If Einstein changed our understanding of space, time and gravity, why do engineers still use Newton’s laws? A new theory can extend an old one while preserving it as an exceptionally useful approximation.
Einstein formulated special relativity in 1905, established an important connection between mass and energy, and completed the equations of general relativity, a new theory of gravity, in 1915. In 1905 he also made separate contributions to light quanta and Brownian motion. These are distinct results, rather than one formula explaining everything. AIP: papers and chronology.
Newtonian mechanics did not become useless
For a ball crossing a room, Newton’s laws usually supply the required accuracy. We describe force, mass, acceleration and Earth’s gravity without calculating spacetime geometry. We explored these foundations in the article on forces and Newton.
Problems arise when conditions or required precision exceed the approximation’s limits. At speeds comparable to light, Newtonian relationships between energy, momentum and motion become inadequate. Precise comparisons of clocks at different heights need gravity’s effect on time, even at low speeds. JILA/NIST: measuring gravitational clock-rate differences.
The question is therefore which effects matter in a measurement, rather than whose surname is more correct. In appropriate limits, the new equations reproduce familiar classical results.
1905: making light, motion and clocks consistent
In On the Electrodynamics of Moving Bodies, Einstein began with electromagnetic phenomena: choosing a moving observer should not invent a physical difference. He combined identical physical laws in inertial frames with constant vacuum light speed. The original 1905 paper in English translation.
The consequences changed measurement itself. Observers in uniform relative motion compare distances, time intervals and distant simultaneity differently. This is neither broken clocks nor arbitrary facts. Exact transformations connect their measurements.
Special relativity describes these relationships when gravitational effects can be neglected. In a separate short paper that year, Einstein linked changes in a body’s energy content with changes in its inertia. Modern notation writes rest energy as E_(0) = m(c)^(2). This is not the gravity equation. Library of Congress: the four 1905 papers.
1915: gravity becomes spacetime geometry
General relativity relates mass, energy, momentum and material stresses to spacetime geometry. That geometry determines the free motion of bodies and light. It involves space and time together, beyond a bent three-dimensional “surface of space.”
On 25 November 1915, Einstein presented The Field Equations of Gravitation. It contained the final form of the equations for that stage of the theory; the printed issue is dated 2 December. The primary paper.
One result explained an extra rotation of Mercury’s orbit. The direction of its closest point to the Sun slowly shifts, and observations left a residual beyond calculations including known Newtonian influences. The new theory explained this residual, rather than discovering the planet’s entire motion for the first time. Caltech Einstein Papers Project: field equations and Mercury’s perihelion.
Compare the questions in the map: high speed and strong gravity are not the only reasons to need a more precise theory.
Choose a model for the question and precision
- QuestionEveryday macroscopic motionWhat matters
Speed is far below c; gravity is weak and nearly static. Relativistic corrections fall below the allowed error.
Useful descriptionNewtonian approximation - QuestionA hypothetical free body at 0.8cWhat matters
Motion and energy are linked differently: kinetic energy is about 2.08 times the classical result. Gravity is neglected.
Useful descriptionSpecial relativity - QuestionPrecision clocks at different heightsWhat matters
Different gravitational potentials alter the comparison of clock rates; even a small effect matters.
Useful descriptionGeneral relativity
Branch · comparing modelsOptional · you can skip this
How different are the energies at 0.8c?
Take a body of rest mass m moving at speed v in a chosen inertial frame; neglect gravity. Classical kinetic energy, the energy of motion, is:
K_(N) = (m(v)^(2))/(2).
Special relativity gives:
K_(SR) = (γ − 1)m(c)^(2),
γ = (1)/(√(1 − (v)^(2)/(c)^(2))).
At v = 0.8c, γ = 5/3. The classical result is 0.32m(c)^(2); the relativistic result approximately 0.667m(c)^(2). Their ratio is about 2.08. This is a hypothetical body at an assigned speed, not actual launch data.
For v≪c, the relativistic expression approaches the classical one. The difference is tiny for an everyday ball, but cannot be ignored for our fast body. Both energies have units of m(c)^(2): kg·m²/s², or joules. OpenStax: the classical limit of relativistic energy.
The other 1905: light quanta and visible particle motion
Light striking matter can release electrons: the photoelectric effect. Einstein proposed describing light’s energy transfer in separate quanta. For the ordinary single-photon photoelectric effect, the fastest electrons’ energy depends on light frequency; increasing brightness alone does not replace sufficient frequency. A light quantum is called a photon in modern terminology. The light-quanta paper, introduction and Section 8.
Another paper linked the erratic movement of small suspended particles with thermal molecular motion in the liquid. This offered a quantitatively testable route to matter’s molecular structure. Einstein neither first saw Brownian motion nor observed atoms through an ordinary microscope. His model related visible movements of larger particles to unseen molecular impacts. The original Brownian-motion paper.
Einstein’s Nobel Prize for 1921, announced in 1922, especially recognised the law of the photoelectric effect. It should not be called a prize for general relativity. IAS: prize year, Max Planck: announcement and reason.
Branch · rest energyOptional · you can skip this
What does E₀ = mc² say about a heated box?
In E_(0) = m(c)^(2), E_(0) means rest energy, beyond energy of motion. A system’s internal energy also contributes to its mass. Imagine a box at rest before and after heating. No matter is added, but an extra 1 MJ, or (10)^(6) J, remains inside:
Δm = (ΔE)/((c)^(2)).
With c = 299 792 458 m/s, its mass increases by approximately 1.11 × 10⁻¹¹ kg, or 11.1 nanograms. Heat did not create new atoms; the system’s overall energy state changed. Energy that left the box is excluded from this difference. The formula does not guarantee a technical method to extract all rest energy from any object. OpenStax: rest energy and stored energy.
A new picture grew from shared science
Einstein’s work built on Maxwell’s electrodynamics and Planck’s quantum ideas. Developing general relativity included collaboration with mathematician Marcel Grossmann, who helped him with the geometrical tools; their joint preliminary theory was not yet the final one. Acknowledging this help describes scientific discovery more accurately without diminishing Einstein’s contribution. Max Planck: Grossmann’s role.
Test the claim: “After 1915, Newton’s laws stopped working everywhere.” No: they remain a practically accurate approximation for many slow macroscopic motions and weak gravitational fields. Low speed alone, however, does not guarantee that gravitational differences between precision clocks can be ignored.
Einstein changed the boundaries of explanation and how questions about measurement are posed. When you next read that new physics has overturned old physics, check when the predictions differ and whether the new model recovers established results in the appropriate limit.