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This is conceptually hard to grasp, Imma gunna have to watch it again, I was feeding this into A.I. chat while watching. Just got myself confused, lol.
To be fair, I've seen the psychic damage inflicted on a math major by a physics professor cancelling out 3 and pi, in a first semester physics class. I think the mathematicians were done with our bullshit LONG before getting to quantum physics.
A brand new electron! Q. How long can you keep it? A. You can't. After mere fractions of a second it will be gone, replaced by another brand new electron. All electrons are brand new.
Mainly because this video summarizes the techniques used to fix a problem without explaining how those techniques actually work -- techniques that would be a whole video on themselves.
It's over many people's heads. But hey, I'll tell you a secret: it was for me at first too. Just keep watching. Keep learning, piece by piece. Every time you listen to something like this, you may only understand 20% of it. That's ok! Keep going. Every month, every year, you'll understand more. What helped me to feel less intimidated at first was to learn the derivation of some basic physics concepts. That and reading alot of things over my head.
Don't forget, you can pause anytime and hit up Wikipedia for understanding, to some degree. It's not part of our biology to inuit this sort of stuff. We aren't even as good as chimpanzees at recognizing less than or more than a pile of objects.
When Feynman and Schwinger were awarded the Nobel prize in 1965 there was a third scientist Tomonaga who independently discovered renormalisation I just thought he deserved a mention.
I once saw a video of Feynman remembering how he was grappling with the electron mass problem and it was a really fun watch but I can't find it anymore.
This question reminds me of the arguments I used to have in 2nd grade. "Oh yeah well I have infinity points." "Yeah well I have infinity plus one points." "You can't have infinity plus one, infinity is everything." "Can too!" "Can not!"
The 'science' behind it is just as rudimentary as that argument would imply also. Not to mention that anyone with a proper math background would tell you that you can't add or subtract infinities
The mass of the electron field being infinite if the electron is point like, sounds a bit like the ultraviolet catastrophe where the graph suggested an infinite temperature of the sun before the rest of the graph line was understood.
That's not quite what the ultraviolet catastrophe was. It wasn't a prediction of an infinite temperature for the sun, it was a prediction of classical physics that any object of any finite temperature would emit an infinite amount of thermal radiation. As Feynman put it, "[classical physics says] that if we have a box at any temperature at all, and if we look at the x-rays that are coming out, there will be a lot of them!" That said, you are right that there is a striking similarity here. In both cases, we see the appearances of infinities arising from adding up contributions at higher and higher energies. We call such infinities in QFT "ultraviolet divergences" exactly because of their reminiscence to the ultraviolet catastrophe. There are also "infrared divergences" that come from low-energy physics, but these are much easier to understand and deal with. They essentially come down to the fact that, if e.g. you have a finite energy density in an infinitely large box, the total energy is infinite! This poses no real difficulty, though. Just phrase all of the questions you ask in terms of finitely-sized chunks of the universe instead of trying to calculate the total amount in an infinite universe.
It makes sense if you view an electron as a wave. Any single-frequency wave has an infinite extent. TO be localized you need to sum multiple waves of differing frequencies. The smaller volume you want to localize the wave the more and higher frequencies you need to sum. A pointlike electron then would need to be a sum of infinite waves of infinitely short wavelength, thus infinitely high energy. It's like saying a photon of pointlike wavelength would be infinite energy. Of course it would, that's how waves work.
@@thechurchofsupersampling To be fair, its wavelength can be as point like as physics allows (up to a wavelength larger than its Schwarzschild radius). So we know at certain energies it no longer exists as an electron. So of course it can't be a point, but using a point makes a lot of maths easier.
Entity 1: Our last hack blew up the mass of particles. Entity 2: Let's just set the internal mass to negative to counter that. Entity 1: Yeah, that should work. Entity 2: It's an internal constant, no one will ever know. _14.5 billion years of simulation time later_ Electric impulses in groups of carbon and hydrogen atoms: "Hey wait a minute. Why is the bare mass negative? And how is it so unnaturally fine tuned??"
@ItzMorgaNpvp The so-called equation "infinity minus (infinity minus one) = one" is an *invalid* use of the equal sign *=* because infinity is not a number. This is one small reason physicists run into problems using mathematics.
Great video. The last video was amazing. Seeing how you visually presented pair productions that occurred around the "real" electron and then randomly annihilate causing the electron to appear to jump around was the best way to think about the Hesenberg Uncertainty Principle in visual form in my opinion. I was really inspired by that! Thank you for advancing science and teach us all! Merry Xmas!
I got lost right around 13:44 where it feels like it glosses over the key point. I think it's because I don't fully grasp the concept of self-energy. So the virtual positrons perfectly cancel out the electrons but then where does the mass come from and why/how does it scale with the bare mass? What is meant by first and second order in this context?
that part both kinda blew my mind in a good way (woah that makes sense!) and a bad way (wait I want to understand more/exactly!) so I would 100% also love a more in depth explanation about that
First order interactions are simplest, virtual photon stuff. Second order is a two-step process, virtual photon->particle pair. There's third, fourth and so on too, but each 'step' decreases in importance exponentially. The core issue is that smaller phenomena are higher energy, if we say the electron is pointlike (infinitely small) we involve infinitely energetic processes. If instead we have a minimum scale like the Planck Length we get a finite energy\mass since we no longer involve infinite energy phenomena. But the Planck Length result is too massive. Fortunately it turns out that the limit is far larger, so the resulting mass far smaller. At a certain scale the electron-positron 'static' in the field blurs out particles. Anything too high in energy (too small in scale) is blurred away and doesn't contribute. The video just approaches this from a maths perspective, describing how the 'blurring' works on a calculation level.
At each step in that diagram energy and momentum are conserved, so even if we could watch this process (which we can't) we would never measure the electron as having a different mass. It's important to remember that this is all "under the hood".
It's the movement of the photons back and forth I would say. If you were to calculate the vectors, the up and down difference is the mass. The bare mass does not matter, it's just the horizontal vectors, so they can be anything. It scales normally because of the conservation of energy. It's just a diagram though. The math checks out, but it's probably not what actually happens. Maybe it might be best to imagine it like a wave. We can measure the electron when it's up or down. They are the same "mass" because they move in the same way in parallel. So one cancels the other. What is not cancelled is whatever is in-between, whether you call it the two photons or the positron, it's what create the mass differential because there is energy there that is not accounted for one one axis. I guess it's the best way I can explain it. Or the teleportation is what causes the mass, no matter how you represent it.
At 4:45, the parenthesis makes it confusing, since it would normally be *negative* 511 eV in the way you present it. You have minus sign before the both terms. Also, shouldn't it be 511 keV? Anyway, still a very solid episode, I'm looking forward to where you take it, since it's such an interesting subject.
This video makes me feel like the point of the universe is to solve how the universe works. So essentially some entity started an algorithm to (1) Spawn infinite universes, (2) Some universes create life, (3) Some of those universes make life smart enough to determine how they work and create life in the first place. Thus we end up with an algorithm that can solve its own problems.
There's a theory that states that if anyone should discover the true meaning of the universe it will instantly collapse in on itself and be replaced by something even more bizarre and obtuse. There's an addendum to this theory that states that this has already happened.
And even with infinite universes there will only be one that is ours to live in. This one, right now. There's nowhere else to be than here. The point of the universe is to be experienced. Measuring and understanding are simply additional layers we apply to the experience of the universe unfolding.
Really excited for this series of topics, we're going deep! In materials for laypeople I usually encounter renormalization just as "a thing you gotta do" and even working (experimental) physicists and physics students I meet seem mostly uninterested in examining the underpinning philosophy. I have too many times heard the idea that quantum mechanics is just the math and if the math works that's the reality. But it so clearly isn't how any of the first couple generations of quantum physicists thought, and this video so clearly demonstrates why poking at the mathematical philosophy gets us closer to understanding reality! Love it.
The idea stems from trying to regurgitate the bigbang if its infinitely dense the sphere of influence from the electrons extends further than infinity since everything has to fit inside the electron clouds probability dispersion
You mentioned that the electron's mass is "protected by the chiral symmetry of the particle" (14:30). This is my ignorance, but in what way are electron's chiral? I'm only familiar with chirality in terms of molecular structure. Would love an elaboration on this point.
I think every mathematician had a migraine when he said "infinity minus infinity-minus-one equals one! No problem!" No problem? We're subtracting one from infinity now and acting as if that's not the most wrong thing ever. Obviously this isn't math, this is physics where this sort of thing makes sense and you can't even compare "infinity" in physics with "infinity" in math, I still find it funny though. 🤣
TL;DR: "whoosh." More-detailed reply below. Did you read a transcript of when Dr. O'Dowd said that, rather than actually watching the video, or do you have difficulty picking up on the use of voice tone to adjust the meaning of statements? Dr. O'Dowd's tone is very clearly jocular when he says "infinity minus infinity-minus-one equals one. No problem!" He isn't suggesting that that's a valid mathematical calculation. He's *not* "subtracting one from infinity and acting as if that's not the most wrong thing ever" like you say he is. He's making a joke.
"Obviously this isn't math, this is physics where this sort of thing makes sense and you can't even compare "infinity" in physics with "infinity" in math," "I still find it funny though. 🤣"
"Infinity minus (infinity+1) equals...1" Oh my brain felt like it sprained itself for a moment there...but, well, it also makes sense! Also, for the lulz of it..."1 part in 20,000" isn't by any chance part of the reason why matter exists, is it?
wait... 13:17 with the electron changing positions because of the pair then annihilation, does that mechanism give rise to the fuzziness of its location, or is that just another component of its existence at that scale?
Good to know every electron in my body annihilates with antimatter 10^17 times per second. 😅 Almost makes one think of particles less as discrete entities, and more as relational distributions of charge; eddies in "the black sea of infinity," as Lovecraft put it.
This is PHYSICS. PHYSICS. Physicists often use terminology that gets jumbled up with the public -- people like you -- but that's okay. You just have to learn about what they mean by it before mindlessly assuming things.
@@sicfxmusic What is "translate"? Do you mean LLM's ? I don't think any of what we currently have is informing us of all that is coming - it's all a stepping stone to new paradigms Huge changes, huge advances won't resemble any of the cute toys we are currently using. As soon as self improvement or any hint of self awareness happens, it will immediately change the world forever and there is no going back. Why is it that humans have this insane desire to forge ahead without looking or stopping to plan ? It must be encoded in our DNA. We forged ahead to new lands, spread across the world, we are terrible at long term planning and have a 'look before you leap' attitude in everything we do. This might be the last time the human race ever gets to do that. I mean, it's going to happen whether we want it to or not. But we can't resist opening Pandora's box, can we? We just have to peak at a superintelligence that is way beyond us. Does that even sound sensible?
I am coming to believe (possibly because I don't understand something) that the idea of measurement is itself flawed. It's like in order to refer to any event or object in the spacetime continuum, we can use measurement because in the continuum itself (which we, the measured event and the measurement devices are) those measurements results remain consistent across time. When we get in deeper and start asking about the actual nature of the events or the continuum itself, the order of the questions the measurements are asking matters to the consistency of the results. So essentially, I believe science is the best possible way to describe the continuum, but it's reliance on consistency in measurement results regardless of order of questions asked is screaming that some updated idea of measuring or a separate domain of logic that undermines how we think of measurement is what rules the nature of reality itself. Measurable results are themselves emergent properties of a nature that can't be measured without context of the measurement parameters already existing to begin with. By the time you're measuring, you're part of the measurement, so the underlying nature of the emergent measurable universe remains beyond measurable results. It's like the true nature of reality is everywhere you look, but nowhere you dig into it. And that is why physics breaks down at certain points. It's essentially trying to apply "continuum logic" to something that the continuum doesn't apply to. Please correct me if you understand better than me. Im happy to research anything I'm pointed towards.
A solid enough take. You can never measure something in isolation, every measurement involves two objects interacting, it is the behavior of a system, not knowledge of a singleton. Possibly the idea of what something is in isolation doesn't even make sense, like asking about the wetness of a single water molecule.
All the hand wringing about infinites in QFT is frustrating. We have no problem accepting the results from complex analysis that are well characterized (integrating around poles, conformal maps integratd at the boundary, etc.). None of this stuff, strictly speaking, is always explicitly necessary in many problems... these techniques merely make the mathematics easier to work with, but even without it, you can nearly always get a solution or an approximate solution that's "good enough for calculus" once you factor in considerations like error convergence, analytical functions, or bounded terms... and good enough for calculus is often good enough for chonkier things like the universe or uncooperative parameterized functions defined on stuff as gossamer and deformable as spacetime (and if quantum mechanics and information theory viewed through the lens of Neother offer any hints, all that REALLY matters here is the algebra of conserved quantities and abstract symmetries outside the context of realism or representation). Up until now the infinities are usually artifacts of embeding these symmetries into an unnatural artificial linguistic or computational system (ie explicit parameterized REPRESENTATION). It's the mathematical "technology" not the universe, or the current understanding of physics that's the real issue here.
Well, when your calculated vacuum energy density is divergent, you have a BIG problem with gravity: such Universe must contract in a Big Crunch. It's not "hand wringing", it means "we are totally off with experimental results on this one".
@denysvlasenko1865 not necessarily. If you integrate below the cutoff of reality and that cutoff is fuzzy, you have no problem (this is the entire point of working with analytic functions). The same problem would happen if you said let's assume that because special relativity exists and things like the wavelength of a photon are meaningless it's valid to say that light scales with the size of objects we want to image instead of the wavelength used to image it... there's a HUGE logical fallacy built into that statement (the wavelength depends on our "lab" frame relative to the emmiter of the photon, relative to the frame the object it will scatter off of as well as the RELATIVE quantum uncertainty in all of the above properties)... all those details fuzz up and difuse every singularity that we build into our unnaturally perfect equations and hence, into the tame reality we witness. The math is just a guide. The physics is what happens when we eliminate all but the minimum level of detail and complexity to see how matter and energy behave... eliminate too much, and things will diverge as you throw out or inadvertently add information or resolution into a system incapable of supporting those information densities. Thus far, this phenomenon has been seen at every scale of nature, and in many instances you simply are prevented from seeing across the IR or UV firewalls to the other side of whatever phase transition is separating one energy scale from another, and for very deep reasons, that are often married to something like the second law of thermodynamics. To learn more about this check out professor Laughlin's book: A Different Universe. If you're not a layman you can look into the subject of universality, the final chapters of Peskin and Schroder as well as Huang are good introductions to this topic. But unless you were spoonfed this as a grad student like I was, it's a few years commitment to come up to speed on this stuff even for most theorists. Working through Churchill's Complex Analysis prior to this and seeing how this stuff is useful in practical engineering and how/why the idealized methods like conformal mapping break down will guide your intuition towards understanding the straightforward resolution to the dilemma your statement/question implies. We are missing a big piece of the puzzle which will only be revealed once we have made a measurement in a system capable of probing the regime on the other side of the transition. Until this happens, we can speculate and try to understand how things might look, but 4 d is special, and the lessons from spontaneous symmetry breaking in 2d and 3d don't always apply. The stuff we're talking about here is on firm experimental footing at all orders and energy scales. The paradoxes up till now have exclusively been computational artifacts. What you're talking about is reaching beyond Noerther's theorem or the landscape of psudopotentials described by Jaynes. If they're fundamental, then the anomalies are artifacts. If there's another fundamental organizing principle on the other side of the transition, of which spacetime is the order parameter we have ZERO evidence for what that might be or how it might look... string theory is the only thing that's ever done anything remotely like this and in AdS5 ... we don't live in 5d anti deSitter space or on its conformal boundary. We live in 4d deSitter space... 5d like 3d&2d is soooooo comparatively EASY... 4d is just hard as ballz. Cheers m8
Here is my, hand wavy, alternative approach. Actually I expect that this has been investigated before and proved wrong or irrelevant. But having someone explain the problems with it would be enlightening. First take the particle like properties to be purely a function of interactions. So we can ignore them when considering a single particle. This leaves you with a field with a large mostly stable wave and a lot of unstable small fluctuations. The mass is the mass energy of the large wave. This should be a small finite value that will vary slightly as it interacts with the small waves. The observed mass is function of the wave mass and the interaction mechanism. Since the wave is not a point and is continuously being modified by the fluctuations in this field and probably other fields as well, we get the quantum weirdness that we observe. The descriptions I have seen are mostly consistent with this. But they then seem to force the "particle" concept onto the waves. Doing this seems to lead to some of problems in the math. Hopefully my ramblings make some sense. If any experts can help enlighten me on the subject, I would really appreciate it.
The only flaw in your argument is that the only stable wave in a quantum field would have a single wavelength and infinite extent, being spread across the entire universe. It wouldn't change because nothing would make any difference. (A wave cannot just stop at some point, and it can't diminish in frequency towards the 'ends' either, what would be making the wave do that?) For an object to NOT be everywhere, to be something like an electron, it needs to be the sum of infinite waves over a certain range of frequencies. (This is related to the phenomenon of 'beats' where two soundwaves of nearly identical frequency interfere to produce distinct beats of sound.) Which is fine, we can absolutely model an electron as the result of infinite 'perfect' waves in the electron field summing up into a little wave packet. That's what all of those Feynman diagrams are, waves of differing wavelengths in various fields. The higher energy, smaller waves we make a part of it, the smaller the end particle becomes. BUT... WHY is it like it is? Why that mass? Your argument works for ALL particles, why isn't an electron as massive as a proton? A top quark? Nothing in the underlying theory says the electron can't be made of more energetic waves, or even be pointlike. If the electron is pointlike, infinitely small, we need infinitely high energy waves in it. But... well we have the Planck Length, that gets rid of infinity by saying we just CAN'T have infinitely energetic and tiny waves involved. As you say, the electron is NOT pointlike and can never be. Even better, the 'static' in the electron field will blur and swamp any waves smaller than those inherent quantum fluctuations, cutting out even MORE high energy waves and giving us the low mass we see today. Which is... almost exactly what you said. Except, rather than a wave AND a field interacting, the field controls what the wave can even BE. The quantum messiness of the electron field limits what it can use to MAKE a stable wave. If the electron field was more messy it'd eliminate more stuff and the electron would be less massive.
No such thing as a discrete point along a wave or around a circle in my mind. If you zoom out far enough a circle may appear point like, but it always fuzzy. If you zoom in far enough a circle appears flat and it's almost impossible to find the curve and is always fuzzy. So for me, the universe has no inherent discrete values even though we may have some concept of the peak of a wave going past and be able to count them, we never really know where the absolute point of that peak is. It's always fuzzy, always contains some infinitesimal uncertainty :)
The way renormalization has been described here looks like just using the fact that for any divergent series with infinite positive and negative contribution where the sequence still converges to zero, you can rearrange the terms to make it sum to anything. Why wouldn't be exactly what's happening here, where we choose this "anything" to be the observed electron mass? If that's the case, the actual solution provides an order that makes physical sense. So if renormalization works, but we don't have a solution, wouldn't it just mean that we don't know why the "right" order of terms physically makes sense? (or even precisely which one it is)
"This is infinite. That is infinite. Out of That infinite manifest This infinite. Substrate This infinite from That infinite, Infinite alone remains." - Upanishads
🎯 Key points for quick navigation: 00:00 *🔬 Introduction to the Hierarchy Problem* - The concept of subtracting infinite masses to yield an electron is introduced. - Overview of the Hierarchy Problem, focusing on the unexpectedly small mass of the Higgs boson. - Comparison to the historical electron hierarchy problem, setting up the discussion. 01:48 *⚛️ Electron's Mass and Quantum Field Theory (QFT)* - Classical physics predicts unrealistically high or infinite self-energy mass for electrons. - Quantum mechanics, specifically QFT and QED, provide the framework to address these issues. - Introduction of terms: bare mass, self-energy, and dressed mass, with renormalization as the method to reconcile infinities. 05:32 *🧮 Renormalization and Fine-Tuning Challenges* - Explanation of renormalization to cancel out infinite self-energy with an infinite negative bare mass. - Highlighting the unnatural fine-tuning required for near-perfect cancellation of large terms. - Renormalization is critical for electron mass but introduces new questions about the Higgs boson. 06:27 *💡 Virtual Particles and Quantum Field Dynamics* - Virtual photons and electron-positron pairs drive the quantum electromagnetic field’s activity. - Feynman diagrams are used to model possible interactions, contributing infinite energy if summed without limits. 09:16 *🚨 Regularization and Limits of Quantum Mechanics* - Regularization imposes a cutoff at scales like the Planck length, yielding finite masses. - Discussion of the limits of quantum mechanics as an effective theory, acknowledging that deeper physics must exist. 13:13 *⚖️ Symmetry and Natural Mass for Electrons* - Matter-antimatter symmetry protects the electron’s mass, avoiding unnatural fine-tuning. - Chiral symmetry ensures that the electron’s small mass emerges naturally from the interplay of positive and negative components. 14:39 *🌌 Implications for the Higgs Boson and Beyond* - The electron's mass is resolved, but the unnaturalness of the Higgs boson’s mass remains a mystery. - Renormalization and regularization illustrate the emergence of effective theories, hinting at deeper physics. 15:04 *🛠️ Sponsor: Radiacode and Scientific Exploration Tools* - Promotion of the Radiacode radiation detector and its features for scientific enthusiasts. - Introduction of holiday discounts and merchandise sales for PBS Space Time viewers. Made with HARPA AI
Mathematically-speaking, you have to be careful with applying arithmetic operations to infinities, bc not all infinities are the same size. Some infinities are larger than others; so, 00-00 often ≠ 0 (and, given that 00 isn't actually a number, the "value" 00-1 is utterly meaningless) That being said, "infinities" in pure mathematics refers to infinite numerical sets (which explains why there can be comparative infinities larger and smaller than others); whereas, in the context of the problem presented here as a mathematical descriptor for the electron (via QM), we very likely don't have to concern ourselves with different sizes of different infinities, because we're dealing with a singular value assigned as infinity presented twice (with opposing polarities*)
it contains both infinities though so the assumption is that they are equally large which makes sense as you would have to specify how large any of the infinities is in the first place.
All infinite sets are the same size but they aren't all constructible. Mathematicians were just confused when they equivocated their way into thinking unconstructible is bigger than constructible. Uncountable infinite isn't greater than countable infinite, it's just uncountable.
I couldn't finish that book. The science ideas were a lot of fun, but the way they were revealed was just a series of scenes where 2 people are in a room doing plot exposition.
Amazing how renormalization aligns theoretical predictions with observations. It’s a striking example of how physics bridges abstract math with empirical data.
Hi Dr. O'Dowd! Renormalization seems unsatisfying, even if it's relatively useful. But for some reason, I can't stop thinking about taking the integral of an infinite polynomial and setting x equal to 0. All the higher-order craziness vanishes and we're left with just the constant of integration. Even if that constant is small or seems strangely fine-tuned, no other terms needed to magically cancel out to produce it. We're still calibrating the constant to reality, but there's nothing weird about it.
excellent episode. i got the basic principle now, but to truly understand it, i think i need some maths to back that up. but hey there are worse ways to spend what could have been a night of good sleep other than a deep dive into the maths of the hierarchy problem.
Some years ago as a undergraduate, I attended a lecture by visiting speaker Arthur Jaffe. I could understand almost none of what he said, and probably our faculty in attendance didn't either. I do remember he tried to take some of the mystery of subtracting infinity from infinity. It was something like "form A sub n minus B sub n, and then take the limit as n goes to infinity." Ah! So that's how it's done! What could be more simple?
Right. So, for ∞ - (∞ - 1) you start with x=1 and move up. 1 - (1 - 1) = 1. 2 - (2 - 1) = 1 and so on. The limit is 1 so ∞ - (∞ - 1) = 1! Seems pretty solid to me.
@garethdean6382 Jaffe's explanation is a more more subtle than that and is exposing why you can't just look at inf-(inf-1) and say "yeah that's 1". (x+n)-x for your favorite number n is inf-inf as x goes to infinity, but every step of the way it evaluates to n. So inf-inf could reasonably be any finite number. 2*x-x is inf-inf as x goes to infinity, but every step of the way the value was x as it grew to infinity, so inf-inf could reasonably be infinity x-2*x is inf-inf as x goes to infinity, but every step of the way the value was -x as x grew to infinity, so inf-inf could reasonably be -inf There is literally no way to rule out any evaluation at all without understanding how you ended up with inf-inf, and even then there's still a chance it is something that can't be evaluated (afterall, I only went over 3 unreasonably well behaved ways or could happen)
This equation is actually meaningful in Conway's surreal numbers. Highly recommend Knuth's book surreal numbers. It's a maths book in the form of a story.
It feels so wrong to use virtual particles as a solution to our problems. It just feels like a way to explain what’s happening without having a good understanding of the truth.
You know how a moving electric field will generate a magnetic field? And that magnetic field will propel electrons creating a moving electric field? It's like that but on a very small scale. Everything is constantly interacting with itself and also interacting with those interactions. It's turtles all the way down.
I remember reading about renormalization a few years ago, but I don't remember having any real understanding of it. This makes a bit more sense. Thank you! Having said that, it gives me the overall impression of building ikea furniture with the wrong parts. You can still get it all to fit together and work mostly correctly, but you still haven't built it properly, lol. God be with you out there, everybody. ✝️ :)
If the hierarchy problem is problematic, just dox it and write emails to its boss with false allegations of racism and sexism. Or any other form of fascistic social pressure should also do…
Honestly, this is a rather well-put higher explanation of "why out of necessity" are we sweeping the energy infinities under the rug and letting them be. All the while looking at the post-renormalization energies...and somehow we are calibrating or reassessing under our current reality. It's like you have to ask the universe what you are looking at while ensuring your reality of measurement is also accounted for before the universe teases you with a truth or novel finding.
My first thought after this was “what if there’s an anti-Higgs particle and that’s dark energy?” Which is, I’m sure, not a new or particularly useful idea, but I just love how this channel makes me marvel and wonder at the inner workings of the universe like that.
I think that quantum and classical eoectromagnetism predicting the same infinities on the point like scale is a good showcase of the theories converging.
No one would be bothered by the destruction of the universe. Now, bothered by being aware of the imminent destruction of the universe before they are finished using it, sure, but that's differrent.
Since this is continuation of the previous episode, I find the mass of electron problem quite fascinating. As I understand it, photons are basically fluctuations in the EM field traveling at a particular frequency yet they have a mass. Why can’t an electron be a fluctuation in the EM field as well? For the mass predicted would the frequency be too large? If so, is that a problem? Isn’t having a high frequency mean that the vibrations are too fast which would align with the elusive nature of the electron where it cannot be seen. Is this fluctuation traveling through the EM field by self destruction i.e. it causes positrons to popup annilating itself and the next paired electron moves forward which does the same thing again and again. The mass calculation would theoretically lead to one calculation but measurement would also account for the positron pair that keeps forming near electrons to anhilate it and possibly another electron paired to the positron. This would also explain the mass descrepancy. I wish I knew mathematics as well as physicists, would love to try and do the calculations.
I'd love to see a little more examples of cancelling terms out - the descriptions are all very high level, and a bit hard to grok. I was also confused about "blowing them up to the size of the planck scale" - isn't that incredibly tiny? Or do you mean that the electron is presumed to be smaller (more point-like) than the planck size?
Yes, if the electron involves phenomena smaller than the Planck Scale, the numerical result 'blows up' towards infinity. The Planck Scale is MOSTLY tiny, the Planck Mass is about that of a dust mote -huge in particle terms. In terms of cancellation, imagine that I have a theory to measure the average mass of fur on a cat. It simply take the mass of one hair then multiply that by all the hairs that could fit on a cat. I sum over all numbers and lengths. Which gives me infinity, I'm counting all possible lengths from zero to infinity after all. Which is foolish, I can't have hairs that are infinitely long, that's not reality. If I just don't count those, if I put in a sensible cutoff I get a finite answer. Mathematically I can do this by taking every 'silly' measurement and pairing it with an opposite silly measurement. The infinities cancel out but perhaps it's more sensible to say I just don't bother with them in the first place. They're unphysical.
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This is conceptually hard to grasp, Imma gunna have to watch it again, I was feeding this into A.I. chat while watching. Just got myself confused, lol.
How come come like Charges repelling Doesn't count as negative mass
Effective mass = true mass / time real?
How can we be sure those infinities are the same and this subtraction is valid...? 🤔
Isn't the mass of electron is 511kev not 511ev
Mathematicians: you can't do ∞ - ∞
Physicists: Don't be so negative bro, here's an electron.
Of course, in doing so you made the mathematician one unit of charge more negative
To be fair, I've seen the psychic damage inflicted on a math major by a physics professor cancelling out 3 and pi, in a first semester physics class. I think the mathematicians were done with our bullshit LONG before getting to quantum physics.
Mathematicians: Get that thing away from me, I'm trying to concentrate on my new therory/proof!
A brand new electron!
Q. How long can you keep it?
A. You can't. After mere fractions of a second it will be gone, replaced by another brand new electron. All electrons are brand new.
But electron is negative
This is what you get when you leave physicists alone.
Physicists’ math 😭
I'm trapped in my mind and my brain is my cell
But I have a key, it's called insanity
I stick in my brain to unlock eternity
@@michaelmayhem350 If you aren’t your mind… what are you?
This is what u get when you leave them alone, imagine what you'll get if you leave them alone with some magic mushrooms...
They become allone?
"Calibrating to reality" is my take-away phrase from this episode. Sadly, it was mostly way over my head.
Mainly because this video summarizes the techniques used to fix a problem without explaining how those techniques actually work -- techniques that would be a whole video on themselves.
It's over many people's heads. But hey, I'll tell you a secret: it was for me at first too. Just keep watching. Keep learning, piece by piece. Every time you listen to something like this, you may only understand 20% of it. That's ok! Keep going. Every month, every year, you'll understand more.
What helped me to feel less intimidated at first was to learn the derivation of some basic physics concepts. That and reading alot of things over my head.
Don't forget, you can pause anytime and hit up Wikipedia for understanding, to some degree. It's not part of our biology to inuit this sort of stuff. We aren't even as good as chimpanzees at recognizing less than or more than a pile of objects.
To pick you up again I recommend Angela Colliers “why you can’t explain QCD” 😌
I liked, "This sounds a little hokey for a number of reasons."
"Calibrating to reality" is how you refer to someone that is recovering from social media withdrawal.
I feel attacked
When Feynman and Schwinger were awarded the Nobel prize in 1965 there was a third scientist Tomonaga who independently discovered renormalisation I just thought he deserved a mention.
I once saw a video of Feynman remembering how he was grappling with the electron mass problem and it was a really fun watch but I can't find it anymore.
wow nice
He was the electron left behind..
Shinchiro Tomonaga, luckily was also awarded the Nobel prize
@ Yes, therefore he deserved a mention in the video. Having independently discovered renormalization at the same time as the two Americans.
This question reminds me of the arguments I used to have in 2nd grade.
"Oh yeah well I have infinity points."
"Yeah well I have infinity plus one points."
"You can't have infinity plus one, infinity is everything."
"Can too!"
"Can not!"
The 'science' behind it is just as rudimentary as that argument would imply also. Not to mention that anyone with a proper math background would tell you that you can't add or subtract infinities
I have exponential infinity points!
@@eqminerva Transfinite Numbers have entered the chat.
I have uncountable infinite points.
@@eqminerva you kinda can - you just end up with the entire set of real numbers for your result XD
The mass of the electron field being infinite if the electron is point like, sounds a bit like the ultraviolet catastrophe where the graph suggested an infinite temperature of the sun before the rest of the graph line was understood.
It isn't pointlike we don't understand it properly
That's not quite what the ultraviolet catastrophe was. It wasn't a prediction of an infinite temperature for the sun, it was a prediction of classical physics that any object of any finite temperature would emit an infinite amount of thermal radiation. As Feynman put it, "[classical physics says] that if we have a box at any temperature at all, and if we look at the x-rays that are coming out, there will be a lot of them!"
That said, you are right that there is a striking similarity here. In both cases, we see the appearances of infinities arising from adding up contributions at higher and higher energies. We call such infinities in QFT "ultraviolet divergences" exactly because of their reminiscence to the ultraviolet catastrophe.
There are also "infrared divergences" that come from low-energy physics, but these are much easier to understand and deal with. They essentially come down to the fact that, if e.g. you have a finite energy density in an infinitely large box, the total energy is infinite! This poses no real difficulty, though. Just phrase all of the questions you ask in terms of finitely-sized chunks of the universe instead of trying to calculate the total amount in an infinite universe.
If you zoom-in to the size of an electron in the Sun's core, it would be dark and freezing.
It makes sense if you view an electron as a wave. Any single-frequency wave has an infinite extent. TO be localized you need to sum multiple waves of differing frequencies. The smaller volume you want to localize the wave the more and higher frequencies you need to sum. A pointlike electron then would need to be a sum of infinite waves of infinitely short wavelength, thus infinitely high energy. It's like saying a photon of pointlike wavelength would be infinite energy. Of course it would, that's how waves work.
@@thechurchofsupersampling To be fair, its wavelength can be as point like as physics allows (up to a wavelength larger than its Schwarzschild radius). So we know at certain energies it no longer exists as an electron. So of course it can't be a point, but using a point makes a lot of maths easier.
I love the "You think your brain melted with electrons, just wait until we get to Higgs!".
"I'm gettin' too old for this sh!t, Higgs."
~Detective Murtaw... probably
Human: "How, exactly, does the universe work?'
Universe: "None of your business."
Entity 1: Our last hack blew up the mass of particles.
Entity 2: Let's just set the internal mass to negative to counter that.
Entity 1: Yeah, that should work.
Entity 2: It's an internal constant, no one will ever know.
_14.5 billion years of simulation time later_
Electric impulses in groups of carbon and hydrogen atoms: "Hey wait a minute. Why is the bare mass negative? And how is it so unnaturally fine tuned??"
It's weird reading this while I'm also reading the Parahumans webserial.
@@Duiker36 what's that abt?
I would add a Like to this post but it's at 42 currently.
Be quiet! The devs will notice.
i like to think that all the things which are finely tuned, are so due to resonance.
“Negative Bear Mass” is an excellent band name
In my mind, this evokes pictures of a congregation of depressed ursidae celebrating their nihilism in dead languages...
@@albrecht-sebastianwitte-re4280 and that's the cover of their self-title album
@@albrecht-sebastianwitte-re4280 that is delightfully weird... maybe weird enough for a doom metal band :D
... Or album
Math Rock. It's already close enough to Minus the Bear
"May you remove your self-energy mass so I can measure your bare mass?"
That should be a fun pickup line for parties.
"Hehe that was very smooth"
>the dudes at party removes clothes
Heisenberg says no.
Or maybe he doesn't?
@@josephbenson6301he does, too
I dig seeing equations make their way back into Space Time episodes. They make me feel smart when I kind of know what I'm looking at lol
Be careful. He's just a physicist and not a mathematician.
@@douglaswilkinson5700 not much of a difference at this point 🎉
@ItzMorgaNpvp The so-called equation "infinity minus (infinity minus one) = one" is an *invalid* use of the equal sign *=* because infinity is not a number. This is one small reason physicists run into problems using mathematics.
Great video. The last video was amazing. Seeing how you visually presented pair productions that occurred around the "real" electron and then randomly annihilate causing the electron to appear to jump around was the best way to think about the Hesenberg Uncertainty Principle in visual form in my opinion. I was really inspired by that! Thank you for advancing science and teach us all! Merry Xmas!
So glad to still be on this journey with you all.
Glad I'm not dead, too.
A family in... Spacetime
You will never cease to exist but transform your state.
The background sound effects during Matt's narration at about 6 minutes in is really freaking me out!
I almost understood this for a hot second but then I lost it. It does give me hope that I can maybe understand it if I listen enough times.
No lie, I usually rewind 3-4 times on the bigger points to make sure I got the order of things correct because I got distracted for 2.6 seconds 😂
I actually paused this episode and viewed the previous episode, upon your recommendation. Gold star, please and thank you. ⭐
A bear sat on our hammock sofa.
It did not have negative mass... We still had to renormalize the hammock sofa though
Fantastic video, as always! Super great explanations here!
I got lost right around 13:44 where it feels like it glosses over the key point. I think it's because I don't fully grasp the concept of self-energy. So the virtual positrons perfectly cancel out the electrons but then where does the mass come from and why/how does it scale with the bare mass? What is meant by first and second order in this context?
that part both kinda blew my mind in a good way (woah that makes sense!) and a bad way (wait I want to understand more/exactly!) so I would 100% also love a more in depth explanation about that
First order interactions are simplest, virtual photon stuff. Second order is a two-step process, virtual photon->particle pair. There's third, fourth and so on too, but each 'step' decreases in importance exponentially.
The core issue is that smaller phenomena are higher energy, if we say the electron is pointlike (infinitely small) we involve infinitely energetic processes. If instead we have a minimum scale like the Planck Length we get a finite energy\mass since we no longer involve infinite energy phenomena.
But the Planck Length result is too massive. Fortunately it turns out that the limit is far larger, so the resulting mass far smaller. At a certain scale the electron-positron 'static' in the field blurs out particles. Anything too high in energy (too small in scale) is blurred away and doesn't contribute. The video just approaches this from a maths perspective, describing how the 'blurring' works on a calculation level.
At each step in that diagram energy and momentum are conserved, so even if we could watch this process (which we can't) we would never measure the electron as having a different mass. It's important to remember that this is all "under the hood".
@garethdean6382 Essentially, the heisenberg uncertainty principle kicks in and solves the issue, if I understood correctly?
It's the movement of the photons back and forth I would say.
If you were to calculate the vectors, the up and down difference is the mass.
The bare mass does not matter, it's just the horizontal vectors, so they can be anything. It scales normally because of the conservation of energy.
It's just a diagram though. The math checks out, but it's probably not what actually happens.
Maybe it might be best to imagine it like a wave. We can measure the electron when it's up or down. They are the same "mass" because they move in the same way in parallel. So one cancels the other. What is not cancelled is whatever is in-between, whether you call it the two photons or the positron, it's what create the mass differential because there is energy there that is not accounted for one one axis.
I guess it's the best way I can explain it. Or the teleportation is what causes the mass, no matter how you represent it.
At 4:45, the parenthesis makes it confusing, since it would normally be *negative* 511 eV in the way you present it. You have minus sign before the both terms.
Also, shouldn't it be 511 keV? Anyway, still a very solid episode, I'm looking forward to where you take it, since it's such an interesting subject.
Thank you, I was sure it was 511 keV too
Didn't know the mass of an electron is the sum of the mass of a bear and infinity. The more you know
Normalization in electrical/computer engineering makes things so much easier. It's basically the best way to approach any theoretical calculation.
This video makes me feel like the point of the universe is to solve how the universe works. So essentially some entity started an algorithm to (1) Spawn infinite universes, (2) Some universes create life, (3) Some of those universes make life smart enough to determine how they work and create life in the first place. Thus we end up with an algorithm that can solve its own problems.
There's a theory that states that if anyone should discover the true meaning of the universe it will instantly collapse in on itself and be replaced by something even more bizarre and obtuse. There's an addendum to this theory that states that this has already happened.
@@XeridanusProbably on December 21, 2012 😂
That would imply the universe being Turing complete!
And even with infinite universes there will only be one that is ours to live in. This one, right now. There's nowhere else to be than here.
The point of the universe is to be experienced. Measuring and understanding are simply additional layers we apply to the experience of the universe unfolding.
@@MathiasMelker Considering you typed this comment on a turning complete machine, I'd say this is self evident.
Really excited for this series of topics, we're going deep! In materials for laypeople I usually encounter renormalization just as "a thing you gotta do" and even working (experimental) physicists and physics students I meet seem mostly uninterested in examining the underpinning philosophy. I have too many times heard the idea that quantum mechanics is just the math and if the math works that's the reality. But it so clearly isn't how any of the first couple generations of quantum physicists thought, and this video so clearly demonstrates why poking at the mathematical philosophy gets us closer to understanding reality! Love it.
The title made me go WTF 😂😂
∞ - (∞ - 1) = 1
BOOM! Where is my Nobel?
@@falxnecis♾️ + (-♾️) + 1 = 1
The everything else too...
The idea stems from trying to regurgitate the bigbang if its infinitely dense the sphere of influence from the electrons extends further than infinity since everything has to fit inside the electron clouds probability dispersion
I had a professor for E and M in college that would cancel infinities on the board during lectures and it gave me a lot of anxiety.
Yay, real readable subtitles, thank you PBS
Well, ya just broke my brain. Hope you're happy.
Now that’s a title I’m clicking on. Whoever came up with it deserves a raise! 🎉
Thanks guys these last two episodes have been really insightful ❤
Infinity - infinity = electron .... Wtf man. It's Thursday. You can't break my brain like that before Friday.
I never could get the hang of Thursdays.
Infinity-infinity = everything. Infinity/0 = anything.
Its so much worse than that
Infinity minus infinity = any real number - take your pick
And we have to wait a whole month for clarification! 😝
It's Friday in Australia :)
Thank you for giving me a refreshing new & better appreciation for the incredibly teensy-weensy, tiniest scale of the electron & it's friends.
Thank you PBS SpaceTime for your great videos! Happy Holidays!
You mentioned that the electron's mass is "protected by the chiral symmetry of the particle" (14:30). This is my ignorance, but in what way are electron's chiral? I'm only familiar with chirality in terms of molecular structure. Would love an elaboration on this point.
I think every mathematician had a migraine when he said "infinity minus infinity-minus-one equals one! No problem!" No problem? We're subtracting one from infinity now and acting as if that's not the most wrong thing ever.
Obviously this isn't math, this is physics where this sort of thing makes sense and you can't even compare "infinity" in physics with "infinity" in math, I still find it funny though. 🤣
TL;DR: "whoosh." More-detailed reply below.
Did you read a transcript of when Dr. O'Dowd said that, rather than actually watching the video, or do you have difficulty picking up on the use of voice tone to adjust the meaning of statements? Dr. O'Dowd's tone is very clearly jocular when he says "infinity minus infinity-minus-one equals one. No problem!" He isn't suggesting that that's a valid mathematical calculation. He's *not* "subtracting one from infinity and acting as if that's not the most wrong thing ever" like you say he is. He's making a joke.
How else would you propose resolving a natural system (universe) based upon infinities to a discrete value or measurement?
@@axle.student The natural system is NOT based upon infinities. That's a fairy tale physicists share, just like renormalization.
"Obviously this isn't math, this is physics where this sort of thing makes sense and you can't even compare "infinity" in physics with "infinity" in math,"
"I still find it funny though. 🤣"
Stuff like this makes me hopeful for the existence of negative mass so we can someday have ftl, artificial gravity, perpetual motion machines, etc
Love ur videos, but can u leave some links of research paper related to the videos for nerds
Pretty cool, I'm studying this at the moment and your videos are a nice recap when you haven't seen this stuff in a while
"Infinity minus (infinity+1) equals...1" Oh my brain felt like it sprained itself for a moment there...but, well, it also makes sense!
Also, for the lulz of it..."1 part in 20,000" isn't by any chance part of the reason why matter exists, is it?
wait... 13:17 with the electron changing positions because of the pair then annihilation, does that mechanism give rise to the fuzziness of its location, or is that just another component of its existence at that scale?
Space Time!
❤
Absolutely freakin awesome video
Removing an infinite subset of an infinite set can result in a set of any size not greater than the original set
Listening to this feels like surfing a wave of knowledge that would drown you if you tried to take it all in. But the surfing sure is fun.
Good to know every electron in my body annihilates with antimatter 10^17 times per second. 😅
Almost makes one think of particles less as discrete entities, and more as relational distributions of charge; eddies in "the black sea of infinity," as Lovecraft put it.
I’ve learned so much from this channel - thank you.
I'm amazed all these bare masses aren't grounds for demonetization 😅😂
I misheard it initially and thought bare ass on tv lol Yeah I went there
It's okay, as long as you don't expose her boson.
This is PHYSICS. PHYSICS. Physicists often use terminology that gets jumbled up with the public -- people like you -- but that's okay. You just have to learn about what they mean by it before mindlessly assuming things.
@Gordy-io8sb Did you reply to the wrong comment? Who is assuming things?
@ No, I didn't. Read your comment again.
I'm really excited about the next episode and I'm wondering if the next disvovery of the LHC will be the particle that "protects" the Higgs!
min: 10:55 the subtitle text says: "wweeping the infinities under the rug" 🤣🤣 poor physicists...
Infinite dust under all my rugs has become fairly obvious at this point... .I've run out of places to put it.
@@MOSMASTERING the true mastery is to have just the right amount of infinite space to accomodate it all, except for 511 grains of dust..
AI (translate) is giving us hints on what kind of future humans are going to have.
@@sicfxmusic What is "translate"? Do you mean LLM's ?
I don't think any of what we currently have is informing us of all that is coming - it's all a stepping stone to new paradigms Huge changes, huge advances won't resemble any of the cute toys we are currently using. As soon as self improvement or any hint of self awareness happens, it will immediately change the world forever and there is no going back.
Why is it that humans have this insane desire to forge ahead without looking or stopping to plan ? It must be encoded in our DNA. We forged ahead to new lands, spread across the world, we are terrible at long term planning and have a 'look before you leap' attitude in everything we do.
This might be the last time the human race ever gets to do that. I mean, it's going to happen whether we want it to or not. But we can't resist opening Pandora's box, can we? We just have to peak at a superintelligence that is way beyond us. Does that even sound sensible?
Such a great video! I didn't learn this in either my particle physics nor QFT class. But you gave such a clear explanation of how this works. Thanks!
I am coming to believe (possibly because I don't understand something) that the idea of measurement is itself flawed. It's like in order to refer to any event or object in the spacetime continuum, we can use measurement because in the continuum itself (which we, the measured event and the measurement devices are) those measurements results remain consistent across time.
When we get in deeper and start asking about the actual nature of the events or the continuum itself, the order of the questions the measurements are asking matters to the consistency of the results.
So essentially, I believe science is the best possible way to describe the continuum, but it's reliance on consistency in measurement results regardless of order of questions asked is screaming that some updated idea of measuring or a separate domain of logic that undermines how we think of measurement is what rules the nature of reality itself. Measurable results are themselves emergent properties of a nature that can't be measured without context of the measurement parameters already existing to begin with.
By the time you're measuring, you're part of the measurement, so the underlying nature of the emergent measurable universe remains beyond measurable results.
It's like the true nature of reality is everywhere you look, but nowhere you dig into it. And that is why physics breaks down at certain points. It's essentially trying to apply "continuum logic" to something that the continuum doesn't apply to.
Please correct me if you understand better than me. Im happy to research anything I'm pointed towards.
A solid enough take. You can never measure something in isolation, every measurement involves two objects interacting, it is the behavior of a system, not knowledge of a singleton. Possibly the idea of what something is in isolation doesn't even make sense, like asking about the wetness of a single water molecule.
Beautiful.
I feel like last episode was the start of a semester and last episode was class 1. Im excite!
All the hand wringing about infinites in QFT is frustrating. We have no problem accepting the results from complex analysis that are well characterized (integrating around poles, conformal maps integratd at the boundary, etc.). None of this stuff, strictly speaking, is always explicitly necessary in many problems... these techniques merely make the mathematics easier to work with, but even without it, you can nearly always get a solution or an approximate solution that's "good enough for calculus" once you factor in considerations like error convergence, analytical functions, or bounded terms... and good enough for calculus is often good enough for chonkier things like the universe or uncooperative parameterized functions defined on stuff as gossamer and deformable as spacetime (and if quantum mechanics and information theory viewed through the lens of Neother offer any hints, all that REALLY matters here is the algebra of conserved quantities and abstract symmetries outside the context of realism or representation). Up until now the infinities are usually artifacts of embeding these symmetries into an unnatural artificial linguistic or computational system (ie explicit parameterized REPRESENTATION). It's the mathematical "technology" not the universe, or the current understanding of physics that's the real issue here.
I think I agree but I would love to see a paper from you about it.
Well, when your calculated vacuum energy density is divergent, you have a BIG problem with gravity: such Universe must contract in a Big Crunch. It's not "hand wringing", it means "we are totally off with experimental results on this one".
@denysvlasenko1865 not necessarily. If you integrate below the cutoff of reality and that cutoff is fuzzy, you have no problem (this is the entire point of working with analytic functions). The same problem would happen if you said let's assume that because special relativity exists and things like the wavelength of a photon are meaningless it's valid to say that light scales with the size of objects we want to image instead of the wavelength used to image it... there's a HUGE logical fallacy built into that statement (the wavelength depends on our "lab" frame relative to the emmiter of the photon, relative to the frame the object it will scatter off of as well as the RELATIVE quantum uncertainty in all of the above properties)... all those details fuzz up and difuse every singularity that we build into our unnaturally perfect equations and hence, into the tame reality we witness.
The math is just a guide. The physics is what happens when we eliminate all but the minimum level of detail and complexity to see how matter and energy behave... eliminate too much, and things will diverge as you throw out or inadvertently add information or resolution into a system incapable of supporting those information densities. Thus far, this phenomenon has been seen at every scale of nature, and in many instances you simply are prevented from seeing across the IR or UV firewalls to the other side of whatever phase transition is separating one energy scale from another, and for very deep reasons, that are often married to something like the second law of thermodynamics.
To learn more about this check out professor Laughlin's book: A Different Universe. If you're not a layman you can look into the subject of universality, the final chapters of Peskin and Schroder as well as Huang are good introductions to this topic. But unless you were spoonfed this as a grad student like I was, it's a few years commitment to come up to speed on this stuff even for most theorists. Working through Churchill's Complex Analysis prior to this and seeing how this stuff is useful in practical engineering and how/why the idealized methods like conformal mapping break down will guide your intuition towards understanding the straightforward resolution to the dilemma your statement/question implies.
We are missing a big piece of the puzzle which will only be revealed once we have made a measurement in a system capable of probing the regime on the other side of the transition. Until this happens, we can speculate and try to understand how things might look, but 4 d is special, and the lessons from spontaneous symmetry breaking in 2d and 3d don't always apply. The stuff we're talking about here is on firm experimental footing at all orders and energy scales.
The paradoxes up till now have exclusively been computational artifacts. What you're talking about is reaching beyond Noerther's theorem or the landscape of psudopotentials described by Jaynes. If they're fundamental, then the anomalies are artifacts. If there's another fundamental organizing principle on the other side of the transition, of which spacetime is the order parameter we have ZERO evidence for what that might be or how it might look... string theory is the only thing that's ever done anything remotely like this and in AdS5 ... we don't live in 5d anti deSitter space or on its conformal boundary. We live in 4d deSitter space... 5d like 3d&2d is soooooo comparatively EASY... 4d is just hard as ballz. Cheers m8
whew, that one took a couple of watches! Still don't fully understand a lot of it, but the Feynman diagrams really helped.
Here is my, hand wavy, alternative approach. Actually I expect that this has been investigated before and proved wrong or irrelevant. But having someone explain the problems with it would be enlightening.
First take the particle like properties to be purely a function of interactions. So we can ignore them when considering a single particle. This leaves you with a field with a large mostly stable wave and a lot of unstable small fluctuations.
The mass is the mass energy of the large wave. This should be a small finite value that will vary slightly as it interacts with the small waves. The observed mass is function of the wave mass and the interaction mechanism.
Since the wave is not a point and is continuously being modified by the fluctuations in this field and probably other fields as well, we get the quantum weirdness that we observe.
The descriptions I have seen are mostly consistent with this. But they then seem to force the "particle" concept onto the waves. Doing this seems to lead to some of problems in the math.
Hopefully my ramblings make some sense. If any experts can help enlighten me on the subject, I would really appreciate it.
The only flaw in your argument is that the only stable wave in a quantum field would have a single wavelength and infinite extent, being spread across the entire universe. It wouldn't change because nothing would make any difference. (A wave cannot just stop at some point, and it can't diminish in frequency towards the 'ends' either, what would be making the wave do that?)
For an object to NOT be everywhere, to be something like an electron, it needs to be the sum of infinite waves over a certain range of frequencies. (This is related to the phenomenon of 'beats' where two soundwaves of nearly identical frequency interfere to produce distinct beats of sound.) Which is fine, we can absolutely model an electron as the result of infinite 'perfect' waves in the electron field summing up into a little wave packet. That's what all of those Feynman diagrams are, waves of differing wavelengths in various fields. The higher energy, smaller waves we make a part of it, the smaller the end particle becomes.
BUT... WHY is it like it is? Why that mass? Your argument works for ALL particles, why isn't an electron as massive as a proton? A top quark? Nothing in the underlying theory says the electron can't be made of more energetic waves, or even be pointlike. If the electron is pointlike, infinitely small, we need infinitely high energy waves in it.
But... well we have the Planck Length, that gets rid of infinity by saying we just CAN'T have infinitely energetic and tiny waves involved. As you say, the electron is NOT pointlike and can never be. Even better, the 'static' in the electron field will blur and swamp any waves smaller than those inherent quantum fluctuations, cutting out even MORE high energy waves and giving us the low mass we see today.
Which is... almost exactly what you said. Except, rather than a wave AND a field interacting, the field controls what the wave can even BE. The quantum messiness of the electron field limits what it can use to MAKE a stable wave. If the electron field was more messy it'd eliminate more stuff and the electron would be less massive.
@garethdean6382 thanks for filling in important parts of my idea that I missed.
No such thing as a discrete point along a wave or around a circle in my mind. If you zoom out far enough a circle may appear point like, but it always fuzzy. If you zoom in far enough a circle appears flat and it's almost impossible to find the curve and is always fuzzy.
So for me, the universe has no inherent discrete values even though we may have some concept of the peak of a wave going past and be able to count them, we never really know where the absolute point of that peak is. It's always fuzzy, always contains some infinitesimal uncertainty :)
The way renormalization has been described here looks like just using the fact that for any divergent series with infinite positive and negative contribution where the sequence still converges to zero, you can rearrange the terms to make it sum to anything. Why wouldn't be exactly what's happening here, where we choose this "anything" to be the observed electron mass?
If that's the case, the actual solution provides an order that makes physical sense. So if renormalization works, but we don't have a solution, wouldn't it just mean that we don't know why the "right" order of terms physically makes sense? (or even precisely which one it is)
So if you add a whole pie to my belly then take away my appetite that somehow equals happiness? I approve of this math.
Lol
Eating makes me happy 😊
Finally finished with my exams, still haven’t gotten enough of physics though :P not that videos like this really resemble courses at all though haha
"This is infinite. That is infinite. Out of That infinite manifest This infinite. Substrate This infinite from That infinite, Infinite alone remains." - Upanishads
this channel does not miss
I don't understand sh*t. I use this channel as ASMR.
I try to Understand most of the time but I'm either too baked or too stupid 😅
But it is good background sound for some reason, good to sleep or eat to
Thank you. Outstanding presentation. Bravo!
How many of you also try to anticipate when Matt is going to end the video with "space time"? 😂
like "smoke week every day" at the end of Dre Dre's track "the next episode"
and i never get it right
🎯 Key points for quick navigation:
00:00 *🔬 Introduction to the Hierarchy Problem*
- The concept of subtracting infinite masses to yield an electron is introduced.
- Overview of the Hierarchy Problem, focusing on the unexpectedly small mass of the Higgs boson.
- Comparison to the historical electron hierarchy problem, setting up the discussion.
01:48 *⚛️ Electron's Mass and Quantum Field Theory (QFT)*
- Classical physics predicts unrealistically high or infinite self-energy mass for electrons.
- Quantum mechanics, specifically QFT and QED, provide the framework to address these issues.
- Introduction of terms: bare mass, self-energy, and dressed mass, with renormalization as the method to reconcile infinities.
05:32 *🧮 Renormalization and Fine-Tuning Challenges*
- Explanation of renormalization to cancel out infinite self-energy with an infinite negative bare mass.
- Highlighting the unnatural fine-tuning required for near-perfect cancellation of large terms.
- Renormalization is critical for electron mass but introduces new questions about the Higgs boson.
06:27 *💡 Virtual Particles and Quantum Field Dynamics*
- Virtual photons and electron-positron pairs drive the quantum electromagnetic field’s activity.
- Feynman diagrams are used to model possible interactions, contributing infinite energy if summed without limits.
09:16 *🚨 Regularization and Limits of Quantum Mechanics*
- Regularization imposes a cutoff at scales like the Planck length, yielding finite masses.
- Discussion of the limits of quantum mechanics as an effective theory, acknowledging that deeper physics must exist.
13:13 *⚖️ Symmetry and Natural Mass for Electrons*
- Matter-antimatter symmetry protects the electron’s mass, avoiding unnatural fine-tuning.
- Chiral symmetry ensures that the electron’s small mass emerges naturally from the interplay of positive and negative components.
14:39 *🌌 Implications for the Higgs Boson and Beyond*
- The electron's mass is resolved, but the unnaturalness of the Higgs boson’s mass remains a mystery.
- Renormalization and regularization illustrate the emergence of effective theories, hinting at deeper physics.
15:04 *🛠️ Sponsor: Radiacode and Scientific Exploration Tools*
- Promotion of the Radiacode radiation detector and its features for scientific enthusiasts.
- Introduction of holiday discounts and merchandise sales for PBS Space Time viewers.
Made with HARPA AI
Mathematically-speaking, you have to be careful with applying arithmetic operations to infinities, bc not all infinities are the same size. Some infinities are larger than others; so, 00-00 often ≠ 0 (and, given that 00 isn't actually a number, the "value" 00-1 is utterly meaningless)
That being said, "infinities" in pure mathematics refers to infinite numerical sets (which explains why there can be comparative infinities larger and smaller than others); whereas, in the context of the problem presented here as a mathematical descriptor for the electron (via QM), we very likely don't have to concern ourselves with different sizes of different infinities, because we're dealing with a singular value assigned as infinity presented twice (with opposing polarities*)
(* positive and negative signs, that is)
it contains both infinities though so the assumption is that they are equally large which makes sense as you would have to specify how large any of the infinities is in the first place.
physicists know but don't care
3= 3x1=30x0.1=3........0 x 0.0.......1= infinity x 0. I'm guessing something similar is true for adding and subtracting infinity.
All infinite sets are the same size but they aren't all constructible. Mathematicians were just confused when they equivocated their way into thinking unconstructible is bigger than constructible. Uncountable infinite isn't greater than countable infinite, it's just uncountable.
Mind blowing stuff!
I'm slightly disappointed you didn't mention Feynman calling renormalization a "dippy process"
this series is brilliant, nice one, more math's please. too many videos skip the details
You get a Sophon. Obviously.
😉
WORST. MACGUFFIN. EVER.
I couldn't finish that book. The science ideas were a lot of fun, but the way they were revealed was just a series of scenes where 2 people are in a room doing plot exposition.
I say you get a Vogon.
@@murunbuchstanzangur I honestly VASTLY preferred Quinns Ideas summary, revie, and exploration of the books MORE than the books themselves.
@@TheOtherSteel I'm totally good with that if I get to play halflife 3 first.
Amazing how renormalization aligns theoretical predictions with observations. It’s a striking example of how physics bridges abstract math with empirical data.
I got to chat with Freeman Dyson for a few minutes at a book signing.
Hi Dr. O'Dowd!
Renormalization seems unsatisfying, even if it's relatively useful. But for some reason, I can't stop thinking about taking the integral of an infinite polynomial and setting x equal to 0. All the higher-order craziness vanishes and we're left with just the constant of integration. Even if that constant is small or seems strangely fine-tuned, no other terms needed to magically cancel out to produce it. We're still calibrating the constant to reality, but there's nothing weird about it.
0:51 are you saying the higgs mass should be MASSIVE?
I've heard that you're the commenter who asks the heavy questions.
excellent episode. i got the basic principle now, but to truly understand it, i think i need some maths to back that up. but hey there are worse ways to spend what could have been a night of good sleep other than a deep dive into the maths of the hierarchy problem.
If the universe is infinite in all directions, then i declare : i am the center of the universe right now ! And for all my life ! … prove me wrong 😅
You are at the center of your universe.
Light cones would agree. 🙃
You can still be at the center of a boundary-free, finite universe.
Some years ago as a undergraduate, I attended a lecture by visiting speaker Arthur Jaffe. I could understand almost none of what he said, and probably our faculty in attendance didn't either. I do remember he tried to take some of the mystery of subtracting infinity from infinity. It was something like "form A sub n minus B sub n, and then take the limit as n goes to infinity."
Ah! So that's how it's done! What could be more simple?
Right. So, for ∞ - (∞ - 1) you start with x=1 and move up. 1 - (1 - 1) = 1. 2 - (2 - 1) = 1 and so on. The limit is 1 so ∞ - (∞ - 1) = 1! Seems pretty solid to me.
@garethdean6382 Jaffe's explanation is a more more subtle than that and is exposing why you can't just look at inf-(inf-1) and say "yeah that's 1".
(x+n)-x for your favorite number n is inf-inf as x goes to infinity, but every step of the way it evaluates to n. So inf-inf could reasonably be any finite number.
2*x-x is inf-inf as x goes to infinity, but every step of the way the value was x as it grew to infinity, so inf-inf could reasonably be infinity
x-2*x is inf-inf as x goes to infinity, but every step of the way the value was -x as x grew to infinity, so inf-inf could reasonably be -inf
There is literally no way to rule out any evaluation at all without understanding how you ended up with inf-inf, and even then there's still a chance it is something that can't be evaluated (afterall, I only went over 3 unreasonably well behaved ways or could happen)
∞ - (∞ - 1) = 1 ... BOOM! Where is my Nobel?
🏆
EinsteinHawking_CalmDownMeme.jpg
They finally found their limits
lim x→∞ [x−(x−1)]=lim x→∞ 1=1
You forgot to account for the smartarse factor. Try again next year.
This equation is actually meaningful in Conway's surreal numbers. Highly recommend Knuth's book surreal numbers. It's a maths book in the form of a story.
8:51 😆 you just described what happens in order for us to view this episode on our screens, especially the led ones 😎👍👍
It feels so wrong to use virtual particles as a solution to our problems. It just feels like a way to explain what’s happening without having a good understanding of the truth.
You know how a moving electric field will generate a magnetic field? And that magnetic field will propel electrons creating a moving electric field? It's like that but on a very small scale. Everything is constantly interacting with itself and also interacting with those interactions. It's turtles all the way down.
I remember reading about renormalization a few years ago, but I don't remember having any real understanding of it. This makes a bit more sense. Thank you! Having said that, it gives me the overall impression of building ikea furniture with the wrong parts. You can still get it all to fit together and work mostly correctly, but you still haven't built it properly, lol.
God be with you out there, everybody. ✝️ :)
"Wait it's all infinite?"
"Always has been"
That's a mighty long time ⌛️
This is fascinating stuff
If the hierarchy problem is problematic, just dox it and write emails to its boss with false allegations of racism and sexism. Or any other form of fascistic social pressure should also do…
Honestly, this is a rather well-put higher explanation of "why out of necessity" are we sweeping the energy infinities under the rug and letting them be. All the while looking at the post-renormalization energies...and somehow we are calibrating or reassessing under our current reality. It's like you have to ask the universe what you are looking at while ensuring your reality of measurement is also accounted for before the universe teases you with a truth or novel finding.
who is the bigger idiot, the person who purposed this formula or me for thinking the person who purposed this formula is an idiot?
Both
If you can't spell "proposed" you don't get to ask questions.
My first thought after this was “what if there’s an anti-Higgs particle and that’s dark energy?” Which is, I’m sure, not a new or particularly useful idea, but I just love how this channel makes me marvel and wonder at the inner workings of the universe like that.
I mean heah, the anti-Higgs does exist, but why would it be dark energy?
9.5k views in 30 mins? That's a lot of electrons
I think that quantum and classical eoectromagnetism predicting the same infinities on the point like scale is a good showcase of the theories converging.
My current bank account balance is a negative infinite balance + a positive infinite balance + my current balance
Sounds an awful lot like the Government. Negative infinity in deficit, positive infinity money printer goes brrr
Feynman, Schwinger and not to be forgotten Tomonaga ...
physicists are the kinds of people who wouldnt mind if the universe was destroyed as long as it makes their theories simpler.
No one would be bothered by the destruction of the universe. Now, bothered by being aware of the imminent destruction of the universe before they are finished using it, sure, but that's differrent.
They weren't sure if a nuclear detonation would set fire to the atmosphere, but they went ahead anyway..
PBS Space Time always asks the question no one else would
Since this is continuation of the previous episode, I find the mass of electron problem quite fascinating. As I understand it, photons are basically fluctuations in the EM field traveling at a particular frequency yet they have a mass. Why can’t an electron be a fluctuation in the EM field as well? For the mass predicted would the frequency be too large? If so, is that a problem? Isn’t having a high frequency mean that the vibrations are too fast which would align with the elusive nature of the electron where it cannot be seen. Is this fluctuation traveling through the EM field by self destruction i.e. it causes positrons to popup annilating itself and the next paired electron moves forward which does the same thing again and again. The mass calculation would theoretically lead to one calculation but measurement would also account for the positron pair that keeps forming near electrons to anhilate it and possibly another electron paired to the positron. This would also explain the mass descrepancy. I wish I knew mathematics as well as physicists, would love to try and do the calculations.
Finally something we can all agree on!
Magnificent video! Thank you!
I'd love to see a little more examples of cancelling terms out - the descriptions are all very high level, and a bit hard to grok. I was also confused about "blowing them up to the size of the planck scale" - isn't that incredibly tiny? Or do you mean that the electron is presumed to be smaller (more point-like) than the planck size?
Yes, if the electron involves phenomena smaller than the Planck Scale, the numerical result 'blows up' towards infinity. The Planck Scale is MOSTLY tiny, the Planck Mass is about that of a dust mote -huge in particle terms.
In terms of cancellation, imagine that I have a theory to measure the average mass of fur on a cat. It simply take the mass of one hair then multiply that by all the hairs that could fit on a cat. I sum over all numbers and lengths. Which gives me infinity, I'm counting all possible lengths from zero to infinity after all.
Which is foolish, I can't have hairs that are infinitely long, that's not reality. If I just don't count those, if I put in a sensible cutoff I get a finite answer. Mathematically I can do this by taking every 'silly' measurement and pairing it with an opposite silly measurement. The infinities cancel out but perhaps it's more sensible to say I just don't bother with them in the first place. They're unphysical.
This will be great for my kids grade 1 home work
❤
Silly question, but what’s the background music used from the beginning until almost the 6 minute mark?