Friday, March 19, 2021

The Folly of Brain Copying: Conscious Identity vs. Physical Identity

The notion of “identity” is a recurring problem both in physics and in the nature of consciousness.  Philosophers love to discuss consciousness with brain-in-a-vat type thought experiments involving brain copying.  The typical argument goes something like this:

i)          The brain creates consciousness.

ii)         It is physically possible to copy the brain and thereby create two people having the same conscious states.

iii)        Two people having the same conscious states each identifies as the “actual” one, but at least one is incorrect.

iv)        Therefore, conscious identity (aka personal identity) is an illusion.

I spent a long time in Section II of this paper explaining why questioning the existence of conscious identity is futile and why the above logic is either invalid or inapplicable.  Yes, we have a persistent (or “transtemporal”) conscious identity; doubting that notion would unravel the very nature of scientific inquiry.  Of course, you might ask why anyone would actually doubt if conscious identity exists.  Suffice it to say that this wacky viewpoint tends to be held by those who subscribe to the equally wacky Many Worlds Interpretation (“MWI”) of quantum mechanics, which is logically inconsistent with a transtemporal conscious identity.

I showed in Section III of the above paper why special relativity prevents the existence of more than one instantiation of a physical state creating a particular conscious state.  In other words, at least one of assumptions i) and ii) above is false.  For whatever reason, the universe prohibits the duplication or repeating of consciousness-producing physical states.  In Section IV(A) of the same paper, I suggested some possible explanatory hypotheses for the mechanism(s) by which such duplications may be physically prevented, such as quantum no-cloning. 

Nevertheless, the philosopher’s argument seems irresistible... after all, why can’t we make a “perfect” copy of a brain?  If multiple instances of the same conscious state are physically impossible then what is the physical explanation for why two consciousness-producing physical states cannot be identical?  I finally realized that conscious identity implies physical identity.  In other words, if conscious identity is preserved over time, then physical identity must also be preserved over time, and this may help explain why the philosopher’s brain-copying scheme is a nonstarter.

I’d been struggling for some time with the notion of physical identity, such as in this blog post and this preprint.  The problem can be presented a couple ways:

·         According to the Standard Model of physics, the universe seems to be made up of only a handful of fundamental particles, and each of these particles is “identical” to another.  For example, any two electrons are identical, as are any two protons, or any two muons, etc.  The word “identical” is a derivative of “identity,” so it’s easy to confuse two “identical” electrons as being indistinguishable and thus having the same (or indistinct) identities.  So if all matter is made up of atoms comprising electrons, protons, and neutrons, then how can any particular clump of atoms have a different identity than another clump made of the same type of atoms?

·         Let’s assume that consciousness is created by physical matter and that physical matter is nothing but a collection of otherwise identical electrons, protons, and neutrons.  In the above paper I showed that if conscious identity exists, then conscious states cannot be copied or repeated.  And that means there is something fundamentally un-copiable about the physical state that creates a particular conscious state, which would seem odd if all matter is fundamentally identical. 

·         Consciousness includes transtemporal identity.  Assuming physicalism is true, then conscious states are created by underlying physical states, which means those physical states must have identity.  But physics tells us that physical matter comprises otherwise identical particles.

I finally realized that this problem can be solved if particles, atoms, etc., can themselves have identity.  (I do not mean conscious identity... simply that it makes sense to discuss Electron “Alice” and Electron “Bob” and keep track of them separately... that they are physically distinguishable.)  An object’s identity can be determined by several factors (e.g., position, entanglements and history of interactions, etc.) and therefore can be distinguished from another object that happens to comprise the same kind of particles.  Two physically “identical” objects can still maintain separate “identities” to the extent that they are distinguishable.  And we can distinguish (or separately identify) two objects, no matter how physically similar they may otherwise be, by their respective histories and entanglements and how those histories and entanglements affect their future states. 

Where does physical identity come from?  It is a necessary consequence of the laws of physics.  For instance, imagine we have an electron source in the center of a sphere, where the sphere’s entire surface is a detector (assume 100% efficiency) that is separated into hemispheres A and B.  The detector is designed so that if an electron is detected in hemisphere A, an alarm immediately sounds, but if it is detected in hemisphere B, a delayed alarm sounds one minute later.  The source then emits an electron, but we do not immediately hear the alarm.  What do we now know?  We know that an electron has been detected in hemisphere B and that we will hear an alarm in one minute.  Because we know this for certain, we conclude that the detected electron is the same as the emitted electron.  It has the same identity.  The following logical statement is true:

(electron emitted) ∩ (no detection in hemisphere A) à (detection in hemisphere B)

But more importantly, the fact that the above statement is true itself implies that the electron has identity.  In other words:

[(electron emitted) ∩ (no detection in hemisphere A) à (detection in hemisphere B)]

à (the electron emitted is the electron detected in hemisphere B)

(On retrospect, I feel like this is obvious.  Of course physical identity is inherent in the laws of physics.  How could Newton measure the acceleration of a falling apple if it’s not the same apple at different moments in time?)

So if electrons can have identity, then in what sense are they identical?  Can they lose their identity?  Yes.  Imagine Electron Alice and Electron Bob, each newly created by an electron source and having different positions (i.e., their distinct wave packets providing their separate identities).  The fact that they are distinguishable maintains their identity.  For example, if we measure an electron where Electron Bob cannot be found, then we know it was Electron Alice.  However, electrons, like all matter, disperse via quantum uncertainty.  So what happens if their wave functions overlap so that an electron detection can no longer distinguish them?  That’s when Bob and Alice lose their identity.  That’s when there is no fact about which electron is which.  (As a side note, Electron Bob could not have a conscious identity given that when he becomes indistinguishable with Electron Alice, even he cannot distinguish Bob from Alice.  This suggests that conscious identity cannot even arise until physical identity is transtemporally secured.)

This realization clarified my understanding of conscious identity.  My body clearly has an identity right now in at least the same sense that Electron Bob does.  What would it take to lose that physical identity?  Well, it wouldn’t be enough to make an atom-by-atom copy of the atoms in my body (call it “Andrew-copy”), because Andrew-copy would still be distinguishable from me by nature, for example, of its different location.  Rather, the wave functions of every single particle making up my body and the body of Andrew-copy would have to overlap so that we are actually indistinguishable.  But, as I showed in this paper, that kind of thing simply can’t happen with macroscopic objects in the physical universe because of the combination of slow quantum dispersion with fast decoherence.

What would it take for me to lose my conscious identity (or copy it, or get it confused with another identity, etc.)?  Given that and conscious states cannot be physically copied or repeated, if conscious identity depends only the particular arrangement of otherwise identical particles that make up matter, then we need a physical explanation for what prevents the copying of that particular arrangement.  But if conscious identity depends on not just the arrangement of those (otherwise identical) particles but also on their physical distinguishability, then the problem is solved.  Here’s why.  Two macroscopic objects, like bowling balls, will always be physically distinguishable in this universe.  Bowling Ball A will always be identifiably distinct from Bowling Ball B, whether or not any particular person can distinguish them.  So if my conscious identity depends at least in part on the physical distinguishability of the particles/atoms/objects that create my consciousness, then that fact alone would explain why conscious states (and their corresponding transtemporal identity) cannot be copied.

Let me put this another way.  Identity is about distinguishability.  It is possible for two electrons to be physically indistinguishable, such as when the wave states of two previously distinguishable electrons overlap.  However, it is not possible, in the actual universe, for a cat (or any macroscopic object) and another clump of matter to be physically indistinguishable because it is not possible for the wave states of these two macroscopic objects to overlap, no matter how physically similar they may otherwise be.  A cat’s physical identity cannot be lost by trying to make a physical copy of it.  It is not enough to somehow assemble a set of ≈10^23 atoms that are physically identical to, and in a physically identical arrangement as, the ≈10^23 atoms comprising the cat.  Each of those constituent atoms also has a history of interactions and entanglements that narrowly localize their wave functions to such an extent that overlap of those wave functions between corresponding atoms of the original cat and the copy cat is physically impossible.  (See note below on the Myth of the Gaussian.)

Imagine that someone has claimed to have made a “perfect copy” of me in order to prove that conscious identity is just an illusion.  He claims that Andrew-copy is indistinguishable from me, that no one else can tell the difference, that the copy looks and acts just like me.  Of course, I will know that he’s wrong: even if no one else can distinguish the copy from me, I can.  And that alone is enough to establish that Andrew-copy is not a perfect copy.  But now I understand that my conscious identity implies physical identity – that my ability to distinguish Andrew-copy from me also implies physical distinguishability.  There is no such thing as a perfect physical copy of me.  Even if the atoms in Andrew-copy are in some sense the same and in the same configuration as those in my body, and even if some arbitrary person cannot distinguish me from Andrew-copy, the universe can.  The atoms in Andrew-copy have a history and entanglements that are distinguishable from the atoms in my body, the net result being that the two bodies are physically distinguishable; their separate physical identities are embedded as facts in the history of the universe.

So if the universe can distinguish me from Andrew-copy, then why should it be surprising that I can distinguish myself from Andrew-copy and that I have an enduring conscious identity?  The question is not whether some evil genius can make a physical copy of my body that is indistinguishable to others.  The question is whether he can make a copy that is indistinguishable to me or the universe.  And the answer is that he can’t because making that copy violates special relativity. 

 

Note on the Myth of the Gaussian:

Physicists often approximate wave functions in the position basis as Gaussian distributions, in large part because Gaussians have useful mathematical properties, notably that the Fourier transform of a Gaussian is another Gaussian.  Because the standard deviation of a Gaussian is inversely related to the standard deviation of its Fourier transform, it clearly demonstrates the quantum uncertainty principle whereby the commutator of two noncommuting operators is nonzero.  An important feature of a Gaussian is that it is never zero for arbitrarily large distances from the mean.  This treatment of wave functions often misleads students into believing that wave functions are or must be Gaussian and that: a) an object can be found anywhere; and b) the wave states of any two arbitrary identical objects always overlap.  Neither is true. 

Regarding a), physics students are often given the problem of calculating the probability that his/her body will quantum mechanically tunnel through a wall, or even tunnel to Mars; the calculation (which is based on the simple notion of a particle of mass M tunneling through a potential barrier V) always yields an extremely tiny but nonzero probability.  But that’s wrong.  Setting aside the problem with special relativity – i.e., if I am on Earth now, I can’t be measured a moment later on Mars without exceeding the speed of light – the main problem is physical distinguishability.  The future possibilities for my body (and its physical constituents) are limited by their histories and entanglements. 

While some electron may, due to quantum dispersion or being trapped in a potential well, develop a relatively wide quantum wave packet over time whose width “leaks” to the other side of the wall/potential barrier, this requires that the electron remain unmeasured (i.e., with no new correlations) during that time period.  But the particles and atoms in a human body are constantly “measuring each other” through decoherence so that their individual wave packets remain extremely tightly localized.  In other words, my body doesn’t get quantum mechanically “fuzzy” or “blurry” over time.  Thus none of the wave packets of the objects comprising my body get big enough to leak through (or even to) the wall.  More to the point, the QM “blurriness” of my body is significantly less than anything that can be seen... I haven’t done the calculation, but the maximum width of any wave packet (not the FWHM of a Gaussian, which extends to infinity, but the actual maximum extent) is much, much, much smaller than the wavelength of light. 

As I showed above, physical distinguishability is an inherent feature of the physical world.  An object that appeared on the other side of the wall that happened to look like my body would be physically distinguishable from my body and cannot be the same.  That is, there is no sense in which the body that I identify as mine could quantum mechanically tunnel to Mars or through a wall – that is, there is ZERO probability of me tunneling to Mars or through a wall.  If I have just been measured in location A (which is constantly happening thanks to constant decohering interactions among the universe and the objects comprising my body), then tunneling to location B requires an expansion of the wave packets of those objects to include location B – i.e., my tunneling to B requires a location superposition in which B is a possibility.  But past facts, including the fact that I am on Earth (or this side of the wall) right now have eliminated all configurations in which my body is on Mars (or on the other side of the wall) a moment later.

No comments:

Post a Comment