Saturday, August 07, 2021

Why the Hype around Hypersonics?

[This is a transcript of the video embedded below.]



Recently, we’ve seen quite a few headlines about traveling faster than the speed of sound. For example, the startup Venus Aerospace wants to reach 12 times the speed of sound. That’s nine-thousand miles per hour, and would bring you from New York to Frankfurt in less than half an hour.

NASA is working on a Quiet SuperSonic airplane called X fifty-nine, that’s supposed to have a reduced sonic boom and be ready in twenty-twenty-four. The American Airline United announced they want to offer supersonic flights by twenty-twenty-nine. And Boeing as well as some other companies have made deals with the US military about developing hypersonic missiles. How seriously should you take these headline? What’s the difference between supersonic and hypersonic? And what’s with those missiles? That’s what we’ll talk about today.

First things first, what is hypersonic flight? Is it just a fancy name to mean really fast? You know… hyperfast! No. Hypersonic flight is defined as flight above Mach 5. The Mach number tells you how many times faster than the speed of sound you are moving. So, moving at Mach 1 through a medium means you are moving at the speed of sound in that medium. Below Mach 0.8 you’re subsonic. The range from 0.8 to 1.2 is called transonic. Between Mach 1.2 and 5 you’re Supersonic, and faster than Mach 5 is hypersonic.

What happens once you fly faster than sound? A plane emits noise that travels outwards into all directions, at the speed of sound, but in rest with the air, not with the plane. If the plane moves below the speed of sound, some of the sound moves ahead of the plane. But if you reach the speed of sound, the plane moves exactly with the sound, and the sound piles up along a cone creating a shock-wave. This is what creates the supersonic boom. You can’t hear the plane coming, but you hear a loud bang once it’s passed by.

Actually, a plane usually creates two shockwaves, one at the front and one at the back of the plane. This means there are really two supersonic booms and if the plane is large enough, you can hear them separately. Here’s an example from the Concorde.

The supersonic boom happens at any speed above the speed of sound though it’s the loudest directly at the sound barrier since the sound spreads out somewhat more at higher speeds. For this reason, supersonic flights are currently forbidden over populated areas, they’re just too loud.

But what’s so special about Mach 5 that everything above is “hypersonic”? It’s somewhat of an arbitrary definition, but it’s roughly at about Mach 5 that some “funny effects” start to become important, effects that either don’t happen or aren’t important at lower speeds.

What are those “funny effects”? The issue with hypersonic flying is what physicists call “stagnation points.” If you have an object that’s flying through a gas fast enough, it’ll basically stop the flow of gas at some places. But the kinetic energy from the gas molecules has to go somewhere, and that increases the temperature to what’s called the “stagnation temperature”. Problem is, this stagnation temperature increases quickly with the Mach number.

The equation that relates the two looks like this, where T naught is the stagnation temperature and T the temperature before stagnation. M is the Mach number, and γ is a constant that depends on the medium. For air, γ is about 1.4. As you can see, the temperature increases with the square of the Mach number. That’s a problem.

Let’s plug in some numbers for illustration. If you are flying at an altitude of about twelve kilometers, like an average overseas flight, T is about 219 Kelvin, or a little below -50C. For Mach 1 this gives a stagnation temperature of about 260 Kelvin, so not much happens.

But already for Mach 2 the stagnation temperature is 390 Kelvin, that’s 117 Celsius. Next time you fly on a fighter jet don’t stick your hand out of the window. At Mach 5 the stagnation temperature is 1300 Kelvin and by Mach 8 you have 3000 Kelvin. At that temperature, most metals melt. That’s not good.

And it’s not enough to keep the metal from melting, because materials weaken long before they melt and also, the pressure increases along with the temperature. Worse, in these conditions out-of-equilibrium chemical processes occur, causing molecules to split or ionize.

Well, you may say, what about rockets, seems to work for them. Indeed, for example, the space shuttle was flying regularly at Mach 25. But. The thing with rockets is they go up. And if you go up, the atmosphere thins out and eventually ends, so air resistance is no longer a problem. The space shuttle left the atmosphere at “only” about Mach 3. Flying hypersonic in the atmosphere, that’s what’s the problem.

And we don’t want to do it with a rocket engine, but with a jet engine. The difference is that a rocket uses combustion with additional oxygen supply, and the rocket carries the source of the oxygen with it. That’s why they work in outer space. Jet engines on the contrary, take in and push out air. They are what’s called “air-breathing” machines. This requires less fuel and makes them lighter.

So how do you get to hypersonic speeds without melting the aircraft? Well the obvious thing is to use materials with extraordinarily high melting points. Among the most promising materials are Tantalum carbide and hafnium carbide with melting temperatures above four-thousand Kelvin. But that isn’t enough. To get beyond Mach 5, you need to redesign the whole engine. Interestingly, and maybe contrary to what you might have expected, you do this by removing parts.

In a jet engine, air enters the engine from the front is compressed with rotating blades. This heats the air, which is then mixed with fuel in the combustion chamber. But above about Mach 3 the air which enters the engine is hot and compressed just because it’s being slowed down so much, so one doesn’t need the compressor. The thing that’s left is called a ramjet, called that way because it “rams” into the air.

A ramjet can’t fly below Mach 3 because it doesn’t have a compressor, so it needs to be launched by other planes. But it works up to about Mach 6. Above that, temperature and pressure get too high to have good combustion

So why don’t we just keep the air flowing through the engine, instead of slowing it down, which causes the heating? Indeed, great idea. If you do this, you get what’s called a scramjet, short for Supersonic Combustion Ramjets.

The Scramjet design greatly alleviate the heating problem inside the engine. Scramjets are basically tubes with some divisions inside where fuel is injected into the air – they don’t even have moving parts. The problem with Scramjets is that the air goes in and out the other end in about a millisecond, and it’s also turbulent. So the challenge is to find the right shape to control the turbulence and get the fuel where it needs to be. Scramjets work from about 4 Mach upward. The current speed record is Mach 9.6 and is held by NASA’s X-43 jet.

In 2013 Boeing’s X-51 scramjet broke a record. It was the first scramjet to use jet fuel instead of hydrogen and had a more lightweight design. The record that it broke was not that of speed (it just flew a bit over Mach 5) but that of duration: it flew for 3.5 minutes.

Yes, you heard that right. 3.5 minutes. That’s the record. And don’t forget that to launch, it first had to be carried aboard a B-52, then accelerated to Mach 4.5 with a rocket booster.

The leader of the team that designed the X-51, Kevin Bowcutt, delivered a TED talk in which he envision a future when people take hypersonic flights regularly and he claims that a way to do it would be to use antimatter as fuel... Hahaha.

Ok, so I’m somewhat skeptic we’ll see hypersonic commercial flights in the near future. Not only, as you have seen, isn’t the technology ready, the whole process is also ridiculously fuel consuming. When it comes to supersonic flights, NASA seems to have made good progress in alleviating the problem with the supersonic boom by smart design. This is neat but doesn’t really do anything about the fuel problem.

This makes me think we might see some supersonic flights but they’ll probably remain rare and expensive. Personally I think it makes much more sense to look for a mode of transportation in which you excavate a tube or tunnel to lower air pressure, such as the hyperloop, because that way it becomes dramatically easier to reach high speeds.

So much about hypersonic travel, but what’s with those hypersonic weapons? It seems we’re in the middle of a hypersonic arms race between the United States, Russia and China. Russia recently became the first nation to deploy a hypersonic missile, tested in December 2018. And the Chinese have created a new hypersonic wind tunnel that, if you trust the Chinese media reaches up to 30 Mach. If you don’t trust them it’s still 22 Mach.

The budgets for this research are, one could say, stratospheric. For 2021, U.S. research agencies have allocated 3 point 2 billion US dollars for hypersonic weapons research, up from 2 point 6 billion in the previous year.

The attraction is easy to understand: at these speeds the enemy just doesn’t time have to react to the missile. The path of “normal” ballistic missiles is easy to predict, so anti-missile systems can target and destroy them. They’re also easy to see coming by radar because they fly high. But hypersonic missile are fast, can fly low and only appear on the radar late, and can unpredictably change direction, so by the time you see them it might be too late to do anything about it.

But is it all advantages? No, according to a paper by researchers from MIT, that appeared in January 2021. That’s because common ballistic missiles fly at high altitudes where the air pressure is really low and reaching hypersonic speeds is fairly easy. They then simply fall down, but even so still hit the ground at hypersonic speed. According to the MIT researchers, with an optimal trajectory, a ballistic missile would even be faster than a hypersonic glider.

They calculate that for a distance of 8500 kilometers, the hypersonic glider would take 28 minutes, and the optimized ballistic path only 25 minutes. They claim that the threat from hypersonic weapons has been exaggerated by military officials, quite possibly to get funding. In their paper, they write:
“It is commonly claimed that hypersonic weapons can reduce warhead delivery times by reaching their targets faster than existing ballistic missiles could. In 2019 testimony before the U.S. Senate Committee on Armed Services, the Commander of U.S. Strategic Command addressed this delivery time issue. Asked how long it would take a Russian hypersonic glide weapon to strike the United States, he responded: “it is a shorter period of time. The ballistic missile is roughly 30 minutes. A hypersonic weapon, depending on the design, could be half of that, depending on where it is launched from, the platform. It could be even less than that.””

The researchers then explain “The implication that a hypersonic missile could halve the time necessary to deliver a warhead between Russia and the United States—while false—subsequently permeated the U.S. discourse, fueling narratives of the revolutionary nature of these weapons.”

They also claim that even though land radars cannot detect missiles flying low until they are too close, because they are behind the Earth curvature, hypersonic vehicles flying inside an atmosphere are actually easy to detect. That’s because they become so terribly hot that they can be seen from satellites with infrared detectors. They conclude that the performance and strategic implications of hypersonic weapons would be comparable to those of established ballistic missile technologies.

So, my conclusion from all this is that we might well see some supersonic passenger flights again in the next decades, but I doubt they’ll become common, and hypersonic missiles are an overhyped threat. We have better things to worry about.

84 comments:

  1. "researchers from MIT ... claim that the threat from hypersonic weapons has been exaggerated ... to get funding... We might well see some supersonic passenger flights again in the next decades, but ... hypersonic missiles are an overhyped threat. We have better things to worry about."

    My thanks to you and MIT for this excellent and insightful analysis. Yes, there are cases where governments allocate billions of dollars to military research programs based on overhyping of the arms-race risk. This sounds like it may be one of them.

    Such funding argument works well for historical reasons. A famous and highly respected physicist once assessed the probability of exponentially expanding nuclear fission reactions existing in real materials to be so low that his country chose not to allocate significant funds to such research. The subtler details of why he did that are so interesting that an excellent play was made about the event.

    Even now, many decades since that profoundly impactful event, the risks of not funding basic physics research has provided a powerful funding argument. Particle collider research funding arguably has also benefited from this fear that "someone else" might land first upon some unexpected and incredibly dangerous new bit of fundamental physics.

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    1. Hi Terry (8)
      The version of the story I heard had less to do with a misjudgment of the probability than with the timeframe that management had set for developing the end product resulting from the probability considerations...
      So basically with the misjudgment of the management about the impact of the probability considerations...
      But that also extended to other areas at the time.
      ...
      In my opinion, this special case represents a rather fortunate misjudgment of reality for us.

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    2. But then there was that time when we took fully 1/3 of our war economy and built and elaborate process to build just a few nuclear weapons based on the advice of just a hand full of people. Remember that?
      Good times.

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  2. When it comes to claims of military threats it is important to listen for the sound to possible cash registers and to train the nose for the smell of cash. The introduction to Pink Floyd’s “Money” helps. The whole industry is a cynically dishonest enterprise meant to tie a nation down with ever more exorbitant military budgets. Those at the top walk all the way to the bank, “Money, it’s a hit … .” The song “Us and Them” is on the same album.

    The supersonic boom is not just the pile up of sound from an object moving faster than sound. It is a shock wave generated in a medium. I had the dubious experience of having a bullet fly close to me, where there was a loud snap sound followed by the sound of the gun. In America these things can happen, and a lot of people see it as a sort of freedom. Anyway, the snap sound was the shock wave generated by the bullet moving faster than sound in air. It is my understanding that the crack sound of a bullwhip is a miniature sonic boom.

    The shock wave bleeds energy away from a moving body at a rate proportional to v^4. This can be adjusted based on the geometry of the object, where a moving plate or blunt end of a reentry capsule will have more and a more arrow shaped object less. This is a big attenuator of energy for supersonic aircraft, and most combat aircraft do not fly much above Mach 2. At Mach 2 there is a second conical shock wave generated that bleeds more energy.

    I have pondered whether Cherenkov produces an electromagnetic analogue of this double shock wave. That would require a material with an index of refraction n > 2. Maybe some particle channeling of neutrons through diamond?

    A transonic aircraft is such because there can be over wings and the rest air moving relative to that surface faster than sound. Notice that commercial aircraft have max speed at 960km/hr or 600mph. They generally cruise at a somewhat slower speed. This keeps them from the aerodynamics of transonic flight. Similarly, a body traveling faster than sound can have air speed relative to a surface shower than sound.

    As for commercial travel faster than sound I seriously doubt that will become the everyman’s mode of flight. The kinetic energy scales of course as v^2 and that will require more fuel. Also, the shock wave will bleed energy. Even if there is an improvement over the Concorde the ticket cost will be steep. Hypersonic travel will be prohibitively expensive. The antimatter comment is clearly wrong. It is produced by colliding particles at relativist velocities and maybe some for a time stored in a ring. I seem to remember the going price is around $50 trillion per gram.

    In the early days of space flight there were the Mercury astronauts who were lofted by Redstone and Atlas rockets, where the latter went into orbit. There as a competing program called the X-15 that was a rocket plane that reached Mach 6. Neil Armstrong was an X-15 pilot. This did not become the space standard, for the rocket approach gets one out of the atmosphere quickly and the shock waves and dynamic pressure/heating is gone.

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  3. Continued: The Russian have claims of a hypersonic missile. There are even videos of these, where it lofts into the air, stops, turns horizontal and then takes off. The idea is that antimissile systems will not work as well. Of course, given the heat they generate an IR system might work. This just represents the latest iteration of a technocratic game of military one-upmanship. Since this involves nuclear warheads, it is connected to weaponry we really cannot hope to use in a war with any positive outcome.

    The nature of conflict is changing. We now have cyberwar, and the world is curiously almost constantly in cyberwar now. We also have terrorists and asymmetrical war. A purpose for war is to dominate other powers or nations, and there are those in power in certain regions of the world who see fecundity as their main strategy for world domination. Very costly and energy intensive systems may not really be the wave of the future. However this is promoted, humanity is best to see those at the top of any nation or society trying to hustle these things for the gangsters they really are.

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    1. My worry is that they'll come up with something else extra-deadly instead.
      I believe MIT and Dr. Hossenfelder but the fact that there are still people working on this in the first place tends to dampen my hope for humanity a fair bit.

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    2. Look up slaughterbots on Youtube. It is somewhat dated now, I think it was 2017 when it came out. It is a disturbing look at the future prospect for killer drones. I read an article a few months back about a contract to make a type of killer drone. To be honest these worry me more than nypersonic missiles.

      To be honest, what concerns me with the prospect of a nuclear war is that these systems are tied into command and communication systems that are very complex. A computer failure, maybe malware uploaded into the system and so forth could give a false reading of an attack. Events similar to this have already occurred. In the age of self-driving cars etc, will we have before long AI based launch systems?

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    3. I agree.

      When I was a teenager, I wrote an essay on nuclear bombs and the efforts to contain the threat to humanity through international treaty for school. Nevertheless, it was seriously depressing to contemplate that a man or a woman could wipe out a city and all its citizens to the last man, woman and child through the push of one button. And that we have come to this.

      Leonardo da Vinci drew a picture called Vitruvius Man. It's a famous picture. He drew a naked man with his arms and legs all stretched out and whose tips are on the boundary of a surrounding square and circle. Traditionally, its seen as a comment on proportion as in the golden ratio and the like. Given da Vinci's interest in science, it can also be seen as da Vinci's prophesy on the relationship between science and man. That the two would be in harmony. Here, we use his use of Euclidean geometry as a metaphor for science. In a way, it's a picture of a new cosmogony. Since harmony is also about proportion, it is about proportion on a higher level than the more literally minded proportion of measure. It's the kind of picture that Francis Bacon, the advocate and philosopher of science might have endorsed.

      But in the 20th C, after two world wars and after the atomic bomb, such a picture, such a prophesy has to be revisted. This was done by Bacons namesake and distant relation, the painter Francis Bacon. He painted pictures of a brutalised, mutilated and isolated figure of a man imprisoned in a cubic prison of white lines.

      Here, the new cosmography of our own times. Science and technology, far from being the hand-maiden of freedom, of liberty and wisdom has turned into his curse. It's his answer to da Vinci's prophesy, or hope.

      Some Christian and Islamic philosophers will not have been surprised, knowledge and know how does not neccessarily bring contentment and happiness in its train. David Hilbert is famous for having said: Wir Wirden Wissen (We must know, we will know). What are we to make of this in the light of the 20C, a centurybof atrocities without parallel in human history? That we are capable of this?

      In Simone Weil's opinion, scientific and technological development outran the development of moral and social institutions. Whereas Francis Bacon painted a scrotum at the base of a cross. He was (a lapsed) catholic. For him, blind, relentless and megalomaniac desire was the culprit.

      A couple of days ago it was the anniversary of the dropping of two atomic bombs on Hiroshima and Nagasaki by the United States of America. This was after Japan had made overtures for a conditional surrender to the USA, the main proviso being that the Emperor Hirohito would maintain his position without loss of face. This would have bedn possible through a constitutional monarchy, the arrangement that we have in Britain. Given all this, it was the opinion of Dwight Eisenhower, Supreme Commander of the Allied Expeditionary Force in Europe and later the 34th President of the USA, "it was not neccessary to hit them with that awful thing."

      But we did, because we wanted to show a newly unified USSR that we meant business and that we were gunning for worldwide dominance. Something that we have achieved - it's called globalisation. I'd call it - megalomaniac desire.








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    4. @Lawrence Crowell:

      Slaughterbots have been covered by Phillip K Dicks SF short story, Second Life with the twist that they autonomously evolve.

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    6. I watched the 'Slaughterbots' movie, and the scary thing is how already credible it seems. I was wondering for a few minutes what the hyperspeed missiles were meant to distract us all from, then I hugged my cat and remembered what the source of my info was (close enough to infallible).
      It's a pretty grim possibility to entertain even as a thought exercise though.

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  4. Dr. Hossenfelder totally looked 'the bomb' in this week's video, speaking of armaments.

    After reading the discussion a few days ago about a car as a real object vs. models, diagrams etc. of that car, I wondered what an exact copy of that vehicle built with chocolate and confectionery would represent conceptually since it could not function like the original car.

    I think the most appropriate comparison would be with the 'anti-matter engine'.

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  5. Calm, cool, rational thinking-- analytical and clear, is as bracing as a stroll through a forest glade, and in many ways much finer because you are less likely to be bitten by something.

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    1. I seriously think Dr. Hossenfelder should be some sort of political/diplomatic advisor in the future. I'm not just saying that out of a surplus of enthusiasm, we need as much clear, thoughtful thinking and rational persuasion as we can find.

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  7. What about the claim that the Russians are using MHD on some of their hypersonic weapons to limit overheating?

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    1. Well, do you find this claim credible? And if true, would that not be a technological breakthrough that justifies at least some of the hype?

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    2. Addendum: for readers who do not know what is the MHD claim I am asking about, you can look up the wikipedia page on ayaks: https://en.wikipedia.org/wiki/Ayaks.
      Besides heat reduction, MHD would also be used in the propulsion system according to that article.

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  8. A couple of points: one other strategy for hypersonic engines is to COOL the incoming air using liquid hydrogen as the heat sink.

    Then the air can be compressed and combusted with the now warm gaseous hydrogen in a normal jet engine. British SABRE (Synergetic Air Breathing Rocket Engine) project is trying this.

    The advantage is that it can work all the way down to 0 speed, no need for rockets.

    The most demanding part of this is the heat exchanger. It has truly ridiculous requirements, but it might be possible to create.

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  10. For any given speed the Mach number goes like the inverse squareroot of absolute temperature 1/SQRT(T), so the Mach number changes as altitude changes, sometimes decreasing, sometimes increasing as in the Troposphere, Stratosphere, or the Chinese Hyposphere. :)

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  11. The August 2021 edition of Scientific American has an article about hypersonic flight.

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    1. Well, hmm, I didn't know this when I recorded this video.

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  12. I agree that hypersonic missiles are an overhyped threat. If we, or our enemies, decided to nuke each other I'm pretty sure the first step would be to employ some sort of electronic warfare, with the hope of disabling communications and radar detection capabilities, so that supersonic or even subsonic carriers, like World War 2 type bombers could be employed to deliver their weapons of mass destruction, without the fear of any timely retaliation.

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    1. I Worked on the Grumman EA6B aircraft. It was an electronic warfare airplane. I have no secrets to share about it. I was just a mechanic. But you can be sure that the CIA is monitoring this blog to see if anyone is saying too much.
      Lose lips sink ships.

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  13. I remember when the Concorde was being built and they said it would become the future of air travel and bring air travel within the budget of everyone. That was an early lesson for me to 'waut and see' about new technology.

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    1. We're supposed to be colonising the Moon and Mars by now, too.
      :)

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    2. On the other hand, we do have the internet, email and the final encyclopedia, ie Wikipedia (the final encyclopedia was a trope in Gordon Dickson's SF novel of the same name). Plus smartphones and induction hobs.

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  14. Sabine, I think you’ve misunderstood why hypersonic missiles are a threat - the reason is none of the ones in your article.
    The fundamental problem isn’t targeting, or even speed in itself, it’s about actually hitting it with a counter-missile due to manoeuvrability.
    A ballistic missile is just that: ballistic. After the launch phase, it is unpowered and its trajectory is extremely predictable. An SBIRS satellite will detect in fact its hot launch plume, and direct an counterstrike based on predicting trajectory up to *8 minutes* later.
    A hypersonic missile, being within the atmosphere, can and does use its flight surfaces to perform violent avoidance manoeuvres, achieving up to 5g lateral accelerations. It would be absolutely pointless to launch countermeasures from a thousand kilometres away based on a linearly predicted trajectory.
    Within the atmosphere, a merely supersonic mIssile is simply too slow to either catch up with a hypersonic, or keep up with violent avoidance manoeuvres.
    The only way you can destroy a hypersonic missile is with another hypersonic missile, and that’s a real problem.

    It is also believed to be impossible, or at least very hard, to destroy a hypersonic missile using a laser. Even though the airborne laser weapons are still not fully operational, so we don’t know their exact capabilities. The optical distortion due to atmospheric ionisation and shockwave produced by the hypersonic are likely to strongly defocus a laser beam before it hits the missile rendering it harmless. You need a dwell time of over ten seconds, and perfect focusing, for a laser beam to do any damage at more than a couple of kilometers, and a hypersonic just doesn’t hang around long enough.

    So that’s why we are worried about hypersonics. Because the only defence is another hypersonic

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    1. ThoughtForTheDay,

      Thank you for your thoughtful comment which I appreciate very much. I originally had a paragraph on this in the script. Alas, this means they'd be a threat because they're not ballistic, not because they're hypersonic, which made it rather off-topic for a video that was about speed. Did you have a look at the MIT paper that I referred to? Did you find anything wrong with their analysis? With best regards,

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    2. ThoughtForTheDay, I too was impressed with your analysis and concur with it. I would add that difficulty of local detection is also a problem for countering hypersonics. Unlike ballistic missiles, near-ground hypersonics can take advantage of hiding behind the curvature of the Earth and smart use of ground-level obscurations such as mountains.

      While satellite detection of the infrared signature of hypersonics is possible in principle, both signal delay and processing time could easily end up making such detections too slow to be relevant. For hypersonics even microseconds of reaction time delay count. By the time a location is received on the ground, the missile's hypersonic maneuvers may have redirected its trajectory too much for that location to be of much use.

      Invoking satellite detection thus is insufficient to dismiss the importance of local detection of hypersonics. Unfortunately, hypersonics could also make ground detection incredibly difficult.

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      ThoughForTheDay, I too would be interested in your analysis of the MIT paper. I'll be sure to read it this week. There are clearly some concerning issues.

      ----------

      All: The above is just my off-hand analysis based the physics. If I have stepped on any points that some might consider sensitive, please be sure not to confirm that I did so. My simple physics analysis is by definition unclassified -- classification is, after all, a process that must be initiated by the government -- but for anyone looking at similar issues in some more sequestered context, you could risk violating the rules, even if we are saying the same thing. Take your no-confirmation briefings on issues like that seriously, please.

      Final point: It is counterproductive and a bit dumb to classify basic physics analyses. Doing so makes the technical analysis process needlessly harder, and doesn't truly protect anything, since the results are too easy to replicate independently. Technical classification works best for highly innovative ideas that are neither obvious nor trivial, and cannot be surmised simply from applying physics to public domain descriptions.

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    3. All these arguments apply of course not only to missiles carrying a nuclear payload, but to conventional payloads as well. Just picture a Chinese missile flying at hypersonic speed toward an American aircraft carrier during an invasion of Taiwan, and you can see why the U.S. military establishment is worried.

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    4. What they say seems reasonable - matches back-of-the-envelope anyway. They calculate that a glide vehicle can’t really manoeuvre “a lot” cross-range, because it will lose too much range, and I will believe them on that.
      But they aren’t analysing the case of it being smart and active, which is more likely. It would have radar, and can just do a single hard jink to avoid an interceptor.

      At 4km/s, the hypersonic could literally just deploy an airbrake to drop 0.2 km/s in the last 2 seconds when the interceptor is still 8km away, forcing it to overshoot by 200 meters, and there’s not a lot the interceptor could do about that. I’m sure there’s neater ways to do it.

      It’s probably true though that each intercept will bleed a significant amount of speed. Perhaps ten or twenty intercepting missiles could force one down.

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    5. I agree it’s a bit off-topic from the physics!
      I looked at the MIT paper. The short version is that I think they are right that a hypersonic glider has much less scope to maneouvre than I thought. But, they don’t take any account that it is likely to have powerful radar and actively avoid interceptors at the last moment.
      At 4km/s, it easily can detect incoming 30km away, and have 8 seconds to bleed 0.2 km/s in any direction it likes, including backwards. That’s going to be enough to avoid intercept.
      But the authors are likely correct in a wider sense, that its energy may only be sufficient for maybe 10 avoidance manoeuvres. So, it could be overwhelmed by 10:1 numerical superiority, that’s always an option.

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    6. The reference for the MIT paper, including the download site, is:

      [1] Tracy, C. L.; Wright, D. Modeling the Performance of Hypersonic Boost-Glide Missiles. Science & Global Security 2020, 28 (3), 135–170.
      http://scienceandglobalsecurity.org/archive/2020/12/modelling_the_performance.html

      The paper was done jointly by the Union of Concerned Scientists (Tracy) and MIT (Wright).

      Upon getting the actual paper, I have several concerns:

      (1) The paper is not “new” from January 2021; it is from March 2020.

      I am concerned about the date because this is by no means the first time I’ve seen a glowing popular press article about an MIT paper that was published months or even years ago. The forum, in this case, was the New York Times [2], which is primarily a real-time newspaper. One suspects someone strongly recommended this paper to them.

      Even when a paper truly is spectacular and for some reason got overlooked by the relevant community of technical peers, using forums such as the New York Times to push its conclusions is problematic. The New York Times is good, but they do not have the right resources to assess all such papers.

      However, more worrisome to me is that in several other instances of someone sending me this kind of glowing popular-press article about some overlooked MIT paper, my subsequent detailed analysis of the actual paper was always a disappointment. None lived up to the hype, and a few were frankly below average for their journals. I recall in particular one paper about a minor electrolysis innovation. It was not a bad idea, but neither was it impressive. Yet, from the general press article written about it, one would have thought it to be a sure bet for next year’s Nobel Prize.

      What irks me most is that the popular articles are so well-written that I keep falling for the same scenario: An MIT paper gets a glowing writeup in some famous popular forum, usually a year or so after its initial publication. A friend then sends me a link to the popular article, which I read first and think, “Wow, this sounds interesting and important!” I then dig up the actual article, read it, and find out it’s either mediocre or, in at least one case, flatly not what the popular article claimed. I then walk of my office and say to my family, “@#$#, I fell for one of those @#$@ PR articles again!” (Please note that except for cases involving malicious manslaughtering old folks and children via COVID, my profanity mostly ranges from “Dang it!” to “crap!”, and occasionally the initials of some famous university.

      Alas, it appears I will again be gifting my family with mild profanity this evening.


      (2) This is an incomplete analysis.

      Despite the bold claims of the popular press article [2], this paper does not cover a sufficient range of issues to qualify as an exhaustive analysis of a massively complex topic. I think my main concern boils down to this: Never, ever underestimate what some clever and goal-driven engineer or developer might come up with as a solution or workaround to some seemingly insurmountable set of issues. Skunkworks engineers, in particular, have a habit of taking some different approach that avoids an issue entirely.

      Much of the paper deals with spectral issues and graphs related to satellite detection. That’s fine, but it occupies a surprising amount of turf for what’s supposed to be a comprehensive analysis.

      I’ll leave it there for now, as it’s time for me to eat both supper and humble pie again (“#@$# I fell for it again!”)

      --------

      [2] Broad, W. J. Hypersonic Superweapons Are a Mirage, New Analysis Says. The New York Times. January 2021.
      Abstract: Two scientists find revolutionary claims about the evasion of detection and defenses to be “nonsense.”
      https://www.nytimes.com/2021/01/15/science/hypersonic-missile-weapons.html

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    7. Hi Terry,

      It's common to quote the publication date, which we took from this page

      https://www.tandfonline.com/doi/full/10.1080/08929882.2020.1864945

      I actually hadn't seen the NYT article.

      You are right of course that the MIT article is a limited analysis. But they are very clear what they are an aren't talking about. I see nothing wrong with that. I believe I have likewise been very clear that I was talking about the supposed threat from the speed advantage, though I guess I could have been clearer.

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    8. This comment has been removed by the author.

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    9. Sabine,

      Yes: For the topics it lists, the original 2020 paper is thorough and well done. I have biases and freely admit it. I used to perform similar analyses in my day job -- Google 'dod foss' for the most famous and impactful public example -- so I have a personal style of analysis of complex issues. My style differs from the one in this paper primarily in how broad of a view one takes in looking for unexpected 'gotchas!'

      Still, the 2020 paper (I won't bother to discuss the 2021 'hype' publication) makes a number of good and none-obvious points, especially in the critical area of comparative risks between technologies. So it's a good paper, just to me not as complete in coverage as the later 'hype' paper suggests. In particular, categorically dismissing the need for defensive hypersonics research based on this paper alone would be both stupid and dangerous.

      Which brings me to my final point: I hate arms races, yet I have more than once found myself advocating them due to the extreme dangers that can arise from assuming there is 'no significant threat' in some topic. A good example is how idiots like me did not adequately anticipate and warn folks of just how maliciously the Internet might end up being used in the future. Sure, folks like me worried and pointedly warned about physical resource cyber attacks, but what we missed assist completely was the devastating threat of destructive psychological and propaganda attacks using social media.

      The very concept of 'social media' popped up so suddenly and unexpectedly that one of the most brilliant and future-seeing venture capitalists I've ever met, Don Rainey, had to spontaneously offer to give our group a talk about it a year before most folks ever heard of social media. If I had to do it over, we would have red-teamed the idea right after that meeting and sent a screaming warning up the chain about how new tech was going to give some of the most destructive leaders on the planet direct and chummy access to the thought patterns and working presumptions of everyday citizens. Instead, like morons we did not follow up on the importance of what Don was telling us. Now I get to watch people I know and care about die needlessly and horribly (asphyxiation is not a fun way to die) due ultimately to mind-boggling levels of insane and very much maliciously intended misinformation spread over those very pathways.

      My first hope, always, is for politicians to get treaties with real teeth in place to halt arms races in any number of scary areas, some old and some new. But as demonstrated horribly by how some of us dropped the ball on anticipating psyops attacks via social media, we should also never just assume everything will turn out 'okay' in an emerging technology domain.

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  15. Vadim: Just to let you know, I belatedly saw and replied to your thoughtful comment under last week's "Is math real?" blog. I'm slowly getting the hang of this "Load more" issue!

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    1. IT guys having no idea how to use blogs. You're blowing the cover. :-)

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    2. I would like to point out that one of the worst "#@$#" words used in this industry branch is "user interface" (x)

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  16. [QUOTE]A protection racket is a racket or organized crime scheme where a potentially hazardous group guarantees protection, outside the sanction of the law, from violence, robbery, looting, raiding, piracy, and other such threats to polities, businesses, individuals, or other entities and groups in exchange for payment in cash or kind.[/QUOTE]
    But if it's inside "the sanction of the law" it's the "natural order" ...

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  17. Saturn V completed 13 successful missions to our moon and back without a flight failure - a remarkable success record. Spiro Agnew then Chair of the National Aeronautics and Space Council reporting to President Nixon, planned a Mars mission by 1986 (even earlier in press briefings). The hardware is sound, but politics is everything.

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  18. C Thompson, I left a long reply to your “Is math real?” comment made at 2:19 AM, August 07, 2021. After a LOAD MORE, my reply will be near the bottom of the main thread. This is the last time I'll do this, as it's time to move on.

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    1. Thanks. :) We're getting ba handle on this!

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    2. Part 1 of 2:

      Thanks for your reply, my response ended up being even longer but I hope is worth the reading. I found that I had a lot of Thoughts to Share.

      I found Superdeterminism a la Hossenfelder somewhat overlaps predestination but for the whole 'purpose' that religion brings. 'No Free Will' runs counter to the idea we choose to follow our deity and do their will. I have enough trouble taking No Free Will on board as an atheist. If there is no way a deity can alter what happens in life, all the 'Omnis' go out the window anyway.

      The earliest conundrum I found is, why does God exist? I asked that as an adolescent/teen to a young leader of the Christian-run youth organisation I was part of; I didn't really get an answer. A similar question is, why the Universe, why something instead of nothing?
      My answer to your question of an irresistible force encountering an immovable object as a problem for God is that, of course God could move it, they control everything. The irresistibility and immobility are what human beings would encounter, not the mover of all the Universe's forces and matter. As for 'she', I figured you were seeing what I'd say. I'm not attached to the Christian God having a gender and the designation is seen as likening God to being a father to their followers, not that God is a male (or even gendered) being.

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    3. Part 2 of 2:

      I pointed out to Steven Evans at least once that there are examples of scientifically-minded people who were also religious, (Gregor Mendel being a well known one) but he did not grasp that point. Wonder at creation and curiosity about how it works seem rather natural together. I think it's not faith that turns away intellect, it's the abuse of religion for manipulation and self-aggrandisement.

      The Middle East and Islam have seen the creation of buildings with breathtaking interiors full of dazzling geometric designs.

      There are any other number of spectacular religious buildings and artifacts that are mathematical and creative marvels, so I think that belief in and yearning for 'something more' is part of human creativity. I assert that even non-theist, non-spiritual people manage to find a way into that realm, if they come up with ideas and models that are striving to explain the Universe from mathematics and physics.

      Humans want to find the ways and rules to bring different parts of reality to bear, in so many different ways. (I'm getting tired now and long-winded) so I think it's natural that we end up with numbers and geometry, writing, astronomy, medicine, etc. along with myths, superstitions, religions, mystic orders, various ways to divine the future, talk to gods and spirit guides, aliens and the dead. Much of the latter gets in the way of gaining and using scientifically valid knowledge so for me, the vital thing is to keep looking past all the woo and hype for true knowledge.

      Dr. Hossenfelder has also explained how scientific thought was formerly coupled to the conviction that it would work a certain way because God created it but that as understanding grew, God as a factor diminished.

      The framing of religion, the Multiverse etc. being outside of science meshes with my thought that humans will believe all sorts of things (including Christianity) as a matter of course. It's not wrong or bad to believe thus, just not always helpful and sometimes dangerous.

      All this to say - we are indeed sitting in a soup of cultural and religious biases. (Hello, moralistic-conservative, pseudo-Christian kyriarchy!)

      As for 'good', 'bad', morality, and emotional reactions, I was involved on-and-off for almost a decade with a personal development company where participants were encouraged to jettison such judgements and focus on whether things worked or not. If people are hurt and exploited, there's no workabiity. Or, if one's communication is effective in maintaining relationships, that works. I have had resistance to that idea (very long discussions with my brother about God-given morals vs. whether things 'work' or not).

      Thinking in terms of 'workability' does give one more flexibility in thinking of solutions to problems, and more objectivity vs. emotional reactions. (To 'calm the farm', as it were.)

      Such objectivity is vital for testing assumptions and reproducibility. It's not easy to keep up all the time but it's a mindset worth cultivating.
      I hope that makes enough sense.

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    4. "an irresistible force encountering an immovable object" is not only not a problem for God, it is not a problem for nobody. The definition of "irresistible force" excludes the possibility of the existence of an "immovable object"; the definition of "immovable object" excludes the possibility of the existence of an "irresistible force." In other words, the question is meaningless. I can't lay claim to any philosophical or logical breakthrough here; the "shield and spear paradox is centuries older than I am.

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    5. @Jonathan Camp - My reply to Terry is above

      @giralua: Interesting, but I'm not sure I quite follow your reasoning.

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  19. Mike Carr
    Thanks for your videos. I often enjoy viewing them and learn what you present is often different than what a video title brings to my mind at first. Thanks for your insights. While hypersonic travel seems impractical, what do you think about the idea to do travel using ICBM type trajectories with rockets?

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  20. Great article!

    From a defense perspective, the worry is the threat these missiles might pose to our aircraft carriers. Current naval missile defense primarily relies on the SM3 (against intermediate range ballistic missiles in midcourse phase) and SM6 (short range and possibly intermediate range in terminal phase). However, both defensive missiles use boosters to reach speed and altitude to quickly get to an envelop where they can then coast to where the target will be in a couple minutes or less. If they had to contend with a maneuvering missile, neither would work because the envelop is very small and they would bleed off far too much energy changing course. The hypersonic threat is less to do with speed (versus ballistics) than it is the later detection due to altitude and potential course changes enroute to a carrier (i,e., swinging 400 miles out of the way and then circling back in).

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    1. There is one other important aspect to hypersonics that hasn't been mentioned but terrifies defense planners: It turns out that they tend to be naturally stealthy. As the hypersonic travels through the atmosphere, it can become shrouded in plasma. This plasma deflects or absorbs incoming radiation emitted by radars, making them hard to detect.

      There has been some debate about boost/glide versus powered hypersonics. Boost/glide is certainly a heightened threat, but powered hypersonics are the real "game changer" to use lame military parlance. This is because modified SM3's might stand a chance against a boost glide hypersonic, but powered hypersonics could only be countered with other powered hypersonics. An earlier comment discussed lasers but accurately discounted this possibility because even extremely high powered lasers would have limited single-digit-miles range at sea level and remember there is no warhead to target here - you are just trying to ablate some metal in a fraction of a second. There's just not enough time to melt enough metal to make a difference before the rifle bullet puts a hole through your ship.

      Also, I inaccurately minimized the threat to just our aircraft carriers. They are really a threat to any large surface combatant.

      Imagine a scenario where China had 300 of these weapons that worked combined with effective targeting data on our ships from satellites (difficult but not implausible in the next 20 years). The consequence would be that China could sink the entire Western Pacific fleet in less than 10 minutes and we would have no countermeasure. Hypersonics are an existential threat to the US Navy.

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  21. If a military destructive device, be it a nuclear bomb, a chemical bomb or a biological bomb, can be fitted and self powered within a simple commercial container with wireless internet access, then surely, foreign powers can have already deployed them in the center of the targeted cities, harbours, airports... and have no need of missiles, an internet encrypted code sent to those devices at the speed of light will do the destructive evil job just as well at a much lower cost. This is I believe the greatest risk we endure. We should find ways to scan our territories to check we are not already at risk. We should also largely improve the control of the numerous containers that are delivered to our harbours and enter our cities.

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    1. Of all the weapons boasts by the Russians, the one that is most disturbing is their claim of a torpedo drone. This could enter a harbor and stealthily hide for the time a command detonates a nuclear bomb. This strikes me as a very real possibility.

      Small nuclear bombs the size of a pineapple could be easily smuggled into a city, planted in some place to await a command. Of course there is the possibility one of these could be found that would alert the targeted national government. However, you are right that shear velocity may not be required for a surprise nuclear attack.

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    2. We do scan but it’s localized (e.g., D.C. access points) and kept fairly secret. Nuclear devices emit detectable signatures and there are reaction teams. But it’s expensive and hard so not feasible on a large scale.

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  22. Separately, the one inevitable incoming hypersonic missile that not only threatens us but will cause extensive extinction is the rogue asteroid. Meteors are hypersonic and typically enter the Earth's atmosphere at speeds of up to Mach 100. There is no way to protect the Earth from meteor or asteroid strike by intercepting them once they've entered the atmosphere. At that point all we can do is sit back and enjoy the spectacle. The only way to protect ourselves from an asteroid strike is to detect the asteroids early and nudge them out of the way while they are still millions of miles away. Fortunately research programmes to achieve this are already under way.

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  23. Here’s an in-depth response from a military perspective. Essentially, it echoes the post by ThoughtForTheDay
    https://breakingdefense.com/2021/02/pentagon-hypersonics-director-rebuts-the-critics-point-by-point/
    (It’s a two part article so you have to click the link at the bottom to read it all.)

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  24. I was amused to come across the current Scientific American article by David Wright and Cameron Tracy: "Over-hyped, Physics dictates that hypersonici weapons cannot live up to the grand promises made on their behalf" shortly after watching Sabine's video today. This is indeed a very timely topic!

    It occurs to me that it might be possible to apply an air breathing (or perhaps even nuclear powered) hypersonic engine to be used in the decent phase of a conventional ballistic missile approach. The engine would accelerate the missile (perhaps with a solely kinetic payload a'la tungsten "Rods from God"), to deliver the payload in a much reduced flight time - overcomming any speed advantage of a boost-glide hypersonic missle. This could allow for a reduced ballistic trajectory, further increasing the speed advantage ballistic approach and reducing detection capabilities from ground and space based sensors. A high mach kinetic payload might also be able to harness thermal energy with some EMP properties. There may be reduced maneuverabiltiy and targeting circular-error-probable at extreme temperatures and g-loads, but lower costs and increased speed would allow for multiple missle launches per target making up for such deficiencies.


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  25. Nuclear propulsion research was banned back in the 1960s.
    I wonder, if it's carrying a nuclear warhead would it really matter if it was nuclear powered?

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    1. There were ideas of a nuclear powered bomber back in the 1950s. There were tests done to develop this. A B-36, a large plane that looks like a cross between the late WWII B-29 and the B-52, carried a nuclear reactor. There were some radiation issues. Then something went wrong, do not remember exactly, and the reactor had to be dropped. It impacted the ground near Albuquerque NM. The idea was also outcompeted by the missile. Then Kennedy shortly after taking office cancelled the program.

      The Russians claim to be working on a nuclear powered cruise missile that can remain aloft for months. This does not worry me as much as their drone torpedo, but it is maybe troubling. I suspect they are nowhere near a complete development on this.

      The Russians have had the white Tsars, then the red Tsars and now the blue-grey Tsars. They have a pretty consistent history of over extending their military power without the national infrastructure and economy to support that. The Russians then tend to be a bit of the pufferfish, in that they look really big, but their ability to actually project military power is not as large. Now of course if some nation invades Russia, Russians then march in coherent ranks and are a formidable force. Yet in times of peace Russia has a repeated tendency to overextend themselves.

      History does not repeat exactly, but it does sort of rhyme.

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    2. I live in Albuquerque, NM. (From Seattle).
      I always figured that something was in the water supply here. Maybe that's where it landed.

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    3. A little off topic, and not exactly hyper, but in WW2 the Japanese launched several balloon carried bombs towards the United States. Some of them made it! None of them worked. It was just a few years ago that another one, hopefully the last one, was discovered in a heavily wooded area of the Pacific Northwest.

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    4. Strewth.

      (C.f., the song 'Albuquerque' by Weird Al Yankovic)

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    5. I lived 20 years in Albuquerque. I worked on various physics programs in association with Sandia Natl Lab. The reactor or some component of it as I recall had to be dropped and fell between Albuquerque and Bernalillo to the north. I think the exact spot is classified. I hope nobody tries to build property there. The extent of the radioactive material release I think is also classified. The whole incident is considerably shrouded.

      As for the Russian nuclear powered missile, this is a part of a big idea people have had since the 1940s. It is incredibly difficult to realize. The usual idea for propulsion is a hot nuclear reactor that serves as the combustion chamber in a standard jet turbine. The reactor has to be really hot, but stable, which might mean a gas-core reactor, that then heats incoming air force by a turbo-fan and this then drives a turbine.

      Unless I am wrong, I would say this is probably a national boast. I think it is probably far beyond their abilities, or the abilities of any national defense research organization. The NEPA (as I recall it was called) program in the US was cancelled by Kennedy for being a big money eating program that produced nothing.

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    6. Lawrence Crowell,
      Remember the National Nuclear museum here? They moved it just up the road from Sandia Natl Labs. The have a few missiles on display. As an ex-structural mechanic I marvel at the excellent workmanship on those things. Most perfectly bucked rivets and safety-wire jobs that I have ever seen. They definitely took pride in their job building it. It's a shame that such a fine piece of workmanship was destined to be blown up.

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    7. Yes. It used to be on base. but they did move it. There is a Redstone rocket outside. I went there in 2006 or so with my son.

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    8. Sounds like 'a thing of beauty'. What a waste of human talent, I reckon.

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  26. some of the new russian missiles are apparently nuclear powered.

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  27. I do wonder how big a piece of flack it would take to destroy a missile going 4,000 mile per hour. I suspect the collision would be quite spectacular.

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  28. giralua 9:29 PM, August 10, 2021
    The definition of "irresistible force" excludes the existence of an "immovable object"... the question is meaningless.

    Yes.

    At the physical level, formal systems are always and only rules for transforming sequences of symbols. The symbols in such sequences have meaning -- can alter the future state of the universe -- only in the presence of Turing machines customized to know the symbols and take action upon seeing them. By a vast margin, the most common example of custom Turing machines is the cellular ribosomes that translate sequences of RNA symbols (codons) into proteins.

    Some symbol sequences define sets by telling their Turing machines how to find and mark objects in the physical world. However, even if a Turing machine can find and mark all the members of its set within a finite time, the symbol sequence that enabled recognition of that set remains a different object from the set itself, just as the DNA for creating a protein remains a different object from the protein it created.

    Most of the paradoxes of formal systems amount to little more than getting sloppy about the difference between the program-like symbol sequences used to find sets and the resulting sets. In particular, symbol sequences require custom Turing machines to have meaning. Since Turing machines are finite and embedded in causal time, the unsettling implication is that any formal statement that invokes an infinity, no matter how carefully and precisely it was done, is incorrect.

    An irresistible force meeting an immovable object thus is nothing more than a programming error. By twice invoking infinities, this symbol sequence causes its Turing machine interpreter -- that would be you, dear reader -- to enter into a infinite loop that oscillates between "irresistible" and "immovable".

    Getting formal systems back onto solid ground will require a major redo. For starters, the entirely of set theory, which at present is a dreadful mess of bad to exceptionally bad programming, needs rebuilding from the ground up. An example of exceptionally bad programming in the foundations of set theory is its use of asymmetric binary trees to "define" integers. This kind of outdated, noise-intensive, hyper-structured nonsense must be discarded entirely and replaced with axioms based on fundamental physics and a deeper understanding of cognition.

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    1. Part 2 of redoing the foundations of mathematics:

      Why would I say physics is needed to repair mathematics’ devastatingly sloppy deep foundations?

      Look at the standard set theory definition of an integer. It’s a LISP program that uses CAR and CDR commands, left and right binary-tree branch choices. That’s too much information! The phrase “three apples” does not include an implied order for the apples. Quite the opposite: the central concept of “three apples” is that the three apples are interchangeable with each other.

      When pre-computer programmers first designed set theory, they tossed quantity and order into the same module. The correct design is to implement quantity and order as fully orthogonal concepts. The original bad design complicates and needlessly adds noise to everything built on top of it.

      Fixing this requires recognizing that the concept of “integer” also defines the very essence of the word “set.” That is, an integer is an assertion that there exists some group of Turing-recognizable entities that are so easily interchangeable that there is no need to distinguish between them.

      That’s where physics comes in. For three apples to be interchangeable, there must exist one or more physics symmetries under which they can be interconverted, at least approximately. (Quantum objects are a delightfully stranger issue.) The main symmetry applied in the case of “three apples” is translational symmetry, the ability to exchange two or more apples without the Turing recognizer seeing any difference.

      Human-defined sets rely primarily on translational and rotational symmetries, though this is only the starting point for the possible symmetries. More subtly, such set definitions depend profoundly on time-translation symmetry since they assume the recognized objects persist over time.

      In other words, the Poincaré group of Minkowski spacetime symmetries makes integers and sets possible. Without the Poincaré group as the starting point, you cannot create a self-consistent definition of what an integer or set is.

      Delightfully, this means Noether’s Theorem is involved in defining integers and sets. Or, more precisely, its inverse, Rehteon’s Theorem. That is, absolute conservation of certain quantum numbers gives rise both to the ability to count and the ability to define indefinitely precise (but never perfect) continuums that interpolate between such counted quantities.

      There is more to the role of physics in enabling integers, sets, order, and continuums in formal mathematics, such as other symmetries and the role of binding forces, but the Poincaré group is a great start.

      However, the most profound irony in any self-consistent definition of “integer” is not its need for physics, but (tip of the hat here to philosopher Ron Green) its need for approximation. Because one cannot call a string of symbols a “formal statement” without first attaching a Turing recognizer to that string, the foundations of formal mathematics are intrinsically heuristic. That is because a real-world Turing recognizer is a finite state machine, and no finite-state machine can have sufficient complexity to record or observe the full diversity of the universe that surrounds it. Therefore, incomplete states and incomplete knowledge necessarily use approximation. Through their interpretation by human or non-human Turing machines, all formal sequences of symbols begin with Turing-based cognitive approximation.

      Recognizing the need for the Poincaré group of symmetries, Rehteon’s Theorem, and Turing approximations just to define “integers,” “sets,” and “continuums” makes the relationship between math and physics easier to discern.

      Mathematics arises from physics, not the other way around.

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    2. @Terry Bollinger:

      Personally, I think the phrase'an irresistable force meets an immoveable object' is a clever rewording of Aristotles definition of gorce which is, paraphrasing, 'a resistable agent meeting a moveable object'. This definition is in Aristotles physics or metaphysics - I forget which. Obviously, there is nothing to object to this definition, it is entirely intuitive, but of course it is boring compared the paraxodical rewording which catches the eye and mind but otherwise has nothing else to recommend it. Its rather like the zen koan: what is the sound of one hand clapping?

      One might say it illustrates the gap between language and the world; the world is neccessarily so, and language can model that world; but also as act of the free play of the imagination, it need not. And it may be that this free play catches our attention more than reality itself.

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    3. @Terry Bollinger:

      The integers are based on physics. Its a feature of our physical world that putting one stick next to two sticks gives you three sticks. Abstracting this gives the integers. Similarly geometry is also based on physics, the clue is in the name: geo-metry = earth measurement. This is what the anciebt mesopotamians bequeathed us.

      Interestingly enough, the integers can be generalised to higher dimensional integers. The way to do this is to go back to basics and visualise addition as the grouping together of sticks, as above. And then, rather than having them all vertical, allow them to slant or cross over. So for example, 2 is I I, but by crossing them over, we have X, where one stick has gone behind the other. Obviously, we can't call this two - it's a new number. Now, whereas, I + I I = I I I = I I + I, we have I + X = I X != X + I. Thus whilst the commutative law holds for the usual integers, they do not hold for these new generalised integers. However, the associative law still holds: (I + X) + X = (I X) + X = I X X = I + (X X) = I + (X + X). This often happens when generalising - we lose laws. However, in recompense, we gain an anotger addition. This second addition is obtained by stacking the sticks on top of each other:

      X
      X

      It's as simple as that. Again the commutative law fails for this second addition but the associative law still holds. Note, this second addition is not visible for the usual integers, since:

      I I
      I I

      is just

      I I

      That is the same number.

      Furthermore, set theory has already been reconceptualised. Look up topos theory. The idea is to conceptualise the category of sets by categorical properties and to consider all categories of this nature. These are the topoi. And it turns out that here Set, the category of sets, is the terminal Grothendieck topos amd so it occupies a special position. The interesting thing here is that every topos comes with an internal logic that is intuitionistic, that is excluded middle need not hold. In the higher categorical version of topoi, the notion of types enters this game, and we have an intuitionistic typed logic, conjecturally thought to be Martin-Lof typed logic. Now types bring in computer science. So here we see a unification between computer science, logic and set theory. It's likely that such a fundamental shift will allow us to re-evaluate how physics is to be thought conceptually at a fundamental level. For example, Chris Isham, the British physicist, has constructed the Bohr topos which is the presheaf on the category of all commutative subalgebras of any C*-algebras and he considers this to be the topos theoretic incarnation of quantum phase space. Other more radical ventures are being pursued by the Brazilian school of logicians, such as paraconsistency (where we can have true contradictions) in a topos context. I expect in the future there will be much more to say.

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    4. Mozibur, thanks! It's been a long time since I've visited John Baez's pages on category theory, which I just did to look up topos. John Baez has a nice knack, similar to what you just demonstrated with your "hold up some fingers" definition of integers, of helping readers connect everyday ideas with lesser-known mathematics. (A vision of the immense paper-based Mathematics and Statistics collection at Stanford just flashed through my mind.)

      At 10:45 PM, August 12, 2021 you said
      The integers are based on physics... [and] can be generalised to higher dimensional integers... for example, 2 is I I, but by crossing them over, we have X, where one stick has gone behind the other. Obviously, we can't call this two — it's a new number.

      Yes: As beautifully demonstrated by the example you just gave, doing nothing more than subsetting the Poincaré symmetries enables recognition of a larger set of "unique" entities. Here, you abandoned rotational symmetry. More precisely, you increased rotation quantization from one (all rotations give the same object) to two (vertical and horizontal orientations are unique).

      Adding indefinitely more bits to the angle enables complex-number-like orientations of the sticks, though getting to actual complex numbers requires more limits.

      Too many mathematical definitions are noisy — and thus prone to exponential generation of more noise — because they do not explicitly state which subset of the Poincaré symmetries defines their unique entities.

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    5. Or more simply: Imagine the Poincaré symmetries as an unblemished block of multidimensional jade. Mathematicians remove pieces of this block by introducing symmetry-breaking equations. The equations are Turing-enabled bits of classical information, bits that have meaning. The resulting sculpture is better known as a formal system. The definitions, axioms, and equations are the sculpture’s design. The finite Turing machines, often human, are the tools that bring the sculpture to life. Their cuts propagate throughout the Poincaré space, creating details and boundaries. Some of the resulting topologies are finite in the sense that the more the sculptor applies her knife, the sharper and more crisply defined the boundaries become so that after some point in the process, no new details emerge. These sharp-surfaced sculptures, including calculus, are most likely to follow the deeper structure of jade and thus represent objects such as electrons, positrons, quarks, and photons in the physical universe. Dirac, while primarily a physicist, was one of the greatest artists of this class. Other designs are easy to specify but fractally recursive in how they cut, giving rise to sculptures of literally limitless complexity and beauty. The Mandelbrot and Julia sets are examples of this group. But there is one final group of subtle cuts that is arguably the most profound of all in terms of impact. This group is the Boltzmann thermodynamic sculptures, which intertwine with the other sculptures to generate self-preserving chaos. In their endless but always Poincaré-compatible expansion of microscopic details that smooth out at larger scales, they end up creating and preserving both classical time and classical information.

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    6. @Terry Bollinger:

      > Delightfully, this implies that Noethers theorem is involved in defining integers and sets. Or more precisely, its inverse, Rehteons theorem ...

      Do you have a reference for Rehteons theorem? I tried googling it but the only page that came up was this page with your post mentioning this theorem - which is a tad self-referential.

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    7. Mozibur,

      My apologies, I should have been more specific: The phrase "Rehteon's Theorem" is entirely my own. I first posted it publicly in a comment I made here in Backreaction in December 2019 [1].

      No physicist or mathematician (I am neither) of whom I'm aware begins with the premise that absolute mass-energy drives continuity in both the natural world and mathematics. That is just one piece of my Dual Denisyuk Universe (DDU) interpretation of physics, which requires quite the bouquet of modest-to-abject heresies. These include:

      (a) The classical universe is a "low" (~atomic or nuclear) resolution, self-defining, 3D Denisyuk hologram (see [2]) that exists simultaneously in xyz and momentum space. This is as opposed to 't Hooft's Planck-scale, quasi-infinite-precision 2D projected holographic universe. This idea is just me.

      (b) Bits are emergent phenomena, a view that Julian Barbour seems to share [3]. Emergent bits are an important part of my Rehteon's Theorem because they ensure quantum smoothness in the absence of enough mass-energy to holographically project (some would say "observe") more details.

      (c) There are two universes, each of which looks like antimatter to the other. Both evolve with the same causal time, but are moving away from each other under the spatial interpretation of time. Sean Carroll et al had this idea first, Neil Turok et al are proponents of it, and even Julian Barbour et al now has his own version of it. I may be somewhat unique in asserting that the total mass-energy of this pair must be exactly zero, as with virtual particle pairs, of which this universe-antiverse pair is nothing more than a very-large-scale example that stubbornly refuses to self-annihilate due to the emergence of Boltzmann time;

      (d) Mass is a broken symmetry of angular momentum, and thus forms pairs the same way angular momentum does. The universe-antiverse is one such pair. It also means there are four forms of matter, not just two, with matter and antimatter both having negative-energy ("nee") versions with exact CPT symmetry. I'm not aware of anyone besides me who invokes fully symmetric negative mass and four versions of matter. I would argue that the idea is implicit in the Turok et al papers on this topic.

      (e) "Quantum observation" is nothing more than thermal "fractalization" of one side of an attojoule-ish momentum pair [4]. This idea makes observation the most common and fundamental quantum event in the universe. In particular, it means condensed matter continually "self-observes" to keep its atoms from drifting away into quantum nonlocality. This is an interpretation that, as best I can tell, is unique to me. But wow, a lot of metaphysical mumbo-jumbo just goes poof once you recognize that thermal matter constantly self-observes via mundane processes that have nothing to do with consciousness or intelligence. It's all just jiggle-jiggle + entanglement.

      --------

      [1] Bollinger, T., Rehteon's Theorem. Backreaction, Dec 2019.
      http://backreaction.blogspot.com/2019/12/why-laws-of-nature-are-not-inevitable.html?showComment=1576415807278&m=1#c2103696397057925275

      [2] Wikipedia, Yuri Denisyuk: Scientific_work. https://en.m.wikipedia.org/wiki/Yuri_Nikolaevich_Denisyuk#Scientific_work

      [3] Barbour, J. Bit from It. FQXi, Feb 2012.
      https://fqxi.org/community/forum/topic/911

      [4] Bollinger, T. Newton's Cradle and Quantum Observation. TAO Physics 2019 1027.
      http://tarxiv.org/tao.2019-10-27/

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  29. Mach 3 is not a lower limit for ramjets. In fact operational ramjet missiles, Talos, Moskit, Bloodhound... have had top speeds in the M2.2 to M3. There have even been subsonic ramjets, generally called athodyds. They been used at the tip of helicopter rotors to drive the blades, but only experimentally.

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  30. Dr. Hossenfelder,

    Thank you for this much needed clarification about the status of Lambda as a natural constant!

    While working on the history of the cosmological constant (as a history and philosophy of science student, not physics) I stumbled on an article written by the french mathematician Jean-Marie Souriau in 1976 (!) titled “Should we take the cosmological constant seriously?” in which he argues in favor of Lambda as natural constant in the EFEs and mentions that one of its consequences is the accelerated expansion of the universe (problem is, the article was never translated to english!). My point is that, historically, the discovery of cosmic acceleration is not unlike that of cosmic expansion (the whole Lemaître - Hubble fiasco) and that the 1998 results from type Ia supernova should be considered to be the first observation (evidence) of comic acceleration as opposed to the “unexpected discovery” since it has already been predicted in the framework of GR.

    I tried publishing this minor historical clarification but in vain. Nevertheless, I think it’s relevant to the debate about the nature of the cosmological constant and vacuum fluctuations.

    Thank you!

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