How many dimensions are there?

Hyperaxion February 27, 2020 2:53 am

In the most common sense, we know 3 spatial dimensions: length, width and height. Putting the first two together, we have a surface. When the third comes in, we have the volume. Can anyone imagine anything in 4 dimensions?

According to relativistic physics, time would be the 4th dimension.

Currently, scientists are trying to prove the existence of other dimensions besides these 4. String Theory, for example, states that there are 10 dimensions of space and one of time. That is, 11 dimensions in total.

The three spatial dimensions

We learned at school that objects in space can have up to three dimensions. A line, for example, is one-dimensional. A rectangle is two-dimensional. A cube is three-dimensional. But why is this so?

The three spatial dimensions: length, width and height.
The three spatial dimensions: length, width and height. (Source: ClkerPixabay).

From a mathematical point of view, we live in 3 dimensions because we have to use 3 coordinates to define the position of any point in space.

For example, to define the position of a helicopter that is stopped over a city, we need at least 3 geographical coordinates: longitude, latitude and altitude/elevation.

Longitude is the value, measured in degrees, that defines the location of anything on the Earth’s surface in relation to the Prime Meridian.

Latitude is the distance of anything from the line of the Equator. The Tropic of Cancer, for example, is an imaginary line that is approximately 23.5° north of the Equator.

 The major latitudes and longitudes.
The major latitudes and longitudes. (Source: TimeandDate).

If we take a paper map (which is two-dimensional), we can locate any point on that map using only 2 coordinates: longitude and latitude.

Have you played Battleship? This is a great example of using 2 coordinates to locate the position of objects on a surface. There is no need for a third coordinate for players to understand each other during a match.

Now imagine a three-dimensional Battleship game. It would not be enough for a player to say “6H” to try to bomb the enemy aircraft carrier.

One more coordinate would be needed. And this is where altitude/elevation comes in, with it you can tell what is the vertical distance between the object and a reference surface: the sea level.

But as ships will always be at sea level (altitude 0), maybe the 3rd dimension is easier to understand if we go back to the helicopter example.

Knowing the value of its longitude and the value of its latitude, it would be enough to know its distance from the sea level (its altitude) to have its exact location.

So, depending on the number of coordinates needed to define the location of a point in space, we can say how many dimensions there are. A line: 1 dimension. A flat surface, like a map: 2 dimensions. A solid object, like a cube: 3 dimensions.

Time: the fourth dimension

According to the theory of special relativity, developed by Albert Einstein, measurements of space and time are not independent of each other.
According to the theory of special relativity, developed by Albert Einstein, measurements of space and time are not independent of each other.

In relativistic physics, time is the 4th dimension, since every event takes place in a certain space but also in a certain time.

Thus, in addition to the 3 coordinates mentioned above, a fourth is necessary to define any event.

According to the theory of special relativity, developed by Albert Einstein (1879-1955) in 1905, measurements of space and time are not independent of each other, as previously thought.

Space and time are integrated, they are a single entity, they are merged. It is a four-dimensional space-time.

We are used to seeing time as something that flows evenly to anyone and anywhere. We think that time flows like a river, regardless of anything else.

Einstein overthrew that idea. For him, time is relative.

And what does that mean? That time can pass in different ways. Time is not uniform as it seems in our everyday experiences.

According to the German physicist, what really exist are times, in the plural. And this observation stems from the discovery of a connection between space and time.

 The greater the movement in space, the less time passes.
The greater the movement in space, the less time passes.

More specifically, between the movement of a body in space and the passage of time. Roughly speaking, these quantities would be inversely proportional. The greater the movement in space, the less time passes.

Pretty crazy, don’t you think? But believe me: this theory has been proven. The Hafele-Keating Experiment, carried out in 1971, proved Einstein’s theory of special relativity.

The Hafele–Keating experiment

Physicist Joseph C. Hafele and astronomer Richard E. Keating took 4 atomic clocks (the most accurate way of measuring time invented by man) to take a plane ride around the world.

They flew around the world on jet planes twice. The objective was to compare the time measured by the clocks taken on board with clocks that were stationary at the United States Naval Observatory.

At the end of the trip, they found that the time on the clocks did not match. The clocks that were on board were billionths of a second behind those on the ground.

In other words: the movement through space reduces the passage of time, and we just don’t notice it in our daily lives because we are used to very low speeds.

What about the speed of light? Today, with the technology we have, we can travel at 1% the speed of light.

The conclusion of this theory is that, in the 4th dimension, there is no distinction between past, present and future, since the perception of the “present moment” is not uniform.

String Theory: are there other dimensions?

In addition to 3 dimensions of space and one of time, would there be a 5th, 6th or 10th dimension? String theory says there are 11 dimensions!

Although quite popular, string theory has not yet been proven by science.

Uniting the macrocosm and the microcosm, it starts from the idea that fundamental particles – those that cannot be subdivided and that form atoms – are not points, as was thought, but strings.

It is a question of format. Instead of points, strings that move through space-time.

When moving, these strings leave a trail in a cylindrical shape (like a tube). Throughout this movement, these tubes interact with each other, come together and divide. The possibilities for interactions are varied.

Interpreting each string as an object of one dimension, this opens the possibility for other universes to emerge. In the case of a rope that is subdivided, two parallel universes appear. And so on.

Conclusion

Although String Theory proposes the existence of up to 11 dimensions, it has not yet been scientifically proven. Currently, it is safe to say that there are at least four dimensions, three spatial and one temporal. However, the existence of additional dimensions is an intriguing possibility. Let’s wait and see where the future of scientific discoveries will take us.

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