Can one equation unite all of physics?
- "It's no exaggeration to say that the greatest minds of the entire human race have made proposals for this grand final theory of everything," says theoretical physicist Michio Kaku.
- This theory, also known as the God Equation, would unify all the basic concepts of physics into one. According to Kaku, the best, most "mathematically consistent" candidate so far is string theory, but there are objections.
- "The biggest objection is you can't test it," Kaku explains, "but we're getting closer and closer."
How long should one wait until an idea like string theory, seductive as it may be, is deemed unrealistic?
- How far should we defend an idea in the face of contrarian evidence?
- Who decides when it's time to abandon an idea and deem it wrong?
- Science carries within it its seeds from ancient Greece, including certain prejudices of how reality should or shouldn't be.
From the perspective of the west, it all started in ancient Greece, around 600 BCE. This is during the Axial Age, a somewhat controversial term coined by German philosopher Karl Jaspers to designate the remarkable intellectual and spiritual awakening that happened in different places across the globe roughly within the span of a century. Apart from the Greek explosion of thought, this is the time of Siddhartha Gautama (aka the Buddha) in India, of Confucius and Lao Tzu in China, of Zoroaster (or Zarathustra) in ancient Persia—religious leaders and thinkers who would reframe the meaning of faith and morality. In Greece, Thales of Miletus and Pythagoras of Samos pioneered pre-Socratic philosophy, (sort of) moving the focus of inquiry and explanation from the divine to the natural.
To be sure, the divine never quite left early Greek thinking, but with the onset of philosophy, trying to understand the workings of nature through logical reasoning—as opposed to supernatural reasoning—would become an option that didn't exist before. The history of science, from its early days to the present, could be told as an increasingly successful split between belief in a supernatural component to reality and a strictly materialistic cosmos. The Enlightenment of the 17th and 18th centuries, the Age of Reason, means quite literally 'to see the light,' the light here clearly being the superiority of human logic above any kind of supernatural or nonscientific methodology to get to the "truth" of things.
Einstein, for one, was a believer, preaching the fundamental reasonableness of nature; no weird unexplainable stuff, like a god that plays dice—his tongue-in-cheek critique of the belief that the unpredictability of the quantum world was truly fundamental to nature and not just a shortcoming of our current understanding.
To what extent we can understand the workings of nature through logic alone is not something science can answer. It is here that the complication begins. Can the human mind, through the diligent application of scientific methodology and the use of ever-more-powerful instruments, reach a complete understanding of the natural world? Is there an "end to science"? This is the sensitive issue. If the split that started in pre-Socratic Greece were to be completed, nature in its entirety would be amenable to a logical description, the complete collection of behaviors that science studies identified, classified, and described by means of perpetual natural laws. All that would be left for scientists and engineers to do would be practical applications of this knowledge, inventions, and technologies that would serve our needs in different ways.
This sort of vision—or hope, really—goes all the way back to at least Plato who, in turn, owes much of this expectation to Pythagoras and Parmenides, the philosopher of Being. The dispute between the primacy of that which is timeless or unchangeable (Being), and that which is changeable and fluid (Becoming), is at least that old. Plato proposed that truth was in the unchangeable, rational world of Perfect Forms that preceded the tricky and deceptive reality of the senses. For example, the abstract form Chair embodies all chairs, objects that can take many shapes in our sensorial reality while serving their functionality (an object to sit on) and basic design (with a sittable surface and some legs below it). According to Plato, the Forms hold the key to the essence of all things.
Plato used the allegory of the cave to explain that what humans see and experience is not the true reality.
Credit: Gothika via Wikimedia Commons CC 4.0
When scientists and mathematicians use the term Platonic worldview, that's what they mean in general: The unbound capacity of reason to unlock the secrets of creation, one by one. Einstein, for one, was a believer, preaching the fundamental reasonableness of nature; no weird unexplainable stuff, like a god that plays dice—his tongue-in-cheek critique of the belief that the unpredictability of the quantum world was truly fundamental to nature and not just a shortcoming of our current understanding. Despite his strong belief in such underlying order, Einstein recognized the imperfection of human knowledge: "What I see of Nature is a magnificent structure that we can comprehend only very imperfectly, and that must fill a thinking person with a feeling of humility." (Quoted by Dukas and Hoffmann in Albert Einstein, The Human Side: Glimpses from His Archives (1979), 39.)
Einstein embodies the tension between these two clashing worldviews, a tension that is still very much with us today: On the one hand, the Platonic ideology that the fundamental stuff of reality is logical and understandable to the human mind, and, on the other, the acknowledgment that our reasoning has limitations, that our tools have limitations and thus that to reach some sort of final or complete understanding of the material world is nothing but an impossible, semi-religious dream.
This kind of tension is palpable today when we see groups of scientists passionately arguing for or against the existence of the multiverse, an idea that states that our universe is one in a huge number of other universes; or for or against the final unification of the laws of physics.
Nature, of course, is always the final arbiter of any scientific dispute. Data decides, one way or another. That's the beauty and power at the core of science. The challenge, though, is to know when to let go of an idea. How long should one wait until an idea, seductive as it may be, is deemed unrealistic? This is where the debate gets interesting. Data to support more "out there" ideas such as the multiverse or extra symmetries of nature needed for unification models has refused to show up for decades, despite extensive searches with different instruments and techniques. On the other hand, we only find if we look. So, should we keep on defending these ideas? Who decides? Is it a community decision or should each person pursue their own way of thinking?
In 2019, I participated in an interesting live debate at the World Science Festival with physicists Michael Dine and Andrew Strominger and hosted by physicist Brian Greene. The theme was string theory, our best candidate for a final theory of how particles of matter interact. When I completed my PhD in 1986, string theory was the way. The only way. But, by 2019, things had changed, and quite dramatically, due to the lack of supporting data. To my surprise, both Mike and Andy were quite open to the fact that that certainty of the past was no more. String theory has taught physicists many things and that was perhaps its use. The Platonic outlook was in peril.
The dispute remains alive, although with each experiment that fails to show supporting evidence for string theory the dream grows harder to justify. Will it be a generational thing, as celebrated physicist Max Planck once quipped, "Ideas don't die, physicists do"? (I paraphrase.) I hope not. But it is a conversation that should be held more in the open, as was the case with the World Science Festival. Dreams die hard. But they may die a little easier when we accept the fact that our grasp of reality is limited, and doesn't always fit our expectations of what should or shouldn't be real.
Roger Penrose used mathematics to show black holes actually exist. Andrea Ghez and Reinhard Genzel helped uncover what lies at the center of our galaxy.
- Half of the prize was awarded to Roger Penrose, a British mathematical physicist who proved that black holes ought to exist, if Einstein's relativity is correct.
- The other half was awarded to Reinhard Genzel, a German astrophysicist, and Andrea Ghez, an American astronomer.
- Genzel and Ghez helped develop techniques to capture clearer images of the cosmos.
The 2020 Nobel Prize in Physics has been awarded to three scientists who advanced the world's understanding of black holes — the mysterious regions of spacetime from which nothing can escape.
Roger Penrose, a British mathematical physicist, was awarded half of the $1.1 million prize. The other half was awarded to Reinhard Genzel, a German astrophysicist, and Andrea Ghez, an American astronomer.
The Nobel Committee for Physics said Penrose, 89, won the prize "for the discovery that black hole formation is a robust prediction of the general theory of relativity," while Genzel and Ghez (68 and 55, respectively) won for "the discovery of a supermassive compact object at the centre of our galaxy."
BREAKING NEWS: The Royal Swedish Academy of Sciences has decided to award the 2020 #NobelPrize in Physics with one… https://t.co/SC0CzMdllJ— The Nobel Prize (@The Nobel Prize)1601978633.0
"The discoveries of this year's Laureates have broken new ground in the study of compact and supermassive objects," David Haviland, chair of the Nobel Committee for Physics, said in a statement. "But these exotic objects still pose many questions that beg for answers and motivate future research. Not only questions about their inner structure, but also questions about how to test our theory of gravity under the extreme conditions in the immediate vicinity of a black hole."
Penrose, a professor at the University of Oxford, used "ingenious mathematical methods" to show that black holes are a direct consequence of Einstein's theory of general relativity, the committee wrote. (Einstein himself doubted that black holes existed in the real world.)
How a black hole is formed (see figure). The 2020 #NobelPrize in Physics has been awarded with one half to Roger P… https://t.co/qpzd6365Ll— The Nobel Prize (@The Nobel Prize)1601980527.0
Together with the late theoretical physicist Stephen Hawking, Penrose helped to reinvigorate research on general relatively, largely by developing theories about singularities, which are believed to be a boundaries within black holes "at which all the known laws of nature break down." The committee wrote that Penrose's 1965 paper, which described the formation of black holes and singularities, "is still regarded as the most important contribution to the general theory of relativity since Einstein."
"Singularity, that's a place where the densities and curvatures go to infinity. You expect the physics go crazy," Penrose told The Associated Press. "When I say singularity, that's not really the black hole. The black hole prevents you from seeing the singularity. It's the nasty thing in the middle. If you fall into a black hole, then you pretty well inevitably get squashed into this singularity at the end. And that's the end."
Since the early 1990s, Genzel and Ghez have been leading independent teams of astronomers that have helped develop techniques for capturing clearer images of the cosmos from Earth. The teams' primary focus of study was what lies at the center of our galaxy, a region called Sagittarius A*.
Credit: Johan Jarnestad/The Royal Swedish Academy of Sciences
Using some of the world's most sophisticated telescopes, Genzel and Ghez also discovered that one star in this region, known as S2 or S-O2, orbits the galaxy's center in just 16 years. (Compare that to our Sun, which takes 200 million years to complete an orbit around the galaxy.) Measurements from both teams indicated that Sagittarius A* is about the size of our solar system, but is incredibly dense, containing roughly 4 million solar masses. This led them to conclude the center of our galaxy could be only one thing: a supermassive black hole.
Grandfathers, take heart. You'll survive the paradox that's been gunning for you since the 1930s.
Science fiction requires its fans to suspend their disbelief, and there's no greater ask in that department than when trying to enjoy a time travel story. Writers twist their plots into Gordian knots to explain how time travel could logically work in their futuristic worlds. When the simplest explanation is, it probably doesn't.
Many physicists have agreed with that assessment. Einstein wondered whether time travel—more specifically ramifications of Gödel's universe—could be "excluded on physical grounds." In a 1992 paper, Stephen Hawking coined the "chronology-protection conjecture." That's basically a temporal accord baked into the laws of the universe to render time travel impossible and, in Hawking's words, "make the universe safe for historians." And Russian physicists Igor Dmitriyevich Novikov formulated a similar idea with his "self-consistency conjecture."
But physics can't preclude the possibility of time travel entirely. Both general and special relativity shows time to be relative, and general relativity is open to the possibility of temporal shenanigans. But if you could hop into a time machine and jet back in time, would you need to worry about generating history-altering paradoxes? Not according to a new study published in the peer-reviewed Classical and Quantum Gravity. The math shows the universe will sort things out.
A paradox primer
According to the study, the universe would have worked things out whether Marty stole credit for "Johnny B. Goode" or not.
(Photo: Universal Studios)
The classic temporal thought experiment is known as the grandfather paradox. It goes like this: Imagine you decide to go back in time to kill your grandfather. Yes, his election-year posts have been that embarrassing. You travel back and kill him before he conceives one-half of your parents. But then, how is it you can exist to go back and kill him? But if you don't exist, then who killed your grandfather? Paradox. The timeline is no longer self-consistent. (Maybe.)
You can play this game with most time traveling tales. In "Back to the Future," Marty travels back in time and interferes with his parents' dalliance, preventing himself from being born. But if Marty is never born, how does he interfere with his parents' dalliance? But if he can't interfere, what's preventing him from being born? And round we go.
One would think such worries limited to high-minded philosophy debates or low-brow movie riffs. But some solutions to Einstein's field equations allow time travel through closed timelike curves. These theoretical paths would allow someone to be present at an initial event, travel through space and time, and return to that event again. Think a spacetime loop-the-loop. Importantly, the return point is not a repeat of the initial event. It is the initial event.
The implications of closed timelike curves lead to all sorts of wild time travel scenarios. According to physicist Michio Kaku, these have included traveling through a wormhole, through a spinning black hole, around an infinitely-long spinning cylinder, and around two colliding cosmic strings.
The universe is a self-regulating Time Lord
Dr. Fabio Costa (left) and Germain Tobar (right) discuss their findings. Behind them, a process function (w) interacts with localized spacetime regions with closed timelike curves.
Credit: University of Queensland
With time travel on the theoretical table, Tobar Germain, a University of Queensland undergraduate, wanted to test its consistency. Is paradox-free time travel mathematically possible? To answer that question, he teamed up with Dr. Fabio Costa, a University of Queensland physicist, to crunch the numbers.
"Some physicists say it is possible, but logically, it's hard to accept because that would affect our freedom to make any arbitrary action," Tobar said in a release. "It would mean you can time travel, but you cannot do anything that would cause a paradox to occur."
According to their research, time travel can be consistent and free of logical paradoxes. However, that requires the outputs of all but two space-time regions to be fixed. In that case, despite the presence of closed timelike loops, entities can maintain their freedom of choice without resulting in a paradox.
"The maths checks out, and the results are the stuff of science fiction," Costa said in the same release.
To illustrate their findings, Tobar and Costa offer a thought experiment straight out of science fiction. Imagine you travel through time to stop the COVID-19 pandemic. You locate and quarantine patient zero. Mission (and paradox) accomplished, right? Not according to their research. The math suggests that temporal events would adjust to being logically consistent with any action you made. For example, you may catch the virus, become patient zero, and spread the pandemic anyway.
Therefore, future, erm, past you still has the stimulus that sent you back in time initially.
"No matter what you did, the salient events would just recalibrate around you," Tobar said. "That would mean that—no matter your actions—the pandemic would occur, giving your younger self the motivation to go back and stop it.
"The range of mathematical processes we discovered show that time travel with free will is logically possible in our universe without any paradox."
Riding the timelike curve?
Of course, sayings paradox-free time travel is mathematically consistent is a wildly different statement than saying it is practically possible. Even if you could take the plunge into a wormhole, there's a good chance you'd be crushed out of existence before reaching the other end. Souped-up DeLorean or no.
It all depends on how the laws of quantum gravity shake out, and physicists are still exploring that very open question. What about those other scenarios Kaku pointed out? In a follow-up article, he points out that none can be realized using known physical mechanisms.
So, while we may be the time lords of the whiteboard, the universe will be a one-way street for the foreseeable future.
Math doesn't suck. It is one of humanity's greatest and most mysterious journeys.
- There is a pervasive cultural attitude against mathematics, but it is actually a mind-blowing tool for analyzing and predicting the world around us—and far beyond. We asked mathematicians Edward Frenkel and Po-Shen Loh, and physicists Michio Kaku, Michelle Thaller, Janna Levin and Geoffrey West to explain the wonders of math.
- West explains the rule of 'quarter-power scaling' in biology—there is a mathematical equation that predicts how much food an organism needs to eat to survive and it's remarkably consistent, whether you're looking at ladybugs, cats, elephants, and even trees and flowers. Math underpins our lives in incredible ways.
- Infinitesimal calculus—the math that describes how moving bodies change over time—turns out to predict not just phenomena on Earth but far out in the universe. The 11-dimensional math used by physicists turns out to predict the exact results of particle physics experiments. Humanity is on an incredible journey with mathematics and every day it opens up the world and universe in eye-opening ways.