5 ms·

It's a probability cloud of different possible locations, but also it's a probability distribution of different permitted possible speeds, as well. This probabi

It's a probability cloud of different possible locations, but also it's a probability distribution of different permitted possible speeds, as well. This probability distribution has a peak (a mode). When he writes "the faster the electrons have to move", he means this mode for a heavier nucleus is larger than that of a lighter nucleus. Please let me know if I'm not being clear enough.

throwaway_pdp09 6y ago
Actually thanks, that's very clear at that level, however that leads to a further confusion (of mine) about what speed implies, that being that the electron is moving (obviously) from x to y, which apparently contradicts the probability cloud concept of probabilities of a position at instant x, and only for that instant. That is, if it's moving from x to y (because it has speed) then it's more likely to appear on some vector between x and y. Please feel free not to answer that question, as I may drag you down the rabbit hole - but if you can, I'd love to know.
- analog31 6y ago
  On possible way to think about it, is to imagine a probability cloud of something else, but made of classical particles. For instance, all of the cell phones in Chicago. Someone like Google can probably compute an average position, such as maybe a center of mass, but also an average speed based on knowing the speeds of all the phones as they're carried about, driven in cars, etc. Now what we might have done in quantum mechanics class, without thinking too hard about the implications, is to assign mathematical functions to the things that we want to know about the electron using rules of thumb for how to turn functions of classical systems into corresponding functions of quantum systems. Then we apply the "what is your average speed" operator, and out pops a number. I didn't get very far past the basic quantum mechanics where we were able to compute stuff but were left on our own to speculate about the meaning of the philosophical implications. Then I joined an experimental research team where I was able to think my way through problems using electronics, vacuum pumps, and computer code. ;-)
  - throwaway_pdp09 6y ago
    Thank you. I kind of get it but perhaps some things are best not considered too deeply.
- yomly 6y ago
  If you have a probability distribution of position. Then increment time by one tick. If you have a second probability distribution (assuming some time dependence) then you have now a distribution of distance travelled and therefore a distribution of speeds. The alarming thing about QM is that it is fundamentally probabilistic and yet a little classical at the same time.
  - yomly 6y ago
    https://phys.org/news/2014-10-function-electron.amp https://phys.org/news/2014-10-function-electron.amp This was on HN before - it's a fun illustration of QM influencing "position" in a non intuitive classical sense
  - AnimalMuppet 6y ago
    I don't think that's right. If you increment the time by one tick, you have the same position probability distribution. That is, the wave function didn't change. Why should it? But that position probability distribution has a very specific energy. And at each point of that position distribution, the electron has a specific electrical potential energy. So at each point, it also has to have a kinetic energy. It has a kinetic energy probability distribution to match the position probability distribution. And now we can talk about velocity.
- ravar 6y ago
  Its because the object that nature works with is not the probability distribution but the complex (as in real number plus imaginary number) wavefunction. The probability of being at a location is proportional to the wavefunction squared and the velocity is proportional to the derivative of the wavefunction times the wavefunction (? its been a while). take the function e^(i*x) the magnitude is a constant and so is the magnitude of the derivative.
- a1369209993 6y ago
  Consider the simplified example a electron uniformly distributed around a single circular orbit. If we say that it has a speed of 90°/sec, then its position at t=0s is uniformly distributed, and its position at t=1s is uniformly distributed, but those positions are correlated such that, conditional on it being at 12 o'clock at t=0s, it's most likely to be at 3 o'clock at t=1s. If its speed is instead 180°/sec, then (conditioned on 12 o'clock), it would most likely be at 6 o'clock one second later. But it's not more likely to appear between 12 o'clock and whereever, because that's only in the subset of cases where we assume it started at 12 o'clock; if we instead assume it started at 5 o'clock, it'll be moving to 8 or 11 instead. The starting positions are uniformly distibuted, so the later positions are also uniformly distibuted.
- MockObject 6y ago
  Think of it less as an actual particle that has a speed and position at a certain time, and more that "speed", or "position" are just the results of measurements that are made. The electron is a cloudy, blurry mess, yet if you measure its position, you'll find it is in a certain location, but that's all it means. It doesn't mean it "was there" before the measurement! Likewise, if you measure its speed, you'll likewise get a precise speed measurement, but it doesn't mean it had that speed before the measurement! Or that it was actually speeding from any point x to a point y. So, while the measurements work, what breaks down are the regular common sense implications that the measurements normally imply.

throwaway_pdp09 6y ago

Actually thanks, that's very clear at that level, however that leads to a further confusion (of mine) about what speed implies, that being that the electron is moving (obviously) from x to y, which apparently contradicts the probability cloud concept of probabilities of a position at instant x, and only for that instant. That is, if it's moving from x to y (because it has speed) then it's more likely to appear on some vector between x and y. Please feel free not to answer that question, as I may drag you down the rabbit hole - but if you can, I'd love to know.

analog31 6y ago
On possible way to think about it, is to imagine a probability cloud of something else, but made of classical particles. For instance, all of the cell phones in Chicago. Someone like Google can probably compute an average position, such as maybe a center of mass, but also an average speed based on knowing the speeds of all the phones as they're carried about, driven in cars, etc. Now what we might have done in quantum mechanics class, without thinking too hard about the implications, is to assign mathematical functions to the things that we want to know about the electron using rules of thumb for how to turn functions of classical systems into corresponding functions of quantum systems. Then we apply the "what is your average speed" operator, and out pops a number. I didn't get very far past the basic quantum mechanics where we were able to compute stuff but were left on our own to speculate about the meaning of the philosophical implications. Then I joined an experimental research team where I was able to think my way through problems using electronics, vacuum pumps, and computer code. ;-)
- throwaway_pdp09 6y ago
  Thank you. I kind of get it but perhaps some things are best not considered too deeply.
yomly 6y ago
If you have a probability distribution of position. Then increment time by one tick. If you have a second probability distribution (assuming some time dependence) then you have now a distribution of distance travelled and therefore a distribution of speeds. The alarming thing about QM is that it is fundamentally probabilistic and yet a little classical at the same time.
- yomly 6y ago
  https://phys.org/news/2014-10-function-electron.amp https://phys.org/news/2014-10-function-electron.amp This was on HN before - it's a fun illustration of QM influencing "position" in a non intuitive classical sense
- AnimalMuppet 6y ago
  I don't think that's right. If you increment the time by one tick, you have the same position probability distribution. That is, the wave function didn't change. Why should it? But that position probability distribution has a very specific energy. And at each point of that position distribution, the electron has a specific electrical potential energy. So at each point, it also has to have a kinetic energy. It has a kinetic energy probability distribution to match the position probability distribution. And now we can talk about velocity.
ravar 6y ago
Its because the object that nature works with is not the probability distribution but the complex (as in real number plus imaginary number) wavefunction. The probability of being at a location is proportional to the wavefunction squared and the velocity is proportional to the derivative of the wavefunction times the wavefunction (? its been a while). take the function e^(i*x) the magnitude is a constant and so is the magnitude of the derivative.
a1369209993 6y ago
Consider the simplified example a electron uniformly distributed around a single circular orbit. If we say that it has a speed of 90°/sec, then its position at t=0s is uniformly distributed, and its position at t=1s is uniformly distributed, but those positions are correlated such that, conditional on it being at 12 o'clock at t=0s, it's most likely to be at 3 o'clock at t=1s. If its speed is instead 180°/sec, then (conditioned on 12 o'clock), it would most likely be at 6 o'clock one second later. But it's not more likely to appear between 12 o'clock and whereever, because that's only in the subset of cases where we assume it started at 12 o'clock; if we instead assume it started at 5 o'clock, it'll be moving to 8 or 11 instead. The starting positions are uniformly distibuted, so the later positions are also uniformly distibuted.
MockObject 6y ago
Think of it less as an actual particle that has a speed and position at a certain time, and more that "speed", or "position" are just the results of measurements that are made. The electron is a cloudy, blurry mess, yet if you measure its position, you'll find it is in a certain location, but that's all it means. It doesn't mean it "was there" before the measurement! Likewise, if you measure its speed, you'll likewise get a precise speed measurement, but it doesn't mean it had that speed before the measurement! Or that it was actually speeding from any point x to a point y. So, while the measurements work, what breaks down are the regular common sense implications that the measurements normally imply.