A powerful enough engine can make a spacecraft move faster and faster. That familiar sentence contains a trap: it sounds as though every speed will eventually be reached if the engine runs long enough.

Special relativity says otherwise. A spacecraft with nonzero mass can approach the speed of light in vacuum, conventionally written as c, but it cannot reach it. This is not a warning about inadequate fuel tanks or materials that have yet to be invented. It follows from the relationship between speed, energy and momentum.

The limit is also easy to describe badly. You may have heard that an accelerating object becomes heavier until its mass turns infinite. The older idea of “relativistic mass” can reproduce the calculations, but most modern treatments keep an object’s invariant or rest mass unchanged. What rises without limit is the energy needed to push that fixed mass to c, along with its momentum.

That version is both cleaner and stranger. The spacecraft never encounters a physical wall. Every finite burst of energy can move it a little closer. The final step is missing because there is no finite final step.

The infinity is visible in one factor

For a body moving at relativistic speed, its kinetic energy is written as K = (γ − 1)mc². The symbol m is the body’s invariant mass. The Lorentz factor γ is:

γ = 1 / √(1 − v²/c²)

At everyday speeds, v is tiny compared with c. The relativistic equation then gives almost the same answer as the familiar Newtonian expression, one-half mv². That is why cars, aircraft and ordinary rockets can be designed without placing the Lorentz factor at the centre of every calculation.

Near light speed, the denominator changes everything. As v approaches c, v²/c² approaches one. The quantity inside the square root approaches zero, so γ grows without bound. Kinetic energy rises with it.

Set v equal to c and the denominator becomes zero. The equation does not return a very large engineering requirement. It ceases to provide a finite energy at all. Any spacecraft with m greater than zero would require infinite energy to occupy that state.

Adding another nine becomes brutally expensive

The curve begins gently and then turns upward. At 50 per cent of light speed, γ is about 1.155, so kinetic energy is 0.155 times the spacecraft’s rest energy mc². At 90 per cent of c, γ is about 2.294 and kinetic energy is 1.294mc².

At 99 per cent, γ reaches roughly 7.089 and kinetic energy becomes 6.089mc². At 99.9 per cent, γ is about 22.366, requiring 21.366mc². At 99.99 per cent, the factor climbs to about 70.712.

Those are ideal energies for the moving object alone. They exclude the propulsion system, fuel, inefficiency, heat rejection and the energy required to slow down at the destination. A rocket that carries its own reaction mass makes the practical accounting far worse.

The important pattern is not any one number. Speed keeps approaching c while each extra nine after the decimal point demands a steep increase in energy. There is always another gap, however small.

CERN runs this experiment every day

The effect is not confined to thought experiments. CERN’s guide to particle energy and speed gives a useful comparison from the Large Hadron Collider.

At injection, a proton with 450 gigaelectronvolts of energy travels at approximately 0.999997828c. At the LHC’s 7,000 GeV design energy, more than fifteen times the injection energy, its speed is about 0.999999991c.

The additional energy is real, and it is crucial when the protons collide. It does not produce a fifteenfold increase in speed. The beam was already so close to c that most of the added energy appeared as greater relativistic energy and momentum, with only a small change in velocity.

This is why accelerator physicists talk about teraelectronvolts rather than celebrating an ever-longer string of nines. The particles can be given more energy without being pushed through the light-speed boundary.

Photons did not win a race to the limit

If massive objects cannot reach c, why does light travel there?

A photon is not a small material object that began below the limit and was accelerated through it. Photons have zero invariant mass. CERN’s explanation of the Brout-Englert-Higgs mechanism notes that the photon remains massless, unlike particles such as the W and Z bosons.

The energy-momentum relation makes the distinction precise:

E² = p²c² + m²c⁴

For a massless particle, m is zero and the relation becomes E = pc. Such a particle follows a lightlike path through spacetime and has no rest frame. For a particle or spacecraft with nonzero invariant mass, the second term remains, its path is timelike and its local speed remains below c.

It is therefore misleading to imagine a photon sitting still and then being launched. There is no valid inertial frame in which a photon is at rest. Massive and massless objects occupy different kinematic categories from the beginning.

The fastest spacecraft is still nowhere near the boundary

The speed of light in vacuum is exactly 299,792,458 metres per second. NASA’s Parker Solar Probe has reached about 687,000 kilometres per hour, the record for a human-made object.

That is roughly 191 kilometres per second, or about 0.064 per cent of c. Parker is extraordinarily fast by spacecraft standards and still travels less than one-thousandth of light speed.

More ambitious concepts change the scale without challenging the limit. SpaceDaily has examined a proposed gram-scale laser sail targeting about 20 per cent of c. At 0.2c, γ is only about 1.021, but accelerating even a gram to that speed requires an immense, precisely directed energy source. The small payload is the point.

A crewed ship would be vastly harder. Its dry mass, shielding, life support and deceleration system would all enter the energy budget. Long before relativity demanded infinity, engineering would encounter limits from fuel, heat and materials.

Time dilation does not create a loophole

People sometimes wonder whether the crew sees the situation differently. It does, but not in a way that allows the ship to catch light.

Every inertial observer measures the same vacuum light speed. A crew travelling at 99.999 per cent of c still measures a forward light beam moving away at c. Ordinary subtraction, c minus the spacecraft’s speed, does not apply because measurements of distance and time transform between moving frames.

The Max Planck Institute’s Einstein Online explains that c is the same for every inertial observer and acts as the limiting speed for matter, energy and information.

Time dilation and length contraction can make a long journey feel shorter to the travellers than it appears to people who remain on Earth. With enough acceleration, a crew could in principle cross an enormous distance within a finite amount of its own elapsed time. It still could not overtake a light signal sent from the same starting point or arrive before that signal.

Several apparent exceptions are not exceptions

Light moves more slowly through materials such as water or glass than it does through vacuum. A charged particle can exceed light’s speed in that material and emit Cherenkov radiation, the optical equivalent of a sonic boom. The particle remains below c, the vacuum limit.

Very distant galaxies can also recede from us at an effective rate greater than c because the space between us expands. General relativity describes that changing geometry. A galaxy is not locally blasting past a nearby photon with a conventional velocity greater than light.

Warp drives and traversable wormholes are attempts to alter spacetime geometry rather than accelerate a spacecraft locally through c. They remain speculative constructions with severe physical requirements, not demonstrated machines that overturn special relativity.

For an ordinary spacecraft passing through its local region of spacetime, the rule is firm. Give it finite energy and it can remain below c. Give it more finite energy and it can move closer. There is no finite amount that completes the approach.