Why Is the Speed of Light the Limit? Relativity, Muons, GPS and the Cosmic Speed Limit

The speed of light in vacuum, c, is exactly 299 792 458 metres per second. That number is exact because the metre is now defined from it (NIST^[1]; BIPM^[2]). It is also, according to relativity, the fastest any signal or object can travel. Why should the universe have a speed limit at all, and why that one? This post walks through the reasoning, the experiments, and the popular “loopholes.” Our characters Muonaut and Orbitick live it every day.

How was the speed of light first measured?

The first good evidence that light takes time to travel came from Ole Rømer in 1676. Watching the eclipses of Jupiter’s moon Io from the Paris Observatory, he found that their timing drifted as Earth moved toward or away from Jupiter, and he correctly predicted that an eclipse on 9 November 1676 would come about ten minutes late (Phil. Trans.^[3]; Bobis & Lequeux^[4]). Rømer’s figure for light crossing Earth’s orbit was about 22 minutes; the modern value is about 16.6. He never published a speed; Christiaan Huygens turned the timing into one later. Who first proposed the light-delay explanation, Rømer or the observatory director Cassini, is still debated by historians. Our Rømer sticker sums it up: Io isn’t late. Light is.

Why is the speed of light the same for everyone?

By the late nineteenth century, light was understood as an electromagnetic wave whose speed follows from Maxwell’s equations (we tell that story in How Are Electricity and Magnetism Connected?). But speed relative to what? Experiments such as Michelson and Morley’s failed to detect any change in light’s speed as Earth moved through space. Feynman’s chapter on special relativity walks through that experiment and why it mattered (Feynman Lectures I-15^[5]).

In 1905 Albert Einstein built a theory on two postulates: the laws of physics are the same for all observers moving at constant velocity, and the speed of light in vacuum is the same for all of them (Ann. Phys.^[6]). Everything strange in special relativity follows from taking that second postulate seriously.

Why can’t anything with mass reach the speed of light?

In relativity, a moving object’s energy is E = γmc², where

γ = 1 / √(1 − v²/c²)

is the Lorentz factor. At everyday speeds γ is almost exactly 1. As v approaches c, γ grows without limit. Pushing a massive object closer and closer to c takes more and more energy, and reaching c would take an infinite amount (Feynman Lectures I-16^[7]). That is the speed limit in its most practical form: not a wall you hit, but a hill that gets infinitely steep.

Experiments confirm it. The Illinois Physics Van describes William Bertozzi’s “Ultimate Speed” experiment, in which electrons were given more and more energy and their measured speeds approached, but never exceeded, the speed of light (Illinois Physics^[8]).

What does faster-than-light travel have to do with causality?

Relativity also says that observers moving differently can disagree about the order of events that are far apart in space. For events that could be connected by a signal at or below light speed, everyone agrees which came first. If a signal could travel faster than light, some observers would see it arrive before it was sent. The University of Illinois Physics Van puts it plainly: you could see effects before their causes, such as a house destroyed before it was built (Illinois Physics^[8]). That is why the speed limit is often described as a causality limit: c is really the maximum speed at which cause and effect can propagate.

What is time dilation, and how do we know it’s real?

If light’s speed is the same for everyone, then moving clocks must run slow as seen by a stationary observer, by the factor γ. This is not a trick of measurement. It changes what happens.

Muons: particles that live longer by moving fast

Cosmic rays hitting the upper atmosphere make muons, unstable particles with a mean life of about 2.197 microseconds at rest (PDG^[9]). Even at nearly light speed, that is only enough to travel roughly 660 metres on average. Yet muons born many kilometres up reach the ground in large numbers. In 1941 Bruno Rossi and David Hall found that faster muons lived longer, as relativity requires (Phys. Rev.^[10]). In 1963 David Frisch and James Smith selected muons moving between 0.9950c and 0.9954c on top of Mount Washington, New Hampshire, and counted how many survived to sea level (Am. J. Phys.^[11]). Far more arrived than their resting lifetime would allow. In the muon’s own frame, the explanation is length contraction: the atmosphere is shorter. Both accounts agree. That is Muonaut’s sticker.

GPS: relativity in your pocket

GPS satellites carry atomic clocks whose signals must agree with the ground to within nanoseconds, because light travels about 30 cm in a nanosecond. Neil Ashby’s review of relativity in GPS explains the two competing effects: the satellites’ speed makes their clocks run slow, while the weaker gravity at their altitude (a general-relativistic effect) makes them run fast. The net is about +38.6 microseconds per day (Ashby, Living Reviews^[12]). Uncorrected, positions would drift badly within a day, so clocks are deliberately set to tick slightly slow before launch. That is Orbitick, the pre-emptive liar.

Are there things that go faster than light?

Several things seem to. None breaks the rule.

Distant galaxies receding faster than light

Because space itself is expanding, very distant galaxies are receding from us faster than light. As Phil Plait explains in Scientific American, this does not violate relativity, because nothing is moving through space faster than light locally (Scientific American^[13]). The limit applies to motion through space, not to the growth of space. Our Null Beacon and The Silence Beyond tees are about the horizons that result.

Cherenkov radiation

Light slows down in water or glass. A charged particle can move through such a material faster than light does in that material, and it then emits a cone of blue light, like a sonic boom for light. Pavel Cherenkov, Ilya Frank and Igor Tamm shared the 1958 Nobel Prize for discovering and explaining it (NobelPrize.org^[14]). The particle is still slower than c in vacuum. That is our sticker Azurwake.

Quantum entanglement

Measurements on entangled particles are correlated across any distance, but the correlations cannot be used to send a message. See What Is Quantum Measurement, Really?

The faster-than-light neutrino scare

In 2011 the OPERA experiment reported neutrinos apparently arriving early at Gran Sasso, Italy, sent from CERN. In June 2012, four experiments at Gran Sasso (Borexino, ICARUS, LVD and OPERA) reported times of flight consistent with the speed of light, and the original anomaly was attributed to a faulty element in OPERA’s fibre-optic timing system (CERN via ScienceDaily^[15]). It was a good example of science checking itself in public.

Is c really about light?

Not fundamentally. c is the speed limit of spacetime; light travels at it because photons have no mass. Anything massless must move at c, and anything with mass must move slower.

Key terms in plain English

• c: the speed of light in vacuum, exactly 299 792 458 m/s (NIST^[1]).
• Inertial frame: a viewpoint moving at constant velocity. Einstein’s first postulate says physics looks the same in all of them (Ann. Phys.^[6]).
• Lorentz factor (γ): 1/√(1 − v²/c²). It sets how much moving clocks slow and lengths contract.
• Time dilation: a moving clock runs slow as measured by a clock it passes. Measured with muons and GPS (Am. J. Phys.^[11]; Ashby^[12]).
• Length contraction: a moving object is shorter along its direction of motion, by the same factor γ.
• Causality: the principle that causes come before their effects for every observer (Illinois Physics^[8]).

How big is γ in practice?

At highway speeds, γ differs from 1 by less than one part in a trillion, which is why everyday life never shows relativity. At 87% of light speed, γ is 2: clocks run at half rate. The Frisch–Smith muons, at about 0.995c, had γ near 10. In Muonaut’s story, cosmic-ray muons at γ around 23 turn a 2.2-microsecond life into about 50 microseconds by ground clocks, enough to cross the atmosphere. GPS satellites move at only about 3.9 km/s, so their γ is barely above 1, yet the effect still adds up to microseconds per day, which matters because positioning relies on nanosecond timing (Ashby^[12]).

Does the speed limit apply to information?

Yes, and that is the strictest form of it. Relativity forbids sending any signal that could carry a message faster than c, because a signal is exactly the kind of thing that can link a cause to an effect. That is why entangled particles, expanding space and Cherenkov light do not count as violations: none of them lets anyone send a message faster than light through space. It is also why the OPERA anomaly drew so much attention, and why its resolution, a faulty timing component, mattered (CERN via ScienceDaily^[15]).

A short timeline of the speed of light

• 1676: Ole Rømer predicts a late eclipse of Io, the first good evidence that light takes time to travel (Phil. Trans.^[3]).
• 1865: Maxwell’s electromagnetic theory predicts waves travelling at the speed of light.
• 1887: the Michelson–Morley experiment finds no change in light’s speed with Earth’s motion (Feynman Lectures^[5]).
• 1905: Einstein publishes special relativity (Ann. Phys.^[6]).
• 1941 and 1963: muon experiments measure time dilation directly (Phys. Rev.^[10]; Am. J. Phys.^[11]).
• Today: the metre is defined in terms of the speed of light, so c is exact (BIPM^[2]).
• 2012: the OPERA anomaly is traced to a faulty timing component (CERN via ScienceDaily^[15]).

The bottom line

The speed of light is not really about light. It is the speed limit built into spacetime, the fastest that cause can reach effect. Massless things travel at it, massive things approach it at ever-increasing cost, and every apparent exception so far has turned out to respect it. Muons and GPS satellites check it every day.

FAQ

What is the exact speed of light?

299 792 458 m/s in vacuum, exact by definition (NIST^[1]).

Can anything go faster than light?

No object or signal can travel through space faster than c. Cosmic expansion and Cherenkov radiation are not exceptions (Scientific American^[13]; NobelPrize.org^[14]).

Does time really slow down when you move fast?

Yes. Muon survival and GPS clock corrections measure it directly (Am. J. Phys.^[11]; Ashby^[12]).

Why would faster-than-light travel break causality?

Some observers would see the effect before the cause (Illinois Physics^[8]).

See the On Cosmic Time sticker sheet and the Relativity & Cosmos collection. Next: Do Black Holes Evaporate?

References

1. NIST CODATA, speed of light in vacuum. https://physics.nist.gov/cgi-bin/cuu/Value?c
2. BIPM, “Metre” (SI base unit definition). https://www.bipm.org/en/si-base-units/metre
3. Rømer (1677), “A Demonstration concerning the Motion of Light,” Phil. Trans. R. Soc. 12, 893. https://doi.org/10.1098/rstl.1677.0024
4. Bobis & Lequeux (2008), “Cassini, Rømer and the velocity of light,” J. Astron. Hist. Herit. 11, 97. https://articles.adsabs.harvard.edu/pdf/2008JAHH...11...97B
5. Feynman Lectures on Physics, Vol. I, Ch. 15: The Special Theory of Relativity. https://www.feynmanlectures.caltech.edu/I_15.html
6. A. Einstein (1905), “Zur Elektrodynamik bewegter Körper,” Ann. Phys. 17, 891. https://doi.org/10.1002/andp.19053221004
7. Feynman Lectures on Physics, Vol. I, Ch. 16: Relativistic Energy and Momentum. https://www.feynmanlectures.caltech.edu/I_16.html
8. University of Illinois Physics Van, “Why can Nothing Exceed the Speed of Light?”. https://van.physics.illinois.edu/ask/listing/16708
9. Particle Data Group (2024), muon listing. https://pdg.lbl.gov/2024/listings/rpp2024-list-muon.pdf
10. Rossi & Hall (1941), “Variation of the Rate of Decay of Mesotrons with Momentum,” Phys. Rev. 59, 223. https://doi.org/10.1103/PhysRev.59.223
11. Frisch & Smith (1963), “Measurement of the Relativistic Time Dilation Using μ-Mesons,” Am. J. Phys. 31, 342. https://doi.org/10.1119/1.1969508
12. N. Ashby (2003), “Relativity in the Global Positioning System,” Living Rev. Relativ. 6, 1 (open full text). https://pmc.ncbi.nlm.nih.gov/articles/PMC5253894/
13. Scientific American, “How Can Galaxies Recede from Us Faster Than the Speed of Light?”. https://www.scientificamerican.com/article/how-can-galaxies-recede-from-us-faster-than-the-speed-of-light/
14. NobelPrize.org, The Nobel Prize in Physics 1958 (Cherenkov effect). https://www.nobelprize.org/prizes/physics/1958/summary/
15. CERN press release (8 June 2012), “Neutrinos sent from CERN to Gran Sasso respect the cosmic speed limit,” via ScienceDaily. https://www.sciencedaily.com/releases/2012/06/120608152339.htm

Written by Pixelated Physics. Every factual claim is linked to the source we checked; points that are still debated are labelled open.