Why Can't Anything Travel Faster Than Light?
The short answer
Because anything with mass would need infinite energy to reach light speed. Light moves at 299,792 km (about 186,000 miles) per second in empty space. That is fast enough to lap Earth about 7.5 times in one second. The closer an object gets to that speed, the more each extra bit of speed costs.
Only things with no mass, like light, travel at exactly that speed. Gravity does too. Anything with mass can only get closer. And the closer it gets, the slower its clock runs compared with clocks back home.
Why each extra nine costs more
Physics textbooks give an object's kinetic energy as (γ · 1)mc². Here m is its mass, c is the speed of light, and γ (gamma) is a stretch factor that grows without limit as the speed nears c. So the energy needed has no ceiling.
Put in real speeds and the cost climbs fast. From rest, 99% of light speed takes about 6.1 mc². Getting to 99.9% takes about 21.4, and 99.99% about 69.7. Each new nine costs more than twice everything spent before it. That holds for every nine from 90% up, but not for just any step: going from 80% to 85% costs less than getting to 80% in the first place.
Gravity obeys the same limit
On August 17, 2017, detectors caught gravitational waves from two neutron stars colliding about 130 million light years away. Gamma rays from the same crash arrived 1.7 seconds later. After a trip that long, that pins the speed of gravity to the speed of light within about one part in a thousand trillion. The gap came mostly from the explosion taking time to launch its jet of gamma rays. Gravity did not win the race.
Your clock slows down, and it has been measured
Near light speed, a moving clock runs slow compared with clocks at home. At 99.5% of light speed the stretch factor γ is 10.01. So a round trip that takes one year on board takes about ten years on Earth. NASA's JPL uses the same speed: leave at 30, celebrate five birthdays aboard, and come home at 35 to classmates who are 80. You age less than the people you left, so the trip is a one way ride into the future.
In October 1971, Hafele and Keating flew four cesium atomic clocks around the world on airline flights, once eastward and once westward. Compared with the U.S. Naval Observatory's clocks, the eastbound clocks lost 59 billionths of a second and the westbound clocks gained 273. Relativity predicted a loss of 40 and a gain of 275. Both results agreed within the margins of error. Speed and altitude both played a part.
Key numbers
| What | Number | Source |
|---|---|---|
| Speed of light in empty space, exact | 299,792,458 m per second | NIST, The International System of Units (SP 330) |
| Speed of light, rounded | about 300,000 km (186,000 miles) per second | NASA Science, What is a light year? |
| Laps around Earth's equator at light speed | about 7.5 per second | NASA Glenn Research Center |
| Kinetic energy from rest at 99%, 99.9% and 99.99% of light speed | about 6.1, 21.4 and 69.7 times mc² | Our arithmetic from OpenStax College Physics 2e (Rice University) |
| Energy needed to bring anything with mass to light speed | infinite | OpenStax College Physics 2e (Rice University) |
| Time stretch at 99.5% of light speed | about 10 (γ = 10.01): 1 year aboard, about 10 years at home | NASA JPL, Time Travel podcast |
| Gap between gravitational waves and gamma rays, 2017 neutron star collision | 1.7 s (1.74 ± 0.05 s) | LIGO, Virgo, Fermi and INTEGRAL 2017, ApJL 848 L13 |
| Distance to that collision | about 130 million light years | NASA Scientific Visualization Studio #12740 |
| Difference between the speed of gravity and the speed of light | between minus 3 × 10⁻¹⁵ and +7 × 10⁻¹⁶ of light speed | LIGO, Virgo, Fermi and INTEGRAL 2017, ApJL 848 L13 |
| Atomic clocks flown eastward around the world, 1971 | lost 59 ± 10 billionths of a second | Hafele & Keating 1972, Science |
| Atomic clocks flown westward around the world, 1971 | gained 273 ± 7 billionths of a second | Hafele & Keating 1972, Science |
| Relativity's predictions for those flights | minus 40 ± 23 billionths of a second east, +275 ± 21 west | HyperPhysics, Hafele and Keating Experiment |
What the film simplifies
- The film says one year aboard is ten years at home. At 99.5% of light speed the factor is 10.01, and the round trip figure assumes the ship spends almost the whole trip cruising. Speeding up, turning around and slowing down change it a little.
- On board, the rocket's clock ticks normally. It runs slow only when compared with clocks at home. One shot shows the rocket's view of the stars and home's view of its clock at the same time.
- Not every clock flown in 1971 ran slow. The eastbound clocks fell behind and the westbound clocks gained, and the higher altitude, where gravity is weaker, sped both up. The film only says the clocks came back out of sync.
- The race between light and gravity is a cartoon. Light is never at rest, so it would not wait at a start line. In 2017 the two signals arrived 1.7 seconds apart, and that gap came mostly from the explosion, not from a difference in speed.
- The speed limit is light's speed in empty space. Light slows down in water and glass, but nothing with mass ever reaches the empty space speed.
- The rocket, its fuel tanks, the beard and the talking characters are cartoon, and no real rocket comes close to these speeds. The piles of 6, 21 and 70 tanks match the energy at 99%, 99.9% and 99.99%, but the closing recap shows 99.9% while the clock math uses 99.5%.
For teachers
Runtime 1 minute 24 seconds · Topics: Speed of light, Special relativity, Time dilation, Gravitational waves · Full script below
Ask your class
Reaching 99% of light speed takes about 6.1 mc² of energy and reaching 99.9% takes about 21.4 mc². Why can't the rocket just bring more fuel and reach 100%?
Answer
Each extra nine costs more than twice everything spent before it, and the energy needed grows without limit as the speed nears light. Reaching light speed would take infinite energy, so only massless things like light travel that fast.
At 99.5% of light speed, a clock aboard runs about 10 times slower than clocks at home. An astronaut and her classmates are all 30 when she leaves, and she spends 5 years aboard. How old are her classmates when she gets back?
Answer
About 80. Roughly 50 years pass on Earth while she ages 5 and comes home at 35.
In 1971 the eastbound clocks lost 59 billionths of a second but the westbound clocks gained 273. Does the gain mean relativity was wrong?
Answer
No. Relativity predicted a loss of about 40 and a gain of about 275, and both results agreed within the margins of error. Altitude and speed both changed the clocks, so they didn't all run slow.
The script
Lil Sat: Ten years! You were gone ten years!
Rocket: Ten years? Nah, it's been one year, tops!
Host: Rewind. He tried to break the one speed limit nothing in the universe can break.
Rocket: Tour stop three! Speed limits are for chumps!
Host: The limit is light. Seven and a half laps around Earth, every second.
Rocket: Cute! Watch me blow right past it! Full throttle!
Host: Here's the catch. The faster you go, the harder it gets to go any faster.
Host: Ninety nine percent of light speed. Ninety nine point nine.
Host: Each extra nine costs more energy than everything before it.
Host: To hit light speed itself, you'd need infinite energy.
Rocket: Infinite? No problem, I'll just bring extra!
Host: Doesn't work. Only things with no mass, like light, go that fast.
Gravity: Even I can't beat it. And I always win.
Host: But get close, and something wild happens. Your clock slows down.
Host: At ninety nine and a half percent, one year on your clock is ten years back home.
Rocket: A year of joyriding? Let's go!
Lil Sat: I grew a whole beard waiting for you!
Rocket: Worth it! And now I'm younger than you!
Host: And it's real. Atomic clocks flown around the world on jets came back out of sync.
Host: You can't break the speed limit. But get close, and it's a one way time machine to the future.
Host: Next stop: something out there is dragging our whole galaxy. Follow!
Sources
- Light travels 299,792,458 m every second in empty space.NIST, The International System of Units (SP 330)
- Light could circle Earth about 7.5 times in one second.NASA Glenn Research Center
- Reaching light speed would take infinite energy for anything with mass.OpenStax College Physics 2e (Rice University)
- Only massless things, like light, travel at light speed.University of Illinois Physics Van
- At 99.5% light speed, a year aboard is about ten at home.NASA JPL, Time Travel podcast
- A twin who travels near light speed comes home younger.Einstein Online, Max Planck Institute for Gravitational Physics
- Atomic clocks flown around the world came back out of sync.Hafele & Keating 1972, Science
- Light travels about 186,000 miles (300,000 km) per second.NASA Science, What is a light year?
- Kinetic energy is (γ · 1)mc², the formula behind the cost of each extra nine.HyperPhysics, Relativistic Energy (Georgia State University)
- Gamma rays arrived 1.7 seconds after the gravitational waves from GW170817.LIGO Scientific Collaboration, GW170817 and GRB 170817A science summary
- From a delay of 1.74 ± 0.05 s, the speed of gravity differs from the speed of light by between minus 3 × 10⁻¹⁵ and +7 × 10⁻¹⁶ of light speed.LIGO, Virgo, Fermi and INTEGRAL 2017, ApJL 848 L13
- The 2017 neutron star collision was about 130 million light years away.NASA Scientific Visualization Studio #12740
- Predicted and measured clock shifts in the 1971 flights, with their gravity and speed parts.HyperPhysics, Hafele and Keating Experiment
- The flown clocks agreed with special and general relativity within the margin of error.NIST Taking Measure, Putting Einstein to the Test With the World's Most Accurate Clocks
- Traveling near light speed lets you age less than people at home, a trip into the future.Scientific American, Why Einstein's Theories of Relativity Make Time Travel Possible