Time Travel - Theories, Possibilities & Paradoxes

Is it possible to make a time machine? What will happen if we travel back in time and change history? Is the nature of time immutable & fixed or fluid and flexible? These are some of the few burning questions you might have if you are slightly interested in the concept of time travel. The nature of time is so fundamental in our everyday life that we seldom think about it yet it is one of the most ill-understood concepts of physics. 

Let’s talk about the very interesting nature of time, the possibility of traveling back or forth in time, and the repercussions of doing so on recorded history. Unlike Hollywood pop culture movies about time travel, this article is based on established and well-respected concepts of theoretical physics.

In 2009, theoretical physicist and science populariser Professor Stephen Hawking threw a party in his college, Gonville, and Caius in Cambridge. It was not an ordinary party. It was a party only for the time travelers and tourists from the future. What was so special about that party? Well, the party was on Sunday evening, and the invitations were sent out the next Monday so that only genuine time travelers could attend the party. However, to his disappointment (and not to his surprise), no one came.

“I had shown that if General Relativity is correct and energy density is positive, time travel is not possible. I would have been delighted if one of my assumptions had turned out to be wrong.” The Professor later wrote in his book.

Did Professor Hawking prove that time travel is not possible at all? Well, not exactly. 

Let’s first understand what exactly time is.

 What is Time? 

Time is defined as an interval between the occurrence of two events. This is the simplest of the definitions that we can easily understand and use in our everyday lives. It has a specific direction and can be measured with devices that exhibit an inherent periodic motion (rotation of the earth around the sun, the vibration of cesium-133 isotope). The idea of time is so fundamental that we rarely think about the nature of it. But the nature of time is one of the most ill-understood things in modern science.

My personal favorite time statement is that time is the distance between the occurrence of events in the 4th (time) dimension. Just like there is a certain distance between things in 3 space dimensions, there is a distance between events in the temporal dimension. (interesting question: can we use a unit of length like a Meter to measure the distance between two events? If so, what would be the underlying constant? Answer in the comments section)

A more in-depth investigation uncovers some fascinating questions about the nature of time. Where did the time begin? What started the time? Can it only go from the past to the future and not the other way around? Is the passage of time fixed for everyone? Will time ever come to a halt? Can we go forward in time? Can we go backward in time? All these questions are the enigma of the current era.

 Pre-Einstein Era of Time 

Before 1905, time was considered to be a fixed stage on which the events of the cosmos unraveled. It was considered to be fixed, inflexible, and unaffected by the events that took place in the universe. All this changed in 1905 when an unknown clerk from the Swiss patent office named Albert Einstein revolutionized the world of physics with his remarkable insights about Time & Space in his paper.

Einstein argued that two observers, moving relative to each other, will never agree on the time & position of occurrence of an event. This simple but remarkable theory, which came to be known as the Special Theory of Relativity, presented the concept of Space-Time. It presented the idea that space and time are not separate entities; instead, they are inextricably intertwined. Time, which was previously considered to be universally absolute, was replaced with a new notion of time, which is dependent on the reference frame and spatial position. The new time can be elongated and slowed down by the relative motion of the reference frames.

The Space-Time 

Space-time is defined by 3-spatial and 1-temporal dimension, a total of 4 dimensions. Together, they tell exactly where you are in space and time. If you have to meet someone, you will tell them the address of the building (defined by longitude & latitude), which floor you are on (altitude), and what TIME you want to meet. Using these 4 parameters, your guest will be at the right place at the right time.

 Our Motion Through Space-Time

Let’s make a statement first, and then we will dive deep into the details to explore the intricacies of the flow of time. The statement goes something like this;

“We are all traveling through space-time with the speed of light.”

By “we” means every atom in the universe. Yes, we all are traveling through space-time with a speed equal to the speed of light. Doesn’t that make sense?

Let’s take an example of a simple motion in the XY plane. Imagine you are driving your car along the X-axis at a velocity of 30 km/hr. While you are going in a straight line on the x-axis, the Y component of your velocity is zero. Now, after traveling for a few miles, you decide to steer left a little and keep your speed the same. Now, you are traveling between the X-Y axis. Your velocity now has two components; An X component & a Y component. The vector sum of both velocities will be equal to 30km/hr, but individually, both velocities will be less than the sum. 

Now think for a moment about what really happened here. If you understand this correctly, you will be able to get the whole “we are traveling through space-time…” statement quite easily.

When you were traveling on the X-axis, your total motion was concentrated in just one direction. Your displacement through the y-axis was zero. When you steer towards your left (keeping your speedometer reading the same), you distribute your total motion between the x & y axes. Now, a part of your motion is in the X-direction & the other part is in the y-direction. Both are less than your initial total motion in the X-direction. So, we can say that when you started moving in the Y direction, you decreased your total motion in the X direction and assigned a part of it to the Y direction (which was zero initially).

Now let’s replace the X dimension with TIME & Y dimension with SPACE (you can pick any of the 3 spatial dimensions for simplicity). When you are at rest, you are not moving in SPACE. Your total motion is concentrated in the TIME direction (just like the car moving along the x-axis). The moment you start moving in space (start walking, ride a car, get on a plane), a part of your motion through TIME will be distributed in the SPACE dimension, but the sum of your total motion through TIME & SPACE will remain the same as before.

Pay attention now. 

What exactly does this imply? The faster you move in the SPACE dimension, the slower you move in the TIME dimension. This is a direct implication of Einstein’s Special Theory of Relativity that time & space are intertwined. When you speed up in SPACE, you slow down in TIME, and vice versa. Your total speed in space-time will always remain the same, i-e 299792458 m/s.

Can we stop time? 

Now, this is the interesting part. As we discussed above, when you are at rest in SPACE, you are moving through TIME at the speed of light (i-e 299792458 m/s). We can say that if you want to come to rest in TIME, you will have to divert all your motion towards the SPACE dimension i.e. start moving through SPACE at the speed of light.

Interesting, isn’t it? To stop the flow of time, you have to travel at a light speed.

In our daily lives, we move at relatively lower speeds compared to the speed of light, so we never sense the slowing down of time. Time slows down, but with such a minuscule amount that we humans cannot sense it without the use of special equipment, e-g precisely calibrated atomic clocks.

But what if you want to go BACK in time? All you have to do is start traveling at a speed higher than the speed of light. Simple right?

Actually, No. Special Relativity gives us a possible doorway into the past, but at the same time, it locks the door with an unbreakable lock – the speed limit.

The Universal Speed Limit 

Special Relativity puts a speed limit on how fast massive bodies can move – the speed of light. No particle with a positive rest mass can travel faster than the speed of light in a vacuum. 

The speed of light in a vacuum is a universal constant. No matter how hard you try, you will never be able to catch or outrun a beam of light in a vacuum.

Let’s discuss the reason why massive particles cannot reach the speed limit (Note: If you don’t appreciate a bit of simple mathematics, you can skip to the next section and continue without a problem)

Let’s say you somehow build a rocket ship that can travel at an increasing velocity. When the rocket ship is at rest, it has a certain mass(m), and to move it, you will need a certain amount of force (f) by spending a certain amount of fuel as an energy source.

Remember Einstein’s famous equation that implies that mass & energy are inter-convertible? The famous E = mC2. If we rearrange this equation, we will get the definition of rest mass.

m = E/C2

i-e the mass of a body is equal to the amount of energy (matter) it has at rest. Now, when the same body is in motion, another component gets added up to the mass equation and that is the kinetic energy. Now the mass (we call it relativistic mass) is represented with something like this.

m = E/C2 + kinetic energy

Let’s go back to our rocket ship example. Now, when we fire up the rocket engines and our velocity increases, our kinetic energy also increases, and as evident from the equation of relativistic mass, the mass of the rocket ship also increases.

With increasing speed, the force required to push the rocket further also increases (f = m.a). When the speed approaches the speed of light, the relativistic mass, and by correlation, the force required to push it further approaches infinity.

So, to cross the speed of light, we will need an infinite amount of force. An infinite amount of force will require an infinite amount of fuel or energy, which is not possible hence the speed limit.

So, Is it possible to make a time machine to travel back to the past or into the future? Let’s discuss one by one.

Traveling into the future 

Due to the speed limit put on massive objects by Special Relativity, we cannot travel back in time (hold on, we have a workaround coming below). However, there are no such theoretical restrictions on traveling into the future. 

Both Special Relativity & General Relativity propose ways through which one can slow down time for himself and watch the world fast-forward into the future. 

Let’s discuss both.

As we discussed before, whenever you travel at high speed in space, your time slows down compared to everyone else around you. 

That’s a great hack to jump forward into the future. 

All you have to do is get into a spaceship, leave the earth, and travel for some time (let’s say 3 months according to your wristwatch) at a good fraction of the speed of light (let’s say 99.99% of C), turn back and travel at the same speed to return to earth. When you land on earth, you will notice that you have aged only 6 months (ignore the time it took you to accelerate to 99.99%C and slow down) according to your wristwatch, but the world has fast-forwarded almost 35 years. Now you are in the year 2055, and all your college buddies are retired (or dead), but you are still 28 years old (almost the same age as you left the earth in 2020)

I know we have not discussed what General Relativity is, and I am not going to open a whole new chapter here but understand this – General Relativity tells us that mass and energy warp or ‘bend’ space-time around them and gives us the feel of a force we call the gravity. In extreme cases, the bending or warping of space-time is so severe around very massive bodies that even light is bent or even trapped inside the warpage.

In the vicinity of such massive objects like black holes or very massive neutron stars, time is slowed down considerably relative to the surrounding universe.

We can use such massive bodies to jump into the future theoretically. 

Let’s say we discover a nearby supermassive black hole. To jump into the future, we will travel to the vicinity of the black hole and stay just above a region called Even Horizon(EH). EH is the last point in the vicinity of a black hole from where you can possibly turn back. Once you cross the EH, there is nothing you can do to come back. The gravitational pull of the dead star is so massive that even light cannot escape the EH.

Let’s come back to our ‘time travel to the future’ hack.

To jump forward in time, all you have to do is spend some time just above the event horizon and see the world events shoot past you like an old VCR tape film in fast-forward mode. When you are in 2055 or any other preferred era in the future, you can just turn your booster rockets on and come back to the future – easy peasy, right?

Traveling back in time

Since we discussed the possible impossibility of traveling back in time due to the limitation set by Special Relativity on how much fast objects can travel, does that mean we can never go back in time?

It seems that way, but we have a workaround.

It has something to do with manipulating wormholes. Wormholes (also known as Einstein-Rosen bridge) are gravitational anomalies in the space-time continuum where a negative energy density curves the space-time onto itself, allowing for possible travel back in time. Wormholes are a theoretical prediction of General Relativity. Although there is no experimental evidence of the existence of wormholes, the science behind them is very solid.

Wormholes are not a naturally occurring phenomenon. They are inherently unstable and will collapse onto themselves and will need a matter that has repulsive gravity to allow anything to pass through them (even light).

Did you see something unfamiliar in the above paragraph? What are this negative energy density and repulsive gravity? You might ask.

Negative mass is also known as exotic matter, has the opposite effect on space-time compared to the normal mass in our universe. Its gravity is repulsive, and it bends the space-time in the opposite direction of the normal mass/matter. Negative mass is not just a theoretical concept. Its existence has been verified through an experimental setup (read about the Casimir effect if you want to dig down further), but there is currently no economical way of producing the amount required to stabilize a wormhole.

If we somehow create enough exotic matter to open a wormhole and keep it stable for long enough for us to pass through, we might be able to create a working time machine. Of course, it's easier said than done, but an advanced civilization has a real chance of making one such time machine. So this answers our starting question of whether it is possible to make a time machine.

(The exact setup of wormholes to allow time travel can be a topic of a separate discussion but for now, understand that a particular arrangement of two or more stabilized wormholes can allow travel back in time).

Time Travel Paradox

Although time travel at this point is merely a speculation, something we might not see in our lifetime, the mere possibility of it still opens up a bunch of paradoxes. They are as interesting as they are mind-boggling.

Causality is an important concept in physics, which says that every effect had a cause in the past. According to Special Relativity, A cause cannot have an effect outside of its future light cone (due to limitation on the speed of light), and similarly, an effect cannot have a cause outside of its past light cone. 

If you travel back in time and kill your grandfather, will you be born to go back in time and kill your grandfather?

You are traveling back in time (a cause in the future of your grandfather) and cannot have an effect (murder of your grandfather) in the past. If it happens, it will violate the causality law set by Special Relativity.

What if you build a time machine, go back in time, and prevent yourself from building the time machine? Will you still be able to build the time machine to go back in time?

If any future generations were to develop time machines, why haven’t we seen someone from the future visiting us (remember Prof. Hawking’s party)?

It seems like the laws of physics are conspiring against humans traveling back in time and changing an observed history. Stephen Hawking called this Chronology Protection Conjecture.

Of course, the discussion of time travel back into the future and changing history doesn’t end here. It gives rise to more questions than it answers. Is our history fixed? Do we have a unique history or an infinite number of histories with variable probabilities? What will happen to our memories of observed history if we somehow go back and change what we observed? Is our reality even real?

We have barely scratched the surface of the nature of time.

Bonus read: Sum-over-histories by Richard Feynman 

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