According to relativity, information can not be transported at a speed higher than that of light. Therefore, it is important to know if there are physical objects that can not transport information and the role they can play. I think that this idea is at the base of classical quantum mechanics. If ψ is a complex field, then the differential equation ∂ψ / ∂t = iωψ with constant ω is saying that ψ can not modulate neither in amplitude nor in phase; and therefore can not transport information. Obviously the above equation is compatible with the Schrödinger equation.
Thank you.
Dear Enrique,
The wave function alone is not even a physical object.
Well, I guess your affirmation depends on the theoretical model followed; the more so if you do not consider ψ a physical object.
Non-invariant quantities don't transport information; invariant quantities do.
No Enrique, the wave function is not a physical quantity because it is gauge dependent. Its square, within the Max Born interpretation, can have a associated a density of probability. Thus the wave function alone cannot transport any kind of information in one univoque form.
Daniel, you say "the wave function alone"; but what about wave-particle duality?; we can think the wave and the particle are never alone. Born's probability is regarding a particle and with Schödinger equation they are saying that wave and particle are not independent.
I agree the idea that a wave function can not transport any information. In fact quantum mechanics defines the wave function as a linear combination of all possible states. Saying that it can take any possible value is a good way of not assigning information to an object.
Stam: Well may be , the proposed equation ∂ψ/∂t=iωψ is not Lorentz invariant.
Dear all, every physical object transports information. Some real and some imaginary. For example, an observer on dark matter can not receive any information from us and vice-versa. The reason being the two referential frames are having relative speeds greater than the speed of light. Hence, imaginary. However, in absolute sense, there still is a flow. Whether observed or not.
Kasibhatla Surya Narayana : It is interesting what you say about dark matter; but I think there is not much we know yet about its nature.
Dear Enrique,
Please, go through my pre-print THEORY OF UNIVERSALITY. I have clearly explained and proved that dark matter is the matter resulting out of the energy outpouring from the stars. You will really appreciate my pre-print. Please, go through the same from beginning to end of that chapter dark matter, dark energy and ordinary mass of solar system.
Lorentz invariance is relevant for the appropriate systems. So what matters are the transformations of the equation studied and the quantities that transport information are those that are constructed from the solution of that equation and are invariant under the transformations that map one solution to another.
The statements made about the solutions of the equation that is mentioned in the statement of the question are, simply, wrong. It suffices to actually write down its most general solution and work out the consequences. This is another homework problem.
Stam: as you know the general solution of the equation is ψ=Aexp{iφ}, ∂A/∂t=0, ∂φ/∂t=const. Where A and φ are scalar fields. The condition ∂A/∂t=0 indicates there is no modulation in amplitude and the condition ∂φ/∂t=const indicates there is no phase modulation. So ψ can't transport information, neither a map between solutions. Obviously the equation is not invariant Lorentz, not even Galileo and therefore the equation is only valid in a given coordinate system.
every physical object IS information! physical objects which do not transport information do not exist.
Paul: Most likely, nature is not there so we can brag about our knowledge about it. I believe that a fairer position is to think that there is information to which we have access and there is information that we do not have access to. This is valid for both a black hole and a quantum particle.
Enrique ≪Is there physical objects that can't transport information?≫
Some days I get a sinking feeling that the Internet is such an object :-). But I guess this depends on how you define information: How much information is there in data which is composed of an unknown ratio of facts to fictions? How much information is there in encrypted data that can't be decrypted?
Information transmission involves transport of energy too. Since all physical objects have energy (otherwise, we cannot know about their existence), their propagation carry information too.
Kåre: Encryption is itself a problem around information management. But regardless of how information is defined and managed there will be a certain problem in its transport derived from the limit of the speed of light. An object like a black hole censures information about what happens inside it. The wave function of quantum mechanics acts in a similar way by censoring information about the path followed by the particle in the double-slit experiment. The conservation of angular momentum in EPR experiments is another case of information censoring. Not in vain, Heisenberg himself thought that the lack of information is a basic principle of quantum mechanics.
Patrick: It can also be considered that we are facing a physical object if we can make a series of measurements about it. In the case of the wave function, its measurement has a statistical character. But to be able to consider the wave function a physical object must also be able to exchange energy with its environment. In Bohm's theory there is a concept that fits with this: the quantum potential.
dear Enrique, You are pretty right, but one word to Your sentence is absent. ergo there is information to which we have access and there is information that we do not have access to., YET!
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