Relativity

What does relativity mean for motion?

Motion can only be measured relative to an observer, length and time are relative quantities that depend on the observer’s frame of reference.

What is Galileo’s Principle of Relativity?

Galileo’s Principle of Relativity states that the laws of motion are the same for all observers in uniform motion, which is either at rest or moving at a constant velocity. The reference frame of an observer in uniform motion is called an inertial reference frame. Hence, the laws of motion are the same in all inertial reference frames.

What does velocity depend on?

Velocity depends on the reference frame in which it is measured.

Which reference frame is more valid, observer A’s or observer B’s?

Reference frames of observers A and B are equally valid according to the Principle of Relativity which states (…). Hence, no one reference frame is absolute, meaning it is more valid than another reference frame.

What is relative velocity?

Relative velocity is the difference in velocity measured in the two reference frames.

What does Einstein’s theory of special relativity state?

Einstein’s theory of special relativity states that the laws of physics are the same in all inertial reference frames and the speed of light is an absolute constant and is the same in all inertial reference frames.

What does Einstein’s theory of special relativity state in relation to simultaneous events?

Einstein’s theory of special relativity states that events that are simultaneous in one reference frame are not simultaneous in a reference frame that is moving relative to an observer. This means that two events that appear simultaneous for a stationary observer may not be for an observer in motion.

In relativistic mechanics, what is the absolute length and time interval?

In relativistic mechanics, there is no absolute length or time interval.

What happens to time in all reference frames?

In classical physics, time is an absolute quantity, meaning that it progresses at a consistent rate throughout the universe in all reference frames. This means that the time interval between two events is the same for all observers in all reference frames.

What happens to time intervals when observed from a stationary point?

At relativistic speeds, time intervals in moving frames are dilated when observed from a stationary reference frame.

In the context of time dilation, what is the Lorentz factor equal to?

In the context of time dilation, the Lorentz factor is equal to the ratio of the time interval in the stationary observer’s reference frame (t) to the time interval in the moving reference frame (t₀).

What is the minimum value of the Lorentz factor?

The minimum value of the Lorentz factor is one, and this occurs when the time intervals measured in the stationary and moving reference frames are equal. The Lorentz factor increases with the relative velocity of two reference frames.

What is the lifetime of many subatomic particles?

Many subatomic particles have short lifetimes and exist for less than a second before decaying.

What happens when subatomic particles travel at high velocities?

When travelling at high velocities, the lifetimes of subatomic particles measured by stationary observer’s are extended due to the effects of time dilation. Furthermore, the effects of time dilation allow these particles to travel greater distances before decaying.

What are Muons?

Muons are subatomic particles produced by cosmic rays with particles in Earth’s atmosphere at an altitude of approximately 6000m.

How do the effects of time dilation impact Muons?

The effects of time dilation allow muons to travel a greater distance before decaying when measured in the reference frame of a stationary observer on Earth.

What is Length Contraction?

Length contraction is when the length of an object moving at relativistic speeds appears shorter (contracted) to an observer in a stationary reference frame.

What does one postulate of special relativity state?

One postulate of special relativity states that the law of conservation of momentum must be valid in all inertial reference frames. However, when a collision of two particles moving at relative speeds is analysed, it is found that total momentum is not conserved in the moving frame. Therefore it is necessary to modify the equations used to calculate momentum in a reference frame that is moving close to C.

What is relativistic momentum?

Relativistic momentum is defined as the product of classical momentum and the Lorentz factor.

What happens to the momentum of a particle moving at relativistic speeds?

The momentum of a particle moving at relativistic speeds is no longer directly proportional to its velocity because the Lorentz factor approaches infinity as the speed increases.

What is acceleration caused by constant force proportional to?

Acceleration caused by constant force is inversely proportional to the cube of the Lorentz factor.

Why can’t a force accelerate a particle to a speed greater than C?

A force cannot accelerate a particle to a speed higher than C because the particle’s acceleration becomes infinitely large as the speed approaches C. The amount of additional force required for each additional increment of velocity becomes larger and larger until no amount of force can raise the velocity any higher.