up a bit.



This time person B is in a car travelling to the right of screen. Let's say he's travelling at 50 mph (I hope this isn't too many numbers).

Now if we're in person B's frame in the car, then person A is only travelling at 50mph towards us, and the bullet is travelling at 150mph.

If person B were driving to the left of screen, then person A would be approaching him at 150mph, and the bullet would be approaching him at 250 mph.

All of this should be familiar to people from day to day life. Speeds can add up so that things are travelling much faster towards you, or they can add up so that they're not travelling towards you quite as fast.

More on speed (trust me, there's a point to this).

I'm going to draw some more pictures to illustrate this.



Ok, again with the car and the bullet, but this time we've got numbers to make it easier.

From person A's point of view, the speed of the bullet is always the same. It is travelling at 100mph no matter what person B does.

Now, I want you to imagine that you are person B, and you are measuring how fast the bullet is travelling. In the above case, the bullet leaves the gun at 100mph and you're travelling towards the shooter at 50mph, so when you measure the speed of the bullet, you measure it to be 150mph (100 + 50 = 150)



This time, you're heading away from the shooter, so when the bullet hits your car you measure it's speed to be only 50mph (100 - 50 = 50).



And finally, in this case your driving away from the shooter at 100mph, so the bullet never reaches you. If you were to measure it's speed you would say it's travelling at 0mph (100 - 100 = 0).

The speed of light

People often have this idea that Einstein was sitting around in his office, working on some crazy mathematical equations, and eventually came up with the idea that people can't travel faster than the speed of light. It didn't work that way at all. Rather, what happened is that about 150 years ago, people noticed some very unusual things about light...



Above we have the same situation as before, except that instead of firing a gun, person A is firing light out of a torch. Like before, person A measures the speed of the light as it comes out of the torch, and he finds that it is travelling at 100mph (light is travelling slowly in these examples).

Now the question is, how fast does B measure the light to be travelling?

If you've been paying attention the previous posts, you should say that B measures the light to pass him at 150mph. In fact, until 150 years ago, that's what everyone would have answered.

In fact, however, that's incorrect. When B measures the light passing him, he will measure it to be travelling at 100mph.

What about in this case?



Again, if you were paying attention above, and if light behaved like everything else, then you would expect that person B would measure the light to travel past him at 50mph. What B actually measures is that the light is passing him at 100mph.

In fact, no matter what B does, he always measures the light to pass him at 100mph. It doesn't matter whether it's a bright light, a faint light, a blue light, a red light, whether it comes from a torch or from the sun, it always travels at exactly 100mph.



This is the fundamental discovery that led to the theory of relativity. It's weird, and it's difficult to get your head around at first because there's nothing in your day to day life that behaves like this. If you think about it, none of it makes sense - if something passes both person A & person B at exactly the same speed, then person A & person B must be moving at the same speed as each other and in the same direction. But we've just seen above that this isn't true. For the record, I've measured this for myself as part of my undergrad studies, and can assure you that light always passes you at the same speed no matter what you do.

People tried to find ways to solve this for quite some time, and eventually what happened is that Einstein said "Look, we're just going to have to accept that this is the way the universe works, let's see what the implications are." It turns out that the implications are pretty weird - time dilation, for example - but we'll get in to that in another post.

Kazza wrote:The speed of light

People often have this idea that Einstein was sitting around in his office, working on some crazy mathematical equations, and eventually came up with the idea that people can't travel faster than the speed of light. It didn't work that way at all. Rather, what happened is that about 150 years ago, people noticed some very unusual things about light...



Above we have the same situation as before, except that instead of firing a gun, person A is firing light out of a torch. Like before, person A measures the speed of the light as it comes out of the torch, and he finds that it is travelling at 100mph (light is travelling slowly in these examples).

Now the question is, how fast does B measure the light to be travelling?

If you've been paying attention the previous posts, you should say that B measures the light to pass him at 150mph. In fact, until 150 years ago, that's what everyone would have answered.

In fact, however, that's incorrect. When B measures the light passing him, he will measure it to be travelling at 100mph.

What about in this case?



Again, if you were paying attention above, and if light behaved like everything else, then you would expect that person B would measure the light to travel past him at 50mph. What B actually measures is that the light is passing him at 100mph.

In fact, no matter what B does, he always measures the light to pass him at 100mph. It doesn't matter whether it's a bright light, a faint light, a blue light, a red light, whether it comes from a torch or from the sun, it always travels at exactly 100mph.



This is the fundamental discovery that led to the theory of relativity. It's weird, and it's difficult to get your head around at first because there's nothing in your day to day life that behaves like this. If you think about it, none of it makes sense - if something passes both person A & person B at exactly the same speed, then person A & person B must be moving at the same speed as each other and in the same direction. But we've just seen above that this isn't true. For the record, I've measured this for myself as part of my undergrad studies, and can assure you that light always passes you at the same speed no matter what you do.

People tried to find ways to solve this for quite some time, and eventually what happened is that Einstein said "Look, we're just going to have to accept that this is the way the universe works, let's see what the implications are." It turns out that the implications are pretty weird - time dilation, for example - but we'll get in to that in another post.

What if B is traveling at the speed of light away from A and the distance between the two is 1 light year?

If B is traveling at the speed of light towards A and they are 10 light years apart, how long will it take for the light from A to illuminate B?

If I was traveling towards A at 299,792,458 meters per second and I was 100,000,000 meters from A when he turned on his torch, would I see the light from the torch before I passed him?

Good questions, and we'll get to the answers shortly. Well, I can give you the answers now, but you'll see how they come about as we go on with the thread.

catch-22 wrote:What if B is traveling at the speed of light away from A and the distance between the two is 1 light year?

If B were travelling away from A at the speed of light, then the light from A would never reach him

If B is traveling at the speed of light towards A and they are 10 light years apart, how long will it take for the light from A to illuminate B?

5 years in A's frame of reference. No time at all in B's frame.

This is something that we're going to have to deal with as well. When Einstein sat down to see what all this implied, one of the things he found out was that time is not the same for everyone. Different people experience time differently.

If I was traveling towards A at 299,792,458 meters per second and I was 100,000,000 meters from A when he turned on his torch, would I see the light from the torch before I passed him?

Umm, yes and no. Person A would see the light pass you, but from your perspective the emission of the light from the torch, and the light hitting you would happen at the same time, as would every other event in the lifetime of the universe. We'll get to why that happens in a few posts, but this is all related to why it's impossible to travel faster than light.

At the moment, the absolute most important thing to understand is that no matter what, when you measure the speed of light, you always measure the same speed.

I'll show you how time slows down in the next post....

I am enjoying this thread.

Time Dilation

Ok. As long as you can accept the fact that everyone measures the speed of light to be the same, it's pretty easy to show that different people experience time passing at different rates.

Now, if you had a hard time letting go of the fact that speed can only be defined relative to some frame, your going to have an incredibly difficult time letting go of the fact that time is the same. For almost all of history, people thought that there was a "Universal Time". That is to say, that time passed at the same rate for everyone, regardless of what you did in the universe - If you were born in 1909, then you are 100 years old today, no matter what you've done in your life. In fact, that's not true.

Just like people can disagree over what speed something is travelling, they can also disagree over how much time has passed. One person may say that 100 years have passed, and another may say that 50 years have passed. Both can be true simultaneously.

Anyway, an example will help show this...

Let's suppose all this talk of time has got me concerned, so I build a very accurate clock that I'm going to use to keep track of how old I am. Since I know that light always travels at the same speed, I'm going to use a beam of light to record time.

I set up two mirrors, like in the diagram below, and bounce a beam of light between them. I know what the distance between the two mirrors is, and I know how fast the light is travelling, so all I have to do is keep track of how many times the light passes back and forth between the mirrors.



To work out how much time has passed, we take the distance the light has travelled, and divide by the speed. Just like if you were going to travel 200 miles at 50mph, you would say 200 / 50 = 4 hours to make the trip.

In this case, lets say it takes 1 second for the light to complete a trip from the top mirror to the bottom and back again. Every time I see the light hit the top mirror, I know that 1 second has passed, and since we've already established that nothing can change the speed at which light is travelling, I'm extremely confident that this clock will keep accurate time.

Ok, now we introduce a second person into this scenario. You see, it turns out that person A is actually inside a train carriage, and now we're going to look at things from the perspective of someone standing on the ground watching the train go past...



In the above picture, we have an illustration of one "cycle" of the clock. From A's perspective inside the carriage, exactly 1 second has passed between the start position and the end position. But how much time has passed for person B?

Since B is standing on the side of the track, watching the train go past, he sees the light travel a much further distance than A does. However, despite the greater distance, he sees the light travelling at the same speed. Remember that no matter what, everyone measures light to be travelling at the same speed.

So now B does the same calculation that A did. He takes the distance the light has travelled, and divides it by the speed to work out how much time has passed. Since the distance is greater, but the speed of light is the same, he says that more time has passed than A, say 2 seconds (so the distance is twice as far).

In Person A's frame of reference, 1 second has passed. In Person B's frame of reference, 2 seconds has passed. Time is passing slower for person A than for person B! If the train carriage has windows, person B will see person A moving in slow motion.

howdy wrote:I am enjoying this thread.

Me too. And I hate math.

Kazza wrote:Time Dilation

Ok. As long as you can accept the fact that everyone measures the speed of light to be the same, it's pretty easy to show that different people experience time passing at different rates.

Now, if you had a hard time letting go of the fact that speed can only be defined relative to some frame, your going to have an incredibly difficult time letting go of the fact that time is the same. For almost all of history, people thought that there was a "Universal Time". That is to say, that time passed at the same rate for everyone, regardless of what you did in the universe - If you were born in 1909, then you are 100 years old today, no matter what you've done in your life. In fact, that's not true.

Just like people can disagree over what speed something is travelling, they can also disagree over how much time has passed. One person may say that 100 years have passed, and another may say that 50 years have passed. Both can be true simultaneously.

Anyway, an example will help show this...

Let's suppose all this talk of time has got me concerned, so I build a very accurate clock that I'm going to use to keep track of how old I am. Since I know that light always travels at the same speed, I'm going to use a beam of light to record time.

I set up two mirrors, like in the diagram below, and bounce a beam of light between them. I know what the distance between the two mirrors is, and I know how fast the light is travelling, so all I have to do is keep track of how many times the light passes back and forth between the mirrors.



To work out how much time has passed, we take the distance the light has travelled, and divide by the speed. Just like if you were going to travel 200 miles at 50mph, you would say 200 / 50 = 4 hours to make the trip.

In this case, lets say it takes 1 second for the light to complete a trip from the top mirror to the bottom and back again. Every time I see the light hit the top mirror, I know that 1 second has passed, and since we've already established that nothing can change the speed at which light is travelling, I'm extremely confident that this clock will keep accurate time.

Ok, now we introduce a second person into this scenario. You see, it turns out that person A is actually inside a train carriage, and now we're going to look at things from the perspective of someone standing on the ground watching the train go past...



In the above picture, we have an illustration of one "cycle" of the clock. From A's perspective inside the carriage, exactly 1 second has passed between the start position and the end position. But how much time has passed for person B?

Since B is standing on the side of the track, watching the train go past, he sees the light travel a much further distance than A does. However, despite the greater distance, he sees the light travelling at the same speed. Remember that no matter what, everyone measures light to be travelling at the same speed.

So now B does the same calculation that A did. He takes the distance the light has travelled, and divides it by the speed to work out how much time has passed. Since the distance is greater, but the speed of light is the same, he says that more time has passed than A, say 2 seconds (so the distance is twice as far).

In Person A's frame of reference, 1 second has passed. In Person B's frame of reference, 2 seconds has passed. Time is passing slower for person A than for person B! If the train carriage has windows, person B will see person A moving in slow motion.

And as a consequence would not light appear to be traveling in slow motion also?

catch-22 wrote:And as a consequence would not light appear to be traveling in slow motion also?

Nope, that's the weird thing. Light always travels at the same speed, no matter who observes it. So light looks to be travelling at the same speed, it's just that now it's travelling at an angle, instead of straight up and down, so it takes longer to complete a cycle.

Is it possible, since people see time at different speeds, that different people would see light at different times? I mean, it took me three divorces for me to see the light????


Sorry carry on, this is interesting.