28.4 Relativistic Addition of Velocities

28.4 Relativistic Addition of Velocities

The signal is different when the particle goes through a coil.

A particle is traveling through the Earth's atmosphere.

It travels 2.50 km to an Earth-bound observer.

The total velocity of a kayak, like this one on the Deerfield River in Massachusetts, is its speed relative to the water as well as the water's speed relative to the riverbank.

The kayak is being pulled by the river current.
Pushing the oars against the water can move the kayak forward in the water, but it only accounts for part of the speed.
Classical addition of velocities can be seen in the kayak's motion.
In classical physics, the velocities add up.
The kayak's velocity is the sum of the water's and the riverbank's velocities.

We only consider velocity addition to one-dimensional motion.

In one-dimensional motion, velocities add like regular numbers.
A girl is riding a sled at a speed of 1.0 m/s relative to an observer.
She throws a snowball at a speed of 1.5 m/s relative to the sled.
In this example, forward is positive and direction is plus and minus signs.
The velocities of the sled relative to the Earth, the snowball relative to the observer, and the snowball relative to the sled should be considered.

In one-dimensional motion, velocities add like ordinary numbers.

The girl throws a snowball from a sled.
The sled's speed is relative to the Earth.
The snowball's speed relative to the sled is, while its speed relative to the Earth is.

The girl throws the snowball.

The snowball will head towards the observer faster because it is thrown from a moving vehicle.
The girl throws the snowball backwards.
The snowball moves away from the observer.

Classical velocity addition does not apply to light according to the second postulate of relativity.

If classical velocity addition was applied to light, the light from the car's headlights would approach the observer on the sidewalk at a speed.
Light will move away from the car at speed relative to the driver of the car, and light will move towards the observer on the sidewalk at the same time.

Light from the car's headlights moves away from the car at speed and towards the observer on the sidewalk.

Classical velocity addition is not valid.

Light is an exception, or the classical velocity addition formula only works at low speeds.

The latter is true.

The velocity of an object relative to one observer is what is known as the relative velocity.

The term becomes very small at low velocities, and gives a result very close to classical velocity addition.
Classical velocity addition is an excellent approximation to the correct formula for small velocities.
It seems correct to us in our experience.

A spaceship heading towards the Earth at half the speed of light emits a beam of light.

Determine the speed at which the light leaves the ship and approaches the Earth from there.

Simple velocity addition is not possible because the light and spaceship are moving at very fast speeds.

We can use the speed at which the light approaches the Earth to determine the light's speed.

The knowns should be identified.

The appropriate equation can be chosen.

The knowns should be plugged into the equation.

The correct result is given by extrapolation velocity addition.

Light leaves the ship and approaches the Earth.
The relative motion of source and observer does not affect the speed of light.

If the speed of light is less than and does not exceed, velocities cannot add to it.

The following example shows the difference between classical and relativistic velocity addition.

The spaceship in the previous example is approaching the Earth at half the speed of light and shooting a canister.

We need to determine the speed of the canister by an Earth-bound observer using a different method than simple velocity addition.

The knowns should be identified.

The appropriate equation can be chosen.

The knowns should be plugged into the equation.

The knowns should be identified.

The appropriate equation can be chosen.

The knowns should be plugged into the equation.

The canister is heading towards the Earth in part and away in part, as expected, because of the minus sign.

Residual velocities do not add as much as they do classically.
The canister does approach the Earth faster, but not at the simple sum.
The total velocity is not as high as it could be.
The canister moves away from the Earth at a faster pace than you would expect.
The velocities are not symmetrical.
The canister moves faster than the ship relative to the Earth, but slower than the ship.

The frequencies and wavelength of light do not change with relative velocity.

When there is relative motion between source and observer, a Doppler shift occurs.

When the source moves away from the observer, the red shift is longer than the blue shift, which is when the source moves towards the observer.

The observed wavelength, the source wavelength, and the relative velocity of the source to the observer are all part of the equation.

Positive for motion away from an observer and negative for motion toward an observer.

The - and + signs are different from the wavelength equation.

If you're interested in a career that requires a knowledge of special relativity, astronomy is probably the best place to start.

Calculating distances, times, and speeds of black holes, galaxies, quasars, and all other astronomy objects must take into account relativistic effects.
If you want to work in astronomy, you need at least an undergraduate degree in either physics or astronomy, but a Master's or doctorate degree is often required.
A good background in high-level mathematics is required.

A universe is moving away from the Earth at a fast pace.

It emits radio waves.

The classical Doppler shift can't be used because the galaxy is moving at a relativistic speed.

The knowns should be identified.

The appropriate equation can be chosen.

The knowns should be plugged into the equation.

The wavelength of radiation the galaxy emits is expected to be redshifted because it is moving away from the Earth.