Welcome back, been a minute. It’s depressing how much of this material is still out of reach for me, but it’s exciting how much of it I can follow. As always, it’s great that people like you give of themselves so people like me can try to learn. Thanks!!
i feel the same, i suddenly developed a big intuition for the quantum world and started getting deeper into the details theres tons more i need but im so happy with what i can follow and so glad that some people dont dumb it down too much which stimulates gradual improvement for me personally
it is absolutely wild to me that people worked this out in advance of the discoveries of the Z and Higgs bosons. humans are incredible when they put their mind to things like this instead of blowing each other up/screwing each other over for money/etc
The W+ Boson is dual to the W- Boson. Symmetric wave functions (Bosons, waves) are dual to anti-symmetric wave functions (Fermions, particles) -- the spin statistics theorem or quantum duality. Bosons are dual to Fermions -- atomic duality. Symmetry is dual to anti-symmetry -- symmetry breaking is dual. "Always two there are" -- Yoda. Energy is dual to mass -- Einstein. Mass, Fermions and particles are anti-symmetric and pure energy, Bosons and waves are symmetric -- symmetry breaking is dual. The Higgs Boson is dual to the Higgs Fermion -- Duality! The vacuum state is dual to the zero particle state synthesizes mass -- the Hegelian dialectic! Thesis is dual to anti-thesis creates the converging or syntropic thesis, synthesis (mass) -- the time independent Hegelian dialectic. Mass is dual and therefore energy is dual. Duality within duality. Duality (energy) is being conserved -- the 5th law of thermodynamics! Symmetry (duality) is dual to conservation -- the duality of Noether's theorem.
@@zapphysics The W+ Boson is dual to the W- Boson. Symmetric wave functions (Bosons, waves) are dual to anti-symmetric wave functions (Fermions, particles) -- the spin statistics theorem or quantum duality. Bosons are dual to Fermions -- atomic duality. Symmetry is dual to anti-symmetry -- symmetry breaking is dual. "Always two there are" -- Yoda. Energy is dual to mass -- Einstein. Mass, Fermions and particles are anti-symmetric and pure energy, Bosons and waves are symmetric -- symmetry breaking is dual. The Higgs Boson is dual to the Higgs Fermion -- Duality! The vacuum state is dual to the zero particle state synthesizes mass -- the Hegelian dialectic! Thesis is dual to anti-thesis creates the converging or syntropic thesis, synthesis (mass) -- the time independent Hegelian dialectic. Mass is dual and therefore energy is dual. Duality within duality. Duality (energy) is being conserved -- the 5th law of thermodynamics! Symmetry (duality) is dual to conservation -- the duality of Noether's theorem.
Whoohoo welcome back! This video was a mouthful... I'll watch this again because I didn't grasp how a doublet of two neutral particles can be charged. You say that we only ever observe one kind of neutrino. But how do we measure the handedness of neutrinos without assuming that the weak interaction cares about chirality in the first place? Is the charge fixing the required masses an example of a measured parameter predicting a free one that we wouldn't otherwise have a value for? This also seems to suggest a deep relationship between mass and charge. Is this the reason we see no massless particles with electric charge? This also further looks like it is really necessary to stop thinking of charge in a classical electromagnetic field way and start thinking "interacts with photons". I also have an unrelated question which I haven't been able to find an answer to. Feel free to ignore it, since it is off topic. I learned recently that the raising operator has _no_ eigenstates and I am baffled by this. A linear operator in an n dimensional, complex vector space should have n eigenvectors _and_ n eigen-covectors. Instead the lowering operator has the eigenvectors and the raising operator has the eigen-covectors. I don't understand how this can be the case and how to identify which vectors go with which operator. Is this a property of infinite dimensional vector spaces, Hilbert spaces, or is it a "lie" and the raising operator just has no eigenvectors that we care about?
Hey Narf! Fantastic questions as always! I think that the first thing that I want to say is that there seems to be a misunderstanding (I don't think the point was super clear in the video, so I don't blame you...). When I talk about the charges and the Higgs couplings, it isn't so much that the charges determine the mass after symmetry breaking, it is just that the charges of the fermions and Higgs doublet allow us to write down fermion-Higgs couplings at all without breaking the symmetries of the theory. So, it really means that the three fields that I couple together in these interactions (one left-handed fermion, one right-handed fermion, and the Higgs doublet) transform in such a way that this interaction doesn't change under the standard model gauge transformations. The masses of the fermions themselves are determined by the *strength* of this interaction, which is completely independent of the charges under the standard model gauge group. These coupling strengths are free parameters of the theory that have to be determined experimentally (this shouldn't be surprising, though, since they are in one-to-one correspondence to the fermion masses, and we already knew that these are free parameters). I don't think that there is really any deep reasoning that there are no massless charged particles. Actually, as far as we know, the only massless particles that really exist are the gauge bosons. What this probably just means is that any matter particles (non-gauge fields) probably talk to a scalar that obtains a non-zero vev at some point in our universe's history, whether or not that is the standard model Higgs doublet. The best way to really think about the doublets is that they are their own particle and the two elements are analogous to the three color elements of the quark fields. We typically think of the quarks as single fields, but really, they are triplets with three elements, each corresponding to a different color. The doublets are the exact same: the elements now just correspond to different weak isospins. It just happens that when the symmetry is broken, these doublets are broken up (because the elements are no longer related by a symmetry), and the net result is that they can be combined with right-handed singlets to form Dirac fermions. I think that it goes even a bit further than just saying that charge is "interactions with photons." Charge is really a statement about the representation of the fields which transform under the standard model gauge group. So really, charge is deeply rooted in group theory more than anything. Okay, the point about the neutrinos. So the nice thing about neutrinos being (almost) massless is that it means that their chirality, or "handedness" is actually directly tied to their spin. In fact, for massless particles, it turns out that chirality is the same thing as what is known as "helicity," which just refers to the value of the spin along the direction of the particle's propagation (an interesting question for you to ponder if you don't know the answer already: why is this only the case for massless particles?). This is very nice because spin is just a form of angular momentum. So, if you work out the momentum conservation of the decay products in weak decays, you can figure out the direction of propagation of the neutrino. Then, if you know the angular momentum of the initial state and the angular momentum of the final state minus the neutrino (since you definitely aren't going to measure the neutrino directly), you can work out the angular momentum of the neutrino, and therefore its spin. So, in some sense, we can indirectly measure the spin, and therefore, the chirality of the neutrino, at least, to an extremely good approximation. Since they are technically massive, it isn't going to be 100% perfect, but the corrections are going to be so tiny that they have never been measured. Now, onto your unrelated question. I don't know for sure, but I have a hunch that your statement that a linear operator should have n eigenvectors and n eigen-covectors only applies to *hermitian* operators. Since the creation and annihilation operators are not hermitian, I am not surprised that they have some weird behavior that might not align with what you are used to if you only really deal with hermitian operators, which is obviously the case if you are studying QM. Intuitively, this sort of makes sense that each the creation and annihilation operators only define "half" of the space. If I have an arbitrary state, I won't be able to reach any other arbitrary state with just operations involving the annihilation operator. As an easy example, say I start with the |2> state. Then, I will never be able to access the |3> state with just annihilation operators, I need a creation operator for that. So it sort of makes sense that I can really only define the "full" eigenspace if I have both creation and annihilation operators. But that is sort of a guess, I don't think I have a super exact answer for you, unfortunately.
@@zapphysics As always, thank you for your thoughtful answer! I think that is basically how I understood the first point, though I suppose I misunderstood the link between charge and mass vs coupling strength and mass. But you said gauge bosons are, in general, going to self interact. Yet the photon doesn't and is the only massless electroweak boson left. Is that really a coincidence in the standard model? For the QCD triplets the components all carry the charge of the interaction in some way and the resulting triplet is a linear combination. But the doublet components are _both_ electrically neutral yet the linear combination is charged. That seems odd to me. The fields which transform under that gauge group (U(1)?) are going to be the ones that interact with the bosons of the gauge field, aren't they? So that sounds like the same statement from a different perspective. Thanks, the neutrino point makes sense. So to find a measurable correction we'd have to find ourselves some very slow neutrinos? We can transform the helicity to be the oposite by just moving faster than that particle, this is not possible for massless particles because they move at c. I don't think that's correct about Hermitian operators. If I have the Eigenvalues I'm pretty sure I can always solve the eigenvalue equation on either side. For hermitian operators the solutions are just going to be each other's conjugates. For non-hermitian operators they can be unrelated, I think. I'm fairly certain this has to be a result of taking the dimensionality to infinity. I just don't see what that actually changes. Thanks for your input, though. I'll keep looking :)
@@narfwhals7843 If you have a matrix which isn't diagonalizable, such as [[1,1],[0,1]] , the span of its eigenvectors will not be the whole space. However, for any linear operator on a finite dimensional vector space over the complex numbers (or over any algebraically close field, iirc), it *will* have at least one eigenvector. So, if the raising operator is a (bounded) linear operator on a (complex) Hilbert space, and if it can indeed have no eigenvectors, then yes I would attribute this to the Hilbert space being infinite-dimensional. Let me think if I can come up with an example. Let the Hilbert space be \ell^2(\bn) , i.e. the space of functions from natural numbers to complex numbers such that the sum of the squares of the absolute values of the terms, is finite. consider the operator S which sends f to S(f) where (S(f))(n+1) = f(n) and (S(f))(0)=0 . (so, it would send (a_0, a_1, a_2, ... ) to (0, a_0, a_1, a_2, ...) ) Then, if S(f) = \lambda f , then, that would mean that \lambda (a_0, a_1, a_2, ...) = (0, a_0, a_1, a_2, ...) and so a_0 = \lambda a_1 , a_1 = \lambda a_2, etc. , but also 0 = \lambda a_0 , and, yeah, that would imply that either \lambda = 0, but the only eigenfunction with an eigenvalue of 0 would be the zero vector, (0, 0, 0, ... ) , which we generally don't uh, count, when talking about eigenvectors, or that a_0 = 0, but in this case, as a_0 = \lambda a_1 , then, as assuming that \lambda isn't 0, this would imply that a_1 = 0 as well, and similarly that a_2 = 0, and so the only thing it could be is (0, 0, 0, .. ), which, again, we don't count. So, this linear operator has no eigenvectors. But, I said "(bounded) linear operator". Is this operator bounded? Yes. I don't know if the raising operator is bounded. I suspect it isn't, but I don't know the physics to say with confidence. To see that this operator is bounded, note that the norm of the output (the norm being the \ell^2 norm) is always equal to the norm of the input, as it just shifts the sum of squares of absolute values over by a position by adding a 0 at the start. So, the operator norm is 1, which is finite, and so the operator is bounded. So, yes, if you are working over a complex vector space, then having linear operators which don't have any eigenvectors happens only when the space is infinite-dimensional. However, you could maybe uh, like, [what follows is more speculative] come up with a sequence of things that are sorta like, "approaching being eigenvectors", maybe? Like, if you had the sequence (1,r, r^2, r^3, ... , r^n , r^{n+1}, ...) , for some r with |r| > 1 (which isn't actually in the Hilbert space because the \ell^2 norm is infinite), then like, applying S to that wouldn't quite multiply it by a factor of r, but it would match for all the terms after the first one, and if you like, truncated it to the first N terms, and then scaled things to normalize the truncated version, then the larger N was, the closer the first term would get to zero, and the smaller the difference between r times the vector and S applied to the vector, so, in a sense, it is sorta-kinda as if it is an eigenvector of it? However, I don't have a good definition for a sense in which it is as if it was an eigenvector of it. Oh, alternatively, uh, If you took like, the sequence v_N of normalized versions of the truncation at N of the (1,r, r^2, ...) sequence (replacing everything after the Nth entry with 0), and then for like, any fixed vector u, took the inner product of u with (S(v_N) - \lambda v_N), then I think the limit of this $\langle u , (S(v_N) - \lambda v_N) angle$ as N goes to infinity, should be 0? So, I think that's kind of like this sequence being in a way as if it were approaching an eigenvector with eigenvalue \lambda . However, uh, I think there's also a similar sense in which it "approaches" the 0 vector... Though, uh, maybe, if $\langle u , (S(v_N) - \lambda v_N) angle$ approaches 0 substantially faster than $\langle u , v_N angle$, then this could still be a reasonable idea? idk.
@@narfwhals7843 So, the point about gauge bosons being able to self-interact in general is a good question. And actually, this is again rooted in group theory. Since the gauge bosons are tied to the transformations which make up the group, it turns out there is actually a very simple rule for determining if your gauge bosons will self-interact or not: if the transformations commute (the group is abelian), then the gauge bosons will not interact with each other. If the transformations do not commute (the group is non-abelian), then the gauge bosons will self-interact. This sort of makes intuitive sense since the transformations "talk" to each other (their ordering matters) in the non-abelian case, but they don't in the abelian case (the ordering doesn't matter). For the photon, the group governing the transformations is U(1), which only has a single possible transformation (rotations in the complex plane) and therefore is abelian. Hope that makes sense. So I think I am a bit confused about what you mean by both elements of the doublet being electrically neutral. The pairs are (neutrino, charged lepton), (up quark, down quark), and (charged Goldstone, physical Higgs boson + neutral Goldstone) (the last being the Higgs doublet). If you notice, the first component of each doublet is one unit of electric charge greater than the second component. This is because the two components will have the same weak hypercharge, but the first component has weak isospin of +1/2 (analogous to spin up), while the second component has weak isospin of -1/2 (like spin down). After SSB, we get a leftover surviving symmetry of QED, and the charge under QED is determined by charge = weak hypercharge + weak isospin, so the two components of the electroweak doublets should always differ by one unit of electric charge. I'm not sure this answers your question, but I think I am a bit confused as to what the question is. Sorry I couldn't be of more help with the question about raising/lowering operators and @drdca, thanks for contributing to the conversation! Hopefully their response is a bit more insightful!
@@zapphysics Ah the self interaction makes sense. Thanks! I was talking about the w+/-, which are charged under QED. being combinations of the w1/2, which are not charged under QED. But as you explain, the QED charge is a combination of weak hypercharge and isospin, which w1/2 do have. So that makes sense after all. I think, I understand. I don't expect you do know everything:) But I'm going to give @drdca 's comment a thorough read! Also I'm extremely glad to see you back. I hope you're doing well!
So, before the SSB, did electric charge and the electromagnetic field exist? Which gauge bosons were the physical ones? The W±, Z and photon, or the W1,2,3 and B?
When I said "before SSB", I implicitly brought some cosmology into the discussion, since I was vaguely referring to the idea that some phase transition in the early universe broke electroweak symmetry into the residual electromagnetic U(1) symmetry
The W+ Boson is dual to the W- Boson. Symmetric wave functions (Bosons, waves) are dual to anti-symmetric wave functions (Fermions, particles) -- the spin statistics theorem or quantum duality. Bosons are dual to Fermions -- atomic duality. Symmetry is dual to anti-symmetry -- symmetry breaking is dual. "Always two there are" -- Yoda. Energy is dual to mass -- Einstein. Mass, Fermions and particles are anti-symmetric and pure energy, Bosons and waves are symmetric -- symmetry breaking is dual. The Higgs Boson is dual to the Higgs Fermion -- Duality! The vacuum state is dual to the zero particle state synthesizes mass -- the Hegelian dialectic! Thesis is dual to anti-thesis creates the converging or syntropic thesis, synthesis (mass) -- the time independent Hegelian dialectic. Mass is dual and therefore energy is dual. Duality within duality. Duality (energy) is being conserved -- the 5th law of thermodynamics! Symmetry (duality) is dual to conservation -- the duality of Noether's theorem.
Spontaneous Symmetry Breaking happens when a particle chooses a position in the Mexican Hat Potential, so does the un-breaked symmetry require a continuous particle that exist along a closed path in this potential. If so is this particle physically realizible?
Real is dual to imaginary -- complex numbers are dual. The W+ Boson is dual to the W- Boson. Symmetric wave functions (Bosons, waves) are dual to anti-symmetric wave functions (Fermions, particles) -- the spin statistics theorem or quantum duality. Bosons are dual to Fermions -- atomic duality. Symmetry is dual to anti-symmetry -- symmetry breaking is dual. "Always two there are" -- Yoda. Energy is dual to mass -- Einstein. Mass, Fermions and particles are anti-symmetric and pure energy, Bosons and waves are symmetric -- symmetry breaking is dual. The Higgs Boson is dual to the Higgs Fermion -- Duality! The vacuum state is dual to the zero particle state synthesizes mass -- the Hegelian dialectic! Thesis is dual to anti-thesis creates the converging or syntropic thesis, synthesis (mass) -- the time independent Hegelian dialectic. Mass is dual and therefore energy is dual. Duality within duality. Duality (energy) is being conserved -- the 5th law of thermodynamics! Symmetry (duality) is dual to conservation -- the duality of Noether's theorem.
This electroweak force sounds like superconductivity where the fermions pair up into Cooper pairs. These Cooper pairs act like bosons and exert a force by repelling magnetic fields observed by levitating magnets. I wonder if they are another force carrying boson in the Standard Model.
Cooper pairs = duality! The W+ Boson is dual to the W- Boson. Symmetric wave functions (Bosons, waves) are dual to anti-symmetric wave functions (Fermions, particles) -- the spin statistics theorem or quantum duality. Bosons are dual to Fermions -- atomic duality. Symmetry is dual to anti-symmetry -- symmetry breaking is dual. "Always two there are" -- Yoda. Energy is dual to mass -- Einstein. Mass, Fermions and particles are anti-symmetric and pure energy, Bosons and waves are symmetric -- symmetry breaking is dual. The Higgs Boson is dual to the Higgs Fermion -- Duality! The vacuum state is dual to the zero particle state synthesizes mass -- the Hegelian dialectic! Thesis is dual to anti-thesis creates the converging or syntropic thesis, synthesis (mass) -- the time independent Hegelian dialectic. Mass is dual and therefore energy is dual. Duality within duality. Duality (energy) is being conserved -- the 5th law of thermodynamics! Symmetry (duality) is dual to conservation -- the duality of Noether's theorem.
at 11:02? I followed that SU2 doublets are like the color charge in the SU3 qcd interaction. But you completely lost me on my that means we need a new neutrino for each of the charged leptons. The you weren't even talking about the muon can someone help me understand?
Conservation of Spatial Curvature (both Matter and Energy described as "Quanta" of Spatial Curvature) Is there an alternative interpretation of "Asymptotic Freedom"? What if Quarks are actually made up of twisted tubes which become physically entangled with two other twisted tubes to produce a proton? Instead of the Strong Force being mediated by the constant exchange of gluons, it would be mediated by the physical entanglement of these twisted tubes. When only two twisted tubules are entangled, a meson is produced which is unstable and rapidly unwinds (decays) into something else. A proton would be analogous to three twisted rubber bands becoming entangled and the "Quarks" would be the places where the tubes are tangled together. The behavior would be the same as rubber balls (representing the Quarks) connected with twisted rubber bands being separated from each other or placed closer together producing the exact same phenomenon as "Asymptotic Freedom" in protons and neutrons. The force would become greater as the balls are separated, but the force would become less if the balls were placed closer together. Therefore, the gluon is a synthetic particle (zero mass, zero charge) invented to explain the Strong Force. An artificial Christmas tree can hold the ornaments in place, but it is not a real tree. String Theory was not a waste of time, because Geometry is the key to Math and Physics. However, can we describe Standard Model interactions using only one extra spatial dimension? What if we describe subatomic particles as spatial curvature, instead of trying to describe General Relativity as being mediated by particles? Fixing the Standard Model with more particles is like trying to mend a torn fishing net with small rubber balls, instead of a piece of twisted twine. Quantum Entangled Twisted Tubules: “We are all agreed that your theory is crazy. The question which divides us is whether it is crazy enough to have a chance of being correct.” Neils Bohr (lecture on a theory of elementary particles given by Wolfgang Pauli in New York, c. 1957-8, in Scientific American vol. 199, no. 3, 1958) The following is meant to be a generalized framework for an extension of Kaluza-Klein Theory. Does it agree with the “Twistor Theory” of Roger Penrose, and the work of Eric Weinstein on “Geometric Unity”? During the early history of mankind, the twisting of fibers was used to produce thread, and this thread was used to produce fabrics. The twist of the thread is locked up within these fabrics. Is matter made up of twisted 3D-4D structures which store spatial curvature that we describe as “particles"? Are the twist cycles the "quanta" of Quantum Mechanics? When we draw a sine wave on a blackboard, we are representing spatial curvature. Does a photon transfer spatial curvature from one location to another? Wrap a piece of wire around a pencil and it can produce a 3D coil of wire, much like a spring. When viewed from the side it can look like a two-dimensional sine wave. You could coil the wire with either a right-hand twist, or with a left-hand twist. Could Planck's Constant be proportional to the twist cycles. A photon with a higher frequency has more energy. ( E=hf, More spatial curvature as the frequency increases = more Energy ). What if gluons are actually made up of these twisted tubes which become entangled with other tubes to produce quarks. (In the same way twisted electrical extension cords can become entangled.) Therefore, the gluons are a part of the quarks. Quarks cannot exist without gluons, and vice-versa. Mesons are made up of two entangled tubes (Quarks/Gluons), while protons and neutrons would be made up of three entangled tubes. (Quarks/Gluons) The "Color Charge" would be related to the XYZ coordinates (orientation) of entanglement. "Asymptotic Freedom", and "flux tubes" are logically based on this concept. The Dirac “belt trick” also reveals the concept of twist in the ½ spin of subatomic particles. If each twist cycle is proportional to h, we have identified the source of Quantum Mechanics as a consequence twist cycle geometry. Modern physicists say the Strong Force is mediated by a constant exchange of Mesons. The diagrams produced by some modern physicists actually represent the Strong Force like a spring connecting the two quarks. Asymptotic Freedom acts like real springs. Their drawing is actually more correct than their theory and matches perfectly to what I am saying in this model. You cannot separate the Gluons from the Quarks because they are a part of the same thing. The Quarks are the places where the Gluons are entangled with each other. Neutrinos would be made up of a twisted torus (like a twisted donut) within this model. The twist in the torus can either be Right-Hand or Left-Hand. Some twisted donuts can be larger than others, which can produce three different types of neutrinos. If a twisted tube winds up on one end and unwinds on the other end as it moves through space, this would help explain the “spin” of normal particles, and perhaps also the “Higgs Field”. However, if the end of the twisted tube joins to the other end of the twisted tube forming a twisted torus (neutrino), would this help explain “Parity Symmetry” violation in Beta Decay? Could the conversion of twist cycles to writhe cycles through the process of supercoiling help explain “neutrino oscillations”? Spatial curvature (mass) would be conserved, but the structure could change. Gravity is a result of a very small curvature imbalance within atoms. (This is why the force of gravity is so small.) Instead of attempting to explain matter as "particles", this concept attempts to explain matter more in the manner of our current understanding of the space-time curvature of gravity. If an electron has qualities of both a particle and a wave, it cannot be either one. It must be something else. Therefore, a "particle" is actually a structure which stores spatial curvature. Can an electron-positron pair (which are made up of opposite directions of twist) annihilate each other by unwinding into each other producing Gamma Ray photons? Does an electron travel through space like a threaded nut traveling down a threaded rod, with each twist cycle proportional to Planck’s Constant? Does it wind up on one end, while unwinding on the other end? Is this related to the Higgs field? Does this help explain the strange ½ spin of many subatomic particles? Does the 720 degree rotation of a 1/2 spin particle require at least one extra dimension? Alpha decay occurs when the two protons and two neutrons (which are bound together by entangled tubes), become un-entangled from the rest of the nucleons . Beta decay occurs when the tube of a down quark/gluon in a neutron becomes overtwisted and breaks producing a twisted torus (neutrino) and an up quark, and the ejected electron. The production of the torus may help explain the “Symmetry Violation” in Beta Decay, because one end of the broken tube section is connected to the other end of the tube produced, like a snake eating its tail. The phenomenon of Supercoiling involving twist and writhe cycles may reveal how overtwisted quarks can produce these new particles. The conversion of twists into writhes, and vice-versa, is an interesting process, which is also found in DNA molecules. Could the production of multiple writhe cycles help explain the three generations of quarks and neutrinos? If the twist cycles increase, the writhe cycles would also have a tendency to increase. Gamma photons are produced when a tube unwinds producing electromagnetic waves. The “Electric Charge” of electrons or positrons would be the result of one twist cycle being displayed at the 3D-4D surface interface of the particle. The physical entanglement of twisted tubes in quarks within protons and neutrons and mesons displays an overall external surface charge of an integer number. Because the neutrinos do not have open tube ends, (They are a twisted torus.) they have no overall electric charge. >>>>>>>>>>>>>>>>>>>>>> Within this model a black hole could represent a quantum of gravity, because it is one cycle of spatial gravitational curvature. Therefore, instead of a graviton being a subatomic particle it could be considered to be a black hole. The overall gravitational attraction would be caused by a very tiny curvature imbalance within atoms. We know there is an unequal distribution of electrical charge within each atom because the positive charge is concentrated within the nucleus, even though the overall electrical charge of the atom is balanced by equal positive and negative charge. >>>>>>>>>>>>>>>>>>>>>> In this model Alpha equals the compactification ratio within the twistor cone, which is approximately 1/137. 1= Hypertubule diameter at 4D interface 137= Cone’s larger end diameter at 3D interface where the photons are absorbed or emitted. The 4D twisted Hypertubule gets longer or shorter as twisting or untwisting occurs. (720 degrees per twist cycle.) >>>>>>>>>>>>>>>>>>>>>>> How many neutrinos are left over from the Big Bang? They have a small mass, but they could be very large in number. Could this help explain Dark Matter? >>>>>>>>>>>>>>>>>>>>>>>> Why did Paul Dirac use the twist in a belt to help explain particle spin? Is Dirac’s belt trick related to this model? Is the “Quantum” unit based on twist cycles? ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ I started out imagining a subatomic Einstein-Rosen Bridge whose internal surface is twisted with either a Right-Hand twist, or a Left-Hand twist producing a twisted 3D/4D membrane. The model grew out of that simple idea. I was also trying to imagine a way to stuff the curvature of a 3 D sine wave into subatomic particles. .
You make some interesting points but there is a pattern to your thinking:- The W+ Boson is dual to the W- Boson. Symmetric wave functions (Bosons, waves) are dual to anti-symmetric wave functions (Fermions, particles) -- the spin statistics theorem or quantum duality. Bosons are dual to Fermions -- atomic duality. Symmetry is dual to anti-symmetry -- symmetry breaking is dual. "Always two there are" -- Yoda. Energy is dual to mass -- Einstein. Mass, Fermions and particles are anti-symmetric and pure energy, Bosons and waves are symmetric -- symmetry breaking is dual. The Higgs Boson is dual to the Higgs Fermion -- Duality! The vacuum state is dual to the zero particle state synthesizes mass -- the Hegelian dialectic! Thesis is dual to anti-thesis creates the converging or syntropic thesis, synthesis (mass) -- the time independent Hegelian dialectic. Mass is dual and therefore energy is dual. Duality within duality. Duality (energy) is being conserved -- the 5th law of thermodynamics! Symmetry (duality) is dual to conservation -- the duality of Noether's theorem. Your questions or problems lead to reactions and synthesize solutions. Problem, reaction, solution -- the Hegelian dialectic.
@@hyperduality2838 Are the W Bosons real particles, or are they really the process of twisted tube breakage and rearrangement of Beta decay? If you break a twisted rubber band, it breaks into two separate pieces and unwinds at least partially.
@@SpotterVideo Tension, stress or energy = Duality! To create tension or stress in a rubber band requires you to pull on the two dual ends of the rubber band, that is tension, stress or energy requires two perspectives, left hand is dual to right hand, In Einstein's theory of General relativity energy is stress or tension = Duality! Action (thesis) is dual to reaction (anti-thesis) -- Sir Isaac Newton or the duality of force. Attraction (sympathy) is dual to repulsion (antipathy), stretch is dual to squeeze, push is dual to pull. All forces are dual. If forces are dual then energy must be dual:- Energy = force * distance -- simple physics. Energy is duality, duality is energy. Potential energy is dual to kinetic energy -- gravitational energy is dual. Apples fall to the ground because they are conserving duality. Gravitation is equivalent or dual (isomorphic) to acceleration -- Einstein's happiest thought, the principle of equivalence or duality. Waves are dual to particles -- quantum duality. Electro magnetic energy or photons are dual -- pure energy! Everything in physics is made from energy hence duality! Enantiodromia is the unconscious opposite or opposame (duality) -- Carl Jung. There are patterns of duality hardwired into physics, mathematics and philosophy! Yoda is correct -- "Always two there".
@@SpotterVideo Duality is a symmetry and it is being conserved according to Noether's theorem. The principle of equivalence (Einstein) or isomorphism requires two dual perspectives! Injective is dual to surjective synthesizes bijection or isomorphism (duality) -- Group theory! Domains are dual to codomains -- Groups. Subgroups are dual to subfields -- the Galois correspondence. The word co means mutual and implies duality. Sine is dual to cosine or dual sine. Sinh is dual to Cosh -- hyperbolic functions. Vectors are dual to co vectors (forms). Syntax is dual to semantics -- languages, communication. If mathematics is a language then it is dual. Covariant is dual to contravariant -- derivatives. In a communication system messages are predicted into existence according to Shannon's information theorem and this is a syntropic process -- teleological. Sender is dual to receiver. Syntropy (prediction) is dual to increasing entropy -- the 4th law of thermodynamics! Teleological physics (syntropy) is dual to non teleological physics (entropy). "We predict ourselves into existence" -- Anil Seth, neuroscientist, watch at 56 minutes:- th-cam.com/video/qXcH26M7PQM/w-d-xo.html "The brain is a prediction machine" -- Karl Friston, neuroscientist. As an observer you are predicting reality into existence -- and this is a syntropic process! Hence there is a 4th law of thermodynamics. Duality creates reality -- thesis is dual to anti-thesis synthesizes reality or the Hegelian dialectic.
@@SpotterVideo Bosons like to be in the same state -- photons in a laser beam. Fermions like to be in different states. Same is dual to different. Inclusion is dual to exclusion -- the Pauli exclusion principle is dual. Certainty (predictability, syntropy) is dual to uncertainty (unpredictability, entropy) -- the Heisenberg, certainty/uncertainty principle. Duality is two equivalent descriptions of the same thing -- Leonard Susskind, physicist.
How do we know there are no right handed nuetrionos, and instead just havent been detectable due to only interacting via gravity, which is too weak to use for detections? I don't think they're dark matter though.
You have it right. We don't know there aren't right-handed neutrinos but have no idea how to detect them. Since they haven't been observed yet, they're not ruled out at all; they're just not part of the Standard Model right now. They could explain how neutrinos have mass, but they're not the only possible explanation so they haven't been added like the Higgs and Z were.
The W+ Boson is dual to the W- Boson. Symmetric wave functions (Bosons, waves) are dual to anti-symmetric wave functions (Fermions, particles) -- the spin statistics theorem or quantum duality. Bosons are dual to Fermions -- atomic duality. Symmetry is dual to anti-symmetry -- symmetry breaking is dual. "Always two there are" -- Yoda. Energy is dual to mass -- Einstein. Mass, Fermions and particles are anti-symmetric and pure energy, Bosons and waves are symmetric -- symmetry breaking is dual. The Higgs Boson is dual to the Higgs Fermion -- Duality! The vacuum state is dual to the zero particle state synthesizes mass -- the Hegelian dialectic! Thesis is dual to anti-thesis creates the converging or syntropic thesis, synthesis (mass) -- the time independent Hegelian dialectic. Mass is dual and therefore energy is dual. Duality within duality. Duality (energy) is being conserved -- the 5th law of thermodynamics! Symmetry (duality) is dual to conservation -- the duality of Noether's theorem.
Hey 🖖 you have a degree in quantum stuff or? Just asking. I have something of that yeah but just MSc. 😟😔 I believe these are understandable when you have some studies. I don't think most ppl (no offense intended, but a medic, a quantum physics one, an architect etc are specialists in their areas, and no one is going to know the work of the others) anyway. Ok. Now. You are in the spinors, the generators for that stuff. Cool, but that's not a very easy liiitttle thing for architects or chefs 🙂. Now, 4 vectors, the Gauges f that almost appear themselves in the model, then it's Dirac and Yukawa terms the ones that are interesting. So, symmetry here is EASIER with the full lie groups, which you just mentioned, Special Unitary Group (2) thank you. Ok now we are with U(1)🙃 Perfect, now put a cross product there. Nice... Hypercharge always sounded pompous to me. The isos probably got some ppl confused with the spin, the intrinsic one. Ok there's the most important thing. These are degrees of freedom, ok 👌 There comes it, a Gauge Boson... Yeah, there appeared the H boson. Ok I'm satisfied. You got the space U(1)xSU(2). Listo, Fuerza electrodébil 🖖👌
‘I like your funny words, magic man’
Welcome back, been a minute. It’s depressing how much of this material is still out of reach for me, but it’s exciting how much of it I can follow. As always, it’s great that people like you give of themselves so people like me can try to learn. Thanks!!
i feel the same, i suddenly developed a big intuition for the quantum world and started getting deeper into the details theres tons more i need but im so happy with what i can follow and so glad that some people dont dumb it down too much which stimulates gradual improvement for me personally
You helped me in the past when i was graduating in physics, luckily learning/revisiting doesnt stop there
That makes me really happy to hear! Never stop learning!
it is absolutely wild to me that people worked this out in advance of the discoveries of the Z and Higgs bosons. humans are incredible when they put their mind to things like this instead of blowing each other up/screwing each other over for money/etc
The W+ Boson is dual to the W- Boson.
Symmetric wave functions (Bosons, waves) are dual to anti-symmetric wave functions (Fermions, particles) -- the spin statistics theorem or quantum duality.
Bosons are dual to Fermions -- atomic duality.
Symmetry is dual to anti-symmetry -- symmetry breaking is dual.
"Always two there are" -- Yoda.
Energy is dual to mass -- Einstein.
Mass, Fermions and particles are anti-symmetric and pure energy, Bosons and waves are symmetric -- symmetry breaking is dual.
The Higgs Boson is dual to the Higgs Fermion -- Duality!
The vacuum state is dual to the zero particle state synthesizes mass -- the Hegelian dialectic!
Thesis is dual to anti-thesis creates the converging or syntropic thesis, synthesis (mass) -- the time independent Hegelian dialectic.
Mass is dual and therefore energy is dual.
Duality within duality.
Duality (energy) is being conserved -- the 5th law of thermodynamics!
Symmetry (duality) is dual to conservation -- the duality of Noether's theorem.
Even with it being a very technical topic, the general points come across. It's great video.
Thank you! I really appreciate it!!
Thank God, another one
Thanks for being patient! Hopefully I will be able to get some more content out soon!
@@zapphysics The W+ Boson is dual to the W- Boson.
Symmetric wave functions (Bosons, waves) are dual to anti-symmetric wave functions (Fermions, particles) -- the spin statistics theorem or quantum duality.
Bosons are dual to Fermions -- atomic duality.
Symmetry is dual to anti-symmetry -- symmetry breaking is dual.
"Always two there are" -- Yoda.
Energy is dual to mass -- Einstein.
Mass, Fermions and particles are anti-symmetric and pure energy, Bosons and waves are symmetric -- symmetry breaking is dual.
The Higgs Boson is dual to the Higgs Fermion -- Duality!
The vacuum state is dual to the zero particle state synthesizes mass -- the Hegelian dialectic!
Thesis is dual to anti-thesis creates the converging or syntropic thesis, synthesis (mass) -- the time independent Hegelian dialectic.
Mass is dual and therefore energy is dual.
Duality within duality.
Duality (energy) is being conserved -- the 5th law of thermodynamics!
Symmetry (duality) is dual to conservation -- the duality of Noether's theorem.
legend is backkkk
THEYRE BACKKKK
Whoohoo welcome back!
This video was a mouthful...
I'll watch this again because I didn't grasp how a doublet of two neutral particles can be charged.
You say that we only ever observe one kind of neutrino. But how do we measure the handedness of neutrinos without assuming that the weak interaction cares about chirality in the first place?
Is the charge fixing the required masses an example of a measured parameter predicting a free one that we wouldn't otherwise have a value for?
This also seems to suggest a deep relationship between mass and charge. Is this the reason we see no massless particles with electric charge?
This also further looks like it is really necessary to stop thinking of charge in a classical electromagnetic field way and start thinking "interacts with photons".
I also have an unrelated question which I haven't been able to find an answer to. Feel free to ignore it, since it is off topic.
I learned recently that the raising operator has _no_ eigenstates and I am baffled by this. A linear operator in an n dimensional, complex vector space should have n eigenvectors _and_ n eigen-covectors. Instead the lowering operator has the eigenvectors and the raising operator has the eigen-covectors. I don't understand how this can be the case and how to identify which vectors go with which operator.
Is this a property of infinite dimensional vector spaces, Hilbert spaces, or is it a "lie" and the raising operator just has no eigenvectors that we care about?
Hey Narf! Fantastic questions as always! I think that the first thing that I want to say is that there seems to be a misunderstanding (I don't think the point was super clear in the video, so I don't blame you...). When I talk about the charges and the Higgs couplings, it isn't so much that the charges determine the mass after symmetry breaking, it is just that the charges of the fermions and Higgs doublet allow us to write down fermion-Higgs couplings at all without breaking the symmetries of the theory. So, it really means that the three fields that I couple together in these interactions (one left-handed fermion, one right-handed fermion, and the Higgs doublet) transform in such a way that this interaction doesn't change under the standard model gauge transformations. The masses of the fermions themselves are determined by the *strength* of this interaction, which is completely independent of the charges under the standard model gauge group. These coupling strengths are free parameters of the theory that have to be determined experimentally (this shouldn't be surprising, though, since they are in one-to-one correspondence to the fermion masses, and we already knew that these are free parameters).
I don't think that there is really any deep reasoning that there are no massless charged particles. Actually, as far as we know, the only massless particles that really exist are the gauge bosons. What this probably just means is that any matter particles (non-gauge fields) probably talk to a scalar that obtains a non-zero vev at some point in our universe's history, whether or not that is the standard model Higgs doublet.
The best way to really think about the doublets is that they are their own particle and the two elements are analogous to the three color elements of the quark fields. We typically think of the quarks as single fields, but really, they are triplets with three elements, each corresponding to a different color. The doublets are the exact same: the elements now just correspond to different weak isospins. It just happens that when the symmetry is broken, these doublets are broken up (because the elements are no longer related by a symmetry), and the net result is that they can be combined with right-handed singlets to form Dirac fermions.
I think that it goes even a bit further than just saying that charge is "interactions with photons." Charge is really a statement about the representation of the fields which transform under the standard model gauge group. So really, charge is deeply rooted in group theory more than anything.
Okay, the point about the neutrinos. So the nice thing about neutrinos being (almost) massless is that it means that their chirality, or "handedness" is actually directly tied to their spin. In fact, for massless particles, it turns out that chirality is the same thing as what is known as "helicity," which just refers to the value of the spin along the direction of the particle's propagation (an interesting question for you to ponder if you don't know the answer already: why is this only the case for massless particles?). This is very nice because spin is just a form of angular momentum. So, if you work out the momentum conservation of the decay products in weak decays, you can figure out the direction of propagation of the neutrino. Then, if you know the angular momentum of the initial state and the angular momentum of the final state minus the neutrino (since you definitely aren't going to measure the neutrino directly), you can work out the angular momentum of the neutrino, and therefore its spin. So, in some sense, we can indirectly measure the spin, and therefore, the chirality of the neutrino, at least, to an extremely good approximation. Since they are technically massive, it isn't going to be 100% perfect, but the corrections are going to be so tiny that they have never been measured.
Now, onto your unrelated question. I don't know for sure, but I have a hunch that your statement that a linear operator should have n eigenvectors and n eigen-covectors only applies to *hermitian* operators. Since the creation and annihilation operators are not hermitian, I am not surprised that they have some weird behavior that might not align with what you are used to if you only really deal with hermitian operators, which is obviously the case if you are studying QM. Intuitively, this sort of makes sense that each the creation and annihilation operators only define "half" of the space. If I have an arbitrary state, I won't be able to reach any other arbitrary state with just operations involving the annihilation operator. As an easy example, say I start with the |2> state. Then, I will never be able to access the |3> state with just annihilation operators, I need a creation operator for that. So it sort of makes sense that I can really only define the "full" eigenspace if I have both creation and annihilation operators. But that is sort of a guess, I don't think I have a super exact answer for you, unfortunately.
@@zapphysics As always, thank you for your thoughtful answer!
I think that is basically how I understood the first point, though I suppose I misunderstood the link between charge and mass vs coupling strength and mass.
But you said gauge bosons are, in general, going to self interact. Yet the photon doesn't and is the only massless electroweak boson left. Is that really a coincidence in the standard model?
For the QCD triplets the components all carry the charge of the interaction in some way and the resulting triplet is a linear combination.
But the doublet components are _both_ electrically neutral yet the linear combination is charged. That seems odd to me.
The fields which transform under that gauge group (U(1)?) are going to be the ones that interact with the bosons of the gauge field, aren't they? So that sounds like the same statement from a different perspective.
Thanks, the neutrino point makes sense. So to find a measurable correction we'd have to find ourselves some very slow neutrinos?
We can transform the helicity to be the oposite by just moving faster than that particle, this is not possible for massless particles because they move at c.
I don't think that's correct about Hermitian operators. If I have the Eigenvalues I'm pretty sure I can always solve the eigenvalue equation on either side. For hermitian operators the solutions are just going to be each other's conjugates. For non-hermitian operators they can be unrelated, I think.
I'm fairly certain this has to be a result of taking the dimensionality to infinity. I just don't see what that actually changes.
Thanks for your input, though. I'll keep looking :)
@@narfwhals7843 If you have a matrix which isn't diagonalizable, such as [[1,1],[0,1]] , the span of its eigenvectors will not be the whole space. However, for any linear operator on a finite dimensional vector space over the complex numbers (or over any algebraically close field, iirc), it *will* have at least one eigenvector.
So, if the raising operator is a (bounded) linear operator on a (complex) Hilbert space, and if it can indeed have no eigenvectors, then yes I would attribute this to the Hilbert space being infinite-dimensional. Let me think if I can come up with an example.
Let the Hilbert space be \ell^2(\bn) , i.e. the space of functions from natural numbers to complex numbers such that the sum of the squares of the absolute values of the terms, is finite.
consider the operator S which sends f to S(f) where (S(f))(n+1) = f(n) and (S(f))(0)=0 .
(so, it would send (a_0, a_1, a_2, ... ) to (0, a_0, a_1, a_2, ...) )
Then, if S(f) = \lambda f , then,
that would mean that \lambda (a_0, a_1, a_2, ...) = (0, a_0, a_1, a_2, ...)
and so a_0 = \lambda a_1 , a_1 = \lambda a_2, etc. , but also 0 = \lambda a_0 ,
and, yeah, that would imply that either \lambda = 0, but the only eigenfunction with an eigenvalue of 0 would be the zero vector, (0, 0, 0, ... ) , which we generally don't uh, count, when talking about eigenvectors,
or that a_0 = 0,
but in this case, as a_0 = \lambda a_1 , then, as assuming that \lambda isn't 0, this would imply that a_1 = 0 as well,
and similarly that a_2 = 0, and so the only thing it could be is (0, 0, 0, .. ), which, again, we don't count.
So, this linear operator has no eigenvectors.
But, I said "(bounded) linear operator". Is this operator bounded? Yes. I don't know if the raising operator is bounded. I suspect it isn't, but I don't know the physics to say with confidence.
To see that this operator is bounded, note that the norm of the output (the norm being the \ell^2 norm) is always equal to the norm of the input, as it just shifts the sum of squares of absolute values over by a position by adding a 0 at the start. So, the operator norm is 1, which is finite, and so the operator is bounded.
So, yes, if you are working over a complex vector space, then having linear operators which don't have any eigenvectors happens only when the space is infinite-dimensional.
However, you could maybe uh, like,
[what follows is more speculative]
come up with a sequence of things that are sorta like, "approaching being eigenvectors", maybe?
Like, if you had the sequence (1,r, r^2, r^3, ... , r^n , r^{n+1}, ...) , for some r with |r| > 1 (which isn't actually in the Hilbert space because the \ell^2 norm is infinite), then like,
applying S to that wouldn't quite multiply it by a factor of r, but it would match for all the terms after the first one,
and if you like, truncated it to the first N terms, and then scaled things to normalize the truncated version, then the larger N was, the closer the first term would get to zero, and the smaller the difference between r times the vector and S applied to the vector,
so, in a sense, it is sorta-kinda as if it is an eigenvector of it?
However, I don't have a good definition for a sense in which it is as if it was an eigenvector of it.
Oh, alternatively, uh,
If you took like, the sequence v_N of normalized versions of the truncation at N of the (1,r, r^2, ...) sequence (replacing everything after the Nth entry with 0),
and then for like, any fixed vector u, took the inner product of u with (S(v_N) - \lambda v_N),
then I think the limit of this $\langle u , (S(v_N) - \lambda v_N)
angle$ as N goes to infinity, should be 0?
So, I think that's kind of like this sequence being in a way as if it were approaching an eigenvector with eigenvalue \lambda .
However, uh, I think there's also a similar sense in which it "approaches" the 0 vector...
Though, uh, maybe, if $\langle u , (S(v_N) - \lambda v_N)
angle$ approaches 0 substantially faster than $\langle u , v_N
angle$, then this could still be a reasonable idea? idk.
@@narfwhals7843 So, the point about gauge bosons being able to self-interact in general is a good question. And actually, this is again rooted in group theory. Since the gauge bosons are tied to the transformations which make up the group, it turns out there is actually a very simple rule for determining if your gauge bosons will self-interact or not: if the transformations commute (the group is abelian), then the gauge bosons will not interact with each other. If the transformations do not commute (the group is non-abelian), then the gauge bosons will self-interact. This sort of makes intuitive sense since the transformations "talk" to each other (their ordering matters) in the non-abelian case, but they don't in the abelian case (the ordering doesn't matter). For the photon, the group governing the transformations is U(1), which only has a single possible transformation (rotations in the complex plane) and therefore is abelian. Hope that makes sense.
So I think I am a bit confused about what you mean by both elements of the doublet being electrically neutral. The pairs are (neutrino, charged lepton), (up quark, down quark), and (charged Goldstone, physical Higgs boson + neutral Goldstone) (the last being the Higgs doublet). If you notice, the first component of each doublet is one unit of electric charge greater than the second component. This is because the two components will have the same weak hypercharge, but the first component has weak isospin of +1/2 (analogous to spin up), while the second component has weak isospin of -1/2 (like spin down). After SSB, we get a leftover surviving symmetry of QED, and the charge under QED is determined by charge = weak hypercharge + weak isospin, so the two components of the electroweak doublets should always differ by one unit of electric charge. I'm not sure this answers your question, but I think I am a bit confused as to what the question is.
Sorry I couldn't be of more help with the question about raising/lowering operators and @drdca, thanks for contributing to the conversation! Hopefully their response is a bit more insightful!
@@zapphysics Ah the self interaction makes sense. Thanks!
I was talking about the w+/-, which are charged under QED. being combinations of the w1/2, which are not charged under QED. But as you explain, the QED charge is a combination of weak hypercharge and isospin, which w1/2 do have. So that makes sense after all. I think, I understand.
I don't expect you do know everything:)
But I'm going to give @drdca 's comment a thorough read!
Also I'm extremely glad to see you back. I hope you're doing well!
What a wonderful video, can’t wait for the next ones! Thank you so much for your work
So, before the SSB, did electric charge and the electromagnetic field exist? Which gauge bosons were the physical ones? The W±, Z and photon, or the W1,2,3 and B?
When I said "before SSB", I implicitly brought some cosmology into the discussion, since I was vaguely referring to the idea that some phase transition in the early universe broke electroweak symmetry into the residual electromagnetic U(1) symmetry
The W+ Boson is dual to the W- Boson.
Symmetric wave functions (Bosons, waves) are dual to anti-symmetric wave functions (Fermions, particles) -- the spin statistics theorem or quantum duality.
Bosons are dual to Fermions -- atomic duality.
Symmetry is dual to anti-symmetry -- symmetry breaking is dual.
"Always two there are" -- Yoda.
Energy is dual to mass -- Einstein.
Mass, Fermions and particles are anti-symmetric and pure energy, Bosons and waves are symmetric -- symmetry breaking is dual.
The Higgs Boson is dual to the Higgs Fermion -- Duality!
The vacuum state is dual to the zero particle state synthesizes mass -- the Hegelian dialectic!
Thesis is dual to anti-thesis creates the converging or syntropic thesis, synthesis (mass) -- the time independent Hegelian dialectic.
Mass is dual and therefore energy is dual.
Duality within duality.
Duality (energy) is being conserved -- the 5th law of thermodynamics!
Symmetry (duality) is dual to conservation -- the duality of Noether's theorem.
Superb stuff! Thank you
Spontaneous Symmetry Breaking happens when a particle chooses a position in the Mexican Hat Potential, so does the un-breaked symmetry require a continuous particle that exist along a closed path in this potential. If so is this particle physically realizible?
Real is dual to imaginary -- complex numbers are dual.
The W+ Boson is dual to the W- Boson.
Symmetric wave functions (Bosons, waves) are dual to anti-symmetric wave functions (Fermions, particles) -- the spin statistics theorem or quantum duality.
Bosons are dual to Fermions -- atomic duality.
Symmetry is dual to anti-symmetry -- symmetry breaking is dual.
"Always two there are" -- Yoda.
Energy is dual to mass -- Einstein.
Mass, Fermions and particles are anti-symmetric and pure energy, Bosons and waves are symmetric -- symmetry breaking is dual.
The Higgs Boson is dual to the Higgs Fermion -- Duality!
The vacuum state is dual to the zero particle state synthesizes mass -- the Hegelian dialectic!
Thesis is dual to anti-thesis creates the converging or syntropic thesis, synthesis (mass) -- the time independent Hegelian dialectic.
Mass is dual and therefore energy is dual.
Duality within duality.
Duality (energy) is being conserved -- the 5th law of thermodynamics!
Symmetry (duality) is dual to conservation -- the duality of Noether's theorem.
Hi, I am The Grand Unified Theory!
This electroweak force sounds like superconductivity where the fermions pair up into Cooper pairs. These Cooper pairs act like bosons and exert a force by repelling magnetic fields observed by levitating magnets. I wonder if they are another force carrying boson in the Standard Model.
Cooper pairs = duality!
The W+ Boson is dual to the W- Boson.
Symmetric wave functions (Bosons, waves) are dual to anti-symmetric wave functions (Fermions, particles) -- the spin statistics theorem or quantum duality.
Bosons are dual to Fermions -- atomic duality.
Symmetry is dual to anti-symmetry -- symmetry breaking is dual.
"Always two there are" -- Yoda.
Energy is dual to mass -- Einstein.
Mass, Fermions and particles are anti-symmetric and pure energy, Bosons and waves are symmetric -- symmetry breaking is dual.
The Higgs Boson is dual to the Higgs Fermion -- Duality!
The vacuum state is dual to the zero particle state synthesizes mass -- the Hegelian dialectic!
Thesis is dual to anti-thesis creates the converging or syntropic thesis, synthesis (mass) -- the time independent Hegelian dialectic.
Mass is dual and therefore energy is dual.
Duality within duality.
Duality (energy) is being conserved -- the 5th law of thermodynamics!
Symmetry (duality) is dual to conservation -- the duality of Noether's theorem.
at 11:02? I followed that SU2 doublets are like the color charge in the SU3 qcd interaction. But you completely lost me on my that means we need a new neutrino for each of the charged leptons. The you weren't even talking about the muon can someone help me understand?
Hi, are you also going to do a Beyond the SM series?
This would really help me with the course I am taking right now.
Conservation of Spatial Curvature (both Matter and Energy described as "Quanta" of Spatial Curvature)
Is there an alternative interpretation of "Asymptotic Freedom"? What if Quarks are actually made up of twisted tubes which become physically entangled with two other twisted tubes to produce a proton? Instead of the Strong Force being mediated by the constant exchange of gluons, it would be mediated by the physical entanglement of these twisted tubes. When only two twisted tubules are entangled, a meson is produced which is unstable and rapidly unwinds (decays) into something else. A proton would be analogous to three twisted rubber bands becoming entangled and the "Quarks" would be the places where the tubes are tangled together. The behavior would be the same as rubber balls (representing the Quarks) connected with twisted rubber bands being separated from each other or placed closer together producing the exact same phenomenon as "Asymptotic Freedom" in protons and neutrons. The force would become greater as the balls are separated, but the force would become less if the balls were placed closer together. Therefore, the gluon is a synthetic particle (zero mass, zero charge) invented to explain the Strong Force. An artificial Christmas tree can hold the ornaments in place, but it is not a real tree.
String Theory was not a waste of time, because Geometry is the key to Math and Physics. However, can we describe Standard Model interactions using only one extra spatial dimension?
What if we describe subatomic particles as spatial curvature, instead of trying to describe General Relativity as being mediated by particles? Fixing the Standard Model with more particles is like trying to mend a torn fishing net with small rubber balls, instead of a piece of twisted twine.
Quantum Entangled Twisted Tubules:
“We are all agreed that your theory is crazy. The question which divides us is whether it is crazy enough to have a chance of being correct.” Neils Bohr
(lecture on a theory of elementary particles given by Wolfgang Pauli in New York, c. 1957-8, in Scientific American vol. 199, no. 3, 1958)
The following is meant to be a generalized framework for an extension of Kaluza-Klein Theory. Does it agree with the “Twistor Theory” of Roger Penrose, and the work of Eric Weinstein on “Geometric Unity”? During the early history of mankind, the twisting of fibers was used to produce thread, and this thread was used to produce fabrics. The twist of the thread is locked up within these fabrics. Is matter made up of twisted 3D-4D structures which store spatial curvature that we describe as “particles"? Are the twist cycles the "quanta" of Quantum Mechanics?
When we draw a sine wave on a blackboard, we are representing spatial curvature. Does a photon transfer spatial curvature from one location to another? Wrap a piece of wire around a pencil and it can produce a 3D coil of wire, much like a spring. When viewed from the side it can look like a two-dimensional sine wave. You could coil the wire with either a right-hand twist, or with a left-hand twist. Could Planck's Constant be proportional to the twist cycles. A photon with a higher frequency has more energy. ( E=hf, More spatial curvature as the frequency increases = more Energy ). What if gluons are actually made up of these twisted tubes which become entangled with other tubes to produce quarks. (In the same way twisted electrical extension cords can become entangled.) Therefore, the gluons are a part of the quarks. Quarks cannot exist without gluons, and vice-versa. Mesons are made up of two entangled tubes (Quarks/Gluons), while protons and neutrons would be made up of three entangled tubes. (Quarks/Gluons) The "Color Charge" would be related to the XYZ coordinates (orientation) of entanglement. "Asymptotic Freedom", and "flux tubes" are logically based on this concept. The Dirac “belt trick” also reveals the concept of twist in the ½ spin of subatomic particles. If each twist cycle is proportional to h, we have identified the source of Quantum Mechanics as a consequence twist cycle geometry.
Modern physicists say the Strong Force is mediated by a constant exchange of Mesons. The diagrams produced by some modern physicists actually represent the Strong Force like a spring connecting the two quarks. Asymptotic Freedom acts like real springs. Their drawing is actually more correct than their theory and matches perfectly to what I am saying in this model. You cannot separate the Gluons from the Quarks because they are a part of the same thing. The Quarks are the places where the Gluons are entangled with each other.
Neutrinos would be made up of a twisted torus (like a twisted donut) within this model. The twist in the torus can either be Right-Hand or Left-Hand. Some twisted donuts can be larger than others, which can produce three different types of neutrinos. If a twisted tube winds up on one end and unwinds on the other end as it moves through space, this would help explain the “spin” of normal particles, and perhaps also the “Higgs Field”. However, if the end of the twisted tube joins to the other end of the twisted tube forming a twisted torus (neutrino), would this help explain “Parity Symmetry” violation in Beta Decay? Could the conversion of twist cycles to writhe cycles through the process of supercoiling help explain “neutrino oscillations”? Spatial curvature (mass) would be conserved, but the structure could change.
Gravity is a result of a very small curvature imbalance within atoms. (This is why the force of gravity is so small.) Instead of attempting to explain matter as "particles", this concept attempts to explain matter more in the manner of our current understanding of the space-time curvature of gravity. If an electron has qualities of both a particle and a wave, it cannot be either one. It must be something else. Therefore, a "particle" is actually a structure which stores spatial curvature. Can an electron-positron pair (which are made up of opposite directions of twist) annihilate each other by unwinding into each other producing Gamma Ray photons?
Does an electron travel through space like a threaded nut traveling down a threaded rod, with each twist cycle proportional to Planck’s Constant? Does it wind up on one end, while unwinding on the other end? Is this related to the Higgs field? Does this help explain the strange ½ spin of many subatomic particles? Does the 720 degree rotation of a 1/2 spin particle require at least one extra dimension?
Alpha decay occurs when the two protons and two neutrons (which are bound together by entangled tubes), become un-entangled from the rest of the nucleons
. Beta decay occurs when the tube of a down quark/gluon in a neutron becomes overtwisted and breaks producing a twisted torus (neutrino) and an up quark, and the ejected electron. The production of the torus may help explain the “Symmetry Violation” in Beta Decay, because one end of the broken tube section is connected to the other end of the tube produced, like a snake eating its tail. The phenomenon of Supercoiling involving twist and writhe cycles may reveal how overtwisted quarks can produce these new particles. The conversion of twists into writhes, and vice-versa, is an interesting process, which is also found in DNA molecules. Could the production of multiple writhe cycles help explain the three generations of quarks and neutrinos? If the twist cycles increase, the writhe cycles would also have a tendency to increase.
Gamma photons are produced when a tube unwinds producing electromagnetic waves.
The “Electric Charge” of electrons or positrons would be the result of one twist cycle being displayed at the 3D-4D surface interface of the particle. The physical entanglement of twisted tubes in quarks within protons and neutrons and mesons displays an overall external surface charge of an integer number. Because the neutrinos do not have open tube ends, (They are a twisted torus.) they have no overall electric charge.
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Within this model a black hole could represent a quantum of gravity, because it is one cycle of spatial gravitational curvature. Therefore, instead of a graviton being a subatomic particle it could be considered to be a black hole. The overall gravitational attraction would be caused by a very tiny curvature imbalance within atoms. We know there is an unequal distribution of electrical charge within each atom because the positive charge is concentrated within the nucleus, even though the overall electrical charge of the atom is balanced by equal positive and negative charge.
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In this model Alpha equals the compactification ratio within the twistor cone, which is approximately 1/137.
1= Hypertubule diameter at 4D interface
137= Cone’s larger end diameter at 3D interface where the photons are absorbed or emitted.
The 4D twisted Hypertubule gets longer or shorter as twisting or untwisting occurs. (720 degrees per twist cycle.)
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How many neutrinos are left over from the Big Bang? They have a small mass, but they could be very large in number. Could this help explain Dark Matter?
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Why did Paul Dirac use the twist in a belt to help explain particle spin? Is Dirac’s belt trick related to this model? Is the “Quantum” unit based on twist cycles?
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I started out imagining a subatomic Einstein-Rosen Bridge whose internal surface is twisted with either a Right-Hand twist, or a Left-Hand twist producing a twisted 3D/4D membrane. The model grew out of that simple idea.
I was also trying to imagine a way to stuff the curvature of a 3 D sine wave into subatomic particles.
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You make some interesting points but there is a pattern to your thinking:-
The W+ Boson is dual to the W- Boson.
Symmetric wave functions (Bosons, waves) are dual to anti-symmetric wave functions (Fermions, particles) -- the spin statistics theorem or quantum duality.
Bosons are dual to Fermions -- atomic duality.
Symmetry is dual to anti-symmetry -- symmetry breaking is dual.
"Always two there are" -- Yoda.
Energy is dual to mass -- Einstein.
Mass, Fermions and particles are anti-symmetric and pure energy, Bosons and waves are symmetric -- symmetry breaking is dual.
The Higgs Boson is dual to the Higgs Fermion -- Duality!
The vacuum state is dual to the zero particle state synthesizes mass -- the Hegelian dialectic!
Thesis is dual to anti-thesis creates the converging or syntropic thesis, synthesis (mass) -- the time independent Hegelian dialectic.
Mass is dual and therefore energy is dual.
Duality within duality.
Duality (energy) is being conserved -- the 5th law of thermodynamics!
Symmetry (duality) is dual to conservation -- the duality of Noether's theorem.
Your questions or problems lead to reactions and synthesize solutions.
Problem, reaction, solution -- the Hegelian dialectic.
@@hyperduality2838
Are the W Bosons real particles, or are they really the process of twisted tube breakage and rearrangement of Beta decay? If you break a twisted rubber band, it breaks into two separate pieces and unwinds at least partially.
@@SpotterVideo Tension, stress or energy = Duality!
To create tension or stress in a rubber band requires you to pull on the two dual ends of the rubber band, that is tension, stress or energy requires two perspectives, left hand is dual to right hand,
In Einstein's theory of General relativity energy is stress or tension = Duality!
Action (thesis) is dual to reaction (anti-thesis) -- Sir Isaac Newton or the duality of force.
Attraction (sympathy) is dual to repulsion (antipathy), stretch is dual to squeeze, push is dual to pull.
All forces are dual.
If forces are dual then energy must be dual:-
Energy = force * distance -- simple physics.
Energy is duality, duality is energy.
Potential energy is dual to kinetic energy -- gravitational energy is dual.
Apples fall to the ground because they are conserving duality.
Gravitation is equivalent or dual (isomorphic) to acceleration -- Einstein's happiest thought, the principle of equivalence or duality.
Waves are dual to particles -- quantum duality.
Electro magnetic energy or photons are dual -- pure energy!
Everything in physics is made from energy hence duality!
Enantiodromia is the unconscious opposite or opposame (duality) -- Carl Jung.
There are patterns of duality hardwired into physics, mathematics and philosophy!
Yoda is correct -- "Always two there".
@@SpotterVideo Duality is a symmetry and it is being conserved according to Noether's theorem.
The principle of equivalence (Einstein) or isomorphism requires two dual perspectives!
Injective is dual to surjective synthesizes bijection or isomorphism (duality) -- Group theory!
Domains are dual to codomains -- Groups.
Subgroups are dual to subfields -- the Galois correspondence.
The word co means mutual and implies duality.
Sine is dual to cosine or dual sine.
Sinh is dual to Cosh -- hyperbolic functions.
Vectors are dual to co vectors (forms).
Syntax is dual to semantics -- languages, communication.
If mathematics is a language then it is dual.
Covariant is dual to contravariant -- derivatives.
In a communication system messages are predicted into existence according to Shannon's information theorem and this is a syntropic process -- teleological.
Sender is dual to receiver.
Syntropy (prediction) is dual to increasing entropy -- the 4th law of thermodynamics!
Teleological physics (syntropy) is dual to non teleological physics (entropy).
"We predict ourselves into existence" -- Anil Seth, neuroscientist, watch at 56 minutes:-
th-cam.com/video/qXcH26M7PQM/w-d-xo.html
"The brain is a prediction machine" -- Karl Friston, neuroscientist.
As an observer you are predicting reality into existence -- and this is a syntropic process!
Hence there is a 4th law of thermodynamics.
Duality creates reality -- thesis is dual to anti-thesis synthesizes reality or the Hegelian dialectic.
@@SpotterVideo Bosons like to be in the same state -- photons in a laser beam.
Fermions like to be in different states.
Same is dual to different.
Inclusion is dual to exclusion -- the Pauli exclusion principle is dual.
Certainty (predictability, syntropy) is dual to uncertainty (unpredictability, entropy) -- the Heisenberg, certainty/uncertainty principle.
Duality is two equivalent descriptions of the same thing -- Leonard Susskind, physicist.
Love listening
I love your videos! Thank you for being awesome!
How do we know there are no right handed nuetrionos, and instead just havent been detectable due to only interacting via gravity, which is too weak to use for detections? I don't think they're dark matter though.
You have it right. We don't know there aren't right-handed neutrinos but have no idea how to detect them. Since they haven't been observed yet, they're not ruled out at all; they're just not part of the Standard Model right now. They could explain how neutrinos have mass, but they're not the only possible explanation so they haven't been added like the Higgs and Z were.
Amazing Video
What would an SU(4) theory look like?
where did this guy go? ):
The W+ Boson is dual to the W- Boson.
Symmetric wave functions (Bosons, waves) are dual to anti-symmetric wave functions (Fermions, particles) -- the spin statistics theorem or quantum duality.
Bosons are dual to Fermions -- atomic duality.
Symmetry is dual to anti-symmetry -- symmetry breaking is dual.
"Always two there are" -- Yoda.
Energy is dual to mass -- Einstein.
Mass, Fermions and particles are anti-symmetric and pure energy, Bosons and waves are symmetric -- symmetry breaking is dual.
The Higgs Boson is dual to the Higgs Fermion -- Duality!
The vacuum state is dual to the zero particle state synthesizes mass -- the Hegelian dialectic!
Thesis is dual to anti-thesis creates the converging or syntropic thesis, synthesis (mass) -- the time independent Hegelian dialectic.
Mass is dual and therefore energy is dual.
Duality within duality.
Duality (energy) is being conserved -- the 5th law of thermodynamics!
Symmetry (duality) is dual to conservation -- the duality of Noether's theorem.
Wait... but neutrinos aren't massless...
Geezzzz 😵💫
cool
Hey 🖖 you have a degree in quantum stuff or? Just asking. I have something of that yeah but just MSc. 😟😔
I believe these are understandable when you have some studies.
I don't think most ppl (no offense intended, but a medic, a quantum physics one, an architect etc are specialists in their areas, and no one is going to know the work of the others) anyway.
Ok. Now. You are in the spinors, the generators for that stuff. Cool, but that's not a very easy liiitttle thing for architects or chefs 🙂.
Now, 4 vectors, the Gauges f that almost appear themselves in the model, then it's Dirac and Yukawa terms the ones that are interesting. So, symmetry here is EASIER with the full lie groups, which you just mentioned, Special Unitary Group (2) thank you.
Ok now we are with U(1)🙃
Perfect, now put a cross product there. Nice...
Hypercharge always sounded pompous to me. The isos probably got some ppl confused with the spin, the intrinsic one.
Ok there's the most important thing. These are degrees of freedom, ok 👌
There comes it, a Gauge Boson... Yeah, there appeared the H boson.
Ok I'm satisfied. You got the space U(1)xSU(2).
Listo, Fuerza electrodébil 🖖👌
@5:50 "... famously Wu did not receive a Nobel Prize..." 🤮 Hooray for the Swedish nobs. It should be at least "infamously".