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Theory of Relativity


stevenaa

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In a nutshell its that all your observations are relative to you point of view.

Any specific question? Like the thought experiments like going into space at the speed of light and aging less than the ones you left behind on earth?

Its really a pretty big topic.

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This is squarely in the realm of Ignatius J.

What little I know is from AP Physics and two worthless Physics classes I took at Colgate. Essentially, as HOF44 points out, your perspective both in terms of thought and measurement is guided by your vantage point. If I am on the train and I'm walking 5 mph on the train from car to car, then I'm only moving 5 mph. If I'm a person observing the train, that itself is going 35 mph, then I see the person walking at approximately 40 mph--that's the funky thing about relativitly, as you get to speeds that approach the speed of light, the speeds, or more accurately, velocities, don't equal a+b.

Now consider the passenger/train example on a much grander or smaller scale and you'll get a sense of relativitly.

Relativitly, though I believe the Lorentz contraction which was taught as good science when I was in school, provides that mass approaches infinity the closer you get to the speed of light.

It's pretty interesting stuff. Let me know if what I've written makes sense.

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Ok, Tater. I will refine my curiosity. Specifically, Special Relativity.

1) Why, theoretically, can't the speed of light be broken?

Scenario>

I'm traveling at the speed of light. I'm holding a mirror 3 feet in front of my face. The light that travels from my face to the mirror and back to my eyes showing my reflection is traveling at the speed of light relative to me. However, if I'm passing over earth at the time, and the speed of the light going from my face to the mirror is measured relative to earth, would it not equate to twice the speed of light?

Analogy. If I have gun that shoots a projectile at 600 MPH, and I fire it from a plane going 300 MPH, the projectile is moving 900 MPH relative to an observer on Terra Firma. Why does light, theoretically, play differently.

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Ok, Tater. I will refine my curiosity. Specifically, Special Relativity.

1) Why, theoretically, can't the speed of light be broken?

Scenario>

I'm traveling at the speed of light. I'm holding a mirror 3 feet in front of my face. The light that travels from my face to the mirror and back to my eyes showing my reflection is traveling at the speed of light relative to me. However, if I'm passing over earth at the time, and the speed of the light going from my face to the mirror is measured relative to earth, would it not equate to twice the speed of light?

Analogy. If I have gun that shoots a projectile at 600 MPH, and I fire it from a plane going 300 MPH, the projectile is moving 900 MPH relative to an observer on Terra Firma. Why does light, theoretically, play differently.

Because the speed of light is the fastest speed under Einstein's theory. Kind of like the temperature of absolute zero, something like -273.15 degrees Celsius--nothing exists below that temperature.

Light plays differently because it's SO much faster and how that affects moving bodies is very different--so your analogy doesn't quite work.

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Analogy. If I have gun that shoots a projectile at 600 MPH, and I fire it from a plane going 300 MPH, the projectile is moving 900 MPH relative to an observer on Terra Firma. Why does light, theoretically, play differently.

I argue with that, all guns have different muzzle velocities. So lets say that your have a MV of 1000feet per second, if your traveling 1000fps I dont think your bullets will have the velocity to escape the barrel. Im not a physicist, but I dont see how it could be anywhere else since your moving the barrel and the bullet is trying to escape the barrel.

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In Einstein's theory of relativity the speed of light as a constant is a given. For everthing else to work this has to be so.

Is the theory correct? Einstein didn't think so. Now people are looking into string theory, which to be honest I am absolutley no expert on.

Relativity doesen't explain why the expansion of the universe is accelerating. ALot of scientest don't like attributing it to "dark matter". Its really all intersting stuff.

Myabe somebody alot more knowledgable than I will chime in.

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I argue with that, all guns have different muzzle velocities. So lets say that your have a MV of 1000feet per second, if your traveling 1000fps I dont think your bullets will have the velocity to escape the barrel. Im not a physicist, but I dont see how it could be anywhere else since your moving the barrel and the bullet is trying to escape the barrel.

Your using your bullets rated muzzle velocity of 1000f/sec. This is calculated with the gun at rest. Firing the bullett while the gun is traveling 1000f/sec will result in the bullett traveling at 2000f/sec from an observer on the ground. To you who is moving at 1000/sec with the gun, the bullet will appear to travel at 1000/sec. This difference is the basis for relativity.

This of course doesen't take into account the inertia of the forces involved when the gun is fired.

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Ok, Tater. I will refine my curiosity. Specifically, Special Relativity.

1) Why, theoretically, can't the speed of light be broken?

Scenario>

I'm traveling at the speed of light. I'm holding a mirror 3 feet in front of my face. The light that travels from my face to the mirror and back to my eyes showing my reflection is traveling at the speed of light relative to me. However, if I'm passing over earth at the time, and the speed of the light going from my face to the mirror is measured relative to earth, would it not equate to twice the speed of light?

Analogy. If I have gun that shoots a projectile at 600 MPH, and I fire it from a plane going 300 MPH, the projectile is moving 900 MPH relative to an observer on Terra Firma. Why does light, theoretically, play differently.

Light is a constant and it always moves at the same speed relative to an observer. You asked why we go faster then the speed of light, well it is because of Einsteins equations. γ= 1/(1-V²/c²)^.5 where the denominator is inside a squareroot and E=γmc² .

Well, as an object approaches the speed of light, (the v² term) approaches the same thing as the c² term, and the denominator approaches zero. As the denominator approaches zero, the value for γ increases to infinity. When this is used in Einstein's equation E=γmc², the energy required to reach the speed of light is infinate.

Here are the basic equations minus the transformations.

eform07.gif

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I argue with that, all guns have different muzzle velocities. So lets say that your have a MV of 1000feet per second, if your traveling 1000fps I dont think your bullets will have the velocity to escape the barrel. Im not a physicist, but I dont see how it could be anywhere else since your moving the barrel and the bullet is trying to escape the barrel.

Think of it this way. If your on a plane, you can toss a piece of paper to the front of the plane.

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Ok, Tater. I will refine my curiosity. Specifically, Special Relativity.

1) Why, theoretically, can't the speed of light be broken?

Scenario>

I'm traveling at the speed of light. I'm holding a mirror 3 feet in front of my face. The light that travels from my face to the mirror and back to my eyes showing my reflection is traveling at the speed of light relative to me. However, if I'm passing over earth at the time, and the speed of the light going from my face to the mirror is measured relative to earth, would it not equate to twice the speed of light?

Analogy. If I have gun that shoots a projectile at 600 MPH, and I fire it from a plane going 300 MPH, the projectile is moving 900 MPH relative to an observer on Terra Firma. Why does light, theoretically, play differently.

...I guess technically I took all the same special relativity classes as Ignatius, so I can give this a try I suppose...

The basic tenet of special relativity is that nothing can travel faster than the speed of light. As objects start to approach the speed of light, they appear shorter and time will appear to slow down, which prevents any observation of something travelling faster than the speed of light.

In your example of looking in a mirror while flying by the earth, if you were actually travelling at the speed of light, an observer on the earth would perceive the distance between you and the mirror to contract to zero, so the light won't be covering any distance at all.

In fact, if someone on earth observed your spaceship as it accelerated to the speed of light, they would see the distance between the mirror getting smaller and smaller and the clocks on your spaceship running slower and slower so that the light between your face and the mirror would always be travelling at a constant speed - the speed of light. Once you hit the speed of light, it would look like your face was smushed into the mirror and all the clocks in your spaceship (also smushed together) would stop moving, so that nothing in your spaceship could have any additional speed at all. Meanwhile, inside the spaceship, everything would look normal to you, although if you looked out your window, the earth would appear to be smushed and all the clocks outside would be stopped.

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Scenario>

I'm traveling at the speed of light. I'm holding a mirror 3 feet in front of my face. The light that travels from my face to the mirror and back to my eyes showing my reflection is traveling at the speed of light relative to me. However, if I'm passing over earth at the time, and the speed of the light going from my face to the mirror is measured relative to earth, would it not equate to twice the speed of light?

Analogy. If I have gun that shoots a projectile at 600 MPH, and I fire it from a plane going 300 MPH, the projectile is moving 900 MPH relative to an observer on Terra Firma. Why does light, theoretically, play differently.

For the second part of your example, as you approach the speed of light, time slows down for you. Think of it this way.

Say you are travelling 99.999% of the speed of light, and you turn on a flashlight. In your reference frame, you measure the c (the speed of light) to be 3.0X10^8m/s. The observer on earth measeures the beam form your flashlight at the same amount relative to HIS reference frame as well, 3.0x10^8. Well, this seems like a contradiction because the light would have the initial velocity of the observer, but that is not correct. Light is a constant, and to account for this, TIME slows down. So as you sit travelling 99.999% of the speed of light, time is travelling at a MUCH MUCH slower rate then it is on earth. TIME for you is different then time is on earth, thus you can both view light with a constant speed.

There have been many experiments to test for the time slowing effect, and they all agree with Einstein's relativity equations, in other words, time slows down the faster you go.

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Your using your bullets rated muzzle velocity of 1000f/sec. This is calculated with the gun at rest. Firing the bullett while the gun is traveling 1000f/sec will result in the bullett traveling at 2000f/sec from an observer on the ground. To you who is moving at 1000/sec with the gun, the bullet will appear to travel at 1000/sec. This difference is the basis for relativity.

This of course doesen't take into account the inertia of the forces involved when the gun is fired.

like I said Im not a physicist, Im gonna have to agree with ya :D

still I would think that if you had a laser on a vessle going the speed of light, it wouldnt leave the barrel. But then again thats from steven wright and his job interview suggestion although he used car and headlights and lightspeed. thats my extent on physics.

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...I guess technically I took all the same special relativity classes as Ignatius, so I can give this a try I suppose...

The basic tenet of special relativity is that nothing can travel faster than the speed of light. As objects start to approach the speed of light, they appear shorter and time will appear to slow down, which prevents any observation of something travelling faster than the speed of light.

In your example of looking in a mirror while flying by the earth, if you were actually travelling at the speed of light, an observer on the earth would perceive the distance between you and the mirror to contract to zero, so the light won't be covering any distance at all.

In fact, if someone on earth observed your spaceship as it accelerated to the speed of light, they would see the distance between the mirror getting smaller and smaller and the clocks on your spaceship running slower and slower so that the light between your face and the mirror would always be travelling at a constant speed - the speed of light. Once you hit the speed of light, it would look like your face was smushed into the mirror and all the clocks in your spaceship (also smushed together) would stop moving, so that nothing in your spaceship could have any additional speed at all. Meanwhile, inside the spaceship, everything would look normal to you, although if you looked out your window, the earth would appear to be smushed and all the clocks outside would be stopped.

Must have cross posted :D. . . we both basically said the same thing, you through words, me through equations. :D

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About the "mirror" deal....

If you are within a vessel that is moving at the speed of light, and the mirror is inside there with you, wouldn't that have no effect on the transfer of light? I mean it's like a car, you're sitting still in a car moving at 100 mph, and you can still juggle tennis balls with no effect (unless there is a change in motion/velocity). Speed is speed, and if everything is going that speed then it all balances out, right? I know the comparison is slightly flawed (100 mph is not light speed).

On a sidenote, does light speed have to be a "barrier"? Is there that big of a difference if you're 5 mph below the speed of light? It's still damn fast. It's just a speed that light happens to go. And if light can be slowed/diverted by gravity (blackholes, etc.), doesn't that show that light speed is not as powerful and absolute as we think?

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Well, I have always believed that the single best source for this stuff is einstein himself:

http://www.amazon.com/gp/product/0517884410/102-7533986-4052108?v=glance&n=283155&n=507846&s=books&v=glance

and then also:

http://www.amazon.com/gp/product/0807615323/102-7533986-4052108?v=glance&n=283155&n=507846&s=books&v=glance

The second paper is actually the origional paper that einstein published to introduce his ideas into the world. No one understands this stuff better than einstein himself did.

DjTj has a real nice explanation of why the counterexample doesn't happen. The key point to the counter examples is the following:

Skeptic: Imagine that I am on a train which is traveling at 2/3 the speed of light. I am relative to myself standing still. If A friend next to me then beging to walk to the front of the train at 2/3 the speed of light, doesn't the observer on the ground see my friend walking at 4/3 the speed of light?

Relativist: No. Your friend is walking at the speed of 2/3 the speed of light, but only in YOUR reference frame. You cannot simply add your velocity to your friends velocity to get the velocity that someone on the ground would measure. You must take into account all sorts of odd effects including the squishing of distances and the slowing down of clocks, all of which affect the measurement of velocity. Once you take these into acount, you find that the observer on the ground does indeed see your friend moving, but he measures his speed to be faster than you and slower than the speed of light.

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About the "mirror" deal....

If you are within a vessel that is moving at the speed of light, and the mirror is inside there with you, wouldn't that have no effect on the transfer of light? I mean it's like a car, you're sitting still in a car moving at 100 mph, and you can still juggle tennis balls with no effect (unless there is a change in motion/velocity). Speed is speed, and if everything is going that speed then it all balances out, right? I know the comparison is slightly flawed (100 mph is not light speed).

No, the speed of light is always a constant. It is always 3.0x10^8m/s (I think that is the value) in a vacuum. If you are travelling 99.999999% of the speed of light, light, to you still moves away from you at the same rate. The reason there is no contradiction is because TIME slows down, this allows the speed of light remains constant.

On a sidenote, does light speed have to be a "barrier"? Is there that big of a difference if you're 5 mph below the speed of light? It's still damn fast. It's just a speed that light happens to go. And if light can be slowed/diverted by gravity (blackholes, etc.), doesn't that show that light speed is not as powerful and absolute as we think?

THere is nothing that says you can't travel faster then the speed of light, just that you can't approach it. Light can not be slowed, unless you change the medium it is travelling in, but it is effected by gravity. Light speed is about as absolute as you get in astrophysics :)

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