Weird paradox revisited.?

Question

Yesterday I asked a question about what would happen if I fired a bullet on a train traveling near the speed of light. One of the answers I received said that if the train was traveling at 99mph and I fired a bullet at 100mph, I would see the bullet travel at only 1mph. My thought on this is that the answer is flawed because the bullet was already traveling at 99mph before I fired it, the gun added an additional force behind it to make it go 100mph. So the bullet should travel a total of 199mph. So back to my original question of what would happen if I fired a bullet on a train traveling at near speed of light, and the bullet itself traveled at near speed of light. the two speeds total more the the speed of light which is impossible. So each objects speed must total less than the speed of light, making each object highest speed less than half of the speed of light.

But if the bullet had a insect traveling at less than half the speed of light on it, then the speed of each object must be less than half the speed of light, and so on. So giving enough objects on or in each other, all traveling at a certain speed, the total these speeds could never reach more than the speed of light. If you had a insanely high number of objects traveling in or on each other, then the speed of the first object (the train) could be forced to have a max speed of only 1mph.

Comment on the answer below, Yes the bullet was already traveling at 99mph. The bullet is on the train. If a observer measured the speed of the bullet at rest on the train, they would see a bullet traveling at 99mph.

Another comment for one of the answers below. If the total combine speeds are only 99.9% of C. Then simple math tells us that each object must be traveling at less than 50% of C (o.k. one could be travel more than 50% while another travels much less, but I am talking about objects traveling at equal speeds) If a third object is introduced then each would be traveling at 33.3% C, then a fourth 24.9% C. and so on... If you have allot, and I mean allot, of objects, each of their speeds could be something like0.000000000000000000000000000000000
0000000000001% of C. Eventually you would have a situation where each object can only travel at a mere crawl.

Answer 1

Adding Velocities in Relativity

In netwonian physics, you just added velocities.

For example, let's say Jim is on a train and Bob is on the side of the track. The train is going 50 miles per hour. Jim walks forward inside the train at 3 miles per hours relative to the train. In Newton's model of the universe, Bob would observe Jim moving at 53 miles per hour, because 50 + 3 = 53.

Newtonian physics breaks down at very high velocities, because if one simply added velocities, the result might very well exceed the speed of light. If the train in the previous example we moving at 75% the speed of light, and Jim walks forward at 50% the speed of light (a very rare feat indeed), Newtonian physics says he's going 125% the speed of light.

The trick is to realize that Bob see's Jim in slow motion. When Jim thinks he's running along the inside of the train at 50% the speed of light, Bob sees him as moving much slower.

Let's call

w the velocity observed by Bob.
u the velocity of the train.
v the velocity of Jim walking inside the train.
c, of course, the velocity of light.

Here's the formula: w = (U+V) / (1 + UV/C^2)

If you plug in all the numbers, you calculate that Bob sees Jim moving at 90.91% the speed of light. Of course, the difference between Newtonian physics and relativistic physics is only significant at very high velocities.

Answer 2

ouch!
this is complicated because we can only speculate and hypothesize about travel near the speed of light.
Gosh. it brings more questions than answers
can the chemical reaction that fires a bullet even at happen in a near-speed of light condition?
My guess is that the bullet will not travel very far anywhere until the 'train' its on begins to slow down. as you maybe aware, by studying relativity: Time in the vessel approaching the speed of light will slow down. So I'd imagine the bullet not moving anywhere until the vessel slows down, and then only accelerating in response to the slowing of the vessel
ouch, that much thinking hurt

Answer 3

Because of time dialation, you would see the bullet travelling at whatever speed you had fired it, but an outside observer would still see both you and the bullet moving slower than the speed of light.

In other words, suppose you could travel at (c - 100) mph, and suppose you fired a bullet at a velocity of 200 mph. From your frame of reference, the bullet would appear to be moving at 200 mph; however, an outside observer would NOT see the bullet moving at (c + 100) as you would expect.

Answer 4

Subluminal velocities when added together never make a speed higher than c.

You need to get a book on relativity. If you're on a spaceship going at 75% the speed of light and you fire something forward at 75% the speed of light its actual speed will be something like 99.9% the speed of light - if the two speeds are both 90 its more like 99.99999% the speed of light - you need to read up on the special theory.

Whenever the speed of light is measure its the same speed - 300,000 kilometres per second - its not relative, that means that space and time are relative.

Answer 5

We have two reference points or two frames of reference. One frame is relative to some point on the train where one observer stands and the other outside the train where another observer stands.

If the train is traveling at speed less then that of speed of light then the frame of reference on the train is in sync with the frame of reference outside the train and the speed of a bullet will be 199 m/ h regardless of the frame of reference.

However if the speed of train is that of speed of light (or very-very :) close to it) then the speed of the bullet will be 100 mph relative to the train and that of the speed of light relative to the frame of reference outside the train.


To additional info.
The superposition will be done on case by case basis and relative to a particular frame of reference.

Answer 6

You can't combine relativities. The relative speeds of the objects/insects would not approach anywhere near 1/2C or 1/3C or anything like that. You would get 0.0001C, then half of that, then half of that, and so on. The only way you would get a train that can't travel more than a mere crawl would be if the train, the bullet, the ant, and the gnat all had masses relatively the same.

Answer 7

NO, the bullet wouldn't be traveling at all untill you fire it so 99mph was right.