Nobody Knows Why Wave Functions Exist - So We Just Assume They Do (Quantum Mechanics Postulates)
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- Опубліковано 29 чер 2024
- Wave functions are a big part of the current formulation of quantum mechanics. But why do they exist? Well currently nobody knows!
Every theory in physics is based on a set of assumptions, also known as axioms or postulates. In other words, we develop theories by first starting with a set of ideas that we assume are true. Then we apply some mathematics to these ideas and build the theory.
An example of this is the Kinetic Theory of Gases. This theory studies how gases should behave, and the assumptions it works off include the idea that a gas is made up of small, spherical particles, and that the total volume of these particles is much smaller than the volume of the container they are in.
What happens when these assumptions are not true for the real gas we are studying? Simple - the theory becomes less and less accurate at predicting how the real gas should behave.
The important point here though is that every theory is based on some assumptions / postulates / axioms. These can be thought of as the rules of the theory. In this video we take a look at the first postulate of the Copenhagen Interpretation of Quantum Mechanics.
The first postulate says that for any quantum system we're studying, there exists a mathematical quantity known as the wave function. The wave function is a quantity that has some value at every point in space and time. This value can be positive, negative, zero, or even imaginary.
When we take the square modulus of the wave function, we can find information about what we'd expect to see with the system, when we make a measurement on it. For example if our system is a single electron, the square modulus of its wave function can give us information about how likely we are to find the electron between different points in space.
Why is this the case? Nobody knows - quantum theory just seems to be based on this strange idea, and yet makes excellent predictions about how the world around us should behave. This is why we stick with the idea of wave functions in the first place. We don't understand quite why the universe behaves as if wave functions exist, but our mathematical formulation agrees very strongly with experimental data.
The wave function has to have some important properties. Firstly, it has to follow the Schrodinger Equation. This is the equation that determines how wave functions are allowed to evolve over time and through space.
Secondly, the area under the square modulus of the wave function directly corresponds to probabilities of experimental results when we make a measurement on the system - we've seen this idea already.
Thirdly, the wave function's square modulus has to be "normalizable". This means the total area under the square modulus has to be finite, and we must be able to set this area to 1. This is because this total area gives us the probability of finding the electron SOMEWHERE in our universe, and this must be 100% = 1.
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Timestamps:
0:00 - Theories in Physics, and the Assumptions They are Based on
0:57 - Postulates in the Kinetic Theory of Gases
2:20 - The First Postulate of (the Copenhagen Interpretation of) Quantum Mechanics
3:35 - How Does a Wave Function Relate to a Real System? Probability Densities
5:33 - WHY Does a Wave Function Even Exist? Why Do We Use the Wave Function?
7:06 - Properties of the Wave Function
8:32 - Thanks for Watching, Please Check Out my Quantum Merch in the Description!
Hi everyone, thank you very much for watching! If you'd like some more physics content, check out this video I made recently, discussing Potential Energy in 5 levels of difficulty: ua-cam.com/video/Iu48lfJXgww/v-deo.html
Also, do check out my quantum mechanics playlist here for more videos on this topic: ua-cam.com/play/PLOlz9q28K2e4Yn2ZqbYI__dYqw5nQ9DST.html
Finally, let me know what other topics to cover in future videos :)
When the box containing Schrodinger's cat's opened, the wave function collapses into a single spike. Please could you say how/if that spike is made out of a million sine waves added together?
Could you please do a video on general relativity and space time ripping as it reaches the ringularity or singularity inside a black hole? Please do explain the mathematics also in a intensive level. I mean the 4×4 matrix stuff, explained in simplicity like you usually do. And thanks a lot for such spectacular videos.🎉🎉
What's the implication of not setting it to one
Respect for you from India
Can you cover electromagnetism?
"I've lost my electron" "Where did you last have it?" "I'm not sure but I'm 100% certain it's somewhere in the universe"
String theorist: "Maybe you are looking at the wrong dimension."
Heisenberg: "Don't try to measure its velocity. You can't find it."
Einstein: "God knows where it is."
If it ran into a proton in a nucleus at just the wrong moment and participated in inverse beta decay, you're out of luck.
@@hakanevin8545 Richard Dawkins: "God doesn't exist, therefore you cannot find your particle."
Postulates = "We don't know why this works, but it works, so let's say this is how the universe works."
welcome to modelling
If you want to know how the universe works just ask a religious apologist.
Oh I know this. If it looks like a duck, swims like a duck, and quacks like a duck, then it is a duck. I wouldn't think quantum mechanics is so easy 😁
To be fair, it *is* how the universe works, to the best of our knowledge. Which is how we know everything. Not perfectly, but better than before
This happens in coding. When you don't know why it works, but it works
I did maths at Uni, maybe a quarter of a mile south of you, ending up as more of a mathematical physicist by the end. People talk to me about it as if maths is all about numbers and I correct them by telling them it's actually about starting with a set of assumptions and seeing how far we can get by applying logic to them. I'm sure it's the same for historians correcting people who think all they do is memorise stories and dates. It was good to see you starting this video off by saying pretty well the same thing about physics as I do about maths!
Parth please make a similar series on relativity 👍
If Parth does it, it’s going to be from a fundamental mathematics perspective not kindergarten analogies. So it would have to be about hyperbolic geometry and lorentzian transformations?
@n.d.: Yes, please!
I don't know any channel in youtube that goes as deep as you go or talks about complex topics as you do.
That's why I subbed and that's why you should keep going :)
Thank you for the kind words!
PBS Space Time is a pretty good one that's only slightly less technical.
The Science Asylum is worth checking out too: ua-cam.com/users/Scienceasylum
Veritasium just recently released a video on "i" (the square root of -1), and part of it talks about how it ended up in Schrodinger's wave equation.
I watched that two days ago
Extremely big RESPECT for this great video! Excellent explanation, without any superfluities and without the usual "you have to be funny when explaining something difficult" (firstly, it's usually not funny, secondly, it's always incredibly annoying and distracting). This is exactly how I would like to see explanatory videos in science and mathematics. Once again THANK YOU for this great work, I am looking forward to all the other videos on this channel (already available and upcoming).
I wish I had found this channel much earlier. Your explanations are clear, straightforward, and make sense. Thank you for doing this and keep those vids coming.
Yes, and they are also wrong. ;-)
Good talk. I like that you presented qm as a model with postulates. When I try to explain it to people I go right to the particle in a box model, because that shows how boundary conditions dictate quantization. The problem is , many people dont know enough calculus to get the gist, which always makes me wonder why someone would try to tackle quantum mechanics...really ANY topic in physics....without a basic math background!
Love your work. Would like to see a video on Bell's Inequality.
Thanks a lot Parth! Could you someday cover the subject of spontaneous symmetry breaking?
Thanks,Parrth - very clear as always. Couple of comments: When you say 'check out this video here', and point, you points to nothing onscreen! Put the link in the comments, please! The other thing is would you number each video - so that we can see if we've missed any - and also, the correct order to view them for progressive understanding. Many thanks for all the good work. I wish you'd been around when I was doing undergrad physics. But you weren't even born then!
Loving your work!
Your Videos are always enlightening and also entertaining. Thanks for sharing ❤👍
Hello, great video! Would you be able to make a video on what experiments validate the current Quantum mechanics postulates? Thanks!
Hey parth. Love your content but at some point I wish to know more.
Could you make a whole series of classic mechanics? Would love to learn it from you
This is really very, very good. To reduce something complex to something of such clarity takes a mind that really knows its stuff.
Love your videos!
Can you do a video about the size of a photon, in terms of how many wavelengths exist? The single wavelength of a photon is well defined but the number of wavelengths seems rather vague and often described as a "wave packet" with just a few (5-10) wavelengths. There are various experiments that restrict the frequency bandwidth of the photon to very small values. A minimum (Fourier-limited) time-bandwidth product would seem to require a corresponding large number of wavelengths.
Einstein's wife asked him to bring her two things - Time and Space
Einstein replied- what is the second thing?
Einstein's wife was mad at him, so she kicked him out and said "Give me time, I need space!!"
This is, in my opinion, one of the best YT videos on Wave Function.
That was awesome. Thank you!
Thank you for your short, simple and effective explanations with some philosophy alongside
Whenever I get discouraged in my physical chemistry course, I come here for motivation.
Thank you for the video. :)
A better way to look at it is "quantum systems all have a common property - that for certain properties of the system, the probability of finding the system in a given state can be described with a function and that function is derivable from a function that describes a wave-like distribution. We don't understand HOW systems that seem discrete and deterministic can work this way, but they do and this models their behaviour very accurately." I feel it's a mistake to go from the model to the real world as it leads to valuing the model over the experiment.
That's not the history of how we got here. We got here by combining three things from the real world and ended up with the model - not the other way around.
First came the idea that an electron was a solid thing, but at the dawn of the quantum age, we were faced with two questions. Why did electrons cause unique spectral lines for each element? (They seem to occupy only unique energy levels around an atom.)
Are electrons really waves? If true we can characterize them in orbit with a continuous function and we have a well-known equation for finding the mass of a standing wave on a stringed instrument, like a violin. That was the wave function applied to the electron and Schrödinger, along with others, expected it to work for experimental results. It failed.
Now comes the third part - bridging a frequency (like a violin note) with a frequency (how often do you skip breakfast, what is the probability for that). If you look at time to frequency transform equations, you'll rapidly hit complex exponentials (specifically e^(-iωt) and you may recall that Ψ = e^i(kx-iωt)) and if you look at various probability equations, they often include exponential definitions. There's a reason for that. Anyway that's the piece that Born put together - instead of frequency description of a + ib pairs to describe spectral components, get the magnitude of the point from the origin and treat it as a probability value.
That basically worked, that's how we got here. Avoid anyone telling you physicists don't look at the real world or only care about their models because that's just not true. That's the battle cry of con artists and pseudoscience.
The map is not the territory. Parth is trying to explain a very nuanced situation before you're fully equipped to handle the nuances - and it does not matter how we got here at this level, only how to recognize the signposts of what is at this level. It's going to get a lot weirder and none of it is caused by a century of physicists worldwide forgetting or being too stupid to consider the real world.
Hope that helps!
It should really be "for all properties of the system"
Every physical property in QM is described by a wavefunction / the wavefunction of the system as a whole
Combine:
1. cosmological constant in Dxy [m^-2] = lp^2/λ^4= lp^2 nxy ^2 [m^2] [m^-4]
2. schrodinger solution
3. Planck E= h f= h n
4. n = number of superpositions = wave function frequency
And you get: dark matter = superposition of the electron
Dxy [m^-2] = lp^2/λ^4= lp^2 nxy ^2 [m^2] [m^-4]
Nxy = sqrt(Dxy / lp^2)=. (Dxy / lp^2) ^0.5= [m^-1] [m^-1] = m^-2
Then nxy = sqrt ( 10^-52 / 10^ -70) = 10^18 ^0.5 = 10^9
Schrodinger solution:
n^2 h^2 / ( 8 m L^2) = h n
8 m L^2 h n = n^2 h^2
m = n^2 h^2 /( 8 L^2 h n)
m = n h 0.125 L^-2
m= 10^9 10-34
= 10^-25 ( all superpositions).
1 particle = 0.331 10^-25 / ( 0.4 10^9) = 0.828 10^-34 kg = 46 eV
If you count only the positive wave function amplitudes: n = 10^4.5
then 1 particle = 0.331 10^-25 / ( 0.4 10^4.5) = 0.828 10^-30kg 5.6 10^35= 10^5 ev = 0.5 Mev
Superposition of electron causes dark matter?
Whenever I see a video or talk about Quantum Mechanics, it usually refers to everything theoretically - like an electron being constrained to being in a box etc etc. What I'd like to see is some 'real world' experiments that bring the Wave Function (and associated probabilty) alive. An example that brings electron spin alive is the Stern Gerlach experiment. What experiments bring Wave Functions and the Schrodinger equation alive?
I don’t think there are any (and that’s exactly why people disagree on interpretation of QM), unless you count the double slit experiment. And some are claiming even that is widely misunderstood, and that it doesn’t mean quite what others think it means.
: You don't know any experiments that show us that wavefunctions exist??? Do you study physics?
Great video! 👍
Your videos are cool too!
Thank you :D
@@fizyknaut8108 🥰
Ur vdeos r amazing. Love them
I am so greatful for that slow and simple explanation - like that even I get it :-D
I don't know, I feel like wave functions "exist" because they're a useful model for the things they're useful for modeling. Like, the question of why wave functions are normalizable: if they WEREN'T normalizable, they'd be no good for describing particles that aren't uniformly detectable everywhere all the time.
Before we had wave functions, we had the Bohr model of the atom, with electrons moving in tidy circles at fixed distances from the nucleus. And that was a great model ... until it wasn't. Then we found a better model. But both Bohr and wave functions are MODELS, which is to say, they have no reality of their own.
Well, technically, you've just described how modern science works,. You observe, hypothesise a model (with a test that defines a failure and that covers all we know to this point on the same subject), test and if it fails, reject or amend - if it passes, start over and do more observations and see if there are things the model missed..
@@TheoWerewolf I notice people talk about wave functions like they're real things with physical reality of their own, and I think I detect some of that in this video. Maybe this exposes a limited understanding on my part, but as far as I'm concerned, a wave function is nothing more than a versatile description of a quantum mechanical system, to the limits of our ability to measure it. So when people get into arguments about, say, the Many Worlds Hypothesis, I feel like they're confusing the map with the terrain: just because the wave function doesn't provide a great guide as to which event will be measured, doesn't mean that all events will actually take place somehow.
@@kingbeauregard - Can't your model vs reality argument be applied to our mathematical model of macroscopic physical reality as well? After all, neither space nor time can be physically detected - their existence must be inferred from our measurements of the behavior of the physical objects we can detect. Likewise, the existence of a complex-valued quantum domain can be inferred from the verifiable behavior of the subatomic particles described by the quantum wave function.
@@FallenStarFeatures Well, sure, a good map is useful, but no map completely captures all the details of a thing. By all means, use a model; but be mindful of the shortcomings of a model.
Hey Parth, we need a video about the density of states please!
The United States is pretty dense.
Thanks Parth, can you make a video on the many worlds interpretation? thanks
so infinite multiverse and no god? prove it atheist
Hey Parth, do a video on computational physics pls.
I love this video.
Thanks
Please do a video on the second uniqueness theorem in electrostatics
Yo good mornin Parth, theres an awesome book called shell beach on this theory called quantum holonomy- very interesting, and might make a good video
Hi, an intuitive way to understand Psi wavefunction is to think of it as an existence wave in 3D; that is the meaning of what Born said, it is a probability of existence in that 3D zone at a given time. So the wave is the oscillation of quantum 3D space between its 3D space and a 4th dimension that carries the essence of physical values, i.e., its total energy, total momentum, total charge, etc. That is what Schrodinger wavefunction is, an weirdness of QM will almost disappear. I read that in a short amazon book, "Space, main actor of quantum and relativistic theories. Since nature doesn't contain full information, on each fluctuation, the compact particle will assume an exact valid solution (eigenstates, eigenfunctions) and, from cycle to cycle, nature assumes aleatorily a different valid solution; one each time. The expectation value will be the average of all the eigenstates or the eigenvalues pondered by its probability. Imagine a twisting Einstein's dice, the top face will be in fluctuating changing value at a rate of its energetic frequency, the eigenvalues will be from one dot, up to six dots, its expectation value will be 3.5 dots, BUT never a superposition of all six possibilities, just one solution at a time at a frequency near 10^20 per second... think about it and QM is more understandable... maybe you will do a video about this new view-interpretation. Regards
We don't know if it exist or not, so lets assume it does
=Quantum physics in a nutshell.
Keep up the good work parth .👍
Truly thank you
nice concise video - thanks - but it raised a question for me - is the wave function the same wave(s) as appear in QFT or are those waves actually real as opposed being only mathmatical tools? - apolgies if this is a stupid question....?
Plz make some video on other postulate of quantum mechanics..........
Namaskar Partha (Partha Ghosh??).
Your videos are informative and contains in depth touch. Thank you
Make a video on bizarre of double slit experiment !!
Hey would you be making any videos on feyman path integral pls :)
I love your videos
Please do videos on rotational mechanics
Combine:
1. cosmological constant
2. schrodinger solution
3. Planck E= h f= h n
4. n = number of superpositions
And you get dark matter
n^2 h^2 / ( 8 m L^2) = h n
m = 0.3313 10^18 10^-34 = 0.3313 10^-16 kg ( all superpositions).
1 particle = 0.331 10^-16 / ( 0.4 10^18) = 0.828 10^-34 kg = 46 eV
Please make a video on vector potentials in ED.
Our wave function is fundamentally a complex number, such that plotting the wave function should involve a real and imaginary component.
Eulers formula tells us that we draw out a helix of sorts by plotting a complex function.
If we filled in the volume contained by the helix, it should look the same as revolving our real component about the X-axis.
The volume contained between any two cross sections as compared to the total volume would therefore be equivalent to taking the normalized square modulus of the real function.
If the wave function is indeed rotational in nature (hence requiring complex numbers), then it seems the probability of finding a particle between any two points is just the percent of volume that space occupies as compared to the whole.
"Our wave function is fundamentally a complex number" is not the answer for the question in the video. It's just another assioma. The point is that the biggest probability of finding an electron is somehow assumed to be similar to the maximum intensity of a ligth radiation.Since a radiation behaves like a sinus function, the maximum intensity is given by the square of the maximum sinus amplitude. A good way to represnt this is the product:
psi(cos ft - i sen ft) x psi(cos ft + i sen ft)= square psi, always positive.
By the way have you made a video on Higgs Boson or even the Hadron Collider yet?
Which camera do you use to make your videos.?😀
Hey Parth, please, make an video about Yang Mills mass gap problem (one of those millennium problems)?
the interrelation of quantum chemistry to the overall field model, ie VSPER
Following on from some of your recent videos, this question came to mind: given that E=mc^2, can Potential Energy be converted into mass or does the PE need to be converted into another form of energy before that transformation can happen? And if only some forms of energy can be converted to/from mass, what is the distinction given to the different forms of energy?
PE in a system contributes mass. E.g., if you can do relativistic kinematics, consider two relativistic masses (m) moving head on with +/- v. They collide via a massless spring that "catches" them with no losses, and is clamped shut at maximum compression:
What is the final mass M of the system (2m + compressed spring)? If M > 2m, where is the mass-excess coming from? Can it be converted back to kinetic energy?
Don't take my word for it, but as far as I know, yes, potential energy does count. For example, a lot of the mass of a proton comes from interactions between quarks, which has a potential energy associated with the strong force.
You're confusing two concepts. Energy can be converted into _matter_ by creating particles or changing particles into heavier ones.
Energy _is_ mass, always was, and you don't "convert" it. If you have a chemical battery, coiled spring, or anything else that contains potential energy, a careful enough measurement of its mass will indicate that the potential is contributing mass.
For example, take a perfect closed box that nothing can enter or leave, not even neutrinos. You know nothing about what goes on inside but can measure the mass of the whole thing, via gravity. If a sample of uranium decays inside the box, the daughter elements are lighter but contain kinetic energy which you understand adds mass to the system. The mass of the box seen from outside is unchanged.
Now also in the box is a generator and battery. The fast moving atoms spin the turbine and charge the battery while causing those daughter atoms to come to a near stop.
The kinetic energy is gone, no atoms have changed into other kinds of atoms. But the box still registers the same mass. Now the excess mass is held by the potential chemical energy in the battery.
@@JohnDlugosz That's a very clear explanation, thank you.
"1"
(My life was in a quantum mechanic style, that I never knew my position and where I am going!)
mmm *one*
Parth G can you make a video on general relativity. I would like it if you would explain a bit more about the mathematics in simplicity like you usually do.
The mathematics of general relativity is tensor calculus. The channel MathTheBeautiful has an extremely in depth and intuitive explanation of tensor calculus. I learned the math of GR from his tensor calculus playlist, then I read a book about certain solutions to the field equations to fully understand the math.
ua-cam.com/play/PLlXfTHzgMRULkodlIEqfgTS-H1AY_bNtq.html
This is assuming you know multi-variable calculus, and the basics of differential equations, oh and maybe some linear algebra.
6:48 The wave function does not "exist" as a physical entity exists, it is a mathematical model used to explain quantum phenomena, and make testable predictions.
The quantum wave functions exist otherwise we should not have interference phenomena in Young double slit experiments for example, there is no other explanations.
@@GH-li3wj The quantum wave function is a mathematical model of what is happening in the real world. The function itself does not exist in the real world.
The quantum world is modeled by the function and some day we may find a better more complete mathematical model. Quantum phenomena will always be there but the FUNCTION may be obsolete.
My point is that people tend to confuse the mathematical equations with the real world phenomena they model.
Alternatively, there's only one wavefunction, and it's the only thing that "exists" on a fundamental level.
@@wayneyadams wave function is part of the reality otherwise you won't have interference. It's like number Pi Pi is not just a mathematical model, it is a part of the physical reality, without the Pi number you won't have waves , you won't even exist, and nothing else will replace this mathematical being as the Pi number.
@@GH-li3wj Please don't lecture me on Physics, I have an M.S. in physics and taught the subject for 33 years.
Let me try this one more time. The wave function is a MATHEMATICAL MODEL OF THE REAL WORLD, it does not exist on its own, just as pi is not an actual object, but the result of a mathematical calculation.
The reason I am so emphatic about this is because Physicists become so enamored with the math that they forget that results of calculations are meaningless unless they have testable results in the real world.
As long as the wave equation is an accurate model that makes accurate (meaning testable) predictions it is useful, however, if there are predictions that are proven false, it would need to be modified, or in the worst case abandoned.
Hey parth, what if the wave function is just how reality shows itself to us using the lowest amount of energy possible? Example: it doesn't matter where the electrons that make up my body are at any given moment, all that matters to a conscious observer is that we (being two observers) agree that I exist in the same macro-configuration. Since the macro-verse is more important to be specific, the universe won't waste energy showing us specific quantum-verses. Instead, it shows us all the possibilities of a q-verse that make the same m-verse. This amalgamation would show up as the wave function from our PoV. It isn't until we introduce extra energy into the quantum system (say, through a particle detector) that there is enough energy to produce a specific quantum result. Then, we see the wave function collapse (or decohere, depending on Copenhagen vs many worlds), giving us a specific quantum state.
Just thoughts running through my head. No idea how valid they may be.
Thanks yt for recommending this channel .
Hey bro.. am a physicist and did my master's from IIT Bhubaneswar. In the early times when was learning the quantum mechanics for the first time .. i usually Frustrated with QM. Unlike the classical mechanics it do not give any physical meaning. Many of questions becomes clear after reading Beiser and Shanker QM book. Your video is good enough for beginners who like to learn the quantum mechanics .... 💐
THANKS!
Can you make a video about the wave function, and the propagation of light? After listening to Sabine Hossenfelder's video on the delayed choice erasure experiment, it seems the "wave function" is already "pre-established" across time and space. This includes the whole experimental setup. It is "non-local" (does not take time). Yet light travels at the limit described by relativity. And in QFT, I've heard Sean Carroll say interactions also propagate across fields, at the light speed limit. (I have images of waves across the pond.). So can you clarify the "local" and "non-local" descriptions? (They both invoke images of "waves".)
Could you please make a video about the Bogoliubov transformation and how it explains Hawking radiation! 😲
Hi Parth sir,,,please make a video on combination of mathematical topology and Klein bottle.👍👍
Is that physics?
please make a video about momentum and heat energy
Goodman, Pls slowdown the speed. Afteral I am a beginner and many like me is enchanted to follow you
Using postulates in physics goes back to Archimedes, but it was Newton in Principia who established that physics follows the axiomatic method. Laws of physics are axioms. Einstein followed this principle as well. I would argue that the axiomatic method is a main component of the scientific method.
Please cover black holes.. static, non static, stationary ,non stationary.
Rather than probability of electron existing at a location isn’t it also the probability we will be able to ensnare/detect/absorb it at a location?
I've thought this same thing and wondered what the implications would be on test results or the way they interpret them.
Maybe you answered this but it seem they always give meaning to the wave squared. But what is the meaning of the wave itself without squaring?
We DO know that waves are a very efficient way to transport energy, momentum, etc. just as oscillations are an efficient way to store physical observables. Nature seems to utilize the simplest mechanisms that accomplish Her goals and needs. But, what aspect of space-time propagates as a wave to transport the mass, electric charge, angular momentum, momentum, kinetic energy, and other essence of an electron?
1.- Wave functions not only encode the probability of finding a quantum system in different states when measuring it, they also encode the relative phases of the quantum system in the different states (that's why the wave functions take complex values). The phases cannot be directly measured, but they influence the evolution of the wave function.
2.- The wave function is not (necessarily) over space, but it is over a basis of the quantum system. For instance, if we have a system with 2 "particles",
the wave function of the system can be over the six dimensional space product of the 2 3-dimensional spaces of the particles, and in general each of the particles do NOT have a wave function. Even for a single particle, the wave function could be defined over the momentum (or other basis) instead of over space.
3.- Wave functions only apply to quantum system in pure states: if the system is not in a pure state, it does not have a wave function. Systems in pure
states cannot be quantum correlated or entangled with other systems, so the use of wave functions is not a good choice to understand or deal with
entangled systems. Entanglement is a very important and central part of Quantum Mechanics, and the use of wave functions is inadequate to deal with it: the correct tool to use is the density matrix. On the other hand, real systems are always correlated with other systems, so they are not in a pure state and in rigor they do not have wave functions (but they have density matrices), but wave functions are simpler to deal with and in many cases
are very good approximations. So the question "why wave function exist" is like "why planets are spherical" (they are not).
4.- Wave functions (or density matrices, etc.) exist only within the theory (quantum mechanics in this case). Like complex numbers or derivatives etc. they are "tools" of the theory, they exist because we "invented" them and found that they are good tools that allows us to make good predictions (precise enough and reliable enough), we do not have to think that they "exist" in the real world; other future, more advanced theories could use other very different tools.
Hey
Please make a video on vector spaces
Perhaps you didn't know but the wavefunction exists because it tells us how the particle responds to a measurement. This is what Schrodinger was saying in his famous 'heat' equation. I should say in my view.
Aren't the postulates different from axioms in that they need to be at least somewhat consistent with the observations rather than just with each other?
Also, in regards with postulate-axiom similarity do physicists ever worry about the Gödel's incompleteness theorems or are they already in over their head with QM/GR incompatibility?
Axioms and postulates are interchangeable words. Mathematicians just use their axioms for different purposes than physicists so the bar for what makes particular axioms good/useful is different.
As for Gödel, no. Not in the slightest. Even if physical models *were* to correspond to mathematical systems strong enough for Godel to apply, there is nothing to "worry" about. It just says we can't prove the axioms consistent from the axioms themselves. Nothing more, nothing less.
I've always been puzzled by the idea of a field. A field is just a Tendency for something in the field to move or act in a certain way. But what is a tendency and what causes a tendency? It can't be caused by a field since that's circular. So it seems to me there is no such thing as a field. If I move my arm it's just particles moved by fields, which are quite unreal. Every time I pick up my teacup it's "spooky action at a distance."
My personal belief - the wave function is a real wave in a field. The field is a real yet immaterial thing, or medium. This medium seems to be a superfluid, with closer resemblance to Bose-Einstein condensates than normal matter (there are others sharing this idea). This superfluid can explain dark matter.
Particles? They don't exist. At least, they are not little objects. They are interactions of waves. Non-linear interactions, that is. Linear interactions are just normal interference. They are short-lived blips that take place at some place at some time, and look like "particles" only because they gather up energy to some threshold (quantized) value. What about atoms? Only the protons are stable and real particles, because they are not fundamental. They are trapped energy that keeps interacting with itself. And they trap "electrons", that don't exist (as particles). It's only around atomic nuclei things get quantized.
Matter... It's trapped electromagnetic energy, like a tiny hotspot. Many hot yet tiny spots becomes a large boiling soup. Think of earth. This ball of matter is like a boiling pot in space. And due to all this energy, it becomes like bubbles in a pool of water that reduces the surface tension (used for practicing diving from hights) - the density gets lower. And if the density of the medium is lower close to earth, while getting denser with increased altitude... Guess what that is? Spacetime curvature and gravity.
The only little piece that doesn't fit anywhere in this picture is special relativity. That's a theory that has to go. Lorentz ether theory still works though.
Are there other things that can be understood about a quantum system, from its wave function, besides its probable location in space? maybe velocity?
Yup you can have a wavefunction for any physical property not just position
Hlo parth ,
Can you please explain 'Chandrasekhar limit'
Thank you
We don’t have to assume. Simply imagine a giant observing a geodesic on the earth’s surface. What he sees is just wave function.
Hi @Parth, I've got a question to you and I real wanna hear you idea about it. I'm gonna study chemistry at an college of science. It's supposed to learn quantus mechanics during the course. So, I'd like to know if there is a difference between the Quantus Mechanics we're going to learn and QM physics students learn. (I know this question looks stupid, I did it 'cause I also want to know how complex is QM, and if Physics and Chemists are used to studying with specific things (though it all is QM)).
QM is presented in a somewhat simpler way in chemistry than physics. You don't get all the crazy complicated details - it's more how QM is utilised for practical purposes rather than in a deeply theoretical sense.
@@Jehannum2000 Thanks, broh.
Had you studied QM at university, or, are you used to working with that daily?
@@YgorRichardMy observation comes from comparing chemistry and physics QM videos (I've watched a lot!). Chemistry focuses on parts of QM useful for chemistry - electron energies - whereas physics includes many other exotic particles in different situations. I would say the chemistry is the better approach for someone new to QM because you actually see why it's useful right from the start.
@@Jehannum2000 I've watched plenty of videos about QM and I never realised that, I should recognise you're right!
Thanks for loss your time explaining it, dude. 👊👍
Hay we want relativity series too
'Why question' are always the best
"Why question?" Mmmm.... I think it's the best way to understand the universe. Yes just like Kelvin mentioned the answers sometimes end up to be "I don't know" but if you think about it, the world is changing so fast because of our mentality to question again and again. it's literally what researchers do. search again and again for clues and answers. This never ends and so do human endeavour and passion for science.
We have physical evidence that the quantum wave-function must exist in some operational sense. The interference patterns observed in Double-Slit experiments are produced by the complex-valued mathematics of the wave-function, which must operate in some underlying domain outside physical space-time.
The only sense in which wave functions "exist" is as part of the solution theory of quantum mechanical equations. They are primitive tools, too. They do, for instance, not make direct physical predictions. A cursory look into atomic/molecular/nuclear physics textbooks will show you that von Neumann's solution theory has to be translated to be actually physically useful.
What sort of answer do you want to the title question? I don't know why the Von Karman vortex street exists, but I do know how to duplicate it by computer simulation. I would like to duplicate everything in quantum mechanics by computer simulation as well. My working assumption, which I call the hypothesis-in-being, is that the wave function describes a series of transformations in the way that exchanges spacelike and timelike intervals. Orthogonal to this is tachyonic Brownian motion in the other way to travel faster than light. This hypothesis is intended to provide guidance to the computer simulator on how to make use of a random number generator without trashing the wave function. If anyone else has an alternative hypothesis, then please tell us.
You're veering into word salad.
@@Jehannum2000 Then I will be caught out when I try to turn it into a computer simulation. The first rule to comply with is that modification of the Schroedinger equation is prohibited. Tachyonic Brownian motion complies with this rule. For composite objects heavier than the Planck mass we can throw away the Schroedinger equation and replace it with classical Brownian motion while preserving an Uncertainty Principle. That gives us two ways to make use of a RNG. I will be interested in knowing if there is way number three. Any ideas?
@@david_porthouse Tachyonic means faster than light?
@@Jehannum2000 Yes.
Plz make some videos on ktg.. Those things are weird😐
Quick question: If we assume the electrons wave function must me normalizable, since we assume it is *somewhere* in the universe (if it was there before): What happens when it gets destroyed, say by hitting an anti-electron? Do you need to assume this electron is the only thing in the universe for the wave function to be normalizable?
Electrons are not "somewhere". They are not objects. Total electric charge is conserved (at least locally and with high precision for the energy range below 1TeV), but the charge of individual electrons is not. The "electron as an object" ontology is simply a 19th century leftover. You have to learn to avoid it.
Sorry for the late reply but, you are correct that in non-relativistic quantum mechanics, the time evolution of a system is described by the Schrödinger equation, and if the initial wave function of a particle is normalizable, it remains normalizable for all time. This implies that the probability of finding the particle exists throughout time.
In the specific case of an electron and its corresponding antiparticle, the positron (anti-electron), their annihilation process cannot be described solely within non-relativistic quantum mechanics. The annihilation of an electron and positron involves the conversion of their mass into energy, and such processes require the inclusion of relativistic effects (mass energy conversion E = mc^2). A more advanced model. Quantum field theory.
Beautiful parth heads of you
Hang about...
If the area under that graph has to be equal to 1, how do we have particles popping in and out of existence?
Say your electron happens to choose that exact moment in time to turn into a virtual photon and virtual electron, it's no longer there to be found. So what of the wave function then?
Surely there is a probability that it won't have done that and the electron will be there so there has to be a wave function for that moment in time, but if it can disappear altogether for a bit how can the probability of its existence everywhere be 1? Wouldn't it have to be just a little less than 1?
I hope that makes sense.
I am surprised by your definition. My book says nothing about existence of a wave function, however, it does say, a system is described by one for QM to work. The big difference being "described" versus "exists".
I mean the wave function is a tool, existence to me would imply it as a real thing, which it isn't.
So it's a leap of faith, given the Schrodinger equation was seemingly pulled out of a hat. Why was this proposed with confidence in the first place. Let's get into it, how was it created.
Nice
There is a big gap in my understanding or particle physics regarding physical experimentation. Explainers of physics like yourself tend to describe things like electron spin, or quark colour without relating whether or not these things have been demonstrated experimentally or are just postulates. My knowledge of detection doesn't go much further than the cloud chamber. I'm sure there are far superior detectors these days, but what are they and on what principles do they work?
For spin, research the Stern-Gerlach experiment.
How do they what is seen in an atom smasher is not just a destroyed particle?
The reason why they insist on wave functions is because they are limited by what they can imagine and the limitations of our means of perception. Both qualities skew their attempts to figure out going on.
Sir,what are the basic differences between quantum mechanics and statistical mechanics.Regards.
Though I'm not Parth, but in simplest terms, quantum mechanics is a study of elementary particles using methods and hypotheses that probably no one understands why they work. They just do. So we're happy with it (almost). And it's used to study individual particles as well.
Statistical mech on the other hand, also focusses on elementary particles, but in a much more defined and established mathematical way. This is generally used to study groups of particles instead of individuals to actually dig our some macroscopic properties of bulk from microscopic fundamental properties.
I hope it's clear :D
t vs. T.
See: "Wick Rotation", or the work of Kenneth Wilson (for which he won the Nobel Prize, 1982).
@@Seriouslyfunny1 thanks. To. GAMMA TOO.
No Aryabhattas were harmed in making the thumbnail...
Now that you commented about it , I really noticed it lol . That's hilarious
At 5:56, there is a wave function because Schrodinger designed it to model the waves of a medium. What medium? The electrical medium of Maxwell's Aether Electro-Magnetic field, i.e. electric charge density. When Max Born stole the WAVE equation to apply his "rule", he also applied the idea of *material particles* to WAVE math. How does that make any sense? Don't material particles bounce off each other when they collide? ...while waves in a medium will pass through each other...
material particles interact with a scattering amplitude. In the S.E., that would appear as a short (or not) range interaction V = V(|r1-r2|). With that interaction, asymptotic free-particle wave states scattering into one another. QM then says the amplitude connecting an initial state |i> to a final state |f> is , to 1st order. A second order correction would sum over all intermediate (aka virtual) states |k>: , and so on to all orders.
Meanwhile, the asymptotic states remain eigenstates that don't overlap (e.g., superposition is fine):
@@DrDeuteron **
Is that "scattering amplitude" a velocity of a particle?
**
"Wave state" of a particle? I can understand a "wave state" of a set of waves vibrating through a medium. Do you mean a particle wave-state, as in a billiard ball oscillating back and forth?
**
So you are saying a "particle is the same thing as a wave"?
Or that you can model the break-up of a set of billiard balls, just like waves through a medium?
@@itsbs there are no particles.
@@DrDeuteron **
It's all waves from our perspective... now, can we agree that waves require a medium to wave? :)
@@itsbs You want him to say aether is real, don't you?