Albert Einstein is easily one of the most brilliant physicists who ever lived. His theories of general relativity changed our understanding of the cosmos, as did his work on quantum theory. But his genius has also led many to hold him up as a poor stereotype of science. The lone genius who ignores the science of his day to overturn everything with a simple brilliant theory. He’s become the icon of every crackpot who feels compelled to send emails to scientists about their idea that will revolutionize science if we only take the time to listen (and work out all the math for them). But as revolutionary as Einstein’s ideas were, they weren’t entirely unexpected. Other scientists had similar ideas, and developed similar equations. Take, for example, Einstein’s most famous equation, E = mc². 

The equation appears in Einstein’s 1905 paper “Does the Inertia of a Body Depend Upon Its Energy Content?“, and it expresses a fundamental connection between matter and energy. Energy was long known to be a property of matter in terms of its kinetic motion, heat and interactions, but Einstein’s equation proposed that matter, simply by having mass, has an inherent amount of energy. It allowed us to understand how radioactive particles decay and how stars create energy through nuclear fusion. But the idea had been proposed by others before.

Like Einstein, J. J. Thompson wondered about the connection between light and matter. He thought that electromagnetism was more fundamental than Newton’s laws of motion, and tried to figure out how mass could be created by electric charge. In 1881 he showed that a moving sphere of charge would create a magnetic field, and this caused a kind of drag on its motion. This acts as an effective mass of the charge. Thompson found that the electromagnetic mass of the electron is given by m = (4/3) E/c², which is surprisingly close to Einstein’s equation. Thompson’s derivation was rather cumbersome, but other researchers found the same result with more elegant derivations.

Thompson’s model was not without it’s problems. For one, it only applied to objects that have charge, and only when they are moving. Another problem came from Thompson’s assumption of a uniform sphere of charge. If an electron were an extended sphere of charge, some kind of force or pressure must keep the electron from flying apart. This pressure would obviously have some energy. This led Henri Poincaré to propose non-electromagnetic stresses to hold the electron together. When he calculated the energy of these stresses, he found it amounted to a fourth of an electron’s total mass. Thus, the “actual” mass of the electron due to its electric charge alone must be  m = E/c². Poincaré’s paper deriving this result was published in June of 1905, just a few months before Einstein’s paper.

Although the equation is often attributed to Einstein’s 1905 paper, Einstein didn’t actually derive the equation from his theory of relativity. The paper is only two pages long, and only shows how the equation can arise from approximations to relativity. It’s more of a proof of concept than a formal derivation. It took other scholars to definitively prove that the equivalence between mass and energy is a consequence of special relativity.

None of this detracts from Einstein’s brilliance, but it does demonstrate that even radical ideas in science rarely come from a single individual. The ideas of Thompson,Poincaré, and others were on the right track, as were the ideas of Einstein. Over the decades the scientific evidence we’ve gathered has further confirmed Einstein’s theory as the best representation of reality. And in the end it’s the best models that win, regardless of who first thought of them.

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One of the big mysteries of modern cosmology is the fact that the Universe is so uniform on large scales. Observations tell us our Universe is topologically flat, and the cosmic microwave background we see in all directions has only the smallest temperature fluctuations. But if the cosmos began with a hot and dense big bang, then we wouldn’t expect such high uniformity. As the Universe expanded, distant parts of it would have moved out of reach from each other before there was time for their temperatures to even out. One would expect the cosmic background to have large hot and cold regions. The most common idea to explain this uniformity is early cosmic inflation. That is, soon after the big bang, the Universe expanded at an immense rate. The Universe we can currently observe originated from an extremely small region, and early inflation made everything even out. The inflation model has a lot going for it, but proving inflation is difficult, so some theorists have looked for alternative models that might be easier to prove. One recent idea looks at a speed of light that changes over time.

The idea that light may have had a different speed in the past isn’t new. Despite the assertions of some young Earth creationists, we know the speed of light has remained constant for at least 7 billion years. The well-tested theories of special and general relativity also confirm a constant speed of light. But perhaps things were very different in the earliest moments of the cosmos. This new work looks at alternative approach to gravity where the speed of gravity and the speed of light don’t have to be the same. In general relativity, if the speed of light changed significantly, so would the speed of gravity, and this would lead to effects we don’t observe. In this new model, the speed of light could have been much faster than gravity early on, and this would allow the cosmic microwave background to even out. As the Universe expanded and cooled, a phase transition would shift the speed of light to that of gravity, just as we observe now.

Normally this kind of thing can be discarded as just another handwaving idea, but the model makes two key predictions. The first is that there shouldn’t be any primordial gravitational waves. Inflation models predict primordial gravitational fluctuations, so if they are observed this new model is ruled out. But it might be the case that primordial gravitational waves are simply too faint to be observed, which would leave inflation in theoretical limbo. But this new model also predicts that the cosmic background should have temperature fluctuations of a particular scale (known as the scalar spectral index n_s). According to the model, n_s should be about 0.96478. Current observations find n_s = 0.9667 ± 0.0040. So the predictions of this model actually agree with observation.

That seems promising, but inflation can’t be ruled out yet. This current model only explains the uniformity of the cosmic background. Inflation also explains things like topological flatness and a few other subtle cosmological issues this new model doesn’t address. The key is that this new model is testable, and that makes it a worthy challenger to inflation.

Paper: Niayesh Afshordi and Joao Magueijo. The critical geometry of a thermal big bang.  arXiv:1603.03312 [gr-qc]

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With the detection of gravitational waves, we’re now able to observe black holes as they merge. We’re already able to determine the mass and rotation of the merging black holes, but gravitational waves might be able to settle the fierce debates over the conflict between black holes and quantum gravity. 

The signal of a classic black hole merger. Credit: LIGO

The LIGO signals we have so far show the classic properties of a black hole merger. Two orbiting black holes create a regular pattern of gravitational waves that gradually increase in frequency. Eventually the two masses merge, creating a chirp and “ringdown” as the newly formed black hole settles into a stable state. According to general relativity, once the new black hole settles down, it should no longer emit gravitational waves. That’s because a single black hole simply has the properties of mass and rotation (and theoretically charge), but nothing else. This is known as the “no-hair theorem.”

While relativity is a well-tested scientific theory, it runs into problems when you try to incorporate it into quantum theory. The foundational principles of quantum mechanics are very different from that of general relativity, so the two models don’t play well together. Since we have reasons to presume the ultimate theory of gravity is a quantum theory, there has been a lot of research on what such a theory would look like. When we try to develop a quantum version of black holes, weird paradoxes arise. One of them is known as the firewall paradox, where quantum fluctuations would create intense heat near the event horizon of a black hole, though this would seem to violate the equivalence principle, upon which relativity is based. Another is the information paradox, where knowledge of an object disappears when it crosses the event horizon, which violates a fundamental principle of quantum theory. Theorists have developed possible resolutions to these paradoxes, but there hasn’t been any way to test them. We can’t travel to a black hole to look at one up close.

Secondary echoes could be evidence of quantum effects. Credit: Jahed Abedi, et al.

But a new paper argues that LIGO might actually be able to test these ideas. While a classical black hole should be silent after the merger, quantum interactions near the event horizon could create small secondary chirps. These chirps should be regularly spaced, and their timing could put constraints on various quantum models. Interestingly, the team looked at data from the three black hole mergers that have been publicly announced, and found some evidence of these secondary signals. The statistics isn’t particularly strong, so it can’t be confirmed as a real effect, but that will change as we observe more black hole mergers. If these secondary chirps keep showing up, then we might be able to test the quantum behavior of black holes.

It’s an interesting result, and it demonstrates the power of gravitational astronomy.

Paper: Jahed Abedi, et al. Echoes from the Abyss: Evidence for Planck-scale structure at black hole horizons.  arXiv:1612.00266 [gr-qc] (2016)

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As we’ve recently seen, the cosmos is much larger than we’ve thought, with more than 2 trillion galaxies in the observable universe. Actually observing many of the most distant and faint galaxies is a real challenge, but more of them are being detected thanks to a trick that relies on relativity. 

The more distant a galaxy, the more dim it can appear. This is due in part to the fact that the apparent brightness of an object decreases with the square of its distance (known as the inverse square law). For galaxies, this effect is even more dramatic due to cosmic expansion, which further dims objects billions of light years away. Because of this dimming, small dwarf galaxies can be difficult to observe. This is a problem because in the nearby universe dwarf galaxies are the most numerous, so we could be missing a lot of galaxies when we look across great distances.

But it turns out that relativity can help, thanks to an effect known as gravitational lensing. The path of starlight can be deflected by the gravity of a nearby mass, as Arthur Eddington first demonstrated in 1919. This means that light from a distant galaxy can be deflected and focused if a closer galaxy is between us and it. Through gravitational lensing, the distant galaxy can appear brighter than it would otherwise, just as a glass lens can magnify and brighten a distant star.

Recently, a team used this method to observe faint dwarf galaxies at a redshift between z = 1 and z = 3.  We see these galaxies as they were when the Universe was 2 to 6 billion years old, which is a period of peak star formation. They found that dwarf galaxies were most abundant at the greatest redshifts, and thus the earliest period. Since most of the stars in these early dwarf galaxies were hot and bright, they flooded the Universe with ultraviolet light, driving the reionization period of the early Universe.

When the James Webb telescope launches in 2018, we should have an even better view of these dim and distant galaxies. Until then, gravitational lensing will help us explore this critical period of galaxy formation.

Paper: Anahita Alavi, et al. The Evolution Of The Faint End Of The UV Luminosity Function During The Peak Epoch Of Star Formation (1<z<3). The Astrophysical Journal, Volume 832, Number 1 (2016)  arXiv:1606.00469

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One of the most popular questions asked about relativity concerns what would happen as an object approaches the speed of light. If it were moving fast enough, would it become a black hole? The same question could be asked another way: are you a black hole? The answer to the second question is obviously no. So is the answer to the first question. Confused? 

The basic argument is as an object approaches the speed of light from our perspective, three things happen. It’s time appears to slow down (time dilation), it appears to get shorter along its direction of travel (length contraction), and its mass appears to increase (relativistic mass).

These are all consequences of relativity and the fact that light has the same speed in all frames of reference. Relativity also says that a large enough mass in a small enough volume becomes a black hole. So it seems reasonable that an object near the speed of light should become a black hole.

If that were true, you must be a black hole.

Here’s why: the Universe is expanding. It’s not just that galaxies are racing away from us, space itself is expanding. This means that the more distant an object is from us, the faster it is moving away from us. There are distant galaxies moving away from us at nearly the speed of light. That means we are moving away from them at nearly light speed, so we should appear to be a black hole to them.

But the thing about black holes is that you either are one or aren’t one. A black hole’s event horizon must exist in all frames of reference. So if you aren’t a black hole in your frame of reference (and you’re not) then you’re not a black hole in any frame of reference. So a fast moving object does not become a black hole.

So what gives? It turns out the original argument is flawed. It’s true that an object’s relativistic mass does increase with speed. This means they are increasingly difficult to push, making it impossible for them to reach the speed of light. But everything is relative. From our perspective we have to keep pushing harder. From the object’s perspective our pushes keep getting smaller. As far as the object is concerned it’s mass hasn’t changed. So naturally it doesn’t become a black hole.

Just as you aren’t a black hole because you’re speeding away from distant galaxies. An object speeding away from us doesn’t become a black hole.

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The Earth rotates on its axis. If you watched the Earth from the Moon, for example, you would see the oceans and continents drift past. The surface features of Earth would make it very clear that the Earth is rotating. The same is true for any object. If you were to spin a ball, for example, the texture of the ball’s surface would make it easy to see the ball is rotating. But what if the ball were perfectly smooth? Not just kind-of smooth, but so smooth its surface was absolutely uniform. In that case a rotating ball would look just like a stationary one. So how could you tell if it was rotating? 

This puzzle of rotation is more troublesome than you might think, and it strikes at the heart of some very basic physics. In physics terms, it raises the question of what constitutes an inertial frame of reference. Basically, if you were in an inertial frame of reference, you wouldn’t feel any forces pulling on you. If you were floating freely in deep space, for example, you would be in an inertial frame. Galileo used the idea of inertial frames to explain why objects seem to keep moving even when nothing is acting on it. The motion of an object is relative, Galileo argued, and an object moving at a constant speed is in an inertial frame, just as if it were sitting still.

Newton agreed with Galileo to a point, but he struggled with the idea of rotation. As an example he proposed a theoretical bucket experiment, where a perfectly symmetrical bucket was filled with water. If the bucket is rotating, the water should flare out a bit, making a dip in its surface. If it isn’t rotating the water’s surface would be flat. Since the bucket and water are perfectly symmetrical, why should there be a difference? For Newton the answer was that there must be some universal inertial frame. There is a particular absolute frame of reference against which everything can be said to move. When the bucket rotates, it rotates relative to the cosmic inertial frame, and thus the water flares out a bit.

While this seems perfectly reasonable, it was problematic for Einstein. In Einstein’s relativity there shouldn’t be any absolute frame of reference, since all reference frames can only be observed relative to each other. What would happen, Einstein wondered, if you were floating in deep space and saw the stars rotating around you. Since reference frames are relative, how would you know that you were rotating and the universe wasn’t? To address this issue Einstein invoked what he called Mach’s principle. It was originally proposed by Ernst Mach, and argued that an inertial frame is determined by the overall distribution of matter throughout the cosmos. Since all the stars in the Universe appear to be moving around you, it must be you that is rotating, and not the other way around. This all might seem like theoretical navel gazing, but it has real consequences for astrophysics, particularly for objects like black holes.

A black hole is an object so dense that not even light can escape it. One of the properties of black holes is the no-hair theorem, which means that no matter what shape a mass had before collapsing into a black hole, the resulting black hole (technically its event horizon) will be perfectly spherical. So in a very real sense a black hole is an example of a perfectly smooth sphere, rotating or not. So how do we know whether a black hole is rotating? Without any surface features to observe, we instead have to rely upon something known as momentum.

The momentum of an object is a measure of its motion. In Newtonian physics the linear momentum of an object is the product of its mass and velocity. If an object is rotating, it has an angular momentum determined by its rotational speed and how mass is distributed in an object (moment of inertia). In Einstein’s relativity things are a bit more complicated, but objects still have a linear and angular momentum. What makes these quantities useful is that momentum is conserved, meaning that whatever momentum a system has, it always has. So if a rotating mass collapses into a black hole, the angular momentum it had before collapsing must still exist for the black hole. Since a rotating black hole must be spherical thanks to the no-hair theorem, how do we distinguish between a rotating and non-rotating black hole? It turns out angular momentum twists space.

In general relativity gravity is not a force, but a curvature of spacetime. This means that gravity affects the overall structure of space and time. According to Mach’s principle, the overall structure of space and time must be inertial, and any rotation (angular momentum) must be relative to the global structure of spacetime. This means that angular momentum must twist spacetime near a rotating mass. As a result, any object near a rotating black hole wouldn’t simply fall straight in, but would appear to spiral around the black hole as it falls toward it. This effect is known as frame dragging, and we’ve actually observed it in Earth orbit. Frame dragging is how we can distinguish a rotating from a non-rotating black hole.

So long after a rotating mass collapses into a black hole, and long after all that matter is hidden behind the black hole’s event horizon, the angular momentum of the mass still leaves its mark by twisting space around the black hole.

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Black Holes are where God divided by zero, so the saying goes. As short sayings go, that’s not a bad description of a black hole’s singularity, and it gives one a good idea why singularities are so problematic in physics.

In my last post I wrote about the cosmic censorship conjecture, and how it might be violated in hypothetical 5-dimensional black holes. I didn’t delve too deeply into the conjecture itself because there are actually multiple versions of the conjecture. The weak cosmic censorship conjecture is basically as I stated, that a singularity must be enclosed by an event horizon. It’s a bit more subtle than that, since an event horizon isn’t a local object in space, but rather a global structure in spacetime. So the formal definition is that a singularity can’t be seen by an observer sitting far away from a black hole (what is called null infinity). If you were close to a black hole you might catch a glimpse of a singularity, but the structure of spacetime is such that you couldn’t tell someone far from a black hole what you saw.

The upshot of all this is that anybody reasonably distant from a black hole could never see a singularity or interact with it. Since it can’t effect things outside a black hole, we don’t have to care about how it would affect things. As long as Pandora’s box stays closed, there’s no need to worry. As I mentioned in the earlier post, there are theoretical examples in general relativity where a singularity can be seen by a distant observer, but none of them seem likely to occur in a real situation.

The strong cosmic censorship conjecture takes a different approach. This is where the “dividing by zero” idea comes in. If you were to divide a number by zero, you might think the answer is infinity. After all, zero can go into a number like 1 an infinite number of times. But the actual answer is undefined. The formal reason has to do with the subtleties of mathematics, but for our purposes suppose we first divided by a very small number. For example, if we divide 1 by 0.01, the answer would be 100. If we divided 1 by 0.0001 we get 10,000. If we kept dividing by an ever smaller number, our answer would get bigger and bigger. This seems to say that 1/0 is infinity, but suppose instead we divided 1 by -0.01. In that case the answer would be -100. Dividing by -0.0001 we get -10,000. That would make 1/0 negative infinity. Starting with a small negative number or a small positive number gets us to the same 1/0, so is the answer positive or negative? The ratio 1/0 is meaningless without knowing how we approached zero.

A singularity is similar to this in that it is indeterministic. If all you have is a singularity, you have no idea how it became a singularity. Likewise if a singularity were to interact with other objects in the universe, the outcome would be unpredictable. So the strong cosmic censorship conjecture proposes that general relativity must be deterministic. As a result, singularities must be excluded from interaction with the rest of the universe.

It turns out there are solutions to Einstein’s field equations that satisfy the weak conjecture but not the strong conjecture, and vice versa. By itself general relativity is not bound by either censorship conjecture. But general relativity is also perfectly fine with warp drive and time travel as well, and they don’t seem to be physically possible for reasons beyond relativity. So it’s likely that some physical process prevents these kinds of weird singularities from occurring.

Then again, we’ve been wrong before.

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LIGO announced that they have detected gravitational waves from a black hole merger. If verified it will be the ultimate confirmation of Einstein’s theory of general relativity. But what are gravitational waves, and why is their detection such a big deal? 

Water is perhaps the most common example of a wave. Drop a stone into a calm pond and you can see ripples expand over the surface of the water. This occurs because water is a fluid. When the stone is dropped into the water, it pushes the water around it out of the way. The water closest to the stone is pushed into the surrounding water, causing it to bunch up a bit. As the bunched up water tries to go back to its original state, it pushes into water further out. Thus a ripple moves through the water.

This is the basic process of any wave. A disturbance in a material affects the region around it causing the disturbance to move through the material. Thus we have ripples in water, sound waves in air, and even seismic waves from earthquakes. Since it takes time for the disturbance to move through the material, waves move through the material at a finite speed.

For a long time it was thought that waves could only move through a physical material, like sound through air. When it was shown in the 1600s that light travels at a finite speed, it sparked much debate over whether light was made of “particles” as Newton suggested, or whether it was a wave traveling through some material. In the early 1800s experiments showing light’s wave behavior seemed to answer the question in favor of waves. We now know light’s behavior is more subtle than that, but in the 1800s it seemed clear that light was definitely a wave. So there must be a material through which light propagates.

Light passing through two small slits creates an interference pattern, proving the wave behavior of light. Credit: Wikipedia user Jordgette.

The most popular candidate was known as the luminiferous aether. The difficulty with the aether was that it would have to be completely invisible and insubstantial to physical objects, so there was no way to detect it directly. The only evidence that the aether existed came from the fact that light travels in waves. Odd as the aether was, it clearly had to exist since waves always move through some material.

Then in the late 1800s it was found that the speed of light was always the same regardless of ones motion through the aether. This is a deeply un-wavelike behavior. If light really moved through the aether at a particular speed, the Earth’s motion through the aether should make the speed of light appear faster or slower at different times of the year. An unchanging speed of light meant our assumption about the aether must be wrong.

If the Earth moved through the aether, we could measure its effect. Credit: Wikipedia

In the early 1900s it was shown that light waves could be explained through special relativity. Instead of moving through a material, the energy fields of electricity and magnetism could be disturbed like a fluid. Light waves are thus waves of electromagnetic energy moving through space. Because physical objects are made of charged particles that have electromagnetic fields, this meant they could never travel through space faster than the speed of light. Relativity showed us that waves didn’t need a physical material to travel through. Waves could move through fields of energy.

But if physical objects couldn’t move faster than light, what about gravity? In Newton’s model of gravity, masses exert forces on each other instantly. As a result, energy could pass from one mass to another with infinite speed. It seemed odd that light energy could only travel at the speed of light while gravitational energy could travel instantly. This puzzle led Einstein to develop a general theory of relativity.

The basic idea of special relativity is that no frame of reference can be favored over any other. This allows the speed of light to be the same in all frames of reference, but it does so by making the behavior of space and time relative to the observer rather than an absolute background. Even the concept of “now” is relative. In general relativity the central idea is the principle of equivalence. Since all bodies fall at the same rate regardless of their mass, a body floating freely in space must be equivalent to a body falling freely. As a result, gravity is not a force between masses, but rather an effect of spacetime curvature. Under Eisntein’s model space and time become flexible and relative, and take on a fluid-like behavior. Masses moving through space should create disturbances in spacetime, just as running your hand through water creates ripples. If general relativity is correct, then there must be gravitational waves.

A visualization of gravitational waves. Credit: NASA

Over the years various tests of general relativity have confirmed the theory works, and so it has widely assumed that gravitational waves exist. But observing gravitational waves directly has been notoriously difficult. Even the strongest of gravitational waves would be extraordinarily weak, and since they are a warping of spacetime itself, effects such as the finite speed of gravity are impossible to measure. The best evidence we’ve had so far has been indirect evidence. In the 1970s observations of a pulsar orbiting another star found that it slowly spirals closer to its companion. According to relativity this is because gravitational waves radiate away from the binary system, causing it to lose energy and spiral closer together.

But without a direct observation of gravitational waves, there is the chance that general relativity could be wrong. We could, for example, come up with a model that gives us all the effects of Einstein’s theory without gravitational waves. It wouldn’t be as elegant as general relativity, but it would work. Gravitational waves are an absolute necessity for general relativity, and if they don’t exist the model is wrong. So even though we expect gravitational waves to exist, without proof there would always be a small bit of doubt about relativity.

That’s why we’ve been looking for gravitational waves for so long, and that’s why the result is so important.

This post originally appeared on Forbes.

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A fast radio burst (FRB) is a short burst of intense radio energy originating from outside our galaxy. We aren’t sure what causes FRBs, though the likely candidate is a white dwarf or neutron star falling into a black hole. They only last a few milliseconds, which makes them a challenge to study, but their brief duration may also allow us to test the limits of general relativity.

If relativity is wrong, then different wavelengths from an FRB should arrive at different times. Credit: Purple Mountain Observatory, Chinese Academy of Sciences

The foundational idea of general relativity is known as the principle of equivalence. On a basic level it states that two objects of different masses should fall at the same rate under the influence of gravity. The principle is necessary to equate the apparent force of gravity with a curvature of spacetime. So far all tests of the equivalence principle have confirmed it to the limits of observation, but there’s an interesting catch. Since relativity also states that there is a connection between mass and energy, the equivalence principle should also hold for two objects of different energy. Specifically, two beams of light with different wavelengths (and therefore different energies) should be affected by gravity in the same way.

We know that the path of light is changed by the curvature of space (an effect known as gravitational lensing), but the curvature also affects the travel time of light from its source to us (known as the Shapiro time delay). According to relativity, the amount of curvature and the time delay shouldn’t depend upon the wavelength of light. This means we can in principle use FRBs to test this idea.

Since FRBs only last milliseconds, they provide a sharp pulse of light at a range of frequencies. If relativity is correct, then the pulse we observe won’t be affected by gravity. If the equivalence principle is wrong, then shorter wavelengths of radio waves from the burst could arrive at a different time than longer wavelengths. We already see different wavelengths arrive at different times due to the interaction between the radio waves and the interstellar plasma in our galaxy, but we know from other observations how much that shift should be. The key is to test whether there is an additional shift not accounted for by standard physics.

Relativity is an extremely well-tested scientific theory, so I wouldn’t count on FRBs showing an energy-based effect, but it’s great that we could have yet another way to test our model. It’s a win-win, since we’ll either confirm our theory yet again, or we’ll discover something new to explore.

Paper: Y. F. Huang & J. J. Geng. Collision between Neutron Stars and Asteroids as a Mechanism for Fast Radio Bursts. arXiv:1512.06519 [astro-ph.HE] arxiv.org/abs/1512.06519

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In an earlier post I talked about the astronomical unit, and how it was standardized in 2012 because the old definition (the distance from the Earth to the Sun) was gradually increasing due to the Sun’s loss of mass. It turns out that’s not the completely correct story.

Using radar telemetry we can measure the astronomical unit to an accuracy of a few meters. In my earlier post I had stated the accuracy was 3 parts per billion, but that wasn’t quite right. In 2009 the IAU defined the astronomical unit to be 149,597,870,700 meters, with an uncertainty of 3 meters. Since the change in distance due to the Sun’s mass loss is only about 1.5 centimeters, it would seem an uncertainty of 3 meters is too large for the Sun’s effect to make a difference.

It turns out that analysis of telemetric data for the solar system seemed to point toward a change in the astronomical unit of about 15 meters per century, which is much larger than the effect of the Sun. But other observations haven’t confirmed such a drift, and so the result remains highly controversial.

So why did the IAU adopt a fixed standard for the astronomical unit? In the actual 2012 resolution, the possible drift due to the Sun’s mass loss is listed as one reason, but the main reason was the need for self consistent units in the framework of general relativity. The big problem is not the Sun’s mass loss, but the fact that (because of relativity) an astronomical unit when measured by a spacecraft orbiting Jupiter is different than one made when orbiting Earth. When all of our measurements were made from Earth, relativity didn’t play a big role. But we now have a flotilla of spacecraft across the solar system, so relativity is an issue.

So now the astronomical unit is 149,597,870,700 meters exactly by definition. The Earth’s distance from the Sun is pretty close to that, but your results may vary depending on where you are in the universe.

Paper: Krasinsky, G. A., Brumberg, V. A.  Secular increase of astronomical unit from analysis of the major planet motions, and its interpretation. Celest. Mech. Dynam. Astron. 90 (3–4): 267–288 (2004)

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While general relativity is an extremely well tested theory, we’re always looking for more precise ways to test it further. Either relativity will pass the test yet again or we’ll find evidence of something beyond relativity. But tests of general relativity are hard to come by, particularly for the most subtle effect of the theory, gravitational waves.

The best tests we have of gravitational waves is through binary pulsars. The first indirect evidence came from the Hulse-Taylor system, which consists of a pulsar orbiting a neutron star. Most of the systems we can use to test GR contain a pulsar orbiting another object such as a neutron star or white dwarf. But a system known as J0737-3039 consists of two pulsars. One pulses at a rate of 23 milliseconds, while the other at about 2.8 seconds. Their orbital period is only about 2.4 hours, so they are quite close to each other.

The regular radio pulses of a pulsar allow us to determine their motion with great accuracy, and since we can measure the motion of both pulsars we can test relativity with greater precision. While Hulse-Taylor system confirms relativity to within 0.2% of the theory, J0737-3039 allows for confirmation to within 0.04%. So far, general relativity still wins.

Paper: Michael Kramer. Experimental tests of general relativity in binary systems. 28th Texas Symposium on Relativistic Astrophysics, (2015)

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One of the predictions of special relativity is that the speed of light in a vacuum is a universal constant. This prediction has held up so well that we now use the speed of light to define part of the metric system. The first verification of special relativity is typically seen as the Michelson-Morley experiment, which demonstrated there wasn’t a luminiferous aether. But this experiment was actually done before Einstein proposed relativity, and so it wasn’t technically a prediction. It took two other experiments to completely verify Einstein’s model.

The Michelson-Morley experiment focused on determining the speed of the Earth through the aether. It wasn’t designed as a test of special relativity, and so it only tested that the speed of light was the same with different orientations. No matter which way you orient your device, the travel time back and forth along your experiment is the same. That’s certainly a prediction of relativity, but the theory goes further to claim that light speed is the same even if you’re moving at different speeds.

It took two other experiments to fully pin down the veracity of relativity. One, known as the Ives-Stilwell experiment looked at the time dilation effects of the model. In order for the speed of light to be the same in every reference frame, the clock of an experiment moving relative to you must appear to tick more slowly than that of an experiment sitting next to you. This effect is known as time dilation, and is one of the stranger aspects of relativity.

The Ives-Stilwell 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 experiment confirmed the Doppler shift just as relativity predicts.

But relativity also predicts that space and time are connected, so a time dilation must also create a change of apparent length (known as length contraction). In other words not only must the clock of a moving experiment appear slower, then length of the experiment must appear shorter. Ives-Stilwell confirmed the first part, but not the second. To do that took a different test known as the Kennedy-Thorndike experiment.

Schematic of the Kennedy-Thorndike experiment.

The Kennedy-Thorndike experiment is similar to the Michelson-Morley. A beam of light is split to travel along two different paths. The separate beams of light are then recombined to create an interference pattern. The main difference is that the path length of the two beams is radically different. Since (according to Michelson-Morley) the speed of light is independent of orientation, the travel time of each path is different. Since Ives-Stilwell verified time dilation, as the apparatus moves with Earth, the amount of time dilation along one path is different from the other. This would produce a shift in the resulting interference pattern unless the lengths of the two paths also contract as relativity predicts.

The Kennedy-Thorndike experiment found no apparent shift in the interference pattern. Combined with the results of Michelson-Morley and Ives-Stilwell, this confirms that the speed of light is constant, and time dilation and length contraction both occur in agreement with special relativity.

And that’s why relativity is the strangest theory we know is true.

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