Tuesday, July 5

What are light cones and why are they a very valuable tool to better understand the amazing properties of space-time

Although he is less known to the general public than some of his contemporary colleagues, the American theoretical physicist John Archibald Wheeler has bequeathed us one of the best condensing descriptions the geometric essence of the space-time continuum: “Space-time tells matter how to move, and matter tells space-time how to bend.”

The notion that time is inextricably linked to the three spatial dimensions is a direct consequence of the two expressions of the theory of relativity formulated by Albert Einstein at the beginning of the 20th century, the special and the general. However, as the mathematical model that it is, spacetime gives rise to a continuum that brings together all the events that have taken place in the universe from the first moments of its formation.

In a completely natural way we have just introduced the need to represent the space-time continuum using a strategy that respect its geometric essence, and that, at the same time, allows us to describe the evolution in time of a certain event. This is precisely the role of light cones, a very valuable resource that in the field of relativistic physics has another essential role: to establish the relationship that exists between the cause and the effect of a certain phenomenon.

Light cones help us understand the relationship between space and time

Before we see in the most intuitive way possible what a light cone is and what it is for, it is worth it. let’s formalize the definition of event to leave our starting point well tied. An event is any event that occurs at a specific point in space and at a specific instant in time. This notion is essentially the same one that we have all arrived at intuitively from our everyday experience.

Light always travels at the speed of light. It does not even matter how fast the source that is emitting it is traveling

At this point it is necessary that we introduce light into the recipe that we are making. One of its most surprising properties is that in a particular medium always travels at the same speed. In a vacuum, light moves at approximately 300,000 km / s, and in this particular medium the photons that make it up always travel at this speed. They do not accelerate. Nor do they slow down. If they do not change the medium, their speed is always the same.

And if they do, if they change their medium, for example, when passing from the vacuum of space to the Earth’s atmosphere, their speed changes instantaneously. Without experiencing any type of acceleration or deceleration. Definitely, light always travels at the speed of light. It doesn’t even matter how fast the source is moving. These properties are somewhat unintuitive because they contradict the behavior of the objects that we observe in our everyday surroundings. But the light is like that. Strange and amazing.

When expanding from a certain event, the light acquires the shape of a three-dimensional cone in the space-time continuum, which has four dimensions.

When a source emits a pulse of light from a specific point in space and at a specific instant in time, as the latter elapses the light is spreading, acquiring the geometric configuration of an imaginary sphere whose size and position are completely independent of the speed of the source. As time passes, the light ‘scatters’, so that the diameter of that imaginary sphere expands.

In his ‘History of time’ Stephen Hawking describes this phenomenon quite intuitively: “After a millionth of a second the light will have scattered forming a sphere with a radius of 300 meters; after two millionths of a second the radius will be 600 meters, and so on. ‘ When expanding from a specific event (we are interested in keeping in mind the definition of an event that we have reviewed a few lines above), the light takes the shape of a three-dimensional cone in the space-time continuum, which has four dimensions (it brings together the three space and time).


Physicists call this object future event light coneFrom it, using the same idea, we can represent the past cone of light, which contains the set of events from which a light pulse is capable of reaching the event that we have taken as a starting point. From this premise, any event A ‘that can be reached from an initial event A by a particle or a wave that travels through space-time as very fast at the speed of light will form part of the future of A. By this reason, the event A ‘will be included in the interior or on the future light cone of A in the diagram representing space-time.

To fully understand this idea it is necessary to make a small effort of abstraction, but I trust that the illustration that we publish above these lines will help you to intuit with some precision what we are talking about. What we have just seen has a very important consequence: only the events contained in the future light cone of A can be influenced so it happens in A because nothing can travel faster than light.

All events in the space-time continuum have their own cone of light, and, furthermore, all cones of light are identical and oriented in the same direction.

If we look at the last cone of light we can carry out the same operation. The past of A contains all the events from which it is possible to reach event A by traveling at the speed of light or slower. In this way, everything that conditions these events can influence A. Once we have reached this point, we can intuit that all the events of the space-time continuum have their own cone of light, and, furthermore, since the speed of light is always the same and does not vary with direction, all cones of light are identical and oriented in the same direction.

What we have just seen invites us to introduce in a natural way the idea of ​​causality, which intuitively establishes the relationship that exists between two given events. In this way one of them is to some extent the result of what happens in the other. The possibility of violating this principle can trigger the appearance of paradoxes, a problem that becomes very relevant if we consider the possibility of traveling back in time (although a new mathematical model maintains that there is a way to avoid temporal paradoxes).

Everything we have seen throughout this article is helpful in laying the foundations of the physics of time travel, an exciting topic in which science has a lot to say, and that, if it attracts you, we can address in another report. Until then, I can only propose that if you want to investigate a little more about the light cones and their role as representations of the space-time continuum, take a look at any of the scientific publications that I suggest in the bibliography of this article. All of them are very worthwhile.

Images | Pixabay | Ignacio Icke

Bibliography | ‘Einstein’s General Theory of Relativity: With Modern Applications in Cosmology’, by Øyvind Grøn and Sigbjorn Hervik | ‘Theory of Relativity’, by Wolfgang Pauli | ‘History of time: from the Big Bang to black holes’, by Stephen Hawking


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