Relativity: Space, Time, Mass-Energy, and Quantum Effects
Relativity: Concepts and Postulates
The study of relativity establishes that time and space are relative; this means that they cannot be described using an absolute reference system because the measurement of space and time depends on the observer.
Einstein’s Special Theory of Relativity
In 1905, Albert Einstein published the Special Theory of Relativity, based on two postulates:
Postulates of Special Relativity
- Postulate 1: The laws of physics are the same for all reference frames moving at a constant velocity relative to one another.
For example, if you are sitting still on a flying airplane, you are at rest relative to the airplane, but in motion relative to the Earth. - Postulate 2: The speed of light (c) in a vacuum is constant for all observers, regardless of their state of motion or the motion of the light source.
For example, an observer is at rest and watches a train pass by. From the train, a rock is tossed in the direction of the train’s motion. The observer at rest will measure the rock’s speed as the sum of the train’s speed and the speed at which it was tossed relative to the train. However, the person on the train will only observe the speed given to the rock relative to the train. Now, if the person on the train, instead of throwing a rock, turns on a lantern, the speed of light they detect would be the same as the speed detected by the person off the train.
Relativistic effects must be considered when studying a body in motion whose speed approaches the speed of light.
Fundamental Concepts in Relativity
In the study of relativity, there are three fundamental concepts affected by relative motion:
To study each of these concepts, imagine an observer at rest on Earth and another observer on a spaceship traveling near the speed of light.
The observer on Earth will measure a length L, a time interval t, and a mass m for events or objects on the spaceship. The person on the spaceship will measure the proper length 
, proper time interval 
, and rest mass 
.
Length Contraction
The length L measured by the observer on Earth will be shorter than the proper length measured by the person on the spaceship (in the direction of motion). This effect is known as length contraction. The closer the spaceship’s speed comes to the speed of light, the greater the difference between the two length measurements:
When the spaceship is at rest (v=0), the length measured by both observers is the same (L = L₀).
Time Dilation
Regarding time, the opposite occurs compared to length. The time interval t measured by the observer on Earth will be longer than the proper time interval measured by the person on the spaceship. This is called time dilation:
Mass-Energy Equivalence in Relativity
The concepts of mass and energy are not independent quantities. Mass can be converted into energy, and vice versa. Because of this, Einstein proposed that mass and energy are different manifestations of the same fundamental quantity, expressed in different units. He found the conversion factor between mass and energy, known as the mass-energy equivalence:
This equation indicates that total energy (E) is proportional to relativistic mass (m), where the proportionality constant is the square of the speed of light (c²).
The relativistic kinetic energy (KE) is given by:
Quantum Theory and the Uncertainty Principle
Quantum theory studies matter at microscopic scales (like atoms and subatomic particles) where classical physics fails, and the act of measurement inevitably disturbs the system being measured.
Planck’s Postulate and Quanta
One of the foundations of Quantum Theory is Planck’s postulate, which states that electromagnetic energy is absorbed or emitted not continuously, but in discrete packets called quanta (singular: quantum). The energy (E) of a quantum is proportional to the radiation frequency (f):
Where h is the Planck constant and f is the radiation frequency.
The Uncertainty Principle Explained
The Uncertainty Principle, formulated by Werner Heisenberg, states that it is impossible to simultaneously know the exact values of certain pairs of complementary physical properties of a particle, such as its position and momentum. We can only determine a probability distribution for these properties. Specifically, we can only determine the probability of finding a particle in a particular region of space with a particular momentum at a specific time.