The electron passing through both slits at the same time (or any other phenomenon of wavefunctions) has never seemed strange, or any less intuitive than any other explanation, but maybe that’s just me.
Your cite says:
Shouldn’t they be exactly the same, if experiment cannot distinguish the interpretations? Or is that an artifact of their computation?
About 90% of quantum weirdness comes from wave-particle duality, and this is one example. It is possible to intuitively understand wave-particle duality, if you train your intuition properly, though it takes some work. That last 10% of weirdness, though, is where you start getting into Bell’s inequality and the like, and I don’t think that anyone has ever managed to train their intuition into accepting that.
There are dozens of different interpretations of quantum mechanics, all of which produce exactly the same answers. Sometimes one interpretation or another will make it easier to see how to set up some particular calculation, so that’s convenient, at least (that’s the reason why most of the interpretations were developed). But every single interpretation must sacrifice something or another that seems like it ought to be intuitive. Bell proved that, by showing that a reasonable-sounding set of assumptions together imply a mathematical relationship (his eponymous Inequality), which quantum mechanics has been empirically verified to violate.
Since they all give the same answers, and they’re all unintuitive in at least some way, “shut up and calculate” is indeed the preferred stance of most physicists. Some may seem less unintuitive than others, and so if you happen to like one better, sure, knock yourself out: You’re not wrong. But the catch (speaking as a teacher, here, not as a physicist) is that which one seems least unintuitive will vary with the person doing the intuiting: What works best for you might not be what works best for the person sitting in the desk next to you.
And of course, it should be emphasized that the lack of intuitiveness of quantum mechanics isn’t a flaw in the physics, but a flaw in our intuition. The world is what it is, and we’re tasked with describing that: The world is not tasked with conforming to our descriptions.
looking at that cite again, I think maybe the trajectories they chose to plot match approximately. I suppose if they plotted them all, they might match exactly, but then you couldn’t grasp the plot, because too many trajectories.
It uses a different formal framework, mainly because the postulates of quantum mechanics and Bohmian mechanics are different, but the relationship between the two is clear enough that they can be shown to be empirically equivalent.
It is an artifact of the visual representation - you can only approximately recreate a continuous distribution by selecting a finite number of trajectories.
PBS Space Time has put a lot of effort into making some of these topics accessible to a general audience while minimizing the math needs as much as possible. They are great for overviews.
They have a fairly good one related to this effect through the Quantum Eraser experiment
Okay, now I understand. Of course, in the absence of any calculations I haven’t understood anything from a rigorous point of view, but still. Many physicists have forgotten what being a layman is like and tend to have ridiculous expectations or ignore ‘stupid’ questions. But maybe the problem with laymen is that they’re practical people.
Each human community and every individual that these groups consist of face the economic problem, which is the problem of how to make the best of limited resources. Humans have a finite lifespan, which can prove both disadvantageous and advantageous for society but causes individuals to ignore or abandon a wide range of propensities they could attend or choices they could make. Understanding the ultimate nature of reality from a physicist’s perspective takes a lot of time and energy (or money, from a mercantilist’s perspective), which most can’t afford.
I remember when ten or fifteen years ago I took up learning Japanese. It was supposed to be a pure intellectual pursuit, like learning Latin for example. I happen to already speak a Romanic language and people in my country study Latin in 8th grade and throughout the high school, depending on their career orientation. The fact that you can’t speak to people whose native language is ancient Latin has always prevented me from a being fan of studying Latin. But being able to eventually communicate to an exotic person in his or her native language somehow presented a lot of appeal to me at the time. I bought all the resources I found on the market and set up a strict schedule where I woke up an hour earlier and went to bed an hour later every day in order to study Japanese for two hours every day. I gave up after several months not because I got tired in any respect, but because the progress seemed infinitesimally slow. I realized that at that pace I was not going to be able to fluently communicate with those exotic people before I died. So I had to decide whether to increase the number of hours dedicated to this activity, which meant spending less time with my family or sacrificing other hobbies such as learning English for example. And the logical conclusion was that I had to drop the idea of learning Japanese altogether. Even though I am not completely fluent in English, continuing to study the English language has turned out to be a lot more practical due to the access to more knowledge and career opportunities.
The analogy is obvious. Learning how to do all those calculations that may allow one to understand the ultimate nature of reality takes a lot of time and energy (or money) that the average person cannot afford. The incentive is even more minute when you hear that actually nobody understands how things work deep there at the most fundamental layer of reality. But in this increasingly conflicting world I’ve decided that if I don’t have anything nice to say I’d better say nothing.
If there is something nice to say is that analogies are useful. They’ve always been a wonderful tool for people to make sense of the world and advance new theories. I remember the enthusiasm everybody showed during the Scientific Revolution in Europe, when there was an burgeoning sentiment that through reason humans will eventually be able to learn everything there is to know about the entire Universe. Nowadays thinkers and physicists are way more reserved and seem to show a different kind of ‘enthusiasm’ – that no matter how advanced science may become, there will always be something new to know or to discover. Hm, sweetbitter resignation in my opinion. I may have given up studying Japanese, but I am just an average individual with a limited lifespan whereas science enjoys innumerable generations of scientists (many of them), and it should not abandon the ideal of learning everything there is know about every aspect of reality. But if I don’t have anything nice to say I’d better say nothing.
I understand that the behavior of liquid droplets on a liquid bath is just an analogy and that’s not exactly how the quantum reality works but this analogy is a useful instrument to make people understand that what may seem to be an irreducible paradox can in fact be the expression of a more complex reality the nature of which is not clear yet but may be fully revealed one day.
And yes, we should be grateful for the existence of these ‘less practical’ people who devote their time and energy to answer these apparently unanswerable questions even when they know that the chances to find an answer are so small.
Thank you for the answers and the links.
To clarify, no one is dismissing you question as stupid; in fact it takes time everyone learning about this subject to come to term with the fact that they don’t have the ability to visualize it. Our brains have trouble visualizing it because QFT is completely foreign to the experiences we have in normal life.
That we can make any progress at all in understanding quantum mechanics is amazing. It takes time to not berate ourselves because our progress far from perfect. While QFT and GR can and will exceed our ability to visualize, the main problem is that we all think we already know the answer…and we are wrong.
Two of best things you can do to help is to get as much exposure as you can and to adopt a mindset that is happier when you find out you are in error then when you are correct.
Really understanding it will take some math, but there are free resources to get you to a basic level around the Internet. It will take some work by even as an arm chair interest you can get to the point where you will be frustrated trying to build good analogies to share with other people.
What seems weird and impossible becomes really incredibly beautiful once you start to understand it. You will probably want to share that beauty with others and you will realize that the frustration you are detecting is actually on the other side of the equation. It is super frustrating to try and share these concepts when our words and analogies just aren’t quite flexible enough to share just how wonderful our world is.
And now I just want to put forth a little hypothesis even though it comes from a non-mathematical person.
It has probably been said before but I haven’t heard it. It’s about the observer effect, where particles seem to behave in one way when not observed and change behavior under strict observation. My sentiment, which I am sure other people must have felt before, is that ‘the universe’ does not want to conceal information from us or to show us a different face of reality when we pay too much attention. It must be a matter of method, because we live in a soup of radiations and we’ve always kind of looked, haven’t we? But when we set up an experiment, the procedure is completely different. The results may end up looking different not because we’re paying attention but because we’re looking differently. Just like a disc that can look like either a circle or a line depending upon your perspective. Maybe there is something in the nature of reality that makes it look different depending on the way we look at it.
Physicists can understand the desire for simple explanations. Heck, we wish that quantum mechanics was easier to understand, too. But the unfortunate fact is, it isn’t. For some things in quantum mechanics, there aren’t even any good analogies. And that’s not just a failure on our part to find the good analogies: We’ve been able to rigorously prove that good analogies do not exist, period. So we’re left with an uncomfortable choice between bad analogies and no analogies at all.
As for the observer effect, just don’t get misled into thinking that there’s some clever way of doing the observations that we haven’t thought of that would show us the “real” reality, without affecting it. That’s another thing that we’ve rigorously proven isn’t possible. Different kinds of observations will show us different results, but it’s not meaningful to say that one of those results is the “right” one and the others are “wrong”.
How far away can the two slits be from each other before the interference pattern stops showing up?
According the Schrodinger’s wave equation, the probability that an electron will appear at any point on it’s wave front can be precisely measured and, mathematically, it extends infinitely. The catch, of course, is that the probability of it appearing decreases with distance. Electrons “disappear” and “reappear” at different points on their wave fronts with regularity. It’s called “electron tunneling” and is, in fact how LEDs function.
So, in answer to your question, there should be no theoretical limit in distance, though practically the probability plummets the farther the slits are apart.
Feynman famously said “If you think you understand quantum mechanics, you don’t understand quantum mechanics.”
In the case of light waves, the characteristic length defining the distance apart the slits can be is the “coherence length” of the wave. I suppose that, in principle, the coherence length trails off for an infinite distance, but as a practical matter, if you significantly exceed the coherence length, any signal will be lost in the noise.
the coherence length depends, among other things, on the width of the spectrum of the source. Sunlight is pretty broad, and the coherence length is only a few wavelengths. Lasers are narrow, and can have enormous coherence lengths.*
What about electrons? They, too, have a coherence length, and it ought to be related to the spread I energies. The “wavelength” of electrons, determining the spacing of the diffraction pattern, depends upon the accelerating voltage.
I have to admit that I’m not sure exactly what determines the spread in wavelength, having never studied this, but I assume it’s things like the velocity distribution, influenced by a number of factors, including the effective temperature. There are entire papers devoted to this issue:
So the real answer to the question “how far apart can the slits be” is that it really can’t be much larger than the coherence length divided by the sine of the angle at which you put your detectors.
*Holography, being an interference phenomenon, depends upon the characteristic lengths of the object being recorded by hologram being smaller than the coherence length of the light. Holograms were invented by Dennis Gabor in 1948. the longest coherence length he could get was a strong mercury emission line, highly filtered. The coherence length was less than a millimeter. So Gabor couldn’t make “3D” holograms. That had to wait about 15 years until Leith and Upatnieks used a laser, with its coherence length on the order of a meter, to make holograms in which the 3D effect could be conveniently displayed.
I’m guessing that coherence length is probably relevant to any interference pattern?
Does this have any implication for the Michelson-Morley experiment, done long before the age of lasers? What was there light source? A guttering candle flame? A highly filtered mercury emission?
Does it make a difference to that experiment? I think a scientist doing that today would use [airquotes]lasers[/airquotes], especially if they were evil.
Certainly, any experiment done nowadays which even remotely resembles Michelson’s experiment will use lasers (the most ambitious are the gravitational wave detectors, like LIGO, with arms kilometers long). I don’t know exactly what Michelson himself used, but a mercury lamp is a decent guess.