As science explains the flow of time, in many physical equations its directions do not seem to exist, physics often does not see a special point of the present. The most common explanation of the arrow of time is related to thermodynamics: it is the increase in entropy in the universe that determines the direction of the flow of time, not allowing physical processes to reverse.

But Sergey Rubin, a professor at the Department of Elementary Particle Physics at the National Research Nuclear University MEPhI, proposed a new concept of the nature of time: the arrow of time is determined by the expansion of the universe in a wide range of dimensions, including hidden ones. Thus, time would flow even if there were no matter in the universe, but only a vacuum. This is his article in The European Physical Journal C. Kommersant-Nauka talks with Sergey Rubin about the main provisions and problems of his theory.

— In classical physics (Einstein), time is merely a coordinate, on an equal footing with space. In thermodynamics, it is a measure of the growth of entropy. What, according to Professor Rubin, is the essence of time, and why can his approach be called “geometric imperialism”?

— The main problem with the concept of time is that in gravity it is indeed one of four equal coordinates, whereas quantum mechanics singles out the time coordinate, for example, when writing the Schrödinger equation. This is one of the reasons why a theory of quantum gravity has not yet been developed.

From the perspective of gravity, we have a four‑dimensional space defined by four coordinates. There is no arrow of time. The main question is how to choose one coordinate from the four initially equal ones. This is what the article in the journal is devoted to. As for “imperialism” — I’m not at all sure that this approach can be called that.

— The main revolutionary thesis states that time will flow even in complete emptiness. If you remove all particles, fields, and radiation, what exactly will be “ticking” and creating the difference between “before” and “after” in a vacuum?

— It will be the gravity of the additional space that will be “ticking.” If you remove all particles, fields, and radiation, the geometry of the additional space may still change. And it is this change that creates the difference between “before” and “after.”

At present, one of the actively researched areas in modern theoretical physics is the hypothesis about the existence of additional spatial dimensions that are so small that we cannot detect them with any instruments. If additional dimensions exist, then experiments tell us that their size must be at least five orders of magnitude smaller than the atomic nucleus. The properties of additional dimensions can determine the parameters and effective laws of physics observed in our four‑dimensional world. An analogy can be a sheet of paper on which two‑dimensional creatures live. They don’t feel the thickness of the sheet, but it’s the thickness — the third dimension — that determines whether it’s paper or copper foil.

— A new fundamental postulate is introduced: any transition increases entropy. Is this merely a reformulation of the second law of thermodynamics in geometric terms, or does this postulate prohibit something that the second law still allowed (for example, fluctuations in small systems)? Mechanism and difference.

— The second law of thermodynamics states that, purely statistically, a system transitions to a state with a greater number of states, with the assumption that the arrow of time already exists. The second law of thermodynamics relies on the existence of the arrow of time, rather than proving it.

Long‑standing debates among scientists, starting with Penrose, are gradually leading to the conviction that there must be a new law of nature — a postulate that explains how time emerges from four initially identical coordinates. Various forms of such postulates are known in the literature. The article proposes its own formulation.

— We see the ordinary Universe — it is expanding. How exactly does the collapsed (compactified) dimension “expand”? What does “growth in volume” mean for something that, by definition, is smaller than the Planck length, and how can we mathematically describe this growth?

— Imagine an island in the ocean. This is an analogue of compactified space. People can live on this island and know nothing about the ocean. And, by the way, about neighboring islands. The expansion of the ocean is analogous to the well‑known and proven expansion of the Universe.

— The text mentions a gigantic number, 1064106410641064, for the growth of entropy. How is this parameter related to the age of the Universe? If the expansion of hidden dimensions were to stop, would time stop, according to this model?

— This is a rough estimate of the change in entropy over the lifetime of the Universe. If the expansion of hidden dimensions were to stop, there would still be the expansion of our Universe, which provides the well‑known cosmological arrow of time — though it is much weaker than the multidimensional one. What such a change would lead to remains to be seen.

— The brane world model describes us as passengers on a ship who cannot see the current. If we are "glued" to a 3-brane and cannot penetrate the bulk, can we experimentally record this "flow" (for example, through anomalies in the gravitational constant or in the spectrum of cosmic microwave background radiation)?

— This is the most difficult question of modern physics in general. It concerns not only extra dimensions, but also particle physics and the origin of the universe with its known laws. The thing is that it seems that all of physics is formed at Planck scales, while modern instruments can only access much larger scales — 14–15 orders of magnitude larger than what is needed to test the models. Therefore, the answer is yes, generally speaking, all these theories and models are testable, but not at present. This makes it impossible to distinguish one model from another, which is why there are many models, and it’s unclear what to do about this at the current stage.

— Traditionally, physicists have had to postulate that at the beginning of the Universe, entropy was very low (a strange condition). How does the proposed mechanism free us from this “unnatural” assumption? Does entropy arise out of nowhere simply due to the emergence of new volume?

— Entropy increases with volume. In simple terms, the volume is filled with a gravitational field, which generates entropy. The smallness of the initial entropy of the Universe is necessary to justify the current entropy of the Universe, assuming that only the cosmological arrow of time is at work. The growth of the volume of additional dimensions is so rapid that it doesn’t matter what the entropy was initially. Over the lifetime of the Universe, the entropy will increase many times over compared to the initial value.

— In quantum mechanics, the equations are time‑symmetric. If the global arrow of time is determined by the geometry of hidden dimensions, have you tried to estimate at what scales (the size of a particle or the size of a galaxy) this “geometric force” begins to suppress quantum reversibility?

— In fact, time symmetry does not mean reversibility. This applies to the equations of both quantum mechanics and classical physics. If “time is growing” initially, then it is not possible to make it decrease. And vice versa. However, if the spatial coordinate is increasing, then it’s quite possible to reverse it. We all go to work and come back home. At the same time, the spatial coordinate can both increase and decrease, while time only increases. Therefore, we first need to decide whether time is increasing or decreasing for us, and then stick to that perspective all the time.

— Mathematically, does the model allow for the existence of regions where expansion gives way to contraction? And if so, does this mean that in contracting hidden dimensions, time will flow backward for a hypothetical observer?

— The first answer is no. Such a model can probably be constructed, but it’s difficult, and the goal isn’t clear.

— What would need to happen for Rubin’s theory to be refuted? Is there a hypothetical experiment (for example, in a collider or when observing gravitational waves) that could show that the hidden dimensions are not expanding at the required rate or that their geometry is static rather than dynamic?

— If it is shown that the observed properties of the Universe are incompatible with the necessary expansion of the extra dimensions, this will become a serious argument against our model. I would add that the falsifiability of a theory (the possibility of conducting experiments that can explain or refute the theory) is a good thing, but modern theories are such that humanity’s resources will not be sufficient to verify them for a long time to come. Which is unfortunate.

And one last remark. We are striving for a physical theory that, at least in the future, will explain everything. This means that the ultimate theory is not falsifiable.