Does mass increase with speed?
- kieronconway
- Mar 19
- 6 min read
Mass and Light-speed
How often have you heard someone say that as an object approaches the speed of light, its mass increases?
Historically, physicists used a quantity called relativistic mass, which does increase with speed and would approach infinity as the speed of light is approached.
However, modern physics has largely abandoned this idea because it causes so much confusion.
Today, physicists use the term rest-mass (also called invariant mass), which is the same value for everyone, whether they are stationary or in motion.
Two definitions of mass
So, there are two definitions of mass.
Rest-mass (m₀) This is the intrinsic mass of an object and is considered to be a fundamental property of an object.
Relativistic mass (m) This is an older concept where relativistic mass does increase with speed.
Because relativistic mass depends on motion, it cannot be considered to be a fundamental property as it has a different value for each observer, depending on their velocity relative to the body, which is having its mass measured.
This term is now rarely used in modern physics.
The two values are related.
How are m₀ & m related?
Rest-mass is independent of motion, either motion of the mass itself or motion of the observer measuring the rest-mass.
Relativistic-mass includes the speed of the object and of course this depends on the relationship between the movement of the mass and the observer measuring the mass.
The relationship between the two values is defined in terms of their energy.
Energy and motion
Let's start with Einstein’s famous equation: E = mc², which is often misunderstood.
In modern physics it really means: E₀= m₀c² , which is the rest-energy of a body at rest. This is the intrinsic energy of a body, which is an invariant constant.
When an object moves, its total energy becomes: E=γm₀c², where γ is known as the “Lorentz factor” after the man who first formulated it and it shows up everywhere in Einstein's special relativity.
Basically, the Lorentz factor allows you to use your version of a parameter, measured in your own frame of reference, to determine how it looks in a frame of reference that is in motion relative to you.
The Lorentz factor is:
The squiggle (γ) is the Greek letter gamma. Note that v is the velocity of the object as you measure it and c is the velocity of light.
In the following text, it is written as; γ = 1 / SQRT(1-(v²/c²))
The Lorentz factor only becomes significant as a body starts to approach the speed of light.
When v is much smaller than c, then v²/c² becomes very small and one minus a very small number is close to 1, so gamma becomes 1 and the relativistic effect vanishes.
You'll see the relationship v²/c² pops up everywhere and what it does in the equation E=γm₀c² is provide a value for energy that accounts for the body's velocity.
Relativistic Energy
Let's look at E=γm₀c² in full: it becomes;
E = (m₀c²) / SQRT(1-(v²/c²))
Squaring both sides of the equation to get rid of the square root, we get;
E² = (m₀c²)² / (1-(v²/c²))
and with a simple bit of algebra and using the definition of relativistic momentum, where p = γm₀v (momentum is normally designated 'p'), this produces;
E² = p²c² + (m₀c²)²
(NOTE: For a full derivation of this equation go to the following URL: https://energywavetheory.com/equations/epc/ and follow from section 2.6.8 onwards.)
This is known as the full energy momentum equation and shows how the relativistic energy of a body of rest-mass m₀ is composed of relativistic momentum and invariant rest-mass.
This is the most fundamental equation describing a particle and this includes photons as we'll see.
What happens to a particle as its velocity approaches c?
A particle's momentum grows rapidly as speed approaches the speed of light making further acceleration increasingly difficult because both total energy and momentum grow without bounds.
To reach light speed, a particle's total energy and momentum would become infinite and this is a physical impossibility. This limitation also applies to spaceships!
You are reduced to pumping in more and more energy into a particle travelling at close to light speed, just to get a minute amount of additional velocity.
The rest mass of the particle remains unchanged throughout.
What about a photon?
Photons have no rest-mass so, for a photon, the energy momentum equation reduces to;
E² = p²c² so, E = pc
Even though a photon has no mass, it has energy and is in motion so, it must have momentum 'p'.
The velocity of light is equal to its frequency times its wavelength, c = fλ so,
E = pfλ
From quantum mechanics we know that a photon's energy is also given by;
E = hf
where h is Planck's constant. So,
E = pfλ = hf
Dividing both sides of pfλ = hf by fλ gives us the momentum of a photon;
p = h/λ
This makes perfect sense as blue light, with the shortest wave-length of visible light, has more momentum (and hence energy) than red light, which has a longer wave-length.
This concept was extended to particles because of the wave/particle duality by Louis de Broglie, who assigned a wavelength to a particle, which is known as the de Broglie wavelength, named after the physicist who gave matter a wavelength.
λ = h/p
The big difference between a photon and a particle is that a photon's momentum depends on its wavelength (or frequency) and not on its speed, which is always c.
The modern viewpoint of mass
Physicists today say:
Mass (rest-mass) is invariant and does not increase with speed.
As an object's velocity increases, its energy and momentum increase, making further acceleration increasingly difficult.
So if someone says “mass increases with speed,” they are using outdated terminology, which is no longer used in modern physics.
The key takeaway is:
Rest-mass is always constant, only energy and momentum increase with speed.
E² = p²c² + (m₀c²)²
Photons, with no rest-mass, travel at a constant velocity of c, but their energy is proportional to frequency.
E = pfλ = hf
How do you measure rest-mass?
Mass needs to be measured in the mass's rest frame.
You can measure a macroscopic body (something you can see with the naked eye) by weighing it, which measures the gravitational force on the body. This measurement of weight allows mass to be inferred for a macroscopic body.
A particle or atom's mass is measured indirectly by a number of methods. We'll only look at one method, which involves; E² = p²c² + (m₀c²)²
Measuring mass in a particle accelerator
In particle accelerators, you can measure the energy and momentum of a particle and derive the rest-mass from the energy-momentum equation.
Specialised detectors track the particle trails and provide measurements of energy and momentum.
Momentum of charged particles
If charged particles are directed into strong magnetic fields, they bend and there is a relationship between the strength of the magnetic field and the radius of curvature of the particle's track that can be used to calculate momentum.
At places like CERN, computers are used to analyse the curved tracks and provide a measurement of momentum.
And, if the particles are moving really fast, then the calculations must include relativistic effects.
Momentum of neutral particles
To measure a neutral particle's momentum, physicists measure the momentum of charged particles produced when the neutral particle decays or collides with charged particles and through conservation of momentum, the momentum of the neutral particle can be determined.
Total energy measurements
To measure a particle's total energy, it is directed into a device that stops it dead, releasing a cascade of secondary particles from both its kinetic energy and its rest-mass energy.
By measuring the secondary particles' total energy, that of the unknown particle can be determined.
Once momentum and energy are known, the rest mass can be determined and it never changes with speed!
© 2026 Kieron Conway - All rights reserved.
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