[This is a transcript of the video embedded below. Some of the explanations may not make sense without the animations in the video.]
Happy holidays everybody, today we’re celebrating Isaac Newton’s birthday with a hand selected collection of nerdy Christmas facts that you can put to good use in every appropriate and inappropriate occasion.
You have probably noticed that in recent years worshipping Newton on Christmas has become somewhat of a fad on social media. People are wishing each other a happy Newtonmas rather than Christmas because December 25th is also Newton’s birthday. But did you know that this fad is more than a century old?
In 1891, The Japan Daily Mail reported that a society of Newton worshippers had sprung up at the University of Tokyo. It was founded, no surprise, by mathematicians and physicists. It was basically a social club for nerds, with Newton’s picture residing over meetings. The members were expected to give speeches and make technical jokes that only other members would get. So kind of like physics conferences basically.
The Japan Daily Mail also detailed what the nerds considered funny. For example, on Christmas, excuse me, Newtonmas, they’d have a lottery in which everyone drew a paper with a scientists’ name and then got a matching gift. So if you drew Newton you’d get an apple, if you drew Franklin a kite, Archimedes got you a naked doll, and Kant-Laplace would get you a puff of tobacco into your face. That was supposed to represent the Nebular Hypothesis. What’s that? That’s the idea that solar systems form from gas clouds, and yes, that was first proposed by Immanuel Kant. No, it doesn’t rhyme to pissant, sorry.
Newton worship may not have caught on, but nebular hypotheses certainly have.
By the way, did you know that Xmas isn’t an atheist term for Christmas? The word “Christ” in Greek is Christos written like this (Χριστός.) That first letter is called /kaɪ/ and in the Roman alphabet it becomes an X. It’s been used as an abbreviation for Christ since at least the 15th century.
However, in the 20th century the abbreviation has become somewhat controversial among Christians because the “X” is now more commonly associated with a big unknown. So, yeah, use at your own risk. Or maybe stick with Happy Newtonmas after all?
Well that is controversial too because it’s not at all cl
ear that Newton’s birthday is actually December 25th. Isaac Newton was born on December 25, 1642 in England.
But. At that time, the English still used the Julian calendar. That is already confusing because the new, Gregorian calendar, was introduced by Pope Gregory in 1584, well before Newton’s birth. It replaced the older, Julian calendar, that didn’t properly match the months to the orbit of Earth around the sun.
Yet, when Pope Gregory introduced the new calendar, the British were mostly Anglicans and they weren’t going to have some pope tell them what to do. So for over a hundred years, people in Great Britain celebrated Christmas 10 or 11 days later than most of Europe. Newton was born during that time. Great Britain eventually caved in and adopted the Gregorian calendar in 1751. They passed a law that overnight moved all dates forward by 11 days. So now Newton would have celebrated his birthday on January 4th, except by that time he was dead.
However, it gets more difficult because these two calendars continue running apart, so if you’d run forward the old Julian calendar until today, then December 25th according to the old calendar would now actually be January 7th. So, yeah, I think sorting this out will greatly enrich your conversation over Christmas lunch. By the way, Greece didn’t adopt the Gregorian calendar until 1923. Except for the Monastic Republic of Mount Athos, of course, which still uses the Gregorian calendar.
Regardless of exactly which day you think Newton was born, there’s no doubt he changed the course of science and with that the course of the world. But Newton was also very religious. He spent a lot of time studying the Bible looking for numerological patterns. On one occasion he argued, I hope you’re sitting, that the Pope is the anti-Christ, based in part on the appearance of the number 666 in scripture. Yeah, the Brits really didn’t like the Catholics, did they.
Newton also, at the age of 19 or 20, had a notebook in which he kept a list of sins he had committed such as eating an apple at the church, making pies on Sunday night, “Robbing my mother’s box of plums and sugar” and “Using Wilford’s towel to spare my own”. Bad boy. Maybe more interesting is that Newton recorded his secret confessions in a cryptic code that was only deciphered in 1964. There are still four words that nobody has been able to crack. If you get bored over Christmas, you can give it a try yourself, link’s in the info below.
Newton may now be most famous for inventing calculus and for Newton’s laws and Newtonian gravity, all of which sound like he was a pen on paper person. But he did some wild self-experiments that you can put to good use for your Christmas conversations. Merry Christmas, did you know that Newton once poked a needle into his eye? I think this will go really well.
Not a joke. In 1666, when he was 23, Newton, according to his own records, poked his eye with a bodkin, which is more or less a blunt stitching needle. In his own words “I took a bodkine and put it between my eye and the bone as near to the backside of my eye as I could: and pressing my eye with the end of it… there appeared several white dark and coloured circles.”
If this was not crazy enough, in the same year, he also stared at the Sun taking great care to first spend some time in a dark room so his pupils would be wide open when he stepped outside. Here is how he described this in a letter to John Locke 30 years later:
“in a few hours’ time I had brought my eyes to such a pass that I could look upon no bright object with either eye but I saw the sun before me, so that I could neither write nor read... I began in three or four days to have some use of my eyes again & by forbearing a few days longer to look upon bright objects recovered them pretty well.”
Don’t do this at home. Since we’re already talking about needles, did you know that pine needles are edible? Yes, they are edible and some people say they taste like vanilla, so you can make ice cream with them. Indeed, they are a good source of vitamin C and were once used by sailors to treat and prevent scurvy.
By some estimate, scurvy killed more than 2 million sailors between the 16th and 18th centuries. On a long trip it was common to lose about half of the crew, but in extreme cases it could be worse. On his first trip to India in 1499, Vasco da Gama reportedly lost 116 of 170 men, almost all to scurvy.
But in 1536, the crew of the French explorer Jacques Cartier was miraculously healed from scurvy upon arrival in what is now Québec. The miracle cure was a drink that the Iroquois prepared by boiling winter leaves and the bark from an evergreen tree, which was rich in vitamin C.
So, if you’ve run out of emphatic sounds to make in response to aunt Emma, just take a few bites off the Christmas tree, I’m sure that’ll lighten things up a bit.
Speaking of lights. Christmas lights were invented by no other than Thomas Edison. According to the Library of Congress, Edison created the first strand of electric lights in 1880, and he hung them outside his laboratory in New Jersey, during Christmastime. Two years later, his business partner Edward Johnson had the idea to wrap a strand of hand-wired red, white, and blue bulbs around a Christmas tree. So maybe take a break with worshipping Newton and spare a thought for Edison.
But watch out when you put the lights on the tree. According to the United States Consumer Product Safety Commission, in 2018, 17,500 people sought treatment at a hospital for injuries sustained while decorating for the holiday.
And this isn’t the only health risk on Christmas. In 2004 researchers in the United States found that people are much more likely to die from heart problems than you expect both on Christmas and on New Year. A 2018 study from Sweden made a similar finding. The authors of the 2004 study speculate that the reason may be that people delay seeking treatment during the holidays. So if you feel unwell don’t put off seeing a doctor even if it’s Christmas.
And since we’re already handing out the cheerful news, couples are significantly more likely to break up in the weeks before Christmas. This finding comes from a 2008 paper by British researchers who analyzed facebook status updates. Makes you wonder, do people break up because they can’t agree which day Newton was born or do they just not want to see their in-laws? Let me know what you think in the comments.
[This is a transcript of the video embedded below. Some of the explanations may not make sense without the animations in the video.]
Superdeterminism is a way to make sense of quantum mechanics. But some physicists and philosophers have argued that if one were to allow it, it would destroy science. Seriously. How does superdeterminism work, what is it good for, and why does it allegedly destroy science? That’s what we’ll talk about today.
First things first, what is superdeterminism? Above all, it’s a terrible nomenclature because it suggests something more deterministic than deterministic and how is that supposed to work? Well, that’s just not how it works. Superdeterminism is exactly as deterministic as plain old vanilla determinism. Think Newton’s laws. If you know the initial position and velocity of an arrow, you can calculate where it will land, at least in principle. That’s determinism: Everything that happens follows from what happened earlier. But in quantum mechanics we can only predict probabilities for measurement outcomes, rather than the measurement outcomes themselves. The outcomes are not determined, so quantum mechanics is indeterministic.
Superdeterminism returns us to determinism. According to superdeterminism, the reason we can’t predict the outcome of a quantum measurement is that we are missing information. This missing information is usually referred to as the “hidden variables”. I’ll tell you more about those later. But didn’t this guy what’s his name Bell prove that hidden variables are wrong?
No, he didn’t, though this is a very common misunderstanding, depressingly, even among physicists. Bell proved that a hidden variables theory which is (a) local and (b) fulfills an obscure assumption called “statistical independence” must obey an inequality, now called Bell’s inequality. We know experimentally that this inequality is violated. It follows that any local hidden variable theory which fits to our observations, has to violate statistical independence.
If statistical independence is violated, this means that what a quantum particle does depends on what you measure. And that’s how superdeterminism works: what a quantum particle does depends on what you measure. I’ll give you an example in a moment. But first let me tell you where the name superdeterminism comes from and why physicists get so upset if you mention it.
Bell didn’t like the conclusion which followed from his own mathematics. Like so many before and after him, Bell wanted to prove Einstein wrong. If you remember, Einstein had said that quantum mechanics can’t be complete because it has a spooky action at a distance. That’s why Einstein thought quantum mechanics is just an average description for a hidden variables theory. Bell in contrast wanted physicists to accept this spooky action. So he had to somehow convince them that this weird extra assumption, statistical independence, makes sense.
In a 1983 BBC interview he said the following:
“There is a way to escape the inference of superluminal speeds and spooky action at a distance. But it involves absolute determinism in the universe, the complete absence of free will. Suppose the world is super-deterministic, with not just inanimate nature running on behind-the-scenes clockwork, but with our behavior, including our belief that we are free to choose to do one experiment rather than another, absolutely predetermined, including the “decision” by the experimenter to carry out one set of measurements rather than another, the difficulty disappears.”
This is where the word “superdeterminism” comes from. Bell called a violation of statistical independence “superdeterminism” and claimed that it would require giving up free will. He argued that there are only two options: either accept spooky action and keep free will which would mean that Bell was right, or reject spooky action but give up free will which would mean that Einstein was right. Bell won. Einstein lost.
Now you all know that I think free will is logically incoherent nonsense. But even if you don’t share my opinion, Bell’s argument just doesn’t work. Spooky action at a distance doesn’t make any difference for free will because the indeterministic processes in quantum mechanics are not influenced by anything, so they are not influenced by your “free will,” whatever that may be. And in any case, throwing out determinism just because you don’t like its consequences is really bad science.
Nevertheless, the mathematical assumption of “statistical independence” has since widely been called the “free will” assumption, or the “free choice” assumption. And physicists stopped questioning it to the point that today most of them don’t know that Bell’s theorem even requires this additional assumption.
This is not a joke. All the alleged strangeness of quantum mechanics has its origin in nomenclature. It was forced on us by physicists who called a mathematical statement the “free will assumption”, never mind that it’s got nothing to do with free will, and then argued that one must believe in it because one must believe in free will.
If you find this hard to believe, I can’t blame you, but let me read you a quote from a book by Nicolas Gisin, who is Professor for Physics in Geneva and works on quantum information theory.
“This hypothesis of superdeterminism hardly deserves mention and appears here only to illustrate the extent to which many physicists, even among specialists in quantum physics, are driven almost to despair by the true randomness and nonlocality of quantum physics. But for me, the situation is very clear: not only does free will exist, but it is a prerequisite for science, philosophy, and our very ability to think rationally in a meaningful way. Without free will, there could be no rational thought. As a consequence, it is quite simply impossible for science and philosophy to deny free will.”
Keep in mind that superdeterminism just means statistical independence is violated which has nothing to do with free will. However, even leaving that aside, fact is, the majority of philosophers either believe that free will is compatible with determinism, about 60% of them, or they agree with me that free will doesn’t exist anyway, about 10% of them.
But in case you’re still not convinced that physicists actually bought Bell’s free will argument, here is another quote from a book by Anton Zeilinger, one of the probably most famous physicists alive. Zeilinger doesn’t use the word superdeterminism in his book, but it is clear from the context that he is justifying the assumption of statistical independence. He writes:
“[W]e always implicitly assume the freedom of the experimentalist. This is the assumption of free will… This fundamental assumption is essential to doing science.”
So he too bought Bell’s claim that you have to pick between spooky action and free will. At this point you must be wondering just what this scary mathematical expression is that supposedly eradicates free will. I am about to reveal it, brace yourself. Here we go.
I assume you are shivering in fear of being robbed of your free will if one ever were to allow this. And not only would it rob you of free will, it would destroy science. Indeed, already in 1976, Shimony, Horne, and Clauser argued that doubting statistical independence must be verboten. They wrote: “skepticism of this sort will essentially dismiss all results of scientific experimentation”. And here is one final quote about superdeterminism from the philosopher Tim Maudlin: “besides being insane, [it] would undercut scientific method.”
As you can see, we have no shortage of men who have strong opinions about things they know very little about, but not like this is news. So now let me tell you how superdeterminism actually works, using the double slit experiment as an example.
In the double slit experiment, you send a coherent beam of light at a plate with two thin openings, that’s the double slit. On the screen behind the slit you then see an interference pattern. The interference isn’t in and by itself a quantum effect, you can do this with any type of wave, water waves or sound waves for example.
The quantum effects only become apparent when you let a single quantum of light go through the slits at a time. Each of those particles makes a dot on the screen. But the dots build up… to an interference pattern. What this tells you is that even single particles act like waves. This is why we describe them with wave-functions usually denoted psi. From the wave-function we can calculate the probability of measuring the particle in a particular place, but we can’t calculate the actual place.
Here’s the weird bit. If you measure which slit the particles go through, the interference pattern vanishes. Why? Well, remember that the wave-function – even that of a single particle – describes probabilities for measurement outcomes. In this case the wave-function would first tell you the particle goes through the left and right slit with 50% probability each. But once you measure the particle you know 100% where it is.
So when you measure at which slit the particle is you have to “update” the wave-function. And after that, there is nothing coming from the other slit to interfere with. You’ve destroyed the interference pattern by finding out what the wave did. This update of the wave-function is sometimes also called the collapse or the reduction of the wave-function. Different words, same thing.
The collapse of the wave-function doesn’t make sense as a physical process because it happens instantaneously, and that violates the speed of light limit. Somehow the part of the wave-function at the one slit needs to know that a measurement happened at the other slit. That’s Einstein’s “spooky action at a distance.”
Physicists commonly deal with this spooky action by denying that wave-function collapse is a physical process. Instead, they argue it’s just an update of information. But information about… what? In quantum mechanics there isn’t any further information beyond the wave-function. Interpreting the collapse as an information update really only makes sense in a hidden variables theory. In that case, a measurement tells you more about the possible values of the hidden variables.
Think about the hidden variables as labels for the possible paths that the particle could take. Say the labels 1 2 3 go to the left slit and the labels 4 5 6 go to the right slit and the labels 7 to 12 go through both. The particle really has only one of those hidden variables, but we don’t know which. Then, if we measure the particle at the left slit, that simply tells us that the hidden variable was in the 1 2 3 batch, if we measure it right, it was in the 4 5 6 batch, if we measure it on the screen, it was in the 7 - 12 batch. No mystery, no instantaneous collapse, no non-locality. But it means that the particle’s path depends on what measurement will take place. Because the particles must have known already when they got on the way whether to pick one of the two slits, or go through both. This is just what observations tell us.
And that’s what superdeterminism is. It takes our observations seriously. What the quantum particle does depends on what measurement will take place. Now you may say uhm drawing lines on YouTube isn’t proper science and I would agree. If you’d rather see equations, you’re most welcome to look at my papers instead.
Let us then connect this with what Bell and Zeilinger were talking about. Here is again the condition that statistical independence is violated. The lambda here stands for the hidden variables, and rho is the probability distribution of the hidden variables. This distribution tells you how likely it is that the quantum particle will do any one particular thing. In Bell’s theorem, a and b are the measurement settings of two different detectors at the time of measurement. And this bar here means you’re looking at a conditional probability, so that’s the probability for lambda given a particular combination of settings. When statistical independence is violated, this means that the probability for a quantum particle to do a particular thing depends on the detector settings at the time of measurement.
Since this is a point that people often get confused about, let me stress that it doesn’t matter what the setting is at any earlier or later time. This never appears in Bell’s theorem. You only need to know what’s the measurement that actually happens. It also doesn’t matter how one chooses the detector settings, that never makes any appearance either. And contrary to what Bell and Zeilinger argued, this relation does not restrict the freedom of the experimentalist. Why would it? The experimentalist can measure whatever they like, it’s just that what the particle does depend on what they measure.
And of course this won’t affect the scientific method. What these people were worrying about is that random control trials would be impossible if choosing a control group could depend on what you later measure.
Suppose you randomly assign people into two groups to test whether a vaccine is efficient. People in one group get the vaccine, people in the other group a placebo. The group assignment is the “hidden variable.” If someone falls ill, you do a series of tests to find out what they have, so that’s the measurement. If you think that what happens to people depends on what measurement you will do on them, then you can’t draw conclusions about the efficiency of the vaccine. Alrighty. But you know what, people aren’t quantum particles. And believing that superdeterminism plays a role for vaccine trials is like believing Schrödinger’s cat is really dead and alive.
The correlation between the detector settings and the behavior of a quantum particle which is the hallmark of superdeterminism only occurs when quantum mechanics would predict a non-local collapse of the wave-function. Remember that’s what we need superdeterminism for: that there is no spooky action at a distance. But once you have measured the quantum state, that’s the end of those violations of statistical independence.
I should probably add that a “measurement” in quantum mechanics doesn’t actually require a measurement device. What we call a measurement in quantum mechanics is really any sufficiently strong or frequent interaction with an environment. That’s why we don’t see dead and alive cats. Because there’s always some environment, like air, or the cosmic microwave background. And that’s also why we don’t see superdeterministic correlations in people.
Okay, so I hope I’ve convinced you that superdeterminism doesn’t limit anyone’s free will and doesn’t kill science, now let’s see what it’s good for.
Once you understand what’s going on with the double slit, all the other quantum effects that are allegedly mysterious or strange also make sense. Take for example a delayed choice experiment. In such an experiment, it’s only after the particle started its path that you decide whether to measure which slit it went through. And that gives the same result as the usual double slit experiment.
Well, that’s entirely unsurprising. If you considered measuring something but eventually didn’t, that’s just irrelevant. The only relevant thing is what you actually measure. The path of the particle has to be consistent with that. Or take the bomb experiment that I talked about earlier. Totally unsurprising, the photon’s path just depends on what you measure. Or the quantum eraser. Of course the path of the particle depends on what you measure. That’s exactly what superdeterminism tells you!
So, in my eyes, all those experiments have been screaming us into the face for half a century that what a quantum particle does depends on the measurement setting, and that’s superdeterminism. The good thing about superdeterminism is that since it’s local it can easily be combined with general relativity, so it can help us find a theory of quantum gravity.
Let me finally talk about something less abstract, namely how one can test it. You can’t test superdeterminism by measuring violations of Bell’s inequality because it doesn’t fulfil the assumptions of Bell’s theorem, so doesn’t have to obey the inequality. But superdeterminism generically predicts that measurement outcomes in quantum mechanics are actually determined, and not random.
Now, any theory that solves the measurement problem has to be non-linear, so the reason we haven’t noticed superdeterminism is almost certainly that all our measurements so far have been well in the chaotic regime. In that case trying to make a prediction for a measurement outcome is like trying to make a weather forecast for next year. The best you can do is calculate average values. That’s what quantum mechanics gives us.
But if you want to find out whether measurement outcomes are actually determined, you have to get out of the chaotic regime. This means looking at small systems at low temperatures and measurements in a short sequence, ideally on the same particle. Those measurements are currently just not being done. However, there is a huge amount of progress in quantum technologies at the moment, especially in combination with AI which is really good for finding new patterns. And this makes me think that at some point it’ll just become obvious that measurement outcomes are actually much more predictable than quantum mechanics says. Indeed, maybe someone already has the data, they just haven’t analyzed it the right way.
I know it’s somewhat boring coming from a German but I think Einstein was right about quantum mechanics. Call me crazy if you want but to me it’s obvious that superdeterminism is the correct explanation for our observations. I just hope I’ll live long enough to see that all those men who said otherwise will be really embarrassed.
Yes, I have taken traveling back up and optimistically agreed to a public event in Vancouver on April 14, together with Lawrence Krauss and Chris Hadfield. If you're in the area, it would be lovely to see you there! Don't miss the trailer video
[This is a transcript of the video embedded below. Some of the explanations may not make sense without the animations in the video.]
A few weeks ago I talked about hypersonic flight and why that doesn’t make sense to me. A lot of you asked what’s with Elon Musk’s hyperloop. Does it make any more sense to push high speed trains through vacuum tubes? Can we maybe replace flights with hyperloops? And what’s a hyperloop in the first place? That’s what we’ll talk about today.
As I told you in my previous video, several companies have serious plans to build airplanes that fly more than five times the speed of sound. But physics gets in the way. At such high speed, air resistance rises rapidly. Even if you manage to prevent the plane from melting or simply falling into pieces, you still need a lot of fuel to counter the pressure of the atmosphere. You could instead try flying so high up that the atmosphere is incredibly thin. But you have to get there in the first place, and that too consumes a lot of fuel.
So why don’t we instead build airtight tubes, pump as much air out of them as possible, and then accelerate passenger capsules inside until they exceed the speed of sound? That’s the idea of the “hyperloop” which Elon Musk would like to see become reality. He is a busy man, however, so he made his take on the idea available open source and hopes someone else does it.
The idea of transporting things by pushing them through tubes isn’t exactly new. It’s been used since the eighteenth century to transport small goods and mail. You still find those tube systems today in old office buildings or in hospitals.
In 1908, Joseph Stoetzel, an inventor from Chicago sent his own child through such a tube to prove it was safe. Yeah I’m not sure what ethics committees would say about that today.
The idea to create vacuum in a tube and put a train inside is also not new. It was proposed already in 1904 by the engineer and physicist Robert Goddard, who called it the “vactrain”.
The quality of a vacuum can be measured either in pressure or in percent. A zero percent vacuum is no vacuum, so just standard atmospheric pressure. A one hundred percent vacuum would be no air at all. An interest group in Switzerland has outlined a plan to build a network of high speed trains that would use tunnels with a 93 percent vacuum in which trains could reach about 430 kilometers per hour. That’s about 270 miles per hour if you’re American or about one point four times 10 to the 9 hands per fortnight if you’re British.
It doesn’t look like the Swiss plan has much of a chance to become reality, but about 10 years ago Elon Musk put forward his plan for the hyperloop. Its first version should reach about 790 miles per hour, which is just barely above the speed of sound. But you should think of it as a proof of concept. If it works for reaching the speed of sound, you can probably go above that too. Once you’ve removed the air, speed is really far less of a problem.
Hyperloop is not the name of a company, but the name for the conceptual idea, so there are now a number of different companies trying to turn the idea into reality. The first test for the hyperloop with passengers took place last year with technology from the company Virgin Hyperloop. But there are other companies working on it too, for example Hyperloop Transportation Technologies which is based in California, or TransPod which is based in Canada.
Why the thing’s called the hyperloop to begin with is somewhat of a mystery, probably not because it’s hype going around in a loop. More likely because it should one day reach hypersonic speeds and go in a loop, maybe around the entire planet. Who knows.
Elon did his first research on the hyperloop using a well-known rich-man’s recipe: let others do the job for free. From 2015 to 2019 Musk’s company Space X sponsored a competition in which teams presented their prototypes to be tested in a one kilometer tube. All competitions were won by the Technical University of Munich, and their design served as the base for further developments.
So what are the details of the hyperloop? In 2013 Elon Musk published a white paper called “Hyperloop Alpha” in which he proposed that the capsules would carry 28 passengers each through a 99.9 percent vacuum, that’s about 100 Pascal, and they would be levitated by air-cushions. The idea was that you suck in the remaining air in the tunnel from the front of the capsule and blow it out at the bottom.
This sounds good at first, but that’s where the technical problems begin. If you crunch the numbers, then the gap which the air-cushion creates between the bottom of the capsule and the tube is about one millimeter. This means if there’s any bump or wiggle or two people stand up to go to the loo at the same time, the thing’s going to run into the ground. That’s not good.
This is why the companies working on the hyperloop have abandoned the air cushion idea and instead go for magnetic levitation. The best way to achieve the strong fields necessary for magnetic levitation is to use superconducting magnets.
The downside is that they need to be cooled with expensive cryogenic systems, but magnetic levitation can create a gap of about ten centimeters between the passenger capsule and the tunnel which should be enough to comfortably float over all bumps and wiggles.
But there are lots of other technical problems to solve and they’re all interconnected. This figure from Virgin Hyperloop explains it all in one simple diagram. Just in case that didn’t explain it, let me mention some of the biggest problems.
First, you need to maintain the vacuum in the tube, possibly over hundreds of kilometers, and the tube needs to have exits, both regular ones at the stations and emergency exits in between. If you put the tube in a tunnel, you have to cope with geological stress. But putting the tube on pillars over ground has its own problems.
A group of researchers from the UK showed last year that at such high speeds as the hyperloop is supposed to go, the risk of resonance catastrophes significantly increases. In a nutshell this means that the pillars would have to be much stronger than usual and have extra vibration dampers.
The other problem with putting the tube over ground is that temperature changes will create stress on the tube by expansion and contraction. That’s a bigger problem than you may expect because the vacuum slows down the equilibration of temperature changes in the tube. Since temperature changes tend to be larger over ground, digging a tunnel seems the way to go. Unfortunately, digging tunnels is really expensive, so there’s a lot of upfront investment.
This brings me to the second problem. To keep costs low you want to keep the tunnel small, but if the space between the capsule and the tunnel wall is too small you can’t reach high speeds despite near vacuum.
The issue is that even though the air pressure is so low, there’s still air in that tunnel which needs to go around the capsule. If the air can’t go around the capsule, it’ll be pushed ahead of the capsule, limiting its speed. This is known as the Kantrowitz limit. Exactly when this happens is difficult to calculate because the capsules trigger acoustic waves that go back and forth through the tunnels.
The third problem is that you don’t want the passengers to stick flat to the walls each time the capsule changes direction. But the forces coming from the change of direction increase with the square of the velocity. They also go down inversely with the increase of the radius of curvature though. The radius of curvature is loosely speaking the radius of a circle you can match to a stretch of a curve, in this case to a stretch of the hyperloop track. To keep the acceleration inside the capsule manageable, if you double the speed you have to increase the radius of curvature by four. This means basically that the hyperloop has to go in almost perfectly straight lines, or slow down dramatically to change direction.
And this brings me to the fourth problem. The thing shakes, it shakes a lot, and it’s not clear how to solve the problem. Take a look to the footage of the Virgin Hyperloop test and pay attention to the vibration.
It’s noticeable, but you may say it’s not too bad. Then again, they reached a velocity of merely 100 miles per hour. Passengers may be willing to accept the risk of dying from leaks in a capsule surrounded by near vacuum. But only as long as they’re comfortable before they die. I don’t think they’ll accept having their teeth shook out along the way.
So the hyperloop is without doubt facing a lot of engineering challenges that will take time to sort out. However, I don’t really see a physical obstacle to making the hyperloop economically viable in the long run. Also, in the short run it doesn’t even have to be profitable. Some governments may want to build one just to show off their technological capital. Indeed, small scale hyperloops are planned for the near future in China, Abu Dhabi and India, though none of those will reach the speed of sound, and they’re basically just magnetically levitated trains in tubes.
What do governments think? In 2017, the Science Advisory Council of the Department of Transport in the UK looked at Musk’s 2013 white paper. They concluded that “because of the scale of the technical challenges involved, an operational Hyperloop system is likely to be at least a couple of decades away.” A few months ago they reasserted this position and stated that they still favor high speed rail. To me this assessment sounds reasonable for the time being.
In summary, the hyperloop isn’t just hype, it may one day become a real alternative to airplanes. But it’s probably not going to happen in the next two decades.
[This is a transcript of the video embedded below. Some of the explanations may not make sense without the animations in the video.]
Is it ant-ee-matter or ant-ai-matter? What do ants think about it and why isn’t aunt pronounced aunt. These are all good questions that we’ll not talk about today. Instead I want to talk about why the universe contains so little antimatter, why that’s not a good question, and if there might be stars made antimatter in our galaxy. Welcome to another episode of science without the gobbledygook.
Last year, I took part in a panel debate on the question why there’s so little anti-matter in the universe. It was organized by the Institute of Art and Ideas in the UK and I was on the panel together with Lee Smolin from Perimeter Institute and Tara Shears who’s a professor for particle physics in Liverpool. This debate was introduced with the following description:
“Antimatter has fascinated since it was proposed by Dirac in the 1920s and confirmed with the discovery of the positron a few years later. Heisenberg - the father of modern physics - referred to its discovery as “the biggest jumps of all the big jumps in physics”. But there’s a fundamental problem. The theory predicts the disappearance of the universe within moments of its inception as matter and antimatter destroy each other in a huge cataclysm.”
Unfortunately, that’s wrong, and I don’t just mean that Heisenberg wasn’t the father of modern physics, I mean it’s wrong that Dirac’s theory predicts the universe shouldn’t exist. I mean, if it did, it would have been falsified.
When I did the debate I found this misunderstanding a little odd… but I have since noticed that it’s far more common than I realized. And it’s yet another one of those convenient misunderstandings that physicists don’t make a lot of effort clearing up. In this case it’s convenient because they want you to believe that there is this big mystery and to solve it, we need some expensive experiments.
So let’s have a look at what Dirac actually discovered. Dirac was bothered by the early versions of quantum mechanics because they were incompatible with Einstein’s theory of special relativity. In a nutshell this is because, if you just quickly look at the equation which they used at the time, you have one time derivative but two space derivatives. So space and time are not treated the same way which, according to Einstein, they should be.
Dirac found a way to remedy this problem, and his remedy is what’s now called the Dirac equation. You can see right away that it treats space and time derivatives the same way. And so it’s neatly compatible with Einstein’s Special Relativity.
But. Here’s the thing. He also found that the solutions to this equation always come in pairs. And, after some back and forth, it turned out that those pairs are particles of the same mass but of opposite electric charge. So, every particle has partner particle with opposite charge, which is called it’s “anti-particle”. Though in some cases the particle and anti-particle are identical. That’s the case for example for the photon, which has no electric charge.
The first anti-particle was detected only a few years after Dirac’s derivation. In my mind this is one of the most impressive predictions in the history of science. Dirac solved a mathematical problem and from that he correctly predicted a new type of particle. But what Dirac’s equation tells you is really just that those particles exist. It tells you nothing about how many of them are around in the universe. Dirac’s equation doesn’t say any more about the amount of anti-matter in the universe than Newton’s law of gravity tells you about the number of apples on earth.
The number of particles of any kind in the universe is an initial condition, which means you have to specify this number at some moment in time, usually early in the universe, and then you can use Dirac’s and other equations to calculate what happens later.
This means that the amount of particles is just a number that you must enter into the model for the universe. This number can’t be calculated, so one just extracts it from observations. It can’t be calculated because all our current theories work with differential equations. And those equations need the initial conditions to work. The only way you can explain an initial condition is with an even earlier initial condition. You’ll never get rid of it. I talked more about differential equations in an earlier video, so check this out for more.
The supposed problem with the amount of antimatter is often called the matter anti-matter asymmetry or the baryon asymmetry problem. Those terms refer to the same issue. The argument is that if matter and anti-matter had been present in the early universe in exactly the same amounts, then they’d have annihilated and just left behind a lot of radiation. So how come we have all this stuff around?
Well, was it maybe because there wasn’t an equal amount of matter and anti-matter in the early universe? Indeed, that solves the problem.
Case closed? Of course not. Because physicists make a living from solving problems, so they have an incentive to create problems where there aren’t any. For anti-matter this works as follows. You can calculate that to correctly obtain the amount of radiation and matter we see today, the early universe must have contained just a tiny little bit more matter than anti-matter.
A tiny little bit means a ratio of about 1.0000000001.
If it had been exactly one, there’d be only radiation left. But it wasn’t exactly one, so today there’s us.
Particle physicists now claim that the ratio should have been 1 exactly. That’s because for some reason they believe that this number is somehow better than the number which actually describes our observations. Why? I don’t know. Remember that none of our theories can actually predict this number one way or another. But once you insist that the ratio was actually one, you have to come up with a mechanism for how it ended up not being one. And then you can publish papers with all kinds of complicated solutions to the problem which you just created.
To see why I say this is a fabricated problem, let us imagine for a moment that if the matter anti-matter ratio was 1 exactly that would actually describe our universe. It doesn’t, of course, but just for the sake of the argument imagine the theory was so that 1 was indeed compatible with observer. Remember that this is the value that physicists argue the number should have. What would they say if it was actually correct? They would probably remember that Dirac’s theory actually did not predict that this number must have been exactly. So then they’d ask why it is equal to one, just like they do now ask why its 1.0000000001. As I said, it doesn’t matter what the number is, we can’t explain it one way or another.
You sometimes hear particle physicists claim that you can shed light on this alleged problem with particle colliders. They say this because you can use particle colliders to test for certain interactions that would shift the matter anti-matter ratio. However, these shifts are too small to bring us from 1 exactly to the observed ratio. This means not only is there no problem to begin with, even if you think there is a problem, particle colliders won’t solve it.
The brief summary is that the matter antimatter asymmetry is a pseudo-problem. It can be solved by using an initial value that agrees with observations, and that’s that. Of course it would be nice to have a deeper explanation for that initial value. But within the framework of the theories that we currently have, such an explanation is not possible. You always have to choose an initial state, and you do that just because it explains what we observe. If a physicist tries to tell you otherwise, ask them where they get their initial state from.
You may now wonder though how well we actually know how much anti-matter there is in the universe. If Dirac’s theory doesn’t predict how much it is, maybe we’re underestimating how much there is? Indeed, it isn’t entirely impossible that big chunks of antimatter float around somewhere in the universe. Weirder still, if you remember, anti-matter is identical to normal matter except for its electric charge.
So for all we know you can make stars and planets out of anti-matter, and they would work exactly like ours. Such “anti-stars” could survive in the present universe for quite a long time because there is very little matter in outer space, so they would annihilate only very slowly. But when the particles floating around in outer space come in contact with such an anti-star that would create an unusual glow.
Astrophysicists can and have looked for such a glow around stars that might indicate the stars made of antimatter. Earlier this year, a group of researchers from Toulouse in France analyzed data from the Fermi telescope. They identified fourteen candidates for anti-stars in our galactic neighborhood which they now investigate closer. They also use this to put a bound on the overall fraction of anti-stars which is about 2 per million, in galactic environments similar as ours.
While such anti-stars could in principle exist, it’s very difficult to understand how they would have escaped annihilation during the formation of our galaxy. So it is a very speculative idea which is a polite way of saying I think it’s nonsense. But, well, when Dirac predicted anti-matter his colleagues also thought that was nonsense, so let’s wait and see what further observations show.
