35: Relativity
- Page ID
- 166364
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Einstein and Newton are heading out for the evening. Einstein phones to say he will wait, at rest, in his car until Newton arrives so they can drive to the bar together. Newton points out that he doesn’t drive. “No matter,” says Einstein. Ten minutes later Einstein pulls up at Newton’s house, rolls down the window, and says, “Thanks for coming to pick me up!” Newton, baffled, protests: he never moved; Einstein clearly drove over. Einstein only smiles and says: prove it.
It sounds like a joke, but the challenge is serious, and answering it overturned three centuries of physics. How would you prove which of two people moving at constant velocity is “really” moving? Every test you can think of fails. The bumps of the road would betray motion, but those come from acceleration, so let us agree to compare only inertial frames, frames moving at constant velocity (this restriction is what makes the theory special relativity). Within that rule, toss an apple, launch a toy rocket, pour a drink: every mechanical experiment comes out the same whether you call yourself moving or at rest, because every particle carries inertia. Newton himself knew this. The trouble began when physicists asked the same question of light, and the answer broke the old physics. This chapter follows that question to its conclusions: that moving clocks run slow, moving objects shorten, simultaneity dissolves, mass and energy are the same thing, and gravity is the bending of spacetime itself.
Learning Objectives
- Explain the experimental and conceptual roots of special relativity, including the Michelson–Morley result.
- State Einstein’s two postulates and the meaning of an inertial frame.
- Apply time dilation and length contraction using the Lorentz factor \(\gamma\).
- Identify which frame measures the proper time and which measures the proper length.
- Add velocities relativistically and transform coordinates with the Lorentz equations.
- Explain the relativity of simultaneity.
- Apply the relativistic Doppler effect to light, including cosmological redshift.
- Use relativistic momentum and the mass–energy relation \(E = \gamma mc^2\).
- Describe the equivalence principle and the basic predictions of general relativity.
We will return to Einstein’s challenge (“prove it”) throughout, for it is the thread that ties the whole theory together.