Topic: Composition of velocities...
Anonymous A started this discussion 14 years ago #17,479
Physics before Relativity would have thought up a thought experiment like this (if they had trucks at the time):
A truck is traveling at 100 kms per hour 'constant velocity' and there is a platform on the back of it; on this platform one person is pitching a ball to the catcher at 100 kms per hour.
What speed does the observer see the ball is traveling at if he is stationary on the ground and the ball is being thrown in the same direction of the truck?
It would be equal to 200% pre-relativity. Post-relativity, it would be very close, so close you would never notice the difference ordinarily but not quite. 100 kms per hour is 0.000009% of the speed of light. The difference between the two is so marginal I couldn't express them without using a lot of decimal points. If both were traveling at 10% of the speed of light, the composite would be 19.8% rather than 20%. If both were traveling at 1% of the speed of light, the composite would be 1.9998% rather than 2%.
For every day velocities, regular composition of velocities are almost an exact approximation.
I think this would fly in the face of conventional logic. If you throw a ball in the direction that a vehicle is traveling at the same speed shouldn't it fly back into your face? You might argue that the pitcher is attached to the vehicle, so travels along with it, and the ball is attached to the pitcher, so travels along with it, but once the ball is in the air it's traveling by itself and therefore can't have an additional velocity of the truck moving. If it travels at an average velocity of 100 kms per hour from the pitcher to the catcher, then it must travel at faster than 100 kms per hour early in the journey, move out from the pitcher and then decelerate to a speed less than 100 kms per hour and back into the pitchers shoulder or face. This is not what happens and what they mean by 'speed is relative' not absolute.
I think logically it can be explained as the ball being given forward momentum by being attached to the pitcher who is attached to the vehicle which is burning extra fuel due to the additional weight of both. That momentum is carried by the ball when it leaves the pitchers hand and stays that way until acted against.
Another way of looking at it is to have this truck travel at 100 kms per hour and have someone jump vertically on the back of it instead. Conventional logic would assume once he becomes detached from the truck, he must fly off the back of the truck. But that's not what should happen, I think! Don't go and try to do it based on my comprehension of it, I may be way off! Essentially the jumper has forward angular momentum and at no point in his jump is he decelerating that momentum. In fact, from his perspective he is jumping straight up vertically. From a stationary observers perspective, he is jumping up on an angle in the direction of the vehicle, but he thinks he is jumping vertically only.
(It would also be dangerous to not mention that this law is broken if the truck changes speed (accelerates or decelerates) after the person is in the air. If the truck is decelerating before you jump and after you jump continues to decelerate then you're going to be flung off the front of the vehicle and off that back if it accelerates.)
In addition to possessing this momentum, relativity also says the faster he travels the more mass he possesses (relativistic mass). From my understanding, this would translate to the ball being thrown at a slightly slower velocity, so in that sense it would travel slower. But from an outside perspective, he will Lorentz contract by an equal measure, which means his metre has compressed, including the distance between pitcher and catcher, and the ball will appear to him unaffected by a change in velocity and weight. Presumably this is what creates the difference in composite velocities.
On the other end of the scale, if both the ball and truck were traveling at 90% of light speed, the composite would not be at or even remotely near 180%, instead it would be 99.4%. At 99% for each, the composite would be 99.995%. So at faster and faster velocities, it would agree to a more absolutist sense. Relativity (at least as it applies to mass velocity) is a theory of absolutes, not relatives.
Which makes me revisit my faulty conclusions some time ago (why it's not good to jump up and down on a moving truck! ). I thought for instance that if you have a straight line on earth and the earth didn't rotate and just moved 'southwards', that in order to shoot a target over distance you would need to predict where that target would be, hence you would need to shoot on a 'southwards' angle. If observed from a stationary perspective out in space, that would appear to be so. But a straight line on earth is pretty much a straight trajectory in an relativist sense... but not quite.
This galaxy is moving through the universe at about 2.1 million kilometres per hour. So when you are standing still, you are actually moving 2.1 million kilometres per hour. Although that sounds like a lot, it is actually about 0.2% the speed of light. And as illustrated above, the 'absolute' effect of that is miniscule (indeed, the famous time dilation effect would be just 1.000002), so when thinking of the earth traveling through space I do believe a straight line observed trajectory is pretty close to ... straight relative to an observer on the moving planet. It doesn't affect my speculations, because my speculations depend on difference of angles and there is still that albeit miniscule.
The interesting thing I think about this is ... Let's start again. If you have a straight line on earth and the earth is moving in 1 direction, then you might argue that you need to shoot on an angle to predict where the target you are aiming it is going to be. But this movement is vastly relative. From an outside perspective, it would appear that way, but from an observer moving with the planet the line it needs to be shot at would be straight.
Now accelerate the planet to speeds near light speed. This enhances how absolute this movement is, and indeed would affect this concept of angles. You would much more definitively say that the bullet must follow a predicted angled trajectory taking into account the earths velocity. So the faster the planet travels, the more of an angle a thing needs be shot at to travel in a straight line.
But the interesting thing here is the inversion of logic. If you shot the bullet at an instantaneous velocity, it'd travel in a straight line no matter the speed of the planets relative velocity. So although the earths velocity creates a steeper angle, much more dramatic and absolute an effect at speeds much closer to light speed, by accelerating the bullet to speeds at much greater velocities you can reduce this effect. This is a bit of an inversion in logic, one I've been looking for in my sinister quest to rule the world.
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