Question

You are floating in space when you notice a flying saucer circling you. Each time it passes in front of you, you note the reading on its clock. Do you see its clock advancing faster or slower than your wristwatch? Does the space alien see your wristwatch advancing faster or slower than his clock? Explain.

Short answer

Observing from the stationary frame of reference, both you and the alien would each see the other's clock as advancing slower due to the time dilation effect in special relativity.

Step-by-step solution

Understanding Time Dilation

Time dilation is a difference in the elapsed time measured by two observers, due to a relative velocity between them. According to Einstein's theory of special relativity, the time interval between two events is longer for an observer in whose frame of reference the events occur at different places than for an observer in whose frame of reference the events occur in the same place.

Applying Time Dilation to the Given Exercise

When you're floating in space and the flying saucer is circling around you, you're in a stationary frame of reference and the saucer is in a moving frame. This means the clock on the saucer, as observed by you, will appear to run slow because of time dilation.

Understanding the Alien's Perception

Similarly, from the alien's point of view, they are stationary and you are moving. Hence, they would also observe your wristwatch to be running slower than their clock.

Explanation

So, based on the concept of time dilation in special relativity, if you are stationary and the flying saucer is moving, you will see its clock advancing slower than your wristwatch. And the alien will see your wristwatch advancing slower than his clock. It's because in your respective frames of reference, the other party appears to be in motion.

Key concepts

Special Relativity

Einstein's theory of special relativity revolutionized our understanding of space, time, and motion. It brought about the radical notion that the laws of physics are the same for all non-accelerating observers, irrespective of their relative motion. This theory introduced the concept of spacetime, a four-dimensional continuum in which events occur.

An intriguing consequence of special relativity is that time does not pass identically for everyone. For two observers in relative motion, each will perceive the other's clock ticking at a different rate. Imagine observing a rocket ship flying past at close to the speed of light; to you, time on the rocket ship seems to slow down. However, for the astronaut inside, time feels normal, but they see time on Earth moving quickly. These differences are not due to mechanical malfunction but are fundamental features of how time behaves at high speeds.

Relative Velocity

The concept of relative velocity is vital when discussing motion in physics. It refers to the velocity of an object as observed from a particular frame of reference. Simplified, it's how fast something appears to be moving from your perspective. For example, if you're standing still and a car passes by you at 60 mph, the car's relative velocity to you is 60 mph.

In the context of special relativity, the relative velocity between objects can lead to surprising effects, such as time dilation. If two observers are moving relative to each other at significant fractions of the speed of light, each observer will measure the other's time as moving slower. However, if they compare notes, they'll find they both agree on the relative velocity between them - a symmetrical relationship.

Frame of Reference

A frame of reference is essentially the 'point of view' from which you measure and observe phenomena in physics. It can be stationary or moving, and consists of a coordinate system and a clock, allowing for measurements of position and time.

The choice of frame of reference can greatly affect what an observer perceives. For example, from your point of view on Earth, the sun appears to move across the sky. However, with a frame of reference centered on the sun, the Earth is seen to move around it. In the context of special relativity, events can appear very different depending on the relative speeds of different frames of reference, leading to effects such as time dilation or length contraction.

Einstein's Theory

Albert Einstein's theory of relativity comprises two theories: special relativity and general relativity. Special relativity, published in 1905, focuses on observers moving at constant speeds in straight lines. One of the key principles introduced in special relativity is the constancy of the speed of light. No matter your frame of reference, light travels at the same speed - about 299,792 kilometers per second.

Another central tenet is the relativity of simultaneity: Events that appear simultaneous to one observer may occur in a different sequence for another observer moving at a different speed. These principles lead to profound consequences, such as time dilation. For instance, time proceeds more slowly for someone moving at high speeds compared to someone at rest, explaining the scenario witnessed with clocks on a fast-moving spaceship versus those on Earth.