Entanglement is one of the most important features — arguably, when you get down to it, the most important feature — of quantum mechanics, but it’s often glossed over in how we introduce the subject to students. Here we dive in, and I use this as an excuse to eventually talk about some of the different physical theories vying to be a complete formulation of quantum mechanics.
Update: I originally uploaded the wrong file, this should be the right one!
The Biggest Ideas in the Universe | 8. Entanglement
And here is the associated Q&A video. (Sorry I was in a hurry and didn’t do the lighting correctly … I’ll never make it big in Hollywood at this rate.)
The Biggest Ideas in the Universe | Q&A 8 - Entanglement
Hi Sean Carroll! Thanks a lot for the videos! Really! =)
So, in many worlds interpretation, there’s a branch of the wavefuncion that every spin ever measured was “spin up”?
And a universe that the spin is always up, except if the experiment is made in mondays, in mondays it’s always down?
Also, seemingly, this other universes must have different laws of physics then ours, since it behaves in a solid repetitive pattern that are different than ours…
Thanks
Hi Dr. Carroll,
You may have explained something I always found mysterious. The text books seem to ignore part of the story. Say you have a large collection of particles prepared in a superposition of two energy states. Let’s say for simplicity that you get either state with probability .5. We can figure out an expectation value, but there is a chance, all be it small, that a preponderance of the measurements will be in the higher energy state. It always seemed to me that this would represent a violation of the conservation of energy. How does the universe have a book keeper to balance things out? Am I right jumping to the conclusion that the collection may be entangled with the preparing device such that the increase in energy measured in the collection is balanced by a decrease in energy in the preparing device. Thank you again for the great videos.
Prof. Carroll, thank you very much for your thought provoking “Biggest Ideas” videos that are making me (and I believe others) look at the concepts/facts we learned in school in a new/interesting light.
I had question. I understand from your earlier video that you support eternalism and the “block universe” view. In this “Entanglement” lecture, you say you believe in Everett’s “many worlds” idea. Are these two consistent? If I understand “many worlds” correctly, it seems to me that in that view a future state of the universe isn’t as predictable (or “already there”) as the “block universe” would suggest. Or are we to suppose that regardless of how many possibilities that “many worlds” might suggest, we can tell with certainty (in line with “block universe”) that there will always be one unique path of reality that is traced through these possibilities?
Your description of different QM interpretations was very helpful; I’m glad you included your own opinions, and flagged them as such. I would be interested in what you think about transactional interpretations, and how they compare to others (e.g. if we have signals travelling backwards in time, do those count as local hidden variables?).
Hi,Sean! How does Many Worlds explain the double slit experiment? Why doesn’t the wavefuntion decohere when it touches the slits or even when it bumps into the air molecules which are present in the experiment?Thanks!
Sean, you appeared to use the terms “entanglement” and “superposition” interchangeably. Don’t the two terms have different meanings in QM?
Do we need extra hidden variables? Nobody knows what the variable TIME is. Nobody knows what the “variable” CAUSALITY is. They are both hidden in the sense that they are hidden from our understanding, and they are both everywhere/everywhere in physics. We are definitely missing, or is it, ignoring them?
Hi Dr. Carroll. I have a separate question. In many worlds, how does the transition from a superposition to a pure state occur and how is it explained that repeated measurements produce the same result. When I have heard of many worlds the observable seems to be the focus but not the other aspects of collapse. Thanks again.
What are some “non-obvious” predictions of many worlds? You mentioned the Schrödinger equation not being violated, but I suspect you could make some other predictions which take many worlds a little further.
And if many worlds somehow turns out to be falsified, what do you think will be the next best theory of quantum mechanics?
Since the arrow of time doesn’t seem to be a feature of quantum mechanics why isn’t time non-locality talked about? Or is that super-determinism?
You said the wavefunction is in infinite dimensional Hilbert space.
But in the double-slit experiment, the wavefunction is in physical 3D space going through both slits.
So which is it?
Does the instantaneous influence of a particle on its entangled partner mean there is such a thing as a universal “now” ?
I’ve heard that one of the challenges in the development of quantum computers is maintaining superposition. How do they know if it’s being maintained? Is there a way to determine whether a particle is in superposition or not?
Bell’s inequalities and the experiment based on his idea sound intriguing. Is there a simplified description that might help us understand how this seemingly impossible result was achieved?
Thanks for these fascinating videos.
I’d like to ask a question about the wave function in Hilbert space.
The description given at the end of the previous QA video seems very analogous to what a complex transfer function of a system with respect to frequency is. We can see how the complex vector changes with frequency in the same way the wave function vector changes with space. I have never thought of a transfer function as a kind of vector in infinite frequency vector space, but it seems we can? Would this sort of analogy between transfer functions and wave functions be a correct line of reasoning?
Would non-local hidden variables make parallel universes unnecessary? Because, to be honest, a bit of non-locality seems much more reasonable than bazillions of parallel universes.
Einstein believed that quantum mechanics wasn’t fundamental but must emerge from some deeper principles. This seem very reasonable to me. Is this a minority view today or do most physicists believe that the equations of quantum mechanics represent something truly fundamental about physical reality?
Who first brought the idea of the epistemic approach? According to this interpretation, does it mean that the wave function is a prediction of something beyond the observable universe like dark matter or dark energy? If our discovery of dark matter and dark energy fit with the explanation of the epistemic approach, would that falsify the many-worlds interpretation?
am I to understand that there is another world in which a copy of me observes the cleveland browns winning a super bowl? that would be a super position to be in.
My question goes in line with that of LINEU MIZIARA above: there are system that can be prepared in a lab where entanglement is maintained (not only the double slit experiment, but I suppose Bose-Einstein condensates, Cooper pairs in superconductors, even Q-bits in quantum computers). Those entanglement processes do not seem to “branch” the universe, otherwise the corresponding systems will not behave so “quantumly” in our branch as they actually do in the experiments. Does that means that some subset of entanglement processes branch the wave function of the universe but others do not ? If yes, does that means that many-wolds needs an extra rule to tell which entanglement processes create a branch and which ones do not, so we can see in the latest all the quantum fun?
Many thanks for all your work!
Dr. Carroll, I can’t thank you enough for your commitment to the communication of popular scientific understanding. I especially enjoyed your debates with William Lane Craig and Eben Alexander.
**Can you, in your view, explain some of the specific problems with the pilot wave theory formulation of quantum mechanics, and why you subscribe to the many worlds interpretation, i.e. are there any phenomena which strain its credulity?**
The allure of a theory which seems to cherry-pick the right flavors of classical mechanics seems to be a deceptively enticing interpretation. The modest, undergraduate physics major, in me would be extremely grateful.
What if we perform the double slit experiment with a monitor recording which slit the photons pass through, but the monitor doesn’t reveal that information instantly, just stores it in a sealed box like the one Schroedinger’s cat was in? If that prevents the observer from being entangled with the photons, does he/she see an interference pattern?
Does the entanglement need to happen instantly for the interference to disappear?
Could the wavefunction extend outside spacetime and this is how it can bring about apparent non-local effects?
Hi Dr. Sean! Thanks a lot for the videos! Please, did I understood many worlds correctly?
Let me exemplify working in an example you gave in your blog, with a little changes, regarding a double slit experiment and electrons.
Electrons are being fired, goes through a double slit, and can be detected in a one dimension detector, in places “a”,”b”,”c”,”d”,”e”, “f”, “g” and “h”
If the electrons hit mostly detectors “c” and “f”, and mostly doesn’t hit detectors “a”, “d” and “h”, t’s a particle pattern.
If the electrons hits “a” a little, “b” a lot, “c” a little, “d” a lot, “e” a little, “f” a lot, “g” a little and “h” a lot, it’s a wave pattern.
We also have a “which way” device we can put if we want to.
And we also can make a quantum eraser, like this: an electron is fired (e1), goes through the slits, a second electron (e2) is entangled with e1 in this ways:
If e1 goes through the slit “1”, e2 is spin up. If e1 goes through the slit “2”, e2 is spin down.
If we measure e2 in the vertical axis, we have an which way experiment. If we measure e2 in the horizontal axis, we have a quantum eraser.
Normal double slit:
The electron is fired, its wave function goes through the slit and hits the detector, and the universe branches into the many places the electron could be detected (place “a”, place “b”, and so on). The universe splitted in 8 universes.
Which way;
The electron is fired, it wave function hits the which way detector, becomes entangled with it and the universe branches into two, one that the particle went through the slit “1” and other that the particle went through the slit “2”, and is detected a particle pattern. The universe splits into 16 universes.
Delayed choice
The electron is fired. It hits the which way detector and the universe branches into two, one that the particle went through the slit “1” and one that the particle went through the slit “2”. It hits the detector and makes a particle pattern.
Now, we have (at least) 16 universes, just like the which way experiment (e1 went through slit 1 and hit the detector in a, e1 went through slit1 and hit the detector in b, and so on…
Now comes the tricky part:
When we choose to measure the spin of e2, we can do it in the horizontal axis or vertical axis.
Let’s say we put a random number generator to choose if we are going to measure in the vertical or horizontal.
Now the e2 gets entangled with the measuring device. And the universe splits 2 more times.
By now we have 32 universes.
Now, supposing the random number generator makes the measure to occur in the horizontal axis, not giving the which way information.
So, the universe splits into two more, one that the electron was spin left and one that the electron was in the spin right.
Now, suppose the random number generator chooses to measure in the vertical axis…
Now here comes the tricky part!
The universe doesn’t splits anymore!!!! Because if e1 hit the detector in a place it only could hit if it went through the slit 1, then e2 MUST be spin up! Likewise, if it hits in a place or only could hit if going through the slit 2, then it MUST be spin down!
So, please, is it right? Thanks! =))))
Hi Dr. Carroll,
Love the lectures! If you would humor me with these questions, borne out of thinking of spin and the angular momentum of the system interchangeably, maybe that’s preposterous:
1) Why is spin (and therefore angular momentum) quantized, when the building blocks of angular momentum, i.e. mass and velocty, are continuous in nature?
2) The spin of a planet is the sum of the spins and the orbital angular momenta of all its elementary particles. Let us say we have a hypothetical device that can measure the spins and orbital angular momenta of all the particles that make up Earth, at any given point of time. Furthermore, this device can be setup to measure this along our choice of x/y/z axis. Let us separately say, that we have a very real orientation for planet Earth’s spin (?) , where is the logical fallacy?
3) Does the conservation of angular momentum have anything to do with why electrons can not be made to spin any faster/slower, i.e. the magnitude is intrinsic?
Thanks again for the fantastic lecture.
I had a troublesome thought about the many worlds theory that I am sure I am just misunderstanding. You said both that in many worlds, whenever entanglement occurs a “copy” is made of the world, but you also mention that all the worlds that will ever be are already there. So my question is – how can energy be conserved if, for every entanglement (too many to count per second) whole new universes are “copied/created”. Does this not violate all thermodynamic and conservation laws? Where do the energy come from to create these new worlds? Are they even real in the sense that they are like our world just in a different dimension? You also mentioned orthogonal vector spaces – how does that translate to our sense of space and time?
Thanks Prof Carroll for the videos! You seemed to imply that decoherence is a relevant phenomenon only w/in Everettian QM. But isn’t decoherence, or some process that eliminates the interference term for objects in superposition, relevant in one-world theories as well? Given the same evidence needs to be explained: double-slit interference, plus no observed macroscopic objects in superposition?