Question

Choose the best answer to each of the following. Explain your reasoning with one or more complete sentences. Which of the following is not relative in the special theory of relativity? (a) motion; (b) time; (c) the speed of light.

Short answer

(c) The speed of light.

Step-by-step solution

Understanding the Concept of Relativity

In the special theory of relativity, many quantities are considered relative, meaning they can change based on the observer's frame of reference. Motion and time are relative concepts as they appear differently to different observers.

Understanding the Concept of Invariance

In contrast, some quantities in physics are invariant, meaning they remain unchanged regardless of the observer's frame of reference. The speed of light is one such invariant quantity, as per Einstein's postulate that it is constant in a vacuum and for all observers.

Identifying the Invariant Quantity

Given the options, motion and time are relative, as their values or perception can change with different frames of reference. The speed of light, however, is invariant as it remains unchanged no matter the observer's motion or position.

Selecting the Correct Option

Based on the analysis that the speed of light is the only invariant quantity among the options, the correct answer to the question of what is not relative in the special theory of relativity is option (c) the speed of light.

Key concepts

Invariance

In the realm of physics, the term "invariance" holds a crucial role. It refers to quantities that remain unchanged regardless of who is observing them and from where. In the context of the special theory of relativity, an essential example of such an invariant quantity is the speed of light. Unlike time and motion, which change due to different observers' perspectives, the speed of light remains constant across all frames of reference.

This constancy of the speed of light suggests that no matter how you are moving or which direction you are traveling, the speed of light observed stays the same. This invariance is a central tenet of Einstein's theory, fundamentally challenging our understanding of space and time. It implies that the laws of physics are the same for all observers, no matter their motion, providing a universal constant against which other movements can be measured.

Speed of Light

The speed of light plays an extraordinary role in Einstein's special theory of relativity. It is denoted by the constant "c" and is approximately equal to 299,792,458 meters per second in a vacuum. One remarkable aspect is its constancy; the speed of light does not change, regardless of the observer's speed or direction.

This constancy leads to some fascinating implications. For instance:

• The speed of light is the same in all inertial frames, meaning it is unaffected by the relative motion of the sources or observers.
• It leads to the conclusion that nothing can travel faster than light in a vacuum, setting a universal speed limit.

The speed of light's invariance is not just a curious fact but also a cornerstone of modern physics, helping to structure our understanding of the universe on a more profound level.

Relative Motion

Relative motion describes how the movement of objects appears to change based on the observer's own motion. In classical physics, motion is straightforward, but in relativity, it's all about perspective. Imagine you're on a train moving smoothly along a track. From inside the train, it feels like you're stationary, and it's the scenery outside that is zipped by. However, to someone standing on the ground, you and the train are speeding along.

In relativity, this concept extends further:

• Observer A moving relative to Observer B will measure different values for the same event (like seeing a clock tick slower).
• This is why time and distances can vary for different observers, leading to surprising effects such as time dilation and length contraction.

The understanding of relative motion revolutionizes how we perceive the universe, emphasizing that our experiences of time and space are not absolute but relative.

Frames of Reference

A frame of reference is essentially the perspective from which observations are made. In the special theory of relativity, understanding frames of reference is fundamental. Imagine two people watching a moving car: one standing on the roadside and the other in another car driving alongside the first car. Each one has their own frame of reference.

The special theory of relativity says:

• Different observers (different frames) can experience different realities, such as different measurements of time and space.
• Inertial frames of reference, those moving at constant velocities, are particularly important because the laws of physics are identical in all of them.

Understanding these frames allows us to interpret how the same event can be observed differently depending on one's motion, making it a crucial element of understanding relativity.