Can spacekime help us make headway on some of the most pernicious inconsistencies in physics?
- Our linear model of time may be holding back scientific progress.
- Spacekime theory can help us better understand the development of diseases, financial and environmental events, and even the human brain.
- This theory helps us better utilize big data, develop AI, and can even solve inconsistencies in physics.
We take for granted the western concept of linear time. In ancient Greece, time was cyclical and if the Big Bounce theory is true, they were right. In Buddhism, there is only the eternal now. Both the past and the future are illusions. Meanwhile, the Amondawa people of the Amazon, a group that first made contact with the outside world in 1986, have no abstract concept of time. While we think we know time pretty well, some scientists believe our linear model hobbles scientific progress. We're missing whole dimensions of time, in this view, and our limited perception could be the last obstacle to a sweeping theory of everything.
Theoretical physicist Itzhak Bars of the University of Southern California, Los Angeles, is the most famous scientist with such a hypothesis, known as two-time physics. Here, time is 2D, visualized as a curved plane interwoven into the fabric of the "normal" dimensions—up-down, left-right, and backward-forward. While the hypothesis is over a decade old, Bars isn't the only scientist with such an idea. But what's different with spacekime theory is that it uses a data analytics approach, rather than a physics one. And while it posits that there are at least two dimensions of time, it allows for up to five.
In the spacekime model, space is 5D. Besides the ones we normally encounter, the extra dimensions are so infinitesimally small, we never notice them. This relates to the Kaluza–Klein theory developed in the early 20th century, which stated that there might be an extra, microscopic dimension of space. In this view, space would be curved like the surface of Earth. And like Earth, those who travel the entire distance would, eventually, loop back to their place of origin.
Kaluza-Klein theory unified electromagnetism and gravity, but wasn't accepted at the time, although it did help in the search for quantum gravity. The concept of additional dimensions was revived in the 1990s with Paul Wesson's Space-Time-Matter Consortium. Today, proponents of superstring theory say there may be as many as 10 different dimensions, including nine of space and one of time.
The Spacekime model
Spacekime theory was developed by two data scientists. Dr. Ivo Dinov is the University of Michigan's SOCR Director, as well as a professor of Health Behavior and Biological Sciences, and Computational Medicine and Bioinformatics. SOCR stands for: Statistics Online Computational Resource designs. Dr. Dinov is an expert in "mathematical modeling, statistical analysis, computational processing, scientific visualization of large datasets (Big Data) and predictive health analytics." His research has focused on mathematical modeling, statistical inference, and biomedical computing.
His colleague, Dr. Milen Velchev Velev, is an associate professor at the Prof. Dr. A. Zlatarov University in Bulgaria. He studies relativistic mechanics in multiple time dimensions, and his interests include "applied mathematics, special and general relativity, quantum mechanics, cosmology, philosophy of science, the nature of space and time, chaos theory, mathematical economics, and micro-and-macroeconomics."
Drs. Dinov and Velev began developing spacekime theory around four or five years ago, while working with big data in the healthcare field. "We started looking at data that intrinsically has a temporal dimension to it," Dr. Dinov told me during a video chat. "It's called longitudinal or time varying data, longitudinal time variance—it has many, many names. This is data that varies with time. In biomedicine, this is the de facto, standard data. All big health data is characterized by space, time, phenotypes, genotypes, clinical assessments, and so forth."
A better way to manage big data
"We started asking big questions," Dinov said. "Why are our models not really fitting too well? Why do we need so many observations? And then, we started playing around with time. We started digging and experimenting with various things. And then we realized two important facts.
"Number one, if we use what's called color-coded representations of the complex plane, we can define spacekime, or higher dimensional spacetime, in such a way that it agrees with the common observations that we make in (the longitudinal time series in) ordinary spacetime. That agreement was very important to us, because it basically says, yes, the higher dimensional theory does not contradict our common observations.
"The second realization was that, since this extra dimension of time is imperceptible, we needed to approximate, model, or estimate, one of the unobservable time characteristics, which we call the kime phase. After about a year, we discovered that there is a mathematically elegant tool called the Laplace Transform that allows us to analytically represent time series data as kime-surfaces. Turns out, the spacekime mathematical manifold is a natural, higher dimensional extension of classical Minkowski, four-dimensional spacetime."
Our understanding of the world is becoming more complex. As a result, we have big data to contend with. How do we find new ways to analyze, interpret and visual such data? Dinov believes spacekime theory can help in some pretty impressive ways. "The result of this multidimensional manifold generalization is that you can make scientific inferences using smaller data samples. This requires that you have a good model or prior knowledge about the phase distribution," he said. "For instance, we can use spacekime process representation to better understand the development or pathogenesis to model the distributions of certain diseases.
"Suppose we are evaluating fMRIs of Alzheimer's disease subjects. Assume we know the kime phase distribution for another cohort of patients suffering from amyotrophic lateral sclerosis, Lou Gehrig's disease. The ALS kime-phase distribution could be used for evaluating the Alzheimer's patients," and many other neurodegenerative populations. Dinov also thinks spacekime analytics could help improve political polling, increase our understanding of complex financial and environmental events, and even the innerworkings of the human brain, all without having to take the huge samples required today to make accurate models or predictions. Spacekime theory even offers opportunities to design novel AI analytical techniques. But it goes beyond that.
The problem of time
Spacekime theory can help us make headway on some of the most pernicious inconsistencies in physics, such as Heisenberg's uncertainty principle and the seemingly irreconcilable rift between quantum physics and general relativity, what's known as "the problem of time."
Dinov wrote that the "approach relies on extending the notions of time, events, particles, and wave functions to complex-time (kime), complex-events (kevents), data, and inference-functions." Basically, working with two points of time allows you to make inferences on a radius of points associated with a certain event. With Heisenberg's uncertainty principle, according to this model, since time is a plane, a certain particle would be in one position or phase, time-wise, in terms of velocity, and another phase, in terms of position.
This idea of hidden dimensions of time is a little like Plato's allegory of the cave or how an X-ray signifies what's underneath, but doesn't convey a 3D image. From a data science perspective, it all comes down to utility. Dinov believes that if we can calculate the true phase dispersion of complex phenomena, we can better understand and control them.
Drs. Dinov and Velev's book on spacekime theory comes out this August. It's called "Data Science: Time Complexity, Inferential Uncertainty, and Spacekime Analytics".
Two new studies examine ways we could engineer human wormhole travel.
- Sci-fi movies and books love wormholes—how else can we hope to travel through interstellar distances?
- But wormholes are notoriously unstable; it's hard to keep them open or make them big enough.
- Two new papers offer some hope in solving both of these issues, but at a high price.
Imagine if we could cut paths through the vastness of space to make a network of tunnels linking distant stars somewhat like subway stations here on Earth? The tunnels are what physicists call wormholes, strange funnel-like folds in the very fabric of spacetime that would be—if they exist—major shortcuts for interstellar travel. You can visualize it in two dimensions like this: Take a piece of paper and bend it in the middle so that it makes a U shape. If an imaginary flat little bug wants to go from one side to the other, it needs to slide along the paper. Or, if there were a bridge between the two sides of the paper the bug could go straight between them, a much shorter path. Since we live in three dimensions, the entrances to the wormholes would be more like spheres than holes, connected by a four-dimensional "tube." It's much easier to write the equations than to visualize this! Amazingly, because the theory of general relativity links space and time into a four-dimensional spacetime, wormholes could, in principle, connect distant points in space, or in time, or both.
A wormhole connecting two points in space.
Credit: TDHster via Adobe Stock
The idea of wormholes is not new. Its origins reach back to 1935 (and even earlier), when Albert Einstein and Nathan Rosen published a paper constructing what became known as an Einstein-Rosen bridge. (The name 'wormhole' came up later, in a 1957 paper by Charles Misner and John Wheeler, Wheeler also being the one who coined the term 'black hole.') Basically, an Einstein-Rosen bridge is a connection between two distant points of the universe or possibly even different universes through a tunnel that goes into a black hole. Exciting as the possibility is, the throats of such bridges are notoriously unstable and any object with mass that ventures through it would cause it to collapse upon itself almost immediately, closing the connection. To force the wormholes to stay open, one would need to add a kind of exotic matter that has both negative energy density and pressure—not something that is known in the universe. (Interestingly, negative pressure is not as crazy as it seems; dark energy, the fuel that is currently accelerating the cosmic expansion, does it exactly because it has negative pressure. But negative energy density is a whole other story.)
If wormholes exist, if they have wide mouths, and if they can be kept open (three big but not impossible ifs) then it's conceivable that we could travel through them to faraway spots in the universe. Arthur C. Clarke used them in "2001: A Space Odyssey", where the alien intelligences had constructed a network of intersecting tunnels they used as we use the subway. Carl Sagan used them in "Contact" so that humans could confirm the existence of intelligent ETs. "Interstellar" uses them so that we can try to find another home for our species.
If wormholes exist, if they have wide mouths, and if they can be kept open (three big but not impossible ifs) then it's conceivable that we could travel through them to faraway spots in the universe.
Two recent papers try to get around some of these issues. Jose Luis Blázquez-Salcedo, Christian Knoll, and Eugen Radu use normal matter with electric charge to stabilize the wormhole, but the resulting throat is still of submicroscopic width, so not useful for human travel. It is also hard to justify net electric charges in black hole solutions as they tend to get neutralized by surrounding matter, similar to how we get shocked with static electricity in dry weather. Juan Maldacena and Alexey Milekhin's paper is titled 'Humanly Traversable Wormholes', thus raising the stakes right off the bat. However, they are open to admitting that "in this paper, we revisit the question [of humanly traversable wormholes] and we engage in some 'science fiction.'" The first ingredient is the existence of some kind of matter (the "dark sector") that only interacts with normal matter (stars, us, frogs) through gravity. Another point is that to support the passage of human-size travelers, the model needs to exist in five dimensions, thus one extra space dimension. When all is set up, the wormhole connects two black holes with a magnetic field running through it. And the whole thing needs to spin to keep it stable, and completely isolated from particles that may fall into it compromising its design. Oh yes, and extremely low temperature as well, even better at absolute zero, an unattainable limit in practice.
Maldacena and Milekhins' paper is an amazing tour through the power of speculative theoretical physics. They are the first to admit that the object they construct is very implausible and have no idea how it could be formed in nature. In their defense, pushing the limits (or beyond the limits) of understanding is what we need to expand the frontiers of knowledge. For those who dream of humanly traversable wormholes, let's hope that more realistic solutions would become viable in the future, even if not the near future. Or maybe aliens that have built them will tell us how.
Night owl or early bird?
As with almost all life on Earth, human beings also function in cycles of light and dark. Look what happens to the human organism (and psyche) every day.
2am: Highest level of lymphocytes. The body heals well overnight.
3am: Blood flow through the brain is at its greatest at night.
4am: Growth hormone is secreted at night. It is responsible for tissue regeneration in adults and growth in children. The level of vasopressin is also raised, thanks to which we don't have to run to the bathroom for a pee. In children, where the endocrine system is still developing, bed-wetting is more likely. At night, the level of prolactin, the hormone responsible mainly for lactation, is at its highest.
5am: Body temperature is at its lowest. For night owls, the minimum temperature occurs during the middle of the sleep cycle. For early birds, this occurs at the end of their sleep.
5am–7am: Large intestine movement and body detox.
6am: Reveille! When light hits the retina, the hypothalamus reduces production of melatonin (the sleep hormone). Within 30 minutes of waking up, we observe a steady increase in our cortisol level, which reaches its maximum at about 7am. Cortisol accelerates gluconeogenesis (the production of glucose, mainly from amino acids) above all in the liver, but also in the kidneys and small intestine. It accelerates the breakdown of fatty acids (allowing them to be converted into energy), and inhibits the immune system. Cortisol increases the secretion of vasopressin and noradrenaline, which mobilizes the body to action. The effect of this is to increase the concentration of glucose in the blood, thanks to which we have the energy to start the day. During these hours, it is a good idea to move a bit, stretching our tendons and muscles, stiff from sleep. Cortisol also participates in the laying down of short-term memories (it is worth looking at your timetable in order to start the day better prepared). This is also a good time for meditation.
7am: Melatonin production stops. Its level falls. The body is now particularly sensitive to gentle stimuli.
7am–9am: Stomach activity. A high level of digestion and nutrient absorption. A good time for breakfast.
8am: Noradrenaline raises our body temperature. The highest concentration of cortisol (the stress hormone). A jump in the concentration of ghrelin, the hunger hormone; we eat breakfast.
9am: High concentration of glucose in the blood due to the high concentration of cortisol.
9am–11am: Spleen and kidney activity. Production of digestive enzymes. Work and exercise.
10am: An increase in body temperature increases vigour and alertness.
11am–1pm: Concentration and cognitive abilities at a high level.
2pm: The highest concentration of glucose in the blood. Glucose is the main fuel for muscles and the brain. Its concentration is directly correlated with physical and mental activity.
3pm: Noradrenaline and body temperature increase the coordination of movement and muscle activity.
3pm–6pm: The best results from intensive physical activity and the least vulnerability to injury. The mitochondria of the skeletal muscles exhibit their most active cell respiration. Increased oxygen uptake in the lungs. By the by, intensive muscle activity can reset a disturbed biological clock.
8pm: The pineal gland starts to produce melatonin. It is made from tryptophan. Pumpkin seeds and dried spirulina (seaweed) are excellent sources of this. It may be worth snacking on these during the day to have the raw materials for sweet dreams. The production of melatonin is inhibited by light, so during these hours we should avoid intensive screen time and the solarium.
9pm: The melatonin level rises. It can be detected in plasma and saliva.
10pm: Intestinal activity slows. It is not a good idea to stuff your face now, although food at this time of day tastes best.
11pm: Low cortisol level. It will rise while we sleep and, reaching a high level, will be the signal to wake up.
12am: High level of testosterone; it peaks after three hours of sleep. During the night the level of ghrelin, the hormone that signals hunger, rises. If we are sleeping lightly, we may feel hungry.
Nobel 2017: Proteins CLOCK and BMAL1 activate the transcription of the PER and CRY genes. The created PER and CRY proteins connect together and inhibit the work of the genes CLOCK and BMAL1. Over time, the PER and CRY proteins break down which allows CLOCK and BMAL1 to appear, again activating PER and CRY…
This sequence repeats and, in some sense, pulsates in a 24-hour cycle.
The most important influence on synchronizing the biological clock ('zeitgeber') is light. The suprachiasmatic nucleus is located in the hypothalamus, above the intersection of the optic nerves (hence its name). This is where the synchronization of the biological clock with the daily rhythm takes place. Other things that influence the clock are food intake and physical activity.
Blue light (emitted by the screens of electronic equipment), inhibits the production of melatonin much more so than orange light. This is why it is hard to fall asleep right after switching off your computer or putting down your smartphone.
In 1962, the caver Michel Siffre, as part of an experiment, shut himself in a cave for two months. It turned out that he ate, slept and woke up according to his internal clock (in a cycle lasting 24.5 hours). Interestingly, his perception of time changed. Every day he counted to 120 at the tempo of one number per second. After some time spent in the dark this exercise took him as long as five minutes.
Depending upon the time of day, plants not only open and close their flowers but they also raise and lower their branches.
It was once thought that bacteria are too primitive to count time. But it turns out that cyanobacteria also have an internal clock. Those that have an inactivated biological clock fare worse with the day/night cycle.
Mushrooms also have a biological clock, which evolved independently from that of bacteria and animals.
Animals fed at a time when they ought to be resting have a tendency to gain weight.
Depression, sleep disruption and metabolic disruption can be caused by impairment of the circadian rhythm (the 24-hour cycle).
The efficacy of medicines and their toxicity depends upon the time of day they are given.
The signals between two selected neurons always run at the same time and with high accuracy. This is how our internal stopwatch works.
The metaphor of Indra's diamond net, which originates from the Garland Sutra, postulates that everything that exists creates an endless net of diamonds, extending throughout the universe. Each point in this net is a jewel whose facets reflect all others, and each is also a universe containing its entire past, present and future. If a new element appears in one of the diamonds, even a speck of dust, the whole net will react to its presence. The human body resembles a net of common interactions and dependencies. An external or internal stimulus causes a whole range of physiological changes, whose effects spread and affect each other like waves on the surface of a lake. There's no way we can reduce such a complicated system to a binary description, but we can see in it some repetitive events and tendencies that seem to pulse in time with the repetition of sunrises and sunsets. The biological clock is a masterful achievement of evolution, and understanding how it works can play a significant role in setting the rhythm for a successful day.
Translated from the Polish by Annie Jaroszewicz
Interactive globe shows where your hometown was at various stages of Earth's deep geological past.
- If you love travelling, a pandemic like this is not the greatest of times.
- But here's a way to go somewhere else without even leaving the house.
- This interactive tool lets you travel up to 750 million years back in time.
Travels in the fourth dimension
Image: Ancient Earth Globe, reproduced with kind permission.
Berlin in deep time. Left to right: in the Neocene Period (20 million years ago), Berlin is on a vast plain that includes what would become the Baltic Sea; in the Devonian (400 million years ago), it's on the southern edge of a turtle-shaped continent; and in the Ordovician (470 million years ago), Berlin is on an island south of what was to become, many millions of years later, the Black Sea.
No matter where in the world you are, the virus continues to be out there somewhere, as keen as ever on making your acquaintance. The best policy remains: avoid contact with others, avoid unnecessary travel. In short: we're all stuck at home a whole lot more than we'd like to.
After the better part of a year spent under various forms of lockdowns and other restrictions, many are suffering from an increasingly itchy version of wanderlust – the urge to travel – and it's becoming harder and harder not to scratch.
Here's an interesting alternative: instead of traveling through space, why not stay put in the first three dimensions and travel through the fourth one instead? It's a trick performed to great acclaim by H.G. Wells in "The Time Machine."
The protagonist in Wells' 1895 novella travels to the terrifying future populated by Eloi and Morlocks and even further forward to the final days of Earth, without having to leave the laboratory attached to his house.
750 million years into the past
Image: Ancient Earth Globe, reproduced with kind permission.
New York City through the ages. Left to right: Early Triassic (240 million years ago), in the middle of a megacontinent opposite future Morocco; Carboniferous (340 million years ago), still coastal, but mirrored – the ocean to the west, the land to the east; Late Ordovician (450 million years ago), near the tip of a very Long Island indeed.
And thanks to the Ancient Earth Globe, you can now travel 750 million years in the other direction, also without leaving your house. You don't even need a lab; just go to the interactive map built by paleontologist Ian Webster. Here's how it works.
- Type in the name of your hometown.
- Its coordinates are 'geolocked' onto the globe.
- As you scroll through the past ages of the Earth, the continents shift shape and change place.
- Watch the surroundings of your location modify accordingly. Now you're high up in the mountains. And now you're getting your feet wet in the middle of a nameless ocean.
- From the drop-down menu on top, you can pick one of 25 specific times, from zero to 750 million years ago.
- Or pull one of 19 significant events from the menu on the right-hand side: the time of the first dinosaurs or the first flowers, the time of the supercontinents of Pangaea or Pannotia, the Jurassic or Cretaceous era.
- Or you can time-travel casual style, by using the left and right arrows on your keyboard to flip through prehistory.
The map of the world isn't 'fixed'
Image: Ancient Earth Globe, reproduced with kind permission.
Time travel in Buenos Aires. Left to right: Late Jurassic (150 million years ago), glued to Southern Africa; Carboniferous (340 million years ago), in the middle of a giant bay; Silurian (430 million years ago), on the north shore of a large continent, facing a Hawaiian-like chain of islands.
The purpose of the Ancient Earth Globe is to provide its users with an appreciation of the dynamic nature of our planet's appearance. The map of the world that we experience as 'fixed' is anything but. The tectonic forces that shift, split and collide entire continents are constantly at work. Except that our lives are too short to really experience the changes they bring about.
But go back far enough into the past, and what's familiar becomes strange. Dry land transforms into ocean floor. Seaside towns move to the middle of strange continents. Cold climes turn tropical, and vice versa. Imagining such exotic pasts may not be the same as actually going there. But it sure beats watching the news in this Groundhog Day of a year.
Images from the Ancient Earth Globe reproduced with kind permission by Ian Webster
Strange Maps #1052
Got a strange map? Let me know at email@example.com.
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.