Special Relativity: Length Contraction

10 Questions

What does the concept of special relativity reveal about time and length?

Both time and length are relative.

What phenomenon occurs when objects appear shorter when moving at high speeds?

Length contraction

How does the measurement of space change according to special relativity?

It changes depending on the observer's velocity.

What is the relationship between L0 and L in special relativity?

L = L0 / sqrt(1 - v^2/c^2)

What do the two observers, one on Earth and one on a spaceship, record differently?

Both spans of time and distances for the same event

What is Δt0 in the context of special relativity?

The proper time interval, measured by the inertial reference frame

What is the significance of muons existing for longer and traveling further than expected?

It is an example of length contraction in action

What is the purpose of the concept of proper length?

To measure the length of an object in its rest frame

What is the relative velocity v in the context of special relativity?

The velocity of the spaceship relative to the Earth

Which observer sees the spaceship as shorter?

The earthbound observer

Study Notes

In special relativity, not only time but also length is relative, and it changes when approaching the speed of light.
The faster an object moves, the smaller objects appear to be, and the shorter the distance traveled seems to be.
This phenomenon is known as length contraction, where the measurement of space changes depending on the observer's velocity.
An observer on Earth and an observer on a fast-moving spaceship will record different spans of time and distances for the same event.
The earthbound observer sees the spaceship moving at velocity v, measures a distance L0 (proper length), and experiences time at the familiar rate.
On the spaceship, the relative velocity v is the same, but the time interval is different (Δt0), and the contracted length of the journey is L.
The relationship between L0 and L is given by an equation derived from the time-dilation equation.
The two observers arrive at different values for the length of the journey and the length of the spaceship, with the earthbound observer seeing the ship as shorter.
Length contraction explains how fast-moving particles can defy certain expectations, such as muons existing for longer and traveling further than expected when moving near the speed of light.
Δt0 is the proper time interval, measured by the inertial reference frame where the two events occur in the same location, while L0 is the proper length, measured by an observer at rest with respect to the objects.
In a scenario where a ship travels from Earth to another system at 90% light speed, the person on board measures the journey as 8.2 light-years, while the person on Earth would measure it as 18.8 light-years (proper length).