The time formula

In the society we live in, we are always looking at the clock. We set an alarm for a specific time, we wake up, have breakfast and head to work to start at a specific time. We spend eight hours and return home. At home we rest for a few minutes and go to pick up our children from school since they leave at a specific time.

We base our entire lives on time and hours. We organize our lives around this concept.

But... What is time?

Does it really exist or have we invented it?

Well, it turns out that time is a very complicated concept to define. Physicists from all over the world try to give definitions. However, we still don't really understand what it is.

Today, we will try to give a view of time from different points of view of modern physics. We will start with classical mechanics, continue with statistical mechanics and quantum mechanics, and finally end with Einstein's general relativity.

Do you want to discover the mysteries that time holds?

Forward!

Classical mechanics are the physical laws that derive from Newton's three principles. Newton's second law tells us that force is equal to the derivative of linear momentum with respect to time, which is equivalent to saying that force is equal to acceleration times mass.

In this theoretical framework, time is considered an absolute value, which occurs in the same way for all observers.

Furthermore, the formulas in classical physics have temporal symmetry. That is, the equations are fulfilled in the same way whether time goes forward or backward.

In classical physics we use time to calculate velocities, accelerations or positions through the equations of motion.

It is a simple number that we enter into our equations to make calculations. Time is absolute, linear (it runs in one direction and reversible.

In fact, this concept of time is the one that is most deeply rooted in our society. Time happens the same for everyone.

We meet our friends at a specific time since we know that time passes the same for all of us and that if at a certain time we are in the same place, we will share that point in space-time and we can go have a beer and chat.

But is time really absolute? Or it is simply a product of our mind where we remember the past and forget the future, having a false sense of the present and an illusion of the fluidity of time.

Let's continue our search...

Mathematical equations say nothing about the meaning of time. These are applicable both to go forward in time and backward.

However, our intuition tells us that a glass breaks, but is not regenerated, or that a sugar cube dissolves in coffee, but once disposed of, the cube is not converted again. Therefore, it seems that there is only one meaning.

This is where the second law of thermodynamics or also known as the arrow of time comes into play, which postulates that the entropy of the universe always increases.

But... What is entropy?

Well...

This concept is also difficult to define since it does not represent any palpable magnitude in our daily lives.

In institutes and universities around the world, entropy is defined as disorder. That is, the greater the entropy, the greater the disorder. Therefore, we could redefine the second law of thermodynamics as that the universe always tends toward disorder.

Personally, I don't really like this definition. I prefer the definition used by the famous theoretical physicist Leonard Susskind in his presentations (you can see them on YouTube). He defines entropy as the degree of misinformation we have about a system.

For example, before breaking, a glass has all its atoms arranged in a specific way. When the glass falls and breaks, the components that make it up can take many different positions.

Therefore, the degree of accessible information about when it is broken is much lower since there are many ways in which the glass can be broken, but only one way for it to be whole.

Entropy, in the end, is a probabilistic concept. Disorder means that a system can take on many different conformations, increasing the system's degrees of freedom and decreasing the amount of information we can obtain from it.

Let's take another example: when water is at absolute zero, its molecules are completely still, arranged in only one way. In this case, its molecules can only be found in one position and the system is completely “ordered”, so its entropy is zero.

However, if we increase the temperature, the water molecules begin to move, so the positions in which the molecules can be found are many, or in other words, there are many microstates of the system. This causes the degree of misinformation in said system to increase, thereby increasing entropy.

In short, the concept of entropy establishes a temporal arrow. Mark what events occur in our universe and the direction of these.

In the 20th century, one of the most revolutionary theories of all time arrived: the theory of general relativity, formulated by Albert Einstein.

General relativity is very complex to understand in depth since it makes use of complex mathematics such as tensor algebra or differential geometry.

Don't worry!

We will try to give a few glimpses of this beautiful theory.

General relativity introduces the concept of space-time. Space-time can be visualized as a fabric that includes three spatial dimensions and one temporal dimension.

This space-time fabric can be deformed by matter and this is exactly what the equations of general relativity relate: How much matter do I need to be able to deform space-time?

Therefore, time is not something linear and flowing, but exists as a block and the future and the past is simply an illusion of ours. Everything has happened and is happening at the same time.

In fact, hypothetical wormholes are portals that would take us from one point in time to another, being able to go to the past ????

What's more, general relativity also tells us that at points where there is greater gravity, time passes more slowly.

Have you seen the Interstellar movie?

At one point in the film they land on a planet very close to the massive Gargantua black hole. Once there he finds Dr. Miller, who was trapped years ago on that planet.

However, the gravity is so high on that planet that for Dr. Miller it has only been a few hours since she was trapped on that planet.

However, for the rest of the people it had been there for years.

Time had passed differently for her!

Once they recover Dr. Miller, they return to the ship where the other crew member was waiting for them.

For the crew member on the ship it had been around 20 years while for the rest on Miller's planet it had only been a few hours!

One hour on Miller was equivalent to seven years on the Endurance mothership.

This is just a movie, but this fact is real.

In fact, did you know that your feet are younger than your head since the force of gravity is greater on the feet as they are closer to the center of the Earth?

Here we come to the big conclusion: time is relative.

Yes, yes, time is relative and not absolute as previously believed.

Einstein's special relativity tells us that two observers in relative motion experience time differently.

What does this mean?

Let's give another example!

Imagine that you are on the platform of a train station and just as a train passes by (without stopping) at high speed, two lightning bolts strike at the same time. For you, lightning has struck at once. However, for an observer inside the train, first one has fallen and then the other.

Who has the reason?

The truth is that both...

There is no absolute reality. There is a reality for each observer. Two events that for you may be simultaneous, for another person may not be. Simultaneity is relative.

Special relativity also tells us that the greater our speed, the slower time passes. This has been verified using the most precise clocks that exist: atomic clocks.

If we leave an atomic clock on the ground and another on a plane, when the plane lands we will see that the one we left on the ground shows that more time has passed than the one that was on the plane.

This is another fact that affirms the power of special relativity and that time is not absolute. Each observer has his own time.

Ok, I accept that it is too much...

Rest your mind a little because we haven't told you the most amazing thing yet...

What does quantum mechanics tell us about time? You're going to freak out...

I want to tell you about an experiment that left me speechless when I discovered it. This experiment is called the delayed selection quantum eraser.

It's a little hard to explain, but I'll try to do the best I can.

Do you remember the double slit experiment initially proposed by Thomas Young?

Let's summarize it:

In the double slit experiment, a source of electrons is launched through a double slit. If we use a device to measure which of the two grids the electron comes out of, we see that the electrons behave like a particle. However, if we do not measure the position of the electron, what we see is an interference pattern. That is, the measurement makes the electron behave like a particle and not like a wave.

The starting point of the delayed selection quantum eraser is the double slit experiment.

Just after the slit, a crystal is placed. When a photon passes through it, the crystal causes two quantumly entangled photons to emerge. We send one of the photons through a meter and the other not.

What happens is incredible...

When we measure one of the photons we see that the other (which we did not measure) behaves like a particle. On the other hand, if we do not measure either of them, then it behaves like a wave (an interference pattern is shown).

What this experiment tells us is as if the photon that is measured could travel to the past and tell the other photon: behave like a particle!

There is a retrocausality from the future to the past.

In this video you can see the experiment visually which will help you understand it better.

This article is titled the formula of time.

However, we still do not know what time is. As we have seen, time seems to behave very differently than we have thought throughout the history of humanity.

This leads me to think...

Does time really exist or is it just a product of our brain?