Can anyone give a clear explanation why information has to be conserved
in quantum mechanics?
I was not taught this when first learning about QM in the 1970's. As
best as I can tell the idea comes from the idea that the QM wave
function evolves per a unitary operator that can, in principle, be
reversed to recover the past state as well as calculate the future
state of the system.
It seems to me that this argument is missing two important facts: -The
wave function is not real, it is only a mathematical tool for predicting
the probabilities of future states -The actual future is one of many predicted by the wave function, and likewise can be the result of many different possible past states.
It seems to me that each time the wave function "collapses" that
information is lost. Is there a good argument why this is wrong?
And *reversibility* itself is already present in classical physics,
namely since the Hamiltonian/Lagrangian approaches, where the dynamics
of a system are described in terms of the evolution of a *system state*
in a state space: *that* evolution has to be reversible, indeed lack of reversibility would simply not be a state space: IOW, given a "law of motion", there must be one and only one next state, and one and only one previous state, or the whole state-space based approach becomes simply meaningless.
I was not taught this when first learning about QM in the 1970's. As
best as I can tell the idea comes from the idea that the QM wave
function evolves per a unitary operator that can, in principle, be
reversed to recover the past state as well as calculate the future state
of the system.
It seems to me that this argument is missing two important facts:
-The
wave function is not real, it is only a mathematical tool for predicting
the probabilities of future states
It seems to me that each time the wave function "collapses" that
information is lost. Is there a good argument why this is wrong?
Julio Di Egidio <ju...@diegidio.name> schrieb:
And *reversibility* itself is already present in classical physics,
namely since the Hamiltonian/Lagrangian approaches, where the dynamics
of a system are described in terms of the evolution of a *system state*
in a state space: *that* evolution has to be reversible, indeed lack of reversibility would simply not be a state space: IOW, given a "law of motion", there must be one and only one next state, and one and only one previous state, or the whole state-space based approach becomes simply meaningless.
And yet, the Second Law of Thermodynamics holds.
On Saturday, 3 September 2022 at 15:50:03 UTC+2, Thomas Koenig wrote:Julio,
Julio Di Egidio <ju...@diegidio.name> schrieb:
And *reversibility* itself is already present in classical physics, namely since the Hamiltonian/Lagrangian approaches, where the dynamics
of a system are described in terms of the evolution of a *system state* in a state space: *that* evolution has to be reversible, indeed lack of reversibility would simply not be a state space: IOW, given a "law of motion", there must be one and only one next state, and one and only one previous state, or the whole state-space based approach becomes simply meaningless.
And yet, the Second Law of Thermodynamics holds.I did say except for the "measurement problem" and thermodynamics. Thermodynamics is indeed another story: the laws of thermodynamics
are not exact laws, in fact thermodynamics is not deterministic, while,
to the point, the laws of quantum mechanics *are* exact and
deterministic: the fact that we measure probabilities has again to do
with "the problem of measurement", i.e. how we go from the quantum
state to a classical outcome, but, to reiterate, the evolution of the wave function, as expressed by the Schroedinger equation, is per se indeed deterministic.
Julio
On Saturday, September 3, 2022 at 7:15:37 PM UTC-5, ju...@diegidio.name wrote:<snip>
On Saturday, 3 September 2022 at 15:50:03 UTC+2, Thomas Koenig wrote:
Julio Di Egidio <ju...@diegidio.name> schrieb:
And *reversibility* itself is already present in classical physics,
Thank you for your detailed response. I have to debate some points where
I think you are being inconsistent.
but the wave function calculated is not real.
The difference is "collapse". Take the two slit experiment with
a single photon. When a photon is detected on the screen [...]
If you try to start from this state and compute backwards [...]
The backward computed wave function includes many
possible sources
QM is not deterministic in that at any given moment there
are several possible mutually exclusive future outcomes.
to me that this means that information is not conserved
Is there an error in my reasoning here?
QM is not deterministic in that at any given momentA naive query: I've known qualitatively that unitarity guarantees
there are several possible mutually exclusive future outcomes. It seems
to me that this means that information is not conserved in the actual physics, despite what the math appears to say. The disconnect is that
the math only predicts probabilities of multiple outcomes, while the
actual physics, in many but not all cases, has only one specific future.
In other words, knowing the exact present state does not tell you which
of many future states the system may evolve to, nor which of several
states it evolved from. It seems to me that this precludes any
conservation of information.
Is there an error in my reasoning here?
Rich L.
On Sunday, 4 September 2022 at 19:54:28 UTC+2, richali...@gmail.com wrote:
On Saturday, September 3, 2022 at 7:15:37 PM UTC-5, ju...@diegidio.name wrote:<snipped>
but the wave function calculated is not real.That *depends* on your ontological stance: and your choice,
which is the standard one, is the one that is *most* problematic.
The difference is "collapse". Take the two slit experiment withWhen the photon is detected, that is a *measurement*, i.e.
a single photon. When a photon is detected on the screen [...]
If you try to start from this state and compute backwards [...]
The backward computed wave function includes many
possible sources
(standardly) you have *collapsed* the wave function, aka
the state: and *that* operation is not reversible, not QM!!
Conversely, do not collapse the wave function (consider
the joint system observer/observed) and you stay quantum
and have reversibility.
QM is not deterministic in that at any given moment thereYes, it is: you are still conflating classical outcomes with
are several possible mutually exclusive future outcomes.
the evolution of the wave function, aka the quantum state.
to me that this means that information is not conservedSure, but it's *collapse* that destroys information.
Is there an error in my reasoning here?Only if you'll insist... :)
HTH,
Julio
On Monday, September 5, 2022 at 12:03:11 AM UTC-5, ju...@diegidio.name wrote:<snipped>
On Sunday, 4 September 2022 at 19:54:28 UTC+2, richali...@gmail.com wrote:
On Saturday, September 3, 2022 at 7:15:37 PM UTC-5, ju...@diegidio.name wrote:
but the wave function calculated is not real.
That *depends* on your ontological stance: and your choice,
which is the standard one, is the one that is *most* problematic.
This clarifies a difference of opinion between us. I don't understand
why you say that is *most* problematic? Can you elaborate? I'm
curious.
For what it is worth, I distinguish the physics of QM from the math of
QM. The math is a model of our understanding that may be imperfect. I
believe there is a reality where the actual physics happens.
Seriously, isn't collapse a part of reality, or required by reality?
For example, back to the photon detected in the two slit experiment,
once the photon is detected there is now a new reality that differs from
the previous wave function.
It sounds like you may follow the many worlds concept.
Thanks Julio for responding, this is clarifying these ideas for me.
[...] Seriously, isn't collapse a part of reality, or required by
reality?
On 9/7/22 6:35 AM, Richard Livingston wrote:
[...] Seriously, isn't collapse a part of reality, or required by
reality?
No. There are interpretations of QM that do not involve any "collapse of
the wavefunction". See, for example:
Ballentine, _Quantum_Mechanics:_A_Modern_Development_.
The basic idea is that whenever one makes a measurement of a quantum
system, that necessarily involves coupling it to a MUCH LARGER measuring instrument, and the comparatively tiny quantum system is "forced" into
an appropriate eigenstate by that coupling.
Tom Roberts
[...] saying "the wave function is not real" means a plain hole in a
theory's ontology
On 9/8/22 4:13 AM, Julio Di Egidio wrote:
[...] saying "the wave function is not real" means a plain hole in a theory's ontology
Say "model" instead of "theory", and you'll more easily see the basic
mistake you are making here:
no human thought has any ontology at all,
because thoughts do not exist in the world we inhabit, they "exist" in
This has been a fundamental evolution in physics: we are NOT "describing
how the world works", we are MODELING how we observe the world to work.
So, for instance, there is no expectation that quantities that appear in<snip>
a model necessarily correspond to some object or process in the world.
It seems to me that this argument is missing two important facts: -The
wave function is not real, it is only a mathematical tool for predicting
the probabilities of future states
On Thursday, September 1, 2022 at 11:30:58 AM UTC-5, rich... wrote:...
It seems to me that this argument is missing two important facts: -TheThere is no such thing as being "only a mathematical tool".
wave function is not real, it is only a mathematical tool for predicting the probabilities of future states
Everything that says anything meaningful about the physical world
is ipso facto physical and physically relevant, and is thus real.
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