Why can't we travel through time?

Updated: July 8, 2006

Well, actually, we can. We do it all the time. Every moment of our life is a travel through time. But what about the movie-style time machines, time portals, worm holes etc? Can be build and use those to go back in time, see dinosaurs, meet Elvis and invest in Coca Cola stocks at the beginning of the 20th century? The answer is: no. Before I delve more deeply into physics, let's define Time.

Time, what is it?

If we accept the Big Bang theory as true or at least plausible, the world began when a tiny bubble of highly condensed something burst and started to expand through a medium we should best call nothing. Traveling at the speed of light, the Big Bang conquered more and more of this empty, physics-less medium and turned it into what we recognize as the matter.

Time also began with the Big Bang. It's a dimension, but it's also the defining parameter that gives our Universe a meaning - it gives it a depth. Our three dimensions have no meaning without time. If we could travel any distance in no time, then there would be no meaning to physical sizes of anything. Without time, our Universe could have remained peacefully locked in its primeval pixel. Apparently, the creation of time forced it to expand. The time we measure is a representation of the big, universal Time. It's our way of handling reality and parceling it into little bits. And herein lies the major problem in our understanding of Time and its limits.

We tend to separate time into seconds, minutes, years, centuries. But the real universal Time is continuous. It must be continuous, because otherwise there would be timeless gaps between its elementary segments that would have no physical definition. If we treat Time as quantized, then there's no problem all explaining all the little mysteries of our world.

If Time is fragmented, then:

We can say anti-matter and dark matter and whatever simply slipped away from our physics through the rents in Time. We can explain why the energy is quantized - the time the particles use to jump between energy levels is fragmented, and we simply cannot measure the "gaps" - they are beyond our physics. We can explain why Black Holes are so small and yet so heavy; they just shovel the matter through the time gaps and into the un-physical world beyond. Hm.

OK, so Time is continuous. This means that you cannot pinpoint any value on it. Precisely defining a value would mean quantizing it. To say the time is 100.332 is incorrect. This means that all the little continuous values after the third decimal point are "bunched" up into the last digit. In other words, 100.3325 would not be physically possible.

Some extremely important and highly defining constants in our world have this continuous behavior. One of these is a magical little number called Pi (~ 3.14). Another is e (~ 2.71). Have you ever wondered about that? Continuous Time will not let us trap it. We will never be able to "select" any single time (date) and go back to it. We will always miss it. But there are other reasons, too.

Speed of light

This speed is the speed. It's the ultimate barrier of movement. I think it's defined by time. Time probably has its constrains when wrapped around our 3D world. And one of them, possibly, is the speed of light. Making things go faster would have probably made the infrastructure of our Universe so much different. Apparently, for our Time, this was the most convenient arrangement.

The Theory of Relativity tells us that Time differs from one reference frame to another. This means that someone flying in a plane experiences Time differently than someone sitting on his front porch. Indeed, this is true. But at human speeds, the differences are so negligible that even if a person spent his entire life orbiting the planet in a jet, he would have gained only a few seconds compared to a pedestrian 10 km below. But as we go faster, things become more interesting.

Damn those BORG are gaining on us! Power on the Adamantium turbo chargers! Gimme Warp 22.2!
This image is taken from Yotophoto and is distributed under CC BY-SA license; courtesy of David Wise

Let's say we're the crew on board Enterprise. Our velocity is 98.5% speed of light in the external reference frame. In our own, we are rather static. The ship moves, but we do not feel the speed. Just like passengers on a bus. Their speed, relative to the bus, is zero. At this speed, a single minute on board our starship is equal to several years of time in the external frame frame, in the world outside. The faster we go, the slower our Time compared to the external, so-called static world. This means that at precisely the speed of light, we would be able to stop the Time.

Now, this is a tricky one. Try to follow me. Aboard our starship, our Time would continue to flow normally. We would live some 50-60 years and die. Meanwhile, in the external world, the entire lifetime of the Universe could pass by. Theoretically, for a particle or an object traveling at the speed of light, distance, hence the Time in the external world would mean nothing. We could magically jump from one galaxy or another. Sounds fun? We almost beat the Time, eh?

Not exactly ...

You see, the Theory of Relativity has one tiny problem. It neglects forces. All of the fancy equations work well for things traveling at constant speed. There's no mention of acceleration or deceleration. And this when, scientifically speaking, merde affronter un ventilateur (for the non-French among us: cacky hits the fan).

Let's say we're on board our starship. We're traveling at a certain percentage of the speed of light that in 60 seconds of our time the external world moved by 2,000,000 years. OK. So we traveled the distance we wanted. It's time to stop. We power down the engines and start slowing down. The question is, for how long are we going to be slowing down?

If we were to slow down in 60 seconds, the transition from our reference frame (our Time) to the external reference frame (external Time) would cause us to age by 2,000,000 years in just one minute. If we wanted to avoid this rather unpleasant experience, we would have to keep decelerating until our times equaled. In other words, we would have to spend the next 2,000,000 years minus 60 seconds slowing down in order to prevent hastened aging. In other words, all the Time we gained would be lost on evil forces of deceleration.

Time does not like to be cheated, and there are no shortcuts. This means that if a crew of a very fast, relativistic ship ever wanted to go back to the world it started in, the net Time bill would be the same for those aboard the ship on those on the ground. So, the only way to beat Time would be to exceed the speed of light. Unfortunately, no can do ... Come on, there must be another way of cheating Time. There is.


This name applies to the arch-nemesis of the energy. While energy to strives to be minimal, entropy strives to be maximal. Entropy is the level of disorder (chaos) in the Universe. In other words, it's the Satan of the physics. And truth to be told, we should be thankful, because without it, our world would be a very peaceful, very quiet absolute-zero graveyard of eternal boredom. Now, how this entro-thingie works? Well, let's take a classic example:

Positive entropy

Entropy wants to grow. Energy wants to shrink. Together, they make a compromise. This is what happens in a world where the temperature is above the absolute zero (-273 °C). Don't ask me why. The equations are like that. In our world, if we want to compact things (i.e. decrease entropy) we must make an effort. Our Universe is growing and trying to maximize its entropy. This entropy governs not only the layout of the galaxies and stars, it also governs Time. Yup. Now, if we could somehow make the temperature go below the absolute zero, we would be able to achieve this:

Negative entropy

Entropy has a positive sign if the temperature is positive. If, however, the temperature was negative, entropy would be negative, too. And then, the increase in entropy would be achieved by minimizing the chaos.

Minimum chaos - entropy = 0 > negative entropy

This is what we want. We want to reach negative temperature somehow. This would cause the Universe not just to physically shrink, it would cause Time to reverse and roll back. This would be a true travel back in time. The only problem is, we would not be able to sit on the outside watching this happen; we would be participating all the way, coming slowly undone. So, neither speed of light nor entropy work. Anything else? Well, I could try to prove this.


What came first, the egg or the omelet? This is a tricky question. And it applies to physics and mathematics, as well. Does the physics define the mathematical equations or do equations govern our understanding of the world?

In our world, most of what happens around us has some sort of mathematical representation. We use a notation called vectors to write down information about parameters. When they grow big, we call the vectors matrices.


A matrix is something that looks like a pair of brackets with rows of numbers inside of them. Matrices obey certain rules. One of the critical rules is that you cannot divide matrices. This means that something that feels so trivial in our life like 5 / 2 is impossible with Matrix A / Matrix B. And the reason? Well, if mathematics decide our physics, it's the limitations that the scientists that lived 200-300 years ago came up with. If it's the other way around, it's the physics that won't let us divide.

I think it's the physics that made the division impossible. Time won't let us take it back. You see, matrices are used to interpret complex physical interactions in a rather simple, algebraic way. They can also be used to describe propagation through time. A practical example: let's say a man drove his car from one city to another. Apart from the obvious physical translation from point A to point B, he also made a shift in Time. This process can be portrayed using matrices.

Now, let's say our man goes back to point B. His coordinates would reverse, but Time would not. He would still advance in Time, forward. This is, once again, easily described using matrices. We can build a chain of matrices when each one represents another stage of his travel. By multiplying matrices, we sequence the events in Time.

Going back in time would be done by dividing matrices. And this is clearly impossible. The mathematics that we use to rationalize the world does not allow it. Still, to describe reversible operations, the mathematics have come up with a clever invention. It's called the inverse matrix. This is a matrix that when multiplied annuls another matrix's effect in the chain of matrices. But the problem is - not all matrices are inversible. And those that are not won't let us delete their effect.

Time is one of them buggers.


Thus, unfortunately, we're stuck in Time. It won't let us do any tricks. Until we master some hyper-physics, which will let us go faster than light or somehow create negative temperature, we will have to entrust the time travel in the hands of the Hollywood movie makers.