# Relative Velocity and Speed of Light: Detailed Explanations

The article discusses about the special theory of relativity concept that includes relative velocity and speed of light.

Relative velocity and speed of light represent the motion of the multiple bodies interacting with each other. The velocity of one of the moving bodies with respect to the other is calculated as their relative velocity. In contrast, the maximum limit to both relative velocities are the ‘speed of light’.

The velocity of any object is frame dependent. That means an object’s velocity must be estimated concerning a frame of another interacting object, even though an object is at rest or moving.

If both objects A and B are moving in the same direction, their relative velocity VAB is the sum of both velocities (VA + VB).

If both objects A and B are moving in the opposite direction, their relative velocity VAB is the difference between their velocities (VA – VB).

The relative velocity is characterized by the frame of reference of another object or observer, represented by spatial coordinates (x,y,z,t).

But there must be the greatest value to the velocity of every object, discovered by the Danish astronomer Ole Roemer. He experimented on the speed of electromagnetic EM waves traveling on the earth. He calculated that light waves required 17 minutes to traverse the diameter of our earth’s orbit. Dividing the diameter of the orbit by the time difference, the speed of light (c) is counted as 186,000 miles per second.

James Maxwell proposed that light, one of the electromagnetic waves, travels at 1,86,000 miles per second or 3.8 x 108 m/s. Einstein cultivated the special theory of relativity by hypothesizing that the speed of light value is constant and independent of the motion of its source.

As per Einstein’s relativity theory, there is a speed limit to every matter, energy, or signal that carries the information through space. That means the relative velocity between two interacting bodies has a speed limit equal to the speed of light.

## Can Relative Velocity exceed Speed of Light?

The relative velocity of any object cannot exceed the speed of light value.

All EM radiation holds massless particles. Hence, they demand less energy to achieve the speed of light. Comparatively, the particles with nonzero mass demand extremely large energy. Therefore, the EM wave travels at the speed of light, despite the frame of reference; but cannot exceed it.

Earlier, physicists assumed that there was no boundary to the speed of an object. But Einstein uncovered the speed of light (c) value in a vacuum as the speed limit for all objects on earth. That means no object can travel faster than the value 3 x 108 m/s. The relative velocity of the particular object with a non-zero mass is calculated in the frame of reference of the other object. But no observer will not witness an observer in another frame of reference approaching or exceeding the c value.

Suppose a man travels on the train and another man is standing outside the train. The man inside the train caught the man outside, passing at 30 km/hr, while the man outside glimpsed the man inside the train, passing at 250 km/hr. The question about ‘what is the actual velocity of the train’ does not have a single answer.

The train’s velocity relative to the standing man outside the train is determined by adding velocities as 30 + 250 = 280 km/hr. In comparison, the train’s velocity relative to the man inside the train is 30 km/hr. Plus, the velocity of the same train relative to the galaxy is 2,20,000 m/s.

Let’s introduce the EM waves in such an example as the train traveling at night, and the man outside the train illuminating a flash of light by torch on the man inside the train. We comprehend the train’s velocity relative to the man outside is 280 km/hr. At the same time, the light has a velocity of 3 x 108 m/s. So, the velocity of light relative to the train is 3 x 108 m/s.

If we like to calculate the speed of light relative to the man inside the train, we would say 280 + 3 x 108 = 3,00,000,280 m/s. But it is not valid. The speed of light relative to the man inside the train is still 3 x 108 as per Einstein’s theory of relativity. Because all speeds are relative, the speed of light is an absolute or universal constant value independent of the medium and frame of reference it traveled.

Therefore, no matter how rapidly the observer is moving relative to the light source, the speed of light is the same when any observer sees it. We understood that the relative velocity is acquired by adding the velocities, but it cannot exceed the c value.

## Why can’t Relative Velocities exceed the Speed of Light?

The relative velocities can’t exceed the speed of light due to the large energy necessity.

The interacting objects must keep large masses to move at a higher speed. The huge an object is, the speedier it travels. However, the objects demand an infinite amount of energy to exceed their relative velocities to the speed of light, which does not practically happen for nonzero mass objects.

Einstein developed the mass-energy equivalence that predicts the amount of energy needed to move an object having nonzero mass. E = mc2. The formula discloses to us that energy and mass quantities are interconvertibleThat means the mass can be transformed into energy and vice versa. The mass-energy equivalence defines the exchange rate between energy and mass.

EM waves discharge as a large amount of energy in the energy conversion process. The light waves only comprise protons that have zero rest mass. In the mass-energy equivalence formula, the small mass of light waves is converted into the highest possible energy to travel at the highest possible speed.

The relative velocities can exceed the speed of light only if;

• The distance between them is zero.
• The time required to travel is infinite.
• No contact or non-contact types of force are acting on both, so their acceleration is zero.
• And their masses are infinite.

So the object having infinite masses is not practical in real life. That’s why no objects or their relative velocities can’t exceed the value of the speed of light.

## Can anything go faster than the speed of light?

An object with zero mass can go faster and even reach the value of light’s speed but never exceed it.

The Large Hadron Collider (LHC) is the particle accelerator that attained the 99.99% speed of light relative to another group of protons. But to go faster than the c value, the needed energy is more than the energy consumed by the whole city.