Relativity, Quantum Theory, and Uncertainty
Relativity: Concepts and Postulates
The study of relativity establishes that time and space are relative. This means that they cannot be handled with an absolute reference system because the measurement of space and time will depend on the observer.
In 1905, Albert Einstein published the Special Theory of Relativity, based on two postulates:
Postulate 1
The laws of physics are the same for all referential frames that move at a constant speed compared to others.
Example: If you are sitting still on a flying airplane, you are at rest regarding the airplane, but compared to Earth, you are in motion.
Postulate 2
The speed of light (c) in a vacuum is constant to all observers, regardless of their state of motion.
Example: An observer is at rest and watches a train passing by. From the train, a rock is tossed in the direction of the train’s speed. The observer will see the rock with the speed of the train plus the speed at which it was tossed. But the person on the train will only observe the speed given to the rock. Now, if the person on the train, instead of throwing a rock, turns on a lantern, the speed at which he detects the speed of light would be the same as that detected by the person off the train.
Every time you study a body in motion and it almost reaches the speed of light, it should be considered relative motion.
In the study of relativity, there are three fundamental concepts:
- Length
- Time
- Mass
To study each of these concepts, imagine there is an observer at rest on Earth, and there is an observer on a spaceship, traveling near the speed of light.
The observer on Earth will measure an L length, a t time, and an m mass; whereas, the person on the spaceship will measure an 
length, a 
time and a 
mass.
L length for the observer on Earth will be shorter than for the person on the spaceship. The closer the spaceship comes to the speed of light, the greater the difference between the two measures of length will be:
When the spaceship is at rest, the speed is zero, and the length that both observers measure is the same.
In the case of time, the contrary happens than with length. The lapse of time for the person on the spaceship will be shorter than for the person on Earth. This is called time dilation:
Relative Relation Between Mass and Energy
The concepts of mass and energy are not quantities independent of each other. Mass turns into energy and vice versa. Because of this, Einstein proposed that mass and energy refer to the same thing but are expressed in different units. He found a conversion factor between mass and energy:
This equation tells us that total energy is proportional to relative mass, where the proportionality constant is the square of the speed of light.
The relative kinetic energy will result as follows:
Quantum Theory and Uncertainty Principle
Quantum theory deals with the study of matter when its dimensions are so small that classical physics is incapable of measuring its properties without affecting the particle itself.
One of the origins of Quantum Theory comes from the Planck postulate, which states that electromagnetic energy is absorbed or emitted in packages of integers’ multiples, known as quanta.
Where h is the Planck constant and f the radiation frequency.
The Uncertainty Principle tells us that it is never possible to know the exact value of magnitudes describing a particle’s state of motion. We can only establish a statistical distribution; specifically, we can only say that there is a certain probability that a particle is in a determined region of space at a determined time.