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Let's take an example, where A is a photon moving with the speed of light, and B is a car, that moves with half of the speed of light

At t=0, a kid in B(thinking that the car is not moving) observes that B is 4.5 million kms away from A(initial position of the photon=4.5 million kms), and both start to move towards each other. After 1 second on the kid's watch, he observes that he and the light are in contact, so that would mean the distance between them is 0 kilometres, so he would consider the final position of the photon=0km

So if he calculates the speed of the photon, by using: (initial position-final position)/time taken, i.e, 1 second on his watch

Won't he get (4.5*10^6)/1 =4.5*10^6km/second?

What else needs to be considered in this calculation?

Edit: Most of you must be downvoting because I haven't considered the time dilation. But the time dilation again is built on the fact that the speed of light is constant, isn't it?

Swaroop Joshi
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This is how the situations looks for us, static external observers – we see a car and a photon separated by $1.5c\cdot 1$s and travelling with $v_{ph}=-c$ and $v_{car}=0.5c$ velocities. After a second they meet.

However, for an observer in the car the situation is completely different: except for $v_{ph}$, every quantity mentioned above is different! We intuitively know that in this frame $v_{car}$ differs (as you observed it's 0), but we are not used to the fact that time and distance also differ between observers.

You can calculate them using appropriate Lorentz boost.

Paweł Czyż
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After 1 second on the kid's watch, he observes that he and the light are in contact, so that would mean the distance between them is 0 kilometres, so he would consider the final position of the photon=0km

Well, that cannot be true. You are arbitrarily taking a value as its speed. There have been so many experiments and measurements proving that the speed of light has an upper bound and it is nearly $3 \times 10^8$ meters per second in vacuum and is slower in other media by their respective refractive indices.

You can try some of them at home to convince yourself.

There are so many successful results derived from taking speed of light as a constant as can be seen from experimental basis of special relativity and tests of special relativity. We are well justified in considering it as an axiom.

PolaroidDreams
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and both start to move towards each other.

If a kid started moving after determining the distance from the photon, then he changed his reference frame. He should measure the distance from he photon again, because it changes due to Lorentz contraction. In your case, the newly measured distance would be exactly one light second, which would lead to no observable change in the light speed.

What is important for measuring the speed is that the time difference and distance need to be measured in the same reference frame.

Adam Latosiński
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