A supernova is a dying star. In a last moment of brilliance a supernova can shine brighter than an entire galaxy. There is still much we don’t understand about supernovae, in part because of how difficult they are to observe. Since we can’t predict when a star will explode, we typically discover supernovae after they have brightened significantly. Ideally we’d like to know where and when a supernova will occur before it happens so we can observe one in its entirety. Thanks to the effects of general relativity, we can. 

In general relativity, spacetime is warped by the presence of mass. Because of this warping, light can be deflected from a straight path, an effect known as gravitational lensing. The effect was first observed by Arthur Eddington in 1919, but is most commonly observed when light from a distant galaxy is deflected by a closer galaxy on its way to reaching us. This lensing effect often produces multiple images of a distant galaxy as its light reaches us along different paths.

Light from a distant galaxy is lensed to produce multiple images of the galaxy. Credit: NASA & ESA.

The speed of light is finite, so it takes time for light from a distant galaxy to reach us, often billions of years. Since the images of a galaxy come to us along different paths, each having a slightly different distance, the time it takes light to reach us along each path is different. This means each image of the galaxy we see is from a slightly different time. Normally this is insignificant, since galaxies change very slowly. But a supernova occurs over a short period of time, so it can appear in one image of the galaxy first, only to reappear in another image years later.

In 2014, astronomers observed a supernova in a galaxy known as MACS J1149.5+2223. Because of gravitational lensing, at least three images of this galaxy can be seen. Using computer models they calculated the path distances of these multiple images, and determined that the supernova should appear in another galaxy image sometime between 2015 and 2020. They’ve been keeping an eye on the galaxy, and this month they were rewarded with a new appearance of the same supernova. The supernova has been nicknamed Refsdal after the Norwegian astronomer Sjur Refsdal, who first proposed the idea of time delayed supernovae in 1964.

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When two black holes merge, the orientation of their axis of rotation can change abruptly. This is known as a spin flip, and typically happens when the orbital plane of two black holes is different from the rotational axes of the black holes. The total rotation (angular momentum) of the orbiting black holes is constant, so when they merge, the orientation of the merged black hole must be in the direction of the total. While we’ve known this for some time, it’s generally been thought that before the merger the rotation of the two black holes is fairly constant. Now new research finds this isn’t the case.

Spin flip when black holes merge. Credit: Wikipedia

The results are published in Physical Review Letters, and are based upon detailed computer simulations of merging black holes. While we know the equations of general relativity extremely well, the complexity of these equations means that even a general two-body solution can’t be solved exactly, unlike Newtonian gravity. While there are ways to find approximate solutions, detailed studies require solving Einstein’s equations numerically. With the rise of powerful supercomputer clusters and advanced software, we’ve finally reached the point were very detailed solutions can be obtained.

The shift of spin orientations over time.
Credit: Lousto and Healy

In this case, the team used the Blue Sky linux cluster at my university (RIT) to analyze the spin orientation of two orbiting black holes as they are close to merging. What they found was that the spins of the two black holes interact gravitationally (what is known as spin-spin coupling) and as a result they can transfer angular momentum between each other. This means that the orientations of their spins change over time.

This has important consequences for observations of merging black holes. We can determine the rotational orientations of black holes by the jets that stream from their poles, so one way to look for mergers is to look for an abrupt shift in the direction of a jet. What this work shows is that there can be gradual shifts leading up to a merger, so there isn’t necessarily a sharp shift in the jet.

Paper: Carlos O. Lousto and James Healy. Flip-Flopping Binary Black Holes. PRL 114, 141101 (2015)

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When you think of the strangest scientific theory ever, you probably think of quantum mechanics. With its particle-wave duality and collapsing wavefunctions, it can certainly be considered a strange theory. But I would argue that even more bizarre is the theory of relativity. In quantum theory objects behave strangely in space and time, but in relativity the very nature of space and time is questioned. Despite all of its consequences such as curved space, time dilation and interchange of mass and energy, we know relativity to be true. Not just “kind of” true, but provably true to a high degree of precision.

Michelson and Morley’s 1887 interferometer.
Credit: Case Western Reserve Archive

The foundational experiment for both special and general relativity is the verification that the speed of light in a vacuum is the same for all frames of reference. This was first demonstrated by the famous Michelson-Morley experiment in 1887. The idea that the speed of light is constant is deeply counterintuitive. It would be as if you are riding a skateboard at 5 mph, and you toss a ball at 15 mph, and someone standing on the sidewalk sees the ball move not at 20 mph, but 15 mph just as you do. Michelson and Morley weren’t trying to prove light speed is constant, they were actually trying to determine how the speed of light changes as the Earth orbits the Sun. Instead of observing a changing speed of light, they found no variation to the limit of their experiment, which was about 1 part in 40,000. Because of this, the Michelson-Morley experiment is sometimes called the most successful failed experiment ever.

Since then, the result has been confirmed numerous times. With the advent of lasers, the experiment could be performed to extremely high accuracies. The results were so precise that in 1983 the speed of light became the standard by which the meter is defined. The most recent tests of the constancy of light speed find that it varies by no more than a few parts per quintillion.

Since the speed of light is constant for all frames of reference, there should be a difference between the way time is observed in different reference frames. We can see how this works if we imagine a clock made with light. Take two mirrors and place one above the other and facing each other, then bounce a pulse of light between them. We can measure time by counting the number of times the light bounces off a mirror. Each bounce is like the tick or tock of a mechanical clock. If you could watch the pulse of light, you would see it move up and down between the mirrors at the speed of light. Up and down at a constant rate. Now suppose you took your clock on a fast moving train. Standing in the aisle of the train, you would see the light pulse move up and down at the same rate as before. Up and down at the speed of light.

Credit: John D. Norton

But an observer watching the train pass by would see something slightly different. They would also see the pulse move at the speed of light, but from their perspective the light can’t move straight up and down because it must also be moving along with you. They would see the pulse move diagonally up then diagonally down, which is a slightly longer distance between each bounce. That means it would take the light longer to travel from bounce to bounce. So from their viewpoint the ticks and tocks of your clock are slower than the ticks and tocks as you see them. Your clock appears to be running slow because of your motion relative to them.

This effect is known as time dilation, and it can be demonstrated by what is known as the Ives–Stilwell experiment. This experiment looks at the light emitted or absorbed by fast moving particles and compares them with the transverse Doppler effect. If an object speeds past you from left to right, when it is directly in front of you would you see any Doppler shift of its light? Since the relative motion along your line of sight at that moment is zero, you might think there would be no shift. But since the object is speeding past you, its time should be dilated. As a result there should be a Doppler shift. The Ives-Stilwell experiment is thus a direct test of time dilation. It was first performed in 1938, and has been improved upon over the years. Just this week, results on a new version of the experiment has confirmed time dilation to 2 parts in a billion.

Other experiments have looked at time dilation by comparing the time of two clocks in motion relative to each other. These experiments assume light obeys special relativity, so they are model dependent rather than the direct Ives-Stilwell experiments. However when comparing the relative time dilation of two atomic clocks, we find that they agree with the predictions of relativity to within one part in 10¹⁶. Special relativity makes our observations of space and time relative, but it is astoundingly accurate.

Of course relativity can be broadened to include the effects of gravity. This general theory of relativity begins with the observation that any two objects will fall in a gravitational field in the same way. It was first noted by Galileo who (according to legend) dropped lead balls of different size from the tower of Pisa. Galileo actually tested the idea by rolling balls down an inclined plane, and could find no observable difference.

Robert DuBois of Missouri Science & Tech, with an Eotvos apparatus

In 1908 Loránd Eötvös made the first precision test of the equivalence principle using a torsion balance, and found that it was true to within one part in a billion. Over the last century this result has been improved to the point that we now know the equivalence principle is true to within 1 part in 10¹⁴.
Using the equivalence principle, Einstein developed a gravitational theory even more strange than special relativity. In his theory the fabric of space and time can be bent and twisted by the presence and motion of masses. One of the first tests of the gravitational curvature of space was the deflection of starlight during a solar eclipse, first observed by Eddington in 1919. Eddington’s results supported Einstein’s model, but not very strongly. Given the radical approach of general relativity, Eddington’s results were initially disputed by some. But subsequent observations confirmed Einstein’s predictions.

A distant galaxy (blue) is gravitationally lensed by a closer galaxy (red). Credit: ESA/Hubble & NASA

The most recent tests of light bending agree with general relativity to within 0.3%. That doesn’t seem very strong, but it’s very difficult to measure accurately. At Earth’s distance, the light of a star seen at a direction 90 degrees away from the Sun is deflected by 4 milliarcseconds. That’s roughly equivalent to the width of a human hair seen from 3 kilometers away.

Our astronomical instruments have gotten so precise that even this small deflection must be taken into account. Satellites such as Hipparcos (and soon Gaia) make very precise observations of the positions of millions of stars. As the satellites orbit the Sun, measured stars are sometimes aligned more closely or more distant from the Sun. As a result, the gravitational curvature of the Sun can shift the observed position of the stars by a measurable amount. In fact, measurements of Gaia will be so precise that it could provide a more stringent confirmation of light bending.

Perhaps the weirdest prediction of relativity is that rotating masses twist space around them. This effect is known as frame dragging, and it is most dramatic around black holes. But even the Earth’s rotation twists space ever so slightly. In 2011 a spacecraft known as Gravity Probe B successfully observed this effect due to the Earth.

Gravity Probe B tests general relativity. Credit: Gravity Probe B Team, Stanford, NASA

The frame dragging effect of Earth is so small that it’s astounding we can perceive it at all. To observe these effects, the team had to create quartz spheres so precise that their surface varied no more than 40 atoms from a mathematically perfect sphere. They were then covered with a thin layer of niobium so they could be suspended within an electric field. Their rotation created a small magnetic field, which was measured by superconducting quantum interference devices. Of course all of this is packed into a probe and shot into space for an 18 month mission. Over the duration of the experiment, the rotation of the spheres had to be measured with milliarcsecond precision. Despite the challenges, Gravity Probe B confirmed the Earth’s gravitational curvature of space to within 1% of predictions, and confirmed frame dragging to within 19%.

Decay of a binary pulsar’s orbital period over time.

Despite all these successes, there is one confirmation of relativity which still eludes us: direct observation of gravitational waves. According to general relativity, when large masses such as neutron stars or black holes orbit each other, they should create ripples in spacetime. These ripples should radiate outward as gravitational waves. Because these waves carry energy away from the system, the orbits of these massive objects should decay. We’ve seen this kind of orbital decay in binary pulsars, so we’re pretty certain these gravitational waves exist. But to truly be certain we’d like to detect them directly.

In principle we should be able to observe their effect as an oscillation in the separation distance of two mirrors. But even if the mirrors were separated by 4 kilometers, the variation in their distance would only be about 10^-18 meters, or about a thousand times smaller than the width of a proton. We haven’t confirmed gravitational waves yet, but with projects such as LIGO, and the proposed space-based LISA, we will likely succeed.

Of course, these experiments are only possible using lasers, and the knowledge of the invariant speed of light. Perhaps it is fitting that we use the first triumph of relativity to strive for its last great confirmation.

Note: This post originally appeared at Starts With A Bang!

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If you toss a ball into the air, it will slow down as it rises.  The Earth’s gravity pulls on the ball as it moves upward, causing it to slow down until it comes to a momentary stop at its highest point. Then it will begin to move downward, speeding up as it does.  Suppose, then, that you were to shine a flashlight upward. What would happen? You might argue that gravity would pull on the photons, causing them to slow down, but we know that light has a constant speed, and can’t slow down. You might argue that since photons are massless gravity doesn’t affect them, but we know that the Earth’s mass, like any other mass, can cause light to change directions. So neither of these can be the answer. The real answer is pretty interesting, and it turns out to be one of the tests of Einstein’s theory of relativity.

To understand what happens to our beam of light, we need to look at gravity in a slightly different way. Normally we think of gravity as a force, but it can also be described in terms of energy. If you take a mass and drop it, it speeds up as it falls, thus gaining kinetic energy.  When you toss a ball in the air, it slows down, thus losing kinetic energy. But energy is conserved, so energy gained or lost by the ball has to come from or go somewhere. This energy is typically called gravitational potential energy, since gravity has the potential to cause the ball to move. So rather than thinking of gravity as a force, we can see it as having a gravitational potential that can give or take away energy from the ball.

This brings us to the case of light. When we shine the flashlight upward, Newtonian gravity would say that the light is unaffected, since light is massless, but under general relativity light is affected by gravity, so as the light travels upward it must lose energy. But how is that possible if it can’t slow down? It turns out that the energy of light doesn’t depend upon its speed, but upon its wavelength. Red light with long wavelengths has less energy than blue light with short wavelengths. So as the light travels upward, its wavelength is stretched, and the light becomes more red. This is known as gravitational redshifting. For those of you wondering what this has to do with curved space, in general relativity the radial distance close to the Earth is shorter than the radial distance farther away.  As the light moves upward its wavelength is stretched by the curvature of space due to gravity, which again means it is redshifted.

This effect is typically quite small, and it wasn’t confirmed until 1959, when Robert Pound and Glen A. Rebka performed an experiment with radioactive iron (Fe 57). This isotope emits gamma rays at a very specific wavelength. To detect these gamma rays they used a detector made of the same element. Since the detector can only catch the gamma rays at the same wavelength, any redshift of the gamma rays would make detection unlikely. Pound and Rebka showed that if you oscillate the detector at a particular frequency it would detect the emitted gamma rays. This is because the oscillation of the detector meant it saw the gamma rays redshifted due to relative motion. In this way they were able to determine how much the gamma rays were redshifted (or blueshifted) by its upward or downward motion. Their results agreed with Einstein’s predictions.

The Pound-Rebka experiment for gravitational redshift is now considered one of the three principal tests of general relativity. The other two are the precession of Mercury’s orbit and the deflection of light by gravity. As strange as general relativity may seem, it really is how the universe works.

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Yesterday’s post on testing the assumption that photons are massless raised a few questions for readers. One of the most common was the idea that the gravitational lensing of light must mean that photons have mass. After all, if a star or galaxy can deflect light gravitationally, doesn’t that mean the light is gravitationally attracted to it? If that is the case, doesn’t that mean that light has mass?

Before we delve into the question, we first need to be clear about what we mean by “mass”. There are actually several different types of mass. The type that best corresponds to our intuitive understanding is known as inertial mass. Inertial mass is determined by its resistance to acceleration. If you push on objects with a force, an object with less inertial mass will accelerate more than one with more inertial mass.

Another type of mass is known as gravitational mass. Gravitational mass is what (in Newton’s gravity) causes the gravitational attraction between objects. When you step on a scale in the morning, you are measuring your gravitational mass. While technically gravitational mass and inertial mass are not the same thing, we generally treat them as the same thing because of the “principle of equivalence”.

If you release a ball from the leaning tower of Pisa, the gravitational force on the ball causes it to fall. The strength of that force depends on the gravitational mass of the ball, but the rate at which it falls depends on the inertial mass of the ball. But experiments have shown that masses all fall at the same rate in a gravitational field, so that means the gravitational and inertial masses must have the same value. This equality between gravitational and inertial mass is called the principle of equivalence. While this was known since at least Galileo’s time, it was Einstein who made the idea central to our understanding of gravity.

The third type of mass is known as relativistic mass. This stems from Einstein’s theory of special relativity and the equivalence of mass and energy (the famous E equals m c squared). In that famous equation, E is the energy of a particle, and c is the speed of light. So if you divide the energy of a particle by the speed of light squared, you get a “mass”, known as the relativistic mass of the particle.

Now if an object is at rest (relative to you) then the relativistic mass has the same value as the inertial mass. This is sometimes called the “rest mass” of an object. But in general, relativistic mass is not the same thing as inertial or gravitational mass. Unfortunately this point isn’t often made clear, so it leads to a great deal of confusion. When someone says “the mass of an object increases as it approaches the speed of light”, that’s really the relativistic mass. A fast moving object has not only energy due to its rest/inertial mass, but also a kinetic energy due to its motion. The relativistic mass due to its total energy is what increases. Its inertial (and gravitational) mass is unchanged.

This is the key difference. Relativistic mass is an apparent mass that depends on how the object is moving relative to you. Inertial and gravitational mass are inherent properties of an object, and don’t depend on your point of view.

So what does this have to do with whether photons have mass? Photons have energy, so we can define the relativistic mass of a photon by taking its energy and dividing by the speed of light squared. The energy of a photon depends upon its wavelength. Long wavelength (reddish light) photons have less energy than short wavelength (bluish light) photons. This means photons have different relativistic masses.

Photons don’t have “rest mass” or inertial mass. Despite popular news articles about “stopping light”, you can’t hold a photon in place. The “light stopping” experiments are effects of light waves, which is a whole other rabbit hole. You also can’t accelerate light with a force. The speed of a photon is constant, so again, no inertial mass. By the equivalence principle, that also means they have no gravitational mass.

At least that is the accepted answer. Maybe for photons, their relativistic mass is their inertial/gravitational mass. How do we know it’s not? Actually, we have an experiment that proves it, and Arthur Eddington first did it in 1919.

In 1919 Eddington photographed the positions of stars near the Sun during a total eclipse. He compared those positions to their positions when the Sun wasn’t there, and found that they had appeared to shift away from the sun. This is because the Sun gravitationally deflected the starlight slightly. This bending of light made the stars appear to be in a different direction. Einstein predicted this light bending due to the curvature of space in his theory of general relativity. Thus, Eddington proved that Einstein’s theory was correct.

When this story is presented, it’s often said that since photons have no mass Newton’s model predicts light shouldn’t bend. Einstein’s theory predicts light bending, so this proved Einstein right. But actually that isn’t entirely the case. If the relativistic mass of a photon is equated to its inertial and gravitational mass, then Newton’s gravity does predict light bending.

The catch is that the amount of bending predicted by Newton’s model is half what Einstein’s model predicted. Eddington actually demonstrated not only that light was gravitationally deflected, but that the amount matched Einstein, and not Newton. You can see this in the figure above, which shows three possible outcomes for light pending: Newton is right, and photons are massless (no deflection), Newton is right and photons have mass (some deflection), or Einstein is right, photons are massless and space is curved (more deflection).

So the gravitational lensing we see from stars and galaxies actually demonstrates that photons aren’t being gravitationally attracted in the Newtonian sense. Instead, space is warped by mass of stars and galaxies, and the path of light is warped accordingly. Light really is massless. You can’t bend it like Newton, but you can bend it like Einstein.

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Black holes are interesting objects, because we know they exist but we don’t know what they are. That isn’t quite true. We know that they are formed from the gravitational collapse of matter, either as supermassive black holes in the centers of galaxies, or as stellar mass black holes from the collapse of a star. We know that they power quasars and radio galaxies, that they can form accretion disks of matter around their equators, and that they can produce powerful jets of matter when they are active.  But buried within our understanding of black holes is a fundamental contradiction that we have yet to resolve.

In our everyday lives we typically view gravity as a force that acts upon solid masses.  This follows the Newtonian model of physics, where objects are solid, and move through space by forces. But by the 1900s we came to understand that Newton’s physics is really an approximation to much more complex phenomena. This led to the development of two physical models, general relativity and quantum mechanics.

In general relativity, gravity is not a force. Instead it is an effect of the curvature of space and time. Masses warp space, and that that warping causes objects to deviate from their linear motion, giving the effect of gravity.  In general relativity Newton’s assumption of solid masses moving in a continuum of space and time still holds, but space and time are malleable by the presence of mass.  While it seems odd to our everyday experience, general relativity has been validated by numerous experiments, and is an extremely accurate description of large objects like planets and stars.

In quantum mechanics, objects are not solid, but are instead made of quanta interacting which each other. The state of these quanta can change as they are measured in different ways. This change occurs in discrete ways, not as a gradual shift through the continuum of space and time. Quantum mechanics also seems counter intuitive, but it has been validated by numerous experiments, and is an extremely accurate description of small objects such as atoms.

While both general relativity and quantum mechanics are accurate descriptions of physical phenomena, their basic assumptions are contradictory. General relativity is a classical (Newton-like) model, while quantum mechanics is a quantum (discrete) model.  Normally this isn’t a problem, but in the case of black holes it is.  One of the predictions of general relativity is that the matter within a black hole will collapse into an infinitely dense point of zero volume. Once inside a black hole there is nothing strong enough to counter gravity.  But this assumes that on small scales we can still treat matter as existing in a continuum of space and time.  Quantum mechanics says otherwise. There should be a quantum aspect to the singularity, likely even preventing the singularity from existing.

There has been a great deal of effort to develop a way to unify these two contradictory models. String theory and loop quantum gravity are two popular approaches. So far we’ve only had partial success.

So for now we know black holes exist, and we can observe their effects in the universe. What we don’t know is what happens if you go down the rabbit hole.

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In the popular science fiction franchise Star Trek, there are two ways in which a ship can move. Impulse engines, and warp drive. Impulse engines actually exist. Impulse is just a physics term for applying a force over a period of time, so impulse engine is just a fancy term for rockets. In the franchise they are usually assume to be some kind of plasma rocket, but they are still just rockets. In fact, any engine that applies a force over time is technically an impulse engine. So the next time you climb into your car you can “engage impulse engine”.

Warp drive is something entirely different. It allows starships to travel among the stars much faster than light, so it is clearly not conventional physics. As its name implies, it seems to rely on warping space to allow for faster than light travel. It is never entirely clear how it works beyond the fact that it relies of warp coils, dilithium crystals, and other things that can break down, threaten to explode or otherwise create drama.

Given its vague description, it is usually assumed that any type of space travel that involves the warping of space is a warp drive. There are other ideas in science fiction, such as hyperspace, wormholes, inertia negation, etc. There are corresponding proposed physics for each of these, such as Heim theory, Dean drives, etc. These are typically viewed as fringe theories, and like perpetual motion machines they either don’t work, or their effects don’t mean what their inventors claim they mean. There’s a deep rabbit hole of “alternative” physics you can find on the internet related to these ideas.

So where does warp drive stand in all this? Although warp drive was popularized by Star Trek in the late 1960s, it wasn’t until 1994 that an actual scientific paper was published on such a drive. It was then that Miguel Alcubierre published an article in Classical and Quantum Gravity titled “The warp drive: hyper-fast travel within general relativity.” This is a refereed paper in a respectable journal, so it’s not fringe theory, but the article is a what-if speculation testing the limits of general relativity.

What Alcubierre showed was that there are solutions to general relativity that allow for an object to travel at any arbitrary speed, even faster than light. It does this by compressing space in front of the object and correspondingly expanding space behind it. This means that while the object itself does not travel through space faster than light, space is warped around it such that the space the object occupies moves from point A to point B faster than light would. This Alcubierre drive sounds like the warp drive of Star Trek, and in fact Alcubierre has said the science fiction concept inspired his idea.

There is, however, a catch with this model, and it’s a big one. Just because something is allowed by general relativity doesn’t make it real. You might remember the Godel Universe I mentioned yesterday, which is allowed by general relativity but doesn’t happen to describe our universe. The same is true in this case. In particular, general relativity only describes the shape of space and time due to a particular distribution of mass and energy. You can make up any distribution you want in general relativity, even ones that are not physically possible. In the case of Alcubierre’s paper, his warp drive solution requires not only regular matter, but some kind of exotic matter with negative mass. All matter has positive mass, so it seems like the Alcubierre drive is only possible if we allow for a type of mass that doesn’t exist. So it’s an interesting idea, but not physically possible.

Except that isn’t entirely true. Once again, physics seems to leave the door open just a crack. There are two things that might (or might not) fit the bill. One of these is dark energy. We see the effects of dark energy in the accelerated expansion of the universe. There are several models to describe dark energy. One of these models proposes a fundamental force known as quintessence. If quintessence is real, then it would have a negative energy density, which is effectively the same as negative mass. So if we could harness quintessence it could be exactly what’s needed for warp drive. Of course we don’t know whether quintessence exists, much less how it might be harnessed, so that possibility is pure speculation.

The other possibility we do know exists. In quantum mechanics, the amount of energy in a region of space can fluctuate by tiny amounts. This is due to the uncertainty principle, which places limits on how precisely things like energy can be measured. These quantum fluctuations exist even in empty space. In an open region of space these fluctuations average out to effectively zero energy. But in an occupied space they may not average out.

The most popular example is to have two metallic plates placed very close to each other (fractions of a millimeter apart). The fluctuations are basically free on either side of the plates, but are constrained between the plates. This means there are less fluctuations between the plates than outside the plates. As a result the plates have a net attractive force between them. This is effect is known as the Casimir effect, and has been observed experimentally. On very small scales the force can be relatively large.

How this relates to warp drive is that outside the plates the quantum fluctuations still average to zero energy, but between the plates the fluctuations are less, which means the quantum energy between the plates is less than zero. In other words, between the plates there is a negative energy density. This is exactly what is needed for warp drive, so we just have to harness this quantum negative energy effect. Right?

Maybe, and maybe not. The Casimir effect is a quantum effect. We don’t have a quantum theory of gravity, so we can’t be sure that this negative quantum energy would act like negative mass. It might, but without an understanding of quantum gravity we can’t be sure. So warp drive is hypothetically possible, but would require a “negative energy”, and we don’t know if that is even possible. Even quantum fluctuations or quintessence does allow for negative energy, warp drive might still require far more of it that we could ever practically gather.

But what about NASA. Isn’t it true that NASA is developing a warp drive? Not quite. It is true that NASA has funded research on warp drive, but you shouldn’t read too much into this. Part of NASA’s mission is to push the envelope of space technology. That means sometimes they will spend a bit of money on a radical idea, and exotic propulsion concepts such as warp drive is one of them. You can think of it at being an investor. If you have a million dollars to invest, you would put some it in fairly safe, moderate yield investments, and some it a riskier, higher yield investments. But every now and then you might toss a few hundred dollars at a really high risk investment with the potential to make millions. You’ll probably lose the money, but you can afford to lose it, and every now and then you might win big. NASA’s funding of warp drive research is just that. Toss a little money at warp drive. It probably won’t work, but if it does it would revolutionize space propulsion.

In the Star Trek universe the first warp drive is created in 2063. That gives us only 50 years to make it so.

Next Time: Wormholes. Can we create shortcuts through space? Would it let us walk through a stargate to another world? Will we find out tomorrow? Indeed.

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When someone mentions time machines, you might think of fantastical machines such as Dr. Who’s TARDIS or the DeLorean in Back to the Future, but several physicists have made a serious study of time machines. Most of this work focuses on “what if” scenarios, which are really about testing the limits of a particular theoretical model, rather than actually engineering a device that can travel to the past.

The physics of time travel is based upon general relativity. If you’ve ever taken a physics course you might remember that the motion of objects is due to forces acting on them. That is, by pushing or pulling on them—either directly or by gravitational or electric fields—you can cause them to move. This is Newton’s physics, where objects fall because a gravitational force acts upon them.

But Einstein had a different way of looking at things. Through his theory of general relativity, Einstein demonstrated that gravity occurs because matter and energy distort space and time. For example, the mass of the Earth curves space around it. The motion of anything near the Earth, such as a satellite, is changed because of this spatial curvature, as if there were a force of gravity acting on it. Since space and time are connected, the mass of the earth also distorts time, which means a clock on the satellite ticks at a slightly different rate than a clock on the Earth. This effect on a satellite’s time is small (on the order of microseconds) but it is a measurable effect. In fact the satellites of the global positioning system have to take this time distortion into effect in order to work properly. If you’ve ever used a GPS receiver to find your way, you’ve counted on Einstein being right.

Although the mass of the Earth really does distort time, it doesn’t allow you to create a time machine. The clocks in satellites tick at different rates because of their motion around the Earth, but they always still tick forward. It is only the rate of their ticking that changes relative to other clocks on Earth. According to general relativity you can change the rate at which time flows but you can never quite stop time completely, and you can never cause your clocks to tick backwards. If that’s the case, it would seem that a true time machine—one that would let you travel into the past—is impossible.

But general relativity leaves the time-travel door open just a little. In Einstein’s theory time is connected to space, which means time can be bent in ways similar to the way space is bent by the Earth’s mass. So in principle time can be bent into a loop in such a way that it connects with its own past. If you found yourself in such a wibbly-wobbly space-time it would be possible to meet your younger self. Such a loop of time would be an actual time machine. As strange as this seems, there are examples of these time loops—what physicists call closed timelike curves (CTCs)—in general relativity.

One place where CTCs appear is in a solution to Einstein’s gravity equations known as the Godel Universe. This is a general relativistic description of a universe with an inherent rotation to it. If this were an accurate description of our universe then we would observe a rotational effect where distant galaxies are not only moving away from us, but also appearing to rotate about us. We don’t see any cosmic rotation among distant galaxies, so the Godel model doesn’t apply to our universe. While it is an interesting model, it is non-physical.

However CTCs also appear inside a rotating black hole. In general relativity, a rotating mass causes space and time to swirl around it a bit. This effect is known as frame dragging, and it has been observed experimentally by a satellite known as gravity probe b. Near a rotating black hole this effect is larger, but still not large enough to make a time machine. However, once you are within the event horizon of the black hole there are CTCs. This would imply that a time machine might be possible inside a black hole. The problem is that though they might exist inside a black hole, you would have to go into a black hole to travel in time, and once inside the black hole you would be trapped there forever. You couldn’t travel to this cosmic time machine, go into the past, and arrive back on Earth in the 1700s. The other problem is that just because general relativity works outside a black hole doesn’t mean it applies inside a black hole. The matter inside a black hole is so small and dense that quantum mechanics and particle physics comes into play, and we don’t have a solid understanding of quantum gravity. There might be something that prevents CTCs from forming inside a black hole.

Most physicists figure this must be the case, because CTCs create all sorts of problems with traditional physics. For example, CTCs can violate the principle of causality (basically cause and effect). This is popularized by the so-called grandfather paradox. Suppose you have a time machine, travel to the past, and accidentally kill your grandfather before he has a chance to woo your grandmother. By preventing their offspring you have prevented your own existence. But that means you couldn’t have travelled back in time, so you couldn’t have killed your grandfather. But that means you didn’t kill your grandfather, which means you were born, which means you did kill your grandfather, which means…

So what would really happen in this case? The answer is unclear, because such a time loop violates causality. The cause and effect contradict each other. In many science fiction stories this is solved by simply declaring that history rewrites itself, or that there are parallel timelines and such. We’ll look at parallel universes later, but this doesn’t solve the problem. The CTCs that general relativity allows exist in a single universe. Following the physics, we can’t simply invoke parallel universes to solve a tricky problem.

One possible solution is to impose what is called the “self-consistency” principle. This requires that any “time machine” example must be self consistent. So the grandfather paradox mentioned above is forbidden because it is not self-consistent. What would be allowed is for you to go back in time and wound your grandfather. While in the hospital he meets a kindly doctor who turns out to be your future grandmother. So your trip back in time caused your grandparents to meet, which allowed you to be born. Perfectly self consistent.

But this solution doesn’t prevent every problem. Suppose when you were 16 a stranger gives you a book. As you read through the book you find it is a set of instructions for building a time machine. It even includes all the background physics necessary to make it work. You go to college, study physics, and your doctoral dissertation is on the physics of time travel (which you got from the book). This groundbreaking work wins you the Nobel prize, and with the prize money you build a time machine, travel back in time and present your younger self with the book on time travel you once received… from yourself.

This is self consistent, but we seem led to ask where the book came from. Yes, you got it from yourself, but that doesn’t seem to be a satisfying answer. Where did the knowledge of time travel originate? The only answer is that the book is itself a closed timelike curve. It doesn’t have an origin. It just is.

Various theories have been proposed to provide a more satisfying answer to examples such as this. They invoke aspects of quantum mechanics, thermodynamics, entropy, information theory, and on and on down the rabbit hole. None of these models provide a completely satisfying description of time travel that makes sense. This is why most physicists figure time travel is impossible. There isn’t a clear way for it to make physical sense. Stephen Hawking went so far as to propose a chronology protection conjecture, which proposes that all macroscopic CTCs are physically impossible.

Still, there are a few physicists who think time machines are possible. For example, Ron Mallett at the University of Connecticut has found a solution to general relativity that allows for CTCs without an event horizon. What Mallett has shown is that light can curve space and time in the same way as mass. By creating a rotating ring of laser light it is possible to distort space and time in a way similar to the way it is distorted by the rotating mass of a black hole, but without the black hole. This, he argues, opens the door to the possibility of creating a time loop you could step into. Critics have pointed out that Mallet’s solution still contains a singularity, so it isn’t a valid physical solution, but Mallett argues the singularity in his solution is an artifact that doesn’t affect the physics.

Even if Mallett is right, his time machine would not allow you to travel anywhere in time. The CTCs could only form in the span of time in which the time machine existed. So you can only go back as far as the moment the time machine was turned on, and you could only travel from the future in which it was still on. In other words, if you wanted to travel 10 years back in time, you’d have to turn on your time machine, keep it running continuously for 10 years, so that you could climb into the machine and arrive when you started. To go back to the future you’d simply have to hang around for another 10 years.

Of course the real question is whether it is possible to distort space and time strongly using only laser light, and whether that distortion could be made into a time machine. Mallet has proposed an experiment to test his model, but so far it hasn’t been performed. Until that happens (and succeeds) time travel is still very hypothetical.

In the end, time will tell.

Tomorrow: Warp Drive. NASA is rumored to be working on it, does that make it so? Find out tomorrow.

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Today is March 14, which many celebrate as Pi Day since the month and day mark 3.14, which is approximately pi.It is also Albert Einstein’s birthday, so it seems fitting to ask whether pi can exist in a universe as Einstein described it.  Just for fun, I’m going to outline why the answer is no, and then explain why that answer is wrong.

The value of pi (3.14159…) is defined as the ratio of the circumference of a circle to its diameter.  But in a physical universe where (as Einstein demonstrated) space is curved, the ratio of circumference to diameter isn’t pi.  For example, if you drew a circle around the Earth, the ratio of circumference to diameter would actually be a little less than pi.  This is because the mass of the Earth curves space around it, making the diameter of your circle a bit longer than it should be.

Geometry of curved space. Credit: The Airspace

This is actually a way you could define a region of space as being curved.  Draw a circle around a region of space, find the ratio of circumference to diameter, and if the value is less than pi then that region of space is curved.  The smaller the ratio, the more strongly that region of space is curved.  If you drew a circle around a black hole, its diameter would be infinite, so the ratio would be zero.

So if we define pi as the ratio of circle’s circumference to diameter in physical space, then pi would actually have lots of values depending the curvature of space around the circle, and none of them would be 3.14159…

Of course that isn’t how pi is defined.  The circumference/diameter definition applies for a mathematically ideal circle, where space isn’t curved.  It can also be defined in other ways, such as an infinite series pi = 4 – 4/3 + 4/5 – 4/7 + …  The geometry definition is just a simple (and perhaps the oldest) one. The key point is that pi is a mathematical concept, not a physical one. 

So even though physical space is actually curved, pi still exists and has the value we all know and love.  So celebrate the day, because it is a perfect excuse to have a slice of pie. 

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One of the predictions of general relativity is that the motion of large masses, such as a binary system of black holes or neutron stars, should produce gravitational waves.  When most people think of waves they typically think of water waves. Drop a pebble in a calm pond and you can watch the waves spread out over the surface of the water.  Gravity waves are similar, but are ripples in the fabric of space and time itself.  There is a project looking for these gravitational waves, known as the Laser Interferometer Gravitational-Wave Observatory, or LIGO.

We actually have a great deal of evidence for gravity waves.  For one, they are a consequence of general relativity, which has passed every observational test we’ve made of it so far.  We also have indirect evidence of gravitational waves through an effect known as inspiralling.  When two stars orbit each other, they produce gravitational waves. The gravity waves in turn take away some of the energy from the binary system. This means that the two stars gradually move closer together, or inspiral. As the two stars inspiral, their orbital period gets shorter (because their orbits are getting smaller).  We have observed this effect with a pulsar orbiting a companion star, and the result is exactly that predicted by gravitational waves.

A schematic of the LIGO experiment.
Credit: LIGO/MIT

Still, we’d like to detect gravitational waves directly, which is where LIGO comes in.  Because gravitational waves create ripples in space, the distance between objects shift slightly as a gravitational passes by.  This means by making precise measurements of the relative positions of objects, we can in principle detect these waves.  The difficulty is that even gravity waves produced by binary black holes will only cause small distortions of an experiment here on Earth.  This is why LIGO uses laser interferometry along a beam 4 kilometers long.  Even then, the expected distortion would be about a billionth of a nanometer.

So far, the LIGO project hasn’t had a confirmed detection of gravity waves, but it is hoped that upgrades to the project currently under way will allow the project to be successful.

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Previously, I talked about how motion is relative, and how relative motion affects our measurement of space and time.  We ended with a very important aspect of physics:  space and time are not absolute, but rather they depend upon your point of view.  Last time, we saw how space and time can be affected by motion.  Today, we’ll look at what happens when gravity gets involved.

In our everyday lives, gravity is the pull of the Earth holding us to its surface.  We think of it as a force (a push or pull) that acts on us and everything around us.  But gravity behaves very differently from other forces.  Suppose I were to push a tennis ball and a bowling ball with equal force.  The tennis ball would move much faster because it has less mass.  If, however, I drop the tennis ball and bowling ball, they fall at exactly the same rate.  Gravity pulls pulls them in such a way that their masses don’t matter.  In fact, under gravity, everything falls in the same way (a property known as the equivalence principle).  As a result, free fall feels exactly like no gravity at all.  This is why astronauts on the international space station appear to be floating, when in fact they and the space station are all in free fall as they orbit the Earth.

By the principle of general relativity, free fall under gravity and the absence of gravity feel the same because they are the same.  The idea seems ridiculous because we can see the space station orbit the Earth, so something must be pulling it.  But remember that space and time are not absolute.  The astronauts don’t feel any force, and their viewpoint is just as valid as ours.  The solution to this paradox is to recognize  that space and time are actually warped by the mass of the Earth.  This warping of spacetime means that the path of the space station is bent, giving the appearance of a force acting on it.  I’ve written about this in more detail before.

Because of this warping of space and time, time as measured on the Earth differs slightly from time as measured on the space station.  This difference is very small. So small that if we ran a clock on Earth for a billion years, the warping of time by Earth’s mass would only slow it by about a second.  This difference only matters when you are making precise measurements, such as when using the GPS in your phone to find the nearest coffee shop.

For objects with much larger mass, the difference can becomes significant.  As an example, consider the extreme case of a black hole.  If you were to fall into a black hole, how long would it take you to reach the event horizon?  Of course that depends on your point of view.  In the figure below, I’ve plotted radial distance from the black hole as a function of time.  For the red line, the time is that of the person falling into the black hole.  For the black line, the time is that of a person watching the fall from a safe distance.

You can see that something interesting happens.  For the person falling into the black hole, the event horizon is reached (indicated by the dotted line) at around the 30 mark.  But from the outside observer’s view, the event horizon is never reached, but rather the person gets ever closer at an ever slower pace.  The outside observer sees the time of the falling friend get slower and slower as the black hole warps spacetime more and more.  The falling explorer doesn’t experience that slowdown, and so he reaches the event horizon in a finite time. Of course once our explorer crosses the event horizon, he can never leave the black hole.  Space and time have become so warped at the event horizon that it traps anything that crosses the line.

So what happens to light in all this?  Both our outside observer and our free falling explorer still measure the same speed of light, but the difference in observed times means they disagree on a light’s color.

But we’ll look at that next time.

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If you’ve ever watched water drain from a bathtub, you’ve seen that it doesn’t flow into the drain in a straight line, but rather swirls around the drain.  Contrary to popular belief, this is not due to the rotation of the Earth but rather random currents in the water.  The reason the spiral forms is because it is self-reinforcing. Water near the drain spirals a bit due to a random current, which drags the water behind it slightly in the same direction.  Over time, the motion builds up until you have a rapid spiral around the drain.

There is a similar effect with space and time.  I’ve talked before about how gravity is due to a curvature of space and time. The presence of mass bends space around it, and the resulting curvature means that objects follow curved paths rather than straight ones.  As a result, an object’s motion near a large mass like the Earth looks as if it is due to a force, which we call gravity.

It turns out that the rotation of a mass also distorts space and time.  For example, as the Earth rotates, it drags the nearby space along with it (an effect known as frame dragging).  Just like the drain spiral, this effect builds up, and as a result, space spirals a bit around the Earth.  You have to be a bit careful with this comparison.  Spacetime doesn’t “flow” the way water does, but the spiral effect is somewhat similar.

Near the Earth, this frame dragging is very small, but it can be measured through an effect known as the Lense-Thirring effect.  Basically, you put a gyroscope in orbit and see if its axis of rotation changes.  If there is no frame dragging, then the orientation of the gyroscope shouldn’t change.  If there is frame dragging, then the spiral twist of space and time will cause the gyroscope to precess, and its orientation will slowly change over time.

We’ve actually done this experiment, and you can see the results in the figure below.  The black line represents the change in orientation over time, and the red line is the predicted change via the Lense-Thirring effect.  As you can see, they agree very well.

So the next time you watch water circling the drain, you will know that a similar effect occurs with space and time itself.

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