If a spaceship approaching Earth at 0.9 times the speed of light shines a laser beam at Earth, how fast will the photons in the beam be moving when they arrive at Earth?

Special relativity is a theory in physics proposed by Albert Einstein in 1905. This theory revolutionized the way we understand space, time, and motion. The core idea is that the laws of physics are the same for all non-accelerating observers. One major aspect of special relativity is that it introduced the concept that space and time are intertwined into a single four-dimensional continuum known as spacetime.
The theory relies on two postulates:

• The laws of physics are the same in all inertial frames of reference.
• The speed of light in a vacuum is constant and independent of the motion of the source or observer.

These ideas lead to phenomena such as time dilation and length contraction, which have been confirmed by numerous experiments and observations.
For example, as an object moves closer to the speed of light, time for that object slows down relative to an observer at rest. Similarly, lengths contract along the direction of motion.

One of the most fascinating aspects of special relativity is the constancy of the speed of light. Unlike other speeds, which can add up or subtract depending on the observer's frame of reference, the speed of light remains constant at approximately \(3 \times 10^8 \ \text{m/s}\).
Regardless of whether the light source is moving towards you, away from you, or is at rest, the speed of light will always be the same.
This unchanging speed of light has significant implications:

• It means that no matter how fast a spaceship is moving, if it shines a light beam, the light beam will always travel at \(3 \times 10^8 \ \text{m/s}\) relative to any observer.

In our exercise, it doesn't matter that the spaceship is approaching Earth at 0.9 times the speed of light. The photons in the laser beam will still reach Earth at the same constant speed of light.

In classical physics, when we consider the motion of a source and an observer, we usually think about how their velocities add up or cancel out each other. For instance, if you're in a car moving at 60 km/h towards another car moving at 60 km/h, classical mechanics suggests you approach each other at 120 km/h combined.
However, special relativity changes this notion when we deal with light. Light's speed remains constant, no matter how fast the source or the observer is moving.
Let's apply this to our spaceship example. Even though the spaceship is moving towards Earth at 0.9 times the speed of light, any light emitted from the spaceship - like the laser beam from our exercise - will travel to Earth at the speed of light, \(3 \times 10^8 \ \text{m/s}\).
This outcome is a direct consequence of special relativity. It tells us that velocities of objects moving close to the speed of light do not simply add up straightforwardly but are subject to the same laws governing the constancy of light speed.