Understanding Quantum Mechanics #1: It’s not about discreteness

[@joevignolor4u949]

Its wonderful how Sabine calls this a "understandable misunderstanding". This is contrary to the typical practice by some on KZbin of calling people "idiots" and "morons" whenever they are wrong about something. Misunderstanding something does not mean someone has low intelligence. It just means that their knowledge base on that particular subject needs some enhancement.

[@musicalBurr]

Hear hear Joe!

[@Lucky10279]

@Goran Vukovic It's not it about being politically correct. Calling people idiots or morons for misunderstanding something isn't going to do anything but make people mad. If the goal is to teach, as Sabine's goal clearly is, expressing empathy, or at the very least, _not_ expressing contempt, is exactly what she needs to do, as she does. I'm subscribed to a whole bunch of educational KZbin channels, but I'd quickly unsubscribe from any that started calling people idiots or otherwise insulting our intelligence. I might let it slide once or twice if it was a channel I otherwise really like, but if they kept it up, I'd be gone. And if it wasn't a channel I really liked, once would probably be enough to turn me off. And I'm quite sure I'm not the only one who wouldn't want to watch videos by someone who insulted their intelligence.

[@joevignolor4u949]

@Goran Vukovic Yes it matters. I'm not talking about political correctness or politeness. What I'm talking about is not resorting to mean-spirited personal insults when someone is misinformed or mistaken or we just don't agree with them. In any intelligent discussion civility is both desirable as well as a necessity. And by the way even though you and I may disagree on this issue I still respect you as a person and I appreciated your thoughtful and well written comment. Thank you.

[@Blox117]

@@joevignolor4u949 Joe, if you are so triggered over a simple word perhaps you do not belong in any "intelligent discussions". Because the first time someone says something you don't like or agree with, you will cry abuse.

[@Lucky10279]

@Goran Vukovic First, there's a difference between _science_ and _science communication._ This channel is the latter. Second, who cares if your science is good if you can't be a decent person? Science isn't the be all and end all. Third, how exactly do you plan on getting anyone to actually _listen_ to your theories or read your papers if you start off by insulting their intelligence? Science is a collaborative effort. Fourth, none of this is to say that it's not important to actually get things right, but getting things right and being a decent person who doesn't insult others' intelligence for no reason are not mutually exclusive things. You can do both. I'm not sure why you think it doesn't matter if you insult people for no reason as long as your theory is right.

[@balasubr2252]

Clarifying this “understandable misunderstanding” is very appropriate when applying quantum mechanics to social science. Even mathematicians and statisticians fail to appreciate this critical distinction. Sabine’s effort in making this video is worth many saved hours of discussions. Thanks Professor.

[@ComplexVariables]

I did know that there was even a problem with my understanding until watching this; thank you!

[@meahoola]

Thank You Sabine, this is exactly the level I need, you fill a gap in the available presentations of science on KZbin. Most popular presentations way too trivial, most lectures too formal.

[@robertopacheco2943]

Well said!

[@KpxUrz5745]

Hosssenfelder is a superb teacher. Her informative videos are filled with comprehensible facts, and none of the fluff that most videos are filled with. Really outstanding.

[@philochristos]

That last sentence was what I was wanting to know the whole time--whether quantizing gravity means that space is quantized.

[@DanielL143]

Sabine, thank-you so much for the most 'coherent', non-trivial explanations of a field of science that has been convoluted (especially for consumption by the general public, not to mention students) by the misuse of language. I've been waiting for you to show up for years. Please, keep producing these videos but not discretely.

[@Nickelodeon81]

I really appreciate this explanation. As an engineer I often deal with the continuous continuum of mechanics being modelled simply i.e. being broken down into something we can model e.g. Finite Element Analysis. In reality, the discretisation is not real, just a way to handle the information in a practical way. Real life is not FEM, but simply a model.

[@noeckel]

Very true! In fact, the operators representing position and momentum in Heisenberg's uncertainty relation have a continuous spectrum themselves. Observables that have a discrete spectrum (more precisely trace-class operators) cannot obey a Heisenberg-type uncertainty relation (with a constant lower bound for the uncertainty product).

[@tiredlmao3226]

If a system has discrete energy levels, does it indicate that system is 100% Quantum? Is there any classical system with discrete energies?

[@frun]

​@@tiredlmao3226Classical system of which only partial information is available = quantum system(ensemble interpretation). Example of a quantum/classical system kzbin.info/www/bejne/pJ6mYaydp5Vrqqc

[@stefanolacchin4963]

Thank you Sabine. Today I learned (somewhere else) that particles are not really "particles", then that quantum mechanics doesn't really imply a quantised reality. Every time I feel like my mind is grasping some basic notion about the nature of reality, I discover it's just a gross simplification and I'm back at square one. As a layman lacking the mathematical tools to really wrap my mind around these concepts, I want to thank you for your rigorous yet comprehensible insights. Your channel is priceless.

[@andybucmo]

The older I get (currently 59), the more I realize I don't understand our world as well as I thought I did. But I also get more comfortable with that. Sometimes I think of it as being on the side of a mountain (various levels of understanding). Sure, it would be more "comfortable" to be sitting on a flat surface (confidence, certainty), assuming I'm at the top, but how can I be sure I'm not actually at the bottom (ignorance)?

[@stefanolacchin4963]

@@andybucmo Actually these very days another renown physicist has self-published a work that claims to promise to spark a revolution in our understanding of the natural world, and seems to point to an underlying quantised nature of reality, though at a scale of several orders of magnitude smaller than the Planck length. These are interesting times. I'm in a superposition of states (hopeful-puzzled) both rooted in utter ignorance so I'll just wait for what Sabine has to say about that.

[@theshermantanker7043]

@@stefanolacchin4963 Did you learn that "particles are not really particles" by Dr. David Tong? If so I can say he's my favourite theoretical physicist to date. Very enjoyable man to be around, humble yet so full of life, but more importantly to me doesn't share Sabine's fatal flaw of arrogance (It's not apparent in this video, but when it comes to topics she feels strongly about she turns from empathetic, helpful scientist to a condescending, passive aggressive monster while describing any of her skeptics, usually implicitly labelling them as drooling idiots who don't deserve any of their accomplishments whatsoever. Her true colours however, really start to show when in a live debate with someone else that simply doesn't agree with her)

[@Levon9404]

Yes you are right Sabine, "energy is proportional in magnitude to the frequency of radiation it represent". And that proportional frequency of radiation starts from Hydrogen atoms and it reaches to the largest black hole known to human kind. You may ask why is that black holes do not emit radiation according to their size? You know Sabine when nucleus growing by size, it just reserving the energy using all the strength pull additional energy just to grow size wise, and that goes on as long as enough supply exits within the reach close by. AS soon as supply slow down or stops slowly but surely large nucleus in is way to become a planet or star, it start to emit radiation, in mean time slow energy movement toward the formation all energy or clouds of energy starting formations all close by after horizon, all formation after horizon expanding their own energy reach. Because main formation is more powerful pulling everything is noticeable to giant formation, with powerful pull of main formation robs most of the energy from small formation it turned them into rocks because main formation pulled so hard out of sadden new formations hot surface get covered with crust and scientists are losing track of this formations and have no clue what happened to them. after that planet size formations start to go self destruction, that is when they create lava and force volcanic activity over the surface of newly formed planets for stars it goes little bit to extreme instead of lava it goes total destruction of energy. The one we get heat form and we except as sun and main star .

[@maxtabmann6701]

What I have lerned long time ago is that one should not mix up the terms quantization and discretization. Discretization refers to spatial or temporal coordinates that are not discrete in nature but they may discretized on a computer for calculation purposes. Quantization refers to charge appearing in quantized units. Therefore, momentum and energy, because they are Fourier conjugate to time and position, are naturally not discrete. Only in a bound system, frequencies or k-vectors can be discrete. This is true for both classical and quantum systems, for guitar strings as well as for energy levels, as frequency and energy are connected by Plancks constant. So the only thing really quantized is the charge or the spin.

[@SabineHossenfelder]

I am not sure what "charge" you are referring to, but largely what you say is correct. Energies (frequencies) are generically discrete in bound systems and discretization does not necessarily have something to do with quantum theory, it's a geometrical requirement, usually coming from boundary conditions.

[@robmorgan1214]

Wonderful content as usual! I like to tackle the aporoach to understanding quantum from the historical perspective of thermodynamic and statistical mech: ie Plank black body and Einstein AB coefficients maybe the Gibbs paradox, then add in the statistical/algebraic constraints to recover the effects of commutation and ultimately the idea of Lie algebra and spinnors and wave mechanics to motivate and "derrive" the schrodenger/dirac eq's. People usually don't "understand" QM because it's an example of a theory that places statistics and algebra/topology on equal footing with geometry. This combined with the problem of integrating a conserved quantity into a theory (such as basis independent total probability aka the Bohrn rule) without an associated charge per Noether's theorem is difficult to comprehend... for me it was this realization, namely that the born rule places something akin to a Goldstone boson (aka something required for mathematical consistency but not DIRECTLY observable in reality: aka complex probabilistic wave functions that permit superposition... until you look for phase effects ala Aharanov Bohm and the EPR predictions and other entanglement effects) straight into the heart of the theory for no reason other than the fact that probability must be conserved (ie sum to 1). Now it's possible to liberate one's self from the confusion by reflecting on the consequences that might result in a statistical theory from introducing a charge and it's associated field from an implicit rather than explicitly conserved quantity into the partition function (like the total probability or the "unfreezing" of degrees of freedom in your state space in the grand canonical partition function). This like any other poorly formulated constraint is essentially swept up into the entropy of the grand canonical partition function and the conjugate temperature/chemical potential that creates the psudo forces coupling "the system" to its own phase space and it's environment in unusual/unexpected or "unnatural" ways. You only notice the problem when your experiment reveals a heat capacity that exceeds your predictions. I'm sympathetic to the guys studying extra dimensions since this is very much analogous but the difference here is profound. After all it was the ultra violet catastrophe, Gibbs parodox and other problems in thermodynamics that illuminated the path forward for the development of quantum mechanics. The string theorists and phenomenologists were trying to figure out WHERE to look next instead of searching for and attacking problems living in experimental data head on. As you point out in your book, It's the "unnaturalness" of this statistical approach that tends to offend most physicists who prefer to work fully in the geometric picture...which mostly makes sense if you like Lagrangian dynamics, GR, or E&M. The irony is statmech is very good at allowing you to basically set up your geometry a priori via the real constraints your experimental observations place on your partition fn (as pointed out by Jaynes)...and hence your Lagrangian... oh well. I've wasted years tilting at this particular windmill. Looking forward to seeing what's next!

[@jaycorrales5329]

Usually they jump right into the math of probabilities and Schrödinger equation when talking about QM, so I am glad you didn't do that. I think you have a better understanding of the student's thought process than 95% of all professors teaching this subject! As they say, those that can't teach, have taught the professors, but you've jumped the shark on this one.

[@davidwright8432]

Thanks Sabine! Clear and helpful, as always. The way one is taught physics - even in grad school! - is poor at understanding other people's misunderstanding of the course content! One is taught to solve problems, not think about them. Your series provides a very good counterbalance. I also enjoy your musical numbers. Lotte Lehmann, eat yer heart out! Likewise Edith Piaf.

[@raminagrobis6112]

Yes, and no, Sabine :) Yes, you're absolutely right, quantum mechanics does not preclude a "free" particle from taking momentum values from a continuum (or "scale", as you refer to it) of such values. But the very definition of a system being quantized IS about it taking only discrete values. And this happens whenever a particle is bound to another or others - a pretty common situation, to say the least (!). That's the very essence not only of the word but of the concept as well, and it's what troubled Planck so much that he long thought the introduction of his constant (h) was a kind of "fudge factor" that had no real intrinsic meaning and reflected a lack of theoretical "classical" explanation rather than a new, fundamental and more accurate way to describe reality than Newtonian mechanics. So, yes, quantum mechanics does not "discretize" (!) energy per se, but quantization of a system truly means constraining energy to acquire only discrete values. But I think you have been saying more or less the same thing. I just wanted to emphasize the important point that it IS about reducing a system to adopt only discrete values of momentum (or of energy, or related parameters) whenever we're dealing with an interaction between particles.

[@talldarkhansome1]

Thanks for clarification. I was wondering.

[@sonofode902]

Could you made a simple parable/illustration of your explaination?

[@rc5989]

I have learned some important caveats regarding quantized vs discrete. Thank you Sabine! My opinion that comes to mind often from your videos is that nature is much more messy and disorganized than undergrad physics would lead us to believe.

[@Andrey.Balandin]

Sabine, my life has been a lie until now.

[@mikicerise6250]

I imagined that a quantum theory of gravity would necessarily mean quantizing spacetime into discrete chunks.

[@christianlibertarian5488]

@Aaron Jones As an aside, you should investigate medical physics as an occupation. High-ish pay, reasonable hours, low stress. Best job in any hospital. Just a suggestion.

[@yomismosoyelregalo2266]

Aaron Jones before you do that watch the latest season of Bosch on Prime Video.

[@RWin-fp5jn]

To be very honest, Sabine is not quite clear enough. A quantum is a quantum, meaning a discrete amount of something, period. It is just that ENERGY can come in the form of a quantum (namely when discussing the sub-atomic realm), but when traveling through the macro world of our spacetime, particles (also the very small ones) basically can have any energy. So the discussion is not whether a quanta is discrete or not but that ENERGY has BOTH a quantum and continuous property. The fundamental explanation is that in the subatomic world the GRID itself consists of energy. It comes in the form of a wound up spiral. Our eyes (and sensors) look 'head on' at this spiral and interpreted the discrete number of windings as 'quanta' of energy, but actually we are simply seeing the distance of e.g. an electron in eV terms. In contrast, in our macro spacetime world physics (outside of the atom), Energy is no longer the GRID but a particle property. This is also the fundamental solution behind particle wave duality; it is not the particle that acts weird, it is just that there are two orthogonal setups for our continuum that BOTH apply. One setup for the subatomic world (which is why we see a particle's energy 'behave' like a wave ) and one macro world setup where energy is a particle property (which is why we see it as a 'particle'). Top physicists (even Sabine) are not aware of this double setup. That's why the confusion has been going on for 100 years now...

[@frankdimeglio8216]

@@RWin-fp5jn The page Nexus of Physics has now given the following two writings the thumbs up on their page. ALSO consider this: E=mc2 is DIRECTLY and fundamentally derived from F=ma, AS E=mc2 IS F=ma; AS time DILATION proves that electromagnetism/ENERGY IS GRAVITY. THE UNIVERSAL AND MATHEMATICAL PROOF THAT ELECTROMAGNETISM/ENERGY IS GRAVITY: Energy has/involves GRAVITY, AND ENERGY has/involves inertia/INERTIAL RESISTANCE. "Mass"/ENERGY IS GRAVITY. ELECTROMAGNETISM/ENERGY IS GRAVITY. E=mc2 is DIRECTLY and fundamentally derived from F=ma. GRAVITATIONAL force/ENERGY IS proportional to (or BALANCED with/as) inertia/INERTIAL RESISTANCE, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. SO, gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE consistent with/as what is BALANCED electromagnetic/gravitational force/ENERGY; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. "Mass"/ENERGY involves BALANCED inertia/INERTIAL RESISTANCE consistent with/as what is BALANCED electromagnetic/gravitational force/ENERGY, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity AND ELECTROMAGNETISM/ENERGY are linked AND BALANCED opposites, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. THE SUN AND THE EARTH are described and represented by BOTH F=ma AND E=mc2. F=ma AND E=mc2 PROVE that ELECTROMAGNETISM/ENERGY IS GRAVITY, AS ALL of SPACE is NECESSARILY electromagnetic/gravitational (IN BALANCE). Objects fall at the same rate (neglecting air resistance, of course), AS the SPEED OF LIGHT is RELATIVELY CONSTANT AS WELL. ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity IS ELECTROMAGNETISM/ENERGY. In fact, the rotation of THE MOON MATCHES it's revolution; AS gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. So, THE PLANETS (INCLUDING WHAT IS THE EARTH) are not "falling" in what is "curved SPACE" in RELATION to what is THE SUN. This is nonsense. E=mc2 is DIRECTLY AND FUNDAMENTALLY DERIVED FROM F=ma. This truly explains PERPETUAL MOTION. Very importantly, outer "space" involves full inertia; AND it is fully invisible AND black. The stars AND PLANETS are POINTS in the night sky. A PHOTON may be placed the center of THE SUN (as A POINT, of course), as the reduction of SPACE is offset by (or BALANCED with) the SPEED OF LIGHT; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. By Frank DiMeglio EINSTEIN NEVER UNDERSTOOD PHILOSOPHY, MATHEMATICS, AND PHYSICS, AS HE HAS BEEN TOTALLY OUTSMARTED BY SIR FRANK MARTIN DIMEGLIO: The balance of being AND EXPERIENCE is ESSENTIAL. BALANCE AND completeness go hand in hand. THE SELF represents, FORMS, and experiences a COMPREHENSIVE approximation of experience in general by combining conscious and unconscious experience. MOREOVER, the ability of THOUGHT to DESCRIBE OR RECONFIGURE sensory experience is ULTIMATELY dependent upon the extent to which THOUGHT IS SIMILAR TO sensory experience. THOUGHTS ARE INVISIBLE. Dream experience is/involves true/real QUANTUM GRAVITY, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. MOST IMPORTANTLY, in dreams, BODILY/VISUAL EXPERIENCE is invisible AND VISIBLE IN BALANCE. IMPORTANTLY, dream experience is possible/potential AND actual IN BALANCE. THE EYE is ALSO the body. Dreams improve upon memory AND UNDERSTANDING. Indeed, there is no outsmarting the GENIUS of dreams. OVERLAY what is THE EYE in BALANCED RELATION to/with what is THE EARTH. NOW, get a good LOOK at what is the translucent, SEMI-SPHERICAL, QUANTUM GRAVITATIONAL, AND BLUE sky. Excellent. The DOME of a person's EYE is ALSO VISIBLE. THE EARTH IS also BLUE (as water). F=ma AND E=mc2 PROVE that, why, and how ELECTROMAGNETISM/ENERGY IS GRAVITY. This NECESSARILY represents, INVOLVES, and describes what is possible/potential AND actual IN BALANCE. SO, it is NECESSARILY a matter of precisely how these equations are understood in a BALANCED, EXTENSIVE, AND INTEGRATED fashion in RELATION to/with WHAT IS THOUGHT. The INTEGRATED EXTENSIVENESS of THOUGHT (AND description) is improved in the truly superior mind. E=mc2 is DIRECTLY and fundamentally derived from F=ma. Very importantly, outer "space" involves full inertia; AND it is fully invisible AND black. The stars AND PLANETS are POINTS in the night sky. A PHOTON may be placed at the center of THE SUN (as A POINT, of course), as the reduction of SPACE is offset by (or BALANCED with) the SPEED OF LIGHT; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Get a good LOOK at what is THE EYE. POINTS are points. Gravity IS ELECTROMAGNETISM/ENERGY. ELECTROMAGNETISM/ENERGY IS GRAVITY. GRAVITATIONAL force/ENERGY IS proportional to (or BALANCED with/as) inertia/INERTIAL RESISTANCE, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. "Mass"/ENERGY involves BALANCED inertia/INERTIAL RESISTANCE consistent with/as what is BALANCED electromagnetic/gravitational force/ENERGY, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. "Mass"/ENERGY IS GRAVITY. ELECTROMAGNETISM/ENERGY IS GRAVITY. Energy has/involves GRAVITY, AND ENERGY has/involves inertia/INERTIAL RESISTANCE. F=ma AND E=mc2 PROVE that ELECTROMAGNETISM/ENERGY IS GRAVITY, AS ALL of SPACE is NECESSARILY electromagnetic/gravitational IN BALANCE; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. GREAT. The stars AND PLANETS are POINTS in the night sky. OPEN your EYES. NOW, LOOK at what is the FLAT, SETTING, AND ORANGE SUN (with the SPACE around it THEN going invisible AND VISIBLE IN BALANCE). This ORANGE SUN manifests or forms at what is EYE LEVEL/BODY HEIGHT as well. This ORANGE SUN is manifest ON BALANCE as what is NECESSARILY the BODILY/VISUAL EXPERIENCE of THE EARTH/LAVA. The viscosity of LAVA IS BETWEEN what is manifest as WATER AND THE EARTH/GROUND. ALL of SPACE is NECESSARILY electromagnetic/gravitational IN BALANCE, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. F=ma AND E=mc2 do provide absolute, BALANCED, THEORETICAL, and CLEAR proof that ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. THEREFORE, the rotation of THE MOON MATCHES it's revolution. MOREOVER, a given PLANET (INCLUDING WHAT IS THE EARTH) sweeps out equal areas in equal times; AND this is THEN consistent with/as what is F=ma, E=mc2, AND what is PERPETUAL MOTION; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. It ALL makes perfect sense. BALANCE AND completeness go hand in hand. THE PLANETS (INCLUDING WHAT IS THE EARTH) are NOT "falling" in what is "curved SPACE". In fact, this is nonsense. It is PROVEN. By Frank DiMeglio

[@S489_20mg]

I am considering switching from synthetic organic chemistry and math to just math and physics thanks to your videos and how you connect the concepts to the mathematics. Thank you immensely you are gifted at teaching.

[@jakehayes1345]

This is great. Perfect... I had always thought that quantum mechanics implied that ultimately there is a grainyness of space. That there was some smallest unit of space that had to be incorporated into theories of gravity. Thank you for your amazing and informative videos! p.s. always thought provoking!!

[@priteshsrivastava5850]

But if not particle form of space, then what does this quantisation implies? Is it different than quantisation of EM field due to existence of photon ?

[@Arboldenrocks]

@@priteshsrivastava5850 she's not saying particles aren't discrete. she's saying energy and distance aren't discrete. there may be a minimum possible length of space, but that's not part of quantum theory. afaik the 'planck distance' comes from trying to unite quantum theory and general relativity.

[@jakehayes1345]

@@Arboldenrocks check out this @6:12 kzbin.info/www/bejne/eZOziIygo7Z8hZo

[@davidwuhrer6704]

@@Arboldenrocks The Planck distance is just the distance covered at the speed of light in Planck time. The reference points for that distance (and time) are still on a continuum.

[@ZeeThird]

There IS a grinyness of space, and energy and distance ARE discrete.

[@davidschneide5422]

Even the textbook definition of "quantum" is confusing. How appropriate.

[@JB-ym4up]

Its different if you don't read it.

[@clmasse]

Even in textbook, there are errors that come from history, and the quantum has a long history. The first occurrence have been the charge of the electron, measured by Millikan. That's when the term has been coined. Then came Planck who found out that to explain the radiation of black body, the energy levels of the harmonic oscillators must be discrete, at that time they said "quantised." Einstein explained this through the hypothesis that the energy of an electromagnetic field of a given frequency is an integer multiple of a quantum. Things changed when Schrödinger reduced the problem of the energy levels in an atom to a eigenvalue problem for a continuous wave function. Then "quantisation" means transforming a classical equation of motion to a quantum one, with a wave function, and thus the uncertainty relation appears. Both senses are still valid, but I prefer to use the word "discretisation" for the former one.

[@davidschneide5422]

@@clmasse well composed. Even with extensive research, before the internet was invented, it's still difficult to see reality in terms of wave functions. My personal ability to picture the quantum realm stops many orders of magnitude higher than that, in quarks & chromodynamics. I understand quantum "stuff", not quantum "math" & an 'impossible' reality. It's simple to imagine how Hawking visualized an event horizon & virtual particles, but hard to picture a hole as a "blackbody" in an experiment. It seems more wordplay than actual naming of things, hence the indecipherable definitions. Not allowed to have just a general interest here, it takes effort to really, really GET IT.

[@jamestheotherone742]

It is very intentionally obfuscated.

[@RWin-fp5jn]

To be very honest, not just the tekst book but also Sabine is not quite clear enough. A quantum is a quantum, meaning a discrete amount of something, period. It is just that ENERGY can come in BOTH the form of a quantum (namely when discussing the sub-atomic realm), AND in a continuous form, namely when traveling through the macro world of our spacetime. So the discussion is not whether a quanta is discrete or not, but that ENERGY has BOTH a quantum and continuous property. The fundamental explanation is that in the subatomic world the GRID itself consists of energy. It comes in the form of a wound up spiral. In case of e.g. observing an atom, our eyes (and sensors) look 'head on' at this spiral and interpreted the discrete number of windings as 'quanta' of energy, but actually we are simply seeing the distance of e.g. an electron in eV terms. In contrast, in our macro spacetime world physics (outside of the atom), Energy is no longer the GRID itself but a particle property and no longer discrete. This is also the fundamental solution behind particle wave duality; it is not the particle that acts weird, it is just that there are two orthogonal setups for our continuum that BOTH apply. One setup for the subatomic world (which is why we see a particle's energy 'behave' like a wave ) and one macro world setup where energy is a particle property (which is why we see the energy as a 'particle'). Top physicists (even Sabine) are not aware of this quite basic fundamental double setup. That's why the confusion has been going on for 100 years now...

[@RWin-fp5jn]

Great video once more! We badly need these core PHYSICS questions asked (and solved) before we try to capture them in complex MATHEMATICAL constructs. Mathematics without underlying tangible physics is a dead end and we wasted a century following this unholy route. As for this specific subject: The answer to the question of a ‘quantum’ being discrete vs. continuous is indeed that both apply. It is simply yet another example of fundamental duality between the four FUNCTIONS of the continuum (Grid, Clock, Potential, Inertia) and the four MEASURES (Space, Time, Energy, Mass) as explained in my comments below Sabine’s previous two video’s. Energy is DISCRETE in its function of grid, e.g. at the subatomic realm. In our Spacetime (ST) dominated realm however, Energy has its dual and continuous continuum function of particle potential. It is really a rather basic insight if one accepts the dual structure of physics. As for the electron: in its atom-bound form, we must see the electron as a stroboscopic ‘energy’ discharge at both sides of the atom caused by a bend EM fieldline (the very folding caused by the atom’s nucleus) which is constantly being wound-up clockwise and anti-clockwise in a double spiral. Reaching its furthest position, the outer fold of the EM spiral arm causes a geometric double intersection point with our ST continuum, leading to a double discharge at each side of the atom. The Max Planck Institute has photographed this double electron discharge on either side of a Helium atom many times, PROVING this concept is correct. As such we must see the electron ‘orbit’ as a collection of stroboscopic double discharges. In fact we may see the atom bound electron as an ST superposition of an atom bound EM photon. This explains why an incoming photon can merge its energy, increasing the eV distance by which the original photon can discharge its energy (‘quantum leap’). Furthermore; The dual setup requires that this double electric discharge must be compensated with a coinciding orthogonal shortening of the spacetime fieldine that is being wrapped ('gravity'). This compensating effect is mass based not time based. This field effect can also be described as a particle: This mass based particle must then have the inverse spin of the electron (1 / ½ thus spin 2) , which would mean a spin 2 boson, a.k.a. the ‘mysterious ‘graviton’. We cannot ‘see’ this ‘mysterious’ particle because it is not time-based. But now at least we understand how an atomic energy discharge (electron) always has the orthogonal equivalent of a shrinkage of the ST fieldline (graviton). Again we can explain EVERYTHING if only we accept the dual nature of our continuum. I hope the likes of Sabine can make this ‘jump’ in insight one day…..

[@bjorncedervall5291]

It feels almost like a birthday present to find Sabine's lectures and singing today. I spent all my life since childhood with focus on interdisciplinary scientific challenges (math->biology and also other areas). Please pardon this self centered perspective - I am deeply impressed however. Will check out more of Sabine's videos later.

[@luudest]

Thank you for this video! I always wondered why Quantum Mechanics is associated with discrete values.

[@Arijit_Bose2308]

Outstanding explanation❤️❤️❤️❤️❤️❤️...No one can explain the basic concept of quantum theory like this method in long academic lectures.

[@craigwall9536]

Well YOU are easily amused....

[@terryg4795]

Thanks for the clarification, Sabine. In semantic studies, which is my research area, the notion quantizedness largely means discreteness. Great to know how physicists use this term.

[@Chaos------]

Took me a long time to figure out that the words for certain phenomenon in physics are not meant to be taken literal and instead describe something much more subtle. Like waves in light. Its not a literal physical wave, its an oscillation in field strength which can then be mathematically abstracted as a two dimensional wave. Small things like that completely turned me off form mathematics and physics all together when I was younger, but now I feel extremely intrigued by all of this and want to absorb as much of it as I can. Your videos help me immensely in this endeveour!

[@ericjorgensen6425]

How do the ideas of Planck time and Planck length fit into this discussion?

[@SabineHossenfelder]

They are scales. They set orders of magnitude. This does not necessarily mean they correspond to an actual duration of time or a length of space. The Planck length and Planck time sets orders of magnitude for quantum gravitational effects to become important, for example in the curvature. But as I said, just because you quantize something does not mean you make it discrete. These are just different things.

[@davidschneide5422]

Were we discussing the size of Trump's brain, or was it his heart?

[@guyincognito.]

@@davidschneide5422 His tolerance for idiots and liberals but I repeat myself.

[@Techmagus76]

@@davidschneide5422 No this is a science discussion. Weird old men can be taking a part in the discussion, but we do not talk about them.

[@dupazelli1]

david schneide -> Who said he has a brain ??

[@thesoppywanker]

I was very recently wondering about this. Very helpful and concise. Thanks!

[@slash196]

What is a "particle" if not a discrete unit of interaction within or between fields? Isn't that what the Born rule gives us a probability distribution for?

[@obsidianjane2267]

The fields are the sum of waveform interactions with which a probability distribution defines a particle property. Distinct from the physical particle itself, which is irrelevant from a quantum mechanical model. This is often confused/ignored even by people who should know better.

[@markoposavec9240]

The other day I thought about how photons supposedly had discrete energy values and it did not make sense to me. I thought Redshift effect should smoothly change the color of light and concluded that photons should not come only in discrete energy values. Now I'm thinking about the Doppler effect, same... Awesome video and explanation!

[@thesparetimephysicist9462]

Hi Sabine, I love your videos. This time I disagree with your point though. 
Yes, the distribution of photon states in empty space is continuous. But the number of photons is not. Each wavelength is associated with an energy, and within that wavelength you have to have a whole number of photons. If you manage to cut a photons energy in half it will no longer be associated with the same wavelength. You are focusing on the distribution of states, but the discreetness is not about the distribution, it is about the individual states. Either a state is occupied or it is empty. Nothing in between.

[@markfernee3842]

I agree that this explanation also fails to really capture the essence of QM. However, this is probably due to the fact that the essence of quantum mechanics is difficult to pin down. Consider that Planck's constant is a quantum of the action. Then we have that any exchange of quanta must be local. That means some local action propagates a change by the emission of a quantum, which can only result in a distant local action. This seems like a particle theory. Yet the propagation of the action is described by a wave equation. Thus we have the wave-particle duality quality of quantum mechanics, except the particles are just the concept of local action. For example, a photon is only particle-like in some aspects and wave-like in others. In fact, the proper quantum optical description of a photon is rather complex, and certainly not point-like. In fact it's impossible to uniquely describe the size of a photon.

[@TonalWorks]

Yeah, you are correct. I think this video is creating a bit of a straw man argument.

[@johnm.v709]

@@markfernee3842 Q. M. kzbin.info/www/bejne/i6rQi4WVg5l6f68

[@johnm.v709]

Sir, Photon... kzbin.info/www/bejne/pJ_Op6J_fd-nhtk Quan... Mech.... kzbin.info/www/bejne/i6rQi4WVg5l6f68

[@chrisgriffiths2533]

Obviously I have more to Learn about the Proportional Relationship between Frequency and Energy. My Simple understanding of Energy and Frequency Tells me that if you want to Increase the Frequency or Energy of an AC Alternator. You can Simple Speed up the Alternator. This will increase the Frequency, but it will Also Increase the Volts. In this Example the Energy Increases mostly in Proportion to the Volts or Speed Increase. The Frequency Increase will have some effect on the Energy but not as much as the increase in Volts. Maybe I have missed Something?. Interesting Topic Doctor Sabine, I have more to Think about with Discreteness and Uncertainty.

[@physics_enthusiast_Soorya]

Thank you! I was really confused on why many people refer it to discrete, where it isn't...

[@rv706]

For me quantum mechanics is: 1) Linearity: can (essentially) sum states, that is "quantum superposition"; 2) Probability theory done with complex numbers instead of positive reals, so there can be "destructive interference"; 3) Noncommutativity of the algebra of observables, which forces the "uncertainty principle".

[@sadface7457]

What distinguishes a quantum system from statistical system?

[@rv706]

@@sadface7457 Point 2, at least

[@obsidianjane2267]

@@rv706 Only because the maths require it.

[@simontist]

@@obsidianjane2267 the maths is the theory.

[@obsidianjane2267]

@@simontist Not when its a practical application.

[@michaelblacktree]

Thank you for that clarification.

[@bhangrafan4480]

I'm a bit surprised by this video, I understood (in my amateurish way as a non-physics scientist) that in QM every particle had a completely defined, discrete state based on a series of quantum numbers, themselves discrete in character. I am definitely one of the people this video is aimed at!

[@ddimin]

I found out that studying quantum informatics is a clearer and much faster way to understand what "quantum" means (compared to studying quantum mechanics). That's because everything is in finite dimensions, operators are just matrices, you can calculate everything by hand and thinking about bits and qubits is easier than thinking about particles. You still have all the quantum stuff: entanglement, teleportation, measurement, non-commuting operators, etc.

[@jusiphstolin8074]

Quantum mechanics profs use their 70s notes, Quantum information theory people use 2000s notes

[@jamestheotherone742]

@@jusiphstolin8074 Abstracting an abstraction...

[@nHans]

Sabine, I have a very basic doubt about discrete versus continuous values in the real world. Paraphrasing from one of your earlier videos: In physics, and hence in the real world, everything is finite; infinities are a mathematical concept but don't occur in the real world. As an engineer, I believe that. So I've always wondered: Can we have physical quantities represented by arbitrary irrational numbers-numbers with infinite (non-recurring) digits in them? If not, then isn't everything automatically discrete?

[@JohnAzariah]

strictly speaking, the volume of a sphere - a physical quantity - is irrational...so no..

[@Methuzala777]

Insert much praise and appreciation for your candor, work, and decision to present the appropriate nomenclature at an expert level (Its just names. If the first one you learn is the accurate, polysyllabic one, then to you that's the easy one) here.

[@clmasse]

It's a pity Sabine miss some very important ideas of quantum mechanics. On one hand, quantisation (or more exactly discretisation) already exists in classical mechanics, like in the vibrations of a guitar string, and so called quantum effects too, like the tunnel effect. And on the other hand, quantum mechanics necessitates discretisation of some sort, for example the number of particles, otherwise it is impossible to have non commuting observables and thus the uncertainty relation. All that is described with a Hilbert space and Heisenberg type relation is not necessarily quantum. In the long run, the viewers are bound to get confused.

[@paulthompson9668]

2:39 "The other important property of quantum theories is that you can have _____." What was the last word of that sentence?

[@SabineHossenfelder]

Entanglement. Please note that my videos all have captions. You turn them on by clicking on CC in the KZbin toolbar. You also find transcripts to all my videos on my blog: backreaction.blogspot.com/

[@paulthompson9668]

@@SabineHossenfelder Thank you. Keep up the great work! You and Don Lincoln produce good complementary videos on physics. Maybe the two of you could collaborate.

[@TheShootist]

@@SabineHossenfelder We (I speak for the animals) would really enjoy hearing you discuss physics and other topics on Eric Weinstein's The Portal, or with Joe Rogan. Thanks from Texas

[@tothesciencemobile4707]

"...you can _entanglement."_

[@rv706]

Sabine: I know it might be too early now, but are you considering to make a video on the new Stephen Wolfram's speculative proposal for quantum gravity based on hypergraph rewriting rules, in the future?

[@darrennew8211]

If you're truly interested, you can buy "A New Kind Of Science". It's an expensive tome. I'd think Wolfram would need to actually come up with a theory, rather than a speculation of a form of theory to try investigating, before it would be worth reviewing.

[@rv706]

@@darrennew8211 W's collaborator claims to have reproduced general relativity and quantum mechanics (in the form of path integral), in the limit, from the model's first principles (I don't really understand what this means though: e.g. the limit is not always a manifold so what's Einstein eqn in that case? Also, what counts as quantum mechanics in the limit?). But if there's a rigorous mathematical way (or even a physicist style handwaving way) to express that both conventional GR (not necessarily in 4 dimensions) and QM (not necessarily the whole bestiary of the standard model) are limits of their framework in a unified way, it seems already quite interesting to me.

[@NoamWhy]

@Boston is my race track You are so right, there is no shortage of strange ideas which lead absolutely nowhere. What we really need is a theory that would successfully predict the masses and coupling constants of the elementary particles. So far, non of these weird theories was able to deliver that.

[@nowonda1984]

@Boston is my race track Ain't in funny when cave trolls and internet nobodies bash the efforts of decades of someone about five gazdillion smarter than yourself and who has made numerous contributions to other areas of research and computing, all this with the moronic analogy of circles and squares and barking at the moon? Dear know-it-all, celular automaton research has been a thing for decades and it's not only for fun animations on the screen, nor was it done only by Wolfram. Look up the cellular automaton interpretation of QM, for example, which is not a creation of Wolfram. But when your view of complex interactions limits to the visuals and the pretty pictures, I'm not surprised neither of the tone, nor of the laughably naive interpretation of yours. @rv706 Look up Wolfram's channel on twitch, he started giving some lectures on the topic and I suspect at some point others will start chiming in too. I'm not saying it's THE answer or even an answer, but this sort of apriori dismissals done by nobodies is completely moronic.

[@noamwhy1856]

@@nowonda1984 Sounds to me like an argument from authority. A good theory is a theory which allows us to successfully compute new verifiable quantities, e.g. masses of particles. So far, none of the proposed theories offeres that, and there is no good reason to believe that cellular automata would.

[@schontasm]

Thanks for the clear presentation Sabine. I'm still confused: Is space: definitely not discrete, not necessarily discrete, not measurably discrete, not theoretically discrete, not theoretically determinably discrete, or undeterminably continuous etc etc. Basically there appear to be lots of flavours of theoretical and experimental definiteness and determinability. Until this video I had naively assumed the determinability of such categories were themselves undeterminable or at the very least unmeasurable via Schrödinger or Heisenberg. A fringe benefit, if you will, of a quantum framework; packaging those awkward little questions into a "That isn't even really a meaningful question in QM" category. But you seem to be suggesting continuousness has theoretical foundations even if it will never be measurable. Or is that muddleheaded ?

[@Lucky10279]

My understanding is that we _don't know_ if spacetime is fundamentally discrete or not. QM definitely doesn't require it to be (that was her whole point in this video), but I don't think it requires it to be continuous either. I'm not an expert though.

[@JG_1998]

i think people get this idea mainly because their only exposure to quantum mechanics was through chemistry classes. the example with the atomic spectra is the only one most people get, so many assume that the schrodinger equation is only meant to describe the way electrons in an atom behave.

[@tomashull9805]

Doing a video on quantum entanglement in the near future is a good idea provided it is not one about something we already know...Why not cover something controversial, such as quantum mechanics (entanglement) transgresses space and time in a very deep sense? Do we need another theory of space and time; i.e. spacetime, analogous to Einstein's 2 theories of relativity?

[@yzScott]

When I think about the discreteness of QM, I think mostly of the photoelectric effect. Even if the possible energy of a photon can be any continuous value, the photon itself is "discreetness" compared to a wave way of thinking. And energy is carried away from a black body in discreet pieces with the characteristic distribution of energy/frequency of the many photons depending on the temperature. I guess I'm saying, the very existence of photons in place of classical waves was always the "discreetness" I took it to mean.

[@jorriffhdhtrsegg]

That's how i perceived discreteness. Such as measurements that fire single particles, resulting in superpositions, are weird because its a discreet pixel of a wavefunction...but it behaves as if it knows the whole.

[@scottdc2105]

Thank you for your time and effort making these videos, quick question. In an atom is the field between the electrons and nucleus considered a quantum field?

[@schmetterling4477]

The entire universe is quantum fields.

[@scottdc2105]

@@schmetterling4477 In the context of your answer then any theory of gravity associated with fields would be considered a theory of quantum gravity but it isn't. That was the base of my question, if the field between electrons and nucleus was a quantum field then a theory of gravity that includes it is a quantum theory. But that does not describe it as a quantum mechanics process does it.

[@schmetterling4477]

@@scottdc2105 Physics only has to find rational explanations for observed phenomena. Quantum gravity has not been observed, yet. It's not even certain that gravity is a quantum phenomenon. That quantum fields are continuous across the entire universe is not even tangential to gravity, anyway. Your question was if the "inside" of atoms are quantum fields and there simply is no "inside". That's just a kindergarten physics approximation that makes no sense in general.

[@scottdc2105]

@@schmetterling4477 The inside of atoms is basically the field between the electrons and the nucleus without delving into the nucleus. So is that field a quantum field and if so if an explanation of gravity can apply to the field then is it able to be termed a quantum theory of gravity.

[@schmetterling4477]

@@scottdc2105 There is no such thing as an "electron". An electron is a quantum of energy.

[@Alex_Plante]

Here's my simple-minded layman understanding of quantum mechanics : according to our day-to-day experience, objects have definite locations and boundaries, but in quantum world, particles are probability clouds with no definite location or boundary. So that's why a single photon can pass through 2 slits and interfere with itself.

[@AndreaCalaon73]

Well done! It is a common misconception!

[@gatedscs]

I wish if you start a depth course on Quantum Physics. It would be really amazing.

[@jlegassic]

Excellent video -- thanks! This sentence stands out: "A quantum theory has operators for observables that do not commute". Hmm, interesting -- wonder what that all means. :) Hoping one day you can drill down into Renormalization ... why necessary and rules for playing with infinites.

[@quphys5253]

ThankYou! With Your permission, I'll post that in my Moodle-Course "QM-I" ...

[@SabineHossenfelder]

Well, it's a public video, you can post it wherever you wish.

[@kenkoskinen1]

The truth is that Quantum Mechanics does include discrete quantities, even though its a subset of Quantum Field Theory. You can say it isn't ALL about discreteness; but you can't say discreteness isn't involved. Perhaps, we need a clearer video lecture that shows that Quantum Mechanics really does make some things discrete and it's one of it's sign posts...

[@jusiphstolin8074]

Quantum mechanics is not a subset of quantum field theory. Quantum theories are a way of formulating physical theories. So Quantum field theories are themselves some Quantum theories not the other way around

[@sadied0g]

Jusiph Stolin He said Quantum Mechanics, so I believe he’s referring to the “standard Quantum Mechanics” that was done before the development of Quantum Field Theory, not a general umbrella of “Quantum Theories”. In that sense, Quantum Mechanics is a subset of Quantum Field Theory as QFT is more general, and can reproduce Quantum Mechanics when the conditions that Quantum Mechanics works under are applied. But QFT also works under conditions where QM does not. Hence QM being a subset of QFT

[@mhmanley]

@@jusiphstolin8074 Quantum field theory combines classical field theory, special relativity, and quantum mechanics. As such, QM is a part of quantum field theory.

[@Entropy3ko]

Actually electrons in energy bands in solids DO have discrete levels, but the levels are so close together (in the order of like 10^-22 eV) that they can be treated as continuous.

[@SabineHossenfelder]

I said the POSITION is not quantized.

[@jamestheotherone742]

In anything but a simplistic model of a single atom in its own pocket Universe this is irrelevant. Also our concept/observation of electron energy levels are probably an artifact of what we don't know than actual reality.

[@rovosher8708]

Could you please do a video on the contention between unitarity and relativity?

[@PrivateSi]

Quantum = discrete energy in continuous 3D space and 1D time (or 4D space-time), to me.. Discrete space is Cartesian with a fixed sized base component - a fixed base grid size.... I prefer to think of subspace as a close packed lattice of +ve charge cells (discrete charge quanta, +1) held together by an ethereal, analogue, continuous sea of -ve charge... Free, travelling cells form matter as a compression in the lattice and the holes left behind could also form matter, as continuous in-out vibrations. Both could comprise of (looping) in-out flow of -ve or +ve charge, respectively, as well as compressed / stretched surrounding lattice... I like to think of these particles spinning at 90' to the direction of motion, clockwise or anticlockwise..... Solid spheres of different sizes could also move, with compressed lattice cells in front flowing to fill the increasingly stetched, therefore -ve lattice space behind... I can imagine the discrete, blocky nature of the sphere and lattice causing the sphere to spin at 90' to motion... The solid sphere could even stop, with just the energy pattern continuing.. Light could be a travelling compression-stretch fold in space.. streams of dipoles... Tunnelling would be all a cell's radial energy flowing in 1 direction for a while. V=MC2=C2 The more matter in a volume of space, the denser the lattice, with cells pulled closer together, while voids expand as the finite amount of the universe's -ve charge gets concentrated around matter, so less to counter +ve cell repulsion. This thin to super-massive lattice density gradient forms a gravity well and a component of dark energy (with the other component being outward momemtum left over from the big bang).... The big bang blew a hole in the lattice, sending material flying in all directions, with the velocity of ejected matter decreasing over the duration of the explosion.... But there are many ways this simple model can go... Gravity arises as -ve charge is pulled to a point, radially but rebounds at random oblique angles much of the time, so does not cancel the inward force. What's left over is gravity. -ve charge will eventually flow back to voids but the more matter, the longer it will take, with more overall trapped for longer around matter... Quantum-Electro-Gravity... it makes more sense......... to DiscreetSi! TIME could be quantised... I haven't done the maths and I'm not sure but having a (possibly time varying!) constant time it taken for light to travel between cells (+ universe expansion), no matter how absolutely far apart they are (due to varying lattice density), makes the thing more conformal, with general relativity maths working. It could be a fixed ratio to lattice density that is not 1 to 1... I like to believe there is an upper and lower limit to lattice density.. but you never know.

[@mistermxyzptlk3573]

Interesting standpoint. However, there is something that may deserve some additional comments: any particle is in fact an excitation of a quantum field (as lengthily explained in Art Hobson's "There are no particles, there are only fields") and ultimately, the quantum formalism always comes to using the number operator N, built from the creation and annihilation operators. Hence, here lies a good reason why the word "quantum" in "quantum theory" is always associated to discreteness.

[@davidwilkie9551]

The fundamental property of quantization is proportioning integrated ratios of temporal differentiation, otherwise known as wave-particle positioning duration timing modulation duality. The "discrete" aspect is being here-now-forever in real numberness existence. The task of first identifying the existence of the perception paradox of misattribution and incomplete definition of "discrete" phenomena because it's a continuous creation connection Principle of pure relative motion-> mathematical reciprocal positioning formulae of coherent cohesion objectives in pulsed resonances of e-Pi-i interference positioning Perspective.., is well established in the above video, thank you. Ie relative mathematical statements are genuinely discrete relativisms because it's pivotal on e-Pi-i omnidirectional-dimensional substantiation, primary probability dominance, not the connected, paradoxical illusion of particular, absolute/discrete objects. The "problem of perceived reality", is a very naturally dualistic polarization at 1-0D Central Limit Eternity-now Superspin, ie, zero-infinity difference distribution spectrum =>everything is Polar-Cartesian AM-FM Timing-spacing coordination in Temporal omnidirectional-dimensional Origin.., the "exploded view" of a time loop-projection, relative-duration, value-ratio timing, Monopole-Universe. "No one's right if everyone is wrong" about Totality as a static eternal object instead of objective positioning Actuality.

[@drdca8263]

Are you familiar with the psychological phenomenon of “clanging”? It isn’t what is happening here, but,... Clanging is a thing where a person will associate words based on the similar sounds, and may end up stringing them together unintentionally, as if they make sense. For example, one might answer a question with “I took it this morning.” and then follow that up with “It was a warning. A warning of danger.” When “warning” had nothing to do with the original context. And, this phenomenon can apparently happen without the person even realizing that they are doing it / that it is happening to them. It is associated with mania and schizophrenia. It is related to the idea of word salad/schizophasia.

[@ailblentyn]

Yes, photons can have any energy, but light does consist of photons. I think THAT is the discreetness people are thinking of there.

[@i.m.9823]

I'm wondering, if we accept the view that the current quantum state of the universe emerged from the Hartle-Hawking wave function and that there's a single giant wave function describing the entirety of the universe, wouldn't it follow that it's a bound quantum system with discrete eigenvalues? Put differently, aren't "single free particle wave functions" solutions to the Schrödinger's equation basically an artifact of simplification, not actual things that occur in nature? Granted, the eigenvalues of a universal wave function would be 𝙚𝙭𝙩𝙧𝙚𝙢𝙚𝙡𝙮 fine, but still arguably and mathematically discrete and not continuous. Unless I'm missing something. 🙂

[@kennarnett8220]

Greetings! About the 2:44 mark you mentioned a concept that you would cover at another time. I didn't quite make that out because I have a hearing disorder. Can you spell it out for me? Be safe and stay well!

[@paulkohl9267]

At 2:44: attenuation? Strange that at the heart of reality ordering of products matters so much.

[@monkerud2108]

Well photons are discreet in the sense of them being individual particles but they are still part of a broader phenomenon with wave effects. The most discreet thing about how we deal with light is measurement, when we use a photomultiplier the workings of the device is essentially measuring a binary thing, light hitting it or not, this doesn't necessarily mean the light hitting the multiplier is localised like the conjecture of photons suggest. The trouble is that we cannot test our theories beyond the current measuring techniques, and atoms and photomultipliers seem to be consistent with photons, but they can still be consistent with other mechanisms that produce the same statistical outcomes for experiments.

[@robertschlesinger1342]

Interesting and worthwhile video.

[@17ultralimited69]

A definition of discrete as it applies to quantum mechanics would have been helpful.

[@Raging.Geekazoid]

1:45 but the magnitude of the electron field (and all other fields, apparently) is discrete. You can't have fractional particles. Back in the olden days (pre-19th-century), people thought matter might be infinitely divisible.

[@dennisdonovan4837]

I could not have said it any better … it’s all about “exactitude” … absolutely no doubt about … ❤️😎❤️

[@lewhughes3079]

Brilliant explanation, thank you for making me think differently about Quantum Mechanics.

[@jamesblank2024]

Sabine, I interpret you are saying free particles have non-discrete energy as opposed to bounded particles. Both are described by quantum mechanical wave equations.

[@sockenschuh2452]

oh my god, thank you! Ever since I read in my physics textbook that space and time were parted in discrete steps i thought that could not be quite right! (the discreteness part not the quantized)

[@billrock6734]

Or as somebody might have said but probably didn't, Discretion is the better part of valence....

[@MichaelPiz]

Ouch.

[@christianlibertarian5488]

A neutron walks into a bar. The bartender says.......

[@n2185x]

@@christianlibertarian5488 -- "Not very attractive, are you?"

[@mohammedj2941]

In fact, even in a classical theory we can have quantized quantities. An example would be the wavelength of a wave with fixed boundaries.

[@whiteboar3232]

Space and time not necessarily have to be discrete, but they could be... right?

[@SabineHossenfelder]

It is very difficult to make this idea compatible with already existing tests of general relativity.

[@jmcsquared18]

In principle, sure, spacetime could be discrete. But I doubt it. Some recent observations, for instance, cast doubt on the most direct modifications of relativity. kzbin.info/www/bejne/qmXWontsmamXo9U

[@whiteboar3232]

@@SabineHossenfelder I find discretization fascinating because many physical phenomena becomes very simple in discrete spacetime: for example, the Laplace equation becomes the most simple smoothing filter on a discrete grid.

[@Gringohuevon]

@@SabineHossenfelder Which is approximate

[@09bidon]

@Sabine Hossenfelder, every measurement, every concrete calculation give discrete values (what is stored in a computer), how an empirical test of a theory could prohibit a theoretical discretization ?

[@Grstearns]

It's one of those things where after you hear it, it becomes obvious. Even if a photon is released at a very particular wavelength, it can be red shifted an arbitrary amount and you don't have to worry about quantization until it interacts with another atom.

[@최진형-u2q]

What is the meaning of 'discrete'? We should know it first. Are real numbers continuous? Yes. But how about integers? No. Although number of integers is infinite. Same thing happen in hilbert space since hilbert space is always countable as it's definition. The number of eigenvalues of observable operators which are hermitian, operating on wave-function in hilbert space can be infinite if dimension of hilbert space where our wave-function lives in is infinte. But although dimension of hilbert space can be infinite, it is countable infinite. Therefore set of eigenvalues of observable operator can not be continuous. Although physicists treat it is continuous, actually it's not. I think this is the meaning of 'discreteness' of quantum theory. But still it does not have trouble to treat it as a continuous in many practical problems. And quantization does not care much about such 'discreteness' but commutation relation(it's consequence is uncertainty principle) as this video says. One more thing. We should distinguish what are parameters and observables in the model we deal with. Position can be observable, but in many cases we just deal it as a parameter in qft. Since parameters are just living in our mind to develop the theory, it can be continuous(in our mind). However when we want to measure it(like position or crystal-momentum or etc), we can not get the continuous value but discrete.(actually crystal-momentum space in Bloch theorem is not continuous) Therefore we should choose what is parameters and what is observable first to say this should be discrete or not.

[@jusiphstolin8074]

What's continuous depends on the choice of topology on your set

[@scienceexplains302]

Sabine Hossenfelder , Did you explain why not? You said they can have any value. That is the refutation as promised, but if you gave any demonstration of how energy values can be sub-Planck, I missed it. Can light have half a proton of energy? (I am probably not using the terminology correctly)

[@TheBerryheerschop]

Great video but I still don't understand a specific issue. As I understand it, it was Planck who postulated that energy could only be emitted in quantized form, for which the formula E=hv calculates how much electromagnetic energy a specific frequency can emit. Since h is a constant, the way for energy to be continuous is that the frequency is allowed to be any value. Is this correct?

[@fanstream]

Clear, concise - thank you, Bee!

[@bigstroker1300]

Sabine please make a video about quantum entanglement (Einstein - Podolsky - Rosen experiment, Bell inequality).

[@danielpopa4482]

Thank you for explaining such important and awesome subjects!

[@cmilkau]

Absorption lines: if the photon energy is high enough to ionize, does the effect go away? After all, excess energy can go into excess kinetic energy of the free electron in that case.

[@katgirl3000]

Oh nice! I've been thinking of going off and solving some QM exercises!

[@piotrm9260]

When we look at the wave function we think QM is not about discretisation. But when we see how QM or nature deals with the attempt or desire to divide single particle ( or analogous values at it's minimal quantity) we see it is about quantisation indeed, but not in a sense of discrete fields or spaces. Piotr

[@spirogyra9761]

Sabine, there is an error in the graphic showing an electron transitioning from n=1 to n=3 and emitting a photon. Obviously the photon is absorbed not emitted for such a transition..

[@georganatoly6646]

It may have been beneficial to provide some examples you've encountered where people have expressed this misunderstanding. I'm not sure how or why someone would find value in trying to describe energy in relation to frequency discretely versus the more natural continuous approach.

[@SabineHossenfelder]

Plenty of examples of this in my KZbin comment sections... Why embarrass someone in particular? It seems very impolite.

[@georganatoly6646]

@Reckless Abandon Could you describe mathematically this 'discrete energy' those photons have? I'm having a hard time imagining what exactly you mean by photons with a discrete energy.

[@tannerfaust433]

@@SabineHossenfelder politeness has never seemed your mantra, though.

[@davidsweeney111]

Excellent, looking forward to learning from this qm series! thanks :)

[@jimbuono2404]

Perhaps the real issue is with the meaning of 'discrete'. If we take the common meaning 'separate and distinct' we can apply that to planck length which google says is defined as "In physics, the Planck length, denoted ℓ P, is a unit of length that is the distance light travels in one unit of Planck time." Once you define planck time you have specified a distance since we know the speed of light. This value is certainly 'separate and distinct' although in quantum physics it may actually not be so straightforward as language assumes everything to be settled once defined.

[@climbeverest]

Your English is perfect, incredible explanations

[@steenandersen4248]

In the last 6 months I've experienced an unexpected attraction to your videos, perhaps even a mild addiction. Subjects, production, delivery, personality in High quality. A bit puzzling given that I have no real understanding of the presented subjects beside a healthy interest and curiosity in scientific matters. But who cares!? :) Thank you!

[@neilcreamer8207]

@Sabine Hossenfelder You said that "atoms can only absorb and emit light only at certain frequencies" and this is now the agreed view. It makes sense in view of principles of frequency and resonance. However, this is now understood to mean that only whole quanta can be absorbed or emitted. Planck produced a second theory that absorption was continuous while only emission obeyed this 'whole quantum' stipulation. Could you say something about why Planck's view is no longer accepted?

[@massecl]

The whole quantum has the energy equal to the difference of the level energies. This is true as well for emission as for absorption.

[@tomjohn8733]

Thank you for the clarification...!!!

[@michealcherrington6531]

Can anything move a distance smaller than the Planck length? Or can a Schwarzschild radius smaller than the Planck persist/exist? Can any event take less time than Plank time to effect a delta? The interpretation of the "speed" of various frequencies from distant EM sources, a few years ago, seemed to indicate that space is not quantized. So contiguous propagation should be possible but is it in QM?

[@MichaelPiz]

So, relative to what you say in this video, what does the Planck length mean?

[@SabineHossenfelder]

I have a separate video about this kzbin.info/www/bejne/pKqzlXx4o7yCea8

[@MichaelPiz]

@@SabineHossenfelder Wonderful! Now that I've seen both videos, I should have an unshakeable Theory of Everything™ by Tuesday. ;)

[@frankdimeglio8216]

Frank DiMeglio has mathematically unified physics. This is an acknowledged and a clear fact.

[@alphaomega1089]

A discrete function is a function that has individual and separated values. The four forces are measured that way. The idea of discrete meaning individual or detached was given to the atom then that singularity then that unmeasurable Q-bit. Space-time is quantized. Time is taken to be the navigation between one event to another relative (energy consumption) to a space-time coordinate reference point. I should say it isn't about discreteness. That's why there is a need for that TOE or GUT. How are they all bound? How are they separated? It is about measuring events which are noticeably different. Words are not the problem. It is their agreed-on definition by those using it.

[@massimiliano-oronzo]

I prefer the definition that quantum theory has operators for observables which do not commute. If we start from this point, Heisenberg's uncertainty relationships can be deduced. I consider the first definition, the one based on the uncertainty principle, only a consequence of how the theory developed from the historical point of view. But if I have to say what is the profound principle behind quantum mechanics, I say Non-commutativity. I think about this very often.

[@SabineHossenfelder]

Yes, I would agree with this. Alas, the operator algebra is only half of the theory. You also need the space which it acts on.

[@musicalBurr]

"operators for observables which do not commute" - Oooh! Can't wait for that lesson! :-)

[@josephtraficanti689]

Succinct and elegantly put! While I blather on your efficiency is wonderful. I will try to emulate your method. 🗒😯

[@spiderjuice9874]

I have always thought that the energy of a photon emitted by an atom when an electron drops from a higher to a lower energy level can be considered as a 'dependent' (or secondary) quantisation, as the photon's energy can be only certain values depending on the relative energy levels of the electron's atomic orbitals (which can be considered the 'independent' (or primary) quantisation for the system considered - ie., the atom in question). Changing the system (ie. choosing another atom) will result in different dependent quantisation of the photon through a corresponding shift in the independent energy levels of the second atom relative to the first atom. What we see then are photons of discreet energy, but they just reflect the underlying discreetness of a more fundamental property of nature - in this case, the relative energies of atomic orbitals; photons can have any energy in general. Please correct me if I'm wrong!

[@markfernee3842]

Photons are quanta and their energy is related to their frequency by Planck's constant. That's the only constraint. Furthermore, a real photon does not even have a precise energy because it is generally represented by a wave packet. Thus the single quantum can actually have a range of possible energies. The real constraint is that a single quantum can only be absorbed locally. A photon, as a quantum of action, represents the propagation of some local action (emission event) to another local action (absorption event). This is the wave-particle duality nature of the quantum. It propagates as a wave, which is nonlocal, but can only result in a local action. This property of quanta ultimately explains how we can see distant stars and galaxies. In a classical theory, the energy emitted by a distant star would disappear into the thermal noise according to the inverse square law. But because visible quanta have energies about one hundred times the thermal background, they can still be detected by simple accumulation in a CCD camera for example. A classical theory would allow the energy at any frequency to smoothly fall to zero, which would result in a signal to noise threshold below which distant stars couldn't be detected. As no such threshold exists, we are able to see far back towards the beginning of the universe. In fact, the quantization of the action is the real consequence of quantum theory. The fact that one local action must propagate to another local action is really behind all fundamental particle theories, and Feynman diagrams, and explains why all force carriers have an associated particle. Yet propagation is described by a wave equation, which is distinctly nonlocal, and this must be the case to explain quantum interference.

[@calcal5135]

Sabine Which observables are always discrete regardless of the system? Spin? Angular momentum?