The question made. In the title of the article in different formulations, we are asked very often. Sometimes instead of photons in the question, the starships appear, which has a little less sense. Still, to fly at the speed of light to the massive object will not work.
It may seem that to obtain the relative speed of two photons of their speed, you just need to fold. But it is not. The theory of relativity states that for observers located in different systems of reference time flows in different ways. At first glance, this may seem strange, illogical and contradictory to our daily experience. But the only reason for which this seems to us is illogical is that in ordinary life we never move with near-light speeds and therefore faced with relativistic effects.
The slowdown in time caused by the movement with the trumpet speeds is quite simply calculated using the Lorentz transformations. So for example, Lorentz factor, i.e. The proportionality coefficient to which the time is multiplied by the following formula:
The deceleration effect starts becoming noticeable with an increase in the speed of the object: in its reference system, the time starts to flow slower. And this is not just an assumption, but the fact verified experimentally. So, for example, synchronized pairs of atomic watches are always suspended when one watches are sent to orbit, where they move with relatively high speed. At the same time, they are dispersed precisely as much as they should and due to the effect of slowing the time of the predictive relativity theory. So, for example, the watches on the ISS are lagging behind the Earth for 0.01 seconds per year.
Some unable to have this effect, it can first be reliably measured by high-precision devices, and secondly, this effect is always taken into account when designing space technology.
What is the speed of two photons moving towards each other? From the point of view of a third-party observer, the distance between two photons will vary with the double speed of light. It may impress that this is something violates in the theory of relativity, but no.
The double speed of light in this case is not the speed of the movement of a physical object in the observer reference system. This is the rate of change of distance between two photons. But the change in distance is not a physical object, the speed of each photon in the observer reference system will still be equal to the speed of light.
And what will happen if you associate an inertial reference system with one of the photons? Alas, it will not work. There can be no reference system in which the photon rests. For example, if we try to substitute the speed of light instead of V in the formula of the Lorenz factor, we will receive division on zero, which means that such an expression does not make sense.
But nothing bothers to consider us instead of photons electrons or space ships moving with 0.9 speed of light. Here with an electron or cosmic ship moving with a handful speed we can easily associate the reference system.
In the reference system of one of the ships, the clock does not go out as in the reference system of another ship and the usual formula for the addition of speeds, in which the speed of moving objects simply add up not applicable. Instead, relativistic formulas are easily derived from Lorentz transformations for speeds:
Substituting 0.9 light speed instead of V1 and V2, we can easily calculate the relative speed of two ships. It will be equal to 0.9945 light speed, i.e. Pretty close to the speed of light, but still less.