I think I understand it for the most part, but need help thinking through some scenarios:
Let’s say that in the future when things are more advanced, we have a space station with an observation area conducting experiments out in deep space. And we have two launch stations, equidistant from the space station, one directly to the left and one to the right of the space station.
The launch stations begin by each sending a small spacecraft toward the space station at 100mph (relative to the space station). The launch process consists of rapidly accelerating the spacecrafts to the target speed and then letting them coast until impact. The two spacecraft collide head on. The space station analyzes the crash and concludes that the force of impact was equivalent to the spacecraft colliding at 200mph. The black boxes in both spacecraft also concur that the force of impact that of a 200mph collision.
Then the launch stations do it again, but this time they send the spacecrafts out at 100,000mph (again, relative to the space station). This time the space station and both black boxes measure a net impact of 200,000 mph.
This continues, ramping up speed each time until they get to 90% the speed of light. The measure the impact and conclude that the net is a 1.8X light speed collision. They factor in special relatively including the mass increasing of each ship as speed is increased. There are no time adjustments necessary since the space station is motionless relative to itself.
Question 1: Is this correct so far? It doesn’t seem possible. See part 2 below.
Question 2: When the spacecraft are approaching each other at 90% the speed of light, when one looks at the other, what does it perceive the other’s speed to be? For example, I think if you were driving 50mph down the road and you measured the speed of a car coming towards you, also at 50mph, that it would seem like that car is coming at you at 100mph (and I assume that when police cars do this their radar guns must subtract the speed of the police car). But in this case, I don’t think the spacecraft would detect the other spacecraft coming at 1.8 the speed of light since that’s above the maximum. So, what speed would it detect? Lots of factors going on at these speeds such as alterations of time and distance, right?
Our curious scientists decide to run the experiment at 90% the speed of light again. But it turns out that the space station itself is very nimble and is able to run parallel to one of the spacecraft. They decide to do this in order to observe the collision while in motion relative to the collision point in order to get a different perspective. The space station leaves observation equipment behind at the collision point, and the moves itself out to one of the launch stations. The launch proceeds and the space station launches too and runs right next to one of the spacecraft. The two spacecraft and space station all accelerate to 90% the speed of light and then coast. During the time period while they are all coasting, the spacecraft that is next to the space station has a computer failure, loses it’s memory and reboots. After rebooting it assesses the situation and concludes that it is motionless and just sitting next to a stationary space station. And that another spacecraft it hurtling towards them at high speed. Then they collide and all of the black boxes read the same as before, and detect a 1.8X light speed collision. But a robot from the spacecraft that was next to the space station who somehow survives the collision protests and says that’s impossible....they were motionless and this other spacecraft smashed into them... and there is no way that the other spacecraft was going 1.8X the speed of light.
Question 3: What’s wrong with these observations? Would they really conclude that the collision was a net of 1.8X the speed of light? I don’t think so. Also, see Part 3.
They continue their experiments and build a wall in space. They launch a spacecraft at it at 99% the speed of light. The spacecraft collides with the wall and they measure it as a collision at 99% the speed of light.
Then they tear down the wall and go back to launching spacecraft at one another. They accelerate them both up to 99% the speed of light and they collide creating a huge spectacle. They measure the evidence from the collision including the black boxes and they conclude that the net speed of the collision was XXXX.
Question 4: What is XXXX in the situation above (approximately)? It seems as if the max collision speed must be just shy the speed of light. Is that right? If collision speeds also can’t exceed the speed of light, then what happens with all collisions where, relative to an observer, two objects each moving faster than 50% the speed of light crash into each other? You would think that the collisions would become more and more violent as speed increases as well as mass increases. Even so, is the maximum observable collision speed only 99.999999999999etc. for all collisions, even when objects are traveling over 99% the speed of light and run into one another?
Question 5: It seems odd that the collision with the wall should be a net 99% speed of light, but the collision forces of two spacecraft each going 99% the speed of light will be something like 99.9% the speed of light (since 99.9% isn’t much bigger than 99%). Does the math work out since the curves are so steep as you get closer and closer to the speed of light that the forces involved in a collision at ~99.9% the speed of light are double the force of a collision at 99% the speed of light?
I know I put several possibly duplicate questions above but mainly I think it comes down to these two questions:
1) Can collisions speeds exceed the speed of light?
2) If not, how do you calculate collision speeds for objects that are headed towards each other, especially when both objects are going over 50% the speed of light relative to an observer.