Question

According to relativity describe how a falling object looks to an observer outside the bus.

What is the constancy of speed principle?

List three outcomes of the two principles mentioned above?

What is space-time?

Describe the space-time interaction with mass.

Describe the interaction of mass with space-time.

Answer 1

1) According to relativity describe how a falling object looks to an observer outside the bus.

As the bus and person are both traveling together the falling object inside the bus appears to be going in a straight line downwards to that person. But for a person looking from outside the object is traveling in both downwards and forward direction thus appears to be following a parabolic path

2)What is the constancy of speed principle?

The speed of light in a vacuum is the same for all observers drifting through gravity-free space (more precisely: for all inertial observers. In particular, its value it's independent of an observer's motion relative to the source of the light.

3) List three outcomes of the two principles mentioned above?

1. If the speed of light is always the same, it means that an astronaut going very fast relative to the Earth will measure the seconds ticking by slower than an Earthbound observer will — time essentially slows down for the astronaut, a phenomenon called time dilation.

2. GPS-Global positioning system

The GPS satellites use clocks that are accurate to a few billionths of a second (nanoseconds). Since each satellite is 20,300 kilometers above Earth and moves at about 10,000 km/h, there's a relativistic time dilation that tacks on about 4 microseconds each day. The difference is very real: if no relativistic effects were accounted for, a GPS unit that tells us it's a 'x' km to the next gas station would be 4 to 5 'x' off after only one day.

3.Electromagnets and electromagnetic induction

4) What is space-time?

It's a concept where we take the 3 physical dimensions of space and add time as the fourth dimension.

5) Describe the space-time interaction with mass.

Mass in this sense meaning rest mass is not appropriate as the same can be said about a moving photon(rest mass 0) As per Einstein's equations an objects energy and momentum warps spacetime

Answer 2

According to the theory of relativity, the perception of a falling object to an observer outside a moving bus is affected by two principles: the constancy of speed principle and the principle of equivalence.

1. Constancy of Speed Principle: According to this principle, the speed of light in a vacuum is constant for all observers, regardless of their motion. This means that the speed of light remains the same for an observer inside the bus and an observer outside the bus.

Three outcomes of the constancy of speed principle are:

• Time Dilation: When an object moves at high speeds relative to an observer, time appears to pass more slowly for that object. This means that the falling object inside the bus would appear to be moving in slow motion to an observer outside the bus.

• Length Contraction: As an object moves at high speeds relative to an observer, its length appears to contract in the direction of its motion. Therefore, the falling object inside the bus would appear shorter to an observer outside the bus.

• Relativistic Mass Increase: The mass of an object increases as its speed approaches the speed of light. This implies that the falling object inside the bus would appear to have an increased mass to an observer outside the bus.

2. Space-Time: In the theory of relativity, space and time are unified into a four-dimensional framework known as space-time. Space-time combines the three dimensions of space (length, width, and height) with the dimension of time.

3. Space-Time Interaction with Mass: According to the theory of relativity, mass and energy curve the fabric of space-time, creating what we perceive as gravity. Massive objects, such as planets or stars, curve the space-time around them, causing other objects to move along curved paths in their presence.

4. Interaction of Mass with Space-Time: Mass interacts with space-time by creating a gravitational field. This means that massive objects distort the geometry of space-time around them. Other objects in the vicinity, such as planets or particles, then move along the curved paths dictated by this distortion, which we observe as the force of gravity.

In summary, the theory of relativity describes how the perception of a falling object is influenced by the constancy of speed principle and the principle of equivalence. These principles lead to outcomes such as time dilation, length contraction, and relativistic mass increase. Additionally, the theory introduces the concept of space-time, where mass interacts with it by curving space-time and, in turn, is influenced by the curved geometry of space-time.