Conservation of Information in QM

[Richard Livingston]

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?

Rich L.

[Julio Di Egidio]

Post by Richard Livingston
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.

That information is conserved follows from unitarity which in turn
follows from reversibility, i.e. that the laws of physics are the same
whether we let the system evolve forwards or backwards in time (indeed,
except for the "measurement problem" as well as thermodynamics).

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.

Post by Richard Livingston
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.

No to the second part for the reasons said above. The first part is an
issue of ontology: e.g. in pilot-wave theory the wave function *is* real.
And I'd personally agree that physics without a *solid* ontology is very
poor thing.

Post by Richard Livingston
It seems to me that each time the wave function "collapses" that
information is lost. Is there a good argument why this is wrong?

That's exactly what happens with the standard interpretation, aka the
"shut up and calculate". Is(n't) that wrong? Many think that it in
fact means an open problem, just there is sort of a taboo against
wave-particle duality (as in pilot-wave theory), despite it *is*
ontologically solid, and we are rather offered multiverses...

Julio

[Thomas Koenig]

Post by Julio Di Egidio
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.

[Stefan Ram]

Post by Richard Livingston
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.

I think this is correct.
It's not an argument, it's an observation about the
properties of the time evolution.

Post by Richard Livingston
-The
wave function is not real, it is only a mathematical tool for predicting
the probabilities of future states

If you believe that one of those future /states/ will be real,
then you should also acknowledge that the /wave function/ is
real, because a /wave function/ is just a particular
representation of the /state/ of a system. (I assume the
simplified case of a pure state.)

But honestly, I do not care if it's called "real" or not.
It's an element of the theory, and this theory gives correct
predictions. These predictions do not depend upon whether
someone calls the wave function "real", so I deem that
question to be irrelevant.

In one sense it really is not "real". It's values are not
real but complex numbers, and observables must have real
values.

Post by Richard Livingston
It seems to me that each time the wave function "collapses" that
information is lost. Is there a good argument why this is wrong?

Ah, the "collapse"! No one understands this yet. If an
observer interacts with a quantum system, he might observe
a collapse. But when the whole combination of the observer
and the quantum system is seen as a single quantum system
from the outset, there is no collapse.

So, there are two possible descriptions of this history.

A tentative guess for an explanation might go as follows:
When the observer O measures the quantum system with two
possible outcomes A and B, the world is split into two worlds:
One world where the observer (now called OA) observed A,
one world where he (now called OB) observed B. Information
is not lost. However, from the point of view of OA,
information is lost. This is because he now only sees a part
of the unitary evolution - that part with the outcome of A.

[Julio Di Egidio]

Post by Thomas Koenig

Post by Julio Di Egidio
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

[Richard Livingston]

Post by Julio Di Egidio

Post by Thomas Koenig

Post by Julio Di Egidio
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

Julio,

Thank you for your detailed response. I have to debate some points where
I think you are being inconsistent. You say that QM wave function is
reversible because it evolves by a unitary operator. This is true, but the
wave function calculated is not real. I admit that it is simulating something
that is real, as proven by interference patterns, but that is not the same thing.

The difference is "collapse". Take the two slit experiment with a single
photon. When a photon is detected on the screen at one of several
predicted interference spots, the physical situation is now a photon
(or its packet of energy-momentum) in one specific atom/molecule.
If you try to start from this state and compute backwards you do NOT
get that the photon had to come from the single point light source on
the other side of the screen. The backward computed wave function
includes many possible sources, including the one that photon
actually came from.

QM is not deterministic in that at any given moment
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.

[Julio Di Egidio]

Post by Julio Di Egidio
And *reversibility* itself is already present in classical physics,

<snip>

Thank you for your detailed response. I have to debate some points where
I think you are being inconsistent.

Even if you disagree or don't see the point, that doesn't make
what I said (which is anyway just basic QM) inconsistent. In
fact, below you are repeating exactly the same mistakes as
in your opening post. So, I'll just repeat quickly:

<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 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

When the photon is detected, that is a *measurement*, i.e.
(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 there
are several possible mutually exclusive future outcomes.

Yes, it is: you are still conflating classical outcomes with
the evolution of the wave function, aka the quantum state.

to me that this means that information is not conserved

Sure, but it's *collapse* that destroys information.

Is there an error in my reasoning here?

Only if you'll insist... :)

HTH,

Julio

[Richard Livingston]

Post by Julio Di Egidio
<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.

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.

Post by Julio Di Egidio

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

When the photon is detected, that is a *measurement*, i.e.
(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.

Are you saying that measurement is not part of QM? Isn't it part of the
physics? Aren't there some events that permanently refine the wave
function down to a subset of possible outcomes?

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.

Post by Julio Di Egidio

QM is not deterministic in that at any given moment there
are several possible mutually exclusive future outcomes.

Yes, it is: you are still conflating classical outcomes with
the evolution of the wave function, aka the quantum state.

to me that this means that information is not conserved

Sure, but it's *collapse* that destroys information.

Is there an error in my reasoning here?

Only if you'll insist... :)

Oh! I insist!

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. If so I can see
your point being that the wave function describes all the possible
worlds and then no information would be lost. However we live in just
one of those many worlds, and it seems to me that we need a QM theory
that includes the random selection (aka "measurement" or "collapse")
down to just one of the many worlds. Therefore it seems to me that in
our world there is a loss of information every time there is a
measurement.

Or so I believe!

Thanks Julio for responding, this is clarifying these ideas for me.

Rich L.

Post by Julio Di Egidio
HTH,
Julio

[Julio Di Egidio]

<snipped>

Post by Julio Di Egidio

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 the reasons I have hinted at upthread: 1) saying "the wave function
is not real" means a plain hole in a theory's ontology (you may think our
physical theories are full of these "holes": they aren't, and the problem
here is in fact quite serious), and in this respect the standard interpretation
is the weakest of the lot, i.e. as compared to pilot-wave theory or even
many-worlds ("multiverses"); 2) "collapse" of the wave function is indeed
an externally added postulate that simply has no place in any physical
theory proper (under the least-action over a state space paradigm that is);
and, 3) with collapse we break "reversibility", which is really the nail in the
coffin as far as that theory is concerned. So... "shut up and calculate."

Indeed, note that many-worlds was born exactly as an attempt to solve
the problems of the standard interpretation: there is no "collapse" but
rather "branching" in many-worlds, and, while ontologically that remains
quite unjustified (as long as there is no way to probe the existence of
these branches), it at least saves reversibility.

While, as for pilot wave theory, that is fine ontologically and otherwise,
indeed (as I get it) it is the best quantum theory we could have, but it's
simply been "cancelled". Sure, it's dualistic, just as in Yin and Yang...
but this is another story.

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.

No, you are quite not precise enough. Physics already *per se* has two
dimensions, theoretical and applicative (experimental), where the
theoretical part is where you find the (physical!) models: and the more
we probe into realms that we cannot directly experience, the more the
theoretical part becomes relevant and needs to be solid. As for maths,
that is simply a tool, it provides a formal language and algebra, but that's
all about it, it certainly does not dictate anything properly physical.

That said, the belief you express above I agree with (how couldn't I), but
now you are getting into the properly philosophical issue of what one
believes about cosmos: physics per se just needs a solid ontology and
then it is proper physics, whether or not the whole cosmos is somebody's
dream or else... but this too is another story and only marginal to our topic.

Seriously, isn't collapse a part of reality, or required by reality?

Nope, "collapse" is a postulate and then a requirement of *that
theory* to somehow manage to use it at all. Conversely, the fact that
we "measure things" does not per se entail the need for "collapse".

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.

You are being *very* imprecise there. Indeed this is my last reply in this
thread: at this point I think if you want more or even just more confirmation,
you should rather start looking into some course material...

It sounds like you may follow the many worlds concept.

I thought I had to made clear that I am quite unhappy about that, too.

Thanks Julio for responding, this is clarifying these ideas for me.

Fascinating topics. Best luck to you,

Julio

[Tom Roberts]

[...] 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

[stargene]

On Sunday, September 4, 2022 at 10:54:28 AM UTC-7, ***@gmail.com wro=
[[Mod. note -- Quoted text trimmed. -- J.T.]]

Post by Richard Livingston
QM is not deterministic in that at any given moment
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.

A naive query: I've known qualitatively that unitarity guarantees
that no information is ever destroyed. Does unitarity allow for
the creation of information? My sense is that just as our physical
universe evolves in a direction of greater complexity, this also
means toward greater amounts of information.

[Richard Livingston]

Post by Tom Roberts

[...] 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
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

I'm having a real problem with this idea. It seems to me that there
are certain events that clearly result in the wave function changing
radically. I gave one example with a photon detected in one particular
spot on a screen. Another would be a isolated atom that emits a photon.
The QM treatment gives a wave function that expands outward in all
directions. Eventually (perhaps years later) that photon is absorbed
by some distant atom. Energy has been transferred from one location to
another at a later time. This is a very real event and experimentally
verifiable.

If it had been scattered immediately with negligible loss of energy, I
could see that as a possible evolution of the state without any collapse
or loss of information. However if it is absorbed and eventually
converted into heat, isn't that equivalent to collapse of the wave
function? Isn't that irreversible? Doesn't that constitute loss of
information?

I understand that some "interpretations" of QM, such as many worlds,
avoid this by partitioning the information into multiple adjacent but
inaccessible adjacent worlds, but it seems to me that this is an
untestable theory, and therefore unscientific.

I have Ballantines book, I'll go back into it to see what he says about
all this.

Rich L.

[Tom Roberts]

[...] 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
our minds only via a PUN on "exist". This of course applies to our
physical models of the world, such as QM: they are pure thoughts.

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
a model necessarily correspond to some object or process in the world.
The difference is profound, and involves a radical change in outlook and
approach. Remember that "model" inherently implies validity only in a
limited domain....

[So, for instance, the incompatibility between GR and QM
does not imply a fundamental problem, as they are both
excellent models valid in disjoint domains. We are
searching for a better model that will be valid in a
wider domain that hopefully encompasses both of their
individual domains.]

Tom Roberts

[Julio Di Egidio]

Post by Tom Roberts

[...] 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

No, you are simply way out of your depths.

Post by Tom Roberts
no human thought has any ontology at all,
because thoughts do not exist in the world we inhabit, they "exist" in

Nonsense: you apparently just don't know the meaning
of "ontology", or of "theory" for that sake.

Post by Tom Roberts
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.

Nonsense: *every* (scientific, not to conflate with e.g.
mathematical or else) theory needs an ontology to be
a theory at all: with physics, the meaning and value of
models indeed is exactly proportional to their correspondence
to the "object of study", aka, from a theoretical point of view,
the ontology.

Post by Tom Roberts
So, for instance, there is no expectation that quantities that appear in
a model necessarily correspond to some object or process in the world.

<snip>

You must have implicitly internalized the shut up and calculate,
as otherwise that is in no way how physics or any other science
is supposed to work.

And now a word a caution to you specifically, Tom, since you
regularly seem to jump on what I write: while I am relatively new
to physics, I happen to be an expert in foundations as well as,
FWIW, in philosophy generally. So, please, rather ask questions.

HTH and EOD (hopefully).

Julio

[Rock Brentwood]

Post by Richard Livingston
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

There is no such thing as being "only a mathematical tool".
Everything that says anything meaningful about the physical world
is ipso facto physical and physically relevant, and is thus real.

Anything that has any effect or impact on the physical world
is thereby physical; even thoughts and things called "subjective"
(since the brain, itself, is a physical object).
Physicality is the Borg of all attributes.
It assimilates everything that comes into contact with it.

[Richard Livingston]

Post by Rock Brentwood

Post by Richard Livingston
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

There is no such thing as being "only a mathematical tool".
Everything that says anything meaningful about the physical world
is ipso facto physical and physically relevant, and is thus real.

...

I have to clarify my statement on the wave function. It is both a
mathematical tool and also something that somehow, probably imperfectly,
mirrors something real. To take the wave function as something real is,
I think, not justified by the non-physical behaviors, e.g. the
"instantaneous collapse". Never the less, there is something real that
the wave function is representing, and I think more of us should be
trying to figure out what that is.

Rich L.