Fungibility clarification
Alan Forrester
fungibility badly and I should like to clarify my position.
I also think the discussion in BoI is slightly confusing. Let's start
by looking at the apparent conflicts in the BoI discussion.
Fungibility is defined at the end of the chapter as 'Identical in
every respect.' Likewise on p. 265 David writes that fungible objects
are 'identical literally in every way except that there are two of
them.'
However, on p. 268, we see the first sign of apparent trouble. Money
is legally fungible - any two units of the same currency are identical
for the purposes of paying a debt. David then points out that you
could instruct your bank to pay one dollar in taxes on a specific
date. 'Since the dollars in the account are fungible,' David writes,
'there is no such thing as which one belongs to the tax authority and
which belongs to you.' In the very next sentence he writes: ''Everyday
language struggles to describe this situation: each dollar in the
account shares literally all its attributes with the others, yet it is
not the case that all of them have the same owner.'
Now, on p. 293, David writes something that I think helps us to
understand the root of the disagreement about fungibility in quantum
mechanics. '[C]onsider a single cosmic ray particle travelling in the
direction of Earth from deep space. That particle must be travelling
in a range of slightly different directions, because the uncertainty
principle implies that it must spread sideways like an ink blot as it
travels. By the time it arrives the ink blot may well be wider than
the whole Earth - so most of it misses and the rest strikes everywhere
on the exposed surface. Remember, this is a single particle, which may
consist of fungible instances. The next thing that happens is that
they cease to be fungible, splitting through their interactions with
atoms into a finite but huge number of instances, each of which is the
origin of a separate history.'
Now, the different instances are not identical in every respect. They
will be found at different places and produce different histories.
What is true is that there is a sense in which there is no such thing
as which is which. Why? Because we could interfere different instances
of the particle and we would not be able to explain the result by
discussing the instances separately: they would all contribute to the
outcome. The important thing is not that they are identical in every
respect, it is just that there is no such thing as which is which.
What counts as there being such a thing as which is which? The answer
is that when two different instances produce different information
that can in principle be copied then there is a fact about which is
which. (Copied here means that information started out as present in
only one system and was then present in more than one system after the
copying process was over.) For example, if a cosmic ray strikes a rock
in Glasgow then it heats the rock up slightly: this could in principle
be measured and that information could be entered onto a computer,
then sent out in an e-mail to another computer, then a scientist could
look at it and say "oh gosh a cosmic ray hit a rock in Glasgow" and
tell his friend about the cosmic ray over lunch and so on. If it hits
a rock in Oxford instead then that too could be measured and then the
scientist would say that the cosmic ray hit a rock in Oxford instead
of saying it hit a rock in Glasgow. Information that can be copied
reliably is digital as explained in Chapter 6 of BoI pp. 140-142. That
explains the quantum in quantum mechanics.
Now, in an interference experiment there is no such thing as which is
which. So if fungibility is defined in terms there being no such thing
as which is which then during an interference experiment the different
versions of the interfering system are fungible. Defining fungible in
any other way is not helpful for understanding quantum mechanics.
I said in an earlier message that fungibility is relative. I was wrong
about that and woule like to explain the mistake. What I was thinking
of was this. If you have a pair of systems that are entangled with one
another then the joint system is fungible: it could undergo
inteference so there is no such thing as which is which. However, the
subsystems can't undergo interference unless the entangling
interaction is undone so there is such a thing as which is which for
them. I got a bit mixed up between the system and the subsystems.
Any problems?
Alan
Lee Kelly
fungibility:
Several instances of a particle are fungible when interference can
destroy their respective identities. For example, in Mach-Zehnder
interferometers, a single particle takes two different paths, passing
through the half-mirror in one universe and reflecting off it in
another. These particles are not identical, i.e. there are statements
which are true for one particle but not true for the other. However,
by the time both particles reach the final half-mirror, they interfere
and exit the interferometer on the same path. This interference
destroys their respective identities, and the two instances of the
particle become fungible.
Our intuition has it that there are now two particles doing the same
thing in two different universes, but each particle has a different
history, i.e. one where the particle passed through the mirror and the
other where is reflected.
This intuition is wrong, according to Deutsch. We can understand this
by stacking two Mach-Zehnder interferometers one after the other. The
particle passes through the first interferometer, takes two paths in
alternate universes, and then interference forces both particles to
take the same path out. Now suppose the particle immediately enters a
second interferometer and, again, passes through the mirror in one
universe and reflects off it in another. Before the two particles
reach the final mirror and interfere, we again have two separate
particles for which some statements are true for one but not the
other.
If particles are not fungible, it would be sensible to ask which path
each particle took when passing through the first interferomenter,
because each particle in each universe would have a unique history.
For example, we might say that the particle which passes through the
mirror at the second interferometer reflected off the mirror at the
first interferometer. The opposite would then be true for the other
particle. But this is, apparently, not a sensible question or answer
given the laws of quantum physics.
What Deutsch appears to be saying is that when the two particles
interfere coming out of the first interferometer, they become
fungible, i.e. they lose their unique identity. By the time the
particle has entered the second interferometer, it literally makes no
sense to ask which particle did what in the first interferometer, just
like it makes no sense to ask which dollar the bank is adding or
removing from your account. What matters is what is happening to the
multiversal object of the particle, just like what matters is what is
happening to the whole balance of your bank account.
At any rate, this is my (mis)understanding.
Lee Kelly
water.
Droplets of water are fungible. Suppose water is dripping from a
faucet into a leaky container and then dripping again into a second
container (suppose the leak is a few is abotu an inch from the bottom
of the first container). Now, it would be nonsense to ask whether a
droplet falling into the second container is the same as a water
droplet that fell into the leaky container a few minutes ago. It
wouldn't just be false, but couldn't possibly be true. That's just not
how water droplets work. The water droplets falling into the second
container do not have a history of falling from the faucet some time
in the past. The whole system has a history of droplets falling into
the first container and then other droplets leaking into the second
container, but the water droplets themselves do not have unique
histories traceable through these events: the mass of water that
collects in the leaky container is fungible with regard to droplets of
water. It literally makes no sense to ask which one of the droplets
that fell into the container originally is now leaking out.
This is what I get from Deutsch explanation of fungibility with regard
to elementary particles. When a particle becomes differentiated in
alternate universes and is then realigned by interference, it is like
two droplets of water coming together. When the particle is then
differentiated again sometime later, it makes no sense to ask which
particle did what the last time they were differentiated, just as it
makes no sense to ask which of the water droplets is leaking from the
container.
David Deutsch
Suppose a photon is approaching a semi-silvered mirror in direction RIGHT (an eigenstate of a direction observable D). The mirror will change the photon's state to RIGHT+DOWN. (Disregarding normalisation.)
That's not an entangled state, so according to your criterion, the instances of the photon are still all fungible after they have struck the mirror.
However, in another way of describing the same physical process, the mirror causes another observable of the photon, namely its position P, to become entangled with its direction of motion D. I have just called the state after striking the mirror RIGHT+DOWN, but we could more elaborately call it
| RIGHT > |ON TOP PATH> + | DOWN > |ON LEFT PATH >
If we were to do that, your criterion would say that the instances of the photon are no longer fungible.
Thus it would appear that your criterion assigns the attributes 'fungible' and 'not fungible' according to how the process is described. But it should depend only on what is happening objectively.
Hence I'm still a little confused. But it's a healthy confusion...
-- David
Alan Forrester
P and D are not observables of distinct subsystems so there is no
state of the form you have written down. Why? D is a coarse grained
momentum observable and P is a position observable and those are
related by the uncertainty principle. Position and momentum of the
same system can't be entangled.
Alan
David Deutsch
The proviso "coarse-grained" makes that statement false.
At a long time T after the photon strikes the semi-silvered mirror, consider two large, non-overlapping spheres centred on points at distance cT from the mirror on the TOP and LEFT paths respectively. Then let P be the sum, with different coefficients, of the two projectors for the photon being inside those spheres. Because the spheres are very large, P commutes with observables that are very close to being projectors for the photon to be travelling RIGHTwards and DOWNwards. Hence there eixsts an observable D that strictly commutes with P, that is very close to being a 'direction of travel' observable.
So at time T, the photon is indeed capable of being in any one of four states |RIGHT MOTION>|TOP PATH>, |RIGHT MOTION> |LEFT PATH> and so on. And it is capable of being in an arbitrary superposition of those. So it does consist of (more than) two distinct subsystems that may or may not be entangled with each other.
-- David
Alan Forrester
Okay. How does the interference experiment go in terms of the states
you have chosen?
It starts with the state:
| RIGHT > |ON TOP PATH>
that changes to
| RIGHT > |ON TOP PATH> + | DOWN > |ON LEFT PATH >
which then changes to
| DOWN > |ON LEFT PATH >
So the joint system of P and D is always fungible by my criterion.
You're interfering the PD system not the P system alone.
Alan
Elliot Temple
What is normalization?
> That's not an entangled state, so according to your criterion, the instances of the photon are still all fungible after they have struck the mirror.
>
> However, in another way of describing the same physical process, the mirror causes another observable of the photon, namely its position P, to become entangled with its direction of motion D. I have just called the state after striking the mirror RIGHT+DOWN, but we could more elaborately call it
>
> | RIGHT > |ON TOP PATH> + | DOWN > |ON LEFT PATH >
Are "right" and "down" velocities, and "on top path" and "on left path" positions?
And from the next email by David Deutsch:
> Then let P be the sum, with different coefficients, of the two projectors for the photon being inside those spheres. Because the spheres are very large, P commutes with observables that are very close to being projectors for the photon to be travelling RIGHTwards and DOWNwards. Hence there exists an observable D that strictly commutes with P, that is very close to being a 'direction of travel' observable.
What does "commutes" mean, in this context?
Is the next part about he possible of "|RIGHT MOTION>|TOP PATH>", etc, an implication of the observable D? "Right motion" sounds like it *is* a direction of travel rather than being very close to one.
> So at time T, the photon is indeed capable of being in any one of four states |RIGHT MOTION>|TOP PATH>, |RIGHT MOTION> |LEFT PATH> and so on.
The other two are |DOWN MOTION>|TOP PATH> and |DOWN MOTION>|LEFT PATH>, correct?
There are more than four states it can be in. You mentioned these four in particular because they are interesting/notable to you. Right? For example it could also be in
> |UP RIGHT MOTION>|TOP PATH>
The four states that interested you are the ones showing that the motion can be the same for either position, and the position can be the same for either motion. I think there is some implication of this. It matters that that is possible because it means something (about entanglement?). What does it mean?
-- Elliot Temple
http://beginningofinfinity.com/excerpt
Elliot Temple
I think David is concerned with the time before a second mirror is hit (he did not mention any second mirror, he just considered the photon continuing in either direction for a "long time T" and thus ending up cT away, potentially in a sphere, so that should probably be thought of as in space not in some narrow enclosed path like an interferometer might have). It's just one mirror and then spheres at distance cT from that one mirror where photons could be.
Alan wrote previously:
> The important thing is not that they are identical in every respect [BoI's definition of fungibility], it is just that there is no such thing as which is which.
>
> What counts as there being such a thing as which is which? The answer
> is that when two different instances produce different information
> that can in principle be copied then there is a fact about which is
> which.
and
> If you have a pair of systems that are entangled with one
> another then the joint system is fungible: it could undergo
> inteference so there is no such thing as which is which. However, the
> subsystems can't undergo interference unless the entangling
> interaction is undone so there is such a thing as which is which for
> them.
And David wrote in reply to that email:
> However, in another way of describing the same physical process, the mirror causes another observable of the photon, namely its position P, to become entangled with its direction of motion D. I have just called the state after striking the mirror RIGHT+DOWN, but we could more elaborately call it
>
> | RIGHT > |ON TOP PATH> + | DOWN > |ON LEFT PATH >
>
> If we were to do that, your criterion would say that the instances of the photon are no longer fungible.
Trying to make sense of this:
What is Alan's criterion which David refers to? The "no which is which" criterion of fungibility.
It is about copyable information.
Then Alan writes later discussing entanglement. And David's reply speaks of entanglement.
So, what does entanglement have to do with copyable information and fungibility?
My second Alan quote, I think, says that whether things are entangled is *also* a criterion of fungibility: entangled means not fungible (and subsystems and joint systems can be considered separately, it varies by how you divide things up).
Using that link, David is saying that we can describe a photon hitting a semi-silvered mirror in terms of entangled subsystems rather than not-entangled larger systems. That's an example of what Alan was saying: the joint system does not have entanglement (so is fungible?) while the subsystems are entangled (so not fungible?).
Then David says:
> Thus it would appear that your criterion assigns the attributes 'fungible' and 'not fungible' according to how the process is described. But it should depend only on what is happening objectively.
So Alan's position, as I read it, is that whether some particular thing is fungible does not have a single answer. It depends on what system, if any, you consider it a part of. It's fungibility is not a fundamental trait it has but a contextual trait.
David on the other hand says there should be a single objective answer to whether a particular thing is fungible that does not depend on how we look at the world (e.g. which things we regard as joint systems, or not), and he has criticized Alan's position for violating this.
-- Elliot Temple
http://fallibleideas.com/
Elliot Temple
On Aug 22, 2011, at 10:18 AM, Elliot Temple wrote:
> Then David says:
>
>> Thus it would appear that your criterion assigns the attributes 'fungible' and 'not fungible' according to how the process is described. But it should depend only on what is happening objectively.
>
>
> So Alan's position, as I read it, is that whether some particular thing is fungible does not have a single answer. It depends on what system, if any, you consider it a part of. It's fungibility is not a fundamental trait it has but a contextual trait.
>
> David on the other hand says there should be a single objective answer to whether a particular thing is fungible that does not depend on how we look at the world (e.g. which things we regard as joint systems, or not), and he has criticized Alan's position for violating this.
Following up on this, I think the example of money (from BoI, discussed previously in the thread) goes to Alan and contradicts David's take.
For simplicity, suppose electronic bank money is stored in a format where each bit repents 1 dollar, instead of a usual format with higher bits having a value above 1.
So 3 dollars is 111000000000 and 5 dollars is 111110000000000
The number of zeros has no importance, you just count up the 1s.
So now we assign some money to be paid to the IRS. We have 11100 with one of those dollars being owned by the IRS and two by us.
Those bits, in their capacity as dollars, are fungible.
But those bits, *described in a different way*, are not fungible. If you forget about the money they represent, they are physical objects in (slightly) different locations, which are not fungible.
So the same bits are fungible for the purposes of money, but not as physical objects.
SOURCES OF ERROR
Another possibility for what I've described is that it's an example of how money isn't truly fungible in the way multiversal instances of particles are. Being legally fungible isn't necessarily the same kind of thing as being actually fungible.
-- Elliot Temple
http://beginningofinfinity.com/discussion
Elliot Temple
On Aug 21, 2011, at 10:16 AM, Lee Kelly wrote:
> An intuition pump would be to imagine each particle as a droplet of
> water.
>
> Droplets of water are fungible.
No, because they are not identical in every respect. For example, different droplets of water occupy different positions.
> It literally makes no sense to ask which one of the droplets
> that fell into the container originally is now leaking out.
It doesn't make sense because it will be a mix of molecules from many droplets that leaks out. They aren't separate droplets at the time of leaking.
But one can ask which H2O molecules are leaking out, and which droplets they fell into the container as part of. This is a difficult question to answer (involving careful tracking of individual molecules in liquid) but it does make sense.
>
> This is what I get from Deutsch explanation of fungibility with regard
> to elementary particles. When a particle becomes differentiated in
> alternate universes and is then realigned by interference, it is like
> two droplets of water coming together. When the particle is then
> differentiated again sometime later, it makes no sense to ask which
> particle did what the last time they were differentiated, just as it
> makes no sense to ask which of the water droplets is leaking from the
> container.
It's kind of like that, except that it's literally true in the case of physics, while only approximately true with the water.
In general everyday life features approximate fungibility but not actual fungibility. A common example is paperclips. In a big pile of paperclips they are *approximately* fungible: it's easy to lose track of which is which, they are basically all the same, and we don't really care which is which. And they are also legally fungible: if I owe someone five paperclips I don't have to give back the same five but can just pick any five from the pile.
But paperclips are not actually fungible, considered at higher precision. Each one has a unique shape if you look at small enough differences. And while they have the same position at low precision, at higher precision each is in a different place. And it is possible to keep track of which is which, if one cares to.
Alan Forrester
If system 1 contains copyable information about he state of system 2
at a particular time t1, then the versions of system 2 that existed at
t1 are no longer fungible.
> Then Alan writes later discussing entanglement. And David's reply speaks of entanglement.
>
> So, what does entanglement have to do with copyable information and fungibility?
If system 1 and system 2 are entangled then they contain copyable
information about one another. So then system 1 is not fungible and
system 2 is not fungible. However, the joint system composed of system
1 and system 2 is fungible if it's not entangled with anything else.
> My second Alan quote, I think, says that whether things are entangled is *also* a criterion of fungibility: entangled means not fungible (and subsystems and joint systems can be considered separately, it varies by how you divide things up).
>
> Using that link, David is saying that we can describe a photon hitting a semi-silvered mirror in terms of entangled subsystems rather than not-entangled larger systems. That's an example of what Alan was saying: the joint system does not have entanglement (so is fungible?) while the subsystems are entangled (so not fungible?).
Yes.
> Then David says:
>
>> Thus it would appear that your criterion assigns the attributes 'fungible' and 'not fungible' according to how the process is described. But it should depend only on what is happening objectively.
>
> So Alan's position, as I read it, is that whether some particular thing is fungible does not have a single answer. It depends on what system, if any, you consider it a part of. It's fungibility is not a fundamental trait it has but a contextual trait.
I don't think that's quite the right way of thinking about it. When a
system is in a particular state, there is an objective to whether it's
fungible or not. Now if you have access to system 1 and all of the
system's it's entangled (systems 2,3 and so on) with then you can make
system 1 fungible again. That's what happens in the interference
experiment. Before you restore system 1's fungibility you can't do
interference with it on its own, that's an objective fact.
> David on the other hand says there should be a single objective answer to whether a particular thing is fungible that does not depend on how we look at the world (e.g. which things we regard as joint systems, or not), and he has criticized Alan's position for violating this.
I think that is David's position.
Alan
Elliot Temple
Why is this? Is this by definition or an implication (of what?)?
>> My second Alan quote, I think, says that whether things are entangled is *also* a criterion of fungibility: entangled means not fungible (and subsystems and joint systems can be considered separately, it varies by how you divide things up).
>>
>> Using that link, David is saying that we can describe a photon hitting a semi-silvered mirror in terms of entangled subsystems rather than not-entangled larger systems. That's an example of what Alan was saying: the joint system does not have entanglement (so is fungible?) while the subsystems are entangled (so not fungible?).
>
> Yes.
>
>> Then David says:
>>
>>> Thus it would appear that your criterion assigns the attributes 'fungible' and 'not fungible' according to how the process is described. But it should depend only on what is happening objectively.
>>
>> So Alan's position, as I read it, is that whether some particular thing is fungible does not have a single answer. It depends on what system, if any, you consider it a part of. It's fungibility is not a fundamental trait it has but a contextual trait.
>
> I don't think that's quite the right way of thinking about it. When a
> system is in a particular state, there is an objective to whether it's
> fungible or not. Now if you have access to system 1 and all of the
> system's it's entangled (systems 2,3 and so on) with then you can make
> system 1 fungible again. That's what happens in the interference
> experiment. Before you restore system 1's fungibility you can't do
> interference with it on its own, that's an objective fact.
If the fungibility of the instances of the photon in the middle of the interferometer need to be "restored" doesn't that mean they are not, currently, fungible? That they become non-fungible temporarily during the experiment? As BoI said, and I thought you had disagreed with.
Can you explain the relevance/meaning of whether you can do interference with system 1 on its own (with itself?)?
>> David on the other hand says there should be a single objective answer to whether a particular thing is fungible that does not depend on how we look at the world (e.g. which things we regard as joint systems, or not), and he has criticized Alan's position for violating this.
>
> I think that is David's position.
And you disagree or agree? I thought you disagreed but your comments above about
> there is an objective [answer? missing word] to whether it's fungible or not
and
> Before you restore system 1's fungibility
look to me like agreeing with David.
-- Elliot Temple
http://beginningofinfinity.com/interview
David Deutsch
> If system 1 and system 2 are entangled then they contain copyable
> information about one another. So then system 1 is not fungible and
> system 2 is not fungible. However, the joint system composed of system
> 1 and system 2 is fungible if it's not entangled with anything else.
I think that's it!
It means that the definition of 'interference' in BoI is correct, and only the description of how the interferometer works is deficient -- some would say misleading.
Now all I have to do is get my head round the stunning fact that two systems can be fungible while corresponding subsystems of them are not.
-- David
Alan Forrester
Normalisation is when you multiply the state by a number so that the
probabilities add up to one. So in this case we're not bothered about
whether the probabilities add to one.
>> That's not an entangled state, so according to your criterion, the instances of the photon are still all fungible after they have struck the mirror.
>>
>> However, in another way of describing the same physical process, the mirror causes another observable of the photon, namely its position P, to become entangled with its direction of motion D. I have just called the state after striking the mirror RIGHT+DOWN, but we could more elaborately call it
>>
>> | RIGHT > |ON TOP PATH> + | DOWN > |ON LEFT PATH >
>
> Are "right" and "down" velocities, and "on top path" and "on left path" positions?
Yes.
> And from the next email by David Deutsch:
>
>> Then let P be the sum, with different coefficients, of the two projectors for the photon being inside those spheres. Because the spheres are very large, P commutes with observables that are very close to being projectors for the photon to be travelling RIGHTwards and DOWNwards. Hence there exists an observable D that strictly commutes with P, that is very close to being a 'direction of travel' observable.
>
> What does "commutes" mean, in this context?
Two observables A and B commute if AB = BA.
> Is the next part about he possible of "|RIGHT MOTION>|TOP PATH>", etc, an implication of the observable D? "Right motion" sounds like it *is* a direction of travel rather than being very close to one.
That seems to me to be a bit of a sticking point where I'd have to
look up stuff to check what's going on. Specifically what does very
close mean in this context? But see below for why I didn't pursue that
issue.
>> So at time T, the photon is indeed capable of being in any one of four states |RIGHT MOTION>|TOP PATH>, |RIGHT MOTION> |LEFT PATH> and so on.
>
> The other two are |DOWN MOTION>|TOP PATH> and |DOWN MOTION>|LEFT PATH>, correct?
>
> There are more than four states it can be in. You mentioned these four in particular because they are interesting/notable to you. Right? For example it could also be in
>
>> |UP RIGHT MOTION>|TOP PATH>
>
>
> The four states that interested you are the ones showing that the motion can be the same for either position, and the position can be the same for either motion. I think there is some implication of this. It matters that that is possible because it means something (about entanglement?). What does it mean?
Observables can commute under two circumstances.
(1) They are the same except that the outcomes are labelled with
different numbers.
(2) They are different but belong to different systems.
If either (1) or (2) doesn't hold the observables don't commute.
Different systems can be entangled with one another: a system can't be
entangled with itself. So if they don't commute then the issue David
describes doesn't arise. I thought they didn't commute. I'm now not
quite sure whether they do or not, but in any case what happens if I'm
wrong about them commuting is more interesting.
Now, if all four states can happen then P and D belong to different
systems because otherwise there would be less than four possible
states because one or more of the possibilities would be different
ways of describing the same thing, or they wouldn't arise.
It's like if you have a register that supposedly has two bits. If the
register can actually only be in one of three or fewer possible states
then there aren't two independent bits.
Alan
Alan Forrester
Copyable information is information that can be present in one system
before the copying process and present in more than one system
afterward. The significance of copyable information is that branches
of the multiverse are basically structures constituted by copyable
information. We can communicate and that's what tells us we're in the
same branch. For communication to take place we have to both know some
copyable information like either we know the same language or the
language we don't have in common can be taught by conjecture and
criticism: that requires that I should be able to say 'you made
conjecture X, but it's wrong because of fact Y.' So you have know to
know what X and Y are and so there has to be copyable information
about X and Y because it's present in both you and me.
Now, if two systems are entangled they have some copyable information
about one another. For example, if the spins of two electrons are
entangled then electron 1 has information about what spin we will
measure in electron 2 in the z direction if we measure the spin of
electron 1 in the z direction, and vice versa. So that's why
entanglement and copyable information go together.
>>> My second Alan quote, I think, says that whether things are entangled is *also* a criterion of fungibility: entangled means not fungible (and subsystems and joint systems can be considered separately, it varies by how you divide things up).
>>>
>>> Using that link, David is saying that we can describe a photon hitting a semi-silvered mirror in terms of entangled subsystems rather than not-entangled larger systems. That's an example of what Alan was saying: the joint system does not have entanglement (so is fungible?) while the subsystems are entangled (so not fungible?).
>>
>> Yes.
>>
>>> Then David says:
>>>
>>>> Thus it would appear that your criterion assigns the attributes 'fungible' and 'not fungible' according to how the process is described. But it should depend only on what is happening objectively.
>>>
>>> So Alan's position, as I read it, is that whether some particular thing is fungible does not have a single answer. It depends on what system, if any, you consider it a part of. It's fungibility is not a fundamental trait it has but a contextual trait.
>>
>> I don't think that's quite the right way of thinking about it. When a
>> system is in a particular state, there is an objective to whether it's
>> fungible or not. Now if you have access to system 1 and all of the
>> system's it's entangled (systems 2,3 and so on) with then you can make
>> system 1 fungible again. That's what happens in the interference
>> experiment. Before you restore system 1's fungibility you can't do
>> interference with it on its own, that's an objective fact.
>
> If the fungibility of the instances of the photon in the middle of the interferometer need to be "restored" doesn't that mean they are not, currently, fungible? That they become non-fungible temporarily during the experiment? As BoI said, and I thought you had disagreed with.
In that particular paragraph I wasn't referring to the photon. The
photon is fungible throughout the experiment, but some of its
subsystems are not. The direction is non-fungible, the position is
non-fungible but the joint system of direction and position is
fungible, so the photon is fungible.
> Can you explain the relevance/meaning of whether you can do interference with system 1 on its own (with itself?)?
Whether you can get system 1 on its own to do something is an
objective fact and so fungibility is not subjective.
>>> David on the other hand says there should be a single objective answer to whether a particular thing is fungible that does not depend on how we look at the world (e.g. which things we regard as joint systems, or not), and he has criticized Alan's position for violating this.
>>
>> I think that is David's position.
>
> And you disagree or agree? I thought you disagreed but your comments above about
>
>> there is an objective [answer? missing word] to whether it's fungible or not
>
> and
>
>> Before you restore system 1's fungibility
>
> look to me like agreeing with David.
The fact that system 1 and system 2 may not be fungible although the
joint system is fungible doesn't make fungibility subjective or
description dependent. So if David's position was that fungibility is
subjective or decision dependent in my view of fungibility then I
disagree with that position.
Alan
Elliot Temple
On Aug 22, 2011, at 11:23 AM, Alan Forrester wrote:
> On 22 August 2011 17:53, Elliot Temple <cu...@curi.us> wrote:
>
>> Is the next part about he possible of "|RIGHT MOTION>|TOP PATH>", etc, an implication of the observable D? "Right motion" sounds like it *is* a direction of travel rather than being very close to one.
>
> That seems to me to be a bit of a sticking point where I'd have to
> look up stuff to check what's going on. Specifically what does very
> close mean in this context? But see below for why I didn't pursue that
> issue.
>
>>> So at time T, the photon is indeed capable of being in any one of four states |RIGHT MOTION>|TOP PATH>, |RIGHT MOTION> |LEFT PATH> and so on.
>>
>> The other two are |DOWN MOTION>|TOP PATH> and |DOWN MOTION>|LEFT PATH>, correct?
>>
>> There are more than four states it can be in. You mentioned these four in particular because they are interesting/notable to you. Right? For example it could also be in
>>
>>> |UP RIGHT MOTION>|TOP PATH>
>>
>>
>> The four states that interested you are the ones showing that the motion can be the same for either position, and the position can be the same for either motion. I think there is some implication of this. It matters that that is possible because it means something (about entanglement?). What does it mean?
>
> Observables can commute under two circumstances.
>
> (1) They are the same except that the outcomes are labelled with
> different numbers.
(Or also, I'm guessing, the same and labelled with the same numbers.)
>
> (2) They are different but belong to different systems.
In other words, they are independent?
So for example you can commute the length of your cat with the length of your dog. But not the length of your dog with its age.
> If either (1) or (2) doesn't hold the observables don't commute.
>
> Different systems can be entangled with one another: a system can't be
> entangled with itself. So if they don't commute then the issue David
> describes doesn't arise. I thought they didn't commute. I'm now not
> quite sure whether they do or not, but in any case what happens if I'm
> wrong about them commuting is more interesting.
I think we are looking at this in different ways.
You are seeing |DOWN MOTION>|TOP PATH>, and so on, as being commuted versions of things? How does that work?
I saw it as because that a photon on the top path (or anywhere) could be going in any direction at any particular time. That's why David spoke of spheres: because photons don't just go straight in all universes but can end up in a variety of places and have a variety of motions to get there.
If I try to commute |DOWN MOTION>|TOP PATH> I get |TOP PATH>|DOWN MOTION>. I don't see how that's different, at least intuitively, though I can see how mathematically it could matter. Regardless, the four things we were talking about weren't created by commuting from AB to BA like this, they all have the motion on the left and position on the right, never vice versa. So please clarify how commuting comes into it.
Also David previously wrote:
> Because the spheres are very large, P commutes with observables that are very close to being projectors for the photon to be travelling RIGHTwards and DOWNwards.
Can you relate this to what you said about commuting?
Back to Alan:
> Now, if all four states can happen then P and D belong to different
> systems because otherwise there would be less than four possible
> states because one or more of the possibilities would be different
> ways of describing the same thing, or they wouldn't arise.
>
> It's like if you have a register that supposedly has two bits. If the
> register can actually only be in one of three or fewer possible states
> then there aren't two independent bits.
I understand the register example.
OK so there are various concepts: fungible, entangled, copyable-information, commute, projector, independent systems, joint systems, subsystems, interference.
I'll try to use them and then you can correct me.
If all states of subsystems in a joint system are possible that means the subsystems are independent and commute. That means they are not entangled and the subsystems have no copied information about each other. This means the joint system *can* undergo interference.
If some states of subsystems of a joint system are not possible together, that means the subsystems are not independent and do not commute. It means you cannot do interference with the joint system, but you still could with the subsystems. It means the non-independent subsystems at least one of the subsystems has copied information about the other.
Is that correct? If it is, or if it's not and you correct it, could you then relate it back to the scenario being discussed with a photon going RIGHT hitting a semi-silvered mirror and then (instances of it each) going RIGHT (top path) or DOWN (left path)?
-- Elliot Temple
http://curi.us/
Elliot Temple
Right. "Universes" are explanatory concepts to help describe/explain/specify areas of the multiverse in which information flows. Information flow means information copying from one thing to another. Correct me if I'm wrong.
> For communication to take place we have to both know some
> copyable information like either we know the same language or the
> language we don't have in common can be taught by conjecture and
> criticism: that requires that I should be able to say 'you made
> conjecture X, but it's wrong because of fact Y.' So you have know to
> know what X and Y are and so there has to be copyable information
> about X and Y because it's present in both you and me.
If I had no copyable information then there'd be no way for the other guy to get even a single bit of information about what my ideas are, so we couldn't communicate. Makes sense.
> Now, if two systems are entangled they have some copyable information
> about one another. For example, if the spins of two electrons are
> entangled then electron 1 has information about what spin we will
> measure in electron 2
By the definition of "entangled"? Or some (which) implication of it?
> in the z direction if we measure the spin of
> electron 1 in the z direction, and vice versa. So that's why
> entanglement and copyable information go together.
I don't think I understand yet. Maybe I need to be reminded of what entanglement is and how it relates to this.
>
>>>> My second Alan quote, I think, says that whether things are entangled is *also* a criterion of fungibility: entangled means not fungible (and subsystems and joint systems can be considered separately, it varies by how you divide things up).
>>>>
>>>> Using that link, David is saying that we can describe a photon hitting a semi-silvered mirror in terms of entangled subsystems rather than not-entangled larger systems. That's an example of what Alan was saying: the joint system does not have entanglement (so is fungible?) while the subsystems are entangled (so not fungible?).
>>>
>>> Yes.
>>>
>>>> Then David says:
>>>>
>>>>> Thus it would appear that your criterion assigns the attributes 'fungible' and 'not fungible' according to how the process is described. But it should depend only on what is happening objectively.
>>>>
>>>> So Alan's position, as I read it, is that whether some particular thing is fungible does not have a single answer. It depends on what system, if any, you consider it a part of. It's fungibility is not a fundamental trait it has but a contextual trait.
>>>
>>> I don't think that's quite the right way of thinking about it. When a
>>> system is in a particular state, there is an objective to whether it's
>>> fungible or not. Now if you have access to system 1 and all of the
>>> system's it's entangled (systems 2,3 and so on) with then you can make
>>> system 1 fungible again. That's what happens in the interference
>>> experiment. Before you restore system 1's fungibility you can't do
>>> interference with it on its own, that's an objective fact.
>>
>> If the fungibility of the instances of the photon in the middle of the interferometer need to be "restored" doesn't that mean they are not, currently, fungible? That they become non-fungible temporarily during the experiment? As BoI said, and I thought you had disagreed with.
>
> In that particular paragraph I wasn't referring to the photon. The
> photon is fungible throughout the experiment, but some of its
> subsystems are not. The direction is non-fungible, the position is
> non-fungible but the joint system of direction and position is
> fungible, so the photon is fungible.
Position is a "subsystem" of a photon? I thought a subsystem would be more like a portion of a system. So for a photon it might be some of the (multiversal) instances of that photon.
>> Can you explain the relevance/meaning of whether you can do interference with system 1 on its own (with itself?)?
>
> Whether you can get system 1 on its own to do something is an
> objective fact and so fungibility is not subjective.
Yes, but I curious more about the physics of it. What could stop you from doing interference with system 1 on its own? Considered alone it will at least be fungible with itself and capable of interference, right? I'm not sure if I said that right. But like consider particles and MWI in general. A billion years ago there were infinitely many fungible instances of some particle on earth. Then it bounced around a lot and "split" into many different versions. But every single one of those, today, still has infinitely many fungible instances still capable of being used in two slit experiments or whatever. They never lose the ability to do interference no matter how much "splitting" takes place over time, and how much they bump into things and copy information and get entangled and whatever else.
Or in short: the past of a photon can never make it not work in a two slit experiment. So I'm not sure what you're talking about with no longer being able to do interference.
Westm...@aol.com
Alan Forrester
>
> On Aug 22, 2011, at 11:23 AM, Alan Forrester wrote:
>
>> On 22 August 2011 17:53, Elliot Temple <cu...@curi.us> wrote:
>>
>>> Is the next part about he possible of "|RIGHT MOTION>|TOP PATH>", etc, an implication of the observable D? "Right motion" sounds like it *is* a direction of travel rather than being very close to one.
>>
>> That seems to me to be a bit of a sticking point where I'd have to
>> look up stuff to check what's going on. Specifically what does very
>> close mean in this context? But see below for why I didn't pursue that
>> issue.
>>
>>>> So at time T, the photon is indeed capable of being in any one of four states |RIGHT MOTION>|TOP PATH>, |RIGHT MOTION> |LEFT PATH> and so on.
>>>
>>> The other two are |DOWN MOTION>|TOP PATH> and |DOWN MOTION>|LEFT PATH>, correct?
>>>
>>> There are more than four states it can be in. You mentioned these four in particular because they are interesting/notable to you. Right? For example it could also be in
>>>
>>>> |UP RIGHT MOTION>|TOP PATH>
>>>
>>>
>>> The four states that interested you are the ones showing that the motion can be the same for either position, and the position can be the same for either motion. I think there is some implication of this. It matters that that is possible because it means something (about entanglement?). What does it mean?
>>
>> Observables can commute under two circumstances.
>>
>> (1) They are the same except that the outcomes are labelled with
>> different numbers.
>
> (Or also, I'm guessing, the same and labelled with the same numbers.)
Yes.
>> (2) They are different but belong to different systems.
>
> In other words, they are independent?
It means they can be manipulated independently, not that this is
necessarily what happens.
> So for example you can commute the length of your cat with the length of your dog. But not the length of your dog with its age.
You can manipulate you dog's age and its length independently in
principle. For example, you could change the genes that make dogs grow
as they age or something like that. Sodog age and dog length do
commute.
>> If either (1) or (2) doesn't hold the observables don't commute.
>>
>> Different systems can be entangled with one another: a system can't be
>> entangled with itself. So if they don't commute then the issue David
>> describes doesn't arise. I thought they didn't commute. I'm now not
>> quite sure whether they do or not, but in any case what happens if I'm
>> wrong about them commuting is more interesting.
>
> I think we are looking at this in different ways.
>
> You are seeing |DOWN MOTION>|TOP PATH>, and so on, as being commuted versions of things? How does that work?
>
> I saw it as because that a photon on the top path (or anywhere) could be going in any direction at any particular time. That's why David spoke of spheres: because photons don't just go straight in all universes but can end up in a variety of places and have a variety of motions to get there.
>
>
> If I try to commute |DOWN MOTION>|TOP PATH> I get |TOP PATH>|DOWN MOTION>. I don't see how that's different, at least intuitively, though I can see how mathematically it could matter. Regardless, the four things we were talking about weren't created by commuting from AB to BA like this, they all have the motion on the left and position on the right, never vice versa. So please clarify how commuting comes into it.
Your right. It's just that direction is related to momentum which
doesn't commute with position which is why I thought there might be a
problem. But I was wrong about that.
> Also David previously wrote:
>
>> Because the spheres are very large, P commutes with observables that are very close to being projectors for the photon to be travelling RIGHTwards and DOWNwards.
>
> Can you relate this to what you said about commuting?
Projectors are a particular kind of observable. Any observable can be
written as a sum of the form
value1*(projector for value 1) + value2*(projector for value 2) + ...
So if the projectors of P commutes with D then P and D commute.
I currently plan to write more later in a new thread to clear up
remaining problems in as clear a manner as I can.
Alan
Elliot Temple
On Aug 22, 2011, at 2:32 PM, Alan Forrester wrote:
> On 22 August 2011 19:57, Elliot Temple <cu...@curi.us> wrote:
>>
>> On Aug 22, 2011, at 11:23 AM, Alan Forrester wrote:
>>
>>> Observables can commute under two circumstances.
>>>
>>> (1) They are the same except that the outcomes are labelled with
>>> different numbers.
>>
>> (Or also, I'm guessing, the same and labelled with the same numbers.)
>
> Yes.
>
>>> (2) They are different but belong to different systems.
>>
>> In other words, they are independent?
>
> It means they can be manipulated independently, not that this is
> necessarily what happens.
>
>> So for example you can commute the length of your cat with the length of your dog. But not the length of your dog with its age.
>
> You can manipulate you dog's age and its length independently in
> principle. For example, you could change the genes that make dogs grow
> as they age or something like that. So dog age and dog length do
> commute.
Ah, nice point.
So, what are some examples of everyday things which do not commute, given the possibility of highly advanced technological interventions?
tom.harrigan
division
pointing a gun at your head, pulling the trigger.
David Deutsch
> On Aug 22, 10:40 pm, Elliot Temple <c...@curi.us> wrote:
>> So, what are some examples of everyday things which do not commute, given the possibility of highly advanced technological interventions?
> subtraction
> division
> pointing a gun at your head, pulling the trigger.
No, those are all examples of *operations* that don't commute, which are common in classical physics and in everyday life. The most straightforward example is, perhaps, rotations about different axes in three dimensions.
*Observables* that don't commute are a purely quantum phenomenon and are therefore, although ubiquitous, very hard to demonstrate unambiguously outside a laboratory.
I guess the examples closest to everyday experience are the components of the polarisation vector of a photon in two different directions. The fact that they do not commute is manifested in the experiment where one inserts a third polariser between two polarisers crossed at right angles. Inserting the third one allows some photons to pass through. This illustrates (but does not, by itself, unambiguously demonstrate) that two different components of the polarisation vector cannot be sharp simultaneously.
David Deutsch