Explaining Quantum Mechanics | John Horgan & Tim Maudlin [Mind-Body Problems]

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  • Опубліковано 19 гру 2024

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  • @KipIngram
    @KipIngram 2 роки тому +2

    29:41 - I'm glad there was an opportunity to clear this up for the host. People really do get the superposition thing wrong, and it was great that Maudlin pointed out that *all* quantum states are superpositions in infinitely many ways. What you CAN say, that means something, is that each observable defines a *basis* (the set of eigenvectors of that observable), and some arbitrary vector can either be a superposition IN THAT BASIS or else it can be a non-superposition IN THAT BASIS (meaning that it's EQUAL to one of the eigenvectors). Before you can start saying "yes/no" about a state being a superposition, you have to select a basis.
    Also, it just kills me that people talk about quantum systems being in more than one STATE at a given time. No, no, no - the quantum system is always in A state. One. In some chosen basis, you may need more than one basis vector to express the state, or a single basis vector might do the job. But in any case that total state is THE state that the system is in.

    • @Creationweek
      @Creationweek 2 роки тому +1

      "Talk about quantum in more than one state"
      so this seems to be imprtant, but your explanation isn't enough. Super position implys infinite possibility so it seems there is some conflating going on between superposition and quantum state. Can you clarify?

    • @jceepf
      @jceepf 10 місяців тому

      @@Creationweek The equations for sound vibrations are a little analogous. If you take a string, it can produce many harmonics (notes). The harmonics are the eigenstates of the string "energy". Depending how you pinch the string, the state of the string will be different, ie, the sound produced by the sting will differ in timber.
      The state will jn general contains many harmonics. It is not a "pure" state. But it is a "state" by definition. A pure state contains a single harmonic, a single note.
      It is hard to get deeper without pencil and paper.....

  • @DaveGilbertPhD
    @DaveGilbertPhD 3 роки тому +1

    Thank you John and Tim for taking the time to help us learn. I'm grateful!

  • @jps0117
    @jps0117 3 роки тому +18

    Math is easy. Screen sharing is hard.

  • @robbie_
    @robbie_ 3 роки тому +3

    Dr Maudlin is always interesting. Great talk, thanks both.

  • @BarryKort
    @BarryKort 3 роки тому +4

    In QBism, the mathematics doesn't describe the system, but only describes the would-be observer's limited state of knowledge about the system prior to taking a measurement. Yogi Berra famously said, "You can see a lot just by looking."
    The real problem with Bell's Inequality is that it overlooks the fact (from GR) that time-keeping is local. Clocks tick at independent rates when they are separated by any distance from each other. Why does independent time-keeping at a distance matter? It matters if the state of the particle is not a fixed constant but some kind of oscillation. In the case of spin, go back to the simple example of a spinning top. You might initially think that the orientation of the spin axis is a fixed direction in space (and therefore not a function of time). But suppose that the top isn't just spinning on its axis, but also precessing. Now time-keeping does matter because as it precesses, its instantaneous spin axis is leaning in a time-varying cycle. As three otherwise identical tops move off in different directions, the instantaneous phase of their precession desynchronizes (decoheres) unpredictably. When you admit of time-varying precession around a mean spin axis, and you also admit of desynchronization (decoherence) due to the absence of a cosmic clock with uniform time-keeping everywhere and everywhen, the violation of Bell's Inequality becomes obvious and easily explainable.
    So for Einstein, it's not spooky action at a distance, but not-so-spooky time-keeping at a distance that one must fold into the model in order to appreciate the violation of Bell's Inequality.

    • @schmetterling4477
      @schmetterling4477 2 роки тому

      Yes, you completely misunderstand the problem. ;-)

    • @david203
      @david203 2 роки тому

      That's a little like looking at Einstein's view of special relativity and saying, well, maybe the interesting analysis doesn't have to do with having the same physics in different inertial frames of reference, but has to do with the necessary errors in having two local clocks to observe locally. The flaw here, of course, is that the theory doesn't depend on clocks. It only depends on observations of events (via photons) among observers in different frames. If you assume that the speed of light in vacuum is constant (which is shown to high accuracy in experiments), and you assume causation (you want to see a cause happen before its result), then special relativity is true regardless of clocks. All you need is a movie clapper, an event that can be observed from different speeds at the same time.
      Similarly, our choice is not spooky action at a distance or indeterminate local clocks. Theory (John Bell) and experiment (many) both confirm the nonlocality of quantum mechanics, period. Whether any clocks used are accurate or inaccurate.

    • @david203
      @david203 2 роки тому

      @@schmetterling4477 The usual arrogant and insufficient comment from Schmetter...

    • @david203
      @david203 2 роки тому

      @@schmetterling4477 It doesn't require being a king or even very wise to recognize when someone is being arrogant and lazy, as you often do. But I certainly don't expect you to have any objectivity when it comes to your own behavior, and don't expect you to change. I'll just try to let this go. As for the Internet, most folks here can ignore folks like you. I'm a bit more sensitive, since I've got quite a strong ego myself and often get myself into trouble. I'll try to let this go, as squabbling on UA-cam is not good behavior for either of us. But if you're going to disagree with good physics, I do expect you to give reasons for your disagreement. That's my only real point.

    • @BarryKort
      @BarryKort 2 роки тому

      @@david203 ~ Alas, we are not in an inertial frame of reference, so we cannot assume Special Relativity. We are in a non-inertial frame of reference, so we must employ General Relativity, where clocks separated in space do not keep time at the same rate.

  • @stephencarlsbad
    @stephencarlsbad Рік тому +1

    I love the interviewers inquisitiveness! Great questions and desire to understand! It helped cement my understanding of the wave function by verifying it through a respected authority figure like Tim Mauldin.

  • @Fatzers
    @Fatzers Рік тому

    This was great! Hoping for part 2 maybe

  • @MrandMrsStuckey
    @MrandMrsStuckey 10 місяців тому

    I've been working to understand quantum mechanics (QM) since 1994 and I always love watching Tim Maudlin explain the mysteries from a "constructive" perspective (a la Einstein's constructive versus principle theories). Tim is brilliant and has spent over 30 years working out all the consequences of the constructive accounts of QM and he concludes that had Einstein lived to see the violation of Bell inequalities, he would have changed special relativity to include a preferred frame. But, Einstein was faced with a very similar situation concerning constructive accounts of the Michelson-Morley experiment, e.g., luminiferous aether theories, and instead of choosing a preferred frame he went to a principle account. He wrote: "By and by I despaired of the possibility of discovering the true laws by means of constructive efforts based on known facts. The longer and the more despairingly I tried, the more I came to the conviction that only the discovery of a universal formal principle could lead us to assured results." That is, he gave up looking for causal mechanisms ("constructive efforts") that would shrink meter sticks and slow down clocks to fool everyone into measuring the same value for the speed of light c, regardless of their relative motions (an empirically discovered fact known as the light postulate). Instead, he said c is a constant of Nature per Maxwell's equations, so the relativity principle -- the laws of physics (including their constants of Nature) are the same in all inertial reference frames -- demands that everyone measure the same value for c, regardless of their relative motions. The Lorentz transformations of special relativity follow from that fact. As it turns out, the same opportunity for QM has been provided by quantum information theorists. That is, they have reconstructed QM based on an empirically discovered fact called Information Invariance & Continuity that (in non-information-theoretic terms) means everyone measures the same value for Planck's constant h, regardless of their relative spatial orientations. So, I think it's possible that Einstein would have justified this "Planck postulate" with the relativity principle just like he justified the light postulate and gave up "constructive efforts" at understanding QM, accepting QM as a principle theory like his special relativity. My colleagues and I explain all of this in a book forthcoming with Oxford University Press in summer 2024 called, "Einstein's Entanglement: Bell Inequalities, Relativity, and the Qubit." Look for it 🙂

    • @schmetterling4477
      @schmetterling4477 Місяць тому

      You are looking in all the wrong places. Quantum mechanics follows trivially from special relativity. Folks like Maudlin just don't have enough physics intuition to tell you that.

  • @isonlynameleft
    @isonlynameleft 2 роки тому +2

    Love this discussion!

  • @kpunkt.klaviermusik
    @kpunkt.klaviermusik 2 роки тому +1

    I like Mr. Maudlin's explanation of superposition @ 30:20

  • @projectmalus
    @projectmalus 3 роки тому +3

    That diagram sure helps. You guys are awesome!

  • @robocop30301
    @robocop30301 2 роки тому +1

    This is a great talk! Thank for sharing!

  • @zvikabar-kochva3641
    @zvikabar-kochva3641 2 роки тому +2

    Good discussion, l'm really encouraged by Dr. Maudlin approach and clarity of mind. However, I was puzzeled as to why he didn't mention the measurement problem as the most difficult issue within QM. According to this year's physics nobel lauraete, Roger Penrose, this problem makes the theory not only incomprehensible but also inconsitant because, according to him, in a recent conversation with Dr. Jordan Peterson, the collapse, as described by the formulation, is not a physical process, yet, after measurement one must update the quantum state (I.e. the wave function). Moreover, the way he addressed the 2 slits experiment as kind of pretty standard outcome wave pattern, doesn't do it due justice, because if the particles are waves, why, each particle, say I individual electrons, shows as singular concentrated dots, on the photographic plate? Surely, that not classical wave behavior. Moreover, when the electron's wave function collapses, it does it instantly, for the entire detector all at once, as to ensure single location of detection. Thus, this spooky action at a distance correlate to all occurances of collapes, not only to specific kind of entangled states of 2 or more particles.
    doesn't necessa

    • @zvikabar-kochva3641
      @zvikabar-kochva3641 Рік тому

      @@BobbyT-yj1cw Would you care to explain it so Mr. Penrose and I, as well as Sabine Hosenfelder would be enlightened?

  • @mechannel7046
    @mechannel7046 2 роки тому +1

    45:20 Bell's Theorem

  • @aclearlight
    @aclearlight 2 роки тому +1

    Position and spin of a single particle can be entangled? I would like to hear more details on that or get a link to source literature.

  • @MrandMrsStuckey
    @MrandMrsStuckey 10 місяців тому

    Also, John, I don't know why Tim cut you off when you were getting ready to relate superposition to the mystery of entanglement. Tim is right of course that the superposition of product states creates the entangled states and that's important mathematically, but superposition for each particle is also directly related to the mystery of entanglement conceptually. Suppose you send a vertical spin up electron to Stern-Gerlach magnets oriented at 60 deg relative to the vertical. Classical superposition of angular momentum says you should measure (hbar/2)cos(60) = hbar/4 in that direction. [The other component of the classical superposition (the orthogonal direction) would be (hbar/2)sin(60) of course.] But quantum superposition says you always get +/- hbar/2 for a spin measurement, so you can't get what you expect from common sense classical physics. Instead, QM says the probability of a +hbar/2 result is 0.75 and the probability of a -hbar/2 result is 0.25 so the average is (hbar/2 + hbar/2 + hbar/2 - hbar/2)/4 = hbar/4. In other words, quantum superposition means you get the common sense classical result on average only. [Aside: Steven Weinberg pointed out that when you measure the spin of an electron you're measuring Planck's constant h, so you could view quantum superposition like the light postulate of SR. That is, everyone measures the same value for h, regardless of their relative spatial orientations. Quantum information theorists have used this fact for the qubit to derive the Hilbert space of QM (they call it Information Invariance & Continuity), so the kinematics of QM follow from this "Planck postulate" just like the kinematics of SR follow from the light postulate. And the relativity principle justifies both of these empirically discovered facts (No Preferred Reference Frame at the Foundation of Quantum Mechanics, Entropy 2022, 24(1), 12).] Now suppose Alice and Bob are measuring the spin singlet state and Alice obtains +hbar/2 vertically and Bob measures his particle at 120 deg relative to Alice. Obviously, if Bob had measured vertically he would have obtained -hbar/2, so at 120 deg Alice says he should get hbar/4 per our single particle example. But of course Bob must measure the same value for h that Alice does, so he can't get the fractional value of h Alice says he should (otherwise Alice would be in a preferred reference frame). Instead, his outcomes at 120 deg corresponding to Alice's +hbar/2 outcomes vertically average to hbar/4 per quantum superposition just like the single particle case. And, of course, the data are symmetric so Bob can partition the results according to his +/- hbar/2 outcomes and show the same thing about Alice's results. In the end, Alice partitions the data per her +/- hbar/2 outcomes and says Bob's results must be averaged to satisfy conservation of spin angular momentum while Bob's partition shows it's Alice's outcomes that must be averaged (Answering Mermin’s challenge with conservation per no preferred reference frame, Scientific Reports volume 10, Article number: 15771 (2020)). This should remind you immediately of an analogous situation in SR. There when Alice and Bob occupy different references frames via relative motion, they partition spacetime events per their own surfaces of simultaneity and show clearly that each other's meter sticks are short and their clocks run slow. Sorry to prattle on, but I wanted to get that cleared up 🙂

  • @mickdaly2778
    @mickdaly2778 Рік тому +1

    Thanks for this conversation John. Tim Maudlin seems to be one of the few modern physicists with a brain.

  • @Osama_Abbas
    @Osama_Abbas 3 роки тому +12

    Always pleasure to watch Tim Maudlin's interviews. Maudlin does not get the attention he deserves, while mediocre "physicists" get all the attention and they are always invited to give their half baked opinions in matters that they barely understands.

    • @schmetterling4477
      @schmetterling4477 2 роки тому

      He doesn't get attention because he is a babbling fool who doesn't understand physics. That is what philosophy does.

    • @stephencarlsbad
      @stephencarlsbad Рік тому +1

      He's got my attention!😅
      He's the only one that knows what he's talking about.

    • @stephencarlsbad
      @stephencarlsbad Рік тому +1

      ​@@BobbyT-yj1cw Ok, but why are you so desperate for attention?
      I think everyone wants to know why you're so needy?

    • @stephencarlsbad
      @stephencarlsbad Рік тому

      @@BobbyT-yj1cw Why would you think someone as needy as you would be offensive to me or anyone?😂
      I feel sorry for you.
      I wish I knew how to help needy, narcissistic people like you.🙏

    • @stephencarlsbad
      @stephencarlsbad Рік тому +1

      @@BobbyT-yj1cw Btw, Im very happy and you dont offend me. How can someone be offended by someone they look down on?

  • @truebaran
    @truebaran 2 роки тому

    Could someone explain why in 48:40 we get those quantum predictions? I would be grateful

  • @siddhantdas6401
    @siddhantdas6401 3 роки тому +1

    This is therapeutic ... thanks so much !!

  • @abdouabdel-rehim8537
    @abdouabdel-rehim8537 2 роки тому +1

    Man. Finally someone got to say these things instead of saying just shut up and calculate.

    • @schmetterling4477
      @schmetterling4477 2 роки тому

      Yes, and they told you absolute bullshit. That is what philosophers do. ;-)

    • @carlhitchon1009
      @carlhitchon1009 2 роки тому

      @@schmetterling4477 That response is lame. What bullshit? Prove that it's bullshit or shut up.

    • @schmetterling4477
      @schmetterling4477 2 роки тому

      @@carlhitchon1009 Dude, I can't teach you physics. That's 5-8 years of full time study. If you aren't willing to do it yourself, then nobody will do it for you. ;-)

    • @carlhitchon1009
      @carlhitchon1009 2 роки тому +1

      @@schmetterling4477
      OK you've given yourself away.

    • @schmetterling4477
      @schmetterling4477 2 роки тому

      @@carlhitchon1009 You mean as a physics PhD? All you had to do was to ask. ;-)

  • @tractorpoodle
    @tractorpoodle 2 роки тому +1

    Superb. Thanks.

  • @CancelledPhilosopher
    @CancelledPhilosopher 3 роки тому +3

    Quantum mechanics is endlessly fascinating and complex.

  • @KipIngram
    @KipIngram 2 роки тому +2

    32:50 - Ok, this is fascinating. HOW have we done such a poor job conveying these very basic and non-controversial ideas to even *interested* members of the general public? All this stuff being discussed right in here isn't even part of what makes quantum theory "strange" - this is just standard wave theory and applies to all waves of any kind. Maudlin already said it earlier - it's *entanglement*, and particular entanglements that exhibit non-locality, that forces a departure from classical ideas. If early training in quantum theory conveys ANYTHING to the student, it should be a clear picture of these exact things - where these boundaries between what's classical and what's not are. Yes, quantum waves carry probability (well, not quite, but something that can easily yield probability) where as EM waves, for example, carry ENERGY. But they're still both waves, and they still share a lot of behavioral characteristics. The unusual step that comes in in quantum theory doesn't show up until you DETECT something - in the quantum case you don't measure that smooth spread out wave - you get a particle, all in one place. Now THAT is unusual compared to, say, EM theory.

    • @carlhitchon1009
      @carlhitchon1009 2 роки тому

      Yes, the nonlocal aspect is something that many physicists want to sweep under the rug, no matter how complex and indecipherable the broom required to do so.

    • @schmetterling4477
      @schmetterling4477 Рік тому

      @@carlhitchon1009 There is no non-local aspect to quantum mechanics. There are only people who don't understand physics. ;-)

    • @carlhitchon1009
      @carlhitchon1009 Рік тому

      @@schmetterling4477 Big claim, no evidence.

    • @schmetterling4477
      @schmetterling4477 Рік тому

      @@carlhitchon1009 Ma, there is the kid who didn't pay attention in special relativity class! ;-)

    • @schmetterling4477
      @schmetterling4477 Рік тому

      @@BobbyT-yj1cw Jump! :-)

  • @MoshkitaTheCat
    @MoshkitaTheCat Рік тому +1

    Brilliant ❤️

  • @yacc1706
    @yacc1706 2 роки тому

    45:07 shared screen: GHZ state

  • @voidisyinyangvoidisyinyang885
    @voidisyinyangvoidisyinyang885 3 роки тому +2

    "If I live in a two-dimensional world, I can't use the right hand rule because I can't use my thumb sticking out. So there is something incongruous about the mathematics [of scalar curl]"
    Tim Maudlin

    • @david203
      @david203 2 роки тому

      Curl isn't defined for two dimensions.

  • @BS-lk3jg
    @BS-lk3jg 3 роки тому +1

    great talk thank you

  • @MrandMrsStuckey
    @MrandMrsStuckey 10 місяців тому

    I don't know why UA-cam is striking out some of my last post. Hopefully, someone gets that fixed.

  • @glaubs65
    @glaubs65 Рік тому

    I love it when philosophy of science professors from New York struggle with technology

  • @khufu8699
    @khufu8699 3 роки тому +1

    Basically what you are saying is we need to get back to logical models and systems design from a real world perspective. The models should support the math and visa versa.

  • @TheGrahamBrechin
    @TheGrahamBrechin 2 роки тому +1

    This might sound mad, but could it be possible that our observable universe is actually contained within a black hole? .... perhaps the missing matter and energy are outside of our host black hole?

  • @yacc1706
    @yacc1706 2 роки тому +1

    28:00 sorry John! But your face changed to suffering look when Tim began to talk about vector space ;-) BTW superb explanation by Tim 29:07. 36:50

  • @fractalnomics
    @fractalnomics Рік тому

    11:27 14:37

  • @yacc1706
    @yacc1706 2 роки тому

    1:13:18

  • @yacc1706
    @yacc1706 2 роки тому

    7:00

  • @yacc1706
    @yacc1706 2 роки тому

    1:13:57 thanks

  • @isonlynameleft
    @isonlynameleft 2 роки тому

    Single particle quantum mechanics is pretty accessible but relativistic quantum field theory is pretty hard.

  • @yacc1706
    @yacc1706 2 роки тому +1

    14:58 "no,no,no" me too!

  • @h7283
    @h7283 3 роки тому +1

    Quintum meckanicks ain't so difficult ya'll. Juss remember the big old

  • @KaliFissure
    @KaliFissure 2 роки тому +2

    Try having a mind without a body.

    • @schmetterling4477
      @schmetterling4477 2 роки тому

      Let's do this experimentally. I have to wonder how many philosophers will volunteer. ;-)

    • @yourlogicalnightmare1014
      @yourlogicalnightmare1014 2 роки тому +1

      You reject your direct experience as any valid source or measure of truth, so your knowledge will always be limited to the very narrow scope that science provides

    • @schmetterling4477
      @schmetterling4477 2 роки тому

      @@yourlogicalnightmare1014 You sound like a drug user just now.

    • @KaliFissure
      @KaliFissure 2 роки тому

      @@yourlogicalnightmare1014 Duh. Everyone knows that their thinking is limited by their experience and cognitive processes.
      But you can't have anything without a physical foundation. That's what "things" are.

    • @yourlogicalnightmare1014
      @yourlogicalnightmare1014 2 роки тому

      @@KaliFissure
      You misunderstood the comment.
      There's a vast wealth of information to be had in the realm of existence that is out of reach of science. You'll never examine that information because it isn't falsifiable. For example, if you had a massive heart attack and were clinically dead for 20 minutes, and during that time you directly experienced watching doctors work on you from above, then you were shot out of the universe until it was a tiny spec in the vast distance, and you were able to suddenly know, witness, and experience all your past lives instantaneously, interact with relatives who had passed, you merely become curious about something and instantly have full knowing of all that is knowable about said thing, and much more, .... you would reject the entire experience as a pile of materialistic nonsense created by your dying brain.
      In other words, you reject every bit of knowing or knowable information obtained through direct experience that cannot be examined under a microscope or falsifiable by science. That rejection of your own mind drastically limits the knowledge you'll ever be able to "possess"
      Materialist zealotry is as big a chokehold starvation of the brain as is religious belief.

  • @idegteke
    @idegteke 9 місяців тому

    I just don’t understand how this two utterly incompatible expression “quantum” and “mechanics” could ever meet in a single expression. This expression, in itself, has a dual nature:)

    • @idegteke
      @idegteke 8 місяців тому

      ​ @LisaBlooper Mechanics: “the branch of applied mathematics dealing with motion and forces producing motion”, quantum: “a discrete quantity of energy proportional in magnitude to the frequency of the radiation it represents” but what’s actually meant was more like subatomic particles - Now, since “quanta” or rather subatomic particles don’t always seem to have a full set of independently defined physical attributes (like spatial position, momentum) and don’t necessarily interact with all forces, it is not a logically sound idea to try to apply mechanics to them, while mechanics deals with mathematically computable changes in spatial position (which some quanta don’t even have) in connection to forces applied on them (some of which forces might not even effect some “quanta”). Please help me to understand how these two (like weight of colors, almost) could ever form a single expression to begin with. (I can see your blood pressure rising:)

  • @yacc1706
    @yacc1706 2 роки тому

    2:45 a pity

  • @edwardlarson6110
    @edwardlarson6110 Рік тому

    The central dilemma of quantum mechanics? It can't tell a story of nature. It can't answer basic questions of what, where, when, and how.

    • @schmetterling4477
      @schmetterling4477 Рік тому

      Except that it can explain any and all matter and radiation related phenomena. You need to pay better attention in school, kid. ;-)

    • @schmetterling4477
      @schmetterling4477 Рік тому

      @@BobbyT-yj1cw That your mother didn't give you any attention does explain why you are trolling, though. ;-)

    • @schmetterling4477
      @schmetterling4477 Рік тому

      @@BobbyT-yj1cw I am troll hunting. You are making this way too easy. ;-)

    • @schmetterling4477
      @schmetterling4477 Рік тому

      @@BobbyT-yj1cw Now you are mimicking a bot? ;-)

    • @schmetterling4477
      @schmetterling4477 Рік тому

      @@BobbyT-yj1cw That's OK with me, too. ;-)

  • @enochbrown8178
    @enochbrown8178 2 роки тому +1

    OK, listen. You lost me with the GHZ set-up. Maybe I'm too damned stupid to catch on, but I think something is amiss with your explanation.

  • @god_damn9661
    @god_damn9661 3 роки тому +1

    very painful listening at times cuz of the host is out of touch!!!
    Tim very patient correcting his bad formulating long confused questions!!!
    science rocks!!!🤘

    • @david203
      @david203 2 роки тому

      And sometimes physicists themselves make long confused explanations that obscure more than clarify, particularly if they are believers in the standard interpretation of QM (Copenhagen), with all its axiomatized mysteries.

    • @yourlogicalnightmare1014
      @yourlogicalnightmare1014 2 роки тому

      I love the "vast depths of knowing" that science can't touch, as science can't tell you what anything is, only how it behaves.
      Science sucks 🤘

    • @david203
      @david203 2 роки тому

      @@yourlogicalnightmare1014 Science sucks as compared to what? Where do you find out what anything is? Religion? Your imagination? Certainly not your senses, which are almost useless for investigating the atomic scale of nature. No, science is all we have to understand what nature really is, its ontology. The great thing about science is that it doesn't have to pretend that it is complete or accurate. It improves over time, thanks to thousands of scientists who think, theorize, observe, and conduct experiments.

  • @vectorshift401
    @vectorshift401 3 роки тому +1

    Physics has always been about prediction.

    • @schmetterling4477
      @schmetterling4477 2 роки тому +1

      No, it hasn't. Next!

    • @carlhitchon1009
      @carlhitchon1009 2 роки тому

      Do you think Newton had a burning desire to know the precise future positions of the planets?