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While the concepts of space and time were fundamental to the Newtonian world, centuries of digging deeper into the mechanics of our universe have uncovered that it isn’t all as simple as it seems. From Einstein’s Special Relativity to theories of multi-dimensional time, the science behind space and time has evolved into a complex field.

Newtonian Absolutism

At the dawn of classical mechanics, Newton created the foundation upon which all of modern spacetime theory is built. Space and time were considered to be entirely unrelated and absolute concepts. There was no question in his mind that time moves forward and space exists around us. Space was considered a static body within which we exist, while time was described as flowing in only one direction at a steady rate. Imagine space as a box, where events are contained within, and time as a river whose current pulls us along.

Newton coined the terms ‘absolute space’ and ‘absolute time’ to describe the absolutes from the relativity we measure. For centuries, this theory remained unquestioned, so physicists didn’t consider time and space to be real entities, but rather our human way of interpreting the world around us.

Einstein’s Revolution:

Special Relativity

The first true challenge to the Newtonian perspective of space and time came in the form of Einstein’s Special Relativity. He introduced one key revolutionary concept: everything, including space and time, is relative, depending only upon the observer’s frame of reference.

The motivations for Einstein’s work arose from the desire to eliminate the contradiction between Maxwell’s equations and Newtonian Mechanics. A simple way to visualize this contradiction is by imagining the following scenario:

Two rockets in space are flying towards each other at a speed of 500 miles per hour. This would result in a relative speed of 1000 miles per hour. Now, if you were to throw a rock from one ship to another at a speed of 10 miles per hour, it would reach the other ship with a relative speed of 510 miles per hour. However, the substitution of light into this situation instead of a rock changes this because the speed of light is constant. No matter how fast you travel towards light, it will always come towards you at the same constant speed: 3·10⁸m/s, or the speed of light.

Many tests were done to prove that the wave-particle duality of light was the reason for this phenomenon. Rather than trying to disprove or explain away the theory, Einstein decided to take the constant speed of light as a fundamental property. He didn’t explain the speed of light, but used it to explain other things. Einstein was willing to give up the time-honored fundamentals of Newton’s laws in favor of the constant speed of light. 

He began with the basic definition of speed as the distance divided by the time. If the speed of light remains constant as this rocket reduces the distance to be travelled, then the time must also decrease to preserve this equality. When mathematically calculating this, Einstein discovered the concept of time dilation, where objects in motion experience time more slowly than objects at rest. Continuing with similar methods for other properties, such as conservation, he discovered that mass would increase with speed and length would decrease. The true genius in Einstein was his willingness to question his own assumptions and give up some of the most basic qualities of the universe, in favor of the speed of light.

General Relativity

Special Relativity, however, did not incorporate gravity. Before Einstein, physicists believed that gravity was an invisible force that dragged objects towards one another. However, Einstein’s general relativity suggested that the ‘dragging’ was not gravity, but rather an effect of gravity. He theorized that objects in space bent the space around them, inadvertently bringing objects closer to one another.

General Relativity defines spacetime as a 4D entity that has to obey a series of equations known as Einstein’s equations. He used these equations to suggest that gravity isn’t a force but instead a name we use to describe the effects of curved spacetime on the distance between objects. Einstein proved a correlation between the mass and energy of an object and the curvature of the spacetime around it.

His work allowed him to prove that:

“When forced to summarize the general theory of relativity in one sentence: Time and space and gravitation have no separate existence from matter.” -Einstein.

Einstein’s General Relativity predicted many things that were only observationally noticed years later. A famous example of this is gravitational lensing, which is when the path of light curves as it passes a massive object. This effect was noticed by Sir Arthur Eddington in 1919 during a solar eclipse, yet Einstein managed to predict it with no physical proof in 1912.

Closed-Timelike-Curves (CTCs)

Another major prediction made by Einstein’s General Relativity is Closed-Timelike-Curves (CTCs), which arise from mathematical solutions to Einstein’s equations. Some specific solutions to these equations, such as massive, spinning objects, create situations in which time could loop.

In physics, objects are considered to have a specific trajectory through spacetime that will indicate the object’s position in space and time at all times. When these positions in spacetime are connected, they form a story of an object’s past, present, and future. An object that is sitting still will have a worldline that goes straight in the time direction. Meanwhile, an object in motion will also have an element of spatial position. Diagrams of a worldline are drawn as two light cones, one into the future and one into the past, with a spatial dimension on the other axis, as seen in figure 1.

CTCs are created when the worldline of an object is a loop, meaning that the object will go backwards in time at some point to reconnect to its starting point. Closed-Timelike-Curves are, in essence, exactly what they sound like: closed curving loops that travel in a timelike way. Traveling in a timelike way, meaning that their change in time is greater than their change in space, suggests that these objects would have to be static or nearly static. As seen in Figure 2, the worldline of a CTC would be a loop, as there is some point in space and time that connects the end and the beginning.

Two major examples of famous CTC solutions are the Gödel Universe and the Tipler Cylinder:

• Gödel Universe: Suggested by mathematician Kurt Gödel in 1949, the Gödel Universe is a rotating universe filled with swirling dust. The rotation must be powerful enough that it can pull the spacetime around it as it spins. The curvature would become the CTC. This was the first solution found that suggested the potential for time-travel to be a legitimate possibility, not just a hypothetical scenario. 
• Tipler Cylinder: In the 1970s, physicist Frank Tipler suggested an infinitely long, massive cylinder spinning along the vertical axis at an extremely high speed. This spinning would twist the fabric of spacetime around the cylinder, creating a CTC.

Closed timelike curves bring many paradoxes with them, the most famous of which is the grandfather paradox. It states that if a man has a granddaughter who goes back in time to kill her grandfather before her parents are born, then she wouldn’t exist. However, if she doesn’t exist, then there is no one to kill her grandfather, thus meaning that she must exist. Yet if she exists, then her grandfather doesn’t.

Most importantly, CTCs drove further exploration and directed significant attention to the spacetime field for decades. Scientists who didn’t fully believe Einstein’s General Relativity pointed to CTCs as proof of why it couldn’t be true, leaving those who supported Einstein to search extensively for a way to explain them. This further exploration into the field has laid the foundation for many theories throughout the years.

The belief amongst scientists is that CTCs simply don’t exist because, while they are hypothetically possible, the energy requirements to create them are not yet feasible. Many of these setups require objects with negative energy density and other types of  ‘exotic matter’ that have not been proven to even exist yet. Furthermore, even if CTCs were to be formed, the specific region of spacetime where they form would be highly unstable, meaning that these CTCs would not sustain themselves. The situations in which CTCs would be feasible require types of fields of energy that would approach infinity and the Cauchy Horizon (the limit at which causality no longer exists, therefore making these situations physically unviable).

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All references listed on Part 3.

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