Unit 15: Special Relativity
What has to give once every observer must measure the same speed of light: simultaneity, time, length, and the rules for adding velocities together.
9 topics · 33 questions
Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.
The Postulates of Special Relativity
- How it worksHow do Einstein's two postulates, that physics looks the same in every inertial frame and light always moves at c, rebuild mechanics from scratch?
- Common mistakeWhy isn't it true that relativity means everything is relative, including the speed of light itself?
- Common mistakeWhy doesn't a spaceship chasing a beam of light ever manage to measure that beam moving any slower than c?
- Ties togetherHow does insisting the speed of light stays constant for every observer force space and time themselves to bend instead?
Your turn1 of 2
Special relativity says many quantities, like time intervals and lengths, are relative, depending on the observer's frame. Does relativity also say the speed of light is relative between observers?The Relativity of Simultaneity
- How it worksHow does light needing time to travel to each observer make simultaneity depend on your own frame of reference?
- Common mistakeWhy isn't there one single universal now that every observer in the universe would ever agree on?
- Going furtherWhat happens to the order of two events in different frames when those events are too close in time for light to connect them?
Your turn1 of 2
Two lightning strikes hit the front and back of a moving train at the exact same instant according to an observer standing on the ground beside the tracks. Does an observer riding on the train also see the two strikes as simultaneous?Time Dilation
- How it worksHow does a light clock bouncing a photon between two mirrors reveal why a moving clock ticks slow to an outside observer?
- Worked exampleFind how much time a clock moving at 0.8c measures to pass for every 10 seconds a stationary observer measures.
- How it worksWalk me through watching two light clocks, one on a moving train and one on the platform, tick out of step with each other.
- Going furtherWhat happens to the amount of time dilation as an object's speed climbs from a small fraction of c toward c itself?
- Worked exampleFind the speed at which a moving clock runs at exactly half the rate of a stationary clock.
Your turn1 of 2
Find how much time a clock moving at 7 times 0.1c measures to pass for every 13 seconds a stationary observer measures.Length Contraction
- How it worksHow does the same time dilation that slows a moving clock also compress a moving object's length as seen from outside?
- Worked exampleFind the length measured by an observer of a 10 meter ship moving at 0.6c relative to that observer.
- Common mistakeWhy doesn't length contraction shrink a moving object in every direction, only along its direction of motion?
- Going furtherWhat happens to an object's measured length as its speed relative to the observer approaches the speed of light?
- How it worksHow does length contraction leave an object's dimensions perpendicular to its own motion completely unchanged?
Your turn1 of 2
Find the length measured by an observer of a 36 meter ship moving at 6 times 0.1c relative to that observer.The Lorentz Transformation
- How it worksHow does the Lorentz transformation mix space and time together so the speed of light stays the same in every frame?
- Worked exampleFind the Lorentz factor gamma for an object moving at 0.9c.
- Ties togetherHow do time dilation and length contraction both fall directly out of the Lorentz transformation equations?
Your turn1 of 2
Find the Lorentz factor gamma for an object moving at 69 times 0.01c.Relativistic Velocity Addition
- How it worksHow does the relativistic velocity addition formula keep two combined speeds from ever exceeding c?
- Worked exampleFind the combined speed, as measured from the ground, of a ball thrown forward at 0.5c from a ship moving at 0.5c.
- Common mistakeWhy can't ordinary Newtonian velocity addition, just adding the two speeds together, ever be exactly right?
Your turn1 of 2
Find the combined speed, as measured from the ground, of a ball thrown forward at 6 times 0.1c from a ship moving at 6 times 0.1c.The Relativistic Doppler Effect
- How it worksHow does relative motion between a light source and an observer stretch or compress the wavelength they measure?
- Worked exampleFind the observed wavelength of light emitted at 500 nanometers from a source receding at 0.1c.
- Going furtherWhat happens to the observed wavelength shift as a receding source's speed climbs closer to the speed of light?
Your turn1 of 2
Find the observed wavelength of light emitted at 609 nanometers from a source receding at 6 times 0.1c.Relativistic Momentum
- How it worksHow does relativistic momentum grow with an extra factor of gamma to keep momentum conserved at high speed?
- Worked exampleFind the relativistic momentum of a 1 kg object moving at 0.8c.
- Common mistakeWhy isn't ordinary momentum, mass times velocity, exactly conserved anymore once speeds get close to the speed of light?
Your turn1 of 2
Find the relativistic momentum of a 14 kg object moving at 6 times 0.1c. Use c = 3x108 m/s.Mass-Energy Equivalence
- How it worksHow does E equals m c squared show that mass itself is just one more form energy can take?
- Worked exampleFind the energy released by converting 1 milligram of mass entirely into energy.
- Common mistakeWhy doesn't E equals m c squared mean a resting object's mass is somehow secretly moving at the speed of light?
- Ties togetherHow does mass-energy equivalence merge the separate conservation of mass and conservation of energy into one law?
Your turn1 of 2
Find the energy released by converting 14 milligrams of mass entirely into energy. Use c = 3x108 m/s.