Why does dbb need to assume pilot wave?

[San K]

The De Broglie–Bohm (DBB) interpretation conjunctures that:

a) the wavefunction travels through both slits, but each particle has a well-defined trajectory and passes through exactly one of the slits

b) there is a pilot waveNow, one can guess/understand why it needs to assume a) above.

However, what observation/phenomena, in a single particle interference experiments, induces the DBB to assume a pilot wave in addition to (a) above?

 

[kith]

The wavefunction is the pilot wave.

 

[San K]

The wavefunction is the pilot wave.

oops...thanks kith...at what velocity is it postulated to travel?

 

[Demystifier]

oops...thanks kith...at what velocity is it postulated to travel?

The wave is postulated to satisfy the Schrödinger equation, which determines its travel velocity.

 

[San K]

The wave is postulated to satisfy the Schrödinger equation, which determines its travel velocity.

thanks Demystifier

is that velocity at, or above, the speed of light?

 

[Demystifier]

Schrödinger equation describes nonrelativistic waves of massive particles, so the speed of wave is not bounded by the speed of light. Of course, it is only an approximation.

 

[San K]

Schrödinger equation describes nonrelativistic waves of massive particles, so the speed of wave is not bounded by the speed of light. Of course, it is only an approximation.

Thanks Demystifier, What does a massive particle mean? Is a photon/electron considered massive? or is it for all particles starting from the smallest ones till the big ones like Fullerene?

In the DBB - Why is there a need to assume that the speed of the wave is faster than light?

which observation/phenomena in the quantum (interference pattern) experiments is DBB trying to explain/rationalize by assuming waves travel almost instantaneously?

can not the -

the experimental observations, in various scenarios, of placing of an obstacle (and or detector) any time before the passage of the particle (as calculated by the speed of light),

be explained without having to assume that the wave is traveling instantaneously?

 

[San K]

In the DBB - Why is there a need to assume that the speed of the wave is faster than light?

I think I just got the answer, not sure if it's correct -

the photon is assumed to be entangled with some part of the experimental apparatus/environment at all points in time-space and that entanglement changes as the situation changes (due to movement of the particle/photon or change in the experimental setup etc).

this (change in) entanglement is assumed to happen (almost) instantaneously.

 

[nonequilibrium]

But since the pilot-wave is the same as the "normal" Schrödinger wave psi, both can "travel" faster than the speed of light, so it's not specific to dbb. In other words: QM is a non-relativistic theory, so why judge it by relativistic standards? But even still, dbb (for QM) seems to be compatible with relativity (although, as just claimed, there is no actual need for it to be so) since it can be proven that no information can be transmitted faster than the speed of light, which is all relativity requires anyway.

Also, "massive" simply means "mass $m \neq 0$".

EDIT: I believe better two postulates for dBB (in the context of one-particle QM) are
1) There is a wavefunction $\psi(\mathbf r, t) = R(\mathbf r, t) e^{i S(\mathbf r,t)}$ governed by the Schrödinger equation.
2) There is a point-particle with position $\mathbf X(t)$ and velocity $\mathbf v(t) = \frac{1}{m} \nabla S(\mathbf X(t),t)$.

 

[San K]

But since the pilot-wave is the same as the "normal" Schrödinger wave psi, both can "travel" faster than the speed of light, so it's not specific to dbb. In other words: QM is a non-relativistic theory, so why judge it by relativistic standards? But even still, dbb (for QM) seems to be compatible with relativity (although, as just claimed, there is no actual need for it to be so) since it can be proven that no information can be transmitted faster than the speed of light, which is all relativity requires anyway.

Also, "massive" simply means "mass $m \neq 0$".

EDIT: I believe better two postulates for dBB (in the context of one-particle QM) are
1) There is a wavefunction $\psi(\mathbf r, t) = R(\mathbf r, t) e^{i S(\mathbf r,t)}$ governed by the Schrödinger equation.
2) There is a point-particle with position $\mathbf X(t)$ and velocity $\mathbf v(t) = \frac{1}{m} \nabla S(\mathbf X(t),t)$.

thanks mr. vodka...cheers

however why is the (Schrödinger) function assumed/postulated to "travel/effect" faster than light?...in the first place

 

[nonequilibrium]

It does not necessarily travel faster than light, there is just nothing forbidding it in a non-relativistic theory. Think of Newtonian mechanics: particles can travel faster than light; they're not postulated to, it's just that since Newtonian mechanics is non-relativistic, there's no upper bound to velocity.

That being said, it seems like QM is more generally applicable than Newtonian mechanics even on the matter of relativity. For example, non-locality could have been a wrong prediction of QM, due to necessary relativistic corrections in those conditions, however it seems non-locality is a fact, so in a sense although QM is a non-relativistic theory, it is more widely valid than simply in "non-relativistic cases".

 

[jtbell]

Even in relativistic QM, if you start with a plane wave:

$$Ae^{i(kx-\omega t)} = Ae^{i(px-Et)/\hbar}$$

and calculate the phase velocity $v_p = \omega / k$ using the relativistic formulas for momentum and energy, you find that $v_p > c$! This is a common exercise in intro modern physics textbooks.

What matters of course is the group velocity $v_g = d\omega / dk$ which does always turn out to be < c.

 

[San K]

Even in relativistic QM, if you start with a plane wave:

$$Ae^{i(kx-\omega t)} = Ae^{i(px-Et)/\hbar}$$

and calculate the phase velocity $v_p = \omega / k$ using the relativistic formulas for momentum and energy, you find that $v_p > c$! This is a common exercise in intro modern physics textbooks.

What matters of course is the group velocity $v_g = d\omega / dk$ which does always turn out to be < c.

thanks jtbell.

thus...do some "massless effects/cause" have to travel faster than light in order to sustain certain laws of physics...(for example - law of conservation of momentum/energy)?