Relativity theory question?

Question

Relativity makes 2 statements if I have it right: 1 - nothing can go faster than the speed of light and 2 - when two objects are in motion relative to each other you can arbitrarily assign one as "stationary" and attribute all the motion to the other. Ok. So if I am approaching a point, say from the east, at 90% of the speed of light, and you are approaching the same point from the west, also at 90% of the speed of light, then aren't we approaching each other at 180% of the speed of light?

Thanks for any help on this. I can't get past it into the real meat of relativity and it's frustrating.

Answer 1

First and foremost: Never, ever get frustrated or discouraged because you can't get into the real meat of relativity. Take heart in the fact that neither could most of the greatest minds of the 20th century when Einstein introduced it to the world.

Secondly, we need an observer who considers himself at rest relative to the point and is establishing the fact that the two objects you speak of are indeed moving at 90% of the speed of light toward a point in space. In theory, that's easy - we'll put the observer off to the side of the point and have him measure the speeds - ok, one object going east is approaching the point at 90% of the speed of light and another object, going west, is approaching the same point at 90% of the speed of light. So, no problem yet, two different objects, both going less than the speed of light.

Now comes the problem (and the downfall of Newtonian physics): If the first object considers itself at rest and measures the second object, according to what would seem to be common sense, you would have 90% + 90%, or the resulting speed of the second object approaching you at 180% the speed of light!

BUT, and this is a BIG but, as an object approaches the speed of light, both the time and distance recorded by this object shrink. The time slows down and the distance traveled is shortened in the direction of travel - this is why all observers, irregardless of their motion, will measure the speed of light as covering the same exact distance (relative to them) in the same amount of time (relative to them) as any other observer. It's because each one is essentually using his OWN clock rate to measure his OWN distance.

So, in closing, when the first object considers himself at rest and measures the speed of the second object, he will be using a clock that is much slower and measuring the distance covered by the second object (both relative to his motion even though he considers himself - and rightfully so - at rest) and he will find that the second object is coming toward him at 90% of the speed of light.

Think of a yard stick with an observer sitting on the end of it - and this is his tool that he uses to measure distance - when it is accellerated it shortens in the distance it is traveling and time for an observer sitting on the stick is slowed - and this is the clock he uses to measure the length of time - therefore, he will always measure the speed of light approaching him or leaving him as exactly the same.

I hope this will help - it's not an easy concept to understand, mostly because all of our experiences are at speeds so much less than even a fraction of the speed of light this effect is negligible.

Answer 2

actually light in a vacuum always travels at light speed no matter from where it is viewed is the fundamental law. you are trying to assign Newtonian classical physics to the problem and that is where you're getting mixed up.

Any object under non-accelerated motion can claim it is stationary. Stationary is a viewpoint from a place where the motion cannot be attributed because it is constant.

So, let's take you're experiment. You are travelling at 90% the speed of light. But you can claim you are stationary because it is unaccelerated motion. In which case in a vacuum the object coming towards you will not approach at anything faster than light speed. This was einstein's fundamental question of what would light look like if you "caught up to it" because newtonian physics do not apply directly to light, it cannot be slowed down by a viewpoint, because an object and where it is viewed from is relative to each other. The reason why relativity was hard to grasp, initially dismissed and often confused is becasue it applies rules to the universe that work in abstracts and goes against the proven classical physics we work with in our world.

On a final note your objects are not going at the speed of light for a start so their speed is a factor. Speed is a measurement of space travelled in time. But who's time, and from what point to what point and where is the measurer taking place? At light speed these questions don't matter because light speed is the same form all viewpoints, but the object at 90% can claim to be stationary, and this makes it's accurate speed a hard thing to quantify because you need to know precisely where you are when measuring it.

Hope that has at least gotten you thinking of not answering your question.

Answer 3

This is one of my favorite paradoxes. The answer has to do with what it means to be an observer. An observer is really a co-moving coordinate system. You are moving, so is your coordinate system. The other guy is moving, therefore so is his coordinate system. Moving with respect to what? Why, to the third "stationary" coordinate system which your confusion implies.

It is certainly tru that, to this third observer, the distance between the two travellers decreases at a rate larger than the speed of light. But neither traveller on his own is travelling faster than lightspeed.

If you now look at what's happenning from the point of view of one of the travellers, say the one moving left-to-right, you have to remember that you must translate lengths and time intervals into his moving system of coordinates. When this is done properly--according to the Lorentz transformations--the apparent right-to-left motion of the other guy is appropriately below light speed according to this new stationary observer.

So when you handle things properly, using the correct transformations between the coordinates of different observers, the apparent contradictions vanish.

Answer 4

Nothing with rest mass can reach the speed of light. All things without rest mass (photons, gravitons, etc.) move at the speed of light as measured by all frames of reference.

The important thing to remember is that the assumption that velocities are additive (90% + 90% = 180%) is dependent on the assumption that space and time are absolutes. They are not. The reality is the space-time interval, for which the spatial and temporal components will have different lengths from different inertial frames of reference. But all frames of reference will agree on the space-time interval itself.

Answer 5

You are a little off. Relativity doesn't say nothing can go faster than light. It says that nothing with a non-zero rest mass can travel at the speed of light. Something with a zero rest mass could travel faster than light, and something with an imaginary (Remmeber imaginary numbers?) mass could go faster.

As to your second point (this is a VERY common question) you are ignoring time dilation. As you are traveling faster, your perception of the passage of time slows. When factored in, this brings your relative speed down to sub-light speeds.

Answer 6

evaluate the time it takes to blend the components and bake the cakes. The time varies with what proportion bran cakes you should make, as properly because of the fact the dimensions of the cakes. That mentioned, bran cakes will strengthen in mass as they attitude gentle speed and settlement somewhat than improve. See my previous remark on the sci notation of the bran muffin. .

Answer 7

I think that the basic problem here is relativity. Relative to that fixed point you may be moving at .9c, and relative to that fixed point something else may be moving at .9c - BUT you are NOT moving at 1.8c relative to each other....(Doesn't help much, does it?)

Answer 8

http://www.phys.vt.edu/~jhs/faq/sr.html