Every time I see a physical or experimental explanation of superposition it seems like what's actually described is an object that isn't actually "in both states at the same time" but is actually "in neither state" because the actual state is the combination of multiple factors. For example, the 45 degree polarization isn't both vertical and horizontal, it's just describable as a combo of the two, it "is" 45 degrees. And we only say it "collapses" to either vertical or horizontal because our measurement device forces it to align to either vertical or horizontal. That's not a measurement, it's a filter. And the entropy of the experiment means we can only know which way it'll go via probability instead of classical mechanics near 100% certainty.
Nice thanks for the video! A friend of mine works on making quantum computers and it's crazy how the engineering is very exotic condensed matter type physics.
🍎If you want to learn quantum mechanics by doing problems, I'm running a course Jan 6 - 31st 🍎 For 4 weeks you will have homework and weekly tutorials with me📝There's no math prerequisite - it's for curious people from all backgrounds. Last time we had people from many walks of life, but all of them had wanted to understand quantum mechanics for a long time. If you're in the same boat, I think you'll enjoy learning together! looking-glass-universe.teachable.com/p/quantum-mechanics-fundamentals1
@TimoBlacks Geez I'm not sure, but supposedly the math checks out and predicts exactly the same results as observed. Something to do with a caveat Bell made. In it, reality is fundamentally random/probabilistic though. But consider that pilot wave, which has a particle only at one location at all times (uncertainty principle being a lack of knowledge instead of real) does produce the interference pattern because the waves interfere with itself or something. This has been reproduced macroscopically if I understand correctly. It's not pilot wave though and not deterministic like pilot wave.
Kinda, except you can't do calculations with variable resistors xd jokes aside tis more like a wave, where you can tune into a specific wavelenght. While there are multiple waves present. With qubits are two waves present each and when we try to tune into one of the two waves we get one of them at random xd
As an x-ray tech trained in the military, the maths were almost non-existent. The highest math I took was college algebra. If I took the class, would the math be overwhelming? Thanks!
No I don’t think so at all! If you want an idea of the level, check out the first 4 videos in this series. If that looks ok, you’ll be fine! Plus I will be there to help as much as possible, so you can email me with your questions and I can help you before the tutorials
youtube''s algorithm works sometimes! I enjoyed the video and subscribed because the explaination was so good, but I have some questions - 7:15 I don't get how there could be a combination of up and down, I understood the example of the prism projecting the laser's polarity into a basis of two polarities, but "up and down" does not sound like a basis to me because there is no orthonormality, so what is happening? - also I don't get why the use of complex numbers, in this case it does not add any further dimensions it's just making the 1 state complex, or was it just a way of saying that whatever multiplies the two states 0 and 1 can be also complex? that would make sense because then yeah there would be more dimensions -I also still don't get how qbits can make calculations easier, how could I apply these concepts to speed up calculations? this question probably is out of the scope of the video though maybe someone could answer these questions? I would appreciate it
Hey, great questions! Thanks for asking them! -This Is a confusing point; "up" and "down" aren't at right angles to each other, but when you translate them to the mathematical representation as vectors we treat them as orthogonal. The reason for this is that "orthogonality" in QM has a very specific meaning. If two states are orthogonal, then they are mutually exclusive. I.e. in an experiment, these vectors represent opposite outcomes. Since a stern-gerlach experiment has two outcomes: "up" and "down", the vectors for these must be orthogonal in QM. The vectors don't really represent the physical system (where up and down aren't at all at 90 degrees), but instead represent the information in a useful mathematical way. -Yes, you're right! You can make either the "a" or "b" coefficients complex! -I did a video about an actually "useful" thing you can do with a quantum computer once, if you're interested: th-cam.com/video/tHfGucHtLqo/w-d-xo.htmlsi=sQIBKjDQV94aYL0X Thanks again :)
12:40 I think this part was a little misleading how you showed it with your hands. Because the possible spin directions are in physical space, which is three-dimensional over the real numbers, while you show it with your hands in Hilbert space (state space), which is two-dimensional over the complex numbers with basis vectors |0> and |1>. There is no third direction in Hilbert space like you make it seem when you rotate the |1> direction upward. EDIT: Sorry, I think I now get what you meant to say. You attach a complex plane to the |1> direction to visualise one complex dimension as two real dimensions. I think that's correct then. However, it should be stated that the same can then be done with the |0> direction, so that the two-dimensional complex vector space becomes a four-dimensional real vector space. And because of the normalisation |a|^2 + |b|^2 = 1 (where a, b are the prefactors of an arbitrary state a|0> + b|1>) that gives an extra condition, you can identify the three-dimensional physical space with the three free real numbers in Hilbert space.
It seems sort of incorrect to say that a quantum system is in a superposition of the two states, because those two states are defined by the basis you choose, and if you choose a different basis, then you have a different two states that it is in a superposition of. Isn't it really in just one state, which is the state of pointing in the exact direction it actually points?
Thanks a lot, you really helped me get all that! But I still can't help but wonder how quantum computers actually take advantage of these properties, like physically. 🤔
How do we know if the result of a quantum computer operation is correct? It could take decades to validate it using current supercomputers. I image that even one misbehaving q-bit could radically alter the result.
There are many problems that are hard to solve but easy to check once you have an answer. One example is finding factors for very very large numbers, which is one of the kinds of things that quantum computers would be good at while supercomputers are much slower.
The nature of quantum computing is such that we do not use any one trial as the answer to the quantum question we are asking. This is for two reasons. 1. Quantum computing relies upon the spread of measurements across a wavefunction to find the answer. This means that the result is statistical and requires many (thousands of) measurements to gain a spectral understanding of the resulting wavefunction for the system. In other words, the noise will affect the spectrum’s clarity, but any one trial, noise and all, is not the “result”. 2. To reduce noise, quantum computing engineers have come up with ways to “error correct” by using groups of qubits to represent one “logical qubit”. So that when one qubit inevitably flips due to noise, the overall group can still be interpreted correctly. This reduces the effect of noise in the system.
@fullfungo Classical bit have two positions either 1 or 0. Quantum bit can be in any position between 1 to 0. Pendulam like Quantum bit can be in any position between -1 0 +1 and independent of temperature. just an imagination!
You make it sound like it's no different than expressing a vector as components. For example, a vector of magnitude 5 at 45° from the x axis might be expressed as two vectors, one of magnitude 3 at 0° and another of magnitude 4 at 90°. However it can also be expressed as any of infinitely more combinations of other vectors. But that's merely mathematics. Those are three separate vectors (also infinitely many other vectors besides), not one vector in two (or infinite) states. What am I misunderstanding?
This is a very subtle point, but in QM there isn't a difference. I think what's hard to accept about this is that when we say "this light is a superposition of horizontal and vertical" if makes it seem this is the correct or only way to see the light. But yeah, as you said, you could have picked any other basis instead. All these different ways of decomposing the light are equally "physical"- the most useful way to do it though is to use the basis that you're then going to be measuring in later. I'm not sure if that helped at all
@LookingGlassUniverse That does help a bit, thanks. The implication, though, seems to be that there is only one "real" state of the object and we just choose the "lens" through which we observe it to fit the purpose we've set. What does that mean for Copenhagen and the supposed reality of, for example, no definite position for a photon? Does it actually have a definite position and all we do is select the metaphorical angle at which we observe that position, such that it _appears_ that that is the "highest probability" position? (Or however it would be best to say that - I only have a middling layman's understanding of quantum physics.) Also, it's philosophically interesting because it gets into whether mathematics is discovered or invented. Are quantum objects "made of math" such that the infinite mathematical expressions of the object are literally what a superposition of infinite states is? Or is math merely a description of the physical world such that there are any number of ways to describe physical reality, only a few of which we have devised (some better - i.e. more accurate - than others) but none of which are physically real. (I'm very firmly on the side of the latter, BTW.)
@@MichaelPizme: whoosh :) Although I tend to agree we are just forcing two states onto something that isn't in any state at all? I could have got this all wrong, as I said whoosh :)
@@1newme425 Just a few months ago, I saw a video that gave me a new perspective on quantum objects. (I don't remember the title but I'm almost certain it was by Float Head Physics.) The reason we have trouble understanding quantum objects like photons, electrons, and others is that they simply _cannot_ be described, _at all,_ using the concepts we have for macroscopic physics. "Particle," "wave," even "point," simply _do not apply_ and cannot even be "stretched" to make sense of quantum objects. They are something else entirely. We are comfortable with terms like "particle" and "wave" because they have become second-nature to us. However, until we devise entirely new concepts for quantum objects and those concepts become as familiar to us as "particle" and "wave" are now, we will fail to have anything resembling an intuitive grasp of what those objects are. They are _entirely_ different than what we're used to, so the words we use to describe what we're used to _cannot_ apply to, _cannot_ describe, them. Even with that being the case, however, it's easier to grasp what we're dealing with in quantum objects if we keep that fact in mind. They're not particles, not waves, but something else entirely. Saying that an electron doesn't have a definite position fits somewhat with our normal understanding of physics but doesn't accurately capture the reality because "position" just doesn't apply to something that is not a particle. The same applies for the term "wave." We need new concepts that are not like "particle" and "wave," then we need them to pass into common usage the same way that "particle" and "wave" have. Only then will we reach an "everyday" understanding of the quantum world.
No surprise, imaginary corresponds to circular. And I will be ignored and will delete this comment But you describe it in such enhusiastic way (and correctly!) that I will simply listen and wait. (Good morning my future-self: do not hesitate to delete me, as usual, you were either too late = very probably, or... unrealistic)
@@LookingGlassUniverse Surprised, really, I deleted the comment where I stated that I am now subsribed+bell because I want to learn with you... I ment it and I keep my promise (even when I think it was not heard out)
Please! be my physics teacher 🙏. Jokes aside, you are quite good at explaining concepts 👍
Every time I see a physical or experimental explanation of superposition it seems like what's actually described is an object that isn't actually "in both states at the same time" but is actually "in neither state" because the actual state is the combination of multiple factors. For example, the 45 degree polarization isn't both vertical and horizontal, it's just describable as a combo of the two, it "is" 45 degrees. And we only say it "collapses" to either vertical or horizontal because our measurement device forces it to align to either vertical or horizontal. That's not a measurement, it's a filter. And the entropy of the experiment means we can only know which way it'll go via probability instead of classical mechanics near 100% certainty.
1:38 Nitpick: If the first is at 45 degrees, shouldn't the second be at 135 degrees (not 130)?
Nice thanks for the video! A friend of mine works on making quantum computers and it's crazy how the engineering is very exotic condensed matter type physics.
🍎If you want to learn quantum mechanics by doing problems, I'm running a course Jan 6 - 31st 🍎
For 4 weeks you will have homework and weekly tutorials with me📝There's no math prerequisite - it's for curious people from all backgrounds. Last time we had people from many walks of life, but all of them had wanted to understand quantum mechanics for a long time. If you're in the same boat, I think you'll enjoy learning together! looking-glass-universe.teachable.com/p/quantum-mechanics-fundamentals1
Awesome, so cool you doing this.
Sure, Got it, I will be there with Einstein!
Awesome! is it free? i would like to do it so much!
This is brilliant Mithuna, thank you
Wow! Great Video
Never understood the logic behind qubits having two states at once until I saw your video!
Thank you for the great explanation🙏
The electron is sad because its too negative, in case you were wondering.
Dr Jacob Barandes has developed an interpretation of QM that features local realism with no superpositions needed.
What's the general idea?
Eg, how would he explain interference pattern, resulting from at atom source placed in front of 2 slits. Roughly?
@TimoBlacks Geez I'm not sure, but supposedly the math checks out and predicts exactly the same results as observed. Something to do with a caveat Bell made. In it, reality is fundamentally random/probabilistic though. But consider that pilot wave, which has a particle only at one location at all times (uncertainty principle being a lack of knowledge instead of real) does produce the interference pattern because the waves interfere with itself or something. This has been reproduced macroscopically if I understand correctly. It's not pilot wave though and not deterministic like pilot wave.
Every time I hear someone explaining Qubits, my mind automatically goes "so it's basically a variable resistor?". I like your teaching style 👍
Kinda, except you can't do calculations with variable resistors xd
jokes aside tis more like a wave, where you can tune into a specific wavelenght. While there are multiple waves present. With qubits are two waves present each and when we try to tune into one of the two waves we get one of them at random xd
As an x-ray tech trained in the military, the maths were almost non-existent. The highest math I took was college algebra.
If I took the class, would the math be overwhelming? Thanks!
No I don’t think so at all! If you want an idea of the level, check out the first 4 videos in this series. If that looks ok, you’ll be fine! Plus I will be there to help as much as possible, so you can email me with your questions and I can help you before the tutorials
@LookingGlassUniverse I think it was okay for me... But definitely scraping the edge of my defeat. 😄
Your videos are absolutely incredible !thank you!
Finally! It was one of the most confusing things ever! Thank you!
youtube''s algorithm works sometimes!
I enjoyed the video and subscribed because the explaination was so good, but I have some questions
- 7:15 I don't get how there could be a combination of up and down, I understood the example of the prism projecting the laser's polarity into a basis of two polarities, but "up and down" does not sound like a basis to me because there is no orthonormality, so what is happening?
- also I don't get why the use of complex numbers, in this case it does not add any further dimensions it's just making the 1 state complex, or was it just a way of saying that whatever multiplies the two states 0 and 1 can be also complex? that would make sense because then yeah there would be more dimensions
-I also still don't get how qbits can make calculations easier, how could I apply these concepts to speed up calculations? this question probably is out of the scope of the video though
maybe someone could answer these questions? I would appreciate it
Hey, great questions! Thanks for asking them!
-This Is a confusing point; "up" and "down" aren't at right angles to each other, but when you translate them to the mathematical representation as vectors we treat them as orthogonal. The reason for this is that "orthogonality" in QM has a very specific meaning. If two states are orthogonal, then they are mutually exclusive. I.e. in an experiment, these vectors represent opposite outcomes. Since a stern-gerlach experiment has two outcomes: "up" and "down", the vectors for these must be orthogonal in QM. The vectors don't really represent the physical system (where up and down aren't at all at 90 degrees), but instead represent the information in a useful mathematical way.
-Yes, you're right! You can make either the "a" or "b" coefficients complex!
-I did a video about an actually "useful" thing you can do with a quantum computer once, if you're interested: th-cam.com/video/tHfGucHtLqo/w-d-xo.htmlsi=sQIBKjDQV94aYL0X
Thanks again :)
@LookingGlassUniverse quick in the answers too! I should be the one thanking you, I will make sure to watch the video
12:40 I think this part was a little misleading how you showed it with your hands. Because the possible spin directions are in physical space, which is three-dimensional over the real numbers, while you show it with your hands in Hilbert space (state space), which is two-dimensional over the complex numbers with basis vectors |0> and |1>. There is no third direction in Hilbert space like you make it seem when you rotate the |1> direction upward.
EDIT: Sorry, I think I now get what you meant to say. You attach a complex plane to the |1> direction to visualise one complex dimension as two real dimensions. I think that's correct then. However, it should be stated that the same can then be done with the |0> direction, so that the two-dimensional complex vector space becomes a four-dimensional real vector space. And because of the normalisation |a|^2 + |b|^2 = 1 (where a, b are the prefactors of an arbitrary state a|0> + b|1>) that gives an extra condition, you can identify the three-dimensional physical space with the three free real numbers in Hilbert space.
IN YOUR EXAMPLE THE POLARIZED LIGHT QBIT DOESN'T SEEM TO COLLAPSE IN ONE OF THE TWO STATES WHEN YOU MEASURE/OBSERVE IT. PLEASE ELABORATE
It seems sort of incorrect to say that a quantum system is in a superposition of the two states, because those two states are defined by the basis you choose, and if you choose a different basis, then you have a different two states that it is in a superposition of. Isn't it really in just one state, which is the state of pointing in the exact direction it actually points?
Thanks a lot, you really helped me get all that! But I still can't help but wonder how quantum computers actually take advantage of these properties, like physically. 🤔
6:30 Why is your electron so unhappy?
Too negative
@@LookingGlassUniverse Ohhhhhhhh!!!!!! Makes sense.
@@LookingGlassUniverse😂😂😂😂😂😂🎉😊
I find superposition to be disturbing. If physicists ever discover super-duper-position, I'm probably going to have a conniption.
I have a lot of conniptions. I keep them in a dark closet in a dark corner of my dark basement, and I never let them out.
Helps keep me sane.
How do we know if the result of a quantum computer operation is correct? It could take decades to validate it using current supercomputers. I image that even one misbehaving q-bit could radically alter the result.
There are many problems that are hard to solve but easy to check once you have an answer. One example is finding factors for very very large numbers, which is one of the kinds of things that quantum computers would be good at while supercomputers are much slower.
The nature of quantum computing is such that we do not use any one trial as the answer to the quantum question we are asking.
This is for two reasons.
1. Quantum computing relies upon the spread of measurements across a wavefunction to find the answer. This means that the result is statistical and requires many (thousands of) measurements to gain a spectral understanding of the resulting wavefunction for the system. In other words, the noise will affect the spectrum’s clarity, but any one trial, noise and all, is not the “result”.
2. To reduce noise, quantum computing engineers have come up with ways to “error correct” by using groups of qubits to represent one “logical qubit”. So that when one qubit inevitably flips due to noise, the overall group can still be interpreted correctly. This reduces the effect of noise in the system.
I'm totally confused now, and thinking about a purely mechanical bits using pendulums.
How are bits related to pendulums???
@fullfungo
Classical bit have two positions either 1 or 0. Quantum bit can be in any position between 1 to 0. Pendulam like Quantum bit can be in any position between -1 0 +1 and independent of temperature. just an imagination!
Excelent Job.tks
Would it be so difficult to use better and more accurate terminology so that people are not confused into believing that quantum mechanics is magic?
You make it sound like it's no different than expressing a vector as components. For example, a vector of magnitude 5 at 45° from the x axis might be expressed as two vectors, one of magnitude 3 at 0° and another of magnitude 4 at 90°. However it can also be expressed as any of infinitely more combinations of other vectors.
But that's merely mathematics. Those are three separate vectors (also infinitely many other vectors besides), not one vector in two (or infinite) states. What am I misunderstanding?
This is a very subtle point, but in QM there isn't a difference. I think what's hard to accept about this is that when we say "this light is a superposition of horizontal and vertical" if makes it seem this is the correct or only way to see the light. But yeah, as you said, you could have picked any other basis instead. All these different ways of decomposing the light are equally "physical"- the most useful way to do it though is to use the basis that you're then going to be measuring in later. I'm not sure if that helped at all
@LookingGlassUniverse That does help a bit, thanks. The implication, though, seems to be that there is only one "real" state of the object and we just choose the "lens" through which we observe it to fit the purpose we've set. What does that mean for Copenhagen and the supposed reality of, for example, no definite position for a photon? Does it actually have a definite position and all we do is select the metaphorical angle at which we observe that position, such that it _appears_ that that is the "highest probability" position? (Or however it would be best to say that - I only have a middling layman's understanding of quantum physics.)
Also, it's philosophically interesting because it gets into whether mathematics is discovered or invented. Are quantum objects "made of math" such that the infinite mathematical expressions of the object are literally what a superposition of infinite states is? Or is math merely a description of the physical world such that there are any number of ways to describe physical reality, only a few of which we have devised (some better - i.e. more accurate - than others) but none of which are physically real. (I'm very firmly on the side of the latter, BTW.)
@@MichaelPizme: whoosh :)
Although I tend to agree we are just forcing two states onto something that isn't in any state at all? I could have got this all wrong, as I said whoosh :)
@@1newme425 Just a few months ago, I saw a video that gave me a new perspective on quantum objects. (I don't remember the title but I'm almost certain it was by Float Head Physics.)
The reason we have trouble understanding quantum objects like photons, electrons, and others is that they simply _cannot_ be described, _at all,_ using the concepts we have for macroscopic physics. "Particle," "wave," even "point," simply _do not apply_ and cannot even be "stretched" to make sense of quantum objects. They are something else entirely.
We are comfortable with terms like "particle" and "wave" because they have become second-nature to us. However, until we devise entirely new concepts for quantum objects and those concepts become as familiar to us as "particle" and "wave" are now, we will fail to have anything resembling an intuitive grasp of what those objects are. They are _entirely_ different than what we're used to, so the words we use to describe what we're used to _cannot_ apply to, _cannot_ describe, them.
Even with that being the case, however, it's easier to grasp what we're dealing with in quantum objects if we keep that fact in mind. They're not particles, not waves, but something else entirely. Saying that an electron doesn't have a definite position fits somewhat with our normal understanding of physics but doesn't accurately capture the reality because "position" just doesn't apply to something that is not a particle. The same applies for the term "wave." We need new concepts that are not like "particle" and "wave," then we need them to pass into common usage the same way that "particle" and "wave" have. Only then will we reach an "everyday" understanding of the quantum world.
brilliant video
Awesomesauce!!
Your name should be photon
Why? Because she lights up your day?
I both clicked on this video and didn't. If you are reading this it mean to you i probably did. I actually didn't though:)
Any bit you do in your videos is a cute b- oh i seem to have misréad it.
😆
Mmh Mmh yeah... I know some of these words 😂
No surprise, imaginary corresponds to circular.
And I will be ignored and will delete this comment
But you describe it in such enhusiastic way (and correctly!) that I will simply listen and wait.
(Good morning my future-self: do not hesitate to delete me, as usual, you were either too late = very probably, or... unrealistic)
Thanks for your comment
@@LookingGlassUniverse Surprised, really, I deleted the comment where I stated that I am now subsribed+bell because I want to learn with you... I ment it and I keep my promise (even when I think it was not heard out)