Space-time can be understood as the place where all the events that have taken place and will take place are found.
We can imagine space-time as a block of three spatial dimensions and one temporal (better to imagine only two spatial and one temporal for simplicity, like the package of sliced bread).
When an observer takes measurements, she is observing events as "her time" passes.
It is as if we are slicing the block into spatial slices, each slice will be the photograph of what she can see in an instant.
Since when does spacetime exist?
An observer moving at a certain constant speed with respect to the observer will see things differently.
As the speed of propagation of light in a vacuum must be the same for the observer and the observer, this implies that "their time" is different and also their succession of photographs;
in it it will be the observer who is moving.
This means that if we consider two events, the measurements of time intervals and distances between these two events will be different for each person who observes depending on their relative speed.
The intervals of time or distance are relative according to the theory of special relativity, that is, the observer can see that two events are closer together or more apart than the observer;
and others that are simultaneous for him will not be for her.
We can say that the separation between two events (points of space-time) is spatial if it is impossible to send a light signal from one event to the other. If it is possible to send this light signal, the separation of these events is not spatial; whether the signal goes from one to the other or from the other to the first depends on the sense of time. The fact that the space-time interval is an invariant means that the separation between two events continues to have the same nature (spatial or not) for the observer and the observer. All the events that could or could be connected with me through light signals (with my self of this moment, understood as an event) are within what we call "my cone of light" that is defined in space-time. Actually, they are two cones, both with the vertex at the point in spacetime where I am right now,with the height along my timeline, but the past light cone (my past) opens in the opposite direction than the future light cone (my future)… sure. We cannot change the orientation of these cones.
That the space-time interval is an invariant, makes the separation between two events continue to have the same nature (spatial or not)
But if we go one step further and take gravity into account, we are in for a surprise. General relativity is not only a theory of gravity, but a theory of space-time, which becomes a physical entity when it is bent by the material content. The light cones will not all be oriented in the same directions, but depending on the point they can be deformed and have different orientations. Therefore, if we think of my life, drawing my “world line” in space-time as the succession of points where I have found myself and will find myself, the cones with vertex at each point of my line could be tilting, But, so much so that my future cone at some point becomes oriented towards where my past cone was oriented?
Mathematically the equivalent rigorous question that we ask ourselves so that it does not seem that we are considering going to the past would be, are there closed time curves? These curves would allow us to return to the time and place where we already were, although not to travel the same region of the curve (our life) in the opposite direction.
We think that the answer to this question must be negative. Although there are solutions of general relativity that could contain closed time curves, these solutions appear when considering very particular situations or substances that do not seem likely to exist (not only because they have not been observed but because their existence would challenge our understanding of matter). After all, any theoretical space-time can be described by means of general relativity, another thing is that the material content that must generate it exists and, therefore, it occurs in nature.
If the circumstances were to arise for these solutions to describe parts of our Universe, this would open a Pandora's box of paradoxes, so the idea of the scientific community is that these solutions, in principle possible although improbable, should not be given in reality.
The last word does not lie with the theory of general relativity alone.
As observation tells us that this does not happen, we believe that there is some principle of nature, yet to be revealed, that prevents it.
As we still do not know how to combine quantum and gravitational effects completely, a theory that successfully combines them could impose some condition that would rule out the existence of regions of spacetime with closed time curves. In fact, results in this direction have already been obtained through theoretical studies that consider quantum effects near these regions. Stephen Hawking postulated the chronological protection conjecture following this idea, which according to him could be tested experimentally simply by noting that we are not being invaded by hordes of tourists from the future.
So the answer to your question is that according to general relativity in principle it is not ruled out that you could go back to your past, although it seems very unlikely.
If you could do it, the journey would not be watching the movie of your life backwards but following a particular path of space-time.
But the last word does not lie with the theory of general relativity alone.
As observation tells us that this does not happen (there are no hordes of tourists of the future in our world) we believe that there is some principle of nature, yet to be revealed, that prevents it.
Prado Martín Moruno
doctor in theoretical physics, professor and researcher at the
Complutense University of Madrid
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