Core Principles of Modern Physics: Relativity and Quantum Theory
Frames of Reference
- Inertial frame of reference: A frame at rest or moving with constant velocity where Newton’s First Law of Motion holds true and no extra forces are required.
- Non-inertial frame of reference: A frame that is accelerating or rotating where Newton’s laws require fictitious (pseudo) forces to explain motion.
Laws of Radiation
- Wien’s displacement law: The wavelength at which a body emits maximum radiation is inversely proportional to its temperature (λmax ∝ 1/T and λmaxT = Constant).
- Stefan’s law: The total energy radiated per unit surface area of a black body per unit time is directly proportional to the fourth power of its absolute temperature.
Special Theory of Relativity
Postulates
- Principle of Relativity: The laws of physics are the same in all inertial frames of reference.
- Constancy of Speed of Light: The speed of light in a vacuum is constant for all observers, regardless of the motion of the source or observer.
Key Concepts
- Proper Length: The length of an object measured in the frame of reference in which the object is at rest.
- Relativistic Mass: In special relativity, the effective mass of a particle increases as its velocity approaches the speed of light, making it harder to accelerate.
Planck’s Quantum Hypothesis
Energy is not emitted or absorbed continuously, but in discrete packets called quanta. The energy of each quantum is directly proportional to the frequency of radiation (E = hν).
Assumptions
- Energy is quantized: Energy is emitted or absorbed in discrete packets.
- Emission/absorption: Occurs only in integral multiples of hν.
- Frequency dependence: Energy depends only on frequency, not on intensity.
Matter Waves and Duality
Louis de Broglie proposed that every moving particle exhibits wave-like properties, known as matter waves.
- Wave-particle duality: Particles like electrons and protons exhibit interference and diffraction.
- Experimental evidence: Electron diffraction experiments confirmed the wave nature of matter.
- Significance: This concept laid the foundation for Quantum Mechanics.
Black Body Radiation
- Black body: An ideal object that absorbs all incident radiation, regardless of wavelength or angle.
- Black body radiation: Radiation emitted by a black body due to its temperature, characterized by a continuous spectrum.
Black Body Spectrum
A plot of the intensity of radiation versus wavelength at a given temperature.
- Continuous Spectrum: Radiation is emitted at all wavelengths.
- Temperature Dependence: As temperature increases, total energy emitted increases (Stefan-Boltzmann law) and peak wavelength shifts toward shorter wavelengths (Wien’s displacement law).
- Shape: The curve rises to a maximum and decreases at longer wavelengths.
Michelson-Morley Experiment
Conducted in 1887 to detect the luminiferous aether, the hypothetical medium for light propagation.
- Experimental Setup: Used an interferometer to split a light beam into two perpendicular paths.
- Observation: A negative result; no significant fringe shift was observed.
- Significance: Disproved the existence of aether and demonstrated that the speed of light is constant in all inertial frames, providing the foundation for the Special Theory of Relativity.