Ever since H. G. Wells published his Time Machine, walks into the past or into the future, with an inevitable return to their own era, have become firmly established in science fiction. But are they possible from the point of view of modern science, at least purely theoretically?
Together with a group of like-minded people, I study time travel in the context of general relativity with certain quantum corrections. Specifically, the problem is posed as follows: is it possible to construct a curved space-time of general relativity with the help of certain quantum fields, containing closed world lines? If the world line leaves a certain space-time point and returns to it, then movement along this loop will just be time travel. For those who are familiar with the theory of relativity, I will clarify that the world line must be similar to time. This means that no movement along it should exceed the speed of light.
Semi-classical
Our approach to formulating the problem of temporal travel can be called semiclassical, since it is based on combining Einstein's classical theory of gravitation with quantum field theory. Some people say that this travel problem should be studied on the basis of a purely quantum theory of gravity, but it has not yet been created and we do not know what it will look like.
Einstein's equations are symmetric with respect to time, their solutions can be continued both into the future and into the past. Therefore, the irreversibility of time does not follow from them, which would impose a ban on time travel. However, the geometric structure of space-time is determined by the properties of matter filling space, its energy and pressure. So our main problem can be reformulated as follows: what kind of matter allows the loops of world lines? It turns out that the matter we are used to, consisting of particles and radiation, is in no way suitable for this. We need a different kind of matter, which has negative mass, and therefore, if we recall the famous Einstein's formula E = mc2, and negative energy (by the way, do not confuse such matter with antiparticles - their masses and energies are positive). This has long been proven by several physicists,for example Stephen Hawking.
Casimir effect
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Matter with negative mass and energy may seem absurd, but it has been worked out by theory and even confirmed by experiment. True, classical physics does not allow it, but from the point of view of quantum field theory, it is completely legal. This is evidenced by a physical effect named after the Dutch physicist Hendrik Casimir. If you take two polished metal plates and place them strictly parallel to each other at a distance of several micrometers, they will attract with a force that can be measured (which was first done 15 years ago). This attraction is explained precisely by the fact that the space between the plates has negative energy.
Where does it come from? For simplicity, we will assume that the plates are located in an ideal vacuum. According to quantum theory, all the time there are born and disappear a variety of fluctuations of quantum fields, such as virtual photons. They all contribute to the average energy of the free vacuum, which is zero. For this to be possible, some of the fluctuations must have positive energy, and some must have negative energy.
But near physical bodies this balance may not be observed. In particular, in the space between the plates, “minus” fluctuations dominate over “plus” ones. Therefore, the density of vacuum energy there is lower than the energy density of a free vacuum, that is, less than zero. This density is inversely proportional to the fourth power of the width of the gap between the plates, while the volume of the interplate space is proportional to the width itself. So their product has a negative sign and is inversely proportional to the cube of the slot width. As a result, when the plates approach each other, the total vacuum energy of the interplate space falls more and more below the zero mark, and therefore it is energetically favorable for them to be attracted to each other.
Time patrol
But back to time travel. Since ordinary matter has a positive mass, it is impossible to make a device from it that can travel in time. If this problem is solvable, then only with the help of some configurations of quantum fields that provide negative energy throughout the closed world line.
However, it is apparently simply impossible to create such a configuration. This is hampered by a very important limitation called the Averaged Null Energy Condition (ANEC). Mathematically, it is expressed in a rather complex integral, and in simple common human language it states that any contributions from negative energy along the world lines of photons should be exactly or even with excess compensated by additions of positive energy.
According to all available data, nature complies with ANEC with no exceptions. It can be shown that the Casimir effect also obeys this condition. For example, if we make two holes in the plates opposite each other and pass a light beam through them from the outside through the interplate space, the total amount of energy changes along its world line will be positive.
How does this affect time travel? It can be proved that if a certain analogue of ANEC acts in a curved space of general relativity, then such travels are impossible.
In other words, this version of ANEC, which we called achronal, imposes a ban on any projects of time machines made using matter with negative mass.
Now I am working with my students on the mathematical proof of this version, and it seems to me that we have already achieved something.
If we succeed in constructing the required proof, the fundamental impracticability of the time machine will be demonstrated - at least within the framework of the semiclassical approach. And since we do not have a complete quantum theory of gravity yet, this conclusion will have to be accepted at least before its creation.
Ken Olum, professor of physics at Tufts University.
Interviewed by: Alexey Levin, Oleg Makarov, Dmitry Mamontov