General Relativity Question

[lyghtningbyrd]

I find it difficult to get answers for questions that deal with abstract scientific concepts that are explained in a way that I, a moron, can understand.

Here is my problem:

I was driving on the interstate in Atlanta, GA, and the Marta (what they call the mass transit in Atl) going about 75 and the Marta train was driving in the opposite direction. I was staring at the train and relative to the train it appeared that I was going faster than 75. (75 + Train's velocity in opposite direction).

So here is the question:

Theroretically, it is my understanding that it is possible to get close to the speed of light asymptotically, but never reach it. SO, if I were in a school bus in outer space and it was going extremely close to the speed of light, but not quite, and I ran from the back of the bus to the front as fast as i could, or better yet, fired a gun from the back to the front, wouldn't the bullet be travelling faster than the speed of light?

There has to be some concept that I am failing to understand here.

Anyone?

By the way, remember to explain it to me as if talking to a child.

Thanks,

Kevin

 

[Bronze Dog]

I'm curious about the explanation this thread'll get as well.

One tip that's occasionally helped me figure out possible answers to some relativity questions: The speed of light is constant, and time and space will bend over backwards to make sure nothing exceeds it.

 

[Hellbound]

I'm curious about the explanation this thread'll get as well.

One tip that's occasionally helped me figure out possible answers to some relativity questions: The speed of light is constant, and time and space will bend over backwards to make sure nothing exceeds it.

The big things here are length and time dilation, and that helps clear it up. Also, a lot of misunderstanding comes from changing your frame of reference mid-stream.

From inside your near-light school bus, your run (or the bullet, or whatever) would appear to function normally. You'd run at 10 mph, your bullet might travel at 300 m/s. Everything looks normal to you. Note, however, that nothing you measure inside would exceed the speed of light.

The outside observer would see the bullet travelling fractionally faster than the bus, likewise with you running. He would measure botha different distance travelled by the bullet, as well as a different length of time the bullet travelled.

The thing to remember is that the speeds you measure are entirely dependent on what frame of reference you use. And "swapping" frames (such as thinking about firing the bullet inside then comparing it with the speed of the outside universe) are were most problems come in.

The easiest way to explain it is with mathematics, but I can't recall the exact formula off-hand (I remember the one for mass increase, but not length contraction or time dilation). Basically, it boils down to the fact that what you percieve depends on where you percieve it from.

Don't know if this will help or not, but hopefully it will at least get someone more qualified then I to come in and unmuddle my explanation

 

[Orangutan]

You question sounds more like Special Relativity. I cant give you a good answer, but I suggest you read "The Elegant Universe", It has the easiest to understand chapters of special/general relativity I ever read. (and it's right at the start!

Good luck with your problem.

O.

 

[CurtC]

SO, if I were in a school bus in outer space and it was going extremely close to the speed of light, but not quite, and I ran from the back of the bus to the front as fast as i could, or better yet, fired a gun from the back to the front, wouldn't the bullet be travelling faster than the speed of light?

Since there is no preferred reference frame, you, as a passenger on the bus, would see the bullet travelling normally. If you instead shine a flashlight towards the front, you will observe the flashlight beam going towards the front of the bus apparently normally.

When you said that the bus was moving at close to the speed of light, you didn't say relative to whom. The key to your question is what that observer, who already sees the bus moving at almost the speed of light, will see with regards to the bullet or flashlight beam. Of course, he'll see the flash light beam going at exactly c, but it will be travelling a shorter distance than what you observe, so it all works out.

 

[Upchurch]

SO, if I were in a school bus in outer space and it was going extremely close to the speed of light, but not quite, and I ran from the back of the bus to the front as fast as i could, or better yet, fired a gun from the back to the front, wouldn't the bullet be travelling faster than the speed of light?

This is the first big conceptual hurdle you need to cross in understanding Relativity (this is technically still Special Relativity, I believe).

The idea that velocities are simply additive is incorrect. In other words, the speed of your bullet is not:

V_you + V_{bullet from you} = V_bullet

It is actually:

(V_you + V_bfy)/(1 + (V_you*V_bfy)/c²) = V_bullet

see here for a more technical take.

Conceptually, whenever you are talking about a velocity, you have to ask "Velocity compared to what?" In the above example, you are asking what the velocity of the bullet is. Relative to you, the velocity of the bullet is simply the velocity the bullet has as it leaves the gun.

"But," you ask, "I am already traveling near the speed of light. Shouldn't the bullet be traveling faster?"

But from whose perspective?

From your perspective, you are standing still on a bus in space firing a gun (odd hobbies you have there, btw). From your perspective, the bullet is traveling no differently than it would on Earth (presence of planetary gravity aside).

From someone from whom you are traveling near the speed of light, the above equation applies, which is due to a combination of length contraction and time dialation. You'll find that V_bullet never gets above c

 

[Orangutan]

Thanks for the prompting of the other posters. Basically it's what they said.

Anyone outside the bus would see the bus traveling as though time were going very slowly for the bus and it's contents. They might see you running but you would appear almost frozen.

Again I think this is the Special Relativity answer, the General relativity answer may be a little different.

O.

 

[Bronze Dog]

Forgot to include one bad joke in my post: "General Question about Special Relativity or Special Question about General Relativity?"

Another question I saw somewhere, but didn't see the answer to: I'm floating out in space, holding a pole that is one lightyear in length, pointing it at a friend one lightyear away. When I thrust the rod at him, how long will it be before he feels the poke?

I suspect that the answer is 1 year or more, since I'm currently imagining the rod's movement as a wave of collisions starting from the atoms my hand pushes, which collide with the next ones, etc, and that wave can't exceed the speed of light.

 

[Hellbound]

Forgot to include one bad joke in my post: "General Question about Special Relativity or Special Question about General Relativity?"

Another question I saw somewhere, but didn't see the answer to: I'm floating out in space, holding a pole that is one lightyear in length, pointing it at a friend one lightyear away. When I thrust the rod at him, how long will it be before he feels the poke?

I suspect that the answer is 1 year or more, since I'm currently imagining the rod's movement as a wave of collisions starting from the atoms my hand pushes, which collide with the next ones, etc, and that wave can't exceed the speed of light.

It's my understanding that it would be signifigantly longer, but you're on the right track.

No material is perfectly inelastic (in other words, everything squishes to some degree), and IIRC the speed of propogation of a pressure wave (such as a poke) is related or identical to the speed of sound in the medium.

 

[drkitten]

Another question I saw somewhere, but didn't see the answer to: I'm floating out in space, holding a pole that is one lightyear in length, pointing it at a friend one lightyear away. When I thrust the rod at him, how long will it be before he feels the poke?

I suspect that the answer is 1 year or more, since I'm currently imagining the rod's movement as a wave of collisions starting from the atoms my hand pushes, which collide with the next ones, etc, and that wave can't exceed the speed of light.

Yes. Specifically, what you are really asking is "what is the speed at which a pressure wave travels along a rod," or more generally "what is the speed of sound in this rod?"

If your rod is steel, for example, the "poke" will travel at about 6000 metres/second. if your rod is made of gold, it will travel at about 1000 meters per second (but you probably have better uses for a light-year of gold than to use it as a cattle prod. If you don't, well, I certainly do).

 

[Bronze Dog]

(but you probably have better uses for a light-year of gold than to use it as a cattle prod. If you don't, well, I certainly do).

Good point. I think I'll melt it down and see about upgrading my entertainment center, computer, "tricking out" my car, and that sort of thing. Oh, and donating to some charities might be nice.

 

[lyghtningbyrd]

Re: Re: General Relativity Question

This is the first big conceptual hurdle you need to cross in understanding Relativity (this is technically still Special

Conceptually, whenever you are talking about a velocity, you have to ask "Velocity compared to what?" In the above example, you are asking what the velocity of the bullet is. Relative to you, the velocity of the bullet is simply the velocity the bullet has as it leaves the gun.

Okay, but if that is the case, how can there be anything inherently special about velocity, if it is all simply relative to something else?

If you shine a flashlight on a normal bus going 50 mph, should not that light coming from the flashlight be going the speed of light + 50mph?

I guess I just do not understand the importance of the speed of light. Why not sound? Why is it that light is the maximum speed of anything

Well, I think perhaps it is all over my head. Thanks for the articulate responses

 

[Orangutan]

No, no one will measure the speed of light as anything other than c, no matter how the sorce is moving, The frequency will shift but not the speed. That's why you get all sorts of weird effects like time and space dilation. Again this is all covered in "The Elegant Universe", even if you don't care for the string theory stuff later on, it has excellent chapters on Einstinian and Quantum physics.

Don't think about sound too much, while it's analogous to light in some ways it's too different in others to help much when thinking about relativity.

These kind of though experiments are great fun.

o.

 

[drkitten]

Re: Re: Re: General Relativity Question

If you shine a flashlight on a normal bus going 50 mph, should not that light coming from the flashlight be going the speed of light + 50mph?

Well, that's the special bit. The "Theory of Relativity" is actually not very well named; the point isn't the relativity of the speed of light, but the fact that it is unexpectedly absolute.

Experimentally, physicists discovered that the speed of light appeared to be the same no matter how you measured it and no matter how the source was moving.

Mathematically, notice what happens if you set the speed of the bullet to be equal to c (the speed of light) in the equation given earlier. Your speed drops out and the final velocity of the bullet is still c, no matter who is doing the observing.

So we would intuitively (Newtonianly) expect that the speed of light would vary depending upon your motion relative to the light source. But instead it doesn't. Instead, what varies (depending upon your motion relative to the light source) is your perception of time and space. TIme and space are relative, but the observed speed of light is not.

 

[epepke]

Theroretically, it is my understanding that it is possible to get close to the speed of light asymptotically, but never reach it. SO, if I were in a school bus in outer space and it was going extremely close to the speed of light, but not quite, and I ran from the back of the bus to the front as fast as i could, or better yet, fired a gun from the back to the front, wouldn't the bullet be travelling faster than the speed of light?

There has to be some concept that I am failing to understand here.

Yeah, basically.

I won't use equations. They make me sleepy.

Velocities don't add up the way you think. Thinking that they do works really well for small speeds.

You, in the bus, would see nothing unusual (unless you looked out the window). The bullet would go far, fast.

Someone who is "at rest" outside the bus or who is going fast in the opposite direction (it makes no difference; that's why it's relative) would measure a really short bus and a bullet moving really slowly forward within it. At the speed of light, someone would see a bus of no length and a bullet that does not move. Of course, it's impossible to accelerate this fast, but at any lesser speeds, the shortness of the bus and the slowness of the bullet combine in such a way that it is impossible for anyone to measure the bullet as going faster than light.

 

[gnome]

Re: Re: Re: General Relativity Question

Okay, but if that is the case, how can there be anything inherently special about velocity, if it is all simply relative to something else?

You might say, there isn't anything inherently special about velocity.

I guess I just do not understand the importance of the speed of light. Why not sound? Why is it that light is the maximum speed of anything?

WHY is a powerful question that may not have a meaningful answer. What matters is that it seems to be so.

 

[Gwyn ap Nudd]

Re: Re: Re: General Relativity Question

Okay, but if that is the case, how can there be anything inherently special about velocity, if it is all simply relative to something else?

If you shine a flashlight on a normal bus going 50 mph, should not that light coming from the flashlight be going the speed of light + 50mph?

I guess I just do not understand the importance of the speed of light. Why not sound? Why is it that light is the maximum speed of anything

Well, I think perhaps it is all over my head. Thanks for the articulate responses

The problem with trying to explain Relativity without the equations, or trying to explain the equations without the experimental data is that the "common sense" that Newtonian physics is based on breaks down.



One approach that I have found helps is to consider two ships traveling on the ocean. They are traveling on the surface of a sphere. If we track their progress on a flat polar-profection map their positions and velocities do not behave according to "common sense," but they are predictable if we consider that the distance of each position on the map to the pole is a function of the corresponding distance on the globe -- a function that can be discovered.

It is possible to envision our space as a flat three-dimenional projection of a curved three-dimensional "surface" in a four-dimensional space. Using the equation for adding two velocities, it is even possible to derive the curvature. The surface works out to be the three-dimensional analog of the hyperbolic-tangent curve.

All of this is possible as an exercise, but not very helpful beyond a vague understanding of why "common sense" breaks down.

It might have been helpful if understanding this gave us equations we could use, but we derived the equations from the raw data, and this viewpoint does not add any new information.

As for your question: "I guess I just do not understand the importance of the speed of light. Why not sound? " It is not that it is the speed of light, it is that it is the ultimate speed. The speed of light does not restrict the universe; the universe restricts all velocities, including light. If it were not for this limitation, light, having no mass, would be expected to travel infinitely fast.

 

[gnome]

Re: Re: Re: Re: General Relativity Question

If it were not for this limitation, light, having no mass, would be expected to travel infinitely fast.

I believe light does have mass, according to Einstein.

 

[Alkatran]

Re: Re: Re: Re: Re: General Relativity Question

I believe light does have mass, according to Einstein.

It has 0 rest-mass. But it does have energy (and therefore mass) AFTER it's moving.

If you want a great site on special relativity, go here: http://casa.colorado.edu/~ajsh/sr/paradox.html

Best one I've seen by far.

 

[CurtC]

Re: Re: Re: General Relativity Question

I guess I just do not understand the importance of the speed of light. Why not sound? Why is it that light is the maximum speed of anything

I don't know if this will help, but try not to think of it as "the speed of light" - think of it as "the speed limit of the universe," and light, being a massless particle, travels at the speed limit. You, being massive, never can. Other massless particles also travel at c.