More than the speed of light?

Question

modern physics state that moving an object at (or more) the speed of light require infinite energy. This also means that if object 1 is traveling more than the speed of light compared to object 2, then object 2 can get infinite energy from object 1. But making 2 objects having a relative speed of more than the speed of light is possible like this:

Fire object1 from earth to moon with 60% speed of light. Fire object2 from moon to earth with 60% speed of light. Now compared to object 1, object2 is traveling 120% speed of light. So from object 1's point of view object 2 has infinite amount of energy. How it is? Why the contradiction?

Dear Scarlet Manuka,

Thank you for the brilliant answer. Actually you have cleared a doubt that was eating up my mind for a long time.

Can you please provide some web links where these details can be found?

Answer 1

In relativity, it turns out that to find the velocity of object2 relative to object1 is not as simple as adding their two velocities.

In fact, the formula for adding two velocities u and v is
(v + u) / (1 + uv/c^2)
When u and v are small compared to c, uv/c^2 is very small and we effectively have v + u. But at relativistic velocities it has a larger effect. In this case, we have
(0.6c + 0.6c) / (1 + 0.36)
= 1.2 c / 1.36
= 0.88c to 2 s.f.
So object2 is travelling at 0.88c relative to object1.

Note that as u approaches c, the total velocity tends to (v + c) / (1 + v/c) = c(v/c + 1) / (1 + v/c) = c. So if you have one object going at the speed of light, it doesn't matter what speed the other object is going at - the relative velocity will always be the speed of light.

Answer 2

Relativity doesn't work that way. The speed of any physical object is *always* measured to be less than the speed of light, even if two things are approaching each other at 99% c.

The reason Einstein concluded that no object could never achieve light speed (it's always stated wrongly that nothing can go faster than light, implying that some physical things can go as fast as light) is that it would require infinite energy to do so, and that's an impossibility. Therefore something else had to give, and those were time (slowing to zero), thickness (decreasing to zero) and mass (increasing to infinity) - but the speed of light is always measured to be c no matter how an observer is moving.

Answer 3

Thank you. You have given me hope for the educated of this nation.

I really like this theory. It makes sense. But it scares me. Do we want to create that much energy. If I were to try this. I would be no where near earth. To much power. To much risk.

Answer 4

It might be possible, but it requires more than we know.