An astronaut has a heartbeat rate of 66 beats per minute as measured during his physical exam on Earth. The heartbeat rate of the astronaut is measured when he is in a spaceship traveling at \(0.5 c\) with respect to Earth by an observer (A) in the ship and by an observer (B) on Earth. (a) Describe an experimental method by which observer \(\mathrm{B}\) on Earth will be able to determine the heartbeat rate of the astronaut when the astronaut is in the spaceship. (b) What will be the heartbeat rate(s) of the astronaut reported by observers A and B?

Imagine talking on the phone with a friend who's riding the fastest train you've ever seen. As you chat about their journey, the conversation turns to time. You check your watch and notice seconds ticking away normally, but your friend's watch seems to be moving slower. That's time dilation for you! It's a mind-bending phenomenon predicted by Einstein's theory of Special Relativity. When objects move really fast, close to the speed of light, time literally slows down for them compared to someone who is at rest.

For our astronaut in the exercise, his heartbeat appears slower to an observer on Earth, even though nothing changed for him personally. He still feels his heart thumping at 66 beats per minute. Yet the observer on Earth, equipped with a stopwatch and some sophisticated lasers, measures it as just 32.97 beats per minute. This stretching of time is not a magic trick; it's the nature of our universe at high speeds – a cosmic speed limit affecting the passage of time.

The speed of light, denoted by the symbol 'c', is a universal constant, sitting at a whopping 299,792,458 meters per second. It's not just a speed limit for light, but for all matter and information in the universe. To help put this into perspective, if you could travel at the speed of light, you could zip around the Earth's equator approximately 7.5 times in just one second.

Is it possible to go faster than light? According to our current laws of physics, nope—nothing can. Speed of light is crucial to understanding time dilation, as in our spaceship example. The astronaut's movement at half the speed of light, or '0.5 c', leads to the observed slower heartbeat from Earth because his rate of time is intrinsically linked to this cosmic speed limit.

If you've ever tried to have a snack on a bumpy bus ride, you know all about reference frames. Your apple may look still to you, but to someone standing on the side of the road, it's bouncing all over the place. In physics, reference frames are basically viewpoint holders—a set of axes or a grid that you use to measure positions and motions.

When we discuss the astronaut's heart rate from his frame of reference, it remains consistent. However, as seen from Earth's frame of reference, it seems altered. This happens because reference frames can be stationary, like Earth, or moving, like our spaceship. Each frame has its own view of time and space, causing seemingly simple concepts, such as heartbeats, to become relative. Physics is like a complex dance, where every observer sees the moves differently based on where they stand.

Experiments are the heart of physics, helping to uncover the mysteries of the universe. In our example, Observer B on Earth determines the astronaut's heartbeat rate using laser pulses. Lasers are neat because they provide a clear, measurable way to transmit data across the vast reaches of space.

Experimental methods can vary from the simple, such as dropping balls from a tower to measure gravity, to the highly complex, like colliding particles in a Large Hadron Collider. Regardless of the method, the goal is the same: test theories, look for patterns, gather data, and come to conclusions. These methods illustrate how science is very much a hands-on enterprise—whether we're dealing with familiar earthly phenomena or the far-out consequences of traveling at relativistic speeds.