Image: Illustration by Kyle Bean
In Brief
- Stymied by the difficulty of unifying quantum mechanics with Einstein’s general theory of relativity, physicists have turned to a simplified version of the problem: imagining space to be just two-dimensional and asking how gravity would then operate.
- At first, they expected 2-D gravity to be trivial. Shoehorned into one fewer dimension, gravity would become so tightly circumscribed that gravitational waves could not propagate, in which case quantum gravity should be a nonstarter.
- Physicists have found it is not so trivial after all. Waves might not ripple through the continuum, but the universe as a whole could morph. The resulting quantum theory of gravity solves various puzzles of unification, such as how time may emerge from timeless physics.
From its earliest days as a science, physics has searched for unity in nature. Isaac Newton showed that the same force responsible for the fall of an apple also holds the planets in their orbits. James Clerk Maxwell combined electricity, magnetism and light into a single theory of electromagnetism; a century later physicists added the weak nuclear force to form a unified “electroweak” theory. Albert Einstein joined space and time themselves into a single spacetime continuum.
Today the biggest missing link in this quest is the unification of gravity and quantum mechanics. Einstein’s theory of gravity, his general theory of relativity, describes the birth of the universe, the orbits of planets and the fall of Newton’s apple. Quantum mechanics describes atoms and molecules, electrons and quarks, the fundamental subatomic forces, and much besides. Yet in the places where both theories should apply—where both gravity and quantum effects are strong, such as black holes—they also seem incompatible. Physicists’ best efforts to combine them into a quantum theory of gravity have failed miserably, giving answers that make no sense or no answers at all. Despite 80 years of work by generations of physicists, including a dozen or so Nobel laureates, a quantum theory of gravity remains elusive.
This article was originally published with the title Quantum Gravity in Flatland.
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19 Comments
Add CommentBecause the gravity is the shielding force in Le-Sage theory, it would be inversely proportional to first power of distance, instead of second one. You're not required to be an expert to realize it.
Reply | Report Abuse | Link to thisAnytime a scientist says something can come from nothing then you know you are dealing with an amateur scientist.
Reply | Report Abuse | Link to thisThe solution to 2-D gravity is right underneath the science writer's nose and he doesn't see it.
I guess that is what happens when atheist scientists are left with the job of trying to figure out where everything originated.
It appears "Artistic Freedom" has entered into physics. The book Flatland published in the 1800s has interior horizontal lines in its illustrations, but no grid lines. Stephen Hawking’s book ‘A Brief History of Time’ published in 1988 had no grid lines in its illustrations either. As far as I know grid lines did not appear in physics illustrations until Brain Greene’s book ‘The Elegant Universe’ published in 1999. After Brian Greene’s book everybody started using grid lines in their illustrations. Now I could go to the library and look at science books since the beginning of time looking for illustrations with grid lines in them to see where it first started. However, at this moment it appears that grid lines were first put into use between 1988-1999. As people will find out in the short future and as trivial as it sounds, those grid lines do make a big difference! If that is the case then shouldn’t the person who started the idea of using grid lines in physics illustrations be given credit for their hard work?
Reply | Report Abuse | Link to thisDoes anyone out there know when grid lines were first used in physics illustrations?
I swear that, as a child in the 1950s I recall seeing a photograph of Einstein and another guy sitting in front of the now ubiquitous rubber sheet replete with two dimensional grid lines and a ball to illustrate the concept of curved spacetime to the public. I can't find any reference to that (perhaps imaginary) image now.
Reply | Report Abuse | Link to thisThe grid lines are intended to illustrate the system of coordinated used in general relativity to describe the effects of gravitation (and other dynamical motions and energy) on the relative positions of material objects of mass.
Unfortunately, that 2-d rubber sheet illustration has made a 'massive' (sorry) impression on the public's consciousness, seemingly representing the curvature of spacetime, using Earth's gravity to 'curve' spacetime 'down'.
It's always seemed to me to be a tragic misrepresentation. In my mind the effect of gravity on the abstract mathematical coordinates of spacetime could only be adequately illustrated as a three dimensional grid space, with its coordinates contracting from all directions towards the geometric center of a massive object. This more complex illustration of curved spacetime would have been nearly impossible to successfully present to the public about a hundred years ago, however...
I haven't received the April issue yet, but this seems to be a derivation of the causal dynamical triangulation theory of gravity previewed here in 2007: http://www.scientificamerican.com/article.cfm?id=the-triangular-universe
Reply | Report Abuse | Link to thisPlease see: http://en.wikipedia.org/wiki/Causal_dynamical_triangulation
"At large scales, it re-creates the familiar 4-dimensional spacetime, but it shows spacetime to be 2-d near the Planck scale, and reveals a fractal structure on slices of constant time."
I don't see any reference to CDT here...
TabulaMentis wrote, "I guess that is what happens when atheist scientists are left with the job of trying to figure out where everything originated."
Reply | Report Abuse | Link to thisAs opposed to attributing origination to faith-based personal beliefs in ancient deity(s) based on modern translations of other peoples written fables?
@TabulaMentis
Reply | Report Abuse | Link to this"Anytime a scientist says something can come from nothing then you know you are dealing with an amateur scientist."
lrn2quantummechanics
You should read up on some of the physics from the 20th century. If you did, you know that something comes from nothing literally ALL THE TIME.
*you'd
Reply | Report Abuse | Link to thisI have a little book that I bought back in the 1960's,"Abert Einstein and The Cosmic World Order" by Cornelius Lanczos.It is a volume of 6 lectures , and the 4th one "The Geometrical Discoveries of Gauss" states in the very well explained lecture," The crowning achievement of the Gaussian theory was the discovery of the "curvature."
Reply | Report Abuse | Link to thisCarl Friederich Gauss (1777-1855) "was one of the most prodigious mathematical geniuses of all ages."
Anyone notice how snottily @TabulaMentis writes about "the solution ...right underneath the science writer's nose and he doesn't see it"?
Reply | Report Abuse | Link to thisOf course Gravity works in 2 dimensions. If you think of Gravity as acting in all directions simultaneously is it not perfectly natural that if you look at a theoretical 2 dimensional slice consisting of all points on any plane described by all the points which make up the world lines describing such a plane then why would it not be logical to assume that Gravity would be felt by all such points be they on such a 2 dimensional plane as well as the 3 dimensional reality constructed by combining and infinite number of such planes to form such a 3 dimensional realty. I hope this is clear but if it is not feel free to ask for clarification from me and, I will try to be more enlightening as to why I make this statement.
Reply | Report Abuse | Link to this"A clock - as well as anything else that varies in time - runs more slowly in a strong gravitational field." - this article, p.44. Which is, of course, completely wrong. Time dilation is a function of position in a gravitational potential. The deeper down in a gravity well you are, the slower you go. Field strength has absolutely nothing to do with it. Near the event horizon of a galaxy-mass black hole, your time dilation would be immense, but the gravitational field would only be about 1G, the same as on the surface of the earth.
Reply | Report Abuse | Link to thisThe whole idea is nonsense. Gravity is not a force that pulls, because pulling is physically impossible. It is always a push from the opposite direction. Gravity does not pull, but stabilizes the orbits of stars, planets, atoms et all.
Reply | Report Abuse | Link to thisDimension is the perception of the differentiation between the "inner space" and "outer space" of objects. This perception is an ocular perception mediated by electromagnetic forces. Since electric fields and magnetic fields move perpendicular to each other and both move perpendicular to the direction of motion, we have 3 dimensions.
Let us talk science and discard the "established theories", where it is contrary to observation or are proved to be conceptually wrong. Fiction and superstitious belief in "established theories" must be totally discarded. We should not fool the public with such terms like the non-existent God particle, so that the scientists can spend public money for self enjoyment.
basudeba@gmail.com
After a blazingly-fast glance through this article at a coffee-shop, I enjoyed the substance but, of course, was left with many questions.
Reply | Report Abuse | Link to this1) Electromagnetic radiation requires that two orthogonal axes exist to the direction of travel, to contain the electrical and magnetic axes - or the E/M spiral in the condition of circularly-polarized light. How can one postulate EM radiation in flatland?
2) Although a torus is an attractive example of two-dimensional infinity, it is infinitely degenerate for each dimension - and so is the neighborhood of each point. There is no unique spacelike "address" for any particular point, or particle which occupies that point. How does one deal with that?
3) Theological explanations in science are avoided not because of religious bias, but because of irrefutability (see Karl Popper). Assuming there is a God, is there any refutable sentence in the form: "God made (_) such-and-such a way."? I suspect not.
PS: I'm not sure what to make of the terms "pulling" and "pushing" regarding force.
Reply | Report Abuse | Link to thisIf there is any sort of energy field in space, and a particle's differential motion affects its potential energy, then the force experienced is just dE/dq in generalized coordinates - stuff rolls downhill.
There would seem to be an alternative to the cylinder becoming a torus as pictured on page 45.
Reply | Report Abuse | Link to thisThe cylinder is similar to a string, except that it might be hollow or solid. This type of string could be adjusted to almost a torus so that the ends do not meet together perfectly forming a “curl”. The angle of a cylinder from its midpoint is 180 degrees; the “curl” angle could range from about [+ or -] 1 to 79 unitary degrees; in either a left or right hand manner.
Repetitions of the same “curl” will form a helicoid.
Would it be correct to say that in terms of General Relativity gravitational waves are not possible in 2D because GR has solutions for a quadrupole but not a dipole?
Reply | Report Abuse | Link to thisIn my Beautiful Universe (BU) model gravity is the outcome of two effects: 1- The potential energy density of space that acts like an index of refraction to curve light. 2- Gravitational attraction and waves are due to twisting of ether nodes. Twisting is possible in 3D but not in 2D. Read a pdf of the (BU) theory here: http://www.ne.jp/asahi/tamari/vladimir/physicsandmath.html
Sorry for the delay, as we were otherwise occupied and missed to see the mail The questions raised are essentially non-questions couched in languages to sound important. For example, “There is no unique spacelike "address" for any particular point, or particle which occupies that point” simply means there is no uniquely defined position. Torus is neither two dimensional (if you scientifically define dimension) nor infinite (like time or space). It is three dimensional and finite. Thus, there is no question of dealing with some non-question.
Reply | Report Abuse | Link to this“Electromagnetic radiation requires that two orthogonal axes exist to the direction of travel, to contain the electrical and magnetic axes - or the E/M spiral in the condition of circularly-polarized light” is essentially what we told earlier. This leads to the mechanism of perception of dimension that is related to spatial orientation. There is nothing like a “flat land”. Thus, again it is a non-question.
We never wrote about theological reasons or justifications unless anything contrary to “establishment science” is dubbed theological. Hence, again it is a non-question.
“Push” and “pull” are common language for displacement; that is the effect of energy field in space that leads to the particle's differential motion. The quantity dE/dq is a measure of this displacement. Thus, again it is a non-question.
We have recently published a paper on Physics Beyond Standard Model. In case anyone is interested, they can write to us.
Mbasudeba@gmail.com
the email id is mbasudeba@gmail.com.
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