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「弦假說」難以成立-沃伊特教授訪問記錄
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我是物理系畢業生，也唸了三年多的研究所。那時還沒有「弦假說」這門課；三、四十年來雖然看過幾篇介紹性的文章，但從來就沒有搞清楚它到底在說些什麼。以我的「科學方法論」標準來說，「弦『理論』」是稱不上的；故名之以「弦假說」。
我沒有能力就沃伊特教授批評弦假說部分置喙；不過我支持他科學方法論上的觀點。由於當下「弦假說」仍然是熱門話題，轉載《藝術與思想研究學會報導》上這篇訪問於此，湊個熱鬧，聊備一說。有興趣的朋友，可以繼續讀本欄第二篇論文。
String theory is dead
An exclusive interview with Peter Woit
Peter Woit/Alexis Papazoglou, 02/23/23
Peter Woit Woit is a senior lecturer in the Mathematics department at Columbia University, and longstanding critic of string theory. He is the author of Not Even Wrong: The Failure of String Theory and the Continuing Challenge to Unify the Laws of Physics
Alexis Papazoglou Senior editor for IAI News, the online magazine of the Institute of Art and Ideas, and former philosophy lecturer at Cambridge and Royal Holloway.
Following Eric Weinstein’s interview on how String Theory culture has stifled innovation in theoretical physics, longstanding critic of String Theory, Peter Woit, takes aim at the theory itself. He argues that String Theory has become a degenerative research project, becoming increasingly complicated and, at the same time, removed from empirical reality. Even the remaining string theorists of the past have given up on the ontology of strings, as well as the original vision of the theory.
Your book Not Even Wrong: The Failure of String Theory and the Continuing challenge to Unify the Laws of Physics came out in 2006. Could you summarise the main argument against String Theory as put forward in that book?
The story of string theory is rather complicated, so the intent of the book was to fully examine some of those complexities. The main problem with the theory though has always been a simple one: it achieves unification by postulating six or seven unobserved extra dimensions, then tries to explain everything we see in terms of these. The initial hope of 1984-5 was that there would only be a few consistent ways of making those extra dimensions unobservably small, and one of these would give our universe. But all evidence now is that either:
1. There is no consistent way to do this.
2. There is an essentially infinite number of ways to do this (the "landscape"), giving almost anything you want, so unpredictive.
In either case, the idea of string theory unification is simply a failure.
Has anything has changed since then about the way you think about String Theory?
I think that the arguments made in that book have aged very well and there is little that I would change if I were to rewrite it today. Back when I wrote the book I was concentrating on trying to understand exactly what string theorists were doing. In recent years they themselves have mostly given up on their original claims and the field has come to a standstill, so no reason to spend much time on it.
I heard you say in a recent podcast interview that it’s hard to pin down what String Theory even is today. What did you mean by that?
String theory has always suffered from the fact that it is only defined in certain limiting cases. What has happened over the years is that hopes to find a unified theory using one of those limiting cases have collapsed as it became clear this didn’t work. People working on string theory have mostly given up on work using these limiting cases, but they haven’t made any progress on finding a general theory. So, they have moved onto working on other topics, but oddly often still calling themselves “string theorists”. To some extent people now refer to “string theory” as whatever this group of theorists is doing now, but since it’s a range of things, none of them involving strings, it’s hard to now know what the term means.
One aspect of what has happened is that since attempts at a unified theory have collapsed, the string theory community has fallen back on just thinking about quantum gravity, and only a small range of questions within that subject, mainly using techniques that historically have some origin in string theory research, but now have nothing to do with strings.
One of your main critiques of String Theory has been that it doesn’t make predictions that can be tested. Does this invalidate it as a scientific theory in your mind? If it isn’t science, what is it?
There’s no simple answer to the question of what’s “science” and what isn’t. Having testable predictions is something to aim for, but more important for any speculative theory in its early stages is to see what happens as people explore its implications. I believe there’s a concept in philosophy of science of evaluating a research program as progressive or degenerative. Even if a research program hasn’t yet made testable predictions, it could still be progressive in the sense that it looks like a better and better idea the more you work on it. String theory is the opposite, a degenerative program. The more people have learned about it, the more complicated, ugly and unpredictive it gets as an explanation of anything in the real world. So, the problem isn’t so much not arriving at testable predictions, but 40 years of steadily moving in the wrong direction.
Is there a role for philosophy of science when it comes to answering this question about the status of a theory that has been developed by physicists, but doesn’t seem to make predictions we can test?
I do think philosophy of science has a role to play here, by helping to evaluate the string theory research program using a more historically and philosphically informed understanding of what is healthy science and what isn’t. One big problem with this is that the details of the theoretical work in the subject are extremely complex, very hard for a non-expert to understand and evaluate. Some of what I’ve seen philosophers of science (e.g. Richard Dawid) do is rather discouraging. Unable or unwilling to evaluate the theory according to usual standards (since the result would be very negative), they start arguing that failure by a conventional standard means that there’s a problem with that standard and it needs to be changed.
Eric Weinstein’s critique of String Theory is that it has dominated theoretical physics for far too long, thus not allowing any alternative attempts at a theory of everything to develop. Do you agree with this assessment?
Yes, very much so. I completely agree with Eric that the big issue in the field is that of how to get the research community out of the long blind alley it has worked itself down. What’s most discouraging is that even convincing theorists of the obvious fact that they’re in a blind alley seems to be impossible. The institutional pressures to keep doing what one has been doing for decades and not admit to failure are huge.
String Theory also had a strong grip not just within academic physics, but on the public imagination. Why do you think that is?
The sorts of questions about the nature of physical reality and its description by an exotic unified theory that string theory claims to successfully address are ones that many human beings naturally find compelling. Looking at the public claims made for the theory, often in high profile TV specials, it would be strange if these didn’t attract significant interest from the public.
What would you say are the positives, if any, to have come out of String Theory research?
There have been some quite interesting mathematical spin-offs from string theory research. One of the most successful has been the concept of “mirror symmetry”. This was first discovered by string theorists looking at high-dimensional spaces. It’s something that turned out to have no use in a theory of physics but opened up a new perspective in geometry and topology.
If String Theory has failed to live up to expectations, are there more promising candidates for unifying General Relativity with the Standard Model?
I believe so. In particular, for several years now, I’ve been looking at ideas which put together the symmetries of General Relativity and the Standard Model in a new way, using, among other things, the geometry of twistors. I’m quite excited by these ideas, although I have to admit I’ve had little luck getting others excited.
Could you say a bit more about the theory of twistors as a way of unifying General Relativity and Quantum Mechanics?
The idea of twistors was developed by Roger Penrose and others, going back to the 1960s and 70s. The new idea about unification is that of taking seriously the idea of formulating twistor theory in imaginary time, and noticing that when you do this, the usual space-time symmetry becomes a mixture of space-time symmetry and the internal symmetry of the electroweak theory, unifying these in an unexpected way.
Is it possible that the whole project of aiming for a theory of everything is misguided in the first place?
Anything is possible, but from all I’ve seen in a long career, there’s many reasons to believe we can do better than our best current unified theory. We don’t know what the end of the road in this direction will look like, but to me it seems that while string theory is at the end of its road, there are promising other ones to go down.
What are the questions in theoretical physics that you think future research needs to focus on?
We’ve hit technological limits of what we can do experimentally in many directions, and that carries implications for what research is going to be fruitful. My own interest now is mainly at the boundaries of physics and mathematics, finding new ideas about math inspired by physics, and better understanding of fundamental physics by incorporating deeper and more sophisticated mathematics. Others should though follow whatever they see as possible ways forward.
本文於 修改第 4 次
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為弦假說辯護-J. Maldacena/S. Custer
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本文是藝術與思想研究學會研究員卡斯特先生和馬爾達欣納教授就「弦假說」所做的訪談紀錄。
馬爾達欣納教授認為「弦假說」可以解釋「量子力學引力」；從而，它在目前物理學家對宇宙的了解架構中有一席之地。
「弦假說」是否成立不是我有資格說三道四。以下僅僅針對這篇訪談紀錄說說我的感覺：
1) 全文的辯護力道不足。馬爾達欣納教授的確”認定”「弦假說」可以解釋「量子力學引力」；但是，他並沒有說明：前者怎麼解釋後者，他更沒有說明：「弦假說」解釋了些什麼。這很可能是因為受到文章格式的限制(「訪談」相對於「論文」)。
2) 一個有爭議的「陳述」；馬爾達欣納教授說：
“In string theory, the concept is that there is a single field with many components. Excitations of these fields behave like one-dimensional objects, like strings, rather than zero-dimensional particles.
I must mention that this is only a partial view of what we think "string theory" is. The above description is appropriate in situations where these string fields are interacting sufficiently weakly.”
我的疑惑是：
如果「弦假說」假設：一個「場域」以及此「(單一)場域」含有多個「子場域」；則這些「子場域」和「單一場域」的關係是什麼？(比較第一段的single field和第二段的string fields are interacting …。
此外，卡斯特先生(或《藝術與思想研究學會 報導》的編者)認為：在解釋過程中，馬爾達欣納教授也用通俗易懂的話語說明了「全息影像」、「維度」、與「量子場域」等三個概念。我無法苟同這個評論；至少，在讀完全文後，我對以上三個概念的了解並沒有更清楚些。
索引：
excitations -- 「能量數量(等級)的增加」(相對於最低能量等級或初始能量等級而言)
In defence of string theory
String theory explains quantum gravity
Juan Maldacena/Simon Custer, 06/27/23
In light of the recent criticisms of string theory, preeminent physicist Juan Maldacena sheds light on the promise of string theory and how it fits into our current understanding of the universe. In so doing, Maldacena also explains the ideas of holograms, dimensions, and quantum fields in terms everyone can understand.
Most people think that physics tells us that everything that exists is made out of particles, like atoms and quarks. Is that right?
Yes, indeed. The current picture of nature posits that all matter is composed of a few elementary particles. More accurately, the theory is that there are several fields that permeate spacetime. The excitations of these fields are quantized, and each elementary excitation quantum represents a particle. For example, the electromagnetic field's unit of excitation is the photon. There is another, the electron field, whose elementary excitation is the electron, and so forth. All electrons are identical because they are excitations of the same underlying field. While popular descriptions often talk about particles, our current foundational theory, the so-called “Standard Model,” relies significantly on the existence of fields.
And should we think of particles as simply very small bits of matter?
No, we should think of matter as being comprised of particles. Particles are the fundamental concept through which we describe matter. The core point is that particles are simpler than matter in general. Hence, we describe something more intricate, like matter, in terms of something simpler, namely, particles. To be more specific, as we mentioned earlier, all matter is formed from excitations of a few fields.
We think that the Standard Model is the long-distance manifestation of a deeper theory at shorter distances, but we do not yet know what that deeper theory is.
I don't believe that the idea of a dimension is abstract. It is actually very natural and has existed since the time of Euclid. Classical Greek geometry was about points, lines, and planes, which are geometric constructions of various dimensions. Adding time allows us to think in terms of "events" that happen at one time and one location in our three-dimensional space. Events are the fundamental "points" of spacetime.
What is certainly not obvious from our everyday experience is that observers moving relative to each other would perceive a different time. Even less obvious is the fact that these dimensions form a curved spacetime. This was the key insight that Einstein had when he developed general relativity.
In an interview with Closer to Truth, you mentioned that string theory posits that one string ultimately exists, and that the oscillation of that string in different, smaller dimensions generates everything from atoms to galaxies to human beings. What does this mean, exactly?
In the currently accepted "Standard Model," we recognize a few elementary fields. In string theory, the concept is that there is a single field with many components. Excitations of these fields behave like one-dimensional objects, like strings, rather than zero-dimensional particles.
I must mention that this is only a partial view of what we think "string theory" is. The above description is appropriate in situations where these string fields are interacting sufficiently weakly.
What does it mean to say that a dimension is small?
The simplest analogy is to think of the surface of a garden hose, which is two-dimensional, but from a distance, it appears one-dimensional. If you were an ant walking on the hose's surface, you would see a two-dimensional surface. One of the dimensions is small – the direction around the hose. If the ant walks around the hose, it comes back to the starting point. However, if it walks along the length of the hose, it would not return to the starting point. Hence, we say this dimension is large.
In the same way, it could be that there are very tiny, microscopic dimensions of space. They could be so minuscule that we might not be able to measure them. Why would we consider such an outrageous idea? Well, because it's not outrageous at all; it's a very natural possibility. In fact, people proposed the existence of extra dimensions soon after the discovery of general relativity. Of course, we have no experimental evidence so far for the existence of new extra dimensions. They might exist, or they might not. One could safely assume that the universe is four-dimensional all the way to the Planck scale, which is the smallest scale that can be explored according to quantum mechanics, given that we have not observed them. Another possibility is that there are small extra dimensions.
And how can one tiny string give rise to the infinite complexity of the universe?
We think that the universe we observe does not have infinite complexity. Nothing infinite has ever been observed. So, only a finite amount of complexity needs to be explained. We believe that we have an explanation for most matter (except for dark matter) in terms of the particles we already know. We think that simple initial conditions for the universe, combined with known particles, could lead to the complexity we observe. Of course, not all details are understood, and many mysteries remain, from the formation of planets to the emergence of life. However, we have no reason to believe that it couldn't work.
Our description of nature proceeds by layers; we have laws that apply at various distance scales. Biology relies on chemistry, chemistry relies on atomic physics, atomic physics relies on electrons and nuclear physics, nuclear physics relies on the Standard Model.
String theory would add a new layer. The idea is to explain the Standard Model's particles, along with gravity, in terms of a more fundamental theory. We don't know whether it is the right theory. What we do know is that we need a consistent quantum theory that describes gravity along with the elementary particles we know. String theory is the most promising contender. Maybe there are other possibilities we have not yet discovered. The other options that have been proposed don't yet have the level of consistency that string theory has. It is a question that is challenging to study experimentally due to the high energies or very short distances involved. Our hope is that by understanding the theory well enough, we could make an experimental prediction that could be checked by some observation, probably a cosmological observation. But this has not happened yet!
Following up on that, what do you make of the concept of monism, the idea that the universe is undifferentiated? Is string theory monistic?
If by monism we mean that the universe is governed by one field with many components, then yes. The question is whether there is a unified field theory that describes all of the interactions, forces, and matter present in nature. Of course, in nature, there are different objects; they are not the same, so in that sense, it is not just one thing. For example, there are two types of particles, called bosons and fermions. Some could argue that they are so fundamentally different that they cannot be part of the same thing. One could also envision a theory where there is a new type of symmetry, called supersymmetry, which relates them. So, you could argue that supersymmetry is necessary for a completely unified theory. But of course, nature has the final say on whether this is the case or not. Supersymmetry has not been discovered. Furthermore, our current Standard Model has a few different elements, so it is not monistic in the sense of having a single field. But it is monistic in the sense that it posits that the only thing that exists are quantum fields, including one associated with the geometry of spacetime.
Is there a difference between the objects a theory says exist and the laws that govern the behaviour of those objects?
The objects are defined by the laws that govern them, just like a chess piece is defined by how it moves (an old analogy due to Paul Dirac). In a relativistic quantum theory, we postulate the existence of certain fields, and then some dynamical law for their interactions. These interactions can be rather general at short distances, but there are some special types of interactions that survive at longer distances. These are the ones present in the Standard Model. We think that the Standard Model is the long-distance manifestation of a deeper theory at shorter distances, but we do not yet know what that deeper theory is.
If so, doesn’t that mean string theory can’t be monistic?
As I said above, I think that it can be monistic in the sense that only one field exists. It could also be monistic in the sense that the interactions are completely set by the structure of the theory; we think that we have no freedom to modify the interactions.
Is simplicity a guide to truth?
No, I would say that consistency is. Simplicity is preferable. As they say: the theory should be as simple as possible but not simpler! By consistency, I mean mathematical and logical consistency, as well as consistency with the laws of physics we already know, including the fundamental principles of relativity and quantum mechanics. The more general theory should reduce to the currently accepted theories in the regime that these theories have been tested.
Leonard Susskind says that “The three-dimensional world of ordinary experience––the universe filled with galaxies, stars, planets, houses, boulders, and people––is a hologram, an image of reality coded on a distant two-dimensional surface." How can that be possible, and how could we ever know it to be true? Holograms are a kind of visual illusion, so is the world of everyday experience an illusion?
Yes, we think that this is part of gravity. When we talk about an "illusion," we mean that in the description in terms of the distant surface, the description is very different. The third dimension is not present, but it emerges out of the dynamics of the two-dimensional theory. But the world we experience is still real. It is an illusion in the same sense that the surface of a table is an illusion since the table is made out of very tiny particles with empty space between them. Of course, if we hit the table with our hand, it might hurt in a very real way.
The assumption that space-time is a fundamental aspect of the universe leads to a serious problem, which is that the laws of physics break down in the center of black holes and at the beginning of the big bang. Does this mean that space-time is a wrongheaded idea, or should we question whether there are physical laws that govern every aspect of reality?
Yes, it's very likely that spacetime is replaced by some other more fundamental concept, but we do not have a really clear and simple way to say what that is. It's one of the mysteries of quantum gravity. Understanding this mystery is the primary motivation to study quantum gravity, as it's necessary to understand it to understand the beginning of the universe.
Steven Weinberg claimed that the question of why there is anything at all is unanswerable. Was he right?
Maybe. It certainly does not seem to be answerable with our current ways of thinking about fundamental laws.
Might new physics shed some light on the mystery of existence?
As far as I understand, physics is about the laws of the game, but not about the ultimate reason we are playing this game.
For more featuring Juan Maldacena, join IAI LIVE: Fantasy, Faith and Physics this July 3rd. Sabine Hossenfelder, Max Tegmark, Michio Kaku, Juan Maldacena, Lisa Randall, and Mary-Jane Rubenstein debate the role of fantasy and unproven belief in modern physics. Book now.
SUGGESTED READING: String theory under fire Omari Edwards
SUGGESTED VIEWING: The trouble with string theory With Katie Robertson, Roger Penrose, Brian Greene, Eric Weinstein, Tasneem Zehra Husain
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「弦」的輓歌 – Paul Sutter
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撒特教授在《藝術與科技》網站上這篇文章對「弦假說」在理論物理界大起大落有深入的介紹和分析。從標題看，頗有蓋棺論定的意味。此文發表於年初，我的物理程度不足以充分了解它；當時只做存檔備查的動作。最近本城市刊出了沃伊特教授比較通俗的評論，特轉載撒特教授大作於此。謹供資優生參考。
Requiem for a string: Charting the rise and fall of a theory of everything
String theory was supposed to explain all of physics. What went wrong?
PAUL SUTTER, 01/27/23
String theory began over 50 years ago as a way to understand the strong nuclear force. Since then, it’s grown to become a theory of everything, capable of explaining the nature of every particle, every force, every fundamental constant, and the existence of the Universe itself. But despite decades of work, it has failed to deliver on its promise.
What went wrong, and where do we go from here?
Like most revolutions, string theory had humble origins. It started in the 1960s as an attempt to understand the workings of the strong nuclear force, which had only recently been discovered. Quantum field theory, which had been used successfully to explain electromagnetism and the weak nuclear force, wasn’t cutting it, so physicists were eager for something new.
A group of physicists took a mathematical technique developed (and later abandoned) by quantum godfather Werner Heisenberg and expanded it. In that expansion, they found the first strings -- mathematical structures that repeated themselves in spacetime. Unfortunately, this proto-string theory made incorrect predictions about the nature of the strong force and also had a variety of troublesome artifacts (like the existence of tachyons, particles that only traveled faster than light). Once another theory was developed to explain the strong force -- the one we use today, based on quarks and gluons -- string theory faded from the scene.
But again, like most revolutions, whispers remained through the years, keeping hopes alive. In the 1970s, physicists uncovered several remarkable properties of string theory. One, the theory could support more forces than just the strong nuclear force. The strings in string theory had enormous tension, forcing them to curl up on themselves into the smallest possible volume, something around the Planck scale. Once in place, the strings could support various vibrations, just like a taut guitar string. The different vibrations led to different manifestations of forces: one note for strong nuclear, another for electromagnetism, and so on.
One of the possible vibrations of the string acted like a massless spin-2 particle. This is a very special particle because that would be the quantum force carrier of the gravitational force, the holy grail of a quantized theory of gravity. The theorists at the time couldn’t believe their chalkboards: String theory naturally, elegantly included quantum gravity, and they weren’t even trying!
The second big deal to come out in the 1970s was the introduction of supersymmetry, which claimed that all the particles that carry forces (called bosons, a category that includes photons and gluons) were linked to a supersymmetric partner from the collection of particles that build stuff (called fermions, like electrons and quarks), and vice versa.
This symmetry doesn’t appear in everyday settings; it only manifests at extremely high energies. So if you were to go back in time to the earliest moments of the Big Bang or had enough funding to build a particle collider along the orbit of Jupiter, you wouldn’t just see the normal zoo of particles we’re familiar with; you'd see all their supersymmetric partners, too. These were given suitably stupid names, like selectrons, sneutrinos, squarks, photinos, and my personal (least) favorite, the wino boson.
By making this connection, string theory could build a bridge from the bosons to the fermions, allowing it to leap from just a theory of forces to a theory of every single particle in existence. The introduction of supersymmetry also solved the nasty problem of tachyons by replacing those troublesome particles with supersymmetric partners, which was a nice flourish.
At the end of the 1970s, string theory could potentially explain all the particles and all the interactions among them and provide a quantum solution to gravity.
One theory to rule them all, one theory to find them, one theory to bring them all, and in the stringiness bind them.
A string perturbed
It’s been almost half a century since physicists first realized that string theory could potentially provide a theory of everything. Despite decades of work involving hundreds of scientists over several (academic) generations and countless papers, conferences, and workshops, string theory hasn't quite lived up to that potential.
One of the biggest issues involves the way that strings interact with each other. A major pain in the asymptote when it comes to quantum theory is the infinite variety of ways that particles can interact. It’s easy enough to write down the fundamental governing equations that describe an interaction, but the math tends to blow up when we actually try to use it. In string theory, fundamental particles aren’t particles at all; they’re tiny loops of vibrating… well, strings. When we see two particles bouncing off each other, for example, it’s really two strings briefly merging and then separating. That sounds super cool, but there are still an infinite number of ways that process can unfold.
Unlike its quantum cousins, when it comes to string theory, we have no fundamental theory -- we have only a set of approximation and perturbation methods. We’re not exactly sure if our approximations are good ones or if we’re way off the mark. We have perturbation techniques, but we’re not sure what we’re perturbing from. In other words, there’s no such thing as string theory, just approximations of what we hope string theory could be.
The second major difficulty involves the vibrations of the strings themselves. Early on, physicists realized that the strings had to vibrate in more than three dimensions of space if they were to explain the full variety of forces and particles in the Universe. 3D was just too limiting; it constricted the number of potential vibrations so severely that it was no longer a theory of everything, just a theory of some things, which isn’t nearly as exciting.
The earliest versions of string theory needed 26 spatial dimensions, but after supersymmetry and some dimensional layoffs, theorists were able to slim that number down to “only” 10.
Now, the Universe doesn’t have 10 spatial dimensions, at least on large scales, because we would have noticed them by now. So all the extra dimensions have to be tiny and curled up on themselves. When you wave your arm in front of you, you’re traversing these tiny dimensions countless times, but they’re so small (typically at the Planck scale) that you don’t notice them.
The extra dimensions give the strings enough vibrational options to explain all of physics. And the variety of shapes those dimensions can take as they curl up on themselves are known as Calabi-Yau manifolds. If you curl a piece of paper up on itself, you have a few choices: you can connect just one pair of edges (a cylinder) or both pairs (a delicious doughnut), you can introduce one flip (a Mobius strip) or two (a Klein bottle), and so on. That’s only two dimensions. With six, you have somewhere between 10500 and 1010,000 possible options.
We care about all these possible shapes because the way the extra spatial dimensions curl up determines the possible set of vibrations of the strings -- each shape produces a different set of string vibrations, like different musical instruments. A tuba sounds different from a saxophone because of the way it’s structured and the kind of vibrations it can support. But our Universe is only a single instrument (an oboe, perhaps) with a single set of “notes” that correspond to our suite forces and particles.
So which one of the zillions of potential Calabi-Yau structures corresponds to our reality? We don’t know. Because we don’t have a full accounting of string theory, only approximations, we don’t know how the shape of the curled-up dimensions affects the string vibrations. We have no reliable machinery that goes from a given Calabi-Yau manifold to the physics that appears in that universe, so we can’t run the reverse operation and use our unique experience of physics to discover the shape of the curled-up dimensions.
Supersymmetry super-headaches
It gets worse. By the early 1990s, string theorists had developed not one, not two, but five different versions of string theory. The variations were based on how a fundamental string was treated. In some versions, all strings had to form closed loops; in others, they could be open. In some, the vibrations could only travel in one direction; in others, they could travel both, and so on. For the curious (and those eager for edgy names for your kids) the five string theories are Type 1, Type IIA, Type IIB, SO(32) heterotic, and E8xE8 heterotic.
So now we have a slight embarrassment of riches. Five potential theories, all claiming to be the best approximation of the true string theory. That’s pretty awkward, but in the 1990s, physicist Edward Witten declared a winner: all of them.
He discovered dualities, which are mathematical relationships between theories that allow you to transform one to the other. In this case, Witten tied the five string theories into a single knot. This idea has yet to be mathematically proven, but it indicates that the five string theories are really manifestations of a single, unified-for-real-this-time string theory, which Witten called M-theory. We don’t know what M-theory is -- or even what the “M” stands for (my vote is “Manchego”) -- but it should be the actual string theory.
That’s potentially very useful since once we determine whether our approximation schemes are valid, all the five versions of string theory should converge on it, and our Universe should pop out of the math.
But that was almost 30 years ago, and we still don’t know what M-theory is. We still haven’t figured out a solution for string theory.
To be clear, our inability to understand string theory isn’t limited by experiment. Even if we could build a super-duper-collider experiment that achieved the energies necessary to unlock quantum gravity, we still wouldn’t be able to test string theory because we have no string theory. We have no mathematical model that can make reliable predictions, only approximations that we hope accurately represent the true physics. We can test those approximations, I guess, but it won’t help us determine the inner workings of the true model.
Even so, the experiments we do have aren’t exactly helping. When supersymmetry was developed by the string theory community in the 1970s, it proved to be such a popular idea that many particle physicists took it as their own, using those techniques to develop models of high-energy physics beyond the Standard Model.
Supersymmetry isn’t a single theory; it's a family of theories. They all share the same core principle: that bosons and fermions are partners of each other at high enough energies. But the details of the interactions are left as a homework exercise for each individual theorist. Some supersymmetric theories are relatively (and that’s putting a lot of work on the word) straightforward, while others are more complex. Either way, in the 1990s, physicists became so convinced the supersymmetry was super-terrific that they devised a super-powerful collider to test it out: the Large Hadron Collider.
The beams of the LHC began their first test operations in 2008 with two main science goals in mind: finding the elusive Higgs boson and finding evidence of supersymmetry.
Four years later, the Higgs was found. Supersymmetry was not. It’s now 15 years later, and there are still no signs of supersymmetry.
In fact, all the “easy” versions of supersymmetry have been ruled out, and many of the more complicated ones, too. The dearth of evidence has slaughtered so many members of the supersymmetric family that the whole idea is on very shaky ground, with physicists beginning to have conferences with titles like “Beyond Supersymmetry” and “Oh My God, I Think I Wasted My Career.”
Where does that leave string theory? Well, since (and I’ll never stop reminding you of this) there is no string theory, only approximations, it’s not quite pining-for-the-fjords dead yet. It’s possible to build a version of string theory without using supersymmetry… maybe. The math gets even thornier and the approximations even sketchier, though. Without supersymmetry, string theory isn’t gone, but it’s certainly on life support.
Duality of the fates
After 50 years of work on a theory of everything, we’re left with approximate theories that seem so tantalizingly close to explaining all of physics… and yet always out of reach. Work continues on finding the underlying dualities that link the different versions of string theory, trying to suss out the mysterious M-theory that might underlie them all. Improvements to perturbation theory and approximation schemes provide some hope for making a breakthrough to link the dimensional structure of the extra dimensions to predictable physics. Routes around the damage caused by the LHC’s lack of evidence for supersymmetry continue to be laid.
In response to our inability to choose which Calabi-Yau manifold corresponds to our Universe -- and more importantly, why our Universe has that manifold rather than any of the other ones -- some string theorists appeal to what you might call the landscape. They argue that all possible configurations of compact dimensions are realized, each one with its own unique universe and set of physical laws, and we happen to live in this one because life would be impossible in most or all of the others. That’s not the strongest argument to come out of physics, but I’ll save a dissection of the idea for another day.
We don’t have a string theory, so we can’t test it. But it might be possible to perform experiments on string theory-adjacent ideas, and there’s been some progress on that front. Perhaps the event of inflation, which occurred immediately after the Big Bang, can teach us about string theory (or the formation of Universe-spanning cosmic strings). And perhaps there’s more to the dualities than we initially thought.
Recently, theorists have proposed another duality, the AdS/CFT correspondence. It’s not exactly string theory, but the idea is certainly sponsored by it. This correspondence proposes that you can write down a string theory in a special three-dimensional setting and connect it to a special kind of quantum theory on its two-dimensional boundary. In principle, the correspondence should allow you to transform your impossible-to-solve string theory problem into a merely really-difficult-to-solve quantum problem (or vice versa, allowing you to use some of the mathematical tools developed in string theory to solve your thorny quantum problem).
The AdS/CFT correspondence has found some limited applications, but its full utility remains unclear. And while the AdS/CFT correspondence has yet to be proven, theorists claim it should be possible soon (although they said the same thing about string theory itself during the Reagan administration).
Most string theorists of the modern era don’t work on string theory directly but instead mostly on the AdS/CFT correspondence and its implications, hoping that continuing to probe that mathematical relationship will unlock some hidden insight into the workings of a theory of everything.
I wish them luck.
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「弦假說」真的難以成立嗎？ -- Sunny Labh
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《媒介》上賴布先生這篇文章對「弦假說」有簡單的介紹和說明；對「通吃理論」的重要性和目前這方面在「弦假說」以外的研究方向有深入淺出的報導。文章可讀性也很高。請欣賞。
Is String Theory Really a ‘Dead end’?
A compelling theory of everything or an unsuccessful scientific ventur
Sunny Labh, 03/01/23
String theory is a theoretical framework that attempts to unify all the fundamental forces and particles in the universe by describing them as tiny, one-dimensional “strings” rather than point-like particles. The idea of string theory was first proposed in the late 1960s as a way to reconcile two seemingly incompatible theories: quantum mechanics, which describes the behavior of particles on a very small scale, and general relativity, which describes the behavior of gravity on a large scale.
Over the years, string theory has developed into a complex and highly mathematical framework with many different versions, each with its own set of predictions and implications. Despite its promise as a potential “theory of everything,” however, string theory has faced criticism for its lack of experimental evidence and testability and there’s absolutely no denying to that. One of the main challenges of the theory is that it predicts the existence of many more dimensions than the four we experience in our everyday lives. In some versions of the theory, there may be as many as 11 dimensions, most of which are “curled up” into tiny spaces that we cannot directly observe. This has made it difficult to devise experiments that can confirm or refute the theory.
Despite these challenges, there have been some attempts to verify string theory experimentally. For example, the Large Hadron Collider (LHC) at CERN, the European Organization for Nuclear Research, has been used to search for signs of supersymmetry, a key prediction of some versions of string theory. So far, however, no conclusive evidence for supersymmetry or string theory has been found. Some critics of string theory argue that it has become a “dead end” because it has not yet produced any testable predictions that can be verified experimentally. Others argue that it is still a promising theoretical framework that could eventually lead to new discoveries and breakthroughs in physics.
Potential alternatives
LQG: This is a theoretical framework that attempts to describe gravity in terms of loops and networks rather than strings. It is based on the principles of quantum mechanics and general relativity, and seeks to unify these two theories in a way that is testable and experimentally verifiable.
Causal dynamical triangulation: It describes space-time as a network of triangles, rather than as a continuum. It attempts to reconcile quantum mechanics and general relativity by describing space-time as a discrete structure that evolves over time.
Emergent gravity: Explains gravity as an emergent phenomenon, rather than a fundamental force. It suggests that gravity arises from the collective behavior of other, more fundamental particles and interactions.
Asymptotic safety: This is a theory that suggests that quantum gravity may be a “safe” theory, meaning that it does not require any additional input or parameters beyond what is already known. It attempts to reconcile quantum mechanics and general relativity by describing gravity as a fundamental force that behaves in a predictable and testable way.
These are just a few of the potential alternatives to string theory that have been proposed over the years. Each of these theories has its own strengths and weaknesses, and there is ongoing research and debate among physicists and theorists about which, if any, of these theories may ultimately prove to be the correct description of the universe.
Geometric unity
Geometric Unity is a theory of everything proposed by mathematician and economist Eric Weinstein. According to Weinstein, Geometric Unity is a new approach to unifying the laws of physics, which seeks to integrate and generalize existing physical theories, including string theory, loop quantum gravity, and other theoretical frameworks.
The central idea behind Geometric Unity is that the universe is best described in terms of a single mathematical object known as the “E8” manifold, a complex, multidimensional geometric structure that is intimately related to the concept of symmetry. According to Weinstein, the E8 manifold is a fundamental building block of the universe, and all of the fundamental particles and forces in the universe can be derived from its geometry.
In Geometric Unity, the universe is viewed as a complex, self-organizing system that operates according to a set of underlying mathematical principles. These principles are related to concepts like symmetry, topology, and information theory, and are believed to underlie the behavior of all matter and energy in the universe. According to Weinstein, this is achieved by recognizing that the universe is a complex, dynamic system that evolves over time, and that the laws of physics must be able to describe this evolution in a consistent and coherent way. If you want to read in detail about the idea of Geometric unity then you can read this brilliant piece by Timothy Nguyen
While Geometric Unity is still a relatively new and untested idea, it has generated considerable interest among physicists and mathematicians, and is seen by some as a promising new approach to unifying the laws of physics. However, like other theories of everything, it will require extensive testing and validation before it can be accepted as a viable description of the universe. And it isn’t hidden that the theory of GU is also faced by several criticisms.
Why do we even need a theory of everything? Why are scientists so desperate to reconcile quantum mechanics with general relativity and all the fundamental forces of nature? Why this sort of desperation anyway? Here’s why!
A “theory of everything”, as tagged by the modern scientific slang, is a theoretical framework that seeks to unify all the fundamental forces and particles in the universe into a single, coherent description. It would provide a complete and consistent explanation of all the fundamental laws and processes that govern the behavior of matter and energy in the universe. This would allow scientists to understand the universe on the most fundamental level possible.
There are still many outstanding problems in physics that remain unsolved, such as the nature of dark matter, the origin of the universe, and the behavior of black holes. A theory of everything could potentially solve these problems by providing a more complete and accurate understanding of the universe. Quantum mechanics and general relativity are two of the most successful theories in modern physics, but they are incompatible with each other. It would provide a framework for reconciling these two theories and would allow scientists to describe the behavior of matter and energy on all scales, from the smallest particles to the largest structures in the universe. It could potentially lead to new technologies and innovations, as a deeper understanding of the fundamental laws of nature could open up new avenues for research and development. String theory has a rich history of development and has evolved into a highly complex and mathematically sophisticated framework with many different versions. However, its lack of experimental evidence and testability remains a significant challenge, and it remains a topic of debate among physicists and theorists whether it will ultimately prove to be a dead end or a fruitful avenue of research.
The development of a complete comprehensive theory is seen as a major goal for physicists and scientists, as it would provide a complete and comprehensive understanding of the universe and the fundamental laws that govern it.
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