The Theories of Relativity: Galilean-Newtonian Relativity, Einsteinian Special Relativity, and Einsteinian General Relativity Notes

Galilean-Newtonian Relativity Theory

A theory based on intuitive understanding from daily experiences, incorporating the Galilean-Newtonian velocity addition law.

What is Galilean-Newtonian Relativity also known as?

Common-sense relativity.

What law is central to Galilean-Newtonian Relativity?

The Galilean-Newtonian velocity addition law.

How is the Galilean velocity addition law written mathematically?

vAC​=vAB​+vBC​

What does the equation vAC = vAB+vBC represent?

The velocity of object A relative to C equals A's velocity relative to B plus B's velocity relative to C.

Despite being accepted for centuries, Galilean-Newtonian Relativity was challenged by

discoveries in electromagnetic theory

If a train moves at 10 mph and a bullet is fired forward at 100 mph from the train, what is the bullet's velocity relative to the ground?

110 mph

If a person on the ground fires a bullet at 100 mph while a train moves at 10 mph in the same direction, what is the bullet's velocity relative to the train?

90 mph

A car moves at 70 mph and another at 50 mph in the same direction. What is the relative speed between them?

20 mph

Why is the relative speed between two cars moving in the same direction lower than their individual speeds?

Because their velocities are subtracted when they move in the same direction.

Two cars travel at 70 mph and 50 mph in opposite directions. What is their relative speed?

120 mph

Why is the relative speed of head-on collisions higher than rear-end ones?

Because in opposite directions, their speeds add, making the impact more severe.

If two cars are moving at 60 mph in the same direction, what is their relative velocity?

0 mph — they are at rest relative to each other.

Who formulated classical electromagnetic theory and when?

James Clerk Maxwell in the 1860s.

What do Maxwell's equations describe?

Classical electromagnetism and the wave nature of light.

What surprising result did Maxwell's equations reveal about light?

That light is an electromagnetic wave traveling at a constant speed c in a vacuum.

What is the value of the vacuum speed of light?

Approximately 300,000 km/s or 186,000 mi/s.

Why does the speed of light in Maxwell's theory seem to contradict Galilean Relativity?

Because it suggests that light travels at the same speed regardless of the observer's motion.

According to Galilean Relativity, what would be the speed of light relative to the ground if it's emitted forward from a moving train?

c+V

What does common sense say about the speed of light relative to a train if someone on the ground shines it forward?

c-V

If a train moves at speed c and a light beam is shined from the ground also at speed c, what does common sense say the beam's speed is relative to the train?

0 — the light would appear at rest relative to the train.

What does Galilean Relativity predict about a light beam moving at a right angle to a train's motion?

The beam would move at a speed different from c relative to the train.

What did the Michelson-Morley experiment aim to test?

Whether the speed of light depends on the observer's motion or the direction of the light.

What was the result of the Michelson-Morley experiment?

The vacuum speed of light is always the same, regardless of direction or movement.

How did most physicists initially react to the Michelson-Morley experiment?

Many believed the result was incorrect or flawed.

What breakthrough did Einstein make in 1905?

He proposed the theory of Special Relativity, accepting that the vacuum speed of light is constant.

What inspired Einstein's belief in the constancy of light speed?

The mathematical beauty and implications of Maxwell's equations.

What does Einstein's theory say about time and moving objects?

Moving clocks run slower—a phenomenon called time dilation.

What is an example of time dilation from daily life?

A person walking with a phone experiences slightly slower clock time than someone stationary.

OR

If one twin travels at high speeds and returns, they would be younger, than their twin who stayed at home due to time running slower for the traveling twin

Has time dilation been experimentally confirmed?

Yes, with atomic clocks on airplanes and the extended lifetimes of fast-moving particles.

Why is time dilation important in modern technology?

It ensures accuracy in systems like GPS, which rely on precise clock synchronization.

What does Special Relativity predict about moving objects?

They contract in length in the direction of motion—this is called length contraction.

Why don't we notice length contraction in everyday life?

The effect is extremely small at ordinary speeds.

How do time dilation and length contraction preserve the constancy of light speed?

They adjust time and distance so that speed = distance/time remains constant at c.

Why can't the Galilean velocity addition law be correct at high speeds?

Because it doesn't preserve the constancy of the speed of light.

What is the correct law of velocity addition according to Einstein?

The Lorentz-Einstein velocity addition law.

What does the Lorentz-Einstein velocity law account for?

The relativistic effects of time dilation and length contraction at high speeds.

According to Special Relativity, what happens to an object's mass as it approaches the speed of light?

Its mass increases

Why can no object with mass reach the speed of light?

It would require infinite force, as its mass would become infinite.

What is the universal speed limit according to Einstein?

The speed of light, c.

What types of particles can travel at the speed of light?

Only massless particles like photons.

Can anything with mass ever reach or exceed the speed of light?

No, it can only approach but never reach c.

What happens to the mass of a subatomic particle as it approaches the speed of light?

It increases, exactly as predicted by Einstein's equations.

What does the equation E = mc^2 represent?

The equivalence of mass and energy. E is energy, m is mass, and c is the speed of light squared.

How does E = mc^2 apply to nuclear reactions?

In exothermic reactions, mass is lost; in endothermic reactions, mass is gained.

When did Einstein first propose the equation E = mc^2?

In 1906, before the atomic nucleus was discovered.

How did Einstein suggest E = mc^2 could be tested?

By studying radioactivity, before it was known to be a nuclear process.

Who introduced the concept of spacetime?

Hermann Minkowski, Einstein's former teacher.

What is spacetime?

A four-dimensional reality combining the three spatial dimensions and time.

How is time represented in spacetime equations?

As ct, where c is the speed of light and t is time.

Einstein's theory of Special Relativity revealed that we live in a four-dimensional universe, consisting of three spatial dimensions

(length, width, height - x, y, z)

Why is spacetime important in Special Relativity?

It explains phenomena like time dilation, length contraction, and mass-energy equivalence.

What does the term "spacetime" reflect?

The idea that space and time are not separate, but unified.

What is a fictitious (or pseudoforce)?

A force that appears to exist in a non-inertial (accelerating) frame of reference but doesn't correspond to a real interaction.

Why do you feel pushed into the backrest when a car accelerates?

Due to a fictitious backward force felt in the accelerating car frame.

Why does the rearview mirror swing backward when a car accelerates?

Because the car moves forward, and objects inside resist that motion, creating an apparent backward force.

Why do you feel pushed forward when a car suddenly brakes?

Due to a fictitious forward force experienced as the car decelerates.

Why does the rearview mirror swing forward when braking?

Because it continues moving while the car slows down, creating an apparent forward motion.

Why do you feel pulled to the right when a car turns left?

It's a fictitious rightward force caused by the car's leftward acceleration.

What's really happening during a left turn when you feel pulled right?

You're trying to continue in a straight line, while the car turns left around you.

What is the Coriolis force?

A fictitious force that makes moving objects appear to curve in a rotating frame of reference.

What causes the apparent deflection of projectiles in a rotating frame?

The rotation of the frame itself, not an actual force on the object.

How does the Coriolis force behave in different rotations?

Counterclockwise rotation deflects right; clockwise deflects left.

Does the Coriolis force affect an object's speed?

No, it only affects direction, not speed.

What happens to the Coriolis force if the rotation stops?

It disappears completely.

What does acceleration refer to?

Any change in an object's motion—speeding up, slowing down (deceleration), or changing direction.

What do all examples of fictitious forces have in common?

They occur in accelerating (non-inertial) frames of reference.

What is an inertial frame of reference?

A non-accelerating frame where no fictitious forces appear.

What is a non-inertial frame of reference?

An accelerating frame where fictitious forces appear.

How are inertial and non-inertial frames related?

All inertial frames are not accelerating relative to each other; non-inertial frames are accelerating relative to inertial ones.

In which type of frame do the laws of physics apply naturally?

Inertial (non-accelerating) frames.

What is Special Relativity limited to?

Inertial frames of reference.

Why is it called "Special" Relativity?

Because it applies only to special (non-accelerating) inertial frames.

Why was Einstein dissatisfied with Special Relativity?

It didn't apply to non-inertial (accelerating) frames of reference.

What theory did Einstein develop to expand beyond inertial frames?

General Relativity.

What does General Relativity allow that Special Relativity doesn't?

It applies to all frames of reference, including accelerating ones.

How did Einstein relate fictitious forces to gravity?

He realized that fictitious forces in accelerating frames behave like gravitational forces.

How can gravity be simulated in space?

By accelerating a spaceship at 9.8 m/s², astronauts feel gravity like on Earth.

What does this imply about gravity?

Gravity can be turned "on" in accelerating frames of reference.

What happens if an elevator cable breaks and it falls freely?

Passengers feel weightless because they and the elevator are accelerating downward together.

Why do objects inside a falling elevator appear to float?

Because everything falls at the same rate, so there's no relative motion.

Why is gravity "turned off" in a freely falling frame?

A fictitious force cancels out the gravitational force inside the accelerating frame.

What counts as free fall?

Any motion under the influence of gravity alone (e.g., falling, orbiting, projectile motion).

Why do astronauts feel weightless in orbit?

They are in a freely falling frame, even though Earth's gravity is still acting on them.

Do astronauts falling toward a planet feel increasing gravity?

No, they feel weightless the entire time because they are freely falling.

What does General Relativity say about gravity?

Gravity is the curvature of four-dimensional spacetime.

How does spacetime geometry differ between Special and General Relativity?

Special Relativity assumes flat spacetime; General Relativity allows curved spacetime.

What is unique about General Relativity's treatment of frames of reference?

It treats all frames—both inertial and non-inertial—as equally valid.

What two factors cause time dilation in General Relativity?

Motion (kinematic time dilation) and gravity (gravitational time dilation).

How does gravity affect time?

Stronger gravity slows down time more than weaker gravity.

Why don't we notice gravitational time dilation in daily life?

Earth's gravity is too weak to produce noticeable differences over short distances.

What happens to two atomic clocks on different floors of a building?

The lower clock runs slower due to stronger gravity than the higher one.

How would identical twins age if one spent time on the ground floor and the other on the second floor?

The twin on the ground floor would age slightly slower.

Why do our feet age more slowly than our heads?

They are closer to Earth's center of gravity, where gravity is stronger.

Why must GPS systems account for time dilation?

Because satellites experience both gravitational and kinematic time dilation.

Is the speed of light still constant in General Relativity?

Yes, the vacuum speed of light (c) is invariant in both Special and General Relativity.

What causes kinematic length contraction?

Motion, as in Special Relativity.

What causes gravitational length contraction?

Gravity—stronger gravitational fields cause more contraction.

What happens when light travels downward into stronger gravity?

Its wavelength contracts (blueshift); frequency increases.

What happens when light travels upward into weaker gravity?

Its wavelength stretches (redshift); frequency decreases.