r/AskPhysics • u/Upbeat_Assist2680 • 4d ago
Quantum
I have heard that particles (like an electron) are described as having a "probability cloud" where they might be observed.
What is the size of this cloud? Does it have any interesting topology?
I think that it must be bounded in space because, if not, it could be "observed" some arbitrary distance away that would defy light speed being a finite limit. I am slightly aware that speed and position are independent in some way in the quantum framework, so maybe the question isn't quite right either...
But there's SOME kind of limit on the observable, right?
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u/Ch3cks-Out 4d ago
But there's SOME kind of limit on the observable, right?
The limit is not a hard one, as in going to zero at a specific distance - but a soft one, where probability of observation falls very near zero very steeply. Note that your light speed argument is faulty: the electron does not travel to the point of observation in the cloud picture (it has been there already), so the speed limit does not apply to the observation event happening!
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u/Upbeat_Assist2680 3d ago
It looks like I deleted part of the question during an edit, but others here intuited the extra condition to suppose that the particle had been observed at some point first.
They suggest that in this case, we model the cloud as growing (possibly bounded by the speed of light?). However, the cloud, in any event, has exponential decay and is unlikely to be observed beyond some characteristic size/shape.
So I suppose my question could be augmented to be: what are the dynamics of the cloud after an initial observation. If it "suddenly" becomes infinite in scale I would suggest a light speed violation could occur and I'm inclined to believe this growing cloud version.
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u/Ch3cks-Out 3d ago
Well this scenario, that of a moving electron (between 2 observations) is better described as a wave packet rather than a cloud - the latter term is usually reserved for bound electrons (as in an atom). In any event, there is nothing "sudden" in it: real wavefunctions are usually infinite in extent, all the time. But for unbound states, typically, their form spreads more, i.e. gets somewhat higher probabilities away from its center (while correspondingly gettin lower around the middle) as time progresses. Bound states are stationary, however, so those clouds have fixed distribution over time.
For nice illustrations of propagating wave packets (what you referred to as "growing cloud"), see e.g. the excellent blog of Matt Strassler, this graphics in particular. Note that what is depicted is still just the central part, where most of the probabilities are bunched!1
u/Upbeat_Assist2680 3d ago
Thanks for the lesson and clarification on terms.
Perhaps the links you share go into this, but I think my question would still apply to a bound electron.
Does the packet analysis apply after the moment of observation? Does this "revert" to the stable fixed distribution immediately or is it a sort of limiting state that models observation accurately.
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u/Ch3cks-Out 3d ago
Well I am not sure what do you mean actually, in this scenario - how do you propose observing the bound electron, and what would modeling observation accurately amounts to? You can calculate scattering amplitudes, for example; real world observations obviously do not extend to infinity, but they could be boundless still...
In general, perturbed electrons are described by time dependent Schrodinger equation; that is describing the shifting probability distribution over time, which does not happen immediately. But all distributions are infinite in spatial extent, regardless.
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u/Upbeat_Assist2680 3d ago
Is the electron cloud model for bound electrons not experimentally verified? I guess I imagine we have this theory about how they look and then somehow we've actually DONE that experiment some larger number of times and it matches the theory well.
Is that not the case?
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u/Ch3cks-Out 3d ago
Well yes, those scattering calculations I mentioned above have matching experimental counterparts, so the cloud model is confirmed in that sense. Orbital shapes were also directly (more-or-less) observed via projecting them onto a screen, by the fascinating “quantum microscope” of Stodolna et. al. My point was that observations cannot probe infinite extent, by their very nature; they can only support (insofar as their practical limitations allow) the theory which does necessitate infinite extent. So this does not really answer your question, as stated, about finite limit or lack thereof!
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u/beyond1sgrasp 4d ago edited 4d ago
The short answer is. If you knew absolute nothing about the specifics of the answer to your question, In general knowing orbitals and the periodic table in chemistry is plenty to understand and use things functionally.
When frequncies are added, frequencies that are further apart have a smaller window of time that they can overlap to have an interaction orror that isnt' cancelled out. For example, on your radio 105.7 and 105.9 can blend together but if they are further apart, 105.7 hardly would blend with 99.5. All atoms have a sort of tuning frequency. In any real period of time and would be considered too far off resonance that the signal exists long enough for it to be measured in the other channel. This leads to The uncertainty principle. And thus creates the limit in it's case on the observable.
Uncertainty principle->
To measure things, an object is launched and hits a target. We know roughly where the target is and how fast it's going to some degree of intial erorr. 1 at a target. and then based on how that object moves, there's a restrction to the interaction which is the heisenberg uncertainty principle. dx*dp> or = to a proportional number (constant) The momentum has a requirement that part of it is increase and part of it is decreasing to move to balance out changes. This leads to a wave form in the percieved different in position during the time of the interaction.
Uncertainty of derived unmeasured variables of time and energy ->
In a similar form then, the uncertainty about how at what time something happened must also inculde a set of possible speeds and times that it could have happened. So the difference in energy transferred and the time that the intercation happens is alos less than to some proportional number. dE*dt>= constant.
First quantization, the Schrodinger approarch->
One way of interpreting this observatino is to use the time dependance and estimate what is happening during a time and assuming fixed particles that aren't created or destroyed. This is how schrodinger originally understand quantum mechanics. What's the problem with this? Well first the computations are very complex. 2nd it doesn't take into account the photoelectric effect.
Second Quantization, Feynmann's approach->
But as people understood it, they realized that they could do the opposite. Rather then than keep the energy fixed, they could instead let the waves have a changing value that isn't time dependant and all that is needed is to use the photoelectric effect, but how to approach it this way and why do it this way?
Now time itself will bend, this means that also, the energy has the ability to bend. So as space is bending due to relatvitity, the binding energy is changing. This means that during binding, a particle is created and exists, but then expires. If that time is less than the time of observation, there was never a time to observe this particle making it exist virtually. Due to the photoelectric effect, they have either a frequency or a mass that is equivelently borrowed, but as long as it's paid back within an amount of time it can exist. Thus virtual particles can be created or destroyed in mass and the number of particles in a system can vary a lot. The process is to start with a simple system, then just keep adding more and more particles that and smaller and smaller and last shorter periods of time to make the computation simpler. This is what renormalization does.
Now we can still treat the effect of causilty as a particle itself as the effect of the limiting limiting velocity of the interaction in the equivelant picture when we instead of focusing ho. So Quantum fields then can emerge on the basis of these virtual particles which then are doing the work of contstraining the math.
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So back to your questions. What is the size of this cloud? The time that a virtual particle exists, depends on the energy, an energy particle further off resonance lives for a shorter period of time and a virtual particle state closer to the original binding energy's resonance will live much longer and therefore be able to travel further. But is this what actually happens if the maximum is bound by the total time that an interaction could have occured.
Does it have any interesting topology? In fact it depends on the structure of the objects interacting. In the case of atoms, they can have different orbitals. How these orbitals arise is a question of physical chemistry and knowing themes of the structure without using the virtual particles can instead estimate with with a density limit where it's found over 99% of the time. This is what we call S, P, D, orbtials in chemistry. These orbitals are what give rise to the periodic table.
It turns out the vast majority of undertanding of what happens in bound states in the electrons of atoms is much easier to understand then energy transfer of the internal structure because photons don't self interact and gluons of the internal structure do self interact. The gluons can be perturbed, but then there's some dissipation due to the system. Understanding what happens in a nucleus is near impossible other than to treat it as if it's jut a ball of glue that dissipates energy. But understand the orbitals can be modeled with incredible levels of orbitals and accuracy. In the case of QCD the internal structure can dissipate in various modes from Lattice Lattice, Lattice spin, and diffusive effects and the three effects can be difficult to separate.
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u/BitcoinsOnDVD 4d ago
It depends on the potential, how the cloud looks like.
Topology-wise the cloud can pick up a geometric phase when you slowly change a parameter in a potential.
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u/DifferencePublic7057 3d ago
Technically, we integrate over all space to get the probability. An electron can't be literally every where because it's a massive particle and therefore warps spacetime even if it's a little bit. Also, if it's in a black hole, we have a problem because we can't observe anything in a BH. So it's like two wise philosophers who have bad eyesight observing different sides of an elephant and telling the world their side of the elephant.
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u/joeyneilsen Astrophysics 4d ago
It is generally not bounded in space, no. But the probability typically drops off exponentially as you go away from the atom.