The Spacetime Metric
Level 1 · FoundationsGrades 8–9About 6 hours

Matter, energy, fields, and forces

Build a physical vocabulary for what exists, what changes, and what carries influence.

Move from particles and atoms to energy accounting and fields, preparing for electromagnetism, nuclear physics, and vacuum-field ideas.

Established foundations

Before you begin

  • Course 1: Measurement, uncertainty, and evidence
  • Basic arithmetic

By the end, you can

  • Describe matter using atoms, charge, and mass.
  • Track energy transfers without treating energy as a material substance.
  • Use a field model to explain forces acting across space.
  • Apply conservation accounting to an unfamiliar device claim.

Interactive model

Explore before calculating

A field-like medium changing near matter while light follows a curved path.
Fields assign a physical quantity to every location. This advanced scene previews how a spatially varying field can change motion.

Live laboratory

Field-vector sandbox

Move a test point between two charges. Vector addition—not the nearest source alone—sets the local field direction and strength.

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Local field: (0.51, 0.00) relative units; magnitude 0.51, direction 0.0°.

Level 1 · Foundations teaching kit

Record the investigation. Teach the reasoning.

A learner-facing lab record and a course-specific instructor guide turn the live model into a repeatable classroom investigation.

Learner record

Two-source field map

How do source sign, source strength, and observation position combine into one local field vector?

Download learner record

Instructor guide

Teach for evidence, not button pushing

Learners add field contributions as vectors and distinguish a field map from material lines in space.

Download instructor guide
Open the complete print-friendly teaching kit →

Lesson 1 of 3

Atoms, mass, and charge

What common ingredients explain the enormous variety of ordinary matter?

Ordinary matter is built from atoms. Their nuclei contain protons and neutrons, while electrons occupy quantum states around the nucleus.

Mass and electric charge are different properties. Electric forces can attract or repel; gravity between classroom objects is far weaker but always attractive in ordinary situations.

atomnucleuselectronelectric charge

Worked example

A neutral atom loses one electron. What changes?

  1. 1. The number of positive protons stays the same.
  2. 2. One negative electron is removed.
  3. 3. The charges no longer cancel.

The atom becomes a positively charged ion; its identity remains set by its proton count.

Try it

Static-charge investigation

Materials: A balloon or plastic comb and small paper pieces.

  1. 1. Bring the uncharged object near the paper.
  2. 2. Rub it on dry hair or cloth.
  3. 3. Repeat at several distances.
  4. 4. Record what changes and avoid naming a cause until after observing.

Notice: Charge separation creates a distance-dependent force that can move neutral paper by polarization.

Check your understanding: Which particle count determines which chemical element an atom is?

Answer: Its number of protons.

Changing electrons makes an ion; changing neutrons makes an isotope; changing protons changes the element.

Lesson 2 of 3

Energy is an accounting rule

Where did the ability to cause change come from, and where did it go?

Energy is a conserved quantity used to compare motion, position, heat, chemical change, radiation, and mass. It is not a mysterious fluid stored in only one form.

A device can transform energy and still waste much of it as heat. A complete claim states every input, useful output, stored change, and loss over a full cycle.

kinetic energypotential energyworkefficiency

Worked example

A motor receives 100 J electrically, delivers 65 J of motion, and warms by 35 J.

  1. 1. Input: 100 J.
  2. 2. Useful mechanical output: 65 J.
  3. 3. Thermal output: 35 J.
  4. 4. Check the balance: 65 + 35 = 100 J.

The accounting closes and the useful efficiency is 65%. No energy disappeared.

Try it

Energy-chain map

Materials: Paper and a familiar device such as a flashlight or fan.

  1. 1. Draw the energy input.
  2. 2. Draw every useful output.
  3. 3. Add heat, sound, or other losses.
  4. 4. Mark any stored-energy change.

Notice: Naming the full chain prevents one impressive output from hiding a larger input.

Check your understanding: Can a machine be useful even when its efficiency is below 100%?

Answer: Yes.

Efficiency compares useful output with input; many valuable devices intentionally transform only part of the input into the desired form.

Lesson 3 of 3

Fields carry local instructions

How can an object respond to something that is not touching it?

A field assigns a value to each point in space and time. A charged particle responds to the electromagnetic field at its own location; a mass follows the local gravitational geometry.

Field diagrams are maps, not invisible strings. Their arrows or contours summarize what a suitable test object would experience.

fieldforcetest objectpotential

Worked example

Why do field arrows around a positive charge point outward?

  1. 1. Define the direction using a small positive test charge.
  2. 2. Like charges repel.
  3. 3. The test charge would accelerate away from the source.

The outward arrows encode the force direction on a positive test charge.

Try it

Map a magnetic field

Materials: A bar magnet, paper, and a compass if available.

  1. 1. Place the magnet beneath the paper.
  2. 2. Sample compass direction on a grid.
  3. 3. Draw small arrows at each point.
  4. 4. Connect the pattern without implying material lines.

Notice: The local directions form a coherent map even though the compass only samples one point at a time.

Check your understanding: What does an electric-field arrow mean?

Answer: The direction a small positive test charge would be pushed at that location.

It is a local operational definition, not a claim that a visible arrow exists in space.

Continue into the evidence