A warning light in the engine of a fast-moving train flashes once each second according to a clock on the train. Will an observer on the ground measure the time between flashes to be greater than, less than, or equal to 1 second? Explain? A warning light on the ground flashes once each second. Will an observer in a fast-moving train measure the time between flashes to be greater than, less than or equal to 1 second? Why?

Peter volunteers to serve on the first mission to visit Alpha Centauri. Even traveling of 80% of the speed of light, the round-trip will take a minimum of 10 years. When Peter returns from the trip, how will his biological age compare with that of his twin brother Paul, who will remain on Earth?

Is it physically possible for a 30-year-old college professor to be a natural parent of 40-year-old student? Is it possible for length contraction to occur without time dilation? Explain. Suppose the meter stick zips by you at a speed only slightly less than the speed of light. If you measure the length of the meter stick as it goes by, would you determine it to be longer than, shorter than, or equal to 1 meter long? Why?

A constant force acts on a proton and causes it to speed up. Does the magnitude of the proton’s acceleration increase, decrease, or remain constant as its speed gets closer and closer to the speed of light? Why is not correct to claim that “matter can neither be created or destroyed?

Muons are created in the upper atmosphere, thousands of meters above sea level. A muon at rest has an average lifetime of only 2.2 microseconds, which would allow it to travel a maximum distance of 660 meters before disintegrating. However, most muons created in the upper atmosphere survive to strike Earth. This effect is often explained in terms of time dilation. In this explanation, is the observer in the reference system of Earth or the muon? Explain.

General Theory of Relativity

Inertial Mass = Gravitational Mass

Principle of Equivalence

The principle of equivalence states that observations made in an accelerated reference system are indistinguishable from observations made in a Newtonian gravitational field.

An astronaut awakes in her closed capsule, which actually sits on the moon. Can she tell whether her weight is the result of gravitation or acceleration motion? Explain. You wake up at night in your berth on a train to find yourself “pulled” to one side of the train. You naturally assume that the train is rounding a curve but you are puzzled that you don’t hear any sounds of motion. Offer another possible explanation that involves only gravity, not acceleration in your frame of reference.

Bending of Light by Gravity

According to the principle of equivalence, if light is deflected by acceleration, it must be deflected by gravity.

Einstein predicted that starlight passing close to the sun would be deflected by an small, but measurable angle.

Gravity and Time

According to Einstein’s general theory of relativity, gravitation causes time to slow down.

1.Why we do not usually notice bending of light? 2.Spaceship A is traveling through deep space with twice the acceleration of spaceship B. If the passengers on the two spaceships believe that they are actually sitting on planets with identical masses, which passengers believe their planet has the smaller radius? Why?