There is a magic rock in St. Cloud, France. It’s made not of stone, but of a metallic alloy that’s 90% platinum and 10% iridium, and it’s magic not through some supernatural force, but because scientists have declared it to have a mass of exactly 1 kilogram. Now many scientists would like to get rid of it. 

Our civilization is built upon a system of measurement standards. If two people want to trade, they have to agree on what a pound is. If you pay a contractor to build a 100 foot tall building, you have to agree on the length of a foot. Throughout history humans have had standards of measurement, often dictated by governmental decree. But since the early 1800s there has been a quest to create a truly universal standard of measurements. This became the metric system, which was further standardized to the Système international d’unités (SI) in 1960. The SI standard has become the basis for measurement across the globe. They define the physical units we use to measure things. Even in the United States, quantities like the foot and pound are defined in terms of SI units.

The most common SI units are those of the meter (length), second (time) and kilogram (mass). In the 1800s these were based upon the physical characteristics of Earth. A meter was defined by declaring the circumference of Earth to be 40,000 kilometers. A second was defined by declaring the length of an average day to be 24 hours long. A kilogram was defined as the mass of a liter (1000 cubic centimeters) of water. While these definitions initially worked well, as our measurements became more precise things became problematic. As measurement of the Earth’s circumference improved, the length of a meter would necessarily change. Since the volume of a liter is defined in terms of length, the mass of a kilogram likewise shifted. Precise measurements of Earth’s rotation showed that the length of a day varied, so even the second wasn’t entirely fixed.

There are two ways to define a set of units that don’t vary. One is by defining a particular object to be an exact standard, and the other is to define units in terms of universal physical constants. The meter and second are now defined using the later method. For example, in Einstein’s theory of relativity, the speed of light in a vacuum is always the same. No matter where you are in the universe, or how you are moving through space, the speed of light never changes. It is an absolute physical constant. This has been verified through numerous experiments, and in 1983 it was given an exact value. By definition, the speed of light is 299,792,458 meters per second. By defining this value, we also defined the length of a meter. Since the speed of light is a constant, if you know how long a second is, you know the length of a meter.

Emission spectrum of a high pressure sodium lamp. Credit: Chris Heilman

The length of a second is also defined in terms of light. By the 1960s we had developed atomic clocks based upon cesium 133. Like all elements, Cesium 133 emits light at specific frequencies. Light is emitted from an atom when an electron moves from a higher energy quantum state to a lower one, and under the right conditions they are always the same. One particular emission from cesium 133 is known as the hyperfine ground state, and it is used to regulate an atomic clock the way the swing of a pendulum regulates a grandfather clock. In 1967 the frequency of light emitted by this hyperfine transition was defined to be 9,192,631,770 Hz. By measuring the frequency, you know the length of a second.

Since the meter and second are based upon physical constants, they don’t change. They can also be measured anywhere in the universe. If an alien civilization wanted to know what units we use, we could send them a radio message with the definition for meters and seconds, and the aliens could recreate those units. But since 1889, the kilogram has been defined by a specific chunk of metal known as the International Prototype of the Kilogram (IPK). If the aliens wanted to know the mass of a kilogram, they would have to make a trip to France.

The relative mass change of kilogram copies over time. Credit: Greg L at English Wikipedia

Besides the necessary road trip for aliens, there is a big problem with using a magic rock as the standard kilogram. Since the mass of the IPK is exact by definition, it cannot change under any circumstances. If someone were to shave off a bit of metal, it would still be one kilogram by definition. Shaving the IPK down a bit wouldn’t make the kilogram lighter, it would make everything else in the world a bit heavier. Of course, that doesn’t make any sense. Shaving down a bit of metal in France doesn’t make the Statue of Liberty weigh more. The problem is with our definition of mass. And in a sense this kind of thing actually happens. In addition to the official prototype kilogram, there are official copies all over the world. By comparing the copies to the IPK, we can determine the stability of its mass. This has only been done a few times over the years, but on average the mass of the copies has increased slightly compared to the IPK. Either the official kilogram is getting lighter, or the copies are getting heavier.

The standard kilogram hasn’t been replaced by a physical constant because we haven’t been able to measure them with enough precision. The obvious physical constant for mass would be the universal constant of gravity G. But gravity is a weak force, and measuring G is difficult. So far we’ve only measured it to about one part in 10,000, which isn’t nearly accurate enough to define mass. But there is another constant we could use, and it’s known as the Planck constant.

The Planck constant lies at the heart of quantum theory. It was first introduced by Max Planck in his study of light. When objects are heated, they emit light, and the color of that light depends upon the temperature of the object. This is known as blackbody radiation. According to classical theory, most of the light emitted should have very short wavelengths, but experimentally this wasn’t the case. Planck demonstrated that light must be quantized proportional to a small constant h, which we now call Planck’s constant. As our understanding of quantum theory grew, the Planck constant played a role not just in quantization, but quantum ideas of energy and momentum. In SI units, h has units of kg∙m²/s. If the Planck constant is defined to have an exact value, then the kilogram would be defined in terms of Planck’s constant as well as the meter and second.

In principle it’s a good idea, but it can only be done if we can measure it accurately. In 2014 the Conférence Générale des Poids et Mesures  (CGPM) decided that before such a definition could occur, three independent measurements of the Planck constant would need to be made, each with an accuracy of 50 parts per billion, and one accurate to 20 parts per billion. By June of this year three experiments have been done with uncertainties smaller than 20 parts per billion. The CGPM meets again in 2018, where it is expected they will officially define the Planck constant to be exactly 6.626069934 x 10⁻³⁴ kg∙m²/s. When that happens the prototype kilogram will no longer be a magic rock, but simply a part of scientific history.

And the aliens won’t have to make that road trip after all.

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Our fate is written in the stars, so the old stories go. It makes for thrilling drama, but it isn’t the way the Universe works. But there’s an interesting effect of quantum mechanics that might leave an opening for a starry fate, so a team of researchers decided to test the idea. 

The idea stems from a subtle effect of quantum physics demonstrated by the Einstein-Podolsky-Rosen (EPR) experiment. One of the basic properties of quantum objects is that their behavior isn’t predetermined. The statistical behavior of a quantum system is governed by the laws of quantum theory, but the specific outcome of a particular measurement is indefinite until it’s actually performed. This behavior manifests itself in things such as particle-wave duality, where photons and electrons can sometimes behave like particles and sometimes like waves.

One of the more subtle effects related to this property is known as entanglement, when two quantum objects have some kind of connection that allows you to gain information about object A by only interacting with object B. As a basic example, suppose I took a pair of shoes and sent one shoe to my brother in Cleveland, and the other to my sister in Albuquerque. Knowing what a prankster I am, when my sister opens the package and finds a left shoe, she immediately knows her brother was sent the right one. The fact that shoes come in pairs means they are an “entangled” system.

The difference between shoes and quantum entanglement is that the shoes already had a destined outcome. When I mailed the shoes days earlier, the die was already cast. Even if I didn’t know which shoe I sent to my brother and sister, I definitely sent one or the other, and there was always a particular shoe in each box. My sister couldn’t have opened the box to find a slipper. But with quantum entanglement, slippers are possible. In the quantum world, it would be like mailing the boxes where all I know is that they form a pair. It could be shoes, gloves or socks, and neither I nor my siblings would know what the boxes contain until one of them opens a box. But the moment my brother opens the box and finds a right-handed glove, he immediately knows our dear sister will be receiving its left-handed mate.

If all of this sounds really strange, you’re not alone. Even quantum physicists find it strange, and they have confirmed the effect countless times. It’s such a strange thing that some have argued that quantum objects must have some kind of secret information that lets them know what to do. We may not know what the outcome might be, but the two quantum objects do.

The key to doing the EPR experiment is to ensure that entangled objects are measured in a random way. That way the system is truly indefinite until one of the objects is measured. This is usually done by letting a random number generator decide the measurement after the experiment has begun.  But if you really want to be picky, you could argue that while the experiment is being set up, there is plenty of time for the system to know what is going on. Technically, the experiment, random generator, and scientist are all “entangled” as a single system, so the outcome may be pre-biased. What looks like a random choice made after the experiment started may not actually be random. This is known as the setting independence problem.

A light cone diagram showing the range of influence possible for the cosmic EPR experiment. Credit: Johannes Handsteiner, et al.

To address this issue, the team used distant stars to roll the dice for their experiment. Rather than using a local random generator, the team took real-time observations of two stars. One star is about 600 light years away, and the other is about 1,900 light years away. They took observations of each star at particular wavelengths to ensure the light wasn’t influenced by local effects such as Earth’s atmosphere, and use the observations as their random number generator. It would take hundreds of years for the quantum objects of experiment to entangle with these distant stars, so this solves the independence problem. What they found was that Bell’s inequality was violated in their experiment, just as it is in similar experiments, meaning that the system can’t have any hidden information to bias the outcome. So once again the EPR experiment shows there aren’t any hidden variables within the system.

Now it is true that this new experiment doesn’t fully solve the independence problem. Perhaps the experiment, scientists and the entire region of stars within hundreds of light years conspired to ensure the system had inside information. That’s theoretically possible, but it would have had to been given to the experiment at least 600 years ago. As the authors note, the experiment would have been given insider information about the time the Gutenberg Bible was being printed.

So we can safely assume that there aren’t any hidden variables within the system, and quantum theory acts just as we’d expect.

Paper: Johannes Handsteiner, et al. Cosmic Bell Test: Measurement Settings from Milky Way Stars.  arXiv:1611.06985 [quant-ph] (2017)

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Hydrogen is the most abundant element in the Universe. It consists of a single proton paired with an electron. Since the proton and electron are bound together, the electron must reside in particular energy states. When the electron transitions from a higher energy state to a lower one, it releases light with a specific color. Each energy transition for the electron corresponds to a particular color, and together they form the emission spectrum of hydrogen. All atoms have nuclei of protons and neutrons bound to electrons, and the resulting emission spectra allow us to determine what makes up distant objects. It’s one of the most powerful tools in astronomy.

One of the ways we distinguish particles is by their charge. Protons are positively charged, while electrons are negatively charged. In 1932 Carl David Anderson discovered a particle that had the same mass as an electron, but with a positive charge. Later it was discovered that protons also had a twin with the same mass, but negatively charged. Such charge-reversed particles came to be known as antimatter. We found that matter and antimatter could annihilate each other to produce intense gamma ray light, and intense energy could create pairs of particles consisting of one matter and one antimatter particle.

In principle, from basic antimatter particles we could create anti-atoms and anti-molecules. If an anti-proton is bound to a positron (anti-electron) it would create anti-hydrogen. According to our understanding of physics, anti-atoms should be identical to their matter twins except for the reversal of their charges. The positrons of anti-hydrogen should be quantized into the same specific energy states as electrons in hydrogen, and when they transition between energy states they should create the same emission spectrum as hydrogen. At least that’s the theory. Proving it is a much harder challenge.

Although we’ve been creating antimatter in the lab since the 1930s, it wasn’t until 1995 that we were finally able to create anti-hydrogen. That’s because the antimatter we create tends to form with lots of kinetic energy, and getting a positron and anti-proton to slow down enough to bind together is difficult. Once they do form anti-hydrogen we face a second challenge, specifically that anti-hydrogen, like hydrogen, is electrically neutral. When particles are charged we can easily push them around with electric and magnetic fields. It’s harder to to contain neutral antimatter.

But recently we’ve been able to create and hold hundreds of anti-hydrogen atoms for more than 15 minutes. That might not seem like much, but it means we can finally start doing some experiments on anti-hydrogen. In a recent experiment, anti-hydrogen atoms were bombarded with laser light. The positrons of those atoms absorbed some of the light, putting them in excited states. After a bit the positrons transitioned back to a lower energy state and released light of their own. It’s the first case of light being emitted by anti-atoms in the lab. The team that achieved this also measured one emission line of anti-hydrogen, and found that it was the same as that of regular hydrogen.

Although this is only a basic first test of light from anti-hydrogen, it’s a pretty significant achievement. As we’re able to create and store more anti-hydrogen for longer periods of time, we’ll finally be able to test whether anti-hydrogen has subtle differences in its spectrum that points towards new physics through the looking glass.

Paper: M. Ahmadi, et al. Observation of the 1S–2S transition in trapped antihydrogen. Nature (2016) doi:10.1038/nature21040

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There has been a lot of digital ink spilled over the recent paper on the reactionless thrust device known as the EMDrive. While it’s clear that a working EM Drive would violate well established scientific theories, what isn’t clear is how such a violation might be resolved. Some have argued that the thrust could be an effect of Unruh radiation, but the authors of the new paper argue instead for a variation on quantum theory known as the pilot wave model. 

One of the central features of quantum theory is its counter-intuitive behavior often called particle-wave duality. Depending on the situation, quantum objects can have characteristics of a wave or characteristics of a particle. This is due to the inherent limitations on what we can know about quanta. In the usual Copenhagen interpretation of quantum theory, an object is defined by its wavefunction. The wavefunction describes the probability of finding a particle in a particular location. The object is in an indefinite, probabilistic state described by the wavefunction until it is observed. When it is observed, the wavefunction collapses, and the object becomes a definite particle with a definite location.

While the Copenhagen interpretation is not the best way to visualize quantum objects it captures the basic idea that quanta are local, but can be in an indefinite state. This differs from the classical objects (such as Newtonian theory) where things are both local and definite. We can know, for example, where a baseball is and what it is doing at any given time.

The pilot wave model handles quantum indeterminacy a different way. Rather than a single wavefunction, quanta consist of a particle that is guided by a corresponding wave (the pilot wave). Since the position of the particle is determined by the pilot wave, it can exhibit the wavelike behavior we see experimentally. In pilot wave theory, objects are definite, but nonlocal. Since the pilot wave model gives the same predictions as the Copenhagen approach, you might think it’s just a matter of personal preference. Either maintain locality at the cost of definiteness, or keep things definite by allowing nonlocality. But there’s a catch.

Although the two approaches seem the same, they have very different assumptions about the nature of reality. Traditional quantum mechanics argues that the limits of quantum theory are physical limits. That is, quantum theory tells us everything that can be known about a quantum system. Pilot wave theory argues that quantum theory doesn’t tell us everything. Thus, there are “hidden variables” within the system that quantum experiments can’t reveal. In the early days of quantum theory this was a matter of some debate, however both theoretical arguments and experiments such as the EPR experiment seemed to show that hidden variables couldn’t exist. So, except for a few proponents like David Bohm, the pilot wave model faded from popularity. But in recent years it’s been demonstrated that the arguments against hidden variables aren’t as strong as we once thought. This, combined with research showing that small droplets of silicone oil can exhibit pilot wave behavior, has brought pilot waves back into play.

How does this connect to the latest EM Drive research? In a desperate attempt to demonstrate that the EM Drive doesn’t violate physics after all, the authors spend a considerable amount of time arguing that the effect could be explained by pilot waves. Basically they argue that not only is pilot wave theory valid for quantum theory, but that pilot waves are the result of background quantum fluctuations known as zero point energy. Through pilot waves the drive can tap into the vacuum energy of the Universe, thus saving physics! To my mind it’s a rather convoluted at weak argument. The pilot wave model of quantum theory is interesting and worth exploring, but using it as a way to get around basic physics is weak tea. Trying to cobble a theoretical way in which it could work has no value without the experimental data to back it up.

At the very core of the EM Drive debate is whether it works or not, so the researchers would be best served by demonstrating clearly that the effect is real. While they have made some interesting first steps, they still have a long way to go.

Paper: Harris, D.M., et al. Visualization of hydrodynamic pilot-wave phenomena, J. Vis. (2016) DOI 10.1007/s12650-016-0383-5

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The reactionless thruster known as the EM Drive has stirred heated debate over the past few years. If successful it could provide a new and powerful method to take our spacecraft to the stars, but it has faced harsh criticism because the drive seems to violate the most fundamental laws of physics. One of the biggest criticisms has been that the work wasn’t submitted for peer review, and until that happens it shouldn’t be taken seriously. Well, this week that milestone was reached with a peer-reviewed paper. The EM Drive has officially passed peer review. 

It’s important to note that passing peer review means that experts have found the methodology of the experiments reasonable. It doesn’t guarantee that the results are valid, as we’ve seen with other peer-reviewed research such as BICEP2. But this milestone shouldn’t be downplayed either. With this new paper we now have a clear overview of the experimental setup and its results. This is a big step toward determining whether the effect is real or an odd set of secondary effects. That said, what does the research actually say?

The basic idea of the EMDrive is an asymmetrical cavity where microwaves are bounced around inside. Since the microwaves are trapped inside the cavity, there is no propellent or emitted electromagnetic radiation to push the device in a particular direction, standard physics says there should be no thrust on the device. And yet, for reasons even the researchers can’t explain, the EM Drive does appear to experience thrust when activated. The main criticism has focused on the fact that this device heats up when operated, and this could warm the surrounding air, producing a small thrust. In this new work the device was tested in a near vacuum, eliminating a major criticism.

The relation of thrust to power for the EM Drive. Credit: Smith, et al.

What the researchers found was that the device appears to produce a thrust of 1.2 ± 0.1 millinewtons per kilowatt of power in a vacuum, which is similar to the thrust seen in air. By comparison, ion drives can provide a much larger 60 millinewtons per kilowatt. But ion drives require fuel, which adds mass and limits range. A functioning EM drive would only require electric power, which could be generated by solar panels. An optimized engine would also likely be even more efficient, which could bring it into the thrust range of an ion drive.

While all of this is interesting and exciting, there are still reasons to be skeptical. As the authors point out, even this latest vacuum test doesn’t eliminate all the sources of error. Things such as thermal expansion of the device could account for the results, for example. Now that the paper is officially out, other possible error sources are likely to be raised. There’s also the fact that there’s no clear indication of how such a drive can work. While the lack of theoretical explanation isn’t a deal breaker (if it works, it works), it remains a big puzzle to be solved.  The fact remains that experiments that seem to violate fundamental physics are almost always wrong in the end.

I’ve been pretty critical of this experiment from the get go, and I remain highly skeptical. However, even as a skeptic I have to admit the work is valid research. This is how science is done if you want to get it right. Do experiments, submit them to peer review, get feedback, and reevaluate. For their next trick the researchers would like to try the experiment in space. I admit that’s an experiment I’d like to see.

Paper: Harold White, et al. Measurement of Impulsive Thrust from a Closed Radio-Frequency Cavity in Vacuum. Journal of Propulsion and Power. DOI: 10.2514/1.B36120 (2016)

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SpaceX has announced it’s Interplanetary Transport System (ITS), with the goal of sending humans to Mars. While there remains many questions about how such a mission will be achieved, one thing that’s very clear is that the ITS will be the biggest rocket ever constructed. It has to be. Basic physics requires it. 

The ITS is designed to have more than 13 million Newtons of thrust at sea level, compared to the 3.5 million Newtons of the Saturn V rockets used to send Americans to the Moon. All this while having only about 10% heavier. Such a big increase in thrust vs weight is necessary, because it determines not only how much mass you can lift into Earth orbit, but whether you can get that mass all the way to Mars.

Delta-V needed to reach Mars. Credit: Wikipedia user Wolfkeeper

It all comes down to delta-V, or how much you can change the velocity of your rocket. When it comes to reaching Earth orbit, bigger is better. The SpaceX ITS should be capable of lifting up to 550 tonnes of payload into low Earth orbit, compared to the 140 tonnes of the Saturn V. This is necessary because a trip to Mars isn’t a few-day trip to the Moon. It will require a larger crew and significantly more food and resources.

Once in Earth orbit, getting to Mars will require even more rocket power to overcome what is known as delta-V. This is the amount of speed a spacecraft needs to gain or lose to reach your destination. It takes much more delta-v to reach the surface of Mars than it does the surface of the Moon. To reach Mars you not only have to overcome Earth’s gravity, you have to overcome the Sun’s pull as you travel toward Mars. You also have to account for the fact that the orbital speed of Mars is slower than the orbital speed of Earth. Finally you have to overcome the gravity of Mars to land softly on its surface. All of this adds to the total amount of needed delta-V. To meet this need the SpaceX plans to refuel the ITS in Earth orbit with a second launch.

There are ways to minimize your delta-V requirements for an interplanetary mission. One way is to make a close flyby of a different planet. Basically, if you approach a planet in the direction of its orbit (coming up from behind, if you will), then the gravity between the planet and your spacecraft will cause the spacecraft to speed up at the cost of slowing down the planet by a tiny, tiny amount. Making a flyby in the opposite direction can cause your spacecraft to slow down. This costs you nothing in terms of fuel, but takes time because you need to orbit the Sun in just the right way. It’s a common trick used for robotic spacecraft, where we use a flyby of Earth to reach Mars or Jupiter, or a flyby of Jupiter to reach the outer solar system.

A Hohmann orbit between Earth and Mars. Image by the author.

Flybys are cheap and easy for space probes, but they can add years to the time it takes to reach your destination. That’s a big problem for a crewed mission. So the alternative is to look at optimized orbital trajectories. For example, about every two years the positions of Earth and Mars are ideally suited so that a trip needs much less delta-V. This was actually discovered in 1925 by Walter Hohmann, who proposed a trajectory now known as the Hohmann transfer orbit. You could, for example, build a large spacecraft in such an orbit and use it as a shuttle between Earth and Mars. Such an idea was used in the book and movie The Martian.

There are other useful tricks, such as using a planets atmosphere to “aerobrake” a spacecraft, significantly reducing its delta-v once it reaches the planet. Since both Earth and Mars have atmospheres this can be used for landing spacecraft. You can also modify the flyby method by thrusting your spacecraft just as it makes its closest approach, in what is known as an Oberth maneuver (another trick used in The Martian). But these will only take you so far. To reach the surface of Mars in a reasonable time, any rocket will require more delta-v than we’ve ever had, which is why the ITS has to be so big.

The one up-side of all this is that once SpaceX, Blue Origin, or NASA builds a rocket with enough power to send humans to Mars, lots of other destinations open up as well. The delta-V requirements to reach the asteroids, Jupiter or Saturn aren’t significantly different. If we can land on Mars, we can reach the moons of Jupiter, or even start mining asteroids.

Mars is not only an awesome destination, it is also a gateway to the solar system.

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The 2016 Nobel prize in physics has been awarded, and it wasn’t for gravitational waves. This was a huge surprise, since the direct detection of gravitational waves is one of the all-time biggest breakthroughs in astronomy. It’s not only confirmed a prediction of general relativity, and verified the existence of black holes, it’s also opened up an entirely new field of observational astronomy. Gravitational waves was considered such a shoe in for the Nobel that it’s lack of an award has sent science writers scrambling. So what did win? Topological phase transitions. The official notice awarded David J. Thouless, F. Duncan M. Haldane, and J. Michael Kosterlitz “for theoretical discoveries of topological phase transitions and topological phases of matter.”

Topology is an area of mathematics that looks at the geometry of different things, and how they are related. Everything from the curvature of space and time to the social networks of Facebook are related to topology. In the case of this year’s prize, it involved the application of topology to things like superconductivity and superfluids. For example, a typical fluid such as water has a certain amount of viscosity. This is why when you stir your coffee the swirl eventually dies down. But some things like liquid helium can be cooled to the point where it becomes a superfluid with no viscosity. If you were to stir a superfluid, it would keep swirling indefinitely. Such swirls are known as vortices. Because these vortices last indefinitely, they can be considered part of the topology of the superfluid.

Which brings us to this work. One of the interesting questions in condensed matter is how and why materials transitions from regular to super. What’s really going on in the structure of a material that makes a material superfluid or superconductive? To try to figure this out, the laureates focused on thin layers of material. So thin that it can basically be considered a two-dimensional surface. For a long time it was thought that superfluidity, for example, couldn’t exist in such a constrained state, but it turns out that they can, and when they do, things like vortices start behaving in interesting ways. When vortices in a fluid form, they’ll tend to be distributed in a random way. Some might interact with each other, but it’s all rather chaotic. However when a fluid cools below a certain point, the vortices pair up, and move together in pairs. This shift in the topological behavior occurs at a critical temperature, and thus is a topological phase change.

It’s actually a surprising result, because it means not only can materials have phase changes where the macroscopic behavior of a material shifts from solid to liquid to gas, but there are also more subtle phase transitions where the topology of a material changes in discrete ways. As we’ve begun to learn over time, these subtle topological shifts can bring exotic changes to a material, and we’re still learning about their applications.

So while it’s not gravity waves, this award-winning work has made waves of its own, and that makes it a worthy choice for this year’s Nobel prize.

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I’ve been getting a flurry of emails and comments recently from folks who don’t believe the Earth is round. It’s pretty straightforward to demonstrate to yourself that the Earth is indeed round, but this time the argument is about gravity and Earth’s (supposed) rotation. Water droplets on a ball will fly off if you rotate the ball due to centrifugal force. If the Earth rotates once a day, then stuff on the equator is moving at over 1,000 mph, while stuff near the poles is barely moving. How can gravity be strong enough to keep things from flying off the equator without simultaneously crushing things at the poles? 

The basic idea of gravity is that masses are mutually attracted to each other. As Newton described it, masses exert a force on other masses depending on how much mass it has, and how far away it is. Near the surface of the Earth, the gravitational force is about 10 times your mass. This number comes from that fact that force is a product of mass and acceleration, and the acceleration of gravity is about 10 meters per square second. That means that if you took a mass and let go of it, its speed would increase by about 10 meters per second (22 mph) each second. If the Earth weren’t rotating, the force of gravity would be basically the same everywhere on the planet, and “down” would always be toward the center of the Earth. But the Earth is rotating, say the scientists, so surely that would have an effect, right?

It turns out centrifugal force is easy to measure in the lab. Just swing a mass and measure how much the mass seems to pull outward. Yes, I know some of you will point out that this actually involves centripetal force, but the end result is the same. A common introductory physics lab involves performing just such an experiment to see how the speed of an object affects the centrifugal force. What you find is that the force depends upon the square of the speed divided by the radius of the circular motion. At the equator an object is moving about 1,000 mph, and it’s moving in a circle with a radius of about 4,000 miles. Plug these into our equation and that gives 250 miles per square hour. That sounds huge, but if you convert it to metric, you get 0.03 meters per square second. So gravity pulls an object at the equator with a force of about 10 times its mass, while the centrifugal force is pulling it away from the Earth at about 0.03 times its mass. Yes, things at the equator are moving fast, but the radius of the Earth is so large that it doesn’t produce much centrifugal force.

Saturn’s fast rotation means it is wider at the equator than the poles.

Since centrifugal force is only about 0.3% of the gravitational force, gravity always dominates, and we don’t notice the centrifugal force in our everyday lives. But modern gravitational measurements are extremely sensitive. We’ve measured the variation of gravity all over the globe, and we find it varies with latitude just as predicted by Newtonian gravity and centrifugal force. Earth’s rotation means you are slightly lighter at the equator, but Earth would have to rotate much, much faster to overcome gravity. Earth isn’t the only place where centrifugal force has an effect. Saturn, for example, has a day that is only 10 hour long, and as a result it’s equator is moving at more than 23,000 mph compared to its poles. That isn’t enough to make things fly off Saturn, but it does mean that the centrifugal force at the equator is about 19% of Saturn’s surface gravity. As a result Saturn bows outward at its equator.

So Earth’s rotation really does mean that you weigh less at the equator. The effect is small, but we can measure it, and it confirms once again that the Earth is round.

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China recently launched a satellite to test quantum entanglement in space. It’s an interesting experiment that could lead to “hack proof” satellite communication. It’s also led to a flurry of articles claiming that quantum entanglement allows particles to communicate faster than light. Several science bloggers have noted why this is wrong, but it’s worth emphasizing again. Quantum entanglement does not allow faster than light communication. 

This particular misconception is grounded in the way quantum theory is typically popularized. Quantum objects can be both particles and waves, They have a wavefunction that describes the probability of certain outcomes, and when you measure the object it “collapses” into a particular particle state. Unfortunately this Copenhagen interpretation of quantum theory glosses over much of the subtlety of quantum behavior, so when it’s applied to entanglement it seems a bit contradictory.

The most popular example of entanglement is known as the Einstein-Podolsky-Rosen (EPR) experiment. Take a system of two objects, such as photons such that their sum has a specific known outcome. Usually this is presented as their polarization or spin, such that the total must be zero. If one photon is measured to be in a +1 state, the other must be in a -1 state. Since the outcome of one photon affects the outcome of the other, the two are said to be entangled. Under the Copenhagen view, if the entangled photons are separated by a great distance (in principle, even light years apart) when you measure the state of one photon you immediately know the state of the other. In order for the wavefunction to collapse instantly the two particles must communicate faster than light, right? A popular counter-argument is that while the wavefunction does collapse faster than light (that is, it’s nonlocal) it can’t be used to send messages faster than light because the outcome is statistical. If we’re light years apart, we each know the other’s outcome for entangled pairs of photons, but the outcome of each entangled pair is random (what with quantum uncertainty and all), and we can’t force our photon to have a particular outcome.

The reality is more subtle, and vastly more interesting. Although quantum systems are often viewed as fragile things where the slightest interaction will cause them to collapse into a particular state, that isn’t the case. Entangled systems can actually be manipulated in a variety of ways, and you can even manipulate them to have a specific outcome. I could, for example, create pairs of entangled photons in different particular quantum states. One state could represent a 1, and the other a 0. All my distant colleague needs to do is determine which quantum state a particular pair is in. But to do this my colleague would need to make lots of copies of a quantum state, then make measurements of these copies in order to determine statistically the state of the original. But it turns out you can’t make a copy of a quantum system without knowing the state of the quantum system. This is known as the no-cloning theorem, and it means entangled systems can’t transmit messages faster than light.

Which brings us back to the experiment China just launched. The no cloning theorem means an entangled system can be used to send encrypted messages. Although our entangled photons can’t transmit messages, their random outcomes are correlated, so a partner and I can use a series of entangled photons to generate a random string we can use for encryption. Since we each know the other’s outcome, we both know the same random string. To crack our encryption, someone would need to make a copy of our entangled states, which can’t be done. There are ways to partially copy the quantum state, which would still improve the odds of breaking the encryption, but a perfect copy is impossible.

So entanglement doesn’t give us faster than light communication, but it may make it a bit easier to keep our secrets secret.

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The central idea of Einstein’s theory of gravity is the principle of equivalence. That is, objects will fall at the same rate under gravity regardless of their mass or composition. As long as there isn’t air resistance, a feather and a bowling ball dropped at the same time will strike the ground simultaneously. But what if one object is rotating and another is not? Will they fall at the same rate? 

We know that the rotation of a body can affect how things fall. When a body such as Earth rotates, it creates an effect known as frame dragging, which twists space and time slightly. Computer simulations of merging black holes show that two rotating black holes would merge at a different rate than if they weren’t rotating. So on a large scale gravity is affected by rotation.

This has led some theorists to wonder whether such a rotational effect might be a way to connect Einstein’s gravity with the quantum theory of atoms and molecules. It turns out that atoms and other quantum particles have a property known as spin. If we imagined an atom as a small sphere, we can imagine its spin as the rotation of that spin. The catch is that atoms are not little spheres, and spin is not physical rotation. Spin is an inherent property of a quantum object that behaves similar to the type of rotation we see every day.

So, would an atom with spin fall at a different rate than one without spin? More specifically, does the principle of equivalence hold for quantum objects with spin? A recent experiment tested this question by comparing the free fall of rubidium atoms with different orientations of spin.

The team compared the gravitational acceleration of atoms with spin +1 and -1. To use our rotating sphere analogy, this would be like comparing a sphere rotating clockwise about its north pole vs one rotating counterclockwise. They found that the two orientations of spin fall at the same rate to within 1 part in 10 million, which was the limit of observation for their experiment. In other words, spin has no affect on the rate at which an atom falls.

This result isn’t entirely unexpected. It’s been generally thought that the equivalence principle holds for both classical and quantum objects. The experiment does, however, rule out some of the more radical models trying to unify gravity and quantum theory.

Now we know the equivalence principle holds even for a quantum top.

Paper: Xiao-Chun Duan, et al. Test of the Universality of Free Fall with Atoms in Different Spin Orientations. Phys. Rev. Lett. 117, 023001 (2016).  arXiv:1602.06377 [physics.atom-ph]

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An atom is comprised of dense nucleus of protons and neutrons surrounded by a diffuse cloud of electrons. Since an atomic nucleus is held together by the strong force, similar to the way gravity holds stars and planets together, you would think nuclei would be basically spherical. This isn’t always the case, and a few such as barium-144 are even pear shaped. This has to do with a subtle way the Universe works, which could explain one of its biggest mysteries. 

As Emmy Noether demonstrated in the early 1900s, symmetry is connected to the basic laws of physics. The presence of certain symmetries in the world is a property of certain unchanging quantity in the Universe. Noether’s theorem is an elegant demonstration of this connection, and is central to most modern physical theories. Noether showed us how some of the most powerful symmetries are those connected to space and time.

Take, for example, mirror symmetry, also known as parity. When you look in a mirror, the image you see is reversed. If you hold up your right hand, your mirror image would seem to hold up its left. Mirror image clocks would appear to move counter clockwise. So imagine a mirror universe. Not the evil Spock kind of mirror universe, but simply one in which the parity of everything is reversed. Americans would drive on the left side of the road, the Sun would rise in the west and set in the East, but fundamentally nothing would change. It would be no different than if we simply decided to switch the meanings of right and left.

The basic idea of the Wu experiment. Credit: Wikipedia user nagualdesign.

At least that would be the case if parity symmetry were true. While usually things are symmetrical under a switch of parity, there are some cases were parity is violated. This was first demonstrated by the Wu experiment in 1956. Chien-Shiung Wu looked at the radioactive decay of cobalt-60 atoms. If parity was conserved, then mirror image decay experiments should behave in exactly the same way. What she found was that mirrored experiments of cobalt-60 decayed in opposite directions. Since radioactive decay is driven by the weak nuclear force, this meant the weak force violates parity.

Another symmetry is related to electromagnetic charge. In our Universe protons have a positive charge while electrons have a negative charge. Charge symmetry considers what would happen if these charges were reversed. Since antimatter particles have the opposite charge of their regular matter partners, this would be like replacing all matter with antimatter. Since positive charges interact with each other the same way as negative charges, you would think that charge symmetry would hold. After all, it’s why charge is conserved.

The helicity of neutrinos and anti-neutrinos. Credit: Universe Review

But it turns out charge symmetry can be violated in a subtle way, again connected to the weak interaction, specifically neutrinos. While neutrinos don’t have any charge, they do have a kind of rotation known as helicity. If charge symmetry were true, then matter and antimatter should produce neutrinos with the same helicity. But it turns out matter produces neutrinos of one helicity, while antimatter produces antineutrinos of the opposite helicity. So charge symmetry is violated as well.  For a time it was thought that the symmetries of charge and parity could be combined into a more general CP symmetry that would be conserved, but there are radioactive particles that violate it as well.

So what does any of this have to do with pear-shaped atomic nuclei? The shape of a nucleus is determined by the various interactions that occur between the protons and neutrons (and quarks) within the nucleus. If those interactions were CP symmetric, there shouldn’t be a pear-shaped nucleus like barium-144. By studying odd nuclei like barium-144, we can gain clues about the ways CP-symmetry can be violated.

What does this have to do with astrophysics? Remember that charge symmetry is connected to matter and antimatter. Because charge is conserved, when any particle of matter is produced through some physical process, a corresponding particle of antimatter must also be produced. In the early moments after the big bang, when matter was being produced for the first time, there should have been an equal amount of matter and antimatter. But what we see today is a Universe dominated by matter. The origin of this matter-antimatter asymmetry is one of the great unanswered questions of cosmology. It’s been proposed that a violation of CP symmetry could have produced more matter than antimatter, but the currently known violations are not sufficient to produce the amount of matter we see. If there are other avenues of CP violation hidden within pear-shaped nuclei, they could explain this mystery after all.

Paper: C. S. Wu, et al. Experimental Test of Parity Conservation in Beta Decay. Physical Review 105 (4): 1413–1415. (1957)

Paper: B. Bucher et al. Direct Evidence of Octupole Deformation in Neutron-Rich ¹⁴⁴Ba. Phys. Rev. Lett. 116, 112503 (2016)  arXiv:1602.01485 [nucl-ex]

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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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