M4 Two Models for Gravity

Newton’s Law of Universal Gravitation

F = GMm / r²

• Bigger Masses → Stronger Gravity

• Greater Distance → Weaker Gravity

Newton’s First Law

An object at rest stays at rest, an object in motion stays in motion at constant velocity unless acted on by a net external force.

Newton’s Second Law

The acceleration of an object is proportional to the net force acting on it and inversely proportional to its mass

• F = ma

Four Fundamental Forces

The four fundamental forces of nature are the basic ways objects interact in the universe

• Strong Nuclear Force

• Weak Nuclear Force

• Electromagnetism

• Gravity

Newton’s Third Law

For every action force, there is an equal and opposite reaction force.

Strong Nuclear Force

Acts between quarks (and binds protons/neutrons in nuclei)

• Relative Strength: 1

• Range: 10^-15 m

Weak Nuclear Force

Responsible for certain types of radioactive decay

• Relative Strength: 10^-5

• Range: 10^-17 m

Electromagnetism

Acts between charged particles; attractive or repulsive

• Relative Strength: 1/137

• Range: Infinite

Gravity

Acts between all objects with mass; always attractive

• Relative Strength: 10^-39

• Range: Infinite

Field

A medium in which forces (i.e. fundamental forces) are transmitted

• Exists at every point in space

• Produced by objects with a certain “charge” (mass, electric charge, etc)

• Tells other objects how strongly and in what direction to experience a force

Field Example

Electromagnetic forces are transmitted through electric fields

• A positive charge creates an electric field around it

  • Exists even if there are no other charges present

  • Electric field lines show strength + direction

Negative Charge

A negative charge placed in a field with a positive charge already in it

• The negative charge doesn’t “look for” the positive charge

• It simply responds to the local electric field at its position

Attraction happens because the field points toward the positive charge

Moving the Field

What if the positive charge moves?

• The electric field changes

• That change travels through space at the speed of light

• The negative charge feels the change when the updated field reaches it

Gravitational Fields

Gravity works the same way

• Mass creates a gravitational field

• Feld points toward the mass (gravity is always attractive)

Other masses respond to the field

• An object in a gravitational field experiences a force

  • (again, reacts to the field at its location, not directly to the object)

Quantum Field Theory Perspective on Forces

For each field, there is an associated carrier particle

• In quantum mechanics, the field is made up of discrete “quanta”, which are particles

QFT particles

Fundamental forces and their respective particles

• The electromagnetic field is made of photons

• The strong nuclear field is made of gluons

• The weak nuclear field is made of W and Z bosons

• Gravity (hypothetical in QFT) would be carried by gravitons

Virtual Photons

The particle that transmits electromagnetic forces according to QFT

• “Virtual” because they cannot be seen directly

Gravitons

Gravitons would create gravity’s gravitational field but has so far never been detected

Newton’s Gravity Law Exceptions

Newton’s Gravity Law

• Works extremely well for:

  • Falling objects

  • Planetary orbits in most cases

• But fails for extreme conditions:

  • Orbit of Mercury (precession problem)

  • Black holes

  • Gravitational bending of light (observed in 1919 eclipse)

  • Strong gravitational fields and high speeds

Einstein’s General Relativity

Proposes that gravity isn’t a “force” in the traditional sense

• Mass and energy actually bend spacetime → objects move along curved paths

Explained things that Newton’s Law couldn’t:

• Mercury’s orbit

• Black holes, event horizons

• Gravitational lensing

Though Experiment

The scenario

• You’re in a sealed room — no windows, no way to “look outside”

• A ball falls to the floor at 9.8 m/s²

• What could be happening?

1. You’re in Earth’s gravitational field → gravity pulls the ball downward

2. You’re in space, far from any planet, but the room is accelerating upward at 9.8 m/s² → the ball “falls” to the floor just as if gravity existed

Equivalence Principle

Locally, there is no experiment you can do to tell the difference between uniform acceleration and a gravitational field.

• Any experiment in that room (ball drop, pendulum swing, etc.) would behave the same in both cases

led Einstein to think of gravity not as a force, but as curved spacetime

Stage Analog

• Newtonian view:

  • Space and time are fixed, flat stage

  • Gravity is a force acting on objects, like a director moving actors

  • Objects accelerate because a “force” tells them to

• Einstein’s view (General Relativity):

  • Space and time together form spacetime, which can curve or warp

  • Mass and energy shape the stage itself

  • Objects (and light) move along the straightest possible paths in curved spacetime (geodesics)

  • Gravity isn’t a force — it’s the curvature of the stage

Visualizing Curved Spacetime

Imagine a trampoline with a heavy ball:

• The ball creates a dent in the trampoline (curvature)

• Smaller balls roll toward the heavy ball not because a “force pulls them,” but because they follow the curved surface

Precession of the Perihelion

A planet’s orbit isn’t perfectly fixed in space; its ellipse slowly rotates over time

• Perihelion = point in the orbit closest to the Sun

• Precession = gradual rotation of that closest point around the Sun

Mercury

Mercury is the closest planet to the Sun

• Strong gravitational effects and high orbital speed make precession more noticeable

• Observations in the 19th century showed Mercury’s perihelion processed slightly more than Newton’s law predicted

Mercury and General Relativity

GR says that the Sun warps spacetime

• Mercury moves along a straight path (geodisc) in this curved spacetime

• Curvature changes the orientation of Mercury’s orbit slightly with each revolution

Using Einstein’s equations (based of GR), predicted extra precession matches observations exactly

Gravitational Lensing

Objects warp spacetime around them

• Light travels along the straightest path in spacetime

• But if the spacetime is curved the “straightest path” looks bent to an outside observer

Newtonian Gravity

• Newtonian gravity treats light as massless

  • If light has no mass, gravity shouldn’t affect it at all

• General relativity predicts that spacetime itself bends, so even massless photons follow the curvature

Gravitational Lensing Practical Uses

• Discovering distant galaxies that would otherwise be invisible

• Measuring the mass of galaxies and clusters (including dark matter)

• Detecting exoplanets via microlensing

• Mapping the distribution of dark matter in the universe

Space and Time

Space and time are linked

• In general relativity, we don’t just have 3D space — we have 4D spacetime (3 space + 1 time)

• Mass and energy warp both space and time

• So, objects and light follow the straightest paths through curved spacetime, not just curved space

Gravitational Time Dilation

In regions of strong gravity (highly curved spacetime), time slows down relative to regions with weaker gravity

• Happens because mass and energy warp both space and time