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University Physics III · Special Relativity · 8.04

The Lorentz transformation

The unique linear map that keeps c invariant and reduces to Galileo at low speed, x' = γ(x - vt) and t' = γ(t - vx/c-squared), with dilation and contraction as one-line corollaries; written here for a single boost along one axis with aligned axes.

Course-map guide · not a complete lesson or simulation

Scope & orientation

What this subsection covers

The unique linear map that keeps c invariant and reduces to Galileo at low speed, x' = γ(x - vt) and t' = γ(t - vx/c-squared), with dilation and contraction as one-line corollaries; written here for a single boost along one axis with aligned axes.

A strong response uses energy-momentum invariant triangles and states where the model stops being reliable.

Reasoning checklist

Evidence, assumptions and limits

01

Assumptions to state

State the system, observable, approximation, and conditions held fixed before using a model.

02

Evidence to collect

Which measurement would separate time dilation from a speed-dependent decay mechanism internal to the particle?

Read the complete note

Which measurement would separate time dilation from a speed-dependent decay mechanism internal to the particle? Useful evidence includes two competing predictions, a proposed measurement, resolution and sample-size estimates, identified confounders, and the smallest effect the design could resolve.

03

Limits to state

This GioPhysics course map is an adaptable learning sequence, not academic credit, accreditation, or a universal university syllabus.

Read the complete note

This GioPhysics course map is an adaptable learning sequence, not academic credit, accreditation, or a universal university syllabus. Third-semester content is the least standardised of the introductory sequence: departments place oscillations, waves, optics, and thermal physics differently, and the modern-physics units here are a bounded survey rather than a complete course in relativity, quantum mechanics, atomic, nuclear, or particle physics. Follow your institution's published scope, notation, laboratory programme, and assessment rules. A result should be checked against units, signs, limiting cases, and the conditions under which its model was derived.

Diagram & examples

Work the claim before choosing an equation

Interactive concept map

Follow the model from claim to evidence.

01 · Physical claimThe Lorentz transformation

The unique linear map that keeps c invariant and reduces to Galileo at low speed, x' = γ(x - vt) and t' = γ(t - vx/c-squared), with dilation and contraction as one-line corollaries; written here for a single boost along one axis with aligned axes.

02 · RepresentationThe subsection's claim

Model, evidence, and boundary

03 · TestPrediction before measurement

Which response about The Lorentz transformation is most defensible?

04 · Evidence & boundaryDecide, then qualify

Which measurement would separate time dilation from a speed-dependent decay mechanism internal to the particle?

Read the complete note

Which measurement would separate time dilation from a speed-dependent decay mechanism internal to the particle? Useful evidence includes two competing predictions, a proposed measurement, resolution and sample-size estimates, identified confounders, and the smallest effect the design could resolve.

Interactive diagram for The Lorentz transformation: follow the physical claim through its representation, proposed test, evidence, and model boundary.

modelModel, evidence, and boundary turns the stated idea into a representation that can make a prediction.

Example questions

Try the reasoning before revealing the structure.

Diagram check

Which response about The Lorentz transformation is most defensible?

Quick check

Test the reasoning, not recall

Which response about The Lorentz transformation is most defensible?

Choose an answer to test the model.