Your interpretation of de Broglie equation must be incorrect because any particle at rest, zero velocity in your frame, would have an infinite wave length. Whereas in my frame, moving relative to yours, it would have a momentum and therefore a finite wavelength.
((The velocity in the equation is with respect to two entities having an interaction and has nothing to do with a third party observer.
If two electrons approach each other in a wire conveying electricity. The interaction can be modeled by wave mechanics or by particle mechanics. If the "velocity between them" is high enough the interaction will be a particle interaction which results in a particle collision causing heat generation (resistence). If the velocity is low enough then the interaction is governed by wave mechanics which prevents a collusion and does not generate heat. Both of these interactions happen in a wire because velocities are above and below the de Broglie velocity limit. Higher frequencies an alternating current reduce resistance in a wire. This is because the acceleration of the electrons are reversed more often causing velocities to be lower and wave interaction is more prevalent.))
Since rest frames do not affect the properties of particles, your use of his formula must be incorrect. I suggest that you read the text more closely. Electrons have a very short wavelength even at rest, as is known from electron microscopes.
((The wavelength typically assigned to an electron is due to internal motion of the electron. The wavelength of an electron can be calculated from its potential energy using the de Broglie wave length equation. You assume that the energy of an electron is composed of moving particles with a momentum equal to the energy of an electron and the correct wave length is given. I am not saying that there are, or are not particles in an electron, just that the equation works. This was deminstrated by Bohr I believe.))
Information: Information is not separate for physics. The force between objects carries both the vector info and its magnitude. Extra dimensions are only needed for entanglement.
(( If the force carries the vector and its magnitude in normal space then it must travel a light speeds.
A distant galaxy we see now is not even there any more.
The entanglement must contain instantaneous data to give a instantaneous gravity.
If I depend on normal space I will get non instantaneous and old information.
Perhaps I misunderstood.
Does the force travel through normal space?))
Or how can entanglement cause old information to become current information?