The arrow of time and the Archimedes point are new directions for the physics of time

Criticism of the book. Author of the book: Hugh Price. Translated from English: Emmanuel Lotem. Science and Adam series, Zamora-Beitan Publishing, 2004

Can the cat count backwards

https://www.hayadan.org.il/timarrow.html

by Yoram Kirsh (*)
The book by Hugh Price, professor of philosophy at the universities of Edinburgh in Scotland and Sydney in Australia, deals with a fascinating subject - the paradox of the arrow of time. The book has almost no formulas and is not full of concepts from physics either. Although he discusses the problem and its solutions in philosophical terms, he does so in a language that can be understood by anyone. Despite all this, it seems to me that the average reader will have to put in a lot of effort to get through the book, mainly because of the tiresome length that also makes it difficult for the book's natural target audience - physicists and philosophers of science. Furthermore, the theory offered by Price is not part of the mainstream of ideas about the physics of time, and it is not at all certain that it can be justified. In other words, it is very possible that the new directions that Price describes in his book are not the right directions.

For all these reasons, it may have been a mistake to translate the book into Hebrew from the beginning. However, those who are interested in physics and philosophy and have already read other books on the topic of time that appeared in Hebrew (such as "A Brief History of Time" by Hawking, "In Search of the Limits of Time" by John Gribbin, and "Time and Consciousness" by Avshalom Elitzur) will be able to find interest In Price's book, even if he didn't reach the end of his mind on all subjects. Another bonus for the diligent reader is an introduction to a method of theoretical research in physics using logical-philosophical tools, which I will expand on later.

The paradox of the arrow of time is related to the fact that the fundamental equations of mechanics and electricity theory are symmetrical with respect to the direction of time. Therefore, a process that obeys these equations can also occur in "reverse". These equations also correctly describe the movement of molecules (although treating the processes that occur inside the molecules requires the use of quantum theory). Therefore, if we film a collision between two molecules, or the movement of a molecule in an electric field, and then project the film in the opposite direction, we will still see a process that is possible according to the laws of physics. It can be said that the film does not have an "Arrow of Time" marking. On the other hand, in systems that contain many molecules there is usually a clear arrow of time, defined by the second law of thermodynamics (increase in entropy or disorder) and distinguishes between the past and the future. For example, if we shoot a film showing a vase falling from a table and shattering into pieces, or a swimmer jumping from a diving board into a pool, and projecting the film from end to beginning, we will see an illogical process that cannot occur in reality.

Processes that can also occur in the opposite direction are called reversible processes. Movement of a single molecule and collision between two molecules are reversible processes. The paradox related to time pressure arises from the fact that any irreversible process, such as the breaking of the vase, consists of many reversible processes at the molecular level. The question is: how is it possible that a combination of reversible processes, each of which is not subject to time pressure, yields an irreversible process subject to time pressure? If each molecule by itself does not recognize the direction of the flow of time, how is it that in a large cluster of molecules the time clock starts ticking? Is this solely related to the fact that high entropy states (ie less ordered states) have a higher probability? Or is there another, more fundamental principle in nature that determines the direction of time? There is still no clear and universally agreed answer to this question.

To demonstrate the paradox, Price chose an example discussed in 1945 by two well-known physicists, John Wheeler and Richard Feynman, when Feynman was a doctoral student at Princeton working under Wheeler's guidance. This example can be described as follows: a lamp hanging from the ceiling of a room. At a certain moment, it is turned on for a short time and it emits a wave of light, or an accumulation of photons - light particles that spread in all directions and are absorbed by the walls and furniture. This is process A, and there is no difficulty in performing it. Process B is the opposite process: photons are emitted from the walls and furniture and move towards the lamp, in such a way that all the photons reach it at once. This is a process that is almost impossible to make happen. The problem of the arrow of time stems from the fact that if only one photon had exited the lamp, both processes would have seemed reasonable and possible. Therefore for a single photon the film in the opposite direction seems as logical as the original film, and the arrow of time seems non-existent. On the other hand, when there are many photons, the original film looks realistic, while the reverse film looks completely unrealistic, i.e. an arrow of time appears pointing from the past to the future.

Wheeler and Feynman's article from 1945 was not originally intended to deal with the problem of the arrow of time but with a different question: when a body emits an electromagnetic wave such as a light wave, why does the wave not affect the body that emitted it? This question arose while working on quantum electrodynamics (the quantum theory of the electric field), which Feynman later became famous as one of its developers, and even won the Nobel Prize for. The solution proposed by Wheeler and Feynman was based on the idea that the bodies that absorb the light affect the emission process itself, and their influence neutralizes the self-effect of the light wave on the body that emitted it. This idea encountered difficulties and was eventually abandoned by its proponents, but physicists, and especially philosophers like Price, continue to engage in it from time to time.

Price criticizes various points in Wheeler and Feynman's paper, but embraces their central idea: the absorption of the photons affects their emission, even though the emission occurred at an earlier time. He expands on this idea and states that the distinction between the past and the future is artificial and misleading, and stems from the fact that we ourselves are creatures living within the stream of time. If we could look at the world from an "Archimedes point" external to time, it would become clear to us that the past and the future are completely symmetrical in relation to the present. Among other things, we would discover that a physical event can be affected not only by events that occurred in the past, but also by events that will occur in the future, that is, a kind of "backwards causality" exists in nature.

How does this assumption solve the paradox of the arrow of time, in the example of the lamp for example? The solution can be presented like this. Process A seems natural and possible, because it seems to us that it describes photons that randomly exit the lamp and move randomly in all directions. Process B seems to us too complicated to exist in reality, because it involves the coordinated emission of photons from many independent bodies. But if we consider backward causality, it will become clear to us that in process A, the number of photons that exit the lamp and the directions of their exit are affected by the state of the absorbers. Therefore, in fact process A is just as complicated as process B. Every time process A is carried out, a coordinated and unique dispersion of the photons takes place, the probability of repeating it is very low, like the probability of process B occurring.

Backward causality allows Price to solve several paradoxes in quantum theory, most notably the famous paradox associated with the names of Einstein, Podolsky and Rosen and Bell's Theorem. That paradox stems from the fact that quantum theory allows for a situation where two distant particles are correlated, so that a measurement performed on one of them immediately affects the results of a measurement performed on the other particle. This apparently contradicts the theory of special relativity, according to which no effect can spread through space at a speed greater than the speed of light. According to Price, the solution to the paradox is simple: the first measurement affects some future event, and the same event affects the measurement performed on the second particle.

It should be noted that Price's theory is not original. Theories about backward causality appeared in philosophy journals from the mid-XNUMXs and in physics journals (in connection with tachyons - hypothetical particles faster than light) from the XNUMXs. Price's arguments are not the same as those put forward by his predecessors, but overall there is no great innovation in his words. The weakness of all theories that hold backward causation is that they give rise to paradoxes that are difficult to resolve, and that they are not supported by experiment. Almost all the physical experiments we know support the principle that physical events are affected by what happened in the past and not by what will happen in the future. There are a few examples that can hint at backward causality, such as the one related to Bell's Theorem, but even for them it is possible to find an alternative, less problematic explanation. It seems that despite the abundance of words that Price invests to convince us that there is backward causality, he does not manage to overcome the difficulties suffered by the previous theories that dealt with the subject.

Price's book serves as an example of an interesting phenomenon of theoretical research in physics using philosophical tools. It is known that in physics, as in the other sciences, there are two main types of research: experimental research that is based on measurements, experiments and observations, and theoretical research that deals with the development of theories. Between the two types there is mutual dependence because the theory is based on the results of experiments and is tested for its suitability to the experiment.

Articles by theoretical physicists are characterized by a multitude of calculations and formulas, and are generally accessible only to those who are knowledgeable in the specific field in which the article deals, and are familiar with the underlying mathematical theory. However, it turns out that there is also an alternative way to deal with the theory of physics. Anyone who looks through philosophical journals of the last twenty years, such as "Mind" or the British journal for the philosophy of science, will find quite a few examples of articles in physics written by philosophers. These articles usually differ in the purpose of change from the articles of physicists. They contain almost no formulas, their language is not mathematical but verbal-logical, they are usually much longer than physicists' articles, and discuss every detail at length, and they often deal with topics that physicists no longer deal with because they see them as closed topics (for example, topics related to interpretation of quantum theory, and paradoxes from the field of statistical mechanics such as "Maxwell's demon").

The authors of these articles usually, but not always, belong to the branch known as "philosophy of science". The traditional field of activity of this branch is a philosophical discussion of the way in which scientific theories are built, the connection between the theories and reality and similar issues, and this from an "external" point of view to science. Dealing with physical problems from an "internal" point of view, as Price does in his book, goes beyond the range of topics that traditionally belong to the philosophy of science, and places the writer in a position that is closer to a scientist than a philosopher. It should be noted that even though the phenomenon is probably getting stronger in recent years, it is not new. Examples can be found, for example, in the German philosopher of science Hans Reichenbach (1891-1953) who wrote books on the arrow of time, relativity and quantum theory.

Physicists are often suspicious and critical of philosophy, both when it treats physics from an external point of view and when it does so from an internal point of view. The criticism stems partly from instincts to protect the territory, and partly from justified fears about erroneous ideas, which may harm the progress of science and lead it to blind alleys from which there is no way out. Regarding the external treatment, it is argued that although it is sometimes instructive and inspiring, in many cases it misses the mark and makes the physicists feel that someone who does not know physics is trying to teach them how to work correctly from a paternalistic and condescending position. This was expressed by Nobel laureate Steven Weinberg in his book "The Vision of the Final Theory" (see Or in Hebrew in the Ofakim series, published by Am Oved). In the chapter "Against Philosophy", Weinberg launches a sharp attack on the school of logical positivism, whose ideas, according to him, hindered the progress of physics on several occasions during the twentieth century. At the same time, he points out that in some cases this school actually had a good influence on the development of physics. For example, she helped Einstein develop the theory of relativity and influenced the formulation of important principles of quantum theory, including the principle of uncertainty.

As far as the internal treatment is concerned, both its disadvantages and advantages stem from the fact that verbal formulation is more flexible than mathematical formulation. When physical principles are expressed in words instead of formulas, it is easier for the writer to formulate new ideas, and it is also easier for him to make mistakes. Examples of this can be found in the works of Reichenbach. There are some interesting ideas in his books, like the treatment of quantum theory through a logic that does not only have truth and falsehood, but also intermediate states. However, there are also misconceptions in these books. For example, the idea that if one day the universe reverses direction, and contracts instead of expanding, the direction of the second law of thermodynamics will also reverse, in such a way that the entropy of closed systems will tend to decrease instead of increase. In addition, the sense of time of all creatures in the universe will be reversed, in such a way that the past will appear to them as the future and vice versa. This strange idea gained him traction with some physicists. Even Steven Weinberg toyed with it for a while, and later declared that it was the biggest mistake of his life (perhaps this is where his anger at philosophy comes from).

Price's book demonstrates the advantages and disadvantages of verbal treatment of physical problems. With the help of words and diagrams, he manages to describe a subject whose presentation with the help of formulas is accessible only to a limited audience. However, the presentation with the help of formulas requires a few pages, while Price's discussion extends over about 400 pages full of text, and it is difficult for the reader to make sure that no mistakes were made during the long discussion. Therefore, in the end the formulas may be preferable.

* Prof. Yoram Kirsh's essay, "The Theory of Relativity", was published by the Open University Press