# Faster than the speed of light.

1. Nov 6, 2006

### ThinksTooMuch

In Einstein's Theory of Relativity nothing can travel faster than the speed of light. Everything is based off of the speed of light. But speed is relative to to the reference point your measuring from.
Example if im in a car with a radar gun going 20 miles an hour an measure a car passing me at 60 its only going to say the car is going 40 MPH. Everything in the universe is moving in relation to each other.

There is no static reference point for the universe. For all we know the whole universe could be traveling at 5X the speed of light but we are measuring is the points that we could see. Example if someone is in complete darkness an quiet an sees a light in front of them the light moves but so does the person in the same direction so the perception is the light isn't moving.

So what if two objects are traveling towards at each other .75 speed of light from two different points in the universe. When measuring the speed the relative speed would be traveling torwards each other at 1.5 speed of light but measuring from the two points it would only be .75. So if speed is realative to the point that your measuring from I don't understand how this theory works. If anyone could help explain it to me this is for my own curiosity.

2. Nov 6, 2006

### LURCH

You have touched on the very heart of relativity, right here:
The fact is, no they wouldn't. If two objects are travelling toward each other at a speed that we on Earth would measure as .75c, then you got on one of the objects and measured the speed at which the other object is approaching you, you'd measure something like .9c. I don't know the exact number you'd get, but it would be less than c. That is where Special Relativity starts.

3. Nov 6, 2006

### actionintegral

This is not true. Relativity only says the speed of light is the same for all observers. It says nothing about things travelling faster than light.

4. Nov 6, 2006

### ThinksTooMuch

So are you saying that they can only travel towards each other at .9c or that they would be traveling towards each other at 1.5c but it would measure .9c. Further more the exsistance of black holes proves to me that things can travel faster than light. Because a black hole is so dense that light can't even excape it which means it has to be sucking it in faster than the speed of light to be black.

Example if someone were to travel away from the solar system faster than the speed of light. The earth would disappear and so would the solar system plus the stars an everything else.

Now what I wonder is would the a image of the stars an solar sytem would appear infront of the person going back in time because your going faster than the speed of light you would be seeing past light in front of you in super slow motion let say if your going 1.1c you would see the earth going at .10 normal speed going backwards in time. But it would also be cluttered by whats in front of you looking like its going at 2.1c it would look like 2.1X normal speed. Planets would orbit stars 2.1x as fast or atleast thats what it would seem like. But really your just seeing the past speeded up.

5. Nov 6, 2006

### JesseM

For cases like this you must use the formula for relativistic velocity addition described on this page, which says that if I see one object moving at velocity v and another moving at velocity u in the opposite direction along the same axis, each of them will measure the velocity of the other as (v + u)/(1 + uv/c^2). So in your example, each object would measure the other object's velocity as (0.75c + 0.75c)/(1 + 0.75*0.75) = 1.5c/1.5625 = 0.96c. The reason velocity addition works differently in relativity than it does in Newtonian physics is that each observer uses rulers and clocks at rest relative to himself to measure velocity = distance/time, but in relativity rulers moving at different speeds don't agree because of length contraction (each observer measures the other's ruler to be shrunk relative to his own) and clocks moving at different speeds don't agree because of time dilation (each observer measures the other's clocks to be slowed-down relative to his own), and there is also something called the "relativity of simultaneity" which means that a pair of clocks which are at rest in my frame and synchronized in my frame will be measured to be out-of-sync in all other frames.

Note that the formula above insures that if one observer measures a light beam to be moving at c using his own rulers and clocks, and measures a second observer to be moving at v in the opposite direction, then that second observer will also measure the light beam to be moving at c: (v + c)/(1 + vc/c^2) = (v + c)/(1 + v/c) = c*(v + c)/c*(1 + v/c) = c*(v + c)/(c + v) = c.

Last edited: Nov 6, 2006
6. Nov 7, 2006

### LURCH

One of the basic tenants of any physical science is that only that which can be measured (observed) can be said to exist. Otherwise, one could make up any story at all, saying that such-and-such is happening, and include the phrase, "but there's no physical evidence of this", and there would be no way of refuting that claim. Therefore, observability and measurability are used as tools of verification.

You could repeat the experiment with the two objects approaching one another, using different speeds (all of them > .5 c, of course), have the passengers on these objects measure one another's velocity with different clocks and rulers, and all their measurements would agree with the relativistic formula for adding velocities. Scientifically speaking, the fact that the measurement of a velocity comes up the same every time is taken as verification that this measurement is correct, and reflects the actuall velocity of the objects.

In short, I'm saying that every measurement anyone could ever take will allways agree that the two objects are approaching one another at .96 c (thank you Jesse for that more accurate value), so that is the speed they are realy moving.

7. Nov 12, 2006

### tehno

I would second that.
If I remember correctly,observed velocities of distant quasars in some cases exceeded 2c relative to Earth!

8. Nov 12, 2006

### JesseM

That would be due to the expansion of space, the speed-of-light restriction is on anything travelling faster than the speed of light as measured by local observers (local observers near the quasar would always measure it moving slower than c). Relativity does forbid anything to accelerate from slower-than-light to faster-than-light, since that would take an infinite amount of energy. In theory relativity doesn't forbid the existence of "tachyons" which always move faster than c in a local sense, but there is no evidence for their existence in reality.

9. Nov 12, 2006

### tehno

Yes,you got the point.
The key point for understanding the paradox is the expansion of the Space itself.The Universe is expanding due to Big Bang.