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@86congtymienbac80 2 күн бұрын
There is an idea of considering space as a network of nodes without having to count how many D's there are.
@gcarcassi 2 күн бұрын
One can have whatever crazy idea... physics is about what you can experimentally observer.
@kafiruddinmulhiddeen2386 7 күн бұрын
I’ve been searching for this argument. Thank you Professor.
@frankdimeglio8216 7 күн бұрын
Two AND three dimensional SPACE are BALANCED in accordance WITH WHAT IS the fourth dimension/TIME. By Frank Martin DiMeglio
@frankdimeglio8216 7 күн бұрын
WHAT IS GRAVITY IS, ON BALANCE, an INTERACTION that cannot be shielded or blocked. WHAT IS E=MC2 IS dimensionally consistent, AS TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE; AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE) !!! BALANCE AND completeness go hand in hand. GREAT !!! WHAT IS GRAVITY IS, ON BALANCE, an INTERACTION that cannot be shielded or blocked. (WHAT IS E=MC2 IS dimensionally consistent.) Consider what is the man (AND THE EYE ON BALANCE) who IS standing on WHAT IS THE EARTH/ground, AS touch AND feeling BLEND; AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE); AS TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE !!! BALANCE AND completeness go hand in hand. WHAT IS GRAVITY IS, ON BALANCE, an INTERACTION that cannot be shielded or blocked. WHAT IS E=MC2 IS dimensionally consistent, AS “mass"/ENERGY involves BALANCED inertia/INERTIAL RESISTANCE consistent WITH/AS what is BALANCED electromagnetic/gravitational force/ENERGY; AS TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE; AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE); AS gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE (ON BALANCE). INDEED, GRAVITATIONAL force/ENERGY IS proportional to (or BALANCED with/as) inertia/INERTIAL RESISTANCE; AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE); AS TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE !!! The stars AND PLANETS are POINTS in the night sky. WHAT IS E=MC2 IS dimensionally consistent !!! Accordingly, ON BALANCE, THE PLANETS (including what is THE EARTH) sweep out equal areas in equal times. Consider TIME (AND time dilation) ON BALANCE. WHAT IS E=MC2 is taken directly from F=ma, AS TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE; AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE). WHAT IS GRAVITY IS, ON BALANCE, an INTERACTION that cannot be shielded or blocked. WHAT IS E=MC2 IS dimensionally consistent !!! CLEARLY, gravity AND ELECTROMAGNETISM/energy are linked AND BALANCED opposites (ON BALANCE); as the stars AND PLANETS are POINTS in the night sky. Consider TIME (AND time dilation) ON BALANCE. INDEED, TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE; AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE) !!! GREAT !!! ACCORDINGLY, ON BALANCE, the rotation of WHAT IS THE MOON matches the revolution. GREAT !!! WHAT IS E=MC2 IS dimensionally consistent. GREAT !!! It is a very great truth that the SELF represents, FORMS, and experiences a COMPREHENSIVE approximation of experience in general by combining conscious and unconscious experience. INDEED, the INTEGRATED EXTENSIVENESS of THOUGHT AND description is improved in the truly superior mind. BALANCE AND completeness go hand in hand. By Frank Martin DiMeglio
@jnrose2 9 күн бұрын
“ Zero Entropy”…. Do you assign the conventional definition state ‘absolute zero temperature’? Which is NO MOTION. (!). And at that condition…. no “Time” either. No ‘change of state’ is possible. Is this what you mean. ?????? jnrose2
@gcarcassi 9 күн бұрын
On a continuum, zero entropy does not mean "no motion." This is the whole point. You should think of zero entropy more as the level of the noise, which is always present on continuous variables. Zero entropy is the entropy of the vacuum (i.e. empty state, no particles). It is not a convention, it has to be zero or the entropy is not additive for independent systems.
@jnrose2 10 күн бұрын
@gcarcassi. -- I have paused your video at about 08:00 to ask: Can you please convert your new interpretation of Entropy states to reference: the original Carnot/Claussian concern: “the ability to do work”? I have evaluated a problem needing review there too: If the spatial localization is very small and well defined … that is: ‘location is maximally known’ … this a state of HIGH ORDER. -- -BUT- … if we look at the conditions of the Big Bang … the universe started with huge high temperature and (maximal chaotic DISORDER). That is, -also- a condition of ‘inability to do work’ (by ‘formal definition’ … a state of Max Entropy). So, how would you graph this information? 1)BOTH entropy states are present at the Big Bang: Spatial maximum order ; Energy maximum disorder. [TWO ‘Entroepies’ streams, not ‘one’; (separate graphs needed)]. ••••. I have proposed for decades an alternative “Information entropy” different from Shannon. Observer KNOWING … where systems entities are, (from one time~position arrangement to another) provides a separate information about ‘closer or further’ from ‘next interaction location(s) possible. That is: improved or diminished ‘ability to: interact, transfer energies, (which enacts a ‘communication’ via such interaction(s)). Which “communication” … is a “work event”. NOW, explicitly defined … instead of a vague loose ideas of “usefulness”. This is now an improved GENERAL ENTROEPY… not locked to thermodynamics!!! The upshot is: Distributing information ‘entroepically’ [note adjusted spelling] improves the ability to INFLUENCE more ‘next encounter locations’. Improved Order potential (negentroepy) happens … in opposition to energy ‘dissipation by distribution’. ••••••. The entire topic of “entropy” requires dissecting, dismantling, and rebuilding. This now makes energy entropy and information entropy. .. one GENERAL ENTROEPY. Your thoughts, please. @jnrose2. James. [[email protected]]
@mpcformation9646 13 күн бұрын
You build on a dramatic confusion as Poincaré details it in his 1902 best seller « La science et l’hypothèse ». Is « space » an observable ? No more than « time »! So what are you talking about? What you are playing with is not « space » nor « time », it’s not « reality », but a mathematical theory that you which to « model », not even « reality », but only phenomenology, where there’s nor « space » nor « time », but interacting « objects », interacting with »somethings ». Thus in this mathematical world, you have many choices, many possibilities, many models. Several can be « true ». And the most true one may be to complicate. Which leads to chose more accessible ones.
@gcarcassi 12 күн бұрын
Right, physical theories are just idealized models of some experimentally accessible objects. Where is the confusion?
@mpcformation9646 12 күн бұрын
@@gcarcassiThe confusion is that you start pretending physical « space » is 3D, while talking in fact of mathematical models. You didn’t even define «physical space » as if it was obvious. It’s not! And even less « his » number of « dimensions ». You’re talking of a ghost and pretend that mathematical dressings of its effigy is his dressing. What kind of Vaudou is that? You’re making a hell of philosophical mess here. Whereas serious science cannot avoid building on coherent rigorous philosophical ground. And nothing is farther than the truth if you even furthermore pretend that science can avoid philosophy. That also is false. And indeed « space » and « time » are before all concepts. Even if they did « existed out there », one has to have a mind to think of them, conceptualize, study, analyse them, and try to capture some of their phenomenological characteristics with some mathematical representations. They are NOT as Kant recalls it, à priori given, self obvious and directly accessible to consciousness. Thus they have to be philosophically thought. And that’s tricky! But worse, « space » and « time » are not physical observables. They are not. The ONLY thing that we have is emission and absorption spectra. That’s the only thing we actually know about « the something out there not being nothing »! The rest is myths and more or less grounded, coherent, falsifiable, accurate mathematical theories about these spectra. But pretending à priori that « space » exist and has 3D is groundless. It’s even blind since we already observe that whatever it could actually be if it does, it’s at best a sort of weird chaotic and unpredictable « sea of madness », a strange ghost or God, swallowing or creating phenomenons and exotic « particles ». Thus, it’s at best weird and « monstrous ». And actually who knows? Consequently it’s a philosophical mistake to start pretending it exist and worse pretend knowing its number of dimension, before even knowing anything precise about it. In fact anything at all to be honest. So you’re just playing with mathematical models and making a dramatic confusion between arbitrary ideas of ghostlike « physical space », actual bias of physiological atavism full of illusions, and abstract conventional mathematical models. A big mess. The only hope that can be worked on is what Alain Connes is trying to : to retro engineer these spectra to try to deduce some constraints on theoretical models of abstract mathematical spaces. A sort of tomography ! But it’s extremely tricky and difficult. It implies non commutative world at full guided by Von Newman-Connes classification . Hence a vastly yet unknown terra incognita.
@gcarcassi 12 күн бұрын
@@mpcformation9646 Well, I presented this arguments to philosophers of science multiple times. I am somewhat active in that community. 🤣🤣🤣 I routinely discuss ideas with them.
@mpcformation9646 11 күн бұрын
@ Totally empty of scientific arguments, your « answer » is called a « side kick » and an obvious « diversion ». But is factually « stone walling », where you precisely avoid answering nor even address the problem. Not even acknowledge that one has been actually raised. That says a lot. And what is the content of your « side kick » and « diversion »? Vaguely pretending to be in contact with « philosophers of science ». That doesn’t tells much except suggesting an attempt to hide behind a « magical fog » of so call « authoritarian argument » : « I’m legitimate because I’m in contact with legitimate fantoms ». Do you realize the weakness of your logic full of little « power game »? Since first of all, so called « philosopher of science » doesn’t mean much nor guaranty anything. It’s an abstract statement full of air. And a zero guaranty to be well advised. Especially in hard and tricky problems. The Nei Jing Su Wen canon of Chinese Taoist medecine exposes the systematic wrong belief of one of the greatest power, mind and philosopher of his time : the yellow emperor, talking with a true Taoist master. And the same in the Hindou Bhagavad Gita, where a high ranking prince, extremely well educated and knowledgeable, nevertheless gradually surrenders his illusory beliefs, fact checked by the Lord Krishna. These two emblematic exemples among many others, emphasizes the say : « Lots of pretendants. Few elected ones! » In other words having even an academic diploma of « philosophy of science », makes you at best a cultivated historian of science, but very doubtfully a Philosopher. Since Philosophy is little about knowledge, but massively about thinking deeply and correctly. Which is hugely tricky. Rare are the « Socrates », the Kant, the Poincaré… So except the fog behind which you obviously hide, you still didn’t answer anything about my strong objection. In particular : is so called « physical space » itself observable? Is so called « time » itself observable? No! There is no such observations. The only thing we have, the only thing, are emissions and absorption spectra. That’s all. And that is NOT any observation of « space » nor « time ». It’s just a bar code. All the rest is speculations. Not actual observations. And worse for your claim of 3D of chimeric « physical space ». In conclusion, stone walling is a really bad attitude in Science. It’s it antithesis !
@86congtymienbac80 6 күн бұрын
@mpcformation9646 What you say means nothing
@ZorroNumber1 14 күн бұрын
Great job from one physicist to another
@gcarcassi 13 күн бұрын
Thanks!
@carly09et 14 күн бұрын
Slightly more than three dimensions [x,y,z]^(T) as S But only S^2 + (dS)^2 is measurable!
@Zamicol 16 күн бұрын
This is absurd. 🤣
@batmanrobin6711 16 күн бұрын
I also feel that the concept of energy is not very well defined in physics. Sometimes physicists talk about pure energy, sometimes some of them say that we always talk about the energy of something else, the energy of a particle, a field... and there is no such thing as pure energy wandering around. As for the definition they give in highschool regarding work and so on it seems to be circular and not very useful. But you didn't mention energy in this video. Do you think physicists really know what they are talking about when they talk about energy? I have found Ricardo Lopes Coelho's book "What Is Energy?" very useful in this regard.
@gcarcassi 16 күн бұрын
Which energy? 😂 In mechanics, we have the Hamiltonian. In thermodynamics we have internal energy. The two are related... but cannot be the same. The internal energy in thermodynamics must have an absolute zero because it is additive. Therefore a system with zero particles must have a zero entropy. For the Hamiltonian, the zero is relative... So if by "really know" means being aware of these problems and having a solution... then I'd say most physicists do not really know. 😊 There is a general sense that there is a quantity that is conserved for closed system, for whatever reason, and it is a useful tool. I think that's about it. To be fair, you will always have primitives. So, taking "there is this universal quantity, energy, and it is always conserved by closed systems" as your primitive is not so bad... there are worse primitives. 😊
@batmanrobin6711 16 күн бұрын
@@gcarcassi Thank you!
@batmanrobin6711 18 күн бұрын
Beautiful introduction to your book! I kind of went through the same questionning that you mentioned during your high school years and this is what I have settled on: bohmian mechanics is the way to go when it comes to QM. Fields in QFT are mere mathematical constructs enabling us to make sound predictions but particules, not fields, are the fundamental building blocks of matter. When it comes to GR I have settled on Barbour's shape dynamics in which time and space do not really exist but merely emerge from the changes happening to matter. I also really love causal set theory (Helen Dowker) because it sees spacetime as discrete (ie matter and change are discrete since spacetime is a mere mental construct->only matter and the change it goes through are real). And when it comes to mathematics I have settled on strict finitism: mainstream mathematics and cantor set theory in which infinities are deemed to exist are merely a useful approximation to enable us to make some "physics" but the road to real truth is through strict finitism, mathematics without any kind of infinities. And for this I really like this book: "Strict Finitism and the Logic of Mathematical Applications" by Feng Ye (www.amazon.fr/Strict-Finitism-Logic-Mathematical-Applications/dp/9400736312) in which the author is able to derive all the maths needed for modern physics (hilbert spaces and manifolds) without any kind of infinities. As for quantum logic I have settled on a paper by Pr Gabriele Carcassi (i think you know him!) who manages to save classical logic! I also believe in non locality and that Bell really showed that the law of physics should be non local (in line with bohmian mechanics)! Am I crazy? Is this crackpot physics? Are your personal inclinations far from the above? (I do believe you might agree with me on quantum logic lol)
@gcarcassi 17 күн бұрын
I don't think finitism works in physics. The issue is that physics relies on experimental reproducibility, which implies you can test things "one more time". This means that a physical law is a relationship between infinite instances of preparations and measurements (i.e. ensembles). There are some ideas from constructivism/finitism/intuitionism that are carry over, because we can only gather finite information in finite time, but it's not as deep as the mathematicians push it.
@jperez7893 18 күн бұрын
i hope someone can transform all of this notation into geometric algebra notation. i find that GA notation is so much easier to follow and more intuitive. i was shocked how i could follow and understand lectures of astrophysics and quantum mechanics presented in GA. i will still try to follow the hamiltonian lecture but it will take a while. amazing presentation. i loved his interview with curt jaimungal.
@gcarcassi 18 күн бұрын
You'd need to find a way to express information theory, statistics (e.g. covariant matrix) and parts of measure theory in geometric algebra... which I don't think you can. Plus, some of the considerations are pre-geometric, so you are going to have a hard time to express those. There is no silver bullet... Every notation makes some things easier and other things harder.
@jperez7893 18 күн бұрын
@@gcarcassi thanks for pointing that out. i agree, there is no magic bullet indeed for the pre-geometric stuff. i was listening to a david hestenes lecture on modeling the electron, and he mentioned that all electrons are all singularities in the vacuum and all elementary particles are topological defects in the vacuum according to his calculations and interpretation. i wonder what consequence this gives. does his line of research or interpretation on the math of fundamental particles have any consequences on how dark matter or dark energy might be interpreted?
@advaitrahasya 19 күн бұрын
Quite the mathematical exploration. And nicely correspondent to the 3D reality we experience. Hopefully a good escape from extra dimensions, and treating Time as a dimension, and may it eventually lead to modeling Matter as what it is: Momentary vortex-driven cavitations in a superfluid/supersolid.
@howiedewitt6223 20 күн бұрын
This is fascinating and I can’t stop looking for more discussions on this topic but am coming up empty surprisingly. Some thoughts, -the continuous entropy formula is actually identical to one given by Shannon. The problem is that this integral formula actually does not reduce to a discrete distribution in the limiting case as Shannon thought it would. The information theoretic approach is to accept a negative differential entropy or quantize in exactly the way you did here. -in the delta function limit I’m not sure there’s anything actually making us use the integral instead of returning to the discrete case. Would also not be surprised if there’s some obscure measure theoretic way out of this. -still, many times in physics when our formalism breaks down it often is nature telling us something. I think that is the case here and flaws in the differential entropy integral become manifest in this thought experiment. It’s so cool that there are real hints about the quantum world hidden in the classically derived statistics.
@gcarcassi 19 күн бұрын
In the continuous case in information theory, the channel capacity depends on the signal vs noise ratio. So you put zero entropy as the entropy of the noise, and then the entropy above is what is the actual signal. In this light, you can understand the zero entropy as the background noise that is always there, even in a vacuum. Physically, since everything interacts gravitationally, you can understand it as the random interaction given by the unknown configuration of everything else in the universe. There are a bunch of different ways to make sense of it...
@batmanrobin6711 21 күн бұрын
Hi professor! I apologize for the dumb question in advance! Is this about showing that theories in which 10 or 11 dimensions are needed are nonsense?
@gcarcassi 20 күн бұрын
It is not clear to me what string theory actually claims about those extra dimensions, so I cannot say it is nonsense. However, if the claim is that those extra dimensions are spatial directions at the same level of our normal three dimensions, then, yes, that claim is problematic. You can't define things you should be able to define.
@Khashayarissi-ob4yj 21 күн бұрын
So beautiful. Thank you professor. Really a true teacher is able to present complex and intricate discussion to the audience in a clear and understandable way. Hoping for more videos. Happy new year.
@gcarcassi 21 күн бұрын
Thank you for the kind words!
@Heisenberg2097 22 күн бұрын
Because space is not three dimensional. It is n-dimesnional.
@erykpakula 22 күн бұрын
You say that Φxy and Lz are conjugate and units of configuration J * s. Next you say that units for generalized coordinate p cannot be the same as configuration. Does it mean we should not treat rad as dimensionless unit? So units for Φ is rad and L is J * s / rad.
@gcarcassi 22 күн бұрын
Angles are weird. They are dimensionless (they are a ratio), but they do have a unit. You could use degrees, for example. So J * s /degrees would be different from J * S / rad. So you can't sum degrees with radians. Also, solid angles are dimensionless as well. However, you can't sum angles and solid angles.
@scottychen2397 23 күн бұрын
What a breath of fresh air . A well of knowledge .
@Achrononmaster 23 күн бұрын
Why do you have the caption: "The 2-sphere is the only symplectic manifold"? All Kähler manifolds are symplectic. R^{2n} is symplectic. Coadjoint orbits of semi-simple Lie groups are often symplectic. Cotangent bundles are symplectic.
@gcarcassi 23 күн бұрын
Within the spheres, it is the only simplectic manifold
@GeoffryGifari 23 күн бұрын
And starting from the basic assumptions that you have, is the number of spatial dimensions independent from the number of temporal dimensions?
@gcarcassi 23 күн бұрын
Different argument for time. But you can argue for a temporal DOF, which turns out to be (time, - energy).
@GeoffryGifari 23 күн бұрын
Hmmm how can the "independent directional degrees of freedom" requirement be inconsistent with a 2D universe? 2D space is used heavily in demonstrating elementary mechanics, and even orbits are possible in that case
@gcarcassi 23 күн бұрын
You can also study the harmonic oscillator in 1D... and you don't work with the full direction DOF. You can also put a constraint on position and velocity such that you do not explore the full DOF. So, yes, you can put constraints and study a part of something... I am not sure what you want to argue from there...
@alexgoldhaber1786 23 күн бұрын
With this picture, the uncertainty principle is so obvious. The state {x=a} is just a line x=a on the phase plane. This line has no definite momentum. It has all momentum values!
@gcarcassi 23 күн бұрын
Yes! See our other work on the classical uncertainty principle, where we show that a lower bound on the entropy in a DOF gives us a classical version of the bound.
@taraspokalchuk7256 23 күн бұрын
3:10 but you haven't derived the dependence of H on q, p and t. So you wouldn't be able to derive the laws of motion even for a free particle starting only from the axiom of divergenless *S* .
@taraspokalchuk7256 23 күн бұрын
You sometimes talk about a degree of freedom as of a pair of position and momentum (1:07) and other times as of a single variable in the pair of position and momentum (0:15).
@gcarcassi 23 күн бұрын
In the beginning I say "each degree of freedom is two dimensional: position and momentum" meaning that a DOF is made of two variables. I.e. position and momentum are the two variables in a DOF
@taraspokalchuk7256 23 күн бұрын
@@gcarcassi Ok, I understand now, thanks.
@jaydenwilson9522 24 күн бұрын
Length is 1D. Area is 2D. Volume is 3D. Space SHOULD BE whatever you want it to be. If you want Newtonian absolute space, then sure, have a 3D background of no-noun-ness! If you like Einstein, then twist, bend, squash the rubber-sheet that is static spacetime and stretch is as you like into any amount of dimensions you want! Why stop at time being a spatial dimension? Add electricity as a spatial dimension! Put heat in there too! Hell, make breadth another layer!
@gcarcassi 23 күн бұрын
Mathematically, you can do anything. Whether what one does mathematically is physically consistent and physically meaningful is another story.
@jaydenwilson9522 23 күн бұрын
@@gcarcassi That's why I said volume is 3D, as Space itself isn't meaningful. Nature abhors a vacuum. And instead of thinking of space as a backdrop of absolute space, or absolute spacetime. It would be better to think of each entity and medium as its own octree matrix, within another's octree matrix. (IN rather than ON an absolute)
@lexinwonderland5741 22 күн бұрын
you are raising a very interesting pedagogical point, but i feel like Dr. Carcassi's entire program is meant to explain those ambiguities at their roots. your conceptual explanation is even in line with the roots of Kaluza-Klein Theory which gave birth to gauge theory and string theory, but.... the point of his program is to distinguish "what is explicitly definable as physics" vs "what is math/science beyond physical reality". Einstein's reply to LeMaitre comes to mind, something to the tune of "your mathematics may be flawless, but your physics is meaningless."
@jaydenwilson9522 21 күн бұрын
@@lexinwonderland5741 Ty for the reply! I can take a step back as I do support and respect Dr. Carcassi for the work he is doing, as well as appearing on the DemystifySci podcast to talk about it. (Even if he did trip up a bit when asked on Spin. (Pedagogically of course)) But, what do you mean "math/science beyond physical reality" ??? Mathematics is now Metaphysics??? (Meta = beyond) Mathematics is the abstract science of number and measure. (THATS IT!) When they stop measuring stuff, like Set Theory or Topology, then it ceases being mathematics. And thanks for sharing! Einstein also said some funny stuff about Eddington in relation to his ideas on the Gaseous Sun. (It's not Gaseous, its liquid, or at least elastic solid) But I don't think we should be using his quotes when he himself had very questionable metaphysics. Which is why Mach refused to be glorified by Einsteinian Relativity in 1921. (This wounded Einstein A LOT apparently) "We shall not speak of the Machian Principle anymore." - Einstein, paraphrased in 1954 I think it was.
@gcarcassi 20 күн бұрын
@@lexinwonderland5741 "your mathematics may be flawless, but your physics is meaningless." That's a great quote! And you are spot on on our aims. 😊
@wargreymon2024 24 күн бұрын
It appears it's the consequence of relativity. If it is phrased as a theorem, it becomes a milestone in theoretical physics!
@gcarcassi 23 күн бұрын
"Phrased as a theorem" is a bit tricky because you have essentially a physical argument that imposes some math. See my other video "the line between math and physics". Another issue is that we do not have a rigorous mathematical theory of physical dimension and units, which are essentially stripped out. I am still in the process of trying to understand how it would look like...
@whatitmeans 24 күн бұрын
I thought you were going to talk about the Gabor's Limit: the uncertainty among the bandwidth and the time extension of any phenomena: I hope you could make an analogous video for this uncertainty principle
@gcarcassi 24 күн бұрын
My brain still haven't worked out the link between the, let's say, signal processing type bounds (like Gabor's limit, and other related to Fourier transform) and the entropic ones, like the one I present here that bridges CM and QM. I am still missing something... 🤔
@Zebinify 24 күн бұрын
But isn’t the logic a bit circular to invoke the simpletic manifold argument? I would argue that the 2form and “cross product” like structures are inspired by the human intuition of 3D space, instead of the other way around.
@gcarcassi 24 күн бұрын
You use the argument to impose the simplectic structure. You can look in the book where these things are done more carefully. You can also find our article "Hamiltonian mechanics is conservation of information entropy". The whole point is that you can run the argument either way, so you can see that positing the mathematical structure is equivalent to positing the physical starting point. This is what Reverse Physics is about! 😊
@Zebinify 24 күн бұрын
Thanks! I see the point now, "you can run the argument either way" is a crucial point @@gcarcassi
@quarkraven 24 күн бұрын
doesn't treating position and momentum as independent variables intrinsically imply a classical framework? does the argument change in a quantum framework? or does this particular line of reasoning only applicable toward satisfying GR?
@gcarcassi 24 күн бұрын
The same argument works in quantum mechanics. In fact, in quantum mechanics this argument can be used to argue way you need complex projective space (instead or real or quaternionic). The real independence is across DOFs, which works the same in QM.
@whatitmeans 24 күн бұрын
as an engineer, every time I heard a theoretical physicist on a video talking about extra dimensions I get upset: "WTF do you expect me to build with that?!! we live in 3 dimensions ffs!"... if it cannot be tested through an experiment it is just math, and not physics, in my opinion.
@gcarcassi 24 күн бұрын
I feel the same way... but I am an engineer too... 🤣🤣🤣
@ThomasEmilioVilla 24 күн бұрын
This is extremely interesting, Gabriele! It kind of reminds me of the use of the Riemann sphere split into two halves by the Wessel plane as done by Roger Penrose in his twistor theory (he switched the north pole to be the zero and the infinity as the south pole in order to create some sort of projecting space). This would be indeed simplectic, with positive frequency modes on one half and the negative frequency modes on the other half. The conclusion for twistor theory is that spacetime shall be indeed four dimensional (it includes time)...maybe there is a link or...maybe it may not be linked at all with your interesting way of seeing it. For instance, you seem to use the Bloch sphere instead in order to describe two possible orthogonal states, that is a difference...gotta think about it some more time. Interesting indeed! :)
@gcarcassi 24 күн бұрын
Ah! Interesting! Not knowing nothing about twistor theory I can't comment... but I wouldn't be surprised if there is a connection.
@Tititototo 24 күн бұрын
Hello and have a wonderful year! I would rather say, "Why do we need three dimensions to describe space? It’s all related to the observer. 😊
@Achrononmaster 24 күн бұрын
There must be something missing in the postulates. You have to be presuming something like classical mechanics, no? So "CM must have 3D space" is the conclusion? A Lagrangian can be formed, say in String Theory in higher dimensions, so that is a simple counter-example to the general argument, even if not our cosmos.
@gcarcassi 24 күн бұрын
The starting points are fine. In a field theory, the DOF are the values at the point. However, if you want the propagation of a free field to be an independent DOF, you will need space to be three dimensional. Therefore, a field theory in which space does not have three dimension, does not satisfy the requirement. Mathematically, you can do all sorts of things that are not physically consistent. And that's the point of the video.
@gcarcassi 24 күн бұрын
>counter-example to the general argument BTW: String theory is NOT a physical theory. Does not give any prediction that have been validated. The argument is a problem for string theory, not the other way around...
@eternaldoorman5228 24 күн бұрын
@@gcarcassi Ah, thanks. This explains something I missed, because I was wondering why each degree of freedom corresponds to two variables, but I missed the "is charted by" and that's the hint that you're talking about field theories.
@zoetropo1 21 күн бұрын
@@gcarcassiThere are known compact dimensions: the complex ones underlying Yang-Mills fields. I don’t know what string theorists think their compact dimensions look like.
@gcarcassi 20 күн бұрын
@@zoetropo1 I do not know either. Note that I specifically say "spatial dimensions". You must be able to make sense of a "direction" across dimensions, which makes sense only if their dimension is physically homogeneous.
@taktoa1 24 күн бұрын
At 8:00, why is the hypersphere defined by sum_i L_i = 1 instead of sum_i L_i² = 1?
@gcarcassi 24 күн бұрын
Argh! And I can't even change it now! :-(
@jperez7893 24 күн бұрын
@@gcarcassi is it supposed to be squared?
@gcarcassi 23 күн бұрын
Yeah... ☹️ Well, at least it tells me that people actually think with their head when looking at the video! 😁
@lexinwonderland5741 22 күн бұрын
@@gcarcassi i would take that as a sign of success -- every human makes mistakes regardless of their caliber, but not every teacher has students that are sharp enough and invested enough to point out their errors!!
@gcarcassi 20 күн бұрын
@@lexinwonderland5741 Yeah! I am often surprised by the level of comments I get on KZbin. Another "viewer" argues that my videos are technical enough that there is god self-selection on who follows the channel.
@gcarcassi 27 күн бұрын
These are results from our research project Assumptions of Physics. More details on this topic in our open access book: assumptionsofphysics.org/book/ . If you are interested in our active research, see our other channel www.youtube.com/@AssumptionsofPhysicsResearch .