# Is there a maximum speed for the spreading out of a wavefunction after measurement in quantum mechanics?

In my study of quantum mechanics, I've encountered the concept of wavefunction collapse after measurement, followed by the subsequent spreading out of the wavefunction in space. I'm curious to know if there is a maximum speed at which this spreading out occurs.

I understand that the spreading of the wavefunction is governed by the Schrödinger equation and the principles of quantum dynamics, but I'm unsure if there are any inherent speed limits imposed by these equations or other fundamental principles of physics.

Additionally, if there is no explicit maximum speed, what factors influence the rate at which the wavefunction spreads out after measurement? Are there any constraints or bounds on this process?

I would appreciate any insights or references to further reading on this topic.

Thank you.

• This is covered by Time evolution of Gaussian packet though whether this constitutes a duplicate is debatable. Commented Feb 3 at 10:26

It is generally considered that collapse (or however you interpret or describe it) occurs everywhere at once instantaneously. There is no specific upper constraint on speed.

For example, consider the heralded creation of exactly 1 photon. The Fock state is 1, and the existence of it is heralded (announced) by the detection of a previously entangled partner from perhaps a PDC source. So you know you have a photon out there somewhere. Its possible position (more accurately the likelihood of detection at some point in spacetime) appears to spread as you show before measurement.

When that photon is detected at some point post measurement, it is not detected at any and all other points anywhere. That is true of all points, exactly as shown on your graph. The likelihood of detection at all points possible before detection immediately drops to zero. (That also applies to far away points possible in the future, which may also be far away.)

NOTE: My example uses a photon. Some might prefer not to use a photon as an example for technical reasons. But the analogy is the same regardless. Also, there are those that have a different viewpoint based on their preferred interpretation of QM. My explanation is not intended to address those interpretations.

Regardless, any experiment intended to detect the position of a particle will never show any sign of collapse having a speed constraint. Of course, the only thing that actually changes instantly is a probability amplitude.

• The is no actual physical charge in a wavefunction "collapse." It is simply that you stop keeping track of thise parts of the wavefunction where the measurement would have given a differerent answer, as they are no longer relevent to you. Commented Feb 4 at 20:22
• The question is asking about the spread of a wavepacket after a measurement, not the shrinking of a wavepacket because of measurement. Commented Feb 4 at 20:35
• @mikestone Your statement is somewhat interpretation dependent. And it also depends to an extent on the specific example. I would mostly agree with you as it applies to my example. But there are certainly examples in entangled particle pairs where a physical change seems to occur upon collapse (measurement). But that "appearance of change" can be explained by some interpretations without "physical change". Commented Feb 4 at 20:37
• @DrChinese I agree that what one calls "physical" is interpretation dependent, --- but the general idea of no "longer tracking" seems pretty universal among both the Qunatum Information theoriests and experimentalists I talk to. It's basically ways opf thinking about the Mott problem: en.wikipedia.org/wiki/Mott_problem Commented Feb 4 at 20:45
• My question is how fast the wavefunctions spread after collapse, not the speed of the collapse itself Commented Feb 5 at 17:16