Recursion, Renormalization, Representation, and Reality

Where does the air come from when water boils?

If you like to listen rather than read, try this video.

The simplest answer is: energy creates space and pressure contains space.

This yin yang symbol is a nice, recursive, technical representation of boiling water or the sun or love, but if you want the gritty details, read on.

• You add heat energy to water and this energy makes the water molecules speed up until there is no way for them to move faster.
• At this point, they begin to collide and when two particles collide, they squish out a bit of energy.
• When that energy has nowhere to go, it turns into space — a tiny bubble of space.
• Nature hates a vacuum and all of the water is pressing in on that bubble, trying to make it disappear, so the bubble moves to cooler spots where the pressure is less intense.
• But lots of other bubbles have the same idea, so the bubbles collide and make bigger bubbles that rise to the surface.
• The surface tension of the water holds those bubbles in until they are big enough to break through and pop.

The story is complicated by the fact that for very small bubbles the internal pressure is very high — so high that they can’t exist, so how can something that can’t exist come into being? One popular explanation is that the surface of the pot provides a way for fractions of bubbles to come into being, thereby allowing them to be born and survive their trip to the surface, but this doesn’t really mesh well with the story I just told in terms of particles colliding and squishing out energy that has nowhere to go.

Which story is right and how do you decide?

I think the answer is found in the story of what happens when a bubble breaks through the surface of the water and releases its contents into the air.

When something under pressure breaks through a surface barrier into a low pressure space, it quickly cools. This is why your breath feels colder when you purse your lips as you blow out, but if you open your mouth wide and breathe out, you will create a cloud of condensation on a cold day. But the act of condensation releases heat and that is why when steam hits your arm, it will burn you more than direct contact with boiling water would.

Condensation is much like inverse bubble formation and whereas condensation releases heat, bubble formation absorbs heat. The colder the air is, the more condensation will occur and the hotter the water is, the more bubbles will occur. Condensation does not require a surface to occur and that is why I think that explanations of boiling that rely on the surface of the pot are probably wrong.

• If they were correct, a pot of perfectly pure water would boil more slowly than a pot of water with dirt in it.
• If they were correct, you couldn’t lower the boiling point by lowering the air pressure around the water, as it is at higher altitudes where it is easier for bubbles (energy) to break through the surface of the water.
• If they were correct, you couldn’t raise the boiling point by adding salt to water. Salt dissolves into big, heavy charged particles that attach themselves to the water molecules and slow them down. If the water molecules are like cars, the salt ions are like trailers attached to the cars that make it hard for the water molecules to move fast enough to collide with enough energy to make a bubble.
• If they were correct, water boiled in a mug in a microwave wouldn’t get superheated. A mug has a large surface area for bubbles to form, yet they don’t form even when the water has absorbed more energy than would be required to initiate boiling.

When you superheat a cup of boiling water in a microwave, the water will look like it is not hot at all until you touch it with a spoon and it erupts in scalding bubbles. This suggests that the energy or motion required to form bubbles must be sufficiently random, as in a Tibetan bubbling bowl. If the motion in water is too coherent, bubbles won’t form, even if sufficient energy has been absorbed.

The vibrations make the water molecules move in and out from the center of the bowl. Eventually, the amplitude of their oscillations becomes so great that they collide with one another. When they collide, they make a bubble that jumps up out of the pot.

This might seem confusing at first, since we all learned about conservation of energy in our science classes and we didn’t learn about a conservation of space principle… but shouldn’t there be one if energy is defined in terms of motion which is defined in terms of space?

Connecting these concepts to cosmology (ha), one might wonder – if space literally expands, how can there be objects receding at speeds faster than light? and then decide that in Cartesian space, the bubbles observed in boiling water are merely an illusion caused by light losing energy to the vacuum. In Riemannian space, the bubbles are literally caused by space expanding. This is, however, a weird way to think.

Nevertheless, thinking about boiling water is a nice way to understand why a pot of boiling water seems like it doesn’t conserve energy because some of the energy turns into space in the form of bubbles.

In the same way, the sun does not conserve energy if you do not consider the energy delivered to the system by the pressure of the vacuum or the pressure of gravity (which are two ways to say the same thing).

When the sun burns, it must also create space, but that created space adds back into the pressure of the vacuum, keeping the sun bright. Are sunspots like bubbles on the surface of a pot of boiling water or are they distorted gravitational shadows cast by the planets? Are these the same things?

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Why doesn’t everyone learn these stories about how water boils in school? My guess is that either science education is very unevenly distributed or the teachers are afraid that we will figure out how to discover the formula for splitting beer atoms.

I know, I know. That formula was was discovered by Albert Einstein, a Tasmanian who was the first person to figure out how to put bubbles in beer.

Just wait 200 years and it will be in all of the history books. (snark)

But before that happens, people will begin to understand how Einstein’s modern physics (general relativity and quantum mechanics) is an approximation of a recursive system and when that is understood by everyone, there will probably be a crisis which buries this knowledge for a few centuries until researchers find it again. At least, this sort of renewal of foundations and removal of spandrels seems to happen periodically as the planet warms and cools. Today, most people have no awareness of these patterns and have been convinced by their betters that the sea is boiling hot and that pigs will soon have wings as a result of genetic engineering.

What I know is that if you boil physics down to its essence, you are left with four things:

• Recursion is when you take the output of a function and use it as the input again and again.
• Renormalization is when you try to estimate the global properties of a substance based on its local properties and vice versa.
• Representation is when you create a description of a thing that exists in reality.
• Reality is the thing you represent through physics theories involving recursion and renormalization.

This all sounds so straight forward. Where did physics go wrong? I think it got off track when it forgot how boiling water works and gave Albert Einstein a Nobel Prize for the photoelectric effect.

If you shine a beam of light onto a pot of water and heat that water until boiling, would your theory of the average absorption and reflection of the light’s energy tell you exactly how many bubbles would rise to the surface of the water? No. It would tell you about the temperature of the water – a quantity only loosely related to the production of bubbles.

In a metal, the absorption of light’s energy is explained by Drude’s skin effect – a surface resonance that describes how some waves are reflected and some are absorbed. When the distribution of metal is inhomogeneous, this can give rise to quantized, localizations of energy – as modeled by Maxwell’s equations and renormalization.

But Drude’s skin effect + Maxwell’s equations + renormalization does not predict saturation effects – as in the pot of boiling water. Without saturation effects, field intensity can grow and grow and we know that this can’t happen.

Quantum mechanics tells us that after a certain threshold, a quantized emission of energy will occur, like a bubble emerging from the bottom of a pot of boiling water.

If you think of the metal as a film of boiling water heated by light, your water will never boil if you only turn the stove on and off all of the time and on the microscale of a metallic surface, that is what a high-frequency wave is like. Similarly, if your stove heats up too slowly, you’ll also never get it to boil. This is what I think of when I see the black body radiation curve.

Planck realized that if the energy is only absorbed in quantized amounts, that could explain why the shortest and longest wavelengths don’t get absorbed.

Einstein realized that this quantized absorption explained why increasing the intensity of light incident upon a metal plate doesn’t cause more particles (bubbles) to be ejected, but he interpreted this in a way that had been out of fashion since Newton wrote about corpuscles (quanta of light). Einstein concluded that light was both a wave and a particle called a photon.

A minority of physicists still think that the idea of quantized light waves is a stupid idea because if you can only ever measure particles with light and light can only ever be measured with particles, light will act like a particle (quanta), even if it isn’t.

It can’t be denied that treating light as a particle/wave is convenient when making mathematical approximations of these systems, but the history of physics shows us time and again that we make mistakes when we confuse approximations with reality.

This is exactly what happened when the photoelectric effect demonstrated that Drude’s model was merely a static approximation of a more dynamic, quantized process that depended on a sort of saturation threshhold – like a boiling point.

There is a pattern to our efforts to look at smaller and smaller things. We approximate continuous processes with discrete processes and then learn that we need to approximate those discrete processes with continuous processes, and so on. I think this suggests that real physics is recursive.

From this perspective, it was stupid to give Einstein a Nobel Prize for interpreting the photoelectric effect as a rejection of a wave theory of light.

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This stupidity became amplified within the Rube-Goldberg machinations of fundamental particle physics. Three generations of fundamental particles are identified but no reason is given for why there are three generations. Rather, the reason that there are three generations is considered to be mysterious, but whenever physicists see a mystery, they are usually being stupid about something fundamental. They tend to defend themselves from this charge by insisting that their job is to find mechanisms for things but not reasons for things. For people who call themselves scientists, this is a very political maneuver. Their marketing game is even more on point when they insist that the simple explanations are too simple.

The simple explanation of the transition from taus to muons to electrons or from gen III to gen II to gen I particles is that it is a state change as layers are melted away from a decelerating particle, as in a melting snowflake or a molecule breaking apart.

In a Riemannian, relativistic system, the faster something moves, the colder it acts, after all, but any well trained particle physicist would shriek in horror at such an explanation, insisting instead on exclusionary, opaque language that says virtually nothing.

In simple terms, each generation of particles has the same charge and spin, but a different lifetime within Riemannian space — a world where lengths contract and time dilates depending on your relative velocity — a world where there people get terribly confused by clockwise and anticlockwise motion.

But, what if changing one’s perspective to that of a godlike Cartesian in absolute space shows that the lifetimes of the particles are all the same, but the charges are different because they are spinning by different amounts relative to an absolute coordinate system?

This would certainly simplify things.

What if Riemannian and Cartesian vantages provide different yet equivalent ways to describe the same system?

A godlike, Cartesian perspective would see that we have chosen to approximate things in Riemannian space as being in a steady-state in which they all spin by the same amount and, therefore, all have the same charge.

The Cartesian would see motion that we cannot see because we are trapped in a non-inertial reference frame, moving in synch with the things around us.

The Cartesian would see that particles don’t just pop into and out of existence as the Standard Model says. They all exist in a permanent state, but their spin and charge change and make them appear and disappear from our perspective. After all, we can’t see things that are out of phase with our particles – even if they must exist for our world to function in the way it does.

In the most simplified language I can think of, the things we see are in synch with us and the things we feel are out of synch with us.

A Riemannian person indoctrinated in accordance with the Standard Model might insist that these ideas are inconsistent with conservation of charge, but I would say that when you change your perspective, charge will still be conserved; the charges and lifetimes of what you see will just look different.

Likewise, Standard Model people tend to react badly to the idea that spin up and spin down electrons are the same thing as electrons and positrons. They say that shifting one’s perspective from outside of an atom to within an atom seems to violate charge conservation, but they are wrong. (For a detailed explanation see the notes at the end.) Charge is conserved within each perspective. A god can shift its perspective at will and even if we can’t do measurements with an absolute, godlike perspective, we can certainly imagine doing so.

Things get simpler when you realize that a transverse wave can be approximated by a spinning sphere tumbling through space, much like a Gen III particle, an oversized bubble that tends to break apart into two smaller bubbles and some light.

Those two smaller bubbles are spinning in opposite directions and thus glued together in a Gen II particle as they continue to tumble through space, but they are unstable because the angles at which energy must circulate between them are too sharp.

This is why two bubbles break up into three to form a Gen 1 particle. Triangles are especially stable objects and 30,60,90 triangles fit together quite nicely to make an isosceles triangle, a clock, or a Poincare disk.

If this story sounds similar to that of hydrogen, I imagine that it should if physics is as recursive or self-similar as it seems to be. Gen I is analogous to n=1, Gen II is analogous to n=2, and Gen III is analogous to n=3. You might recall that there is no stable n=4 shell within hydrogen, just as there is no Gen IV.

These rules also probably apply on the scale of the solar system and we just can’t see the quantized patterns because they occur on average and the timescales we can observe are too short to see them. On an earthly scale, we can get a lot of information about the Schumann resonances, but still see the limits of our predictive power.

One might have a perfectly accurate, classical, deterministic set of equations for existence within a non-inertial, oscillating reference frame, but if you can’t know the initial conditions, all of your predictions of where the bubbles will appear in a pot of boiling water will have a certain degree of uncertainty in a quantum sense.

… and we all know that a watched pot never boils!

(Ephemeral things like bubbles or fundamental particles can’t exist if you keep disturbing/observing them.)

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Notes:

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There is a surfer who believes that he is able to surf gigantic waves because he has tuned into a specific Schumann resonance that gives him the ability to anticipate patterns that others cannot sense. That would be wild. It is often difficult to figure out why we anticipate certain things that others do not see.

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The thing that puzzles me at the moment is why people tend to make explanations of things like boiling water and fundamental particles more complicated than they need to be. Perhaps this gardener has found the answer.

If we aren’t discerning about which ideas we pass on, we might end up cultivating a garden of weeds and I think that Einstein’s ideas were rather weed-like.

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This post was composed from a number of answers I wrote on Quora but which were deleted for some reason. I was also blocked from the platform – such that I cannot edit any of my answers or write new answers.

Usually this form of censorship gets removed by a person who reviews the blocking function, but without a human in the loop, a single disgruntled person can delete answers you spent a lot of time developing:

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One of the Quora answers which was deleted had a particularly clear explanation of the recursive properties of matter and antimatter:

Matter and antimatter are in perfect balance on the microscale and when you turn around and face the opposite direction, everything you previously called matter becomes antimatter and vice versa. Electrons become positrons and spin up particles become spin-down particles. It is all relative.

You might think I am crazy for thinking that way because only crazy people would ever insist that anti-racism is racism and racism is anti-racism if you turn around and face the opposite direction.

Anthropomorphizing the situation reframes the problem in an interesting way because on the microscale, if you are only tracking a few people, there may be perfect symmetry between racist and anti-racist people such that they are simply two sides of a mirror, however, if you zoom out from the microscale and see that when one group outnumbers another group, there is a clear group of advantaged and disadvantaged people and when the advantaged people exploit their advantages, as they often do, we can label the people as racists and antiracists in a more absolute, non-relative sense.

The mystery of matter and antimatter becomes – why does there appear to be an advantaged group on the macroscale when on the microscale, we see no asymmetry whatsoever?

How do we know that there is an advantaged group is a very good question and I don’t think that we know for sure that there is an advantaged group.

Some physicists might say that what I’ve written is crazy because otherwise there wouldn’t be any matter – all matter and antimatter would’ve annihilated.

I’d say that what I’ve written is not crazy if there is an oscillation of our reference frame that continually provides energy to matter and antimatter, keeping them from annihilating. If the oscillation of our reference frame disappeared, all of the matter and antimatter would disappear in equal measures.

I’ve written a bit about this before in short form, here on Quora:

What potential does antimatter have in the future?

What is wrong with science today?

What is antimatter? Why does it matter to our universe and current understanding of physics?

What would make a more powerful Antimatter bomb electron-positron warhead or a proton-antiproton warhead?

and in long-form on my blog

Magnetic Monopoles

I find explanations given in terms of the Big Bang misleadingly confident since the Big Bang is an extrapolation and we have no direct knowledge of t=0. That should be the domain of religion, not science. This is why I am interested in alternatives to the Big Bang like Tired Light – an idea that is consistent with my favorite interpretation of antimatter.

Just as there are negative and positive entropy systems and just as time seems to flow forwards and backwards on different length scales, there may be length scales where there is an imbalance between matter and antimatter, but how you label the two categories will still be relative to your perspective. Keeping track of pluses and minuses in physics is tough.

In an easier to understand context: if you are the only white person in a neighborhood, you might be subject to racism from the predominantly black community even if that community is subject to racism within a larger, predominantly white city.

This basic truth is why the golden rule is so important for maintaining peace. Do unto others as you would have them do unto you because you never know when you are going to end up in the minority.

Since matter and antimatter have not annihilated, I’d say that they follow a form of the golden rule, as well. (snark)

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I recently found an author named Mark Morris who describes the difference between the three generations of fundamental particles in terms of the number of dipoles contained within each particle.

Gen I has three dipoles and is the most stable

Gen II has two dipoles

Gen III has one dipole and is the least stable

These objects exist in a Cartesian world and he connects them to a Riemannian cosmos with an unmeasurable, dynamic conversion factor that he calls a shell. I believe that it is similar to the concept of an axion from Helen Quinn.

I hadn’t heard this story in this form before and find it interesting, however, I do think that Mark’s view of particle physics as a whole is largely a re-packaging of some old ideas. His unmeasurable electrino-positrino pairs filling a spacetime gas sound like the same thing as an aether filled with magnetic monopoles or a Dirac sea of negative energy particles. Electrino-positrino pairs are just dipoles and a magnetic monopole which moves is also just a dipole. Why aren’t they two ways to say the same thing?

He calls his vision neoclassical particle physics and it makes sense that he and I crossed intellectual paths because the accelerator physics that I studied is basically classical particle physics. I’ve learned that in the larger physics community, accelerator physicists like me are much like Benedictine monks within the Catholic church. They compose an old order that is somewhat disconnected from modern physics and there is a lot of overlap with the order of engineers – by whom Mark was trained.

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The image in the header is of a recursive function that produces the Mandelbrot set and this video really opened my mind about that function.