In the effort to unify the gravitational theory of general relativity with the quantum theory of the very small theoretical physicists explore a lot of wild ideas. One of these is the idea of higher dimensions. While we may live our lives in the three-dimensional volume of space and the temporal dimension of time, that may just be a fraction of the total number of dimensions the Universe has. Some models of string theory, for example, propose an eleven dimensional universe. These extra dimensions give string theory the mathematical space necessary to combine aspects of gravity and quantum mechanics. But if we’re trapped in the subspace of four dimensions, how could we possibly detect these higher dimensions? It turns out that gravity could provide evidence of these higher dimensions (if they exist) because gravity wouldn’t be bound to our regular space. 

One of the arguments against the existence of higher dimensions comes from general relativity. As Newton proposed in his gravitational theory, the force of gravity follows an inverse square relation, where the strength of the gravitational force changes proportional to the square of your distance from an object. Newton strongly suspected this relation had to be exact, but had no way to prove it. In general relativity the inverse square relation comes from the geometry of space and time. In a universe with three spatial dimensions and one time, the gravitational force at close distances must follow the inverse square relation. If the universe had more spatial dimensions the force of gravity would be very different.

If space is noodle-shaped, gravity still might approximate an inverse-square relation. Credit: Pixelbay user rkit (public domain)

Given the well-tested evidence of inverse-square gravity, it would seem that higher dimensions are a non-starter. But theorists have pointed out that higher dimensions could agree with inverse-square gravity if they are compact. Instead of extending off for (at least) billions of light years like our regular dimensions of length, width, and depth, they might wrap around themselves over a short distance. You might imagine space like a piece of tube-shaped pasta. Along its length space would seem large and open, but circling around the tube space would be small and compact. At large scales these compact dimensions would be hardly noticeable, but on the small quantum scale they would allow for the dimensional freedom necessary for models like string theory.

While this sounds like a crazy idea, it actually makes testable predictions. If higher dimensions exist and are compact, then on our large, everyday scale gravity will seem to follow the inverse-square relation. But at smaller scales, approaching the size of the compact dimensions, gravity will look like that of a higher dimensional universe. In other words the gravitational force should deviate from the inverse square relation at small distances.

The problem is that gravity is not a strong force. It can be difficult to measure precisely at small distances and with small masses. So researchers have used a few experimental tricks to get the job done. One of these uses a torsional pendulum, similar to what you might see in an old pocket watch. Any mass near the pendulum would gravitational tug on the pendulum, but that by itself isn’t enough to see an effect. So the researchers move the masses in sync with the natural motion of the pendulum. Just as a child can get a swing to move higher and higher by swinging their legs at just the right rate, the movement of the masses can give the torsional pendulum a measurable oscillation. The rate needed to swing the pendulum depends upon the force of gravity, so any deviation from the inverse-square relation can be seen in the experiment.

As new results in Physical Review Letters shows, at small scales gravity still seems to obey the inverse-square relation. The experiment found no evidence of any deviation. Given the sensitivity of the experiment, that means the force of gravity is inverse-square at least down to the scale of 59 micrometers, which is about the width of a human hair. So either higher dimensions don’t exist, or they are very, very compact.

Even though this is a null result, it’s an amazing experiment given the challenge of measuring small-scale gravity. And it’s a great example of how some of the strangest ideas in physics can be put to an experimental test.

Paper: Wen-Hai Tan, et al. New Test of the Gravitational Inverse-Square Law at the Submillimeter Range with Dual Modulation and Compensation. Phys. Rev. Lett. 116, 131101 (2016)

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Tis the season for claims that the universe is a hologram again. Just to be clear, there’s no observational evidence that the universe is a hologram, and the latest research driving the sensational headlines doesn’t claim that there is. But there is some interesting theoretical work regarding the holographic principle that is worth discussing.

The holographic principle argues that the information contained within a region of space can be determined by the information at the surface that contains it. For example, imagine a road 10 miles long that is “contained” by a start line and a finish line. Suppose the speed limit on this road is 60 mph, and I want to determine if a car has been speeding. One way I could do this is to watch a car the whole length of the road, measuring its speed the whole time. But another way is to simply measure when a car crosses the start line and finish line. At a speed of 60 mph, a car travels a mile a minute, so if the time between start and finish is less than 10 minutes, I know the car was speeding. Mathematically, the space can be represented as a hologram of the surface that contains it. Unfortunately the term hologram invokes images of virtual reality and the idea that we’re living in the Matrix, which couldn’t be farther from the truth.

As a theoretical tool the holographic principle is useful because it is easier to do some calculations on a boundary than it is on the enclosed volume. One of the most popular uses of the principle is in string theory, through something known as the AdS/CFT correspondence, which uses the holographic principle to connect the strings of particle physics string theory with the geometry of general relativity. The AdS stands for anti-deSitter space, which is a non-flat model universe. Anti-deSitter space can’t be used as a model for the physical universe, because we know observationally that the universe is extremely flat.

It would be nice if there were a similar holographic correspondence for a flat universe model, but proving one has been difficult. Now a new paper has shown that the holographic principle can apply to flat space models, at least in some cases. The team looked at an aspect of quantum theory known as entanglement. If two objects such as electrons are entangled, they can be described in quantum theory as a single entity. Entanglement is one of the more strange aspects of quantum theory, and leads to some strange predictions about the universe, but has been experimentally validated. What the team found was that a calculation in standard quantum theory of a particular entanglement property dealing with entropy gave the same result when done using a holographic version. In other words, the standard and holographic versions are mathematically equivalent. They did these calculations in a model universe that’s flat, which demonstrates the holographic principle can work in flat space.

This is not a general proof, and it doesn’t show that the holographic principle does work for a flat universe like ours, only that it might when it comes to quantum systems. There’s a lot more work to do before anyone can say with certainty that there is a flat space version of AdS/CFT correspondence. And even then it won’t mean the universe is a hologram.

Paper: Arjun Bagchi, et al. Entanglement Entropy in Galilean Conformal Field Theories and Flat Holography, Phys. Rev. Lett. 114, 111602 (2015)

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We usually think of efforts to unify Einstein’s theory of gravity with other forces as a more modern trend. Models such as string theory and loop quantum gravity are seen as modern ideas. But in fact, as soon as Einstein presented his model there were efforts to unify it with the other known force at the time, electromagnetism.

In 1919, the same year that Eddington confirmed Einstein’s theory. Theodor Kaluza proposed a generalization of Einstein’s model that had five dimensions, rather than the four (3 space + time) of general relativity. Although the general five-dimensional model was quite complex, Kaluza found that if the fifth dimension was considered to be somewhat independent of the others (known as the cylinder condition), then something interesting happened. The general equations could be broken into three parts: a 4-dimensional model that was Einstein’s equations for gravity, a separate set of equations that matched Maxwell’s equations for electromagnetism, and a scalar field known as the radion. In other words, the 5-dimensional theory seemed to unify gravity and electromagnetism into a single model.

In 1926 Oskar Klein applied quantum theory (as it was understood at the time) to Kaluza’s model. He proposed that the extra spatial dimension was “compact,” which would explain the cylinder condition. Klein then found that the scale of this compact dimension was connected to the quantization of charge. Soon this model came to be known as the Kaluza-Klein model.

At the time, the strong and weak nuclear forces were unknown, so the Kaluza-Klein model held promise as a single unified theory to describe all of known physics. But it didn’t turn out to be the case. There are several reasons for that. One is that while the simplifed “cylinder” form of the model clearly gave rise to general relativity and electromagnetism, the general model was deeply complex and difficult to understand. Another is that as quantum theory became more robust, the Kaluza-Klein model was found difficult to quantize. It wasn’t until the 1940s that the classical version was finally understood, much less a fully quantum model. Finally, the discovery of the strong and weak nuclear forces meant that the Kaluza-Klein model was a partial theory at best. As the standard model of particle physics was developed (unifying electromagnetism with the strong and weak forces), the popularity of the Kaluza-Klein model waned.

In many ways, the Kaluza-Klein model was the string theory of its day. It had some early successes, followed by a deep complexity that made progress difficult and slow.  In fact aspects of the Kaluza-Klein model such as higher dimensions and compact manifolds also appear in string theory and other modern models.

Although not as popular as it once was, there is still some interest in the Kaluza-Klein model. The radion scalar field has some similarities to the Higgs field, and the radion could affect the way the Higgs interacts with photons. So some researchers hope that data from the Large Hadron Collider might show evidence of such an interaction.

But even if such evidence is never found, the Kaluza-Klein model is an interesting bit of theoretical physics history. It showed that gravity and electromagnetism do share a deep mathematical connection, and it introduced theoretical ideas that are central to modern models.

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Yesterday I wrote about the difficulty in understanding black holes. The heart of this difficulty lies in trying to understand how two radically different physical models (general relativity and quantum mechanics) might integrate into a single, unified model. Two major approaches to this problem are loop quantum gravity and string theory.

Loop quantum gravity (LQG) takes the approach of trying to bring space and time into a quantum framework. It gets its name from the fact that solutions to quantized gravity equations are known as loops (or graphs). One consequence of this model is that spacetime has a granularity to it. The granularity only appears at the Planck length scale. A Planck length is extraordinarily small.  If you compared the size of a period in this post to the size of the observable universe, it is about the same as the size of a Planck length to the size of the period. On any normal scale this granularity would average out and look like a continuum, just as general relativity predicts. At high energies and small scales, the quantum aspects come into play. The problems with black hole singularities could be solved by loop quantum gravity.

String theory (or its generalization M-theory) takes a different approach. In string theory elementary particles such as quarks and electrons are not point particles, but rather loops (strings) of energy where the modes of oscillation can determine the properties of the particles. String theory has several advantages, such as an inherent connection between quantum theory and gravity. Some models require more dimensions than the 3 of space and 1 of time we see around us, but more complex versions can be formulated within the 4-dimensional framework we observe.

Both of these approaches hold promise in solving the quantum-GR problem, but both are also based upon a concept known as supersymmetry.  In particle physics we have found that elementary particles can be divided into two main groups: fermions such as electrons and quarks, and bosons such as photons and gluons. This distinction is based upon an inherent property of particles known as spin, but basically fermions constitute matter, and bosons are the quanta of the fields through which matter interacts.  Supersymmetry proposes that each elementary particle as a supersymmetric pair of the opposite type.  Thus, for the fermionic electron, there is a bosonic selectron. For the bosonic photon, there is a fermionic photino, etc.

Unification of forces under supersymmetry. Credit: CERN

This grand symmetry between particles allows both LQG and string theory to unify gravity and quantum mechanics. Supersymmetry also solves a problem in the standard model of particle physics. In the standard model, three fundamental forces (electromagnetic, strong and weak) don’t quite unify at a common temperature (known hierarchy problem), but with supersymmetry they do. Thus supersymmetry not only provides a connection between quantum theory and gravity, it also provides a way to unify fundamental forces. Some supersymmetric particles could even be the solution for dark matter.

Of course supersymmetry also predicts that there should be twice as many elementary particles than we actually observe.  So why don’t we observe them? The answer lies in the fact that supersymmetric particles are more massive than regular particles, so at normal energies we simply don’t see them. But it turns out that in order to unify fundamental forces, the lightest of these supersymmetry particles should be observed in high energy collisions.

And therein lies the problem. The Large Hadron Collider has experimentally excluded the existence of supersymmetric particles at the expected energy levels. It is possible that supersymmetry particles exist at higher energies, but then supersymmetry can’t solve the hierarchy problem, which was the main reason for its introduction.  It is also possible that supersymmetry is simply wrong. If supersymmetry is wrong, then string theory (and M-theory) are also wrong. So are the most straight-forward versions of loop quantum gravity.

So where do we go from here? Proponents of string theory have taken the view that supersymmetric particles are at energies higher than we expected. They may, in fact be at such high energies that any particle accelerators that could conceivably be built will not detect them. Of course that makes string theory effectively untestable. There are versions of LQG that don’t depend upon supersymmetry, but they also make predictions that are untestable. So it may be that neither approach will lead to clear scientific tests of their validity.

This is, of course, the big question regarding scientific discovery. Will there come a day when experimentally and observationally we can go no further? As humans we like to think that there is symmetry in the universe. That somehow our understanding of the cosmos can be unified into a single complete theory. But there’s nothing in the universe that requires such unification. Striving toward that goal has given us a deep understanding of physics, but we may face theoretical and experimental limits that prevent us from reaching the ultimate goal.

Even if that is the case, it won’t stop us from trying. Science is about pushing the limits of our understanding, and even in the face of seemingly insurmountable challenges, we can always keep pushing.

The post A Lack of Balance appeared first on One Universe at a Time.

From measurements of distant supernovae, we now know our universe is not only expanding, but that it is expanding at an ever increasing rate. This cosmic acceleration is driven by what we call dark energy. While we can see the effects of dark energy, and we know it makes up about 68% of our universe, we don’t really know what dark energy actually is. That means while the experimentalists scurry to get more data, the theorists work frantically to explain what’s going on.

In a recent paper in the journal Astronomy and Astrophysics, an interesting theory was proposed to explain dark energy as a quantum effect. The idea is based on an experiment known as the Casimir effect. In quantum mechanics there are energy fluctuations at very small scales. Normally we don’t notice these fluctuations because they average out at larger scales. But you can observe their effect if you constrain the fluctuations. Experimentally this is done by placing two conducting surfaces very close together (on the order of microns). Between these surfaces the fluctuations are limited by the space between the surfaces, but elsewhere the fluctuations aren’t limited. As a result, the conducting surfaces are pulled toward each other, even though there is “nothing” between them.

What the Casimir effect demonstrates is that quantum fluctuations in a vacuum can produce a force. So what if dark energy was due to vacuum energy fluctuations? For that to be the case, there would have to be a constrained geometry. But such a constrained geometry is exactly what is proposed in (wait for it) string theory! String theory (or M-theory as it is now known) proposes that there are actually ten spatial dimensions instead of just the three that we know of. These higher dimensions differ from our usual ones in that they are compact, meaning they are folded around themselves. If you think of a straw as a two-dimensional sheet with one “regular” dimension (the length of the straw) and one “compact” dimension (the circumference of the straw), then you have the basic idea.

Now if these compact higher dimensions exist, then quantum fluctuations would be constrained in those dimensions, and that might produce a cosmic Casimir force that looks like dark energy. The catch is that our observations of gravity place a limit on the size of these compact dimensions. This is because gravity is an inverse-square force, meaning that the force of attraction between masses varies by one over their distance squared. If there are higher dimensions, then the inverse-square relation for gravity would break down at the size of those dimensions. Gravity experiments have shown no such effect, so that means that any higher dimensions (if they exist) can be no larger than 85 microns, which is about the width of a human hair.

This is where things get interesting, because if you calculate the effect of these quantum fluctuations in such compact dimensions you find that having 8 compact dimensions (as string theory proposes) doesn’t work. It only works if you allow for just one compact dimension. But if you constrain the universe to just one extra and compact dimension, and you also constrain the fluctuations to exist within the limits of the observable universe, then this model makes two predictions. The first is that dark energy would be constant throughout the universe. It would, in fact, look like a cosmological constant. The second is that this extra compact dimension would have a size of about 35 microns, which means that around 35 microns we should see gravity deviate from the inverse square relation.

Of course all of this could be wrong, but it is an interesting idea with predictions that should be testable in the near future. Sometimes it takes a bit of theory as well as experiments to solve a cosmic mystery.

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A few years ago a research team measured the force of gravity over very small distances. Their result places very stringent constraints on the space-time structure of our universe. Either the universe consists of only the four dimensions we see around us, or else all dimensions beyond those four must be very small, no more than about 10 microns, roughly one-tenth the width of a human hair. What, you might ask, does proving Newton right (yet again!) have to do with hyperdimensional physics? Quite a lot, it turns out.

We look around and see the usual dimensions of length, width and depth as we move forward through the dimension of time at the rate of one second per second, and it all makes sense to us. However some models of string theory (or more properly its offspring, M-theory) propose that although we may seem to live in these four dimensions, we actually live in a universe of eleven dimensions. According to string theory the universe only appears 4-dimensional because, like Abbott’s flatlanders, we are trapped on a “plane” of four dimensions.

The reason we are trapped is that all the strings we are made of — the electron neutron and proton strings — are open strings. The ends of these strings can’t flop around freely, but instead must be fixed to a membrane surface or “brane”, and are thus only able to move freely along this brane, specifically our usual four dimensions. Closed strings on the other hand can flow freely through higher-dimensional space. In string theory gravity is made of such strings, which would explain why gravity is so much weaker than other forces such as electromagnetism. The basic idea is that all the other forces are trapped on the brane, and are thus very concentrated, whereas gravity is spread throughout all eleven dimensions, and so seems much weaker in our regular space-time.

Still, other than mathematical elegance, why invoke higher dimensions in the first place? If we can’t see them, and physical objects can’t travel through them, then aren’t they superfluous? Not quite. It turns out that even though we can’t see higher dimensions directly, might be able to detect them indirectly.

To see how this might work, consider Newton’s theory of gravity. In three spatial dimensions, Newtonian gravity near a mass is inversely proportional to the square of the distance from the mass. In two spatial dimensions, gravity is inversely dependent on the distance. In general, the number of spatial dimensions determines the power (1, 2, 3) at which gravity is inversely dependent.

It would seem we have a simple rule of observation. By determining the value of of that power for gravity, we can determine the dimension of space. Since we observe that power is 2 (inverse-squared), we must live in a universe of 3 spatial dimensions. However, this only works if space is simple, flat and infinite. If some of the dimensions are compact — that is they loop back on themselves rather than spreading out forever — then all bets are off.

Consider our flatland physicists, who live on the surface of a 2-dimensional plane. They look around and see that gravity behaves as it should for two dimensions, and thus they observe the power of gravity is 1 (inverse linear). If their plane existed in three dimensions, their gravity would be like ours.

But suppose that in their universe, the third dimension isn’t flat and open as it is in our universe, but instead loops back on itself. If they could travel in this third dimension, they would find that after a short journey they would find themselves back where they started. Their universe would be 3-dimensional, just very thin. Put another way, if they assumed the third dimension was flat, they would see images of their universe over and over again.

In such a universe, the force of gravity would be inverse-square, but they would only notice it at small distances. Since the third dimension is compact, all the images of a mass would have the same gravitational attraction as real masses. This is complicated in general, but basically if the size of the compact dimension is really large compared with their distance from the mass, then the result is standard Newtonian gravity in three dimensions. On the other hand, compact dimension is very, very small, then it is almost 2-dimensional gravity.

Our 2-dimensional physicists would see 2-dimensional gravity in their everyday world, but they might detect the third dimension if they take a closer look at gravity on either very large or very small scales. We can apply the same idea to our universe, and what we find is that if all the “extra” dimensions are compact we would never notice their presence unless we look very closely at things small scale, such as the strength of gravity.

So far experiments point to the fact that we live in a four-dimensional world. Either that or the “higher dimensions” are smaller than some string models presumed.

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When we look around the universe we see the usual dimensions of length, width and depth as we move forward through the dimension of time at the rate of one second per second, and it all makes sense to us. However string theory (or more properly its offspring, M-theory) says that although we may seem to live in these four dimensions, we actually live in a universe of eleven dimensions. According to string theory the universe only appears 4-dimensional because, like Edwin Abbott’s flatlanders, we are trapped on a “plane” of four dimensions. The reason we are trapped is that all the strings we are made of — the electron, neutron, and proton strings — are open strings. The ends of these strings can’t flop around freely, but instead must be fixed to a membrane surface or “brane”, and are thus only able to move freely along this brane, specifically our usual four dimensions. Closed strings on the other hand can flow freely through higher-dimensional space. In string theory gravity is made of such strings, which would explain why gravity is so much weaker than other forces such as electromagnetism. The basic idea is that all the other forces are trapped on the brane, and are thus very concentrated, whereas gravity is spread throughout all eleven dimensions, and so seems much weaker in our regular space-time.

Still, other than mathematical elegance, why invoke higher dimensions in the first place? If we can’t see them, and physical objects can’t travel through them, then aren’t they superfluous? Not quite. It turns out that even though we can’t see higher dimensions directly, might be able to detect them indirectly. To see how this might work, consider Newton’s theory of gravity in two dimensions.

For flatland physicists, who live on the surface of a 2-dimensional plane. They look around and see that gravity behaves as it should for two dimensions. In two dimensions gravity is proportional to the inverse of distance, not the inverse square of the distance. If their plane existed in three dimensions, their gravity would be an inverse square force just like ours. But suppose that in their universe, the third dimension isn’t flat and open as it is in our universe, but instead loops back on itself. If they could travel in this third dimension, they would find that after a short journey they would find themselves back where they started. Their universe would be 3-dimensional, just very thin. Put another way, if they assumed the third dimension was flat, they would see images of their universe over and over again. In the first figure, I’ve drawn a simple diagram of a closed dimension. In the second figure I’ve drawn how the mass and all of its images would appear to our flatland physicists.

In such a universe, the force of gravity would be the usual inverse square form with one catch. All the images of a mass would have the same gravitational attraction as real masses. Since the third dimension is compact, to find the force of gravity from a mass we would have to add up the effect of an infinite number of masses spread evenly along the third dimension. The result is a bit complicated in general, but if the third dimension is really thin, then at the scale of our physicists the mass would look like a continuous line of mass. It turns out that the gravitational field from a long line of mass is proportional to the inverse of your distance from the line, just as if space were two dimensional. On the other hand, if our flatland physicists measured gravity on a small scale (on the order of the size of the extra dimension) they would see the effect of the discrete mass images. In other words, they would see that gravity it is almost 2-dimensional, but has a small extra term due to the small compact dimension. Our 2-dimensional physicists would see 2-dimensional gravity in their everyday world, but they might detect the third dimension if they take a closer look at gravity on either very large or very small scales.

We can apply the same idea to our universe, and what we find is that if all the “extra” dimensions are compact we would never notice their presence unless we look very closely at things small scale, such as the strength of gravity. So far, experiments to detect deviations from Newtonian gravity at small scales haven’t found any higher-dimensional effect. What they have shown is that either the universe consists of only the four dimensions we see around us, or else all dimensions beyond those four must be very small, no more than about 10 microns, roughly one-tenth the width of a human hair.

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