Yesterday we had a school project to build a star. Today let’s go for extra credit and see about building a black hole.

As you might recall, building a hypothetical star was basically a matter of gathering enough matter together so that it collapsed under its own weight. With enough mass (about 80 – 90 Jupiter masses) the interior pressure became great enough to start fusing hydrogen into helium, thus lighting our star. The fact that matter will undergo nuclear fusion given enough pressure actually makes building a black hole more difficult than building a star.

The supernova remnant known as the Crab nebula.

One way we could try to build our black hole is to simply create a very massive star and wait. As a star undergoes nuclear fusion, hydrogen is fused into helium. Over time the density of the star increases and the star burns hotter. Eventually the pressure is high enough that helium is fused into elements like carbon, nitrogen and oxygen. Those elements are eventually fused into heavier elements. But fusing elements beyond iron is an energy losing game, so there comes a point where a star can’t produce enough heat and energy to keep itself stable. For large stars, this means they undergo a supernova explosion. Such an explosion rips the star apart, but it can also compress the core of the star so that it collapses into a black hole.

That’s easy enough, but it doesn’t guarantee that a black hole will form. Our star might rip itself apart completely, or the core might not collapse into a black hole. To be sure we make a black hole, we’ll have to take a more gradual route. Instead of a really large star, let’s start with a star similar to our Sun.

Like larger stars, our Sun-like star will fuse hydrogen into helium for most of its lifetime. As it ages, it will gradually grow more dense and hot, and over time will start fusing helium into carbon, nitrogen and oxygen. After about 10 billion years it will run out of hydrogen and helium to fuse, and it will start collapsing under its own weight. For a short period of time it will try to fuse heavier elements, and as a result it will swell into a red giant star. But a Sun-like star simply doesn’t have enough mass to explode as a supernova, so in the end all it can do is collapse. But it doesn’t collapse into a black hole.

Because our old star doesn’t have a way to produce heat and energy through fusion, it once again relies upon hydrostatic pressure, where the pressure of the star’s material is balanced against its weight due to gravity. But instead of being a gas of hydrogen, it’s now a plasma, where the atoms have split into a mix of electrons and nuclei. The electrons move around much more easily than the nuclei, so as the star collapses it is the electron pressure that balances against gravity. When this happens our star becomes a white dwarf.

The size of a white dwarf for a given mass. Credit: Wikipedia

To determine the size of our white dwarf, we just need to know how our plasma (technically known as a Fermi gas) behaves under temperature and pressure (its equation of state) which is quite well known. For a white dwarf about the mass of the Sun, it turns out to be about the size of Earth. It’s hard to imagine the entire mass of a star compressed into the volume of Earth, but we’ve observed lots of white dwarfs in our galaxy.

The pressure of electrons is extraordinarily strong, so in our simple model giving our white dwarf more and more mass will simply make it slightly smaller no matter how much mass we add. But in reality that’s not what happens. The more the Fermi gas of electrons is squeezed, the faster the electrons move. A white dwarf is so dense, and the electrons are moving so quickly that they approach the speed of light. This means we have to take relativity into account.

One of the important consequences of relativity is that mass and energy are related. As a result, gravity acts not just on the mass of an object, but also its energy. Usually the energy contribution is negligible, but when the electrons approach the speed of light their energy becomes much larger than their mass. The faster the electrons move, the heavier they get. So the very act of speeding up to create more pressure against gravity actually ends up helping gravity. There comes a point where the gravitational weight gained is more than the pressure the electrons can make, and the Fermi gas completely collapses. The point at which this occurs is about 1.44 solar masses, which is known as the Chandrasekhar limit. So we simply add mass to our white dwarf beyond that limit, and our white dwarf will collapse. But it still won’t collapse into a black hole.

Neutron star size vs black hole size.

In a white dwarf, the main pressure is caused by the electrons of the plasma, while the nuclei play a much smaller role. But when a white dwarf collapses the pressure of the nuclei is still there. The electrons collapse and merge with protons to create neutrons, and what remains is basically a Fermi gas of neutrons. The resulting neutron star is again a balance of pressure and weight, only this time it is neutron pressure vs gravity. The equation of state for neutrons is similar to that of electrons, so we can again determine the size of our neutron star given a particular mass. What we find is that a star of about 2 solar masses would have a diameter of about 15 kilometers, which is roughly the size of a small city like Rochester NY. Because neutrons are much heavier than electrons, we’d have to add much more mass to our star to approach the point where the neutrons collapse. But it turns out a black hole forms well before that point.

In a simple neutron gas model, the size of a neutron star would level off at about 10 – 15 kilometers even as we add more and more mass. But as we add mass, the density of the star increases to the point where a black hole must form. Technically, a black hole will form if your mass is within a sphere of a particular radius known as the Schwarzschild radius. For any given mass you can calculate this radius quite easily. The Schwarzschild radius of the Earth, for example, is about about a centimeter, so an Earth-mass black hole would be about the size of a large marble.

To create a black hole, we simply need to add mass to our neutron star until its Schwarzschild radius is larger than the radius of the neutron star. This limit is known as the Tolman-Oppenheimer-Volkoff (TOV) limit. In very simple models this limit is about 6 solar masses, but more realistic models put the limit at about 3 solar masses. We’ve observed a lot of neutron stars in the galaxy, and 3 solar masses appears to be about the limit.

So creating a black hole is much like creating a star. It’s a matter of getting enough matter into a small enough volume. That’s how nature does it, and it’s worked out pretty well so far.

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Suppose you wanted to build a star. Perhaps you’re part of an advanced Kardashev Type 3 civilization, and you need to make a star for your third grade science project. How would you go about creating a star?

On a basic level, it’s quite simple to build a star. Simply gather a star’s worth of gas and dust, let it collapse together under its own weight, and given enough time a star will form. This is how stars form naturally. But since we might be graded on this project, it would be nice to have an idea of how much mass we might need, and what the size and temperature of the resulting star might be.

The answer depends quite a bit upon what material you use, and how the material behaves under different temperatures and pressures (what’s sometimes called its equation of state). Since the most common material in the universe is hydrogen, lets keep things simple and assume we’ll build our star out of pure hydrogen. Since hydrogen has a very simple equation of state, it’s an easy matter to calculate what will happen as we build our star.

Size of planets by mass.

When we start to gather hydrogen together, two things will start to happen. The first is that the gravitational attraction between the hydrogen atoms will start to collapse the gas under its own weight. The second is that the pressure of the hydrogen will push back against the weight. Given time the gas will reach hydrostatic equilibrium, where the pressure of the gas is equal its weight, at which point you have a stable ball of hydrogen. This by itself isn’t enough to make a star. If you gathered a Saturn’s mass worth of hydrogen, what you would have is a Saturn-sized planet, not a star. The obvious solution is to simply add more hydrogen, which would make your planet bigger and bigger. Eventually your ball of gas would grow to a Jupiter-sized planet, and you just keep adding more hydrogen.

Peak size for a Jupiter-type planet.

But it turns out that something interesting happens when you keep adding more hydrogen to your planet. The more hydrogen you have, the more mass you have, and that means more weight. The gas is squeezed more strongly, and as a result it compresses. So if you double the mass of your Saturn-sized planet, you don’t get a planet twice as big as Saturn. You get a planet that is a bit bigger than Saturn, but with a higher density. For example, Jupiter is more than three times the mass of Saturn, but only about 15% larger in size. However Jupiter has an average density about twice that of Saturn.

As you keep adding more mass, your planet will get bigger up to about 3 Jupiter masses. At that point, the weight of your ball of hydrogen is so large that adding more actually makes the planet smaller. As a result, a planet 10 times the mass of Jupiter would be about the same size as Jupiter itself. This poses a real challenge for astronomers that study exoplanets. Just because a planet is Jupiter sized doesn’t mean it has a Jupiter mass. The same is true for smaller planets. A “super-Earth” planet a bit larger than Earth could be a rocky planet or a small Neptune-like planet depending upon what it’s made of.

Brown dwarfs vs stars. Credit: P. Marenfeld & NOAO/AURA/NSF

Once your ball of hydrogen reaches about 15 Jupiter masses it enters the regime of brown dwarfs. Adding more mass continues to make it smaller, but by this point the temperature of its interior starts to play a significant role. Our simple model of hydrostatic equilibrium isn’t enough. The hydrogen in the center is being squeezed so strongly that it heats up significantly. So while a brown dwarf is roughly the same size as Jupiter, it can be more than 10 times hotter. Adding more mass continues to shrink the brown dwarf slightly, but there comes a point where the interior becomes so hot that it raises the pressure of the hydrogen faster than the added weight can squeeze. Just as there is a maximum size for a planet, there is a minimum size for a brown dwarf. That minimum size is about 80% that of Jupiter, at which point a brown dwarf has a temperature of about 2000 K. Such a brown dwarf would look like a small, dim star.

Size vs mass for main sequence stars.

But a true star is one in which nuclear fusion occurs in its core. A star’s light and heat isn’t due to gravitational contraction, but rather the creation of energy by fusing hydrogen into helium. This starts to occur when your ball of hydrogen reaches about 90 Jupiter masses, which coincidentally is about the same mass as a minimum-sized brown dwarf. Now that you’ve made a star, adding more hydrogen just makes it larger and hotter. Because stars fuse hydrogen in their core, their size and density changes over time. But if we only consider stable, main sequence stars, then there’s a simple relation between mass and size. So you can just decide how much hydrogen to use, and calculate the size of your star.

Of course this is just a simple hypothetical stars. Real stars aren’t made purely of hydrogen, and depending on their origin and age they can behave very differently than our simple star. The details will be left as a homework exercise for the reader.

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What would the universe be like if the speed of light were infinite? It might seem like a silly question, since the speed of light clearly isn’t infinite, but questions like these are a good way to explore how different aspects of a physical model are interrelated.

For example, in our universe light is an electromagnetic wave. It not only has a speed, but a wavelength. If you think of a wave as an oscillation, then at infinite speed light would have no time to oscillate. So infinite light can’t be a wave. Since the wavelength of light determines its color, that would also mean it has no color. But it gets worse because in classical physics light is produced when electromagnetic waves cause the charges in atoms and molecules to oscillate. Without waves, atoms can’t be induced to emit light, the universe would be a sea of darkness.

But real light actually has both wave and particle aspects, so let’s suppose that for infinite light it’s just some kind of particle so we can still have light and color without all that meddling wave business. What else would change?

Relativity is an obvious choice. Einstein’s theory of relativity depends upon a finite speed of light. With an infinite light speed, all those fun things like time dilation are thrown out the window. So is Einstein’s most famous equation, E = mc². The main consequence of this equation is that matter can be transformed into energy and vice versa. It’s central to things like nuclear fusion, which powers the stars and creates the heavy elements. Stars could still be powered by gravitational contraction, but they would only last for a million years rather than billions of years. They also wouldn’t have any mechanism to explode as supernovae, so there would be no way to make new stars from old ones.

Since Einstein’s theory of gravity is a generalization of special relativity, it goes away too. Our model of the universe, beginning with a big bang and expanding through dark energy, depends upon Einstein’s theory. Without it the universe look very different. No dark energy, possibly no big bang.

Of course this is all just a game of pretend. If you made different assumptions about physical phenomena you would derive different effects. We have no way of knowing what an infinite light speed universe would really be like. But what this shows is just how interconnected different aspects of a physical model actually are. Any tweak to the model has consequences that can ripple into widely different areas, or even cause an entire model to collapse.

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There’s news on the web that cosmologists have proven the existence of negative mass. The news is based upon an article that recently appeared on the preprint arxiv, and has not yet been peer reviewed. The article in no way proves the existence of negative mass, but rather demonstrates the theoretical possibility of a form of negative mass within general relativity. In other words, it is an interesting “what if” paper rather than applied astrophysics.

Usually when we talk about the mass of an object we think of it as a basic property of an object. Mass is always positive in quantity, so negative mass must be the same thing but opposite. But in fact there are three types of mass than an object can have. Theres’s inertial mass, which determines how easy or difficult it is to move an object; passive gravitational mass, which interacts with a local gravitational field (and determines the weight of an object), and the active gravitational mass, which creates the gravitational field.  In this paper the focus is on negative active mass, so that it creates a repulsive gravitational field.

Various forms of negative mass are sometimes referred to as exotic matter, and they are often invoked to create science fiction things like warp drive and wormholes. Of course this leads to effects such as time travel and violations of relativity and causality.  For this reason (and the fact that we’ve never observed anything with negative mass), this kind of repulsive gravity matter is considered impossible.

In general relativity we often describe what is possible for matter by what are known as energy conditions. One of these is known as the dominant energy condition, which basically requires that matter doesn’t move faster than light, which is a big no-no in relativity. What the authors of this new paper have shown is that negative matter can be described in general relativity without violating the dominant energy condition. From this, they’ve found a solution within general relativity that looks like a negative mass object within an inflating universe. It is basically a “toy model” within general relativity.

This doesn’t in any way prove (or even suggest) that negative mass exists. It is interesting, though, because it models an inflating universe such as might have existed in the earliest moments after the big bang. It even makes a prediction, though not a very satisfying one. If the early universe were filled with a sea of both mass and negative mass, then gravitational waves could be damped. If the BICEP2 results are found to be false, and Planck also fails to detect primordial gravitational waves, then negative mass could explain how inflation could exist even though we don’t see primordial gravitational waves.

Of course, using the lack of evidence for gravity waves as evidence for inflation and negative mass is hardly scientific. But again, this is a “what if” paper, pushing the limits of theory to see what useful ideas might come out of it.

Paper: Saoussen Mbarek and M. B. Paranjape. Negative mass bubbles in de Sitter space-time. arXiv:1407.1457 [gr-qc] (2014).

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This week I’ve gotten a number of questions about various proposed models in astrophysics, such as the one about how anti-gravity could explain dark matter and dark energy. Or the one where dark matter is a result of quantum interference on a cosmic scale. Or the one where the cosmic microwave background is actually due to thermal turbulence rather than the big bang. There are lots of ideas that show up in the literature and in the press, so how do you judge the quality of a particular idea?

When I look at a paper, I usually start with broad claims and narrow down to the specific. Initially I look for any obvious red flags. For example, the claim that the cosmic background is thermal turbulence is a big flag. A central claim of the work is that the big bang and all the related physics (redshift, cosmic inflation, etc.) are all wrong.  As I’ve written earlier, there is a great deal of observational support for the big bang. You don’t get to be a robust scientific theory without strong evidence, so a paper claiming a robust theory is fundamentally wrong better have some Nobel prize level evidence.  In this case, the paper makes broad claims but only cites minor observations that the author feels agrees with their revolutionary model. So it is pretty clear the work is unsubstantiated.

The “broad claim” approach is often made by so-called “crank” science, where a revolutionary new approach is proposed that is obviously correct. Since extraordinary claims require extraordinary evidence, they are also the easiest to dismiss. The response is often to accuse “establishment” science as being closed minded, or not willing to learn their new and radical model. But as we’ve seen from the recent BICEP2 drama, even a skilled team of researchers studying well accepted models can overstate their results.  Pointing out obvious flaws in a model isn’t being closed minded, it is actually treating the work scientifically.

The other two papers look at effects attributed to dark matter. They don’t make claims that sweep away established physics. So the next step is to see if they introduce any “new” physics. The anti-gravity paper does this by asserting that virtual particles in empty space could induce an anti-gravity effect. Like an earlier paper looking at a difference in the speed of light, this paper treats virtual particles as real ones, which is a contentious approach. In this paper they go further and claim that matter and antimatter gravitationally repel each other.

This is an idea that has been looked at before. There have even been recent experiments trying to determine if antimatter “falls up” as it were. So far the results are inconclusive, but it is generally thought that antimatter will fall just like matter. If it doesn’t, that would have dire consequences for established models such as general relativity.  So this paper depends upon new physics for which there is no evidence, which puts it on weak ground. But the authors also propose an experimental test, which is a point in their favor.  Specifically they note that if quantum antimatter is a cause of dark matter effects, it should affect the orbit of distant Kuiper belt objects such as (55637) 2002 UX25.

So radical new physics, but also a clear predictive test of the model. This puts the paper in the “fringe” category. That is, very speculative but making testable predictions. If experiments show that antimatter does indeed fall up, then it might be worth looking at Kuiper belt objects for antigravity effects. For now, though, it is just an idea.

The last paper takes a different approach to dark matter.  In this case the paper doesn’t introduce new physics, but takes established physics and applies it in new ways.  The paper looks to address a very specific weakness in the standard cold dark matter (CDM) model. Specifically the fact that dwarf galaxies don’t fit the model as well as we’d like. Combine this with the fact that we haven’t directly observed dark matter particles, and you have a perfect opening for new ideas. Here the paper proposes that dark matter is not only cold, but super-cold. So cold that it acts as a Bose-Einstein condensate. Put simply, this would mean that dark matter could act as a single quantum system.  Computer simulations show that the model could address the difficulty with dwarf galaxies.

So this last paper makes a new approach to a clear difficulty in current models, and doesn’t invoke controversial new physics. It hasn’t made any clear predictions to distinguish it from other models, but it is the type of new idea that mainstream theorists propose to address observational difficulties.  As the model is developed further, and we gather more observational evidence, we’ll be able to determine if the model is viable.

Astrophysics is a difficult field, and it is always good to look at new ideas. But as we can see, some ideas have more potential than others.

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When talking about scientific ideas, you often hear terms such as theories, hypotheses, facts, laws, models, etc. Some of these terms are used in everyday speech, but with meanings other than their scientific ones. Someone might say they have a theory, when they really mean they have an idea. People talk about scientific laws as if they are facts, or use the phrase “just a theory” to distinguish it from some idealized truth.  Even scientists will sometimes interchange terms like theory and law. We know what we mean, but we aren’t always precise with our usage. So what do these terms mean in a scientific sense?

The big three in scientific nomenclature are law, hypothesis and theory.

A scientific law is an empirical relation that can be summarized in a concise way either verbally or mathematically. They are relations that are well validated by experiment, such as Newton’s Laws of Motion. In the strict sense, laws should be valid without exception. It is this sense that is often used when referring to the “laws of nature”. However because of their history there are many things we refer to as laws that we now know aren’t strictly valid. Kepler’s Laws of Planetary Motion, for example, aren’t strictly true because of the gravitational interactions between planets.  Kepler’s Laws are merely a reasonable approximation, but we still refer to them as laws because of their history.  Even worse, we have things like Bode’s Law for planetary distances, which isn’t a valid relation at all. The important things about laws, though, is that they are purely observational. A law doesn’t propose an underlying mechanism, it simply is an observed relation.

A hypothesis is an idea or proposed theory that can be tested either experimentally or observationally. The term generally doesn’t apply to basic ideas or rudimentary concepts, but rather to ideas that have been fleshed out a bit. The important thing about a hypothesis is that it must be capable of being falsified. This is why, for example, intelligent design is not a hypothesis. The premise of intelligent design is that there is an intelligence behind the evolutionary process, which is a tenet that cannot be falsified by scientific methods.  As I’ve noted in an earlier post, it is possible to falsify a hypothesis based on observational evidence alone. Evolution, the big bang, and dark matter can all be falsified without some kind of repeatable experiment. (Though to be clear, evolution has been validated by repeatable experiments in the lab numerous times).

A theory is a comprehensive hypothesis or set of hypotheses that have been validated by confluence of evidence from a range of observational and/or experimental sources.  Usually a theory refers to something so well validated by scientific evidence that it has become a foundational aspect of its field, such as the theory of evolution for biology, atomic theory for chemistry, and the big bang theory for astrophysics. A theory can never be proven true, so it is always possible that such a foundational theory may be found invalid, but it is very unlikely. It would also take a preponderance of incontrovertible evidence to overturn such a theory.  This is something supporters of “fringe” ideas such as the electric universe don’t seem to understand.  It isn’t enough for a new idea to explain an idea here and there, or to simply declare that an established theory is wrong or insufficient. A new hypothesis must be able to account for all the observational evidence of the old theory, and it must account for new evidence that invalidates the old theory.  And it must do this to the same level and precision (if not better) than the theory it supplants.  This has happened, for example when quantum theory supplanted Newtonian mechanics for things like atoms and molecules, and when general relativity supplanted it for larger objects.

One thing to keep in mind is that the amount of “truth” does not increase at each level.  It is not the case that hypotheses become theories become laws.  A hypothesis can become a theory, but more often multiple hypotheses are integrated into a general theory.  Neither, however, become laws, since a law is merely an observed relation.  Usually it is hypotheses and theories that are built up from laws, such as the Theory of gravity built upon the Newton’s laws of motion and law of gravity. In science, the theory is the thing, since it is deeply validated by the reality of scientific evidence.

There is some variation in usage within different scientific fields, and even individuals within a particular field. My own quirk is that I generally don’t refer to things as hypotheses. Since my field of physics and astrophysics tend to be highly mathematical, I generally refer to hypotheses as models. So Modified Newtonian Dynamics (MoND) is a model that has been largely (but not entirely) invalidated by observational evidence, while dark matter is a robust model that has been largely (though not entirely) validated by observational evidence.  To me, the term model strikes a sweet point between common and scientific usage that both indicates that it is more than a mere idea, but also that it is open to being falsified.

With all of these terms, the goal is to pursue a deeper and broader understanding of the universe. So we discover laws, develop hypotheses, and test them until they either fail or are modified and integrated into better hypotheses. Always pushing to create deep, robust theories that represent our best understanding of cosmos.

And then we keep pushing.

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Suppose you count down from five:  5, 4, 3, 2, 1, 0.  Then what?  You could just stop, or you could keep going -1, -2, -3 and so on.  Mathematically there is nothing to prevent you from counting down below zero.  Of course if you apply this idea to cupcakes, something changes when you reach zero.  If you start with five cupcakes and start giving them away, you eventually run out.  At that point you can’t give away any more.  In this case you can’t count down past zero.  Sure, you can hand out slips of paper with “I owe you a cupcake.” written on them, but it would be ridiculous to use the existence of negative numbers to claim that “negative cupcakes” exist and can be handed out to people.

A similar type of thing can occur  in physical models.  One example of this is the legendary “white hole” making the social media rounds of late.  The basic idea of a white hole is that it is some kind of anti-black hole.  Instead of capturing material and trapping it forever, a white hole spews material out.  So they would constantly be generating material around it.  There are even some speculations that black holes and white holes could be connected as a kind of wormhole.

All cool ideas, except for one problem.  White holes don’t exist.  I don’t mean they are hypothetical, but we don’t have evidence for them.  I really mean they don’t exist.  They are about as sensical as negative cupcakes.

The original idea of a white hole comes from the mathematics of general relativity.  One of the key features of general relativity is that you can represent the structure of space and time in all sorts of different coordinate systems.  This allows you to choose a coordinate system that makes your calculations easier, but it also means you have to be careful to recognize when you’re dealing with negative cupcakes.

In this coordinate system the edge is infinitely far away. That doesn’t mean you could walk beyond infinity.
Credit: Claudio Rocchini

When describing a simple black hole, one useful coordinate system is known as Kruskal–Szekeres coordinates.  The coordinates are a good way to describe the spacetime around a simple black hole, but you can also extend them, just like you can count down to zero and keep going.  Mathematically there is nothing to prevent you from extending the coordinates.  When you do, you not only get a description of a black hole, you get a description of a white hole as a negative black hole.  But that doesn’t make white holes real, or even hypothetical.

You can see a similar example in the figure here.  It represents what is known as a hyperbolic coordinate system.  It is a way to represent an infinite surface, and it does it by representing close areas as large, and more distant areas as tiny.  Infinity is then represented as a finite area.  But just because you can represent an infinite surface this way doesn’t mean you could walk off its edge.

Mathematics is a powerful tool in astrophysics, but you need to be aware of what it actually represents.

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Yesterday while doing an AMA on Reddit I was asked an interesting question.  How do we know that dark energy, which is the attributed cause of cosmic expansion, isn’t just gravitationally repulsive matter?  After all, electric charges can attract and repel, so why not masses?  The repelling masses would push against each other and expand the universe.  How do we know that isn’t the cause of dark energy?  The short answer is that the observational evidence doesn’t support the idea.  But it is an interesting demonstration of how you can build and test ideas.

Let’s start with the idea that mass is somehow similar to electric charge.  In electromagnetism, there are positive and negative charges, and they follow the rule that charges of the same kind repel each other, while opposite kinds attract.  With gravity, masses of the same kind attract each other, so we could suppose that there is positive and negative mass, where masses of the same kind attract each other and opposites repel.

With charge, opposite kinds tend to come together to form objects that are electrically neutral.  The atoms in our body, for example, have positive and negative charges, but they tend to be distributed pretty evenly.  For our hypothetical positive and negative mass, you would tend to get clumps of one kind or another.  So we might speculate that some galaxies are formed of positive matter, while others are formed of negative matter.

Galaxy clusters in the universe.
Credit: Sloan Digital Sky Survey.

That’s an interesting idea, but if that were the case, positive mass galaxies would attract other positive mass galaxies, but repel negative mass galaxies.  The same would be true for negative mass galaxies, so we would expect to see galaxies tend to differentiate into clumps of different mass types.  What we actually observe is that galaxies always attract each other.  The clustering of galaxies is consistent with them always attracting each other gravitationally, and there is no evidence of a differentiation.  So that idea doesn’t work.

So let’s try another idea.  Two types of mass, one being the regular kind that gravitationally attracts all other masses, and a second kind that always repels all other masses.  At first blush this might seem to be a good idea.  Regular matter would clump into galaxies and clusters, just as we observe, and this new repulsive matter would tend to spread out evenly and push against all the galaxies.  So you would get clumping and cosmic expansion just like we see.  Right?

Not quite.  The good news is this idea makes a clear prediction.  If cosmic expansion is due to some repulsive matter, then as the universe expands the density of that matter would decrease over time.  If the repulsive matter is more thinly spread, then its effect would be lessened.  So the clear prediction is that cosmic expansion is slowing over time.

This isn’t what we see, so this idea doesn’t work either.

What we actually see is that the universe is  expanding at an exponential rate.  This means that the rate at which the expansion occurs doesn’t decrease.  It is constant.  As the universe expands, the density of dark energy doesn’t decrease.  In general relativity this means that dark energy is a property of spacetime itself.  It cannot be some form of repulsive matter because the effect of cosmic expansion is persistent and unchanging.  Observations of distant galaxies confirm this.

So while we aren’t entirely sure what dark energy is, we do know unequivocally that it is not matter.

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