Objects travelling relatively to each other faster than light? When we say that something is travelling a certain speed, it's really travelling that speed relative to the Earth. When saying the speed of anything, it is, for the most part, relative to something else. That being said. If I have an object moving at half the speed of light, and another moving at just above half the speed of light in the opposite direction, would the second object be moving faster than the speed of light to the first one?
Note: I know this question is similar to some other questions like this one. However, with my limited physics knowledge (taking AP Physics class next year) I found the explanation a bit confusing. So, even though this might be a bit similar to other questions, I'm looking for a simpler explanation that could help me understand this and its foundation.
 A: In Special Relativity, we use Lorentz Transformations to add speed. The relevant formula here is
$$u = \frac{u^{'}+v}{1+\frac{u^{'}v}{c^2}} $$
where $u^{'}$ and $v$ are the speeds of the objects and $u$ (what you are looking for) is the speed that the object at $u$ sees the object at $v$.
This embodies Einstein's postulate that no information can be transferred faster than the speed of light in vacuum. Now using this formula, we can put $u^{'} = 0.5c$ and v = $0.6c$ and still get that $u = \frac{1.1c}{1.3} = 0.85c$. Note that even if $u^{'}=v=c$ we get $u=c$, which tells us that the speed of light in vacuum is the same for all observers (which is really the more-precise text of Einstein's conjecture)
Note what you have learned that you can just add the two speeds up is only a good approximation when $v<<c$.
P.S. See e.g. here for a simple derivation of the formula, which we get from using the lorentz transformations of time and position. It is only after we realise that time and space can be a combination of each other that we arrive at this.
A: so actually you could simplify the equation a lot.
A better way to frame the question to someone might be as follows
"If two objects are moving in opposite directions relative to a third object at just under the speed of light (c), how fast are the two objects moving relative to each other?"
The question doesn't involve trigonometry. It can be solved using simple multiplication and addition. The formula is as follows:
A(c)+B(c)= X, where A is the relative speed of the first object compared with the third, B is the relative speed of the second object compared to the third, c equals a speed just under the speed of light, and X is the total relative speed.
If this equation isn't correct, please explain!
