Speed of Light again...

[OBonio]

So we've ascertained that travelling at the speed of light is nigh on impossible for various reasons.

But what if we manage to get to half the speed of light and have two objects doing this towards each other? Would the two objects be travelling toward each other at the speed of light? What would this prove theoretically?

[Clanad]

Nothing, actually, since it's all relative as Mr. Einstein suggests. In reality, measurements of the speeds of galaxies moving away from each other have been shown to exceed, as a combined speed, that of c...
different pairs of galaxies are moving at different speeds with respect to each other; the further the galaxies are, the faster they move apart...

[jake-the-peg]

This is basically the invariance of the speed of light c.

The speed of light is constant no matter the speed of the observer.

If I measure the speed of a light ray and you measure it, it doesn't matter if you are going towards it or going away from it or if we are travelling at different speeds we'll both measure the same speed of the light ray.

This is the main premise on which special relativity is founded and was shown by the most famous failed experiment where Michelson and Morley tried to measure the speed of the Earth in the ether (which we now know doesn't exist).

Coming back to your example. If I am sitting on a planet and I measure the speed of a rocket coming towards me to be three quarters of the speed of light and I then get on a similar craft and drive off, I can measure the planet recede at 3/4 the speed of light, when I look at the spacecraft coming towards me it won't be travelling towards me at one and a half times the speed of light but at some speed less than c.

Now I'm sorry if you don't like that, I know it's not the way that we think these things work, but busses and trains don't travel at these speeds so we rarely see relativity in action.

In Clanad's example we might measure 2 galaxies to be travelling apart from each other at nearly 2c but when they look at each other they only see themselves flying apart at just under c.

[lightoftruth]

a question thats allways confused me is if you are travelling at near the speed of light and you throw a ball foreward then would the ball be going at the speed of light?

[fo3nix]

lightoftruth: no, for pretty much the same reason as jake-the-peg explains for this question. weird, but that's the way things work...

[jake-the-peg]

I think the confusion arises because people use expressions like "if you're going close to the speed of light" and don't specify "who says they are travelling close to the speed of light"

Light of truth's ball is going at say 2 m/s to him. But to somebody who is watching and sees him going at close to the speed of light the ball is travelling a little faster than him but not quite at the speed of light.

People also seem to have got the idea that relativity says that nothing can travel faster than the speed of light. In actual fact this is an experimental observation that we see - Einstein used this information to explain and predict other startling effects such as time dilation.

[OBonio]

Ok, to surmise my thoughts on this thus far...

A car driving at 40 miles per hour, actually isn't. Its movement is purely based on what we observe. It is actually travelling at the speed of the earth's rotation.... and the speed of the galaxy's movement and... etc etc.

So the 'speed of light', c, is a constant that can be exceeded by combined speeds.

[bernardo]

50% of the speed of light plus 50% of the speed of light equals 80% of the speed of light.
90% plus 90% equals 99%.

[fo3nix]

OBonio: the speed of light can never be exceeded. Ever.

As for the car question: what do you mean travelling at 40mph? The key question here is "relative to what?"

if you're standing at the side of the road, and you have some fancy measuring device with you, and measure a car going past at 40mph, then it is travelling at 40mph *relative to you*.

if you happen to be floating in space, so that you can measure how fast the earth is rotation away from you, then everything that's stationary on the earth's surface is also travelling at that speed. if you have really good eyes, and you can see a car travelling away from you at 40mph on the earth's surface, in the same direction as the earth is rotating, then the car will be travelling at the speed of the earth's rotation + 40mph, *relative to you, in space*.

[fo3nix]

finally! i've been trying to say that for about 4 days.

[JudgeJ]

And the way to calculate this for two bodies A and B (measuring the speed of each body as a fraction of c, the speed of light, where c =1) is:

(A+B)/(1+(A x B).

Under Newtonian physics (where the relative speed is calculated by simply adding the two individual speeds together) it is obviously quite possible to calculate relative speeds greater than c. Under Einsteinian physics, using the above formula, relative speeds greater than c are not possible.

This makes very little difference at low speeds. Two objects, each travelling towards the other at 100mph, have a relative speed of 200mph under Newtonian Physics, and 199.99977mph under Einstein�s model. However, as bernardo points out, there is a significant difference when the individual speeds tend towards c.

[OBonio]

Thanks JudgeJ. That's cleared it up nicely.