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Loren Booda
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When does the wavefunction propagate at a finite speed, and when instantaneously?
Demystifier said:It propagates instantaneosly when you assume objective wave function collapse. Otherwise, it always propagates with a finite speed.
Are you saying there is no mapping between the evolution in configuration space and the probability of finding a possible pattern in real space when a measurement is done with regards to c?vanesch said:The "speed of propagation" is the hamiltonian !
Note that the wavefunction doesn't live in real space, and hence you cannot define such a thing as "speed of propagation" of the wavefunction in things like meters per second or so. The wavefunction lives in hilbert space.
MeJennifer said:Are you saying there is no mapping between the evolution in configuration space and the probability of finding a possible pattern in real space when a measurement is done with regards to c?
But under which circumstances do you think it will propagate less than c (and obviously I do not mean the average velocity).vanesch said:If the hamiltonian defines a local dynamics (which it does in QFT, and which it doesn't in NRQM), then each kind of local "field operator expectation value", which WILL define a field in spacetime, will indeed propagate at less than or equal c, if that is what you hint at.
True, and I am sorry you misunderstood that I did make such a claim.vanesch said:But these "field operator expectation values" are not necessarily "physical quantities in spacetime", and are certainly not identical to the wavefunction itself.
MeJennifer said:But under which circumstances do you think it will propagate less than c (and obviously I do not mean the average velocity).
Well forgive my ignorance but how do we know?vanesch said:When the field operator is the one of a massive field, for instance...
Or when we have a stationary solution !
MeJennifer said:Well forgive my ignorance but how do we know?
For instance are you saying that the amplitude for a mass particle to travel at c is zero for an abritrary short path?
And how can we exclude the possibility that a mass particle has an average velocity of < c but actually moves at the speed of c in different directions?
The wavefunction is a mathematical description of a particle or system's quantum state. It contains information about the probability of finding the particle in a particular location or with a specific energy. The wavefunction propagates through space and time according to the Schrödinger equation, which describes how the quantum state evolves over time.
The propagation of the wavefunction is significant because it allows us to make predictions about the behavior of quantum systems. By understanding how the wavefunction evolves, we can determine the probability of finding a particle in a certain state, and make predictions about its future behavior.
Unlike a classical wave, the wavefunction does not represent a physical disturbance in space. Instead, it is a mathematical representation of the quantum state of a particle or system. The wavefunction does not have a physical location, but it describes the probability of finding a particle at a specific location.
The propagation of the wavefunction is affected by a number of factors, including the potential energy of the system, the mass and charge of the particle, and any external forces acting on the particle. These factors can alter the shape and behavior of the wavefunction as it propagates through space and time.
No, the wavefunction itself cannot be measured or observed. It is a mathematical concept that represents the probability of finding a particle in a certain state. However, the effects of the wavefunction can be observed through experiments and measurements, such as the interference patterns of particles in the double-slit experiment.