Quantum theory is strange. With it’s particle-wave duality, and spooky action at a distance, it is a difficult theory to wrap your head around. But long before we were able to test some of its strangest implications, we used hypothetical thought experiments. One of the most famous was the delayed-choice experiment proposed by John Wheeler in 1978. 

The delayed choice experiment looks at one of the strangest behaviors of quantum systems, specifically that they can sometimes interact like particles, and sometimes like waves. For example, light can behave like a wave, and waves of light can overlap to create interference patterns that can be seen as ripples of bright and dark on a screen. Light can also behave as particles called photons, and a single photon can trigger a detector, similar to the way a baseball can be used to drop someone in a tank of water.

It would seem, then, that a quantum system such as light is sometimes a wave, and sometimes made of particles. But if that’s the case, you should be able to trick the system. What if you set up a wave experiment for light, and then changed it to a particle experiment after the light has already been released? Or what if you randomly chose a particle or wave experiment long after light began its journey. If the light really has to be either a particle or a wave, then it somehow has to choose before the experiment is decided. What would happen if it chooses wrongly? This is what Wheeler called the delayed-choice experiment, because the choice of experiment is only decided after the light is already committed.

Wheeler’s idea was to imagine a “cosmic interferometer.” Suppose light from a distant distant quasar were to be gravitationally lensed by closer galaxy. As a result, light from a single quasar would appear as coming from two slightly different locations. Wheeler then noted that this light could be observed in two different ways. The first would be to have a detector aimed at each lensed image, thus making a particle measurement. The second would be to combine light from these two images in an interferometer, thus making a wave measurement. According to quantum theory, the results of these two types of experiments (particle or wave) would be exactly as we’ve observed in their standard form. But the light began its journey billions of years ago, long before we decided on which experiment to perform. Through this “delayed choice” it would seem as if the quasar light “knew” whether it would be seen as a particle or wave billions of years before the experiment was devised.

It took nearly 30 years before the experiment was successfully done using an interferometer in a lab. The results were exactly what Wheeler predicted. Even though the choice is delayed, the outcome is just what quantum theory predicts. This was considered solid proof for most scientists, but a few argued that because the experiment was done entirely in the lab, some subtle interaction might have given light a clue as to the outcome. So there has been some effort to do the experiment at much greater distances. Now a team has succeeded in doing it between a lab on Earth and a satellite in space.

Their setup is similar to other delayed choice experiments, but with a spacey twist. Light passes through an interferometer in the lab, but instead of simply measuring the result, the combined beams travel out into space, where they strike a mirror on a satellite in low Earth orbit. Only after the light bounces back to the lab is the outcome measured. The choice of measurement isn’t made until the light beam is well beyond the lab. So the lab can’t affect the outcome. As expected, the result matches Wheeler’s prediction.

So quantum theory is right. Quantum systems don’t choose to be particles or waves to fit the experiment. They have both particle-like and wave-like properties at the same time. It’s strange, but it’s not magic.

Paper: Francesco Vedovato, et al. Extending Wheeler’s delayed-choice experiment to space. Sci. Adv. e1701180 (2017)

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Humans are mortal. Not just as individuals, but also as a species. We can defend against many of the existential dangers to humanity. Threats such as global warming and pollution are well understood, and we can take steps to address them if we have the will. Even cosmic threats such as a civilization ending impact can be mitigated given time. But what about a deeper cosmic threat? What if the Universe could destroy not only our planet, but the entire galaxy, and what if we could never see it coming? 

Recently there’s been buzz about an idea known as the false vacuum scenario, and it’s terrifying to think of.

Usually a physical system will try to get to the lowest energy state it can, releasing that energy in some form. In classical physics, if a system reaches a state of low energy it will remain there even if a lower energy state is possible. Imagine a ball rolling into a small valley on the side of a mountain. If the ball could get out of the valley it would roll even farther down the mountain. But the ball has no way to get out of the valley, so it will remain their indefinitely.

However in quantum mechanics this isn’t the case. If a quantum system reaches a state of low energy, it might remain there for a time, but it won’t remain there forever. Because of an effect known as quantum tunneling, a quantum system can break out of its little valley and head toward an even lower energy state. Given enough time, a quantum system will eventually reach the lowest energy state possible.

The observed mass of the Higgs boson supports the idea that the Universe is in a metastable state. Credit: Wikipedia

Our Universe is a quantum system, so one of the big questions is whether it happens to be stable and in the lowest energy state, or in a higher energy state and only metastable. In the standard model of particle physics, the answer to this question can be answered by the mass of the Higgs boson and the top quark. These two masses can be used to determine if the the vacuum state of the electroweak force is stable or metastable. Current observations point to it being metastable, which means the current state of the Universe might be temporary. If so, the Universe could collapse into a lower energy state at any time. If it does, then everything in the Universe would be destroyed. And there would be no way to see it coming. We would just exist one moment, and dissolve into quantum chaos the next.

But how likely is such a scenario? It’s tempting to argue that since the Universe has existed just fine for nearly 14 billion years, it will probably exist for billions more. But that’s not how probability works. If you toss a fair coin ten times and each time comes up heads, that doesn’t mean it will likely come up heads the next ten times. The odds of each toss is 50/50, and just because you got lucky the first ten time doesn’t mean you will on toss eleven. However there is also the possibility that your coin isn’t fair, in which case you would expect to keep seeing heads. So if you get heads ten times in a row, what are the odds that the coin is fair?

The more likely the doomsday scenario, the less likely Earth would have formed later.

We can use this idea to estimate the likelihood of the false vacuum scenario. We live in a Universe that is about 14 billion years old, and Earth formed when the Universe was about 9 billion years old. If the false vacuum scenario were highly likely, then the odds of our planet forming so late in the game would be tiny. The more stable the Universe is likely to be, the more probable a late-forming Earth is. As with the coin toss, the fact that we live on a planet that only formed 5 billion years ago means the odds of cosmic destruction must be quite small. Doing the math, it comes out to a chance of about 1 in 1.1 billion years.

So even if the Universe is metastable (and we still don’t know for sure) it is at least very, very stable. There are lots of other existential threats that are more likely, and we would do well to focus on them. If we rise to the challenge there is still plenty of time to explore the stars.

Paper: Max Tegmark and Nick Bostrom. Is a doomsday catastrophe likely? Nature 438, 754 (2005)

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Quantum theory is probabilistic by nature. Because of fuzzy effects of quantum indeterminacy, the equations of quantum mechanics can’t tell us exactly what an object is doing, but only what the likely outcome will be when we interact with it. This probability is determined by the Born rule (named after physicist Max Born). The rule has various forms, but in the most common approach it means that squaring the wavefunction of an object yields the probability of a particular outcome. The Born rule works extraordinarily well, making quantum theory the most accurate scientific theory we have, but it is also an assumption. It’s a postulate of quantum theory rather than being derived formally from the model. So what if it’s wrong. 

Even if it is wrong on some level, the great success of quantum physics demonstrates that it certainly works in most cases. But we scientists love to test our assumptions even when they work, so there have been attempts to disprove the Born rule. One approach looked at a triple-slit experiment, which is a variation of the famous double-slit experiment.

Interference patterns from a double slit experiment. Credit: Pieter Kuiper

In the double slit experiment, quantum objects such as photons or electrons are beamed through two closely spaced slits. Since we don’t know which slit each object passes through, the possibilities overlap to produce an interference pattern rather than two sharp lines. According to the Born rule, even when we run the experiment one object at a time, the probability distribution of each object follows this pattern. This is exactly what we see experimentally, making it an excellent demonstration of quantum theory.

The triple slit experiment uses three small openings instead of two. While it seems like a trivial change, if done correctly it allows for secondary interactions that could in principle violate the Born rule. Basically, if you just square the total wavefunction of the three slits, you get one probability distribution. If you calculate the secondary interactions you get a different distribution. The difference is extremely small, but in 2010 the experiment was performed, and found the Born rule held within experimental limits.

While this would seem to confirm the Born rule, the precision of the experiment was only to 1 part in 100, which isn’t very high. Unfortunately, even getting that level of precision is difficult with the triple-slit experiment. That’s because the test only works if the wavelength of the experiment is less than the width of the slits. But now a new paper proposes a different approach that might yield even greater precision.

This new approach is a double slit experiment with a twist. Rather than simply letting an object pass through the two slits, an extra level is introduced to shift objects from one slit to the other. This can be done for either slit or both, even without knowing which slit the object passes through. According to the Born rule, any such shift should have no effect on the outcome. If the shift affects the outcome, then the Born rule is violated. Doing this kind of shift in a real experiment will be tricky, but it’s not limited by the wavelengths of the objects, so potentially it would be much more precise than previous experiments.

Given the power of the Born rule thus far, I wouldn’t bet on seeing a violation. But this kind of experiment is a win-win. Either the Born rule continues to reign, or we discover a subtle violation that could lead to a better understanding of things like quantum gravity.

Paper: Sinha, U., et al. Ruling Out Multi-Order Interference in Quantum Mechanics. Science 329, 418-421 (2010).

Paper: James Q. Quach. Which-way double slit experiments and Born rule violation. arXiv:1610.06401 (2016).

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Quantum teleportation brings to mind Star Trek’s transporter, where crew members are disassembled in one location to be reassembled in another. Real quantum teleportation is a much more subtle effect where information is transferred between entangled quantum states. It’s a quantum trick that could give us the ultimate in secure communication. While quantum teleportation experiments have been performed countless times in the lab, doing it in the real world has proved a bit more challenging. But a recent experiment using a dark fibre portion of the internet has brought quantum teleportation one step closer to real world applications. 

The backbone of the internet is a network of optical fibre. Everything from your bank transactions to pictures of your cat travel as beams of light through this fibre network. However there is much more fibre that has been laid than is currently used. This unused portion of the network is known as dark fibre. Other than not being currently used, the dark fiber network has the same properties as the web we currently use. This new experiment used a bit of this dark web in Calgary to teleport a photon state under real world conditions.

The basic process of quantum teleportation begins with two objects (in this case photons) that are quantumly entangled. This basically means the state of these two objects are connected in such a way that a measurement of one object affects the state of the other. For quantum teleportation, one of these entangled objects is measured in combination with the object to be “teleported” (another photon). The result of this measurement is then sent to the other location, where a similar combined measurement is made. Since the entangled objects are part of both measurements, quantum information can be “teleported.” This might seem like an awkward way to send information, but it makes for a great way to keep your messages secret. Using this method, Alice can basically encrypt a message using the entangled objects, send the encrypted message to Bob, who can then make his own measurement of the entangled state to decode the message.

Using dark fibre to teleport photons. Credit: Raju Valivarthi, et al.

This new experiment used a variation of this method using three observers rather than two. Using the Bob and Alice analogy, Bob and Alice each make measurements of an entangled state and a photon, about 8 kilometers from each other. Their results are then sent to Charlie, who combines the two results to achieve quantum teleportation. This method assures that the experiment extends beyond a single lab location, and it was done using existing dark fibre and wavelengths of light commonly used in current fibre internet.

Overall the experiment demonstrates that quantum teleportation can be used as a way to encrypt messages over the web. The next big challenge will be to find a way to make it practical enough for everyone to use.

Paper: Raju Valivarthi, et al. Quantum teleportation across a metropolitan fibre network. Nature Photonics 10, 676–680 (2016) DOI:10.1038/nphoton.2016.180

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We have an intuitive understanding of how the world works. Our intuition works well in our everyday lives, but it doesn’t quite match reality. 

One of the basic assumptions we make about objects is that they are objectively real. For example, when you leave your apartment in the morning, you imagine your house is right where you left it as you go about your day. Barring some calamity, you expect to find your apartment just as you left it when you return in the evening. This idea is known as macrorealism, in that a macroscopic object such as your house is still there even when you’re not looking at it. In scientific terms we would say the state of an object exists independent of an observer. While this seems obviously true, we can test the idea experimentally.

To show this, let’s consider an experiment. Suppose we have a box that contains a coin. At any time we can open the box and see whether it’s heads or tails. The catch is that the box has to follow a certain rule. Whatever you observe initially, you must observe the same thing ten seconds later. If you open the box and see heads, then ten seconds later when you open the box you must also see heads. For the experiment we’ll open the box, then open it five seconds later, then finally open it again at ten seconds. We know the first and last observations have to agree, but what about the observation in the middle?

It depends upon what the box does with the coin. One possibility is that the box does nothing, so if you see tails the first time, you will see tails both other times. Another possibility is that each time you open the box it flips the coin when you close it. So the first time you see heads, the second time tails, and the third time heads again. But we could also make a tricky box that flips the coin at seemingly random times, but does so in such a way that every ten seconds it repeats the pattern. In that case, we would always see the same thing the first and last time, but the middle observation would seem random. If macrorealism is true, then middle observations being always the same as the first and last observation, always opposite or always random are the only possibilities for the experiment.

The MINOS far detector near Soudan, MN.

This reality condition can be expressed in a simple inequality known as the Leggett-Garg Inequality. This is done by looking at the correlation between each observation. Since the first and last observations must always agree, then we can say the correlation C₁₃ = 1. If the middle observation is also the same, then we can say C₁₂ = C₂₃ = 1. If the middle observation is always opposite, then we can sayC₁₂ = C₂₃ = – 1. If the middle observation is random thenC₁₂ = C₂₃ = 0. The Leggett-Garg inequality simply states that C₁₂ + C₂₃ – C₁₃ must be no bigger than 1. This makes sense because the three cases give sums of 1, -3, or -1. If any experiment violates this inequality, we can say it violates the assumption of microrealism.

Measurements of neutrino flavor. The red curve represents the result expected by the Leggett-Garg inequality. The actual observations in blue clearly violate the inequality. Credit: J. A. Formaggio, et al.

What’s interesting is that quantum systems violate this inequality all the time. Take, for example, a recent experiment on neutrinos. Neutrinos have a strange property known as oscillation, where the “flavor” of a neutrino changes. Each flavor interacts with other matter in a unique way, so when we observe neutrinos we also observe their flavor. It’s tempting to imagine the three flavors of a neutrino as being like the state of a traffic light. It’s always red, green, or yellow, but changes over time. If that were the case, then the Leggett-Garg inequality should hold for neutrino oscillation. But it doesn’t. Recently a team measured the flavor of neutrinos beamed from Fermilab to the MINOS far detector near Soudan, MN. They found a clear violation of the Leggett-Garg inequality, which means that neutrino flavor violates microrealism. In other words neutrino flavor is a truly quantum state. A particular neutrino doesn’t have a specific flavor that changes over time, because flavor isn’t macroscopically real.

It’s one more example of how our intuition fails when it comes to quantum theory.

Paper: A. J. Leggett and Anupam Garg. Quantum mechanics versus macroscopic realism: Is the flux there when nobody looks? Phys. Rev. Lett. 54, 857 (1985) DOI:http://dx.doi.org/10.1103/PhysRevLett.54.857

Paper: J. A. Formaggio, et al. Violation of the Leggett-Garg Inequality in Neutrino Oscillations. Phys. Rev. Lett. 117, 050402 (2016) DOI:http://dx.doi.org/10.1103/PhysRevLett.117.050402

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There’s been much buzz about a new paper claiming that it’s observed light acting as both a particle and a wave at the same time. Is this legitimate research? Yes, absolutely. Did they actually observe particles and waves at the same time? Well…

Much of the hype around this paper is driven by some basic misconceptions regarding quantum objects. The popular view of quantum theory is that things like photons are sometimes particles and sometimes waves, and which one they become depends upon how you observe them. But in fact quantum objects are neither particles nor waves. They are quanta, which is a separate thing altogether. Under the right conditions quanta can demonstrate wave-like and particle-like behaviors, and there is complementarity between them so that quanta tend to lean toward one or the other in an experiment. But within the formalism of quantum theory, particle-wave duality is a property of the quanta as a whole. Thinking of quanta as particles or waves is far to simplistic when dealing with quantum theory. This is important to keep in mind when popular articles such as this hit the web.

As research areas such as quantum optics and quantum computing developed, we’ve gained tools to really start looking at sophisticated quantum interactions. It’s how we’ve been able to study things like the connection between the uncertainty principle and entropy, or study phase velocity in a quantum system. But since this kind of work isn’t easy to describe in simple terms, it gets hyped as “quantum mechanics gets simpler!” or “speed of light not absolute!” The same is the case here.

The team maintained a wave pattern while inducing particle-like interactions. Credit: L Piazza, et al.

So what’s really going on in this work? The team pulsed laser light at a tiny wire of conductive material (a nanowire). The light induced what is known as surface plasmon polaritons in the nanowire, which is basically an electromagnetic wave pattern within the electrons of material. Because of the size of the nanowire, the plasmon polaritons form a standing wave within the wire, which is where the “wave” aspect comes into the experiment. They also radiate light, which in a quantum sense means that photons are emanating from this standing wave. The team then aimed a beam of electrons at the set up. Some of the electrons collided with the emanating photons, and thus gained some energy. Since these collisions are particle-like, they gain specific (quantized) energy amounts from the induced photons.  Basically the team found a way to induce particle-like interactions while maintaining the overall wave aspect of the system at the same time.

Does this mean the team caused a specific photon or electron to behave as a particle and wave at the same time? No. The particle interactions with the electrons and the induced wave pattern in the wire are two separate aspects of the system. But their result is useful because it could allow us to study quantum interactions directly. This type of work is really useful for photonics and quantum computing, and it’s a clever way to interact with quantum systems.

But this is not an experiment that somehow violates quantum theory. We’ve known for a while that we should be able to do this kind of thing in theory. The achievement here is that they actually pulled it off.

Paper: L Piazza, et al. Simultaneous observation of the quantization and the interference pattern of a plasmonic near-field. Nature Communications 6:6407 DOI: 10.1038/ncomms7407 (2015)

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Quantum theory is often viewed as a strange and mysterious model where objects behave in illogical ways. While it’s true that quantum objects behave in ways that are counterintuitive, we actually understand the behavior quite well. In fact, many of these strange behaviors are used in modern astronomy. Take, for example, the quantization of magnetic moments.

Most atoms have a small magnetic field. This magnetic field can be approximated as a small magnet, just as the Earth’s magnetic field is sometimes treated as a magnetic. The strength of that imaginary magnet is given by the magnetic moment of the atom. With this in mind, the orientation of an atom’s magnetic field can be represented by the orientation of the magnet.

The basic setup of a Stern-Gerlach experiment. Credit: Wikipedia

Suppose, then, that we were to toss atoms through an inhomogeneous magnetic field. Individually the atoms have no particular orientation, so we would expect that the orientation of their magnetic moments are entirely random. As a result, some of the atoms would be more strongly attracted toward the north direction of the magnetic field, while others would be more attracted to the south, and everywhere in between. If the atoms really did act like tiny magnets, we would expect to see the beam of atoms spread out evenly by the magnetic field. In fact, what we see is that the atoms either move toward the north or south, and that’s it. Instead of spreading out evenly, the atoms lock into specific orientations. This experiment is named the Stern-Gerlach experiment, after the physicists who first performed it in 1922, and it demonstrates one of the basic aspects of quantum theory. When you try to measure the state of a quantum system, the results you get are often snapped to discrete results. It would be like measuring the height of a random collection of people, and finding they are all exactly either 5 ft or 6 ft tall.

The Zeeman effect.

As strange as this is, we actually use a similar effect to measure the strength of magnetic fields in the Sun. Since electrons also have magnetic moments, strong magnetic fields can cause their energy levels in an atom to shift. As a result, the emission lines an atom gives off can be shifted by magnetic fields. Emission lines can even be split slightly, which is known as the Zeeman effect. We see this effect near sunspots, which is how we know that sunspots are cooled by magnetic dampening.

That’s part of the real power of astrophysics. Once we understand a phenomena, however strange, we can use it has a tool to study the stars.

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There’s a story going around the popular press about using quasars to determine whether free will exists.  This stems from an MIT press release which talks about using quasars to “close the free will loophole.”  Needless to say, the actual paper published in Physical Review Letters isn’t really about free will, but rather about an interesting effect of quantum mechanics.  Obviously you have no choice but to keep reading.

The paper is about quantum entanglement, specifically an experiment known as the Einstein-Podolsky-Rosen (EPR) experiment.  Suppose we have a mischievous mutual friend.  She decides to prank us by sending sending each of us one member of a pair of gloves.  She packs each glove in a box and mails one to each of us.  We find out about the prank, so we both know that we’re getting one glove of a pair.  But until either of us open our respective box, neither of us know which glove we have.  Once the box arrives at your door, you open it up, and find you have the left glove.  At that moment you know I must have the right glove.

This is the basic idea of the EPR experiment.  For gloves it isn’t a big deal, because from the get-go the left glove was heading your way.  You just didn’t know you were getting the left glove.  That’s because gloves are not quantum things.  In the quantum regime, things get much more strange.  In quantum theory, things can be in an indefinite state until you observe them.  It would be as if our boxes contained a pair of something (gloves, shoes, salt and pepper shakers, etc.) but it is impossible to know what specific something until one of us opens their box.

In quantum theory we would say the boxes contain a superposition of possible things, and the outcome only becomes definite when the outcome is observed.  Now even though you can’t know what specific object you have, you know that I must have its pair.  So if you open the box to find a red right shoe, you know immediately that I must have a red left shoe.  We both know this without opening the box, so we can say that the outcomes of opening our boxes are entangled.  Knowing the contents of one box tells us the contents of the other.  We’ve actually done this experiment with photons, atoms and the like, and it really works.

Of course this is really hard to wrap your head around.  If I’m thousands of miles away from you, and I open my box to find a salt shaker, I know you must have a pepper shaker.  But your box couldn’t have known that until I opened the box.  How is that possible?  How can the opening of my box instantly affect your box thousands of miles away?  Do the boxes communicate faster than light? (No.)  Is there some secret (hidden variable) so that the boxes know what they will become when observed? (No.)  That is part of what makes entanglement so strange, and the EPR experiment so popular.

Schematic of the quasar EPR experiment. Credit: Jason Gallicchio, Andrew S. Friedman, David I. Kaiser

Now the standard interpretation of this experiment is that it shows that fundamentally things are quantum mechanical.  The experiments we’ve done have pretty much eliminated any possibility for things like hidden variables or faster than light communication.  Usually this is done by waiting until the two “boxes” are sent on their way, and then use a random number generator to determine whether you test for “gloves” or “shoes” or whatever.  Since the choice of what to look for is random, and that choice is made after the experiment has started, there is no way for the system to have advance knowledge of the outcome.

But if you really want to be picky, you could argue that while the experiment is being set up, there is plenty of time for the system to know what is going on.  Technically, the experiment, random generator, and scientist are all “entangled” as a single system, so the outcome may be pre-biased.  What looks like a random choice made after the experiment started may not actually be random.  This is known as the setting independence problem.  It is generally seen as far fetched, but technically it hasn’t been experimentally eliminated.

This new paper proposes a way to address this issue.  Instead of using a random generator, you use light from distant quasars.  The fluctuations of light from quasars billions of light years away would then determine what to test for, rather than a local random generator.  The fluctuations began billions of years before the experiment was even thought of, so there is no way for the system to be biased.  This idea isn’t new, but the authors have presented a realistic way to actually do the experiment.

Needless to say, this doesn’t really deal with existence or non-existence of free will.  Philosophers are still likely to debate that topic whatever the outcome of this experiment.  What this experiment will do is test a basic feature of quantum mechanics on a cosmic scale.  We expect the outcome to be the same as before, but the fact that we could actually do the experiment is pretty cool.

Paper:  Jason Gallicchio, Andrew S. Friedman, David I. Kaiser,  Testing Bell’s Inequality with Cosmic Photons: Closing the Setting-Independence Loophole, arXiv:1310.3288v2 [quant-ph] (2014).

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Suppose I put a plastic cup on a table, and put a ping pong ball beside the cup. Then suppose I asked you to put the ball in the cup without touching either the ball or the cup.  You might suggest moving the table or some such “out of the box” trick, but I don’t allow that.  You might then say what I ask is impossible, and for the cup and ball you’d be right.  On the scale of atoms and nuclei, however, it isn’t impossible.  In fact, it happens all the time in the core of our sun.

Atoms and nuclei are not governed by the familiar rules of Newton but rather by the rules of quantum mechanics.  Quantum mechanics can be a bit hard to wrap your head around, but one of the central principles is that you can never be entirely certain of things.  If you want to know where an atom is, or what its energy is, you can never get an exact measurement.  This “fuzziness” factor leads to a number of strange effects, of which one is quantum tunneling.

To use our ball and cup analogy, it would be as if the ball just happened to find itself inside the cup by chance.  One moment the ball is outside the cup, and the next moment it is inside the cup.  It is as if the ball “tunneled” into the wall of the cup, hence the name quantum tunneling.  For the ball and cup this is impossible, but for the nuclei of atoms it is possible.  This quantum tunneling effect is necessary for the sun to be a star.

The sun produces heat and light by fusing atoms.  For example, hydrogen nuclei are slammed together so hard that they stick and produce helium atoms.  The problem is that most of the hydrogen atoms in the sun’s core don’t have enough energy to stick together.  To do that, they have to overcome the repulsion of their positive charges, and they generally don’t have enough energy.  To use our analogy, the ball is outside the cup, and it doesn’t have the energy climb up over the rim to get in the cup.

With quantum tunneling, however, the nuclei can cheat.  They have enough energy to get relatively close to each other, and then they have a chance of tunneling through the remaining barrier to stick together.  This window of opportunity is known as the Gamow peak, and it is a product of how much extra energy it needs and the odds of it quantum tunneling.  Because of the Gamow peak, the nuclei in the sun can fuse despite the fact that they don’t have enough energy to fuse on their own.  Sometimes nature says “close enough” and gives them a bye.  Without quantum tunneling, the sun wouldn’t be able to fuse nuclei in its core in any significant amount, which would mean it couldn’t be a star.

The fact that our sun is a star might seem magical, but it’s really just quantum mechanical.

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