StudySmarter - The all-in-one study app.

4.8 • +11k Ratings

More than 3 Million Downloads

Free

StudySmarter AI is coming soon!

- :00Days
- :00Hours
- :00Mins
- 00Seconds

A new era for learning is coming soonSign up for free

Suggested languages for you:

Americas

Europe

Einstein's theory of special relativity is a scientific theory that focuses on how time, speed, and space interact and how the laws of physics are the same in all inertial frames. The first step to take when studying Einstein's theory of special relativity is to study the two postulates that Einstein put forward for special relativity.Einstein's theory of special relativity…

Content verified by subject matter experts

Free StudySmarter App with over 20 million students

Explore our app and discover over 50 million learning materials for free.

Einstein's Theory of Special Relativity

- Astrophysics
- Absolute Magnitude
- Astronomical Objects
- Astronomical Telescopes
- Black Body Radiation
- Classification by Luminosity
- Classification of Stars
- Cosmology
- Doppler Effect
- Exoplanet Detection
- Hertzsprung-Russell Diagrams
- Hubble's Law
- Large Diameter Telescopes
- Quasars
- Radio Telescopes
- Reflecting Telescopes
- Stellar Spectral Classes
- Telescopes
- Atoms and Radioactivity
- Fission and Fusion
- Medical Tracers
- Nuclear Reactors
- Radiotherapy
- Random Nature of Radioactive Decay
- Thickness Monitoring
- Circular Motion and Gravitation
- Applications of Circular Motion
- Centripetal and Centrifugal Force
- Circular Motion and Free-Body Diagrams
- Fundamental Forces
- Gravitational and Electric Forces
- Gravity on Different Planets
- Inertial and Gravitational Mass
- Vector Fields
- Conservation of Energy and Momentum
- Dynamics
- Application of Newton's Second Law
- Buoyancy
- Drag Force
- Dynamic Systems
- Free Body Diagrams
- Normal Force
- Springs Physics
- Superposition of Forces
- Tension
- Electric Charge Field and Potential
- Charge Distribution
- Charged Particle in Uniform Electric Field
- Conservation of Charge
- Electric Field Between Two Parallel Plates
- Electric Field Lines
- Electric Field of Multiple Point Charges
- Electric Force
- Electric Potential Due to Dipole
- Electric Potential due to a Point Charge
- Electrical Systems
- Equipotential Lines
- Electricity
- Ammeter
- Attraction and Repulsion
- Basics of Electricity
- Batteries
- Capacitors in Series and Parallel
- Circuit Schematic
- Circuit Symbols
- Circuits
- Current Density
- Current-Voltage Characteristics
- DC Circuit
- Electric Current
- Electric Generators
- Electric Motor
- Electrical Power
- Electricity Generation
- Emf and Internal Resistance
- Kirchhoff's Junction Rule
- Kirchhoff's Loop Rule
- National Grid Physics
- Ohm's Law
- Potential Difference
- Power Rating
- RC Circuit
- Resistance
- Resistance and Resistivity
- Resistivity
- Resistors in Series and Parallel
- Series and Parallel Circuits
- Simple Circuit
- Static Electricity
- Superconductivity
- Time Constant of RC Circuit
- Transformer
- Voltage Divider
- Voltmeter
- Electricity and Magnetism
- Benjamin Franklin's Kite Experiment
- Changing Magnetic Field
- Circuit Analysis
- Diamagnetic Levitation
- Electric Dipole
- Electric Field Energy
- Magnets
- Oersted's Experiment
- Voltage
- Electromagnetism
- Electrostatics
- Energy Physics
- Big Energy Issues
- Conservative and Non Conservative Forces
- Efficiency in Physics
- Elastic Potential Energy
- Electrical Energy
- Energy and the Environment
- Forms of Energy
- Geothermal Energy
- Gravitational Potential Energy
- Heat Engines
- Heat Transfer Efficiency
- Kinetic Energy
- Mechanical Power
- Potential Energy
- Potential Energy and Energy Conservation
- Pulling Force
- Renewable Energy Sources
- Wind Energy
- Work Energy Principle
- Engineering Physics
- Angular Momentum
- Angular Work and Power
- Engine Cycles
- First Law of Thermodynamics
- Moment of Inertia
- Non-Flow Processes
- PV Diagrams
- Reversed Heat Engines
- Rotational Kinetic Energy
- Second Law and Engines
- Thermodynamics and Engines
- Torque and Angular Acceleration
- Famous Physicists
- Fields in Physics
- Alternating Currents
- Capacitance
- Capacitor Charge
- Capacitor Discharge
- Coulomb's Law
- Electric Field Strength
- Electric Fields
- Electric Potential
- Electromagnetic Induction
- Energy Stored by a Capacitor
- Equipotential Surface
- Escape Velocity
- Gravitational Field Strength
- Gravitational Fields
- Gravitational Potential
- Magnetic Fields
- Magnetic Flux Density
- Magnetic Flux and Magnetic Flux Linkage
- Moving Charges in a Magnetic Field
- Newton’s Laws
- Operation of a Transformer
- Parallel Plate Capacitor
- Planetary Orbits
- Synchronous Orbits
- Fluids
- Absolute Pressure and Gauge Pressure
- Application of Bernoulli's Equation
- Archimedes' Principle
- Conservation of Energy in Fluids
- Fluid Flow
- Fluid Systems
- Force and Pressure
- Force
- Conservation of Momentum
- Contact Forces
- Elastic Forces
- Force and Motion
- Gravity
- Impact Forces
- Moment Physics
- Moments Levers and Gears
- Moments and Equilibrium
- Pressure
- Resultant Force
- Safety First
- Time Speed and Distance
- Velocity and Acceleration
- Work Done
- Fundamentals of Physics
- Further Mechanics and Thermal Physics
- Bottle Rocket
- Charles law
- Circular Motion
- Diesel Cycle
- Gas Laws
- Heat Transfer
- Heat Transfer Experiments
- Ideal Gas Model
- Ideal Gases
- Kinetic Theory of Gases
- Models of Gas Behaviour
- Newton's Law of Cooling
- Periodic Motion
- Rankine Cycle
- Resonance
- Simple Harmonic Motion
- Simple Harmonic Motion Energy
- Temperature
- Thermal Equilibrium
- Thermal Expansion
- Thermal Physics
- Volume
- Work in Thermodynamics
- Geometrical and Physical Optics
- Kinematics Physics
- Air Resistance
- Angular Kinematic Equations
- Average Velocity and Acceleration
- Displacement, Time and Average Velocity
- Frame of Reference
- Free Falling Object
- Kinematic Equations
- Motion in One Dimension
- Motion in Two Dimensions
- Rotational Motion
- Uniformly Accelerated Motion
- Linear Momentum
- Magnetism
- Ampere force
- Earth's Magnetic Field
- Fleming's Left Hand Rule
- Induced Potential
- Magnetic Forces and Fields
- Motor Effect
- Particles in Magnetic Fields
- Permanent and Induced Magnetism
- Magnetism and Electromagnetic Induction
- Eddy Current
- Faraday's Law
- Induced Currents
- Inductance
- LC Circuit
- Lenz's Law
- Magnetic Field of a Current-Carrying Wire
- Magnetic Flux
- Magnetic Materials
- Monopole vs Dipole
- RL Circuit
- Measurements
- Mechanics and Materials
- Acceleration Due to Gravity
- Bouncing Ball Example
- Bulk Properties of Solids
- Centre of Mass
- Collisions and Momentum Conservation
- Conservation of Energy
- Density
- Elastic Collisions
- Force Energy
- Friction
- Graphs of Motion
- Linear Motion
- Materials
- Materials Energy
- Moments
- Momentum
- Power and Efficiency
- Projectile Motion
- Scalar and Vector
- Terminal Velocity
- Vector Problems
- Work and Energy
- Young's Modulus
- Medical Physics
- Absorption of X-Rays
- CT Scanners
- Defects of Vision
- Defects of Vision and Their Correction
- Diagnostic X-Rays
- Effective Half Life
- Electrocardiography
- Fibre Optics and Endoscopy
- Gamma Camera
- Hearing Defects
- High Energy X-Rays
- Lenses
- Magnetic Resonance Imaging
- Noise Sensitivity
- Non Ionising Imaging
- Physics of Vision
- Physics of the Ear
- Physics of the Eye
- Radioactive Implants
- Radionuclide Imaging Techniques
- Radionuclide Imaging and Therapy
- Structure of the Ear
- Ultrasound Imaging
- X-Ray Image Processing
- X-Ray Imaging
- Modern Physics
- Bohr Model of the Atom
- Disintegration Energy
- Franck Hertz Experiment
- Mass Energy Equivalence
- Nuclear Reaction
- Nucleus Structure
- Quantization of Energy
- Spectral Lines
- The Discovery of the Atom
- Wave Function
- Nuclear Physics
- Alpha Beta and Gamma Radiation
- Binding Energy
- Half Life
- Induced Fission
- Mass and Energy
- Nuclear Instability
- Nuclear Radius
- Radioactive Decay
- Radioactivity
- Rutherford Scattering
- Safety of Nuclear Reactors
- Oscillations
- Energy Time Graph
- Energy in Simple Harmonic Motion
- Hooke's Law
- Kinetic Energy in Simple Harmonic Motion
- Mechanical Energy in Simple Harmonic Motion
- Pendulum
- Period of Pendulum
- Period, Frequency and Amplitude
- Phase Angle
- Physical Pendulum
- Restoring Force
- Simple Pendulum
- Spring-Block Oscillator
- Torsional Pendulum
- Velocity
- Particle Model of Matter
- Physical Quantities and Units
- Converting Units
- Physical Quantities
- SI Prefixes
- Standard Form Physics
- Units Physics
- Use of SI Units
- Physics of Motion
- Acceleration
- Angular Acceleration
- Angular Displacement
- Angular Velocity
- Centrifugal Force
- Centripetal Force
- Displacement
- Equilibrium
- Forces of Nature Physics
- Galileo's Leaning Tower of Pisa Experiment
- Inclined Plane
- Inertia
- Mass in Physics
- Speed Physics
- Static Equilibrium
- Radiation
- Antiparticles
- Antiquark
- Atomic Model
- Classification of Particles
- Collisions of Electrons with Atoms
- Conservation Laws
- Electromagnetic Radiation and Quantum Phenomena
- Isotopes
- Neutron Number
- Particles
- Photons
- Protons
- Quark Physics
- Specific Charge
- The Photoelectric Effect
- Wave-Particle Duality
- Rotational Dynamics
- Angular Impulse
- Angular Kinematics
- Angular Motion and Linear Motion
- Connecting Linear and Rotational Motion
- Orbital Trajectory
- Rotational Equilibrium
- Rotational Inertia
- Satellite Orbits
- Third Law of Kepler
- Scientific Method Physics
- Data Collection
- Data Representation
- Drawing Conclusions
- Equations in Physics
- Uncertainties and Evaluations
- Space Physics
- Thermodynamics
- Heat Radiation
- Thermal Conductivity
- Thermal Efficiency
- Thermodynamic Diagram
- Thermodynamic Force
- Thermodynamic and Kinetic Control
- Torque and Rotational Motion
- Centripetal Acceleration and Centripetal Force
- Conservation of Angular Momentum
- Force and Torque
- Muscle Torque
- Newton's Second Law in Angular Form
- Simple Machines
- Unbalanced Torque
- Translational Dynamics
- Centripetal Force and Velocity
- Critical Speed
- Free Fall and Terminal Velocity
- Gravitational Acceleration
- Kinetic Friction
- Object in Equilibrium
- Orbital Period
- Resistive Force
- Spring Force
- Static Friction
- Turning Points in Physics
- Cathode Rays
- Discovery of the Electron
- Einstein's Theory of Special Relativity
- Electromagnetic Waves
- Electron Microscopes
- Electron Specific Charge
- Length Contraction
- Michelson-Morley Experiment
- Millikan's Experiment
- Newton's and Huygens' Theories of Light
- Photoelectricity
- Relativistic Mass and Energy
- Special Relativity
- Thermionic Electron Emission
- Time Dilation
- Wave Particle Duality of Light
- Waves Physics
- Acoustics
- Applications of Ultrasound
- Applications of Waves
- Diffraction
- Diffraction Gratings
- Doppler Effect in Light
- Earthquake Shock Waves
- Echolocation
- Image Formation by Lenses
- Interference
- Light
- Longitudinal Wave
- Longitudinal and Transverse Waves
- Mirror
- Oscilloscope
- Phase Difference
- Polarisation
- Progressive Waves
- Properties of Waves
- Ray Diagrams
- Ray Tracing Mirrors
- Reflection
- Refraction
- Refraction at a Plane Surface
- Resonance in Sound Waves
- Seismic Waves
- Snell's law
- Spectral Colour
- Standing Waves
- Stationary Waves
- Total Internal Reflection in Optical Fibre
- Transverse Wave
- Ultrasound
- Wave Characteristics
- Wave Speed
- Waves in Communication
- X-rays
- Work Energy and Power
- Conservative Forces and Potential Energy
- Dissipative Force
- Energy Dissipation
- Energy in Pendulum
- Force and Potential Energy
- Force vs. Position Graph
- Orbiting Objects
- Potential Energy Graphs and Motion
- Spring Potential Energy
- Total Mechanical Energy
- Translational Kinetic Energy
- Work Energy Theorem
- Work and Kinetic Energy

Lerne mit deinen Freunden und bleibe auf dem richtigen Kurs mit deinen persönlichen Lernstatistiken

Jetzt kostenlos anmeldenNie wieder prokastinieren mit unseren Lernerinnerungen.

Jetzt kostenlos anmeldenEinstein's theory of special relativity is a scientific theory that focuses on how time, speed, and space interact and how the laws of physics are the same in all inertial frames. The first step to take when studying Einstein's theory of special relativity is to study the two postulates that Einstein put forward for special relativity.

Einstein's theory of special relativity covers movement across colossal distances with a cosmic speed, the speed of light.

Einstein stated that the laws of physics are the **same **for all non-accelerating observers, and the **speed of light **in a vacuum is **constant **regardless of the observer's speed. He backed up his theory with **two simple postulates **and cautious consideration of how measurements are made.

Einstein's first postulate is about **reference frames**. A reference frame is a viewpoint used to determine the movement of an object. According to the first postulate, all velocities are measured relative to some frame of reference.

So what are **inertial frames of reference**? An inertial frame of reference is a reference frame in which a body at rest remains at rest and a body in motion continues at a constant speed in a straight line unless impacted by an outside force. This may sound familiar, since **Newton's first law **of motion says the same thing because it is based upon inertial frames of reference. Let's look at some examples.

- If a car is going on a road, its motion is measured relative to the road it is going on.
- If you throw a ball off a large cliff, the motion of the ball is measured relative to your standing point.

The laws of physics are the same and can be stated in much more simple forms in all inertial frames of reference than non-inertial ones.

Imagine you are in the back seat of a car, and the car is driving at a constant speed. The laws of physics appear to function the same way as when you're standing on the surface of the earth. Things get a little trickier when the car is moving.

**F**, the net force of an object, does not equal the multiplication of mass and acceleration (**ma**) in many instances like these. Instead, it equals **ma **plus a **fictitious ****force**. Imagine the car is going at a velocity of **10 km****/h** and you throw a ball inside the car with a velocity of **2 km/h**. You will see the ball moving at a velocity of **2km/h **while an observer standing on the side of the road will see the ball moving at a velocity of **12km/h**.

The famous equation \(E = mc^2\), which is discovered by **using the formula for the force in a near light moving frame**, is one of the most notable implications of this postulate.

Einstein's second postulate about the theory of special relativity is about the speed of light and it being a constant independent of the reference frame. Even though in the late 19th century the major tenets of classical physics predicted that light travels at \(c = 3.00 \cdot 10^8 m/s\)** **in a vacuum, they didn't specify the frame of reference in which light has this speed.

There was a contradiction between this prediction and **Newton's laws **in which velocities add like simple vectors. If this were true, then the observer moving at a velocity of c would see light as stationary, which went against Maxwell's equations. So Einstein came to the conclusion that **an object with mass **can't travel at speed c.

As a result of this reasoning, light in a vacuum must **always move at **** c** relative to any observer. Maxwell's equations are correct, and

**The general outcome **of the second postulate is that in a vacuum, the speed of light is constant at \(c = 3.00 \cdot 10^8 m/s\).

The speed of light is slower in matter, as the impact of the index of refraction from the law of refraction shows. Also, this is where special relativity is different from **general relativity**. Only **unaccelerated motion **is covered by special relativity, while **accelerated motion **is covered by general relativity.

Can time intervals or the distance travelled be different from one observer to another? Normally we expect the answer to be no, but in some circumstances, the answer may be yes to both of these questions.

The elapsed time of a class is the same for all students (observers). However, at relativistic speeds, the observer's relative velocity and the event being observed impact the elapsed time.

Time dilation is a concept that occurs when one observer moves through space relative to another observer, causing **time to flow more slowly. ** Let's imagine an observer is moving at ** v**, and the

\[\Delta t = \frac{\Delta t_0}{\sqrt{1 - \frac{v^2}{c^2}}} = \gamma \Delta t_0\]

Where

\[\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}\]

When traveling at everyday speeds, observers can and will measure the length of a car journey the same, always independently of the velocity observers are traveling at. But that does not apply under **relativistic speeds, **which are close to the **speed of light**.

Under relativistic speeds, the length that an object is moving through is measured to be less than its proper length, this is called length contraction. **The proper length** (**L0**) is the length obtained when the distance between two points is measured by an observer who is at rest relative to both points. Take a look at the example below to get a better understanding of the concept:

Let's imagine a spaceship is observed by someone on Earth and travels at a velocity of 0.750c for 9.05µs from the moment it is spotted until it vanishes. It covers the following distance:

\(L_0 = v \Delta t = (0.750) \cdot (3.00 \cdot 10^8 [m/s]) \cdot (9.05 \cdot 10^{-6} [s]) = 2.04 [km]\)

The observer on Earth will observe the proper length, Camacho - StudySmarter Originals

This is relative to Earth. In the spaceship's frame of reference, its lifetime is Δt0:

\(\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} = \frac{1}{\sqrt{1-\frac{(0.950 c)^2}{c^2}}} = 1.512\)

In the question, it says 'to an observer on Earth' so 9.05µs is Δt and you need Δt_{0} to find the length from the spaceship's reference. As we saw before:

\(\Delta t = \gamma \cdot \Delta t_0\)

Let's put the knowns in place, to get \(\Delta t_0 = 5.99 \mu s\)

Now you can find the length relative to the observer inside the ship (L)

\(L = v \Delta t_0 = (0.750) \cdot (3.00 \cdot 10^8 [m/s]) \cdot (5.99 \cdot 10^{-6} [s]) = 1.348 km\)

The observer in the spaceship will observe the length relative, Camacho - StudySmarter Originals

Finally, the distance between when the spaceship appears and when it vanishes, is **determined by who is measuring it **and how the observer moves relative to it.

While the distances are observed the same by all observers in everyday life, they can be observed differently in relativistic speeds.

The law of the conservation of energy states that energy has many forms, and each form can be converted to another without being destroyed; the energy in a system remains constant.

Energy is still conserved relativistically if its definition is changed to include the possibility of **mass converting to energy**. If we define energy to include a relativistic element, Einstein demonstrated that the law of the conservation of energy can be applied relativistically, which led to the concepts of **total energy **and **rest energy**.

Total energy ** E **can be defined as

As you may remember we defined \(\gamma\) as:

\[\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}\]

** v**, is velocity in m / s.

You can see that ** E **is related to relativistic momentum. But notice that if the velocity is zero, it will not equal zero but

The rest energy is actually defined as the famous equation below.

\[E_0 = mc^2\]

, is the rest energy in joules.

This is the **correct version **of Einstein's most famous equation, which demonstrated for the first time that energy is proportional to an object's mass when it is at rest. When energy is stored in an object, for example, its rest mass increases. This also suggests that **energy may be released by destroying mass**. Let's look at the example below to understand the concept better.

Calculate the rest energy of a 1 gram mass.

**Solution**:

Let's apply the equation.

\[E_0 = mc^2\]

In the question, m is given as 1 gram which is equal to \(1 \cdot 10^{-3}\) kg.

\(E_0 = (1 \cdot 10^{-3}) \cdot (3 \cdot 10^8)^2 = 9 \cdot 10^{13} kg \cdot m^2/s^2\)

Let's convert the unit to joules to see how much energy there is. We know that \(1 kg \cdot m^2/s^2 = 1 \space Joule\).

So the result is \(E_0 = 9 \cdot 10^{13} J\)

This is an enormous level of energy. It is about twice the amount of energy released by the Hiroshima atomic bomb.

- Einstein's theory of special relativity is a scientific theory that focuses on how time, speed, and space interact and how the laws of physics are the same in all inertial frames.
- Einstein's first postulate upon which he based the theory of special relativity is about reference frames. Einstein's second postulate is about the speed of light.
- Length contraction occurs when the length that an object moving on at relativistic speeds is measured to be less than its proper length.
- Time dilation is a concept that occurs when one observer moves through space relative to another observer, causing time to flow more slowly.
- Relativistic energy states that the energy is conserved relativistically if its definition is changed to include the possibility of mass converting to energy.

More about Einstein's Theory of Special Relativity

60%

of the users don't pass the Einstein's Theory of Special Relativity quiz! Will you pass the quiz?

Start QuizHow would you like to learn this content?

Creating flashcards

Studying with content from your peer

Taking a short quiz

94% of StudySmarter users achieve better grades.

Sign up for free!94% of StudySmarter users achieve better grades.

Sign up for free!How would you like to learn this content?

Creating flashcards

Studying with content from your peer

Taking a short quiz

Free physics cheat sheet!

Everything you need to know on . A perfect summary so you can easily remember everything.

Be perfectly prepared on time with an individual plan.

Test your knowledge with gamified quizzes.

Create and find flashcards in record time.

Create beautiful notes faster than ever before.

Have all your study materials in one place.

Upload unlimited documents and save them online.

Identify your study strength and weaknesses.

Set individual study goals and earn points reaching them.

Stop procrastinating with our study reminders.

Earn points, unlock badges and level up while studying.

Create flashcards in notes completely automatically.

Create the most beautiful study materials using our templates.

Sign up to highlight and take notes. It’s 100% free.