Question

1. Provide an example of an inertial frame of reference and a non-inertial frame of reference. Explain the difference.

2. Using the Michelson-Morley experiment as an example, explain why classical mechanics was unable to explain natural phenomena.

3. Using at least one of Einstein's "thought-experiments", explain how special relativity addresses how it is possible for observers in two different inertial reference frames to “disagree” about time and distance intervals.

4. Describe how special relativity explains the conditions under which classical mechanics breaks down. (When would you, as an observer begin to notice the effects of time dilation and length contraction?)

5. In the early 20th century, the law of conservation of mass was replaced by the law of conservation of mass-energy. Why was this change needed, and how does E=mc² relate to the special theory of relativity?

Answer 1

1. Provide an example of an inertial frame of reference and a non-inertial frame of reference. Explain the difference.

Inertial Frame of Reference : An inertial frame of reference is a non-accelerating frame of refernce (FOR). In all frames of reference which are moving uniformly relative to each other, the laws of nature must be the same. All frames of reference in which the Law of Inertia is correct are called "inertial frames".

For example, if a person is observing a moving car while at rest or while moving at constant velocity, then he is in an inertial frame of reference (FOR).

Non-inertial Frame of Reference : A non-inertial frame of reference is an accelerating frame of reference (FOR). If our frame of reference has a non-uniform or accelerated motion, then the law of inertia will appear to be wrong and we must be in a non-inertial frame of reference. Frame of reference in which the law of inertia is not correct are called "non-inertial frames".

For example, a rotating frame of reference (FOR).

4. Describe how special relativity explains the conditions under which classical mechanics breaks down.

"Special theory of relativity" is applicable to an empty, local and flat spacetime. If we extend the local frame at some distance away, then free-falling objects will looks like accelerating with respect to this local frame. In the presence of gravity, the spacetime would no longer be flat.

General relativity replaces the special relativity.

It can be shown that special relativity breaks down because there is a clear disconnect between its axiomatic concept of length contraction which is in contradiction with Maxwell's first equation. Special relativity (SR) cannot deal with mutual velocities of inertial reference systems.

5. In the early 20^th century, the law of conservation of mass was replaced by the law of conservation of mass-energy.

Why was this change needed and how does E=mc² relate to the special theory of relativity?

We know that, energy can neither be created nor destroyed but can be change from one form to another. The "law of conservation of mass" states that the total amount of mass remains constant in an isolated system in spite of any physical or chemical changes that may take place.

The law of 'conservation of energy' is one of the basic law of physics along with the 'conservation of mass' and the 'conservation of momentum'. Einstein’s theory of relativity is that mass and energy are equivalent and convertible one into the other.

Equivalence of the mass and energy is described by Einstein’s famous formula which given below as :

E = m c²

In special theory of relativity, a certain types of matter may be created or destroyed. In all of these processes, the mass and energy associated with such matter remains unchanged in quantity. It was found the rest mass an atomic nucleus is measurably smaller than the sum of the rest masses of its constituent protons, neutrons and electrons.