The laws of physics imply that the passage of time is an illusion, and to avoid this conclusion, we may have to rethink the reality of infinitely accurate numbers. Although, in the sense, there is a knife between the fixed past and the open future, we have been through it. But strangely, the knife – the “now” — is not found in the existing laws of physics.
In Einstein’s theory of relativity, for example, time is intertwined with three-dimensional space to form a curved four-dimensional space-time continuum, known as the “block universe”, encompassing the whole past, present and future. Einstein’s equations depict everything in the universe that has been decided from the start; the initial conditions of the universe determine what happens after that, and surprises don’t happen — just seem to happen. In 1955, a few weeks before his death, Einstein wrote, “For those of us who believe in physics, the differences between the past, the present and the future are nothing more than a stubborn illusion.” “
Nicolas Gisin in his family office overlooking the garden
Einstein’s view that reality is timeless and predetermined is still popular today. “Most physicists believe in block cosmology because it is predicted by general relativity, ” said cosmologist Marina Cort?s of the University of Lisbon in Portugal. “
However, she also noted that “if someone is asked to think more deeply about what the block universe means, they will begin to question and shake its meaning.” “
Quantum mechanics is a physical branch of the study that describes the probability behavior of particles. On a quantum scale, irreversible changes distinguish the past from the future: a particle can hold multiple quantum states at the same time until you measure it, and the particle falls into one of those states. Mysteriously, individual measurements are random and unpredictable, even if particle behavior generally follows statistical patterns. This obvious inconsistency between the nature of time in quantum mechanics and the mode of operation of time in relativity creates uncertainty and confusion.
Swiss physicist Nicolas Gisin has published four papers in 2019 trying to dispel the fog of time in physics. In Gissing’s view, the problem has always been a mathematical one. In general, he argues, time in general is easily expressed in “intuition math” as we call it “now”. This is a century-old mathematical language that opposes the existence of an infinite number, such as a collection of all natural numbers. According to Gissing, when intuitive mathematics is used to describe the evolution of physical systems, it can be clearly stated that “time is really passing and new information is created.” Moreover, in this formal system, the strict determinism implied by Einstein’s equation gives way to the unpredictability of quantum patterns. If the accuracy of numbers is limited, then nature itself is imprecise and therefore unpredictable.
It is not uncommon for people to try to revise the laws of physics in new mathematical languages. Physicists are still digesting Gissing’s work, but many of those involved in the debate argue that they may be able to bridge the conceptual divide between the calves of general relativity and the inherent randomness of quantum scales.
“I think it’s interesting,” nicole Yunger Halpern, a quantum information scientist at Harvard University, said in response to Nicholas Gissing’s recent article in Nature Physics. “
Marina Cortez said Gissing’s approach was “very interesting” and its meaning was “shocking and provocative”. “It’s really a very interesting form system that solves the problem of limited precision in nature,” she said. “
‘What we’ve experienced has shown that the future is open, and now it’s very real, and it’s important to make the laws of physics, ‘ says Mr. Gissing. “I’m a down-to-earth physicist, ” he said. ” “
Information and time
Gissing, 67, was first and foremost an experimenter. He runs a laboratory at the University of Geneva and has done some ground-breaking research in quantum communications and quantum cryptography. But he is also a rare cross-border physicist, known for important theoretical insights, especially those involving quantum opportunity and non-locality.
On Sunday morning, Gissing went to church, but was used to sitting quietly in a chair at home, holding a cup of oolong tea and thinking about esoteric concept puzzles. About two and a half years ago, on a Sunday, he realized that in Einstein’s theory and other “classic” physics theories, the deterministic picture of time implicitly assumed the existence of infinite information.
In the case of weather, because it is a chaotic system, or highly sensitive to small differences, we cannot accurately predict the weather after a week. But because it’s a classic system, textbooks tell us that in principle we can predict the weather after a week, as long as we can accurately measure every cloud, every gust of wind, and the swing of a butterfly’s wings. The actual physical laws of the weather unfold like clocks, but due to our own shortcomings, we cannot measure weather conditions with sufficient lymes to make accurate forecasts.
Now, extend the idea to the whole universe. In a predetermined world, time seems to only unfold, and what will happen at all times must actually be set from the start, with the initial state of each particle encoded in countless precise numbers. Otherwise, in the distant future, the predictable universe itself will collapse.
However, information is physical. Modern research shows that information requires energy and takes up space. Any volume of space has a limited amount of information (the densest information storage occurs within a black hole). Gissing realized that the initial conditions of the universe required too much information to be stuffed into limited space. “A real number with an infinite number makes no physical sense, ” he says. The block universe implicitly assumes the existence of infinite information and is bound to fall apart.
Gissing looked for a new way to describe time in physics. This method does not assume infinite precision of the initial conditions.
The logic of time
Modern academics have accepted the idea that there is a continuous system of real numbers, most of which are still numerous after the decimal point, but this view does not reflect the heated debate on this issue in the first decades of the 20th century. David Hilbert, the great German mathematician, embraced the view that real numbers existed and could be manipulated as complete entities. To oppose this view is the famous Dutch topological scientist L.E.J. Brouwer leads the mathematical “intuitionist” who believes that mathematics is a construct. Brouwer insists that the numbers must be constructable, that their numbers are calable, or that they can be selected or randomly determined. Numbers, he points out, are finite and process: when more bits appear in the form of what he calls a selection sequence, they become more precise;
Intuitiveism, which builds mathematics on a building basis, has a profound influence on mathematical practice and on determining which statements are true. One of the most complete departures from standard mathematics in the logic of intuitionism is the non-recognition of the rules of the platoon, a principle that has been touted since Aristotle’s time. The meaning of the rules is that a proposition is either true or its no proposition is true. This is a clear set of choices that provide a strong pattern of reasoning. But in Brouwer’s framework, statements about numbers may be neither “true” nor “false” for a given period of time, because the exact value of the numbers has not yet been displayed.
Standard mathematics does not distinguish when it comes to numbers such as 4, 1/2, or thora, or thora, which is the circumference of a circle and the ratio of diameter. Although the crucible is an irrational number, there is no limited fractional part, but an algorithm can be used to generate its decimal expansion so that the crucible is as certain as 1/2. But what if it’s another number, x, which is about 1/2?
Suppose the value of x is 0.4999…, and the number sits after it expands in the selection sequence. Perhaps the sequence of 9 lasts forever, in which case x converges to 1/2 (0.4999… – 0.5 is valid in standard mathematics, because the difference between x and 1/2 is less than any finite difference).
However, if at some point in the following sequence, a number other than 9 appears, for example, the value of x becomes 4.9999999999997… then no matter what happens, x is less than 1/2. Until then, when we only knew 0.4999, “we didn’t know if the number satoutside 9 would appear,” explains Carl Posy, a mathematical philosopher at the Hebrew University of Jerusalem in Israel and an authority on intuitional mathematics. “Proposition ” x is not true, nor is its proposition true. The rules of the platoon do not hold up.
In addition, the continuum cannot be clearly divided into two parts, one of which is less than 1/2 of the number and the other is greater than or equal to 1/2. “If you try to cut the continuum in half, the number x sticks to the knife, it doesn’t break into the left or right,” Posey said. “
Hilbert likened the rule of exclusion from mathematics to “prohibiting boxers from using fists” because this principle is the basis of mathematical reasoning. Although Brouwer’s intuitive framework captivated the likes of Kurt Godel and Hermann Weyl, standard mathematics dominates in real numbers because it is easy to use.
The expansion of time
In May 2019, at a conference attended by Carl Posey, Gissing first came into contact with intuitive mathematics. When the two began talking, Gissing soon discovered a link between the number of decimal places described in the mathematical framework and the physical concept of time in the universe. When an uncertain future becomes a concrete reality, the number of physicalized bits naturally seems to correspond naturally to the sequence of moments that define seinkers. The absence of a platoon law is similar to a non-deterministic proposition about the future.
In a paper published in Physical Review A in December 2019, Gissing and collaborator Flavio Del Santo used intuitive mathematical language to develop another version of classical mechanics and made the same predictions as standard equations, but described events in non-deterministic terms. This creates a new picture of the universe, where unpredictable things happen and time unfolds.
It’s a bit like the weather. Recall that we can’t predict the weather accurately, because we can’t know exactly what the initial conditions of every atom on Earth are. But in Gissing’s non-deterministic version, these infinitely accurate numbers never existed. Intuitive mathematics captures this: when the future unfolds in a selection sequence, the numbers that specify the weather state precisely and indicate their future development are selected in real time. Renato Renner, a quantum physicist at the Swiss Federal Institute of Technology, said Gissing’s argument “points in a direction where deterministic predictions are fundamentally impossible”.
In other words, the world is uncertain and the future is open. Gissing points out that time “doesn’t unfold like a movie in a movie theater.” It’s actually being creatively unfolded, and new numbers are produced over time. “
Fay Dowker, a quantum gravity theorist at Imperial College London, said she “very much agree” with Gissing because “he sided with those of us and thought physics was out of step with our experience and missed something.” Dok agrees that mathematical language shapes our understanding of time in physics, that standard Hilbert mathematics treats real numbers as complete entities, and that this is “clearly static and has untimely properties, which is undoubtedly a limitation for physicists, especially when we try to incorporate something dynamic, such as the experience of the passage of time.”
For physicists like Dok, who are interested in the link between gravity and quantum mechanics, the most important revelation of this new view of time is how it can be linked to two worldviews that have long been considered incompatible. “One of the revelations to me, ” Reiner said, “is that in some ways classical mechanics is closer to quantum mechanics than we thought.” “
Quantum Uncertainty and Time
If physicists want to solve the mystery of time, they will not only have to contrang with Einstein’s space-time continuum, but also to understand the quantum nature of the universe (dominated by chance and uncertainty). The time picture of quantum theory is quite different from Einstein’s theory. “Our two major physics theories, quantum theory and general relativity, make different statements, ” Reiner said. He and several other physicists point out that this inconsistency makes it difficult to establish quantum gravity theory (which describes the quantum origin of space-time) and to understand why the Big Bang happened. “Look at where there’s a contradiction, look at what we have, and ultimately it all comes down to the concept of time,” Reiner said.
Time in quantum mechanics is rigid, not curved, and entangled with the spatial dimensions of relativity. In addition, measurements of quantum systems “make time irreversible in quantum mechanics, and in other ways, quantum theory is completely reversible,” Reiner said. “
In the understanding of many physicists, quantum physics tells us that the universe is uncertain. “You can find two uranium atoms, one decaying after 500 years and the other decaying after 1,000 years, but they are exactly the same in every way,” said Nima Arkani-Hamed, a physicist at the Institute of Advanced Studies in Princeton, New Jersey. “
Nevertheless, other popular interpretations of quantum mechanics, including the interpretation of “multi-worlds”, are trying to perpetuate the classic concept of deterministic time. These theories paint quantum events as an established reality. For example, the multi-world theory holds that each quantum measurement divides the world into branches, resulting in every possible outcome that is pre-set.
Gissing’s idea is the opposite. He wants to provide a common, nondeterminological language for classical physics and quantum physics, rather than trying to turn quantum mechanics into a deterministic theory. However, this approach is largely out of standard quantum mechanics.
In quantum mechanics, information can be disrupted, but not created or destroyed. However, if, as Gissing suggests, the numbers that define the state of the universe grow over time, new information will emerge. Mr Gissing said he was “absolutely” opposed to the idea that information was kept in nature, mainly because “new information was clearly generated during the measurement process”. He added: “I mean, we need to look at these whole ideas in a different way. “
This new way of thinking about information may solve the black hole information paradox. The paradox raises the question: What happens to information engulfed by black holes? General relativity holds that information is destroyed, while quantum theory holds that information is preserved. If quantum mechanics, expressed in intuitive mathematics, allows information to be created through quantum measurements, then destruction of information is also permissible.
Jonathan Oppenheim, a theoretical physicist at University College London, believes that information is indeed lost in black holes. He wondered whether Brouwer’s intuitioncould be the key to demonstrating this, as Gissing claims, but said it was reasonable to believe that the creation and destruction of information might be closely related to time, and that “over time, information is destroyed; it will not be destroyed because you move in space”. There are great differences between the dimensions that make up Einstein’s block universe.
In addition to supporting the concept of creative (and possibly destructive) time, intuitive mathematics provides a novel explanation for our conscious experience of time. Recall that in this frame, the continuum is viscous and cannot be split in two. Gissing links this stickiness to our feeling that “now” has a “thickness”, which is a substantive moment, rather than a zero-width point that completely separates the past from the future. In standard physics based on standard mathematics, time is a continuous parameter that can take any value on the axis. However, Gissing said, “If the continuum is represented by intuitive mathematics, then time cannot be cut in half.” “It’s thick, ” as thick as honey. “
So far, this is just an analogy. Oppenheim said he “feels good about the concept of ‘being thick now.’ I don’t know why we feel this way. “
The future of time
Gissing’s ideas prompted a series of reactions from other theoretical physicists, who also had their own thought experiments and intuitions about time.
Several experts agree that real numbers do not seem physically real, and that physicists need a new formal system that does not rely on real numbers. According to Ahmed Almheiri, a theoretical physicist at the Princeton Institute of Advanced Studies who studies black holes and quantum gravity, quantum mechanics “excludes the existence of continuum”. Quantum mathematics binds energy and other amounts like packing, more like integers than continuums. Infinite numbers are truncated in black holes. “Black holes seem to have an infinite number of internal states, but these numbers are cut off,” he said, because of quantum gravitational effects, “real numbers can’t exist because you can’t hide them in black holes.” Otherwise they can hide endless information. “
Sandu Popescu, a physicist at the University of Bristol in the UK, often agrees with Gissing’s view, but says he is not convinced that intuitive mathematics is necessary. Popsku opposes the idea of real numbers as information.
Akani-Hamid thinks Gissin’s use of intuitive mathematics is interesting and could play a role in the apparent conflict between gravity and quantum mechanics, such as black holes and the Big Bang. “These questions, such as the limitability of numbers, the fundamental existence of things, the existence of an infinite number of numbers, or the creation of numbers, may eventually be linked to how we should see cosmology, especially if we don’t know how to apply quantum mechanics,” he said. He also saw the need for a new mathematical language that would “liberate” physicists from infinite precision and allow them to “talk about things that are always a little vague”.
Gissing’s ideas resonate with many people, but still need to be fleshed out. Next, he hopes to find a way to reconstruct relativity and quantum mechanics with limited, fuzzy intuitive mathematics, as he did with classical mechanics, which could bring the two theories closer together. He already has some ideas on how to deal with quantum mechanics.
One of the ways that “infinite” appears in quantum mechanics is the “tail problem”. When you try to locate a quantum system, like an electron on the moon, “if you use standard math, you have to admit that electrons on the moon have a very small probability of being detected on Earth, ” Gissing said. A mathematical function that represents the particle’s position leaves a “tail” and is “exponentially smaller, but not zero.”
But Gissing wanted to know, “What reality should we attribute to a super-small number?” Most experimentalists would say, ‘Let it go to zero and stop questioning’. But people who are more theoretical might say, ‘Okay, but from a mathematical point of view, something does exist.’ “
“It’s up to what kind of math we’re going to use, ” Gissing continued. ” And in intuitive mathematics, there’s nothing. “Electronics are on the moon, and there is zero chance that it will appear on Earth.
Since Gissing’s paper was published, the future has become more uncertain. For him, every day is Sunday, because the epidemic is shrouding the world. Unable to go to the lab and to see his granddaughter on the screen, his next plan was to carry a teacup and continue to think about time for the garden landscape.