So, time travel is possible after all!

No, you’re not going to step inside a time machine to get physically shredded and transported as tiny packages only to be reassembled in another era where you can wreak havoc by just showing the local people of 1542 BC that you have an iPad 2. Though it might sound very alluring for the aspiring evil scientists among us, it still is possible the other way: traveling forward in time.
Yes yes – not quite that exciting as you’d hoped, but very interesting nonetheless!

The law of universal gravitation

We all know Newton’s laws from high school physics class. Still, for most of us, the equations remained highly abstract and we didn’t get the chance to apply them to real life scenarios. Though the equations were basic, some laws are highly applicable to an enormous amount of the universe. With the first law of Newton: Newton's law of universal gravitation we can have a simple planetary orbit system by applying the equation to the bodies [fig a.1].

The basic principle behind this confirmed idea is that any form of mass – a body – has gravity. You can simply imagine gravity as a force surrounding a body, pulling other bodies to its center. That is the reason we don’t fall off the Earth when we jump!

Newton was convinced that gravity worked instantaniously. For example: if the sun would suddenly evaporate and disappear, the Earth would fall out of orbit immediately and gets hurled into space. This was later proven to be a misconception of how gravity works.

Unification of theories

So now we know that all bodies – or just mass – has its own gravitational well that pulls other bodies towards the center of the body. This theory was the basis for further research on the matter by scientists such as Albert Einstein.

Albert Einstein was working on a theory about light in his early twenties. At the age of 26, he released a paper that proved that the speed of light was the absolute barrier of everything. Yet, light also travels at a certain speed. For example: the time for the rays of light to travel the distance from the sun to the surface of the Earth (150 million kilometers) is approximately 8 minutes. Einstein said that nothing can go faster than light, not even gravity. Yet, Newton’s theory told a different story.
When Einstein noticed this flaw in Newton's law of universal gravitation, he started working on a solution for this problem – in which he succeeded and revolutioninzed the picture of the universe.

Though to understand what Einstein did, we have to take a big jump through time and go back to 1632, when Galileo Galilei came up with the idea of a coordinate system in which objects, where no force at work, are completely still or make a uniform rectilinear motion. So if you’d spill coffee or drop a ball while on an airplane or while sitting on a couch at home, the same laws apply. Even though, in an airplane, you are traveling at 1000km per hour! This effect is called the Galilean invariance.
Einstein unified this theory with Newton's universal gravitation theory to end up with a coordination grid that simplifies the calculations for measuring the amount of deflection of gravity, amongst other physical changes caused by the mass of an object.

After nearly ten years of racking his brain, he found the answer in a new kind of unification. Einstein came to think of the three dimensions of space (length, width and depth) and the single dimension of time, as bound together as a single fabric of space-time.
Like the surface of a trampoline, is warped and stretched by heavy objects like planets or stars [fig b.2]. And it’s this warping or curving of space-time that creates what we feel as gravity. A planet like the Earth is kept in orbit not because the sun reaches out and instantaneously grabs hold of it as of Newton’s theory. Bodies no longer have a force that pulls other bodies towards them. The reason why the Earth orbits the sun is merely because the Earth follows curves in the space-time fabric caused by the sun’s presence.
This theory is named general relativity.

fig b.2 - A symmetric spherical body on a two-dimensional grid that illustrates the space-time universe. body A is surrounded by its gravitational well, defined by an outer ring and a gradient.

You can simply imagine a gravitational well as a ring or more specifically, a funnel surrounding a body [fig b.3] of mass that depicts the curvature of space-time.

fig b.3 - The same scene as fig a.2 illustrated from the side with the forces of the gravitational well of body A applied to the grid. The gravity well shows an exponential distribution (hyperboloid) of the force in this situation, since body A is a symmetric spherical mass. Therefore, there can also be noted that the gravitational force exponentially increases as you get closer to the center of mass of the body, and will theoretically have an endless reach.

So what does time have to do with gravity?

The current state of the general relativity theory also describes the dilation and delay of time, affected by the curvature of space-time.

When general relativity was introduced in 1915, it had no solid empirical foundation (it did not depend on evidence or consequences that are observable by the senses). This lead to a quest for proof, obtainable through experiments and testing.

General relativity at its best

A very good example of general relativity is a natural phenomenon called gravitational redshifting. It describes how light has to “climb” uphill a gravitational well and thereby losing some energy, shifting the light-waves to a lower energetic frequency and longer in wavelength, resulting in the optical color red [fig c.4].

fig c.4 - The gravitational redshift of a light wave as it moves uphill against a gravitational field (caused by the yellow star body C).

The deflection of light caused by bodies with great mass was already foretold by John Michell in 1783 and Pierre-Simon Laplace in 1796, who predicted that some stars could have a gravity force so strong that light would not be able to escape. It was in 1801 that Johann Georg von Soldner calculated the amount of deflection of a light from a distant star, by the sun. He arrived at the Newtonian answer which is half the value predicted by general relativity. All of this early work assumed that light was a particle, a corpuscle with kinetic energy, which was inconsistent with the modern understanding of light waves.

In 1861 when James Clerk Maxwell published his paper, it was clear that light is in fact an electromagnetic wave rather than a particle. Einstein’s theory on light told that light does not simply “slow down” and combined with the fact that light is an electromagnetic wave, it all made sense. One way around this conclusion would be if time itself was altered – if clocks at different points had different rates! This effect is called time dilation.

What about special relativity

When Einstein came up with general relativity, a problem popped up when he faced calculations in the vacuum of space (or, hypothetically far from all gravitational mass). He did not have a reference of time nor space to make his calculations. So special relativity (SR) was his second invention: a way to make space-time calculations based on a “the inertial frame of reference”. This basically means that you will refer to a force that does exist in that space-time field you are doing calculations in, but only to measure differences between the two forces.

This also means that when making calculations in SR, you are excluding every practical cause of errors in measurements or formulas for a better understanding of what is happening.

Being able to make calculations like that gave a lot of new ways for calculating space-time ratios for different velocities. Now imagine two clocks that get shot into outer space to orbit the Earth. Clock A gets launched to orbit Earth with a velocity of almost the speed of light, while clock B gets launched to orbit at the speed of a regular space shuttle [fig d.5].

fig d.5 - Both clocks are launched at 00:00 hours and are measured 00:21, revealing that clock A has spent less time in space due to its high velocity compared to earth and clock B.

After one year, the time on both clocks would be measured and compared to one another. You would see that clock A would be far behind on clock B. This does not mean that clock A is broken, but simply that the speed time would pass depends on how fast the subject is moving. So clock A would have spent less time in space than clock B, even though they both spent a year in outer space. (Yes, the measurement of a year would be also relative, since the Earth is moving at a different velocity too!)

Welcome on board

In theory, time dilation is the key for travelling into the future without spending the same amount of time you normally would, compared to the speed time moves on Earth. You would need a very, very fast vehicle to have a dramatic difference. For example, one year of travel might correspond to ten years at home. A constant 1g acceleration would permit humans to travel through the entire known Universe in one human lifetime. The space travellers could return to Earth billions of years in the future. A scenario based on this idea was presented in the novel Planet of the Apes by Pierre Boulle, which… really didn’t give hope for having a nice welcome home party.

“YOU! Get off my planet!”