# Physics of Time Travel

## Abstract

## Scene 1 - Clock

Time travel has long been a fascination for human beings, offering the possibility of fixing past mistakes or exploring new worlds and opportunities in the future. This allure has been used by writers to make their stories unique, while scientists have made considerable efforts to find a precise and reliable description of time itself. Today, we are able to measure time with great precision by using the oscillations of the wave emitted by an atom of cesium 133 during a particular transition – a second is defined as the amount of time it takes for 9,192,631,770 oscillations to occur.

we could potentially swap out atomic clocks for optical clocks. Optical clocks are more precise and can only lose up to 100 seconds over a time period equivalent to the age of the universe. This increased precision would allow us to gain a full understanding of many phenomena, including dark matter and the most basic elements of the theory that describes space-time: the theory of General Relativity.

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## General Relativity and Time Travel

Space acts on matter, telling it how to move.

In turn, matter reacts back on space,

telling it how to curve.

## Scene 2 - The Documentary

Albert Einstein presented the Theory of Relativity in 1905, revolutionizing our understanding of space, time, and gravity. According to Einstein’s theory, space and time form a four-dimensional continuum that is curved by the presence of matter. Moving objects follow the curvature of space. In this space-time, as Einstein puts it, “the distinction between before and after must be abandoned for points that are very far away in a cosmological sense, although this gives rise to those paradoxes that concern the direction of causal connection.”

Thanks to the constancy of the speed of light, regardless of the inertial reference system from which it is observed, we deduce that space and time must be redefined. Descriptions of space and time reveal that time can dilate and space can contract in different reference systems. When factoring in the effects of gravity on the shape of space-time, interesting solutions to Einstein’s equations arise that suggest time travel, especially to the past, may be possible – at least in theory.

In simple terms, time travel is closely tied to velocity (specifically the speed of light) and gravity.

## A journey toward the Future

Verily, the black hole may be a portal true,

but an thou seek’st to return, be wary, too

For time doth flow as a swift and murky river,

whose course and direction oft make us to shiver

## Scene 3 - Vivaldi's Madness

Since Einstein formulated his theory of relativity, we have thoroughly analyzed his equations. The consequences and predictions of this theory are revolutionary, sometimes shocking, and so outlandish that even Einstein himself seriously doubted that they could be true and physically verifiable in our reality.

Despite this, experimental evidence has confirmed some of the most bizarre predictions of general relativity, namely black holes and gravitational waves. Black holes, in particular, would be a fundamental ingredient for anyone wishing to take a trip through time.

As seen in the movie Interstellar, we could park ourselves near a black hole and time, far away from its grasp, it would flow at a much faster rate. After returning to a safe distance from the event horizon, we could go back to Earth where several years would have passed. For example, a black hole of 10,000 solar masses would have a Swarztchild radius of 30000 km. If we are at a distance of 3 mm away from the event horizon, 1 second for us would correspond to 28 hours on Earth. But as we approach the smallest fraction of a millimeter from the event horizon, time slows down until it approaches infinite time dilation.

## Scene 3 - The Black Hole

Another way to travel to the future is to consider the relationship between time and velocity. Put simply, the faster we move in space, the slower our time will be. To observe significant time dilation, we must travel at speeds very close to the speed of light.

Let’s make a quick estimate. If a spaceship travels at a speed equal to 99.99% of the speed of light for a year, it would return to a world that would have aged about 80 years in their absence. If the speed is increased to 99.99999% of the speed of light, more than 2000 years would pass on Earth in just one year.

Well, given these circumstances, wouldn’t you say that a black hole is a more practical solution for time travel to the future?

As we have seen, time travel to the future is completely possible and accepted by the scientific community. According to Michio Kaku, “There are many experiments that prove the possibility of traveling to the future. In fact, the only problems are of a technical nature. We are not yet able to build spaceships capable of reaching the necessary speeds.”

However, traveling to the past is a much more complicated matter. Physics tells us that time machines capable of taking us back to the past can not yet be invented. If it were possible to travel to the past, as Stephen Hawking observed, why haven’t we met any tourists from the future? Most importantly, how can we solve the logical paradoxes that arise from time travel to the past?

## Traveling to the Past

Time doth rage, a tempest lost to all

Wherein we’re all but flotsam in its thrall

## Scene 4 - The Magic clock

Which solutions physicists have proposed to allow time travel?

In General Relativity, there are closed timelike curves. They are worldlines that form closed loops, implying that the object represented by them, by continuing to travel into the future, goes back to the point from which the worldline began, both in space and in time. These trajectories would allow time travel, but the first issue with them is that by traveling into the past along a closed timelike curve, we would arrive before the moment we left.

Among the various discussions advanced by physicists, the following solutions to the equations of general relativity are noteworthy:

– The Einstein-Rosen one-way Bridge, now known as the Wormhole

– Godel’s solution, which requires a rotating universe as an ingredient

– Tipler’s variant of Godel’s solution, which uses a rotating cylinder of infinite length instead of a rotating universe

– Kip Thorne’s two-way spacetime wormhole

It seems that the fundamental ingredient for time travel (i.e., on a closed timelike trajectory) is to exceed the speed of light, which seems impossible according to the laws of physics. However, some physicists have tried to develop theoretical strategies to deceive nature and, therefore, exceed the speed of light.

An example is the warp drive, which I’m mentioning for its charm. The warp drive is an engine that would allow the manipulation of spacetime, curving it in a particular way, i.e., contracting it in front of the ship and expanding it behind it. In this way, it would be possible to move at superluminal speeds even without moving. Unfortunately, however, this method would only be useful for moving extremely quickly in spacetime but would not be of any help in time travel. To travel on a closed timelike curve, the ship would have to be accelerated and travel at superluminal speeds, which is not possible.

Another strategy would be to use a wormhole, a sort of shortcut between two points in spacetime. In this case, too, we would not actually be traveling at the speed of light, but we could still cover extremely distant spacetime distances in the blink of an eye.

Moreover, unlike the warp drive, wormholes would allow time travel to the past. Let’s see how.

## Einstein-Rosen Bridge (or Wormhole)

“Only a few know, how much one must know

how little one knows”

-Heisenberg

## Scene 5 - Autumnal Glow

According to General Relativity, space-time can have some peculiar properties, such as the ability to tear (form holes or create tunnels). These tunnels are called wormholes, and if they exist and function, they would allow us to travel from one point to another in space-time.

Wormholes could be useful as time machines because they would enable travel to points in space, time, or both. However, since they have not yet been observed, they remain hypothetical and speculative for the time being.

The term Wormhole comes from a visual analogy. Imagine a worm on an apple representing the universe. If the worm wanted to travel from point A to point B, it could move on the surface or dig a hole, making the distance shorter. The hole represents the space-time tunnel, also called the Einstein-Rosen Bridge.

Wormholes can be classified in different ways, but for the purpose of this discussion, we will focus on two types:

– Intra-universe space-time tunnels, which connect different positions within the same universe. A gravitational tunnel could theoretically connect distant points in the universe through space-time deformations, allowing for faster travel than a normal journey.

– Inter-universe space-time tunnels, or Schwarzschild wormholes, which connect one universe to another. Such tunnels could potentially be used for inter-dimensional or time travel. In the latter case, the wormhole would allow for instantaneous travel between different points in space-time.

Wormholes are promising for both interstellar and temporal tourism, but there is a catch. To enter a wormhole, one would have to enter a black hole and use its center as a “portal,” which is likely to be fatal.

Furthermore, it seems like a one-way trip, since to exit a black hole, one would have to surpass the speed of light. However, physicist Kip Thorne, one of the world’s leading experts on General Relativity who worked on the Interstellar project, believes that artificial wormholes can be built.

## Double-sided Wormhole

The energy needed would be the one of a star,

or a black hole itself

## Scene 6 - Autumnal Glow Piano solo

In 1988, Kip Thorne proposed a model for a double-sided wormhole that allows for easy travel back and forth. This model is the most promising, as it would leave travelers unharmed. However, its use would require negative mass or energy to keep the wormhole entrance open. The repulsive force of negative mass would prevent gravity from devastating the entrance and the travelers.

Producing a human-sized wormhole would require an impressive amount of positive and negative energy. For a one-meter wormhole, the negative mass would need to be equivalent to the mass of Jupiter.

To make this idea feasible, we would need to solve the instability problem of wormholes and find a way to escape the radiation generated by the tunnels and inside the black hole.

Even if we could achieve this, time travel would still be extremely dangerous and costly in terms of energy. For larger tunnels, the energy needed would be equivalent to that of a star or a black hole.

## Rotating Universe by Kurt Godel (and Tipler)

“I don’t believe in empirical science.

I only believe in a priori truth”

– Kurt Godel

## Scene 7 - Reflective

It is important to acknowledge the contribution of Kurt Godel, a friend of Einstein and “the greatest since Aristotle,” to the field of logic.

Godel was the first person to find solutions to Einstein’s equations regarding the possibility of time travel, which greatly disturbed Einstein himself.

He simulated an alternative universe that was rotating and could complete a full revolution every seventy billion years. In this universe, time would be cyclical, and centrifugal force would prevent gravitational collapse. The rotation was crucial in making time cyclical. Godel believed that this universe would act as the greatest time machine, allowing a hypothetical space traveler to journey to their own past (they would need to move at the speed of light and travel incredibly far).

Unfortunately, the current evidence suggests that the net rotation of our universe is zero.

However, physicist Tipler proposed a variation of Godel’s theory, which eliminated the complication of a closed, rotating universe and instead used a rotating cylinder within the universe. According to Tipler’s theory, this cylinder could drag the space-time continuum, providing access to the past beyond certain rotation speeds. The only issue was that the cylinder would have to be infinitely long to work. To address this problem, Tipler hypothesized a finite cylinder, but this would require an even faster rotation.

## Conclusions

The only reason for time is so that

everything doesn’t happen at one

– Albert Einstein

## Scene 8 - Suspense

Beyond the technical issues that prevent time travel, we must consider ethical and legislative issues as well. For example, imagine the possibility of space-time theft or murder against someone who has not yet been born. There are also paradoxes, such as the grandfather paradox, in which going back in time and killing one’s own grandfather would prevent one’s own existence. Enabling the possibility of interacting with the past and altering the future would lead to other speculative discussions. The simplest and most promising solution to the grandfather paradox is that of the parallel universe. This is favored by quantum theory. Without it, we would have to surrender to the idea that 1) traveling into the past and altering it is something that is already foreseen, making the loop itself possible and unalterable. 2) Traveling into the past is possible for us, but alterations would not be allowed, except in the slightest form. It would be as if the guardians of time were coming to control us and prevent us from doing foolish things.

To date, it seems that the cosmic guardian preventing us from doing nonsense is interpreted by the second law of thermodynamics, which does not approve of time travel at all.

It is stated indeed that the entropy of an isolated system can increase with time but cannot decrease.

However, this is not always true. There are exceptions and, as expected, we can find them in the world of quantum mechanics. Here, there are systems for which time can go forward and backward simultaneously. As always, quantum mechanics offers us an extremely imaginative and complex alternative reality where quantum superposition occurs. Thus, the occurrence of one temporal evolution does not exclude the other because both occur in a state of superposition. This is a theoretical model that has been experimentally demonstrated on multiple platforms. Many physicists discuss a possible inaccuracy of quantum mechanics, otherwise, we would once again have to question the concept of time, as Einstein did about a century ago.

While some physicists question the correctness of quantum mechanics, this theoretical model may be a key element in understanding time travel and black holes, if it can be combined with General Relativity through a future theory of everything.

No matter which path we take, we are sure to discover exciting and incredible new physics.

### Bibliography

Michio Kaku: Physics of the Impossible – Amazon Link

Stephen Hawking: A Brief History of Time: From the Big Bang to Black Holes – Amazon Link

Palle Yourgrau – Godel meets Einstein: time travel in the Godel Universe – Amazon Link

Miguel Alcubierre – The Warp Drive: hyper-fast travel within general relativity- Link

Jean-Pierre Luminet – Closed Timelike Curves, Singularities and Causality:

A Survey from Gödel to Chronological Protection – Link