Fairly Simple Math Could Bridge Quantum Mechanics and General Relativity

The following article is taken from the email received from Scientific American magazine  {Noor Salik}

Some of the comments are interesting:

<–for example —>

Nonsense.  I suppose you don’t consider the transistor to be practical. The transistor could not have been invented without quantum mechanical solid state physics.


Actual article:

Fairly Simple Math Could Bridge Quantum Mechanics and General Relativity

A framework that relies on college-level mathematics could describe what happens to particles in so-called space time rips, gravity fluctuations such as those that occur during the birth of a black hole

By Eugenie Samuel Reich and Nature magazine



Image: wylieconlon/Flickr

From Nature magazine.

Could an analysis based on relatively simple calculations point the way to reconciling the two most successful — and stubbornly distinct — branches of modern theoretical physics? Frank Wilczek and his collaborators hope so.

The task of aligning quantum mechanics, which deals with the behaviour of fundamental particles, with Einstein’s general theory of relativity, which describes gravity in terms of curved space-time, has proved an enormous challenge. One of the difficulties is that neither is adequate to describe what happens to particles when the space-time they occupy undergoes drastic changes — such as those thought to occur at the birth of a black hole. But in a paper posted to the arXiv preprint server on 15 October (A. D. Shapere et al. http://arxiv.org/abs/1210.3545; 2012), three theoretical physicists present a straightforward way for quantum particles to move smoothly from one kind of ‘topological space’ to a very different one.

The analysis does not model gravity explicitly, and so is not an attempt to formulate a theory of ‘quantum gravity’ that brings general relativity and quantum mechanics under one umbrella. Instead, the authors, including Nobel laureate Frank Wilczek of the Massachusetts Institute of Technology (MIT) in Cambridge, suggest that their work might provide a simplified framework for understanding the effects of gravity on quantum particles, as well as describing other situations in which the spaces that quantum particles move in can radically alter, such as in condensed-matter-physics experiments. “I’m pretty excited,” says Wilczek, “We have to see how far we can push it.”

The idea is attracting attention not only because of the scope of its possible applications, but because it is based on undergraduate-level mathematics. “Their paper starts with the most elementary framework,” says Brian Greene, a string theorist at Columbia University in New York. “It’s inspiring how far they can go with no fancy machinery.”

Wilczek and his co-authors set up a hypothetical system with a single quantum particle moving along a wire that abruptly splits into two. The stripped-down scenario is effectively the one-dimensional version of an encounter with ripped space-time, which occurs when the topology of a space changes radically. The theorists concentrate on what happens at the endpoints of the wire — setting the ‘boundary conditions’ for the before and after states of the quantum wave associated with the particle. They then show that the wave can evolve continuously without facing any disruptions as the boundary conditions shift from one geometry to the other, incompatible one. “You can smoothly follow this process,” says Al Shapere at the University of Kentucky in Lexington, a co-author on the paper, adding that, like a magician’s rings, the transformation is impossible to visualize, but does make mathematical sense.

The desire to escape the mathematical headaches caused by such transformations is one motivation for string theory, which allows smooth changes in the topology of space-time, says Greene. He suggests that the approach developed by Wilczek, Shapere and MIT undergraduate student Zhaoxi Xiong could be applied within string theory too.

Although Wilczek originally believed that the result was new, a 1995 paper by Aiyalam Balachandran of Syracuse University in New York proposed a similar strategy for describing changes in topology in quantum mechanics (A. P. Balachandranet al. Nucl. Phys. B 446, 299–314; 1995). Balachandran acknowledges that his work hasn’t hit the mainstream and says that he hopes Wilczek’s paper will prompt others to take a closer look. “Conventional approaches to this problem don’t get very far,” he says. “This opens up a new technique.”


A framework that relies on college-level mathematics could describe what happens to particles in so-called spacetime rips, gravity fluctuations such as those that occur during the birth of a black hole

By Eugenie Samuel Reich and Nature magazine



The framework might also provide inspiration for experimentalists working on condensed matter. Rob Myers, a string theorist at the Perimeter Institute for Theoretical Physics in Waterloo, Canada, says that he expects it to be relevant to an area called quantum quenches, in which quantum systems evolve in isolation from the environment and are then kicked out of equilibrium by an action of the experimentalist. Condensed-matter physicists have developed several quantum systems — including cold-atom traps and superconducting circuits — that can be used to test this idea.

Although the authors lay out their solution in only one dimension, Myers expects that the approach will readily generalize to describe real experiments in three dimensions. But he cautions that the paper represents only a first step. “To really see the impact of this work, that will take a while,” he says.

This article is reproduced with permission from the magazine Nature. The article wasfirst published on October 30, 2012.




Add Comment

  1. 1.    1. owlafaye08:57 PM 10/30/12

Bridging a 100 year old theory to a theory that has yielded nothing of practical value is a great way to continue wasting resources on roads that lead nowhere.

The protons were upset enough before quantum came along…leave them alone, admit you fell off the path somewhere, go back to a more promising idea and stop making fools of yourselves.

  1. 2.    2. robert schmidtin reply to owlafaye09:52 PM 10/30/12

Never have to wait long before some idiot comes along and says essentially that the world should take his word for it that the scientists are all wrong. Thanks for your contribution. You have made the world a much better place.

  1. 3.    3. slackerkeithin reply to owlafaye10:24 PM 10/30/12

@ owlafaye – You’re claiming quantum mechanics has “yielded nothing of practical value”? Man, you are a tool of the highest order.

  1. 4.    4. owlafayein reply to slackerkeith10:58 PM 10/30/12

Its a matter of your understanding of the word “practical”.

Physicists and their theories are at loggerheads with each other. You might say they always have been but in the past it led to great revelations and progress.

We are going nowhere towards the discovery of free energy solutions and travel amongst the stars.

Most physicists no longer have a “holy grail” relevant to humanity. Directed energy matters lay on the laboratory floor.

Leedskalnin, Tesla and other brilliant men were ignored by the rapaciousness of people like Westinghouse…once their research and goals are claimed and enhanced on by today’s scientists, we might just get somewhere.

Quantum mechanics only leads to answers that needed no question. They chase foolishness.

There is another scientific path to knowledge.

  1. 5.    5. Of NoImportance in reply to owlafaye11:55 PM 10/30/12

You speak as if, at present, every application of quantum mechanics is known – that there will never be a need to further study a certain science that works yet clashes with another.

And it’s not like the world is short on physicists. People can specialize; can pursue seemingly pointless goals for the purpose of finding out why – much like mathematics.

It is foolish to discard knowledge when it exists and no one knows why.

  1. 6.    6. negabladein reply to owlafaye12:13 AM 10/31/12

You haven’t actually said what that path is, other than something about upset protons which I’m assuming isn’t a literal description. If you have a self consistent framework with testable theories you should follow that path yourself and report on where it leads you. Or you could pay others to follow that path on your behalf. Your current approach is unlikely to succeed.

  1. 7.    7. And Then What?07:32 AM 10/31/12

Any theory that appears to constructs a mental bridge that allows us to understand why our current theories seem to be in conflict is worth exploring. To me it is a foregone  conclusion that the information we have at this point in time is just a glimpse of Reality. What lies in wait beneath and teases us with small bits of information about its true nature does not purposely hide from us. It simply is. We are curious, and want to know what drives everything, but unfortunately our vision of everything is not really everything, and so we interpret according to our perceptions. In a strange way we may be trying to go down the road with the cart before the horse. It may be that we will solve the true nature of the riddle by observing how the riddle affects its surroundings, but I suspect that any true understanding of how the riddle is constructed will only come once we understand the riddle itself. Mathematics may well describe the effects but in order for it to describe what produces the effects it must be “proven mathematically” that such a result is unique. This will always be open to attack based on the fact that “sample size” cannot be ignored as a determining factor with regard to the uniqueness of the result. Having said this, at our current stage of development, Mathematics and its underlying Logical framework would appear to be the best tools we have and may in fact lead us to our Eureka moment.

  1. 8.    8. bigbopperin reply to owlafaye09:36 AM 10/31/12

Nonsense.  I suppose you don’t consider the transistor to be practical. The transistor could not have been invented without quantum mechanical solid state physics.

  1. 9.    9. jahtez01:30 PM 10/31/12

owlafaye sez: “We are going nowhere towards the discovery of free energy solutions and travel amongst the stars”.

Think about that before you bother to respond.

  1. 10.  10. M Tuckerin reply to owlafaye05:13 PM 10/31/12

You have no idea of what you are talking about. It would be best for you to attempt to get some sort of basic notion of quantum mechanics before you decide it is a waste of resources. You might start with history. When you mentioned, “Bridging a 100 year old theory to a theory that has yielded nothing of practical value…” I was a bit perplexed but the rest of your rant made it clear that you consider general relativity to be the older theory but you are wrong. When general relativity gets to be 100 years old in a few more years I’m sure SA will have a nice article to commemorate the event. Perhaps you could investigate quantum mechanics to find out just what that theory has contributed to both physics and chemistry.


Genesis of the Universe



A Universe from Nothing: Einstein, the Belgian Priest and the Puzzle of the Big Bang

An excerpt from physicist Lawrence M. Krauss’s new book explains why we are not the center of the universe

By Lawrence M. Krauss | February 10, 2012 |25



[Editors’ note: The following is an excerpt from theoretical physicist Lawrence M. Krauss’s new book, A Universe from Nothing: Why There Is Something Rather Than Nothing (Free Press, 2012).]

It was a dark and stormy night.

Early in 1916, Albert Einstein had just completed his greatest life’s work, a decade-long, intense intellectual struggle to derive a new theory of gravity, which he called the general theory of relativity. This was not just a new theory of gravity, however; it was a new theory of space and time as well. And it was the first scientific theory that could explain not merely how objects move through the universe, but also how the universe itself might evolve.

There was just one hitch, however. When Einstein began to apply his theory to describing the universe as a whole, it became clear that the theory didn’t describe the universe in which we apparently lived.

Now, almost one hundred years later, it is difficult to fully appreciate how much our picture of the universe has changed in the span of a single human lifetime. As far as the scientific community in 1917 was concerned, the universe was static and eternal, and consisted of a single galaxy, our Milky Way, surrounded by a vast, infinite, dark, and empty space. This is, after all, what you would guess by looking up at the night sky with your eyes, or with a small telescope, and at the time there was little reason to suspect otherwise.

In Einstein’s theory, as in Newton’s theory of gravity before it, gravity is a purely attractive force between all objects. This means that it is impossible to have a set of masses located in space at rest forever. Their mutual gravitational attraction will ultimately cause them to collapse inward, in manifest disagreement with an apparently static universe.

The fact that Einstein’s general relativity didn’t appear consistent with the then picture of the universe was a bigger blow to him than you might imagine, for reasons that allow me to dispense with a myth about Einstein and general relativity that has always bothered me. It is commonly assumed that Einstein worked in isolation in a closed room for years, using pure thought and reason, and came up with his beautiful theory, independent of reality (perhaps like some string theorists nowadays!). However, nothing could be further from the truth.

Einstein was always guided deeply by experiments and observations. While he performed many “thought experiments” in his mind and did toil for over a decade, he learned new mathematics and followed many false theoretical leads in the process before he ultimately produced a theory that was indeed mathematically beautiful. The single most important moment in establishing his love affair with general relativity, however, had to do with observation. During the final hectic weeks that he was completing his theory, competing with the German mathematician David Hilbert, he used his equations to calculate the prediction for what otherwise might seem an obscure astrophysical result: a slight precession in the “perihelion” (the point of closest approach) of Mercury’s orbit around the Sun.

Astronomers had long noted that the orbit of Mercury departed slightly from that predicted by Newton. Instead of being a perfect ellipse that returned to itself, the orbit of Mercury precessed (which means that the planet does not return precisely to the same point after one orbit, but the orientation of the ellipse shifts slightly each orbit, ultimately tracing out a kind of spiral-like pattern) by an incredibly small amount: 43 arc seconds (about 1⁄100 of a degree) per century.

When Einstein performed his calculation of the orbit using his theory of general relativity, the number came out just right. As described by an Einstein biographer, Abraham Pais: “This discovery was, I believe, by far the strongest emotional experience in Einstein’s scientific life, perhaps in all his life.” He claimed to have heart palpitations, as if “something had snapped” inside. A month later, when he described his theory to a friend as one of “incomparable beauty,” his pleasure over the mathematical form was indeed manifest, but no palpitations were reported.

The apparent disagreement between general relativity and observation regarding the possibility of a static universe did not last long, however. (Even though it did cause Einstein to introduce a modification to his theory that he later called his biggest blunder. But more about that later.) Everyone (with the exception of certain school boards in the United States) now knows that the universe is not static but is expanding and that the expansion began in an incredibly hot, dense Big Bang approximately 13.72 billion years ago. Equally important, we know that our galaxy is merely one of perhaps 400 billion galaxies in the observable universe. We are like the early terrestrial mapmakers, just beginning to fully map the universe on its largest scales. Little wonder that recent decades have witnessed revolutionary changes in our picture of the universe.

The discovery that the universe is not static, but rather expanding, has profound philosophical and religious significance, because it suggested that our universe had a beginning. A beginning implies creation, and creation stirs emotions. While it took several decades following the discovery in 1929 of our expanding universe for the notion of a Big Bang to achieve independent empirical confirmation, Pope Pius XII heralded it in 1951 as evidence for Genesis. As he put it:

It would seem that present-day science, with one sweep back across the centuries, has succeeded in bearing witness to the august instant of the primordial Fiat Lux [Let there be Light], when along with matter, there burst forth from nothing a sea of light and radiation, and the elements split and churned and formed into millions of galaxies. Thus, with that concreteness which is characteristic of physical proofs [science] has confirmed the contingency of the universe and also the well-founded deduction as to the epoch when the world came forth from the hands of the Creator. Hence, creation took place. We say: “Therefore, there is a Creator. Therefore, God exists!”

The full story is actually a little more interesting. In fact, the first person to propose a Big Bang was a Belgian priest and physicist named Georges Lemaître. Lemaître was a remarkable combination of proficiencies. He started his studies as an engineer, was a decorated artilleryman in World War I, and then switched to mathematics while studying for the priesthood in the early 1920s. He then moved on to cosmology, studying first with the famous British astrophysicist Sir Arthur Stanley Eddington before moving on to Harvard and eventually receiving a second doctorate, in physics from MIT.

In 1927, before receiving his second doctorate, Lemaître had actually solved Einstein’s equations for general relativity and demonstrated that the theory predicts a nonstatic universe and in fact suggests that the universe we live in is expanding. The notion seemed so outrageous that Einstein himself colorfully objected with the statement “Your math is correct, but your physics is abominable.”

Nevertheless, Lemaître powered onward, and in 1930 he further proposed that our expanding universe actually began as an infinitesimal point, which he called the “Primeval Atom” and that this beginning represented, in an allusion to Genesis perhaps, a “Day with No Yesterday.”

Thus, the Big Bang, which Pope Pius so heralded, had first been proposed by a priest. One might have thought that Lemaître would have been thrilled with this papal validation, but he had already dispensed in his own mind with the notion that this scientific theory had theological consequences and had ultimately removed a paragraph in the draft of his 1931 paper on the Big Bang remarking on this issue.

Lemaître in fact later voiced his objection to the pope’s 1951 claimed proof of Genesis via the Big Bang (not least because he realized that if his theory was later proved incorrect, then the Roman Catholic claims for Genesis might be contested). By this time, he had been elected to the Vatican’s Pontifical Academy, later becoming its president. As he put it, “As far as I can see, such a theory remains entirely outside of any metaphysical or religious question.” The pope never again brought up the topic in public.

There is a valuable lesson here. As Lemaître recognized, whether or not the Big Bang really happened is a scientific question, not a theological one. Moreover, even if the Big Bang had happened (which all evidence now overwhelmingly supports), one could choose to interpret it in different ways depending upon one’s religious or metaphysical predilections. You can choose to view the Big Bang as suggestive of a creator if you feel the need or instead argue that the mathematics of general relativity explain the evolution of the universe right back to its beginning without the intervention of any deity. But such a metaphysical speculation is independent of the physical validity of the Big Bang itself and is irrelevant to our understanding of it. Of course, as we go beyond the mere existence of an expanding universe to understand the physical principles that may address its origin, science can shed further light on this speculation and, as I shall argue, it does.

In any case, neither Lemaître nor Pope Pius convinced the scientific world that the universe was expanding. Rather, as in all good science, the evidence came from careful observations, in this case done by Edwin Hubble, who continues to give me great faith in humanity, because he started out as a lawyer and then became an astronomer.

Hubble had earlier made a significant breakthrough in 1925 with the new Mount Wilson 100-inch Hooker telescope, then the world’s largest. (For comparison, we are now building telescopes more than ten times bigger than this in diameter and one hundred times bigger in area!) Up until that time, with the telescopes then available, astronomers were able to discern fuzzy images of objects that were not simple stars in our galaxy. They called these nebulae, which is basically Latin for “fuzzy thing” (actually “cloud”). They also debated whether these objects were in our galaxy or outside of it.

Since the prevailing view of the universe at the time was that our galaxy was all that there was, most astronomers fell in the “in our galaxy” camp, led by the famous astronomer Harlow Shapley at Harvard. Shapley had dropped out of school in fifth grade and studied on his own, eventually going to Princeton. He decided to study astronomy by picking the first subject he found in the syllabus to study. In seminal work he demonstrated that the Milky Way was much larger than previously thought and that the Sun was not at its center but simply in a remote, uninteresting corner. He was a formidable force in astronomy and therefore his views on the nature of nebulae held considerable sway.

On New Year’s Day 1925, Hubble published the results of his two-year study of so-called spiral nebulae, where he was able to identify a certain type of variable star, called a Cepheid variable star, in these nebulae, including the nebula now known as Andromeda.

First observed in 1784, Cepheid variable stars are stars whose brightness varies over some regular period. In 1908, an unheralded and at the time unappreciated would-be astronomer, Henrietta Swan Leavitt, was employed as a “computer” at the Harvard College Observatory. (“Computers” were women brought in to catalogue the brightness of stars recorded on the observatory’s photographic plates; women were not allowed to use the observatory telescopes at the time.) Daughter of a Congregational minister and a descendant of the Pilgrims, Leavitt made an astounding discovery, which she further illuminated in 1912: she noticed that there was a regular relationship between the brightness of Cepheid stars and the period of their variation. Therefore, if one could determine the distance to a single Cepheid of a known period (subsequently determined in 1913), then measuring the brightness of other Cepheids of the same period would allow one to determine the distance to these other stars!

Since the observed brightness of stars goes down inversely with the square of the distance to the star (the light spreads out uniformly over a sphere whose area increases as the square of the distance, and thus since the light is spread out over a bigger sphere, the intensity of the light observed at any point decreases inversely with the area of the sphere), determining the distance to faraway stars has always been the major challenge in astronomy. Leavitt’s discovery revolutionized the field. (Hubble himself, who was snubbed for the Nobel Prize, often said Leavitt’s work deserved the prize, although he was sufficiently self-serving that he might have suggested it only because he would have been a natural contender to share the prize with her for his later work.) Paperwork had actually begun in the Royal Swedish Academy to nominate Leavitt for the Nobel in 1924 when it was learned that she had died of cancer three years earlier. By dint of his force of personality, knack for self-promotion, and skill as an observer, Hubble would become a household name, while Leavitt, alas, is known only to aficionados of the field.

Hubble was able to use his measurement of Cepheids and Leavitt’s period-luminosity relation to prove definitively that the Cepheids in Andromeda and several other nebulae were much too distant to be inside the Milky Way. Andromeda was discovered to be another island universe, another spiral galaxy almost identical to our own, and one of the more than 100 billion other galaxies that, we now know, exist in our observable universe. Hubble’s result was sufficiently unambiguous that the astronomical community—including Shapley, who, incidentally, by this time had become director of the Harvard College Observatory, where Leavitt had done her groundbreaking work—quickly accepted the fact that the Milky Way is not all there is around us. Suddenly the size of the known universe had expanded in a single leap by a greater amount than it had in centuries! Its character had changed, too, as had almost everything else.

After this dramatic discovery, Hubble could have rested on his laurels, but he was after bigger fish or, in this case, bigger galaxies. By measuring ever fainter Cepheids in ever more distant galaxies, he was able to map the universe out to ever-larger scales. When he did, however, he discovered something else that was even more remarkable: the universe is expanding!

Hubble achieved his result by comparing the distances for the galaxies he measured with a different set of measurements from another American astronomer, Vesto Slipher, who had measured the spectra of light coming from these galaxies. Understanding the existence and nature of such spectra requires me to take you back to the very beginning of modern astronomy.

One of the most important discoveries in astronomy was that star stuff and Earth stuff are largely the same. It all began, as did many things in modern science, with Isaac Newton. In 1665, Newton, then a young scientist, allowed a thin beam of sunlight, obtained by darkening his room except for a small hole he made in his window shutter, through a prism and saw the sunlight disperse into the familiar colors of the rainbow. He reasoned that white light from the sun contained all of these colors, and he was correct.

A hundred fifty years later, another scientist examined the dispersed light more carefully, discovered dark bands amidst the colors, and reasoned that these were due to the existence of materials in the outer atmosphere of the sun that were absorbing light of certain specific colors or wavelengths. These “absorption lines,” as they became known, could be identified with wavelengths of light that were measured to be absorbed by known materials on Earth, including hydrogen, oxygen, iron, sodium, and calcium.

In 1868, another scientist observed two new absorption lines in the yellow part of the solar spectrum that didn’t correspond to any known element on Earth. He decided this must be due to some new element, which he called helium. A generation later, helium was first isolated on Earth.

Looking at the spectrum of radiation coming from other stars is an important scientific tool for understanding their composition, temperature, and evolution. Starting in 1912, Slipher observed the spectra of light coming from various spiral nebulae and found that the spectra were similar to those of nearby stars—except that all of the absorption lines were shifted by the same amount in wavelength.

This phenomenon was by then understood as being due to the familiar “Doppler effect,” named after the Austrian physicist Christian Doppler, who explained in 1842 that waves coming at you from a moving source will be stretched if the source is moving away from you and compressed if it is moving toward you. This is a manifestation of a phenomenon we are all familiar with, and by which I am usually reminded of a Sidney Harris cartoon where two cowboys sitting on their horses out in the plains are looking at a distant train, and one says to the other, “I love hearing that lonesome wail of the train whistle as the magnitude of the frequency changes due to the Doppler effect!” Indeed, a train whistle or an ambulance siren sounds higher if the train or ambulance is moving toward you and lower if it is moving away from you.

It turns out that the same phenomenon occurs for light waves as sound waves, although for somewhat different reasons. Light waves from a source moving away from you, either due to its local motion in space or due to the intervening expansion of space, will be stretched, and therefore appear redder than they would otherwise be, since red is the long-wavelength end of the visible spectrum, while waves from a source moving toward you will be compressed and appear bluer.

Slipher observed in 1912 that the absorption lines from the light coming from all the spiral nebulae were almost all shifted systematically toward longer wavelengths (although some, like Andromeda, were shifted toward shorter wavelengths). He correctly inferred that most of these objects therefore were moving away from us with considerable velocities.

Hubble was able to compare his observations of the distance of these spiral galaxies (as they were by now known to be) with Slipher’s measurements of the velocities by which they were moving away. In 1929, with the help of a Mount Wilson staff member, Milton Humason (whose technical talent was such that he had secured a job at Mount Wilson without even having a high school diploma), he announced the discovery of a remarkable empirical relationship, now called Hubble’s law: There is a linear relationship between recessional velocity and galaxy distance. Namely, galaxies that are ever more distant are moving away from us with faster velocities!

When first presented with this remarkable fact—that almost all galaxies are moving away from us, and those that are twice as far away are moving twice as fast, those that are three times away three times as fast, etc.—it seems obvious what this implies: We are the center of the universe!

As some friends suggest, I need to be reminded on a daily basis that this is not the case. Rather, it was consistent with precisely the relationship that Lemaître had predicted. Our universe is indeed expanding.

From UNIVERSE FROM NOTHING: Why There Is Something Rather than Nothing by Lawrence M. Krauss. Copyright © 2012 by Lawrence M. Krauss. Reprinted with permission by Free Press, a Division of Simon & Schuster, Inc.