Although I’ve read quite a few books on quantum mechanics—popular books, not books intended for physicists—I still don’t understand it. That is, I can understand the history, the controversies and some of the phenomena, as well as the various interpretations of quantum mechanics. But when it comes to stuff like entanglement, I’m baffled—not just by its existence, but what it really means physically and how it could be possible.
Sean Carroll (the physicist) has just published a paper in Nature that is about as clear an explanation of the weirdness of quantum mechanics as I can imagine. I still don’t understand entanglement, but Carroll does point out why people like me have difficulty grasping some of the concepts and predictions.
Since, as Carroll notes, Heisenberg “first put forward a comprehensive version of quantum mechanics” in 1925, it is in one sense the 100th anniversary of quantum theory:
Click below to read for free:
I’ll give a few quotes under headings that I’ve made up:
Why quantum mechanics is qualitatively different from classical mechanics.
The failure of the classical paradigm can be traced to a single, provocative concept: measurement. The importance of the idea and practice of measurement has been acknowledged by working scientists as long as there have been working scientists. But in pre-quantum theories, the basic concept was taken for granted. Whatever physically real quantities a theory postulated were assumed to have some specific values in any particular situation. If you wanted to, you could go and measure them. If you were a sloppy experimentalist, you might have significant measurement errors, or disturb the system while measuring it, but these weren’t ineluctable features of physics itself. By trying harder, you could measure things as delicately and precisely as you wished, at least as far as the laws of physics were concerned.
Quantum mechanics tells a very different story. Whereas in classical physics, a particle such as an electron has a real, objective position and momentum at any given moment, in quantum mechanics, those quantities don’t, in general, ‘exist’ in any objective way before that measurement. Position and momentum are things that can be observed, but they are not pre-existing facts. That is quite a distinction. The most vivid implication of this situation is Heisenberg’s uncertainty principle, introduced in 1927, which says that there is no state an electron can be in for which we can perfectly predict both its position and its momentum ahead of time.
On entanglement.
The appearance of indeterminism is often depicted as their [people like Einstein and Schrödinger’s] major objection to quantum theory — “God doesn’t play dice with the Universe”, in Einstein’s memorable phrase. But the real worries ran deeper. Einstein in particular cared about locality, the idea that the world consists of things existing at specific locations in space-time, interacting directly with nearby things. He was also concerned about realism, the idea that the concepts in physics map onto truly existing features of the world, rather than being mere calculational conveniences.
Einstein’s sharpest critique appeared in the famous EPR paper of 1935 — named after him and his co-authors Boris Podolsky and Nathan Rosen — with the title ‘can quantum-mechanical description of physical reality be considered complete?’. The authors answered this question in the negative, on the basis of a crucial quantum phenomenon they highlighted that became known as entanglement.
If we have a single particle, the wavefunction assigns a number to every possible position it might have. According to Born’s rule, the probability of observing that position is the square of the number. But if we have two particles, we don’t have two wavefunctions; quantum mechanics gives a single number to every possible simultaneous configuration of the two-particle system. As we consider larger and larger systems, they continue to be described by a single wavefunction, all the way up to the wavefunction of the entire Universe.
As a result, the probability of observing one particle to be somewhere can depend on where we observe another particle to be, and this remains true no matter how far apart they are. The EPR analysis shows that we could have one particle here on Earth and another on a planet light years away, and our prediction for what we would measure about the faraway particle could be ‘immediately’ affected by what we measure about the nearby particle.
The scare quotes serve to remind us that, according to the special theory of relativity, even the concept of ‘at the same time’ isn’t well defined for points far apart in space, as Einstein knew better than anyone. Entanglement seems to go against the precepts of special relativity by implying that information travels faster than light — how else can the distant particle ‘know’ that we have just performed a measurement?
Yes, I know that this cannot be understood in terms of everyday observation, but what I fail to understand—and perhaps some reader can explain this to me—is exactly what properties of a particle can be affected by ascertaining properties of another particle light years away.
I’ll leave you to read the various interpretations of quantum theory, the most trenchant involving whether it actually represents physical reality or is merely a theory meant to explain experimental results. I’m not sure where Carroll fits on this spectrum, but I do see that while he describes another interpretation, the “Everttian or many-worlds interpretation,” I thought that Carroll used to favor this explanatin, which of course is deeply, deeply, weird, creating a new but unobservable universe each time an observer measures something. His summary of the state of the field is this:
So, physicists don’t agree on what precisely a measurement is, whether wavefunctions represent physical reality, whether there are physical variables in addition to the wavefunction or whether the wavefunction always obeys the Schrödinger equation. Despite all this, modern quantum mechanics has given us some of the most precisely tested predictions in all of science, with agreement between theory and experiment stretching to many decimal places.
The big remaining problem. If you read even a bit about quantum physics, you’ll know this:
Then, there is the largest problem of all: the difficulty of constructing a fundamental quantum theory of gravity and curved space-time. Most researchers in the field imagine that quantum mechanics itself does not need any modification; we simply need to work out how to fit curved space-time into the story in a consistent way. But we seem to be far away from this goal.
What good is quantum mechanics? But of course quantum mechanics, even if not comprehensible by the standards of everyday experience, has been immensely useful, for we’ve long known that its predictions match observations about as closely as any theory can. Here are the benefits:
Meanwhile, the myriad manifestations of quantum theory continue to find application in an increasing number of relatively down-to-Earth technologies. Quantum chemistry is opening avenues in the design of advanced pharmaceuticals, exotic materials and energy storage. Quantum metrology and sensing are enabling measurements of physical quantities with unprecedented precision, up to and including the detection of the tiny rocking of a pendulum caused by a passing gravitational wave generated by black holes one billion light-years away. And of course, quantum computers hold out the promise of performing certain calculations at speeds that would be impossible if the world ran by classical principles.
And don’t ask me what “quantum chemistry” is, as I know it not.
These are just small excerpts. Go read about the theory in its centenary year.
Entanglement. It’s never about one particle, always at least two. And they don’t exist in two states, but in one state, the classic example being when one necessarily has its spin pointing in the opposite direction from that of the other. (Experiments use other things, such as light polarization.) So you have two particles in a superposition of two states, one with particle A having spin up and one with particle A with spin down. Whatever A’s state, B’s is the opposite. You measure A’s spin and you immediately know what B’s is, even though it may be far away, too far for a subliminal message to have told B in what state A is in. That is a violation of what Einstein called locality. Einstein’s pet theory, Special Relativity, says nature is local, so he was convinced QM is not complete because of this, something must be missing.
Yes, but not just any two particles, right? Do you have to create two particles that are entangled at the outset?
Yes, that’s right. The important (and unsettling) part is that this is not merely the same as saying there are two boxes A and B, one of which contains a marble and the other doesn’t, so if I separate the boxes and open box A and find it empty, I immediately know box B contains the marble.
It’s the following: There are two boxes A and B which collectively contain one marble. Until I check to see which box has the marble, each box behaves as a superposition of boxes which both contain and don’t contain marbles. (This means they behave differently than a filled or empty box would alone.) Once I check box A and see it is empty, box B immediately ceases to behave as a superposition of the states, and starts to behave as a box with a marble behaves.
I stil do not understand. WHICH TWO PARTICLES a million light years apart are we talking about? How did they get entangled in the first place? It cannot be any two randomm particles, as commenters have said.
There are many situations in which two particles are entangled. For instance, an atom may transition to a lower-energy state by releasing two photons. But conservation laws dictate the photon polarizations must be complementary. Experiments show that when you measure the polarization of one of the photons, the other one picks up a polarization of the other orientation. But these photons are separated by a distance too far for any information to have traveled from one photon to the other by the time both measurements are made. In other words, the second photon was affected by the measurement made on the first photon instantaneously. Extrapolate to an arbitrary photon separation (millions or billions of light years apart) and the same phenomenon should hold.
The deep answer is that ALL particles in the universe are entangled. An electron in my living room and an electron in the Andromeda Galaxy are affecting each other, however weakly, through electrostatic force and through their magnetic moments. Weaker still are the gravitational forces. In a deep way, we can only speak of the wave function of the entire universe.
I think the entanglement is described as between two particles that were created simultaneously by some reaction like a decay of an elementary particle, into a positron and an electron, say, that move in opposite directions toward two separated observers. Since angular momentum has to be conserved, if one of the particles has spin “up” as measured by one observer, the other particle created at the same time and entangled has to have spin “down” in the same axis. The other observer will so measure. The weird part is that each particle in the pair has potential spin states in both directions in a state of superposition during its journey to the spin detector. It seems there was no at-birth commitment to one up, the other down when the two particles formed from the decay. Rather it seems that the spin that will be recorded as one of the particles interacts with the spin detector at one location is random. Yet whichever is detected, the positron “knows” to yield the other direction when it interacts with the spin detector at the other location. It can be shown that even if the distance between the observer locations is too great for an imagined controlling signal to have passed from one “driving” particle to the “driven” particle in the time between the two detections, the spins still behave.
Yes. The standard example is of two spin 1/2 particles which in are what is called a singlet state, wherein the total spin of the two is zero — one up and one down. An example is the decay of a pi-zero meson into a positron and an electron. You can imagine it to be 1, but that is a triplet state, not a singlet, and the triplet spins can be aligned in the same direction.
There is something I had read somewhere about photosynthesis which weirded me out, but I don’t know if I had read it right and maybe someone here can comment on it.
Its that when a photon is absorbed by a chlorophyl molecule, it raises the potential energy of electrons. This elevated potential energy is xfered to other pigments without their also absorbing photons, apparently by quantum tunneling (?) I don’t know what that means, but it reads like quantum entanglement to me.
No. Tunneling and entanglement are two different things. Tunneling is when a particle manages to cross a potential barrier which it would not be able to do by classical physics. One particle. Entanglement concerns correlations between more than one particle. Both phenomena are weird, though, or at least non-intuitive.
Ah, thank you. Much better.
Tunneling can happen in classical-physics concepts, if one is dealing with waves. The QM surprise is that it can also happen to particles, by dint of wave-particle duality.
Right; however, entanglement also happens in photosynthesis, and apparently plays an important role. I can try to dig up a reference later, when I’m at a computer.
Here’s an article on it:
https://physicsworld.com/a/is-photosynthesis-quantum-ish/
That also happens between the Rieske iron-sulfur centres of the protein complexes of the electron transport chain.
There is an ongoing debate about whether some of the weirder quantum effects called non-trivial quantum effects* (entanglement is one of them) may be used by biological systems as it might have happened that evolution stumbled upon them. This is called quantum biology and several processes are proposed to make use of the quantum effects including photosynthesis (here the effect in question is called coherent exciton transport and it basically means very efficient transfer of energy from the light absorbing part of the photosystem to where the reactions happen), magnetic compass in animals or olfaction. But the last article I saw on photosynthesis claimed that the classical explanation was sufficient. There are many nice and readable review articles on this topic as well as a popular science book by Jim Al Khalili called Life on the Edge.
*Trivial quantum effects would be just that you need to solve quantum mechanical equations to determine the structure of biomolecules and their properties like chemical reaction barriers. But the distinction is not clear cut.
There is an analogy that can be helpful to conceptualize quantum entanglement. Consider a story about a “glove left home”. You take a walk on a cold winter day. Your hands get cold so you decide to put on gloves. But when you feel at the pockets of your coat you realize you only have one of the gloves with you. You deduce that you must have dropped one of the gloves as you left your home. Now before you take the glove out of your pocket and look at it, it is 50-50 whether you have the right or left glove with you. But if you look at the glove and ascertain that it is the right glove, you instantaneously determine the lefthandedness of the glove left home.
In classical physics there is no real conceptual problem here. We understand that the 50-50 chance describes your knowledge of the gloves, not their actual reality. But QM is fundamentally different. If it were possible for macroscopic things like gloves to behave the way we know particles do, we would have to say that the gloves are “entangled” and that they simply did not have a definite handedness, but rather existed in a superposition of states. It is only the act of observation that caused the handedness of the glove with you and the corresponding opposite handedness of the glove left home to come into existence.
I suspect that human brains really aren’t wired to intuitively understand quantum physics in a deep way. Our ancestors on the veldt had to intuitively grasp certain aspects of Newtonian physics well enough to erect huts, throw spears, invent bows and arrows and hunting darts and boomerangs and such. But never before the 20th century did hominids have to trouble their minds about quantum superpositions.
Different brains are “wired” for different tasks. I am probably much smarter in most respects than a bat. But my primate brain would be helpless to make heads or tails of the sensory data a bat gets about the world from its sonar and echolocation. My brain doesn’t swing that way. I could perhaps study in agonizing mathematical detail the bat’s sensory data, but I could not put it together to get a perception of the world the way a bat’s brain can do. In the same way I might fully understand the mathematical details of a quantum system, but I can’t put it together to intuitively grasp the reality described by the mathematics.
I liked this comment, thanks.
Here’s where you lost me: “Now before you take the glove out of your pocket and look at it, it is 50-50 whether you have the right or left glove with you.” I’d have thought that it was 100% that it was whichever one was actually in your pocket, notwithstanding that you might not know which one that was until you looked.
In classical physics, reality is 100% even if our knowledge is 50%. Quantum physics, which DOES describe reality is different. It is not that reality is vague. Just that intuitions we import from classical physics are wrong. Consider the famous uncertainty principle between position and momentum of a particle. A general particle does not have a precise position, nor a precise momentum. All we have is probability distributions that describe the likelihood of the values we would get if we measure position or momentum. The standard deviations of those probability distributions satisfy the inequality DxDp >= h/4pi where h is the famous Planck constant.
What does that mean? The uncertainty principle is not just a limitation on what we can measure about a particle. It describes the reality of the particle. Suppose, for the sake of argument, that religious people are right and there is an All-Knowing God. If so, God could not tell you the precise position and momentum of an electron. Instead God would tell you that you ask a stupid meaningless question and that you are fundamentally confused about what an electron really is. Our classical intuition of a particle as something that has a precise trajectory and therefore a precise position and momentum at any instant time is simply wrong.
Getting back to my story about “quantum gloves”, our intuition says a glove is right or left handed. Quantum theory says no. A typical state of a glove is a superposition of righthanded and lefthanded states.
If we can’t tell without looking whether what’s in my pocket is a right-handed glove or a left-handed glove, then how do we know without looking that what’s in my pocket is even a glove at all? Why couldn’t it be something else entirely (or for that matter nothing at all)?
I understood some of this when I studied it. But that was fifty years ago. A few points:
1) it describes things within atoms and molecules
2) there are other forces besides gravity and electrical. They only kick in for subatomic particles: nuclear strong force and nuclear weak force. These allow the nucleus of an atom to hold together when one would expect the protons to repel each other by electric force.
3) the quantum levels in an atom fall out of the math that describes these forces. If I recall the equations can only be solved analytically for a hydrogen ion.
4) everything is different from the macro world because of these forces that are only relevant at subatomic sizes.
Can’t remember much else. Wikipedia has an article on it.
https://en.m.wikipedia.org/wiki/Quantum_mechanics
Some mid-scale objects do exist in a quantum superposition of states. Most (all?) require very very low temperatures, since thermal jostling easily collapses the superposition. For example, Bose-Einstein Condensates and Soliton Josephson Junctions.
Note that thermal jostling acts as a “measurement”, so it’s way different from the usual experimental notion. The “measurement problem” is a serious unsolved problem in QM: what is a “measurement” in the first place?
Thanks for the info.
Am I the only one getting a paywall?
No you are not alone. But you can register for free just by giving your email address and making up a 12 character password…oh and giving your “family” name….which can be anything. I am extremely reluctant to give out info, but i was ok with hacking this request with new made up stuff to get a sean carroll article…and you can download a pdf copy.
Richard Feynman once said “If you think you understand quantum mechanics, you don’t understand quantum mechanics”.
If that’s what Feynman thought, the rest of us are probably beat from the git-go.
Even more beat for those whose formal scientific education ended in their early teens.
Usually it’s our host who advances my scientific knowledge a little, but today some of the knowledgeable readers here provided comprehensible explanations. Any moment now, instead of seeing the usual cats on this site, I might glimpse Schrodinger’s cat. 😼
And Heisenberg said, “Not only is the Universe stranger than we think, it is stranger than we can think”. JBS Haldane said something similar.
I snipped this Feynman quote from his lecture-to-laypeople-based book on quantum electrodynamics:
“What I am going to tell you about is what we teach our physics students in the third or fourth year of graduate school—and you think I’m going to explain it to you so you can understand it? No, you’re not going to be able to understand it. Why, then, and I going to bother you with all this? Why are you going to sit here all this time, when you won’t be able to understand what I’m going to say? It is my task to convince you not to turn away because you don’t understand it. You see, my physics students don’t understand it either. That is because I don’t understand it. Nobody does.”
Classic Feynman. I had not seen this quotation before. The Feynman Lectures were part of my undergrad upbringing in the 1960’s, including his presence on some grainy B&W 16mm film if I recall correctly. I used his lectures to supplement the physics high school course I taught in the early 70’s with a three-volume paperback set being one of my first purchases with public taxpayer dollars for our high school library science shelves,
Feynman never said that. What he said, in one of his 1965 Cornell Messenger Lectures, was, “I think I can safely say that nobody understands quantum mechanics.” This was meant as a joke, but also seriously in the particular sense that Quantum Mechanics defies intuitive understanding. Feynman certainly did not mean that nobody understands Quantum in any other sense, for example mathematically. Obviously Feynman and many other physicists understand Quantum Mechanics well enough to use it to make predictions that are verified experimentally.
Reading Edwin Abbott’s book “Flatland” helped me understand that there are dimensions to reality that a two, or three, or four dimensioned thinker simply cannot even imagine. I have christened other dimensions, universes, etc. Absolute Elsewhere, and no longer obsess.
Mind blown. Electrons may not actually exist :
I cannot prove that electrons exist, but I believe fervently in their existence. And if you don’t believe in them, I have a high voltage cattle prod I’m willing to apply as an argument on their behalf. Electrons speak for themselves.
Seth Lloyd Quantum Mechanical Engineer, Massachusetts Institute of Technology
Sean is still an Everettian. Actually, I don’t think the frequent splitting off of new universes is quite as incredible as it sounds. Another way of saying it is that some states of the universe become inaccessible in practice, every time a quantum entanglement decoheres. So inaccessible that you might as well call them a separate universe. But there’s no magic moment when this happens. It just rapidly becomes less and less probable that those states will have any noticeable effect on us.
A problem that I have with many-worlds arises in the double slit experiment with one-at-a-time particles. Where each individual particle ends up is not one of a choice of two positions (splitting) but effectively on a a continuum with varying probability, and thus an infinite set of positions for each particle. Perhaps a “too many worlds” problem?
Can someone help me with this?
Even worse (for me) is simple particle decay. At any instant there’s a probability that an unstable particle (a free neutron, say) will, or won’t, decay. Do we get new universes for each of those instants? When those “instants” can be arbitrarily small?
I think that the many-worlds explanation is that in one world the particle decays and in the other it does not. If one observes decay, then one’s version of self is in the same world as the decay and vice versa.
However, this raises the problem of what observation on oneself dumps one into the appropriate world.
“And don’t ask me what “quantum chemistry” is, as I know it not.”
Well, you know who to ask! Though it might not help. I’ve been asking for 20 years.
An ex chemistry professor once told me that “quantum chemistry is the only real chemistry” (FSVO “real” of course).
Such a great topic. Experiencing confusion over quantum mechanics seems to be essential to an examined life.
The Observer. A particle’s position and momentum don’t exist until they are measured by an observer. Why should a particle’s state depend on whether someone is looking at it? Can an ant be an observer? What if there were no living things capable of observation? Can a rock be an observer? Can the particle under investigation be its own observer? What is it about the observer that “perturbs” the particle such that it makes its appearance known? There must be a perturbation, else the particle would just go about its normal business. No?
I’ve read many books and articles about Quantum Mechanics—and took P-Chem in college—but the entire topic is so counterintuitive that I still feel like I have to relearn what I’ve already learned over and over again before even a little of it sticks.
At least some professional physicists must feel that understanding quantum mechanics is hopeless, even if the mathematics works. The instrumentalist’s approach is to just “shut up and calculate!”*
https://www.quantumdiaries.org/2012/01/13/shut-up-and-calculate/
I like to think that “observer” is an anthropomorphism, and that anything with which a particle interacts is the observer. The trouble is that QM itself prevents us from observing this :).
One thing that puzzles me is this: if, in the Many Worlds interpretation of QM all the possible outcomes occur, what do the probabilities mean?
Can a physicist enlighten me or correct my misunderstanding?
Probabilities relate to the proportion of universes in the multiverse in which a particular outcome is observed. A 70% chance of X occurring with a 30% change of Y occurring means that in 70% of universes X will be observed and in 30% Y will be observed. Both outcomes occur, but in different percentages of all universes.
No, many worlds theory does not work that way. There is no way to say that some universes are more likely than others. They are all equally real to the people living in them.
The EPR reference reminded me of the Alfer Bethe Gamow paper whose third author was selected for the “Alpha Beta Gamma” sound. When will we see a collaboration on a paper by Stephen Wolfram, Kip Thorne and Alessandra Follia? 🙂
Yes, but Bethe was added, not Gamow.
“… all the way up to the wavefunction of the entire Universe.”
Do we actually know that? I suspect not.
In some reasonable sense of “know”, yes. It’s a short equation, but of course a universe worth of data is encompassed by a few variables.
Hi, I’ve been a reader but this is my first comment.
This is something I’ve been musing over since I happened on the work of Donald Hoffman and colleagues. They used evolutionary game theory to support the hypothesis that our senses may not have evolved to perceive a veridical part of objective reality but to accurately perceive fitness payoffs. That may be relevant to these very weird dilemmas of physics like the observer effect (as well as to the philosophical puzzles that neuroscience and consciousness studies are grappling with). When I came across this paper, I was blown away… It makes sense and could have a huge implications if they are right. Unfortunately I lack the math skills to do a critical evaluation of their reasoning.
Hoffman, Singh & Prakash, “The interface theory of perception.” Psychonomic bulletin & review 22, (2015).
https://doi.org/10.3758/s13423-015-0890-8
If I understand correctly and if what the authors claim is right, then maybe the missing piece to the puzzle of unifying physics is a theory that describes the relationship between the human perceptual strategy’s fitness payoffs function and objective reality… ? To get to a Theory Of Everything that reconciles newtonian physics and general relativity, perhaps biology is needed because if the authors are right, newtonian physics relies on measures that emanate from a framework based on premises rooted in our perception of the physical world – and thus it too is based on those fitness payoffs, not on veridical objective truth (see the «Measured World» section of the paper). There has to be a relationship between the fitness payoffs function that our senses are tuned to and objective physical reality but what these authors claim is that this function is akin to the interface of a computer: we can reliably use it but what we use (icons, cursors, etc.) is nothing like the physical inner workings of the computer (chips, circuits, diodes, etc.) that do the work. Thus we can take what our senses give us access to seriously, but not literally.
What do you think?
This is very true. We humans evolved to survive in a world where things are roughly the same size as us, at least to within two or three orders of magnitude, and where those things are moving no faster than a few tens of km/h. That covers pretty much everything that could kill us, or that we could kill and eat.
Evolution did NOT provide us with ways to perceive (still less to interact with) things that are extremely large, like black holes, or extremely small, like the quantum realm. And that’s why, at some level, we find both general relativity and quantum mechanics to be counter-intuitive and disturbing.
And yet, as Sean Carroll and others remind us, both general relativity and quantum mechanics make predictions about the universe that are confirmed to astonishingly high accuracy by experiments. In that sense, at least, they do reflect the universe as it truly is.
I don’t buy the premises of these arguments. We absolutely evolved in the realm of the microscopic and quantum effects. Our immune system is one example, and our vision systems work at quantum levels. The arguments given seem to rely too much on conscious perceptions, but we are after all just amalgams of cells, all of which deal with quantum effects.
I’m reminded of the opening of Douglas Adams’s novel “The Restaurant at the End of the Universe”:
“There is a theory which states that if anyone ever discovers what the Universe is for and why it is here, it will instantly disappear and be replaced by something even more bizarre and inexplicable.”
Article is not actually totally free and half of it is paywalled… 🙁
Please see my reply to Alexander in comment 5 above. You (at least I could) can sign up without revealing any security…just your email address. Your email password is not required.
My impression was that what “quantum chemistry” is, is just what we also call just plain-old “chemistry”. Or do I misunderstand?