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.