What would you do if you just returned from deep space only to find the world in the next century? Many dystopian science fiction narratives use the traveler-out-of-time scenario where a person from one time period moves through time into another era through some sort of scientific or magical plot device. The traveler-out-of-time scenario mainly serves to comment on the fast-paced evolution of our ephemeral normalcy. We often discuss these sociological implications first because they are presented front and center. However, the practicality of how the traveler ages differently from society is often less discussed and is hence, in my opinion, more interesting.

In 1860, James Clerk Maxwell proposed laws of electricity and magnetism akin to Newton’s tried and true kinematic laws. Perhaps the most important law dictated that the speed of light, c was 3.00 × 108 m/s. In introductory physics classes, professors first teach particle mass problems like pushing a box along a rough ramp or rolling a ball down a hill. Near the end of the semester, your professor may focus on sinusoidal objects like waves or oscillations. French graduate student, DeBroglie, hypothesized that all objects behave like both particles and waves. Later experiments on electrons indeed that confirmed objects once considered particle masses behave like waves too. Scientists termed this phenomenon wave-particle duality. Because scientists already knew light behaved like a wave due to the interference properties it exhibited, all they needed to discover was that it behaved like an object too. Einstein consequentially found that light consisted of particle-like photons in his famous paper on the Photoelectric Effect where he illustrated light’s wave-particle duality.

For the longest time, scientists had tried to find the medium light passed through as a wave. Ocean waves crash through the water, and sound waves travel though in the air. It took two decades to experimentally show that no such medium existed. Michelson and Morley’s experiments showed that light moved with speed c even if the source or observer were moving too. Their work laid the foundation for Einstein to publish his paper on special relativity which formally established that speed of light c was invariant or constant. In other words, light moves with speed 3.00 × 108 m/s to both a stationary observer and the observer moving with constant velocity. Einstein once wondered if he moved at speed c next to a beam of light whether he could see a stationary photon beside him. This observation would support the idea that even if he reached such a relativistic speed, the photon would still move with speed c with respect to his frame of reference, regardless of how fast or slow he was moving.

On one hand, Einstein’s findings resolved this paramount issue. On the other, it opened another can of worms by suggesting that phenomena like time dilation and length contraction were also possible. Generally speaking, Newton’s 1st law says:

Velocity = Distance ÷ Time,

$v = \frac{\Delta x}{\Delta t}$.

So, it’s possible for distance to decrease and time to increase for velocity c to remain constant in a few key circumstances.

The Twin Paradox is one such scenario. It occurs when one identical sibling moves at very fast, relativistic speeds, often through space, that are close to c while the other stays stationary often on Earth. Christopher Nolan’s Interstellar explores this famous problem with Cooper and his daughter Murphy. In the film, Cooper leaves his young daughter Murphy behind on Earth to explore space at relativistic speeds on the spaceship Endurance. Cooper eventually falls into the black hole Gargantua where he experiences massive gravitational forces. In the end, Cooper returns to find Murphy on her deathbed while he has barely aged a year. Although the traveler-out-of-time reveal with Cooper and Murphy relies upon the Twin Paradox and special relativity, it also explores the effects of general relativity caused by massive gravitational forces.

To clarify, special relativity as used in the Twin Paradox relies upon discrepancies between different frames of reference like the Earth and Endurance to explain time dilation, and general relativity considers the discrepancies in gravitational forces. But in either instance, the person moving at the relativistic speed or experiencing the large gravitational force will always age slower than the unaffected person. First, we’ll consider special relativity which uses the Lorentz factor to propose:

$\Delta t = \gamma \Delta {t}’$.

Murphy experiences ∆𝑡 in the Earth’s reference frame, and Cooper experiences ∆𝑡′ on the spaceship Endurance. For an object moving with relativistic velocity 𝑣 (m/s), Lorentz factor 𝛾 or gamma is:

$\gamma = \frac{1}{\sqrt{1-\frac{v^{2}}{c^{2}}}}$.

The ratio $𝑣^{2}/𝑐^{2} < 1$ because the speed of light is always c, and nothing moves faster than the speed of light. As a result, 𝛾 >1, and ∆𝑡′<∆𝑡. Thus, time moves faster for Cooper than it does for Murphy, and he ages slower moving at near relativistic speeds while Murphy lives out her life on Earth. To the everyday individual moving no faster than 30 m/s in a car or even 250 m/s in an airplane, 𝛾 ~1, and the effects time dilation are negligible.

Finally, we’ll consider time dilation due to general relativity as proposed by Einstein in 1916. Cooper experiences a massive gravitational field inside the singularity of the massive black hole Gargantua. Yet, nearly infinite gravitational fields are not necessary to observe time dilation.$^{1}$ A team of scientists led by C.W. Chou detected time dilation in Aluminum atoms on Earth separated by less than one meter apart.$^{2}$

It’s hard to believe that Einstein published his theory of relativity just a little over a century ago. Although most of us do not think about the differences in gravitational fields or relativistic speeds every day, the effects of both general and special relativity are not only integral to the complexity of our modern societies but also key to the future of the next ones. In the last century alone, we’ve introduced technological wonders like satellites, particle accelerators, electron microscopes, and the internet.$^{3}$ Such complex devices require measurement re-calculations for objects not in the Earth’s frame of reference like those orbiting around us in the case of satellites or atomic sized masses moving very quickly in the case of a particle accelerator. If we brought Einstein back to the present day and showed him what we’ve accomplished with his work, I’m fairly sure he would be a time traveler just like Cooper. At the rate that our scientific community innovates and discovers phenomena, perhaps we too might also be time travelers within our natural lifespans.

Works Cited:

[1] Tipler, Paul Allen, and Ralph A. Llewellyn. Modern Physics. W.H. Freeman, 2012.

[2] Chou, C. W., et al. “Optical Clocks and Relativity.” Science, vol. 329, no. 5999, 24 Sept. 2010, pp. 1630–1633., doi:10.1126/science.1192720.

[3] “Theory of Relativity.” Wikipedia, Wikimedia Foundation, 27 Dec. 2020, en.wikipedia.org/wiki/Theory_of_relativity.