Quantum suicide and immortality

Quantum suicide is a thought experiment in quantum mechanics and the philosophy of physics. Purportedly, it can falsify any interpretation of quantum mechanics other than the Everett many-worlds interpretation by means of a variation of the Schrödinger's cat thought experiment, from the cat's point of view. Quantum immortality refers to the subjective experience of surviving quantum suicide. This concept is sometimes conjectured to be applicable to real-world causes of death as well.[1][2]

As a thought experiment, quantum suicide is an intellectual exercise in which an abstract setup is followed through to its logical consequences merely to prove a theoretical point. Virtually all physicists and philosophers of science who have described it, especially in popularized treatments,[3] underscore that it relies on contrived, idealized circumstances that may be impossible or exceedingly difficult to realize in real life, and that its theoretical premises are controversial even among supporters of the many-worlds interpretation. Thus, as cosmologist Anthony Aguirre warns, "[...] it would be foolish (and selfish) in the extreme to let this possibility guide one's actions in any life-and-death question."[4]

History

Hugh Everett did not mention quantum suicide or quantum immortality in writing; his work was intended as a solution to the paradoxes of quantum mechanics. Eugene Shikhovtsev's biography of Everett states that "Everett firmly believed that his many-worlds theory guaranteed him immortality: his consciousness, he argued, is bound at each branching to follow whatever path does not lead to death".[5] Peter Byrne, author of a biography of Everett, reports that Everett also privately discussed quantum suicide (such as to play high-stakes Russian roulette and survive in the winning branch), but adds that "[i]t is unlikely, however, that Everett subscribed to this [quantum immortality] view, as the only sure thing it guarantees is that the majority of your copies will die, hardly a rational goal."[6]

Among scientists, the thought experiment was introduced by Euan Squires in 1986.[7] Afterwards, it was published independently by Hans Moravec in 1987[8] and Bruno Marchal in 1988;[9][10] it was also described by Huw Price in 1997, who credited it to Dieter Zeh,[11] and independently presented formally by Max Tegmark in 1998.[12] It was later discussed by philosophers Peter J. Lewis in 2000[2] and David Lewis in 2001.[13]

Thought experiment

The quantum suicide thought experiment involves a similar apparatus to Schrödinger's cat – a box which kills the occupant in a given time frame with probability one-half due to quantum uncertainty.[note 1] The only difference is to have the experimenter recording observations be the one inside the box. The significance of this is that someone whose life or death depends on a qubit could possibly distinguish between interpretations of quantum mechanics. By definition, fixed observers cannot.[12]

At the start of the first iteration, under both interpretations, the probability of surviving the experiment is 50%, as given by the squared norm of the wave function. At the start of the second iteration, assuming a single-world interpretation of quantum mechanics (like the widely-held Copenhagen interpretation) is true, the wave function has already collapsed; thus, if the experimenter is already dead, there is a 0% chance of survival for any further iterations. However, if the many-worlds interpretation is true, a superposition of the live experimenter necessarily exists (as also does the one who dies). Now, barring the possibility of life after death, after every iteration only one of the two experimenter superpositions – the live one – is capable of having any sort of conscious experience. Putting aside the philosophical problems associated with individual identity and its persistence, under the many-worlds interpretation, the experimenter, or at least a version of them, continues to exist through all of their superpositions where the outcome of the experiment is that they live. In other words, a version of the experimenter survives all iterations of the experiment. Since the superpositions where a version of the experimenter lives occur by quantum necessity (under the many-worlds interpretation), it follows that their survival, after any realizable number of iterations, is physically necessary; hence, the notion of quantum immortality.[12]

A version of the experimenter surviving stands in stark contrast to the implications of the Copenhagen interpretation, according to which, although the survival outcome is possible in every iteration, its probability tends towards zero as the number of iterations increases. According to the many-worlds interpretation, the above scenario has the opposite property: the probability of a version of the experimenter living is necessarily one for any number of iterations.[12]

In the book Our Mathematical Universe, Max Tegmark lays out three criteria that, in abstract, a quantum suicide experiment must fulfill:

  • The random number generator must be quantum, not deterministic, so that the experimenter enters a state of superposition of being dead and alive.
  • The experimenter must be rendered dead (or at least unconscious) on a time scale shorter than that on which they can become aware of the outcome of the quantum measurement.[note 2]
  • The experiment must be virtually certain to kill the experimenter, and not merely injure them.[14]

Analysis of real-world feasibility

In response to questions about "subjective immortality" from normal causes of death, Tegmark suggested that the flaw in that reasoning is that dying is not a binary event as in the thought experiment; it is a progressive process, with a continuum of states of decreasing consciousness. He states that in most real causes of death, one experiences such a gradual loss of self-awareness. It is only within the confines of an abstract scenario that an observer finds they defy all odds.[1] Referring to the above criteria, he elaborates as follows: "[m]ost accidents and common causes of death clearly don't satisfy all three criteria, suggesting you won't feel immortal after all. In particular, regarding criterion 2, under normal circumstances dying isn't a binary thing where you're either alive or dead [...] What makes the quantum suicide work is that it forces an abrupt transition."[14]

David Lewis' commentary and subsequent criticism

The philosopher David Lewis explored the possibility of quantum immortality in a 2001 lecture titled "How Many Lives Has Schrödinger's Cat?", his first – and last, due to his death less than four months afterwards – academic foray into the field of the interpretation of quantum mechanics. In the lecture, published posthumously in 2004, Lewis rejected the many-worlds interpretation, allowing that it offers initial theoretical attractions, but also arguing that it suffers from irremediable flaws, mainly regarding probabilities, and came to tentatively endorse the Ghirardi–Rimini–Weber theory instead. Lewis concluded the lecture by stating that the quantum suicide thought experiment, if applied to real-world causes of death, would entail what he deemed a "terrifying corollary": as all causes of death are ultimately quantum-mechanical in nature, if the many-worlds interpretation were true, in Lewis' view an observer should subjectively "expect with certainty to go on forever surviving whatever dangers [he or she] may encounter", as there will always be possibilities of survival, no matter how unlikely; faced with branching events of survival and death, an observer should not "equally expect to experience life and death", as there is no such thing as experiencing death, and should thus divide his or her expectations only among branches where he or she survives. If survival is guaranteed, however, this is not the case for good health or integrity. This would lead to a cumulative deterioration that indefinitively stops just short of death.[2][15]

Interviewed for the 2004 book Schrödinger's Rabbits, Tegmark rejected this scenario for the reason that "the fading of consciousness is a continuous process. Although I cannot experience a world line in which I am altogether absent, I can enter one in which my speed of thought is diminishing, my memories and other faculties fading [...] [Tegmark] is confident that even if he cannot die all at once, he can gently fade away." In the same book, philosopher of science and many-worlds proponent David Wallace[16] undermines the case for real-world quantum immortality on the basis that death can be understood as a continuum of decreasing states of consciousness not only in time, as argued by Tegmark, but also in space: "our consciousness is not located at one unique point in the brain, but is presumably a kind of emergent or holistic property of a sufficiently large group of neurons [...] our consciousness might not be able to go out like a light, but it can dwindle exponentially until it is, for all practical purposes, gone."[17]

Directly responding to Lewis' lecture, British philosopher and many-worlds proponent David Papineau, while finding Lewis' other objections to the many-worlds interpretation lacking, strongly denies that any modification to the usual probability rules is warranted in death situations. Assured subjective survival can follow from the quantum suicide idea only if an agent reasons in terms of "what will be experienced next" instead of the more obvious "what will happen next, whether will be experienced or not". He writes: "[...] it is by no means obvious why Everettians should modify their intensity rule[note 3] in this way. For it seems perfectly open for them to apply the unmodified intensity rule in life-or-death situations, just as elsewhere. If they do this, then they can expect all futures in proportion to their intensities, whether or not those futures contain any of their live successors. For example, even when you know you are about to be the subject in a fifty-fifty Schrödinger’s experiment, you should expect a future branch where you perish, to just the same degree as you expect a future branch where you survive."[15]

On a similar note, quoting Lewis' position that death should not be expected as an experience, philosopher of science Charles Sebens concedes that, in a quantum suicide experiment, "[i]t is tempting to think you should expect survival with certainty." However, he remarks that expectation of survival could follow only if the quantum branching and death were absolutely simultaneous, otherwise normal chances of death apply: "[i]f death is indeed immediate on all branches but one, the thought has some plausibility. But if there is any delay it should be rejected. In such a case, there is a short period of time when there are multiple copies of you, each (effectively) causally isolated from the others and able to assign a credence to being the one who will live. Only one will survive. Surely rationality does not compel you to be maximally optimistic in such a scenario." Sebens also explores the possibility that death might not be simultaneous to branching, but still faster than a human can mentally realize the outcome of the experiment. Again, an agent should expect to die with normal probabilities: "[d]o the copies need to last long enough to have thoughts to cause trouble?[note 4] I think not. If you survive, you can consider what credences you should have assigned during the short period after splitting when you coexisted with the other copies."[18]

Writing in the journal Ratio, philosopher István Aranyosi, while noting that "[the] tension between the idea of states being both actual and probable is taken as the chief weakness of the many-worlds interpretation of quantum mechanics," summarizes that most of the critical commentary of Lewis' immortality argument has revolved around its premises. But even if, for the sake of argument, one were willing to entirely accept Lewis' assumptions, Aranyosi strongly denies that the "terrifying corollary" would be the correct implication of said premises. Instead, the two scenarios that would most likely follow would be what Aranyosi describes as the "comforting corollary", in which an observer should never expect to get very sick in the first place, or the "momentary life" picture, in which an observer should expect "eternal life, spent almost entirely in an unconscious state", punctuated by extremely brief, amnesiac moments of consciousness. Thus, Aranyosi concludes that while "[w]e can't assess whether one or the other [of the two alternative scenarios] gets the lion's share of the total intensity associated with branches compatible with self-awareness, [...] we can be sure that they together (i.e. their disjunction) do indeed get the lion's share, which is much reassuring."[19]

Analysis by other proponents of the many-worlds interpretation

Physicist David Deutsch, though a proponent of the many-worlds interpretation, states regarding quantum suicide that "that way of applying probabilities does not follow directly from quantum theory, as the usual one does. It requires an additional assumption, namely that when making decisions one should ignore the histories in which the decision-maker is absent....[M]y guess is that the assumption is false."[20]

Tegmark now believes experimenters should only expect a normal probability of survival, not immortality. The experimenter's probability amplitude in the wavefunction decreases significantly, meaning they exist with a much lower measure than they had before. Per the anthropic principle, a person is less likely to find themselves in a world where they are less likely to exist, that is, a world with a lower measure has a lower probability of being observed by them. Therefore, the experimenter will have a lower probability of observing the world in which they survive than the earlier world in which they set up the experiment.[14] This same problem of reduced measure was pointed out by Lev Vaidman in the Stanford Encyclopedia of Philosophy.[21] In the 2001 paper, "Probability and the many-worlds interpretation of quantum theory", Vaidman writes that an agent should not agree to undergo a quantum suicide experiment: "The large 'measures' of the worlds with dead successors is a good reason not to play." Vaidman argues that it is the instantaneity of death that may seem to imply subjective survival of the experimenter, but that normal probabilities nevertheless must apply even in this special case: "[i]ndeed, the instantaneity makes it difficult to establish the probability postulate, but after it has been justified in the wide range of other situations it is natural to apply the postulate for all cases."[22]

In his 2013 book The Emergent Multiverse, Wallace opines that the reasons for expecting subjective survival in the thought experiment "do not really withstand close inspection", although he concedes that it would be "probably fair to say [...] that precisely because death is philosophically complicated, my objections fall short of being a knock-down refutation". Besides re-stating that there appears to be no motive to reason in terms of expectations of experience instead of expectations of what will happen, he suggests that a decision-theoretic analysis shows that "an agent who prefers certain life to certain death is rationally compelled to prefer life in high-weight branches and death in low-weight branches to the opposite."[3]

Physicist Sean M. Carroll, another proponent of the many-worlds interpretation, states regarding quantum suicide that neither experiences nor rewards should be thought of as being shared between future versions of oneself, as they become distinct persons when the world splits. He further states that one cannot pick out some future versions of oneself as "really you" over others, and that quantum suicide still cuts off the existence of some of these future selves, which would be worth objecting to just as if there were a single world.[23]

Analysis by skeptics of the many-worlds interpretation

Cosmologist Anthony Aguirre, while personally skeptical of most accounts of the many-worlds interpretation, in his book Cosmological Koans writes that "[p]erhaps reality actually is this bizarre, and we really do subjectively 'survive' any form of death that is both instantaneous and binary." Aguirre notes, however, that most causes of death do not fulfill these two requirements: "If there are degrees of survival, things are quite different." If loss of consciousness was binary like in the thought experiment, the quantum suicide effect would prevent an observer from subjectively falling asleep or undergoing anesthesia, conditions in which mental activities are greatly diminished but not altogether abolished. Consequently, upon most causes of death, even outwardly sudden, if the quantum suicide effect holds true an observer is more likely to progressively slip into an attenuated state of consciousness, rather than remain fully awake by some very improbable means. Aguirre further states that quantum suicide as a whole might be characterized as a sort of reductio ad absurdum against the current understanding of both the many-worlds interpretation and theory of mind. He finally hypothesizes that a different understanding of the relationship between the mind and time should remove the bizarre implications of necessary subjective survival.[4]

Physicist and writer Philip Ball, a critic of the many-worlds interpretation, in his book Beyond Weird, describes the quantum suicide experiment as "cognitively unstable" and exemplificatory of the difficulties of the many-worlds theory with probabilities. While he acknowledges Lev Vaidman's argument that an experimenter should subjectively expect outcomes in proportion of the "measure of existence" of the worlds in which they happen, Ball ultimately rejects this explanation. "What this boils down to is the interpretation of probabilities in the MWI. If all outcomes occur with 100% probability, where does that leave the probabilistic character of quantum mechanics?" Furthermore, Ball explains that such arguments highlight what he recognizes as another major problem of the many-worlds interpretation, connected but independent from the issue of probability: the incompatibility with the notion of selfhood. Ball ascribes most attempts of justifying probabilities in the many-worlds interpretation to "saying that quantum probabilities are just what quantum mechanics look like when consciousness is restricted to only one world" but that "there is in fact no meaningful way to explain or justify such a restriction." Before performing a quantum measurement, an "Alice before" experimenter "can't use quantum mechanics to predict what will happen to her in a way that can be articulated – because there is no logical way to talk about 'her' at any moment except the conscious present (which, in a frantically splitting universe, doesn't exist). Because it is logically impossible to connect the perceptions of Alice Before to Alice After [the experiment], "Alice" has disappeared. [...] [The MWI] eliminates any coherent notion of what we can experience, or have experienced, or are experiencing right now."[24]

Philosopher of science Peter J. Lewis, a critic of the many-worlds interpretation, considers the whole thought experiment an example of the difficulty of accommodating probability within the many-worlds framework: "[s]tandard quantum mechanics yields probabilities for various future occurrences, and these probabilities can be fed into an appropriate decision theory. But if every physically possible consequence of the current state of affairs is certain to occur, on what basis should I decide what to do? For example, if I point a gun at my head and pull the trigger, it looks like Everett's theory entails that I am certain to survive—and that I am certain to die. This is at least worrying, and perhaps rationally disabling."[25] In his book Quantum Ontology, Lewis explains that for the subjective immortality argument to be drawn out of the many-worlds theory, one has to adopt an understanding of probability – the so-called "branch-counting" approach, in which an observer can meaningfully ask "which post-measurement branch will I end up on?" – that is ruled out by experimental, empirical evidence as it would yield probabilities that do not match with the well-confirmed Born rule. Lewis identifies instead in the Deutsch-Wallace decision-theoretic analysis the most promising (although still, to his judgement, incomplete) way of addressing probabilities in the many-worlds interpretation, in which it is not possible to count branches (and, similarly, the persons that "end up" on each branch). Lewis concludes that "[t]he immortality argument is perhaps best viewed as a dramatic demonstration of the fundamental conflict between branch-counting (or person-counting) intuitions about probability and the decision theoretic approach. The many-worlds theory, to the extent that it is viable, does not entail that you should expect to live forever."[26]

See also

Notes
  1. The simplest example of this is a weapon triggered by a two level system. Schrödinger described his as a radioactive decay detector while Moravec's was a device measuring the spin value of protons.
  2. This is not unanimously agreed upon. Sebens argues, as will be detailed infra, that death must be instantaneous, not merely faster than the brain can process the result of the experiment.
  3. By "intensity rule", Lewis and Papineau mean the Born rule, the rule used to apportion probabilities in quantum mechanical events.
  4. By "cause trouble," Sebens means spoiling the expectations of necessary subjective survival.

References
  1. Tegmark, Max (November 1998). "Quantum immortality". Retrieved 25 October 2010.
  2. Lewis, Peter J. (1 January 2000). "What is it like to be Schrödinger's cat?". Analysis. 60: 22–29. doi:10.1093/analys/60.1.22.
  3. Wallace, David (2012). The Emergent Multiverse: Quantum Theory According to the Everett Interpretation. Oxford University Press. pp. 369–372. ISBN 978-0-19-954696-1.
  4. Aguirre, Anthony (2019). "What survives". Cosmological Koans.
  5. See Eugene Shikhovtsev's Biography of Everett: Keith Lynch remembers 1979–1980
  6. Byrne, Peter (2010). The Many Worlds of Hugh Everett III: Multiple Universes, Mutual Assured Destruction, and the Meltdown of a Nuclear Family. Oxford University Press. p. 342. ISBN 978-0199659241.
  7. Squires, Euan (1986). The Mystery of the Quantum World. Hilger. pp. 72–73. ISBN 9780852745656.
  8. Moravec, Hans (1988). "The Doomsday Device". Mind Children: The Future of Robot and Human Intelligence. Harvard: Harvard University Press. p. 188. ISBN 978-0-674-57618-6.
  9. Marchal, Bruno (1988). "Informatique théorique et philosophie de l'esprit" [Theoretical Computer Science and Philosophy of Mind]. Acte du 3ème colloque international Cognition et Connaissance [Proceedings of the 3rd International Conference Cognition and Knowledge]. Toulouse: 193–227.
  10. Marchal, Bruno (1991). De Glas, M.; Gabbay, D. (eds.). "Mechanism and personal identity" (PDF). Proceedings of WOCFAI 91. Paris. Angkor: 335–345. Archived from the original (PDF) on 25 January 2020. Retrieved 13 May 2020.
  11. Price, Huw (1997). "The Puzzle of Contemporary Quantum Theory". Time's Arrow and Archimedes' Point: New Directions for the Physics of Time. OUP USA. pp. 221–222. ISBN 978-0195117981.
  12. Tegmark, Max (November 1998). "The Interpretation of Quantum Mechanics: Many Worlds or Many Words?". Fortschritte der Physik. 46 (6–8): 855–862. arXiv:quant-ph/9709032. Bibcode:1998ForPh..46..855T. doi:10.1002/(SICI)1521-3978(199811)46:6/8<855::AID-PROP855>3.0.CO;2-Q. ISSN 0015-8208. S2CID 212466.
  13. "How Many Lives Has Schrödinger's Cat?," Australasian Journal of Philosophy, Vol. 82, No. 1, pp. 3–22; March 2004
  14. Tegmark, Max (2014). "The Level III Multiverse/Is Time An Illusion?". Our Mathematical Universe. Vintage Books.
  15. "David Papineau, "David Lewis and Schroedinger's Cat", 2004".
  16. Wallace, David. "About me". Retrieved 24 May 2020.
  17. Bruce, Colin (2004). "The Terror of Many Worlds". Schrödinger's Rabbits: The Many Worlds of Quantum.
  18. Sebens, Charles (29 January 2015). "Killer Collapse Empirically Probing the Philosophically Unsatisfactory Region of GRW" (PDF). Synthese. 192 (8): 2599–2615. doi:10.1007/s11229-015-0680-x. S2CID 17259579. Archived (PDF) from the original on 22 September 2017.
  19. Aranyosi, Istvan (15 August 2012). "Should we fear quantum torment?" (PDF). Ratio. 25 (3): 249–259. doi:10.1111/j.1467-9329.2012.00540.x. hdl:11693/21341. Archived (PDF) from the original on 31 October 2012.
  20. Deutsch, David (2011). "The Beginning". The Beginning of Infinity. Penguin Group.
  21. Vaidman, Lev (2018). "Many-Worlds Interpretation of Quantum Mechanics". The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University.
  22. Vaidman, Lev (13 November 2001). "Probability and the Many-Worlds Interpretation of Quantum Theory". arXiv:quant-ph/0111072.
  23. Carroll, Sean (10 September 2019). Something Deeply Hidden: Quantum Worlds and the Emergence of Spacetime. Penguin. ISBN 978-1-5247-4302-4.
  24. Ball, Philip (2018). "There is no other 'quantum you'". Beyond Weird: Why Everything You Thought You Knew About Quantum Physics Is Different. Univ of Chicago Pr. ISBN 978-0226558387.
  25. Lewis, Peter J. (13 November 2001). "Uncertainty and probability for branching selves" (PDF). Archived (PDF) from the original on 8 November 2016.
  26. Lewis, Peter J. (2016). "Immortality". Quantum Ontology: A Guide to the Metaphysics of Quantum Mechanics. Oxford University Press. ISBN 978-0190469818.
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