Faster Than Light and the Big Rip

Einstein’s Relativity tells us the speed of light is the universal speed limit. Distant galaxies, though, are moving away from us much faster due to the expansion of spacetime, which will eventually rip the universe apart.

The Happy Neuron
Dec 31, 2020 · 6 min read
The universe’s final state is an infinitely stretched wasteland, in which no structure of any sort can exist.
The universe’s final state is an infinitely stretched wasteland, in which no structure of any sort can exist.
The universe’s final state might be an infinitely stretched wasteland, in which no structure of any sort can exist.

Way back in 1638, Galileo tried to measure the speed of light. He stood on one mountain top, and his assistant stood on another. Galileo uncovered his lantern, and when his assistant saw the flash, he uncovered his. Galileo believed he could time how long it would take for the returning light to reach him. Needless to say, it didn’t work, and he concluded that light “if not instantaneous, is extraordinarily rapid.”

It wasn’t until 1675 that we gained some sense of how rapid light actually is. Ole Roemer noticed differences in the transit of Jupiter’s moons at different times of the year and estimated the speed of light to be around 200,000 km/s. In 1849, Hippolyte Louis Fizeau sent beams of light through rotating wheels and came surprisingly close at 313,000 km/s. In the years following, scientists refined their experiments, and today the speed of light is known to be 299,792.458 km/s.

However, in 1887, Albert A. Michelson and Edward W. Morley turned their attention not to how fast light travels, but to what it travels through. All waves travel through an elastic medium, in that they’re rhythmic undulations of a substance. Ripples in a pond are the up and down motion of water, sound waves are the compression and rarefication of air or other matter, and light was thought to propagate through the cosmic aether. It was believed that as the Earth moved through it, the aether would create cosmic wind, much like when we put our hands out the window of a moving car. The light waves, then, would be affected differently depending on their angle to the motion of this wind. Michelson and Morley, though, used perpendicular reflections of light to demonstrate that the aether did not exist.

The Michelson-Morley experiment used perpendicular reflections of light to disprove the idea of the cosmic aether. (Creative Commons License)

The now famous Michelson-Morley experiment also found that light traveled at the same speed regardless of motion. This idea became one of the cornerstones of Einstein’s Theory of Special Relativity, which that the speed of light is the universal speed limit.

Einstein’s Gedankenexperiment

Using the results of the Michelson-Morley experiment, Einstein began his famous Gedankenexperiment, or thought experiment. He reasoned that if light is the same speed for all observers regardless of motion and if the laws of physics are the same for all frames of reference, then a stationary observer would make different measurements than a moving observer. These measurements would differ by gamma, as shown below.

The Lorentz factor demonstrates the universal speed limit.
The Lorentz factor demonstrates the universal speed limit.
The Lorentz factor demonstrates the universal speed limit.

In this equation, when velocity v is small, (v^2/c^2) is close to 0, making it trivial and reducing the equation to very close to 1. This means that the measurements taken by a stationary observer and an observer traveling at speeds nowhere near the speed of light c will be essentially the same. However, the larger v becomes the bigger the difference. For example, if v is (.86c), then gamma becomes 1.96. Therefore, we don’t see relativistic effects at the speeds we are used to, but if we travel at significant fractions of the speed of light, then we certainly would.

Gamma also demonstrates why the speed of light is the universal speed limit. If v=c, then (v^2/c^2) is 1, and the bottom of the equation becomes 0. Dividing by 0 is not possible and the equation breaks down. Therefore, it’s only possible for objects with mass to approach the speed of light but never reach it.

After the success of Special Relativity, Einstein expanded his work into the far more complicated General Relativity. In Special Relativity the moving observer moves with a constant velocity in relation to the stationary observer, but in General Relativity the moving observer accelerates. The acceleration creates an ever-changing difference in measurements between the two observers, which can be visualized as a curved 4D space. That is, the 3 spatial dimensions and the 1 time dimension (known as spacetime) would appear different to the two observers, the amount of which depending on the amount of acceleration. Einstein’s key revelation, though, was that this also applies to gravity because it is an accelerating force. In other words, gravity is actually curved spacetime. Therefore, massive objects like a star warp spacetime, and gravity is the illusion of an object moving through this warping.

Faster Than Light

With the equations of General Relativity, Alexander Friedmann showed that the universe is expanding. Edwin Hubble and others corroborated this by observing the light coming from distant galaxies. The light was red-shifted, meaning the light is stretched, making it appear to have longer wavelengths. That is, as an object moves away from an observer, the wave takes slightly longer to arrive, creating longer distances between each crest and trough. Likewise, as an object moves towards an observer, each successive undulation takes slightly shorter time to arrive than the last, making the waves appear to have shorter wavelengths, or blue-shifted. For example, when an ambulance approaches you the sound gets increasingly higher pitched and then increasingly lower pitched as it moves away. With this discovery, Hubble provided some of the first evidence for the expansion of the universe, earning him the privilege of having the Hubble Space Telescope named after him.

Furthermore, Hubble reached the startling conclusion that the universe was accelerating. When looking at the red-shifted light from galaxies, he noticed that the further away the galaxies were, the faster they were moving away from us. He reasoned that at a certain distance away from Earth, galaxies would be moving faster than the speed of light. This means that light emitted from a galaxy while below the speed of light might still reach us, but new light emitted after it accelerated beyond the speed of light would not reach us. In a way, this means that some light and the information it carries is forever lost to us, no matter the age of the universe, as it sits behind a cosmic event horizon.

In fact, this keeps Neil DeGrasse Tyson up at night. If some objects can forever disappear, then what else has disappeared? Are there cosmological structures that we’ve never seen, and will cosmological structures like galaxies someday be hidden from future generations? In an interview with Stephen Colbert, he said “The next generation of cosmic explorers will only have the stars of the Milky Way to think about.” He stays up at night thinking about what chapters of the universe we will never be able to read and don’t even know exist.

Dark Energy and the Big Rip

While faster than light galaxies may seem to violate the universal speed limit, they don’t. The universal speed limit only applies to movement through the universe, not the illusion of movement due to expansion. Put another way, the space in between us and galaxies beyond this cosmic event horizon expands faster than their light travels.

But what causes the expansion? Scientists have named it dark energy, but we still have little idea what it is. Dark Energy forces every point in the universe to expand, and because expansion leads to more points, the expansion accelerates. That is, as galaxies move away from us, there’s more space in between to expand, leading to more space and more expansion.

As of now, gravity is strong enough to keep matter together enough for galaxies, stars, planets, us, etc. to exist. The strong nuclear force is strong enough to keep the nuclei of atoms together. The electromagnetic force is strong enough to hold electrons in place around nuclei. However, if the acceleration continues, then these forces will eventually be overcome, as the space in between protons and neutrons, electrons and nuclei, etc. will expand too rapidly. The fundamental forces will become trivial by comparison.

This is the Big Rip: dark energy accelerates the universe’s expansion to the point that all fundamental forces are overcome. Everything is ripped apart, even subatomic particles. The universe’s final state is an infinitely stretched wasteland, in which no structure of any sort can exist.

Is this how the universe ends? It’s hard to say. It’s possible dark energy weakens, slowing the rate of expansion. In this case, gravity might win in the end, bringing the universe closer together, leading to the Big Crunch and to a new Big Bang. However, as far as we know, the rate of expansion is accelerating, pushing the universe towards not a bang but a whimper.

Originally published at on December 31, 2020.

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