What is Renormalization

Post Reply New Topic

What is Renormalization?

The idea of renormalization is rather simple. Let me use three examples to explain it.

The first example is something that everyone is familiar with: microphone-loudspeaker audio feedback. You place a microphone close enough to a loudspeaker, and it will produce a high-pitched sound. What is happening here? All sounds are made of waves of different frequencies. But when there is self-interaction (audio feedback in this case), one single frequency becomes dominant, and all other frequencies die off. That’s the essence of renormalization. When there are interactions, especially run-away interactions, the final situation simplifies, and is largely independent of how it was triggered. That independence is known as “universality.” The annoying pitch in audio feedback will be the same, regardless of the initial music note or voice tone that has triggered the audio feedback.

The second example is from statistics. In statistics, there is a “Central Limit Theorem.” It says that no matter the initial distribution, if you take the average of several random variables drawn from the same distribution, their average will converge to the Gaussian or Normal distribution. That is, upon self-interaction (taking average in this case), all probability distributions on the real axis will converge to one single final distribution. That is universality.

The third example is dewdrop formation on a leaf. Initially the tiny water droplets condense uniformly on a leaf.


However, as the air moisture keeps adding volume to these droplets, they start to touch upon each other (meaning interaction). Smaller dewdrops then coalesce into larger dewdrops. Not only that, due to the existing slope of the leaf, eventually the larger dewdrops tend to roll to the lower part of the leaf.


The “dewdrop model” of renormalization can be used to interpret all other renormalization phenomena, including the first two examples. In the case of audio feedback, the dewdrops represent sound waves of different frequencies. Upon self-interaction, all dewdrops coalesce into a final gigantic dewdrop at one single fixed point, leading to one single frequency response. In the second example, all probabilistic distributions will roll down to one single final distribution, which is the normal or Gaussian distribution.

We live in a universe made of some quantum fields of tiny entities that we don’t really understand today. Some people think they could be tiny strings, or “branes,” or other entities. We have no way of knowing what’s really going on at the very microscopic level. However, those entities interact with each other. And when you look at the situation at larger scales, the situation simplifies. Pretty much like how in the audio feedback situation one single frequency is selected, or how all probability distributions converge to the normal distribution, or how all dewdrops coalesce into larger dewdrops towards the bottom of a leaf. So, despite not knowing what’s really going on at the microscopic level, at larger scales we have pretty good idea what sort of interactions are allowed. Those interactions are known as “renormalizable quantum field theories.” All the microscopic complications are gone, and we are left with a small set of macroscopic quantum field interactions.

Renormalizable quantum fields by definition are self-similar across scales. So, when you talk about, say, an electron, you need to specify your scale of observation. If you choose a tiny enough scale, you could call that electron a “bare” electron. What happens when you go to a larger scale? You will see that you “bare” electron starts to emit and absorb photons nearby, and that a “physical” electron at a larger scale is actually made of a cloud of particles around it: virtual photons are emitted, some electron-positron pairs are created and reabsorbed, etc. That is, at larger scales, your unit of interaction (a physical electron in this case), is made up of a cluster of “bare” particles, behaving more like a fluffy ball.

The self-similarity is used in the study of critical phenomena in Condense Matter physics as well. That field of study is often known as the Renormalization Group approach. See, though the concept of renormalization is simple, it can be studied from so many different angles. It’s like a 7-headed beast. You talk to 7 different physicists, and they will give you 7 different explanations about renormalization.

Now, let us go to the human brain. If we view the human brain like a Hamiltonian, made of a system of bare particles, with each neuron behaving like a somewhat independent particle. Are there situations when the self-interaction among these neurons are strong enough that the unit of interaction becomes a cluster of neurons instead of a single neuron? That is, can we observe renormalization phenomenon in the human brain? The answer is yes. And that phenomenon is known as autism. Autism is when connected neurons have excessive self-interaction. As a consequence of renormalization, the interactions inside the autistic brain simplifies. If we view the triplet of (visual, verbal, social) interactions inside the human brain, then in the autistic case the visual interaction becomes dominant at the expense of reduced verbal and social interactions. That’s the universality and necessary consequence of autism.

This is the picture of a neurotypical brain in the dewdrop model.


And this is the picture of an autistic brain in the dewdrop model.


Autism is a spectrum, so the intensity of contrast between these three types of interactions varies from one person to another. The clusters form inside the brain are like giant dewdrops, with higher concentration towards the visual cortex. The precise locations of the dewdrops are guided by chaos theory. The two main types of neural networks inside our brain: CNN (convolutional neural network) and RNN (recurrent neural network) respectively capture “concepts” and “processes.” Upon renormalization, often CNN is favored, or RNN is favored. That is, autism seems to have two major fixed points: two main types of autism are observed: the pro-picture type (CNN-dominant) and the pro-video type (RNN-dominant). Just like photon-photon scattering, which does not exist in the bare QED (Quantum Electrodynamics) but is effectively allowed at high-loop level, in the case of autism, as long as you leverage the visual interaction of the children, you can develop them into verbal and social human beings, with amazing creativity and problem solving skills.

So, all in all, renormalization is a pretty general phenomenon in physics and mathematics.

All the computational tools, such as counter-terms, removal of infinities, scale-cut-off, fractional dimensions in the case of dimensional regularization, etc., are just computational devices. The physical understanding of renormalization does not depend on those computational gimmicks. Those devices are not what renormalization is about. You can understand renormalization without needing to understand those operational tools. What happens is that near the fixed points, the physics theories often have some run-away behaviors: imagine a loudspeaker that doesn’t have output volume limitation. So we have to come up with some mathematical formalism that allows us to relate a physical observable to another. That part, is not physics. It’s just math.

So, what is renormalization? If you ask 7 physicists, you will get 7 definitions. Instead of that, let me describe 7 common aspects to all phenomena that exhibit renormalization.

1. There are entities (particles/fields, probability densities, sound waves, block spins in Ising model, dewdrops, effective neurons, etc.)

2. These entities interact. If there is no interaction, there is no renormalization.

3. After interactions, the results are also entities, albeit acquiring somewhat different properties. In this sense, the output belongs to the same class of objects as the input. Or, we can say, the entities undergo “self-similar” interactions/transformations. Mathematically this is known as automorphism, or automorphism group. Most physical phenomena involving renormalization proceed through continuous groups (Lie group) of automorphisms, that is, automorphisms that are themselves composed of other automorphisms infinitesimally close to the identity transformation.

4. The new entities post-interactions can be considered as made up of those entities before interaction.

5. When the self-similar interactions/transformations continue repeatedly, a simplified picture emerges. That’s often called “universality.” Depending on the conditions of renormalization, there could be one or multiple final “fixed points.” The “watershed region” of each fixed point is a “universality class.”

6. Due to the repeated interactions/transformations, certain aspects of these entities are enhanced while others are suppressed. Those aspects that are enhanced are called “relevant,” those aspects that are suppressed are called “irrelevant.” Through the renormalization process, the overall contrast among all aspects is accentuated, leading to the survival of just a few relevant aspects and a simplified situation of interactions.

7. The study of renormalization often is not about what happens at the fixed point(s), but what happens near the fixed point(s). It aims to study the asymptotic behavior near the fixed point(s). “Infinity” is often considered as a valid fixed point, especially in quantum field theory.

2018-09

I recently watched the "Brainman" documentary.



Daniel Tammet, an autistic savant, can recall the value of Pi to 22,514 digits. The thing is, when he sees numbers, he also see colors, shapes, textures, etc. That is known as "synesthesia": triggering of unrelated senses. Synesthesia happens more frequently in autistic people. In particular, Richard Feynman was synesthestic.

Synesthesia is yet another indirect evidence that, inside the autistic brain, the unit of interaction is not an isolated neuron, but a group of neurons. This is akin to the formation of "dressed" particles from "naked" particles in quantum field theory. Here is a picture from the Nobel Prize site, regarding the work done by 't Hooft and Veltman. https://www.nobelprize.org/prizes/physics/1999/press-release/.



So, a physical particle is actually made from a cloud of the original bare particles. The same is true with the autistic brain. Due to the excessive neural connections, clusters of neurons are fired together and the clusters themselves become the units of interaction.

It is very interesting that I also found this video about explaining renormalization to a general audience.



It's a lecture given by Simon DeDeo, a professor in the Department of Social and Decision Sciences at Carnegie-Mellon University. Guess what? He also uses and talks about the Central Limit Theorem to illustrate the renormalization process, just like what I have repeatedly done throughout these years. The lecture is actually rather approachable, and I highly recommend it to anyone with some technical background to watch it.

The title of the lecture was: "Lecture 1: Coarse-Graining, Renormalization & Universality." I want people to pay attention to the very last word in the title: Universality. When I tell people what to do regarding raising their autistic children, there is no lack of parents/psychologists that balk at my ideas. They often laugh at me, and say, each child is different. In the back of their heads, they always think, yeah, you are successful at raising your children with YOUR method, but I am going to find MY method to raise MY children. There is more than one way to do it, right?

Let us look at the case of Helen Keller. She was deaf, mute, and blind. Before she learned to communicate, she was rather violent. She learned to communicate through hand-spelling. Tell me, how many other methods there are to teach Helen Keller to communicate? The answer is: NONE. Why don't people try to give behavioral therapy, speech therapy, arrange play dates, etc. for Helen Keller, and see how much all of that helps to her development? The regular intervention techniques of course wouldn't do iota to develop Helen Keller, because Helen had one and only one channel of communication. Nothing else would have worked. Helen Keller needed to learn hand-spelling. Period.

Similarly, people that don't grasp the concepts of renormalization and universality, they just randomly come up with a sentence like "each child is different" and refuse to develop their children visual-manually. I can only shake my head, because they are trying to raise their Helen Kellers by talking to these children. Look, renormalization always comes with Universality. The channels of communication of autistic children greatly simplify. Certain ways of interaction become "irrelevant." ("Irrelevant" is a technical word in the context of renormalization.) Nope, there are no other ways of raising autistic children. You MUST raise your children visual-manually, via modulation. There is only ONE way, due to universality. Yep, just like Central Limit Theorem. You may not like the Central Limit Theorem, but the fact is, no matter how much you don't like it, you will always end up with the Gaussian (Normal) Distribution. There is just no way around it.

So, for people that want to keep exploring other methods of raising their children, I am not going to argue with them. I am just going to watch them fail, watch them suffer. Go ahead, repeat the mistakes of millions of parents out there, in these 75 years of formal history of autism. Keep wasting your time in cures/treatments. My question to them is: "What have you tried that has not been tried before?" Irrational parents. They have access to plenty of information via Google and via observing other parents, yet they embark on the very same failed paths. Autism is such a trivial issue. It should have been a 5-minute issue. Yet people choose to suffer, for the rest of their lives, and in the process, destroy the lives of their own children. And when their children reach adulthood, the parents then panic: who is going to look after my children after I am gone? "Behavioral problems and intellectual disability"? Who are the ones with real mental disorder here? You tell me.

It's really easy for me to tell which parents are going to be successful. I only need to see what have come out of their hands. Zero manual output? All hot air? There you go. No need to whine. Yep, parents that don't use their hands to communicate and raise their children, are kidding themselves.

renormalization (n): a method used in quantum mechanics in which unwanted infinities are removed from the solutions of equations by redefining parameters such as the mass and charge of subatomic particles (Oxford Dictionary).

renormalization (n): a collection of techniques in quantum field theory, the statistical mechanics of fields, and the theory of self-similar geometric structures, that are used to treat infinities arising in calculated quantities by altering values of quantities to compensate for effects of their self-interactions (Wikipedia).

How you made the leap from a simple method of quantum physics to advocating teaching all autistic children in the exact same way is a misapplication of the method. However, if you have a degree in quantum physics AND a degree in behavioral psychology, developmental psychology, or special needs education, I would be interested in reading more about your idea. Assuming that a degree in physics gives you expertise in all other scientific disciplines as well is erroneous.

And that both your account name and your avatar are advertisements for your book lend credence to the idea that your posts are merely tangential references to your income-making endeavors.

As it stands right now, I wouldn't waste my time on a second read-through.

<_< Not even close to a physicist. Not ever interested in physics. The only time I heard this term was when I regressed slightly and had more therapy. Not a happy association for me.
60s/70s methods to assimilate you (the aspie) into the mainstream could be pretty rough.