I thought about making the title for this week’s Idea simply “Quantum,” since one-word titles are kind of cool, but ultimately decided that accuracy was a higher priority than coolness. That’s why I’ll never be cool.
Anyway, quantum mechanics! This installment runs down the basic ideas; we’ll leave the conceptual heavy lifting for next week.
The Biggest Ideas in the Universe | 7. Quantum Mechanics
And here is the Q&A video. Mostly I talk about the double-slit experiment, and how it implies that the wave function is something other than simply a stand-in for our lack of knowledge about where the particle is.
The Biggest Ideas in the Universe | Q&A 7 - Quantum Mechanics
Not trying to be cool is surely the coolest way to be.
Are there any observable (like position, momentum, energy) present in the wave function which we have not yet measured either because of our limitation or unimportance or do we know about all the possible observables that the wave function conveys?
You’ve told us that you don’t listen to your own lectures and I wonder if you were aware that this one was punctuated by frequent sighs. I guess that says a lot about the frustration of a passionate communicator when dealing with an essentially ambiguous subject.
I have a question about QM that is also related to time. You said “There’s no such thing as at the same time”, which seems unambiguous but I’ve just been watching Brian Greene’s latest Daily Equation video, where he tells us that entangled particles influence each other instantaneously no matter how far apart they are. How can both statements be true?
No better way to spend the lockdown than listening to Sean Carroll explain Quantum Mechanics.
Thanks for this Sean.
If the Wave function is a contentious function (as the bell curve looking curve Shaun showed in the example) spread out over space and if a measurement can find the particle at any one of those points – then in many worlds interpretation it means that the universe will have to split into infinite branches for every possibility not only two branches. Is that correct way to think about it?
For the reasons as to why we never see a wave, has the box analogy ever been followed to our size? By that I mean: the world is full of atoms, so if you try to calculate the solution to the wave function by taking into account all the atoms for say an electron going through a cloud chamber, then would the solution just end up being a discrete particle like path?
Thank you for such a wonderful conceptual explanation of QM to a non physics major. Looking forward to more on the subject.
“If we have to go on with these damned quantum jumps,. then I’m sorry that I ever got involved.” E. Schrödinger (I also understand that he disliked “particles” and wanted them to be “wave packets”)
Are there quantum jumps? Do they occur instantaneously? I have heard that they have been measured… Is that correct and important? Also, are jumps somehow related to the ” instantaneous collapse of the wave function?” Does a theory like GRW address both of these phenomena?
Thank you !
Saying you will never be cool — Is COOL
Could you please talk about what it means for Planck’s h constant to be a measure of ‘joules per *second*’ ?
Remembering that it is ‘allowed’ to think in terms of VSL, (or holding c relative to variable length seconds)…
Q: Can a parallel be considered by holding h relative to variable length seconds?
The probability of finding a particle with(in) the wave function has been proven countless times.
We are then entitled to move to the metaphysical consequences.
The particle must exist with the same probability as of finding it!
Therefore, the wave function actually describes the probability of existence at a certain location.
Then, the wave function contains the secret for the probability of EXISTENCE for a particle in some place.
That secret component is the same as for gravity. A differential in the local rate of time.
One shown everywhere as 1/T.
Funny thing, this background spontaneous time-process that makes dark matter, also makes all our instruments we use to detect it. Good luck!
Shaun, can you please clarify definitively that even in Copenhagen interpretation whether or not the “observer” or “measurement device” in a quantum experiment, does or does not have to be a conscious entity like a human. As I understand it, “observer” is simply a macroscopic thing that interacts with a quantum system – which causes the “collapse” of the wave function according to Copenhagen interpretation. Did any one of Copenhagen club members ever say that “observer” has to be a conscious entity? I know that Jon Von Neumann and Wigner proposed that “observer” has to be a “conscious” entity. But later Wigner changed his mind. How many modern scientists use the word “observer” to mean “conscious” entity? Could you please convince your fellow scientists to clarify the word “observer” as it is used in quantum mechanics.
IMO the use of the English word – observer – for the measuring device in quantum experiments, was a unfortunate choice and has caused countless amount of mischief by new age gurus like Deepak Chopra. I am really annoyed by it.
I am surprised that even at respectable conferences like FQXi there is a discussion about “observer” in quantum mechanics as if it needs to be a conscious entity. Or is it still true many scientist think that “observer” has to be a conscious entity? It is obviously true that a macroscopic conscious entity can play a role of “observer” not because it is it is conscious but because it is macroscopic.
In a double slit experiment with single photon (at one time) it is said that a the photon as acts as a wave and interacts with itself. Ok, so if a single photon was behaving like a wave then how come it produces a single dot on the target screen. A classical wave (single wavefront) after splitting into two and reaching the screen would not create a peak at only one spot at any specific time. It will create a banded peaks. For that reason I do not understand how a single photon is supposed to behave like a wave and interferes with itself analogy works.
Ok, the interference pattern emerges when multitude of photons are sent through the two slits. There can be a huge time gap between two successive photons. But for the interference pattern to occur how can waves corresponding to each separate photon is understandable, but how the waves at different point in time can interfere? That does not make sense either.
Lastly if the wave function is a probability wave function for a given fixed configuration of the photon source, the distance to two slits, the distance between two slits, width of each slit and the distance to screen, then is the wave function associated with the photon or the above configuration. I say this because, if never send any photon, we know that the wave function is still dictating the potential interference pattern that will emerge in future – as soon as the experiment starts. Remember the experiment works even when a single photon is sent though the slits at a time and there can be arbitrary amount to time gap between successive photons.
It is said that energy of a photon is equal to plank constant times frequency. So how does the amplitude of that wave figures into the energy of that photon. Does it mean that a tiny amplitude vs huge amplitude of photon does not make any difference. Or is it wrong to think of amplitude in this case and only frequency makes sense. But then I do not understand what is this frequency of? Because there cannot be a wave with only frequency but no amplitude.
What is the shape of a photon wave packet? Oblong shape extended over short length? Plank length? How many wavelengths fit in that oblong shape assuming that it even makes sense to think of the wave packet like that.
I know I may be applying too much classical thinking here.
When we say that the atom is the wave function of electron and not an empty space, is that true only in the case of many-worlds theory? The spontaneous collapse theory states that the wave function sometimes obeys Schrodinger’s equation. Does that mean the statement “The atom is the wave function of electron” also true in the case of spontaneous collapse theory? In the epistemic approach, the wave function is a prediction, but what does this approach say about the empty space of the atom?
Thank you Sandip.
I too would like to hear more about the “wave packet”. Bluntly, is it ‘real’ (and analogous to an observed particle)? Or is it just a way to calculate probabilities? I’m not sure when we are talking about waves as something real (in the classical sense) or when we are talking about them as tools to calculate. I think the confusion often exists e.g. “the electron is a wave… of probabilities”.
The idea of a real “wave packet” (being equivalent to a particle) is very attractive to talk about the double slit experiment, for example. I can understand how a single photon or electron “wave packet” can interfere with itself i.e. the little waves inside the packet account for it. But if the particle is an irreducible, point like, single “thing”, it rather defies classical intuition.
Yes, I agree, all puzzling! Perhaps Sean with sort through this for us.
My understanding of the double slit is that the interference can start with the very first particle. It, like subsequent particles, may interfere with itself. Of course, not all particles are interfering. Some reinforce and we see the resulting particle image on the screen. We see the interference pattern built up over time. And, as you say. the particles are fired one at a time (so they are not interfering with each other in the classical sense.)
I was just saying that a “wave packet” leaves some wiggle room for a more classical interpretation: at least you have “real” waves passing through the slit vs. indivisible entities. But, personally, I think the wave packet is a suggestive picture and is actually a method for calculating probabilities i.e. it’s not “real”.
Sean, if I may, I would like to speculate about Sandip’s question about the photon.
If one looks at the single (soliton) photon, one sees that the Planck is the amplitude of the wave.
All the waves we know about are travelling variations of the variable of the medium.
Here, the medium is a spontaneous time-process with a variable rate of evolution.
Then, the photon would be a travelling variation of the rate of evolution of this time-process.
This specific Planck amplitude defines our present universe; everything in it is made of this time-process with that amplitude and boundaries. In other words, this is like a FM radio universe where the frequency varies but never the amplitude. Our universe exists in a tiny slice of the amplitude spectrum. The above and below universes at h+x and h-x are out of tune and do not interact with our universe.
At the big bang, the various h bands appeared as a cool way to pack up as much as possible in a same limited space; for each new Planck band, this space simply appeared empty (constraint quantization). Once this proto atom was filled with all possible values for a Planck, it exploded, and spewed a number of overlapping universes all ignoring each other, as in the original limited space.
More speculation: Given a proper “radio”, one could go to other universes or (!) travel in the gap between universes and avoid time and obstacles … But, would stepping into the gap make us a new exploding sub-harmonic universe?
Hello Sean,
Simple question that I’m sure is addressed, but may not have been clear to me:
Is it correctish to say then that electrons behave differently when bound to an atom than when they are liberated? Is this the same thing as saying they act like a wave when not observed (still bound to the atom), but a particle when observed (removed from the atom)?
Guess I’m asking because it obviously sounds crazy to say things act differently when “observed”, but maybe not as crazy to say things act differently when bound in a system like the atom.
Thanks!
If we only see a particle going through a particular slit because of wave function collapse, and If wave function collapse is an explanation resulting from the copenhagen interpretation- does that mean the common interpretation of double slit contains similar contradictions as those found in the cat killing machine?
Hey,
I’m really curious… from what I understood ψ is a function of where and when a particle exists, which represents the particle’s current quantum state. And the quantum state represents its position and momentum (x,p). Therefore ψ is made up of information about position, momentum, and time.
But then what exactly is “ψ” ?
I arrived at this question because I was trying to understand how momentum can be a wave that oscillates without losing energy every time it changes direction. Then I tried to think about what is doing the oscillating in the first place. And it seems that’s the magnitude ψ. Does that mean the quantum state is oscillating as a function of its place in space? And if that is so, then does that mean the cumulative information about the particle’s position, momentum and time is somehow equal to some max value someplaces, zero other places, and increasing or decreasing when looking at different directions?
Thanks for making these videos, I’ve never taken courses in this but very badly want to learn about it. There’s some super helpful (though many times way over my head) conversation happening in the comments too so thanks also to the commenters out there 🙂
Many thanks for these very inspiring videos.
Question: what is wrong in thinking that the electron is the wave function whose norm squared gives me the probability (for position, momentum etc) and that once I know the outcome then the probability is concentrated on that particular outcomes?
For example: imagine I throw a dice and then I go away to drink a coffee; until I come back and check it, for me the outcome of the dice is ANY number between 1 and 6 with probability 1/6 (like the electron is a wave, associated to a probability) even if in reality the dice already assigned a number; now when I check it, and see that it is a 2 say, for me the “probability collapsed” to that given value (like the wave function collapses when I check the outcome).
So, what is wrong if we accept that the electron has a position with a certain probability, but then when we check where it is then we know it forever (like the dice example above)?
It seems to me that there is nothing magic in the “measurement”: just any random event, when I know the outcome of it, then the randomness disappears.
Many thanks in advance for considering my question.
Thank you for doing what you do. It is a blessing to many of us who are trying to become more enlightened, particularly in our later years.
Philosophically, I’m favorable to the idea of the wave function as ontological. However, I also philosophically would prefer not to share a version of my world with other worlds. Also, I don’t like the idea of hidden variables and it’s not that they would have to be nonlocal. Am I missing an alternative? I’ve read your book “Something Deeply Hidden”. It’s great and I’m getting ready to read it again because I miss things, I forget things, and I’m further along the learning curve so some things will make more sense. I’m also looking forward to your QM text book.
My question is along the same lines as that of Sandip and William Harnew.
My personal preference, (purely a philosophical one), would be an as yet unidentified event or sequence of events that results in a nonlocal, spontaneous wave function collapse (back to the measurement problem). In the double slit experiment with a single photon, the screen on which the interference pattern resolves, somehow causes the collapse resulting in a single point displayed for each photon. As Sandip questioned, does many worlds require a world for every probable point on the screen? What event in many worlds causes the worlds to split for each photon? Does each wave function have embedded in it the number of worlds? What event splits the conscious awareness of the world I occupy verses the other worlds that copies of me occupy. Couldn’t that same event just be an ontological collapse to our one world?
Thank you again for helping all of us remove a little ignorance.
My personal conjecture about some of the above questions…
In the micro-world, the value of every free parameter has a normal distribution tapering off on each side as infinities. Whenever this parameter is constrained, in an atom or under measurement (temporary quantization), these infinities are destroyed and boundaries are formed; this parameter becomes quantized and can now only assume, still under constraint, one of a few discrete values.
The direction of a photon is one such parameter, a quantum number. When the direction of the photon is squeezed by the slit … the direction parameter becomes quantized and the photon will take one of a few allowed directions, each direction regaining, after the slit, their normal distribution, creating the fuzzy edged bands. Destructive interference may be a nice explanation with photons (and other waves) but not so much with interfering electrons or other particles because … the particles do not really get destroyed. Here, it is effectively the probability wave of the direction parameter that gets quantized, thus making the (single or double) slit experiment the simplest Quantum Experiment anyone can do.
ENTANGLEMENT: Two particles are “entangled” when they have spent some intimate (or squeezed) moment together. If we measure or “format” parameter M (squeeze M) for two same particles at the same time, the M parameter becomes quantized (a quantum number) and the two particles must each pick a different value for M (Pauli exclusion). Once released, the two particles will always be found to have opposite values for M, no matter how far apart … Is this a real “entanglement”? No, this is just rigging things from the start. By measuring M, we choose M to be the one parameter that will be quantized and shared/split à la Pauli.
Thanks Sean for this amazing series.
I was just wondering what will happen to the “observed” (wave function collapsed) particle after it has been “unobserved”? Does the particle returns back to being wave-like or will remain as a particle perpetually?