In quantum mechanics , the measurement problem is the problem of definite outcomes: quantum systems have superpositions but quantum measurements only give one definite result.
90-449: RQM or rqm may refer to: Relational quantum mechanics , an interpretation of quantum mechanics Relativistic quantum mechanics , a theory in quantum mechanics Rekem, a former name of the archaeological city Petra Regimental quartermaster, a type of military quartermaster Topics referred to by the same term [REDACTED] This disambiguation page lists articles associated with
180-421: A physical interaction, a quantum interaction, and so a complete description of it can only be given by a further observer O ″ {\displaystyle O''} , who will have a similar "M-operator" guaranteeing coherency, and so on out. In other words, a situation such as that described above cannot violate any physical observation , as long as the physical content of quantum mechanics
270-474: A "collapse" is because O {\displaystyle O} has incomplete information on the system (specifically, O {\displaystyle O} does not know its own Hamiltonian, and the interaction Hamiltonian for the measurement). In our system above, O ′ {\displaystyle O'} may be interested in ascertaining whether or not the state of O {\displaystyle O} accurately reflects
360-406: A "decayed atom-dead cat". However, when the chamber is opened the cat is either alive or it is dead: there is no superposition observed. After the measurement the cat is definitively alive or dead. The cat scenario illustrates the measurement problem: how can an indefinite superposition yield a single definite outcome? It also illustrates other issues in quantum measurement, including when does
450-411: A clearly defined state relative to O ′ {\displaystyle O'} . However, because O {\displaystyle O} 's measurement of S {\displaystyle S} breaks its unitary evolution with respect to O {\displaystyle O} , O {\displaystyle O} will not be able to give a full description of
540-414: A full knowledge of the system, we might say, could give a complete and equivalent description of the state of affairs, but that obtaining this knowledge is impossible in practice. But whom? What makes O {\displaystyle O} 's description better than that of O ′ {\displaystyle O'} , or vice versa? Alternatively, we could claim that quantum mechanics
630-405: A general question: How can one establish a correspondence between quantum reality and classical reality? A thought experiment called Schrödinger's cat illustrates the measurement problem. A mechanism is arranged to kill a cat if a quantum event, such as the decay of a radioactive atom, occurs. The mechanism and the cat are enclosed in a chamber so the fate of the cat is unknown until the chamber
720-455: A human observer. The proponents of the relational interpretation argue that this approach resolves some of the traditional interpretational difficulties with quantum mechanics. By giving up our preconception of a global privileged state, issues around the measurement problem and local realism are resolved. In 2020, Carlo Rovelli published an account of the main ideas of the relational interpretation in his popular book Helgoland , which
810-459: A measurement occur? Was it when the cat was observed? How is a measurement apparatus defined? The mechanism for detecting radioactive decay? The cat? The chamber? What is the role of the observer ? The views often grouped together as the Copenhagen interpretation are the oldest and, collectively, probably still the most widely held attitude about quantum mechanics. N. David Mermin coined
900-494: A network of relations could be built up based on the properties of a set of systems, which determines which systems have properties relative to which others, and when (since properties are no longer well defined relative to a specific observer after unitary evolution breaks down for that observer). On the assumption that all interactions are local (which is backed up by the analysis of the EPR paradox presented below), one could say that
990-644: A peaceful co-existence between quantum mechanics and special relativity, but a formal indication of a completely local character to reality. This problem was initially discussed in detail in Everett's thesis, The Theory of the Universal Wavefunction . Consider observer O {\displaystyle O} , measuring the state of the quantum system S {\displaystyle S} . We assume that O {\displaystyle O} has complete information on
SECTION 10
#17327903197191080-472: A similarly incorrect assumption frustrates attempts to make sense of the quantum formalism . The assumption rejected by relational quantum mechanics is the existence of an observer-independent state of a system. The idea has been expanded upon by Lee Smolin and Louis Crane , who have both applied the concept to quantum cosmology , and the interpretation has been applied to the EPR paradox , revealing not only
1170-473: A system S {\displaystyle S} which may take one of two states, which we shall designate | ↑ ⟩ {\displaystyle |{\uparrow }\rangle } and | ↓ ⟩ {\displaystyle |\downarrow \rangle } , ket vectors in the Hilbert space H S {\displaystyle H_{S}} . Now,
1260-449: A way as to exclude (as physically impossible) all value assignments which result in inconsistent probabilities being attributed to observed states of the system. This is done by means of ascribing values to "frameworks", and all values are hence framework-dependent. RQM accords perfectly well with this view. However, the consistent histories approach does not give a full description of the physical meaning of framework-dependent value (that
1350-403: Is a 0 probability of O {\displaystyle O} reflecting the state of S {\displaystyle S} as being | ↑ ⟩ {\displaystyle |{\uparrow }\rangle } if it is in fact | ↓ ⟩ {\displaystyle |{\downarrow }\rangle } , and so forth. The implication of this
1440-474: Is always relative to some observer. There is no privileged, "real" account. The state vector of conventional quantum mechanics becomes a description of the correlation of some degrees of freedom in the observer, with respect to the observed system. The terms "observer" and "observed" apply to any arbitrary system, microscopic or macroscopic . The classical limit is a consequence of aggregate systems of very highly correlated subsystems. A "measurement event"
1530-432: Is an interpretation of quantum mechanics which treats the state of a quantum system as being relational, that is, the state is the relation between the observer and the system. This interpretation was first delineated by Carlo Rovelli in a 1994 preprint , and has since been expanded upon by a number of theorists. It is inspired by the key idea behind special relativity , that the details of an observation depend on
1620-401: Is complete, then so is this description. But, for O ′ {\displaystyle O'} , S {\displaystyle S} is not uniquely determinate, but is rather entangled with the state of O {\displaystyle O} – note that his description of the situation at t 2 {\displaystyle t_{2}}
1710-504: Is describing what that "something" is, how a superposition of many possible values becomes a single measured value. To express matters differently (paraphrasing Steven Weinberg ), the Schrödinger equation determines the wave function at any later time. If observers and their measuring apparatus are themselves described by a deterministic wave function, why can we not predict precise results for measurements, but only probabilities? As
1800-466: Is fundamentally a physical interaction between the system being measured and some form of measuring apparatus. By extension, any physical interaction may be seen to be a form of quantum measurement, as all systems are seen as quantum systems in RQM. A physical interaction is seen by other observers unaware of the result, as establishing a correlation between the system and the observer, and this correlation
1890-520: Is given by log 2 k bits, where k is the number of possible values which this correlation may take – the number of "options" there are, as described by the other observer. Note that if the other observer is aware of the measurement result, there is only one possible value for the correlation, so they will not regard the (first observer's) measurement as producing any information, as expected. All physical interactions are, at bottom, quantum interactions, and must ultimately be governed by
SECTION 20
#17327903197191980-411: Is it does not account for how there can be "facts" if the value of any property depends on the framework chosen). By incorporating the relational view into this approach, the problem is solved: RQM provides the means by which the observer-independent, framework-dependent probabilities of various histories are reconciled with observer-dependent descriptions of the world. RQM provides an unusual solution to
2070-467: Is no "spooky action at a distance" yet . From the "coherence-operator" discussed above, Alice also knows that if at t 3 {\displaystyle t_{3}} she measures Bob's particle and then measures Bob (that is asks him what result he got) – or vice versa – the results will be consistent: Measurement problem The wave function in quantum mechanics evolves deterministically according to
2160-474: Is no actual collapse. A fourth approach is given by objective-collapse models . In such models, the Schrödinger equation is modified and obtains nonlinear terms. These nonlinear modifications are of stochastic nature and lead to behaviour that for microscopic quantum objects, e.g. electrons or atoms, is unmeasurably close to that given by the usual Schrödinger equation. For macroscopic objects, however,
2250-505: Is not factorisable no matter what basis chosen. But, if quantum mechanics is complete, then the description that O ′ {\displaystyle O'} gives is also complete. Thus the standard mathematical formulation of quantum mechanics allows different observers to give different accounts of the same sequence of events. There are many ways to overcome this perceived difficulty. It could be described as an epistemic limitation – observers with
2340-529: Is not a complete theory, and that by adding more structure we could arrive at a universal description (the troubled hidden variables approach). Yet another option is to give a preferred status to a particular observer or type of observer, and assign the epithet of correctness to their description alone. This has the disadvantage of being ad hoc , since there are no clearly defined or physically intuitive criteria by which this super-observer ("who can observe all possible sets of observations by all observers over
2430-451: Is not tied to a specific observer (and hence is "meaningless" in RQM), and because RQM maintains that there is no single, absolute description of the universe as a whole, but rather a net of interrelated partial descriptions. In the consistent histories approach to QM, instead of assigning probabilities to single values for a given system, the emphasis is given to sequences of values, in such
2520-414: Is opened. Prior to observation, according to quantum mechanics, the atom is in a quantum superposition , a linear combination of decayed and intact states. Also according to quantum mechanics, the atom-mechanism-cat composite system is described by superpositions of compound states. Therefore, the cat would be described as in a superposition, a linear combination of two states an "intact atom-alive cat" and
2610-522: Is represented as a correlation between O {\displaystyle O} and S {\displaystyle S} . O {\displaystyle O} itself cannot say anything with respect to its own "state", because its own "state" is defined only relative to another observer, O ′ {\displaystyle O'} . If the S + O {\displaystyle S+O} compound system does not interact with any other systems, then it will possess
2700-433: Is taken to refer only to relations. An interesting implication of RQM arises when we consider that interactions between material systems can only occur within the constraints prescribed by Special Relativity, namely within the intersections of the light cones of the systems: when they are spatiotemporally contiguous, in other words. Relativity tells us that objects have location only relative to other objects. By extension,
2790-453: Is that at time t 2 {\displaystyle t_{2}} , O ′ {\displaystyle O'} can predict with certainty that the S + O {\displaystyle S+O} system is in some eigenstate of M {\displaystyle M} , but cannot say which eigenstate it is in, unless O ′ {\displaystyle O'} itself interacts with
RQM - Misplaced Pages Continue
2880-414: Is that different observers may give different accurate accounts of the same system. For example, to one observer, a system is in a single, "collapsed" eigenstate . To a second observer, the same system is in a superposition of two or more states and the first observer is in a correlated superposition of two or more states. RQM argues that this is a complete picture of the world because the notion of "state"
2970-496: Is the Hilbert space inhabited by state vectors describing O {\displaystyle O} . If the initial state of O {\displaystyle O} is | init ⟩ {\displaystyle |{\text{init}}\rangle } , some degrees of freedom in O {\displaystyle O} become correlated with the state of S {\displaystyle S} after
3060-439: Is thus described as an ordinary physical interaction where two systems become correlated to some degree with respect to each other. Rovelli criticizes describing this as a form of "observer-dependence" which suggests reality depends upon the presence of a conscious observer, when his point is instead that reality is relational and thus the state of a system can be described even in relation to any physical object and not necessarily
3150-494: Is to be observer-dependent, then a description of a system would follow the form "system S is in state x with reference to observer O " or similar constructions, much like in relativity theory. In RQM it is meaningless to refer to the absolute, observer-independent state of any system. It is generally well established that any quantum mechanical measurement can be reduced to a set of yes–no questions or bits that are either 1 or 0. RQM makes use of this fact to formulate
3240-470: Is what is described and predicted by the quantum formalism. But, Rovelli points out, this form of correlation is precisely the same as the definition of information in Shannon's theory. Specifically, an observer O observing a system S will, after measurement, have some degrees of freedom correlated with those of S , as described by another observer unaware of the result. The amount of this correlation
3330-453: Is without interaction, and hence breaking the unitary evolution of the compound system (because he doesn't know his own Hamiltonian). The distinction between knowing "that" and knowing "what" is a common one in everyday life: everyone knows that the weather will be like something tomorrow, but no-one knows exactly what the weather will be like. But, let us imagine that O ′ {\displaystyle O'} measures
3420-451: Is zero. These electrons are fired off at time t 1 {\displaystyle t_{1}} towards two spacelike separated observers, Alice and Bob , who can perform spin measurements, which they do at time t 2 {\displaystyle t_{2}} . The fact that the two electrons are a singlet means that if Alice measures z-spin up on her electron, Bob will measure z-spin down on his, and vice versa :
3510-413: The S + O {\displaystyle S+O} system (since it can only speak of the correlation between S {\displaystyle S} and itself, not its own behaviour). A complete description of the ( S + O ) + O ′ {\displaystyle (S+O)+O'} system can only be given by a further, external observer, and so forth. Taking
3600-424: The S + O {\displaystyle S+O} system. An apparent paradox arises when one considers the comparison, between two observers, of the specific outcome of a measurement. In the problem of the observer observed section above, let us imagine that the two experiments want to compare results. It is obvious that if the observer O ′ {\displaystyle O'} has
3690-400: The EPR paradox . Indeed, it manages to dissolve the problem altogether, inasmuch as there is no superluminal transportation of information involved in a Bell test experiment : the principle of locality is preserved inviolate for all observers. In the EPR thought experiment, a radioactive source produces two electrons in a singlet state , meaning that the sum of the spin on the two electrons
RQM - Misplaced Pages Continue
3780-434: The Schrödinger equation as a linear superposition of different states. However, actual measurements always find the physical system in a definite state. Any future evolution of the wave function is based on the state the system was discovered to be in when the measurement was made, meaning that the measurement "did something" to the system that is not obviously a consequence of Schrödinger evolution . The measurement problem
3870-406: The linearity of Schrödinger evolution to break down. RQM could recover a Copenhagen-like view of the world by assigning a privileged status (not dissimilar to a preferred frame in relativity) to the classical world. However, by doing this one would lose sight of the key features that RQM brings to our view of the quantum world. Bohm's interpretation of QM does not sit well with RQM. One of
3960-477: The other observer involved. As far as Alice is concerned, the specific results obtained on Bob's wing of the experiment are indeterminate for her, although she will know that Bob has a definite result. In order to find out what result Bob has, she has to interact with him at some time t 3 {\displaystyle t_{3}} in their future light cones, through ordinary classical information channels. The question then becomes one of whether
4050-421: The reference frame of the observer, and uses some ideas from Wheeler on quantum information . The physical content of the theory has not to do with objects themselves, but the relations between them. As Rovelli puts it: "Quantum mechanics is a theory about the physical description of physical systems relative to other systems, and this is a complete description of the world". The essential idea behind RQM
4140-434: The "state" of the entire universe. This is because this state would have to be ascribed to a correlation between the universe and some other physical observer, but this observer in turn would have to form part of the universe. As was discussed above, it is not possible for an object to contain a complete specification of itself. Following the idea of relational networks above, an RQM-oriented cosmology would have to account for
4230-516: The Everettian program have not yet reached a consensus regarding the correct way to justify the use of the Born rule to calculate probabilities. The de Broglie–Bohm theory tries to solve the measurement problem very differently: the information describing the system contains not only the wave function, but also supplementary data (a trajectory) giving the position of the particle(s). The role of
4320-522: The GRW theory makes different predictions from orthodox quantum mechanics in some conditions, it is not an interpretation of quantum mechanics in a strict sense. Erich Joos and Heinz-Dieter Zeh claim that the phenomenon of quantum decoherence , which was put on firm ground in the 1980s, resolves the problem. The idea is that the environment causes the classical appearance of macroscopic objects. Zeh further claims that decoherence makes it possible to identify
4410-432: The above scenario is directly linked to Wigner's Friend thought experiment , which serves as a prime example when understanding different interpretations of quantum theory . According to O {\displaystyle O} , at t 2 {\displaystyle t_{2}} , the system S {\displaystyle S} is in a determinate state, namely spin up. And, if quantum mechanics
4500-408: The act of measurement is simply an interaction between quantum entities, e.g. observer, measuring instrument, electron/positron etc., which entangle to form a single larger entity, for instance living cat/happy scientist . Everett also attempted to demonstrate how the probabilistic nature of quantum mechanics would appear in measurements, a work later extended by Bryce DeWitt . However, proponents of
4590-456: The correlation is perfect. If Alice measures z-axis spin, and Bob measures the orthogonal y-axis spin, however, the correlation will be zero. Intermediate angles give intermediate correlations in a way that, on careful analysis, proves inconsistent with the idea that each particle has a definite, independent probability of producing the observed measurements (the correlations violate Bell's inequality ). This subtle dependence of one measurement on
SECTION 50
#17327903197194680-422: The description of the measurement event by the other observer, O ′ {\displaystyle O'} , who describes the combined S + O {\displaystyle S+O} system, but does not interact with it, the following gives the description of the measurement event according to O ′ {\displaystyle O'} , from the linearity inherent in
4770-434: The entire universe" ) ought to be chosen. RQM, however, takes the point illustrated by this problem at face value. Instead of trying to modify quantum mechanics to make it fit with prior assumptions that we might have about the world, Rovelli says that we should modify our view of the world to conform to what amounts to our best physical theory of motion. Just as forsaking the notion of absolute simultaneity helped clear up
4860-525: The expected correlations in results will appear: will the two particles behave in accordance with the laws of quantum mechanics? Let us denote by M A ( α ) {\displaystyle M_{A}(\alpha )} the idea that the observer A {\displaystyle A} (Alice) measures the state of the system α {\displaystyle \alpha } (Alice's particle). So, at time t 2 {\displaystyle t_{2}} , Alice knows
4950-581: The explicit hypotheses in the construction of RQM is that quantum mechanics is a complete theory, that is it provides a full account of the world. Moreover, the Bohmian view seems to imply an underlying, "absolute" set of states of all systems, which is also ruled out as a consequence of RQM. We find a similar incompatibility between RQM and suggestions such as that of Penrose , which postulate that some process (in Penrose's case, gravitational effects) violate
5040-465: The full Hamiltonians of both S {\displaystyle S} and O {\displaystyle O} , he will be able to say with certainty that at time t 2 {\displaystyle t_{2}} , O {\displaystyle O} has a determinate result for S {\displaystyle S} 's spin, but he will not be able to say what O {\displaystyle O} 's result
5130-430: The fuzzy boundary between the quantum microworld and the world where the classical intuition is applicable. Quantum decoherence becomes an important part of some modern updates of the Copenhagen interpretation based on consistent histories . Quantum decoherence does not describe the actual collapse of the wave function, but it explains the conversion of the quantum probabilities (that exhibit interference effects) to
5220-450: The ideas of "state" and spatiotemporal contiguity are two sides of the same coin: spacetime location determines the possibility of interaction, but interactions determine spatiotemporal structure. The full extent of this relationship, however, has not yet fully been explored. The universe is the sum total of everything in existence with any possibility of direct or indirect interaction with a local observer. A (physical) observer outside of
5310-425: The linear evolution of the Schrödinger equation for the system. The many-worlds family of interpretations (MWI) shares an important feature with RQM, that is, the relational nature of all value assignments (that is, properties). Everett, however, maintains that the universal wavefunction gives a complete description of the entire universe, while Rovelli argues that this is problematic, both because this description
5400-517: The measurement, and this correlation can take one of two values: | O ↑ ⟩ {\displaystyle |O_{\uparrow }\rangle } or | O ↓ ⟩ {\displaystyle |O_{\downarrow }\rangle } where the direction of the arrows in the subscripts corresponds to the outcome of the measurement that O {\displaystyle O} has made on S {\displaystyle S} . If we now consider
5490-774: The model system discussed above, if O ′ {\displaystyle O'} has full information on the S + O {\displaystyle S+O} system, it will know the Hamiltonians of both S {\displaystyle S} and O {\displaystyle O} , including the interaction Hamiltonian . Thus, the system will evolve entirely unitarily (without any form of collapse) relative to O ′ {\displaystyle O'} , if O {\displaystyle O} measures S {\displaystyle S} . The only reason that O {\displaystyle O} will perceive
SECTION 60
#17327903197195580-427: The nonlinear modification becomes important and induces the collapse of the wave function. Objective-collapse models are effective theories . The stochastic modification is thought to stem from some external non-quantum field, but the nature of this field is unknown. One possible candidate is the gravitational interaction as in the models of Diósi and Penrose . The main difference of objective-collapse models compared to
5670-463: The observer O {\displaystyle O} wishes to make a measurement on the system. At time t 1 {\displaystyle t_{1}} , this observer may characterize the system as follows: where | α | 2 {\displaystyle |\alpha |^{2}} and | β | 2 {\displaystyle |\beta |^{2}} are probabilities of finding
5760-423: The ordinary classical probabilities. See, for example, Zurek, Zeh and Schlosshauer. The present situation is slowly clarifying, described in a 2006 article by Schlosshauer as follows: Several decoherence-unrelated proposals have been put forward in the past to elucidate the meaning of probabilities and arrive at the Born rule ... It is fair to say that no decisive conclusion appears to have been reached as to
5850-427: The other approaches is that they make falsifiable predictions that differ from standard quantum mechanics. Experiments are already getting close to the parameter regime where these predictions can be tested. The Ghirardi–Rimini–Weber (GRW) theory proposes that wave function collapse happens spontaneously as part of the dynamics. Particles have a non-zero probability of undergoing a "hit", or spontaneous collapse of
5940-469: The other holds even when measurements are made simultaneously and a great distance apart, which gives the appearance of a superluminal communication taking place between the two electrons. Put simply, how can Bob's electron "know" what Alice measured on hers, so that it can adjust its own behavior accordingly? In RQM, an interaction between a system and an observer is necessary for the system to have clearly defined properties relative to that observer. Since
6030-522: The other interpretations do not accord with the "relational world" put forward by RQM. RQM is, in essence, quite similar to the Copenhagen interpretation , but with an important difference. In the Copenhagen interpretation, the macroscopic world is assumed to be intrinsically classical in nature, and wave function collapse occurs when a quantum system interacts with macroscopic apparatus. In RQM, any interaction, be it micro or macroscopic, causes
6120-507: The phrase "Shut up and calculate!" to summarize Copenhagen-type views, a saying often misattributed to Richard Feynman and which Mermin later found insufficiently nuanced. Generally, views in the Copenhagen tradition posit something in the act of observation which results in the collapse of the wave function . This concept, though often attributed to Niels Bohr , was due to Werner Heisenberg , whose later writings obscured many disagreements he and Bohr had during their collaboration and that
6210-523: The problems associated with the interpretation of the Lorentz transformations , so many of the conundrums associated with quantum mechanics dissolve, provided that the state of a system is assumed to be observer-dependent – like simultaneity in Special Relativity . This insight follows logically from the two main hypotheses which inform this interpretation: Thus, if a state
6300-402: The quantum effects being studied and he notes that these processes are irreversible. He considered a consistent account of this issue to be an unsolved problem. Hugh Everett 's many-worlds interpretation attempts to solve the problem by suggesting that there is only one wave function, the superposition of the entire universe, and it never collapses—so there is no measurement problem. Instead,
6390-463: The quantum formalism, exemplified by the "M-operator" defined above, guarantees that there will be no contradictions between records. The interaction between O ′ {\displaystyle O'} and whatever he chooses to measure, be it the S + O {\displaystyle S+O} compound system or O {\displaystyle O} and S {\displaystyle S} individually, will be
6480-422: The quantum formalism: Thus, on the assumption (see hypothesis 2 below) that quantum mechanics is complete, the two observers O {\displaystyle O} and O ′ {\displaystyle O'} give different but equally correct accounts of the events t 1 → t 2 {\displaystyle t_{1}\rightarrow t_{2}} . Note that
6570-554: The same rules. Thus, an interaction between two particles does not, in RQM, differ fundamentally from an interaction between a particle and some "apparatus". There is no true wave collapse , in the sense in which it occurs in some interpretations. Because "state" is expressed in RQM as the correlation between two systems, there can be no meaning to "self-measurement". If observer O {\displaystyle O} measures system S {\displaystyle S} , S {\displaystyle S} 's "state"
6660-569: The sequence of events in this experiment, with observer O {\displaystyle O} doing the observing, as follows: This is the description of the measurement event given by observer O {\displaystyle O} . Now, any measurement is also a physical interaction between two or more systems. Accordingly, we can consider the tensor product Hilbert space H S ⊗ H O {\displaystyle H_{S}\otimes H_{O}} , where H O {\displaystyle H_{O}}
6750-438: The spin of S {\displaystyle S} , and finds it to have spin down (and note that nothing in the analysis above precludes this from happening). What happens if he talks to O {\displaystyle O} , and they compare the results of their experiments? O {\displaystyle O} , it will be remembered, measured a spin up on the particle. This would appear to be paradoxical:
6840-411: The state of S {\displaystyle S} . We can draw up for O ′ {\displaystyle O'} an operator , M {\displaystyle M} , which is specified as: with an eigenvalue of 1 meaning that O {\displaystyle O} indeed accurately reflects the state of S {\displaystyle S} . So there
6930-447: The state of a quantum system (relative to a given observer!) in terms of the physical notion of information developed by Claude Shannon . Any yes/no question can be described as a single bit of information. This should not be confused with the idea of a qubit from quantum information theory , because a qubit can be in a superposition of values, whilst the "questions" of RQM are ordinary binary variables . Any quantum measurement
7020-450: The success of these derivations. ... As it is well known, [many papers by Bohr insist upon] the fundamental role of classical concepts. The experimental evidence for superpositions of macroscopically distinct states on increasingly large length scales counters such a dictum. Superpositions appear to be novel and individually existing states, often without any classical counterparts. Only the physical interactions between systems then determine
7110-453: The system in the respective states, and these add up to 1. For our purposes here, we can assume that in a single experiment, the outcome is the eigenstate | ↑ ⟩ {\displaystyle |{\uparrow }\rangle } (but this can be substituted throughout, without loss of generality, by | ↓ ⟩ {\displaystyle |{\downarrow }\rangle } ). So, we may represent
7200-606: The system, and that O {\displaystyle O} can write down the wavefunction | ψ ⟩ {\displaystyle |\psi \rangle } describing it. At the same time, there is another observer O ′ {\displaystyle O'} , who is interested in the state of the entire O {\displaystyle O} - S {\displaystyle S} system, and O ′ {\displaystyle O'} likewise has complete information. To analyse this system formally, we consider
7290-492: The title RQM . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=RQM&oldid=1175613536 " Category : Disambiguation pages Hidden categories: Short description is different from Wikidata All article disambiguation pages All disambiguation pages Relational quantum mechanics Relational quantum mechanics ( RQM )
7380-412: The two measurement events take place at spacelike separation, they do not lie in the intersection of Alice's and Bob's light cones . Indeed, there is no observer who can instantaneously measure both electrons' spin. The key to the RQM analysis is to remember that the results obtained on each "wing" of the experiment only become determinate for a given observer once that observer has interacted with
7470-509: The two never resolved. In these schools of thought, wave functions may be regarded as statistical information about a quantum system, and wave function collapse is the updating of that information in response to new data. Exactly how to understand this process remains a topic of dispute. Bohr discussed his views in a 1947 letter to Pauli. Bohr points out that the measurement processes such as cloud chambers or photographic plates involve enormous amplification requiring energies far in excess of
7560-473: The two observers, surely, will realise that they have disparate results. However, this apparent paradox only arises as a result of the question being framed incorrectly: as long as we presuppose an "absolute" or "true" state of the world, this would, indeed, present an insurmountable obstacle for the relational interpretation. However, in a fully relational context, there is no way in which the problem can even be coherently expressed. The consistency inherent in
7650-401: The universe as a set of partial systems providing descriptions of one another. Such a construction was developed in particular by Francesca Vidotto . The only group of interpretations of quantum mechanics with which RQM is almost completely incompatible is that of hidden variables theories . RQM shares some deep similarities with other views, but differs from them all to the extent to which
7740-403: The universe would require physically breaking of gauge invariance , and a concomitant alteration in the mathematical structure of gauge-invariance theory. Similarly, RQM conceptually forbids the possibility of an external observer. Since the assignment of a quantum state requires at least two "objects" (system and observer), which must both be physical systems, there is no meaning in speaking of
7830-580: The value of M A ( α ) {\displaystyle M_{A}(\alpha )} : the spin of her particle, relative to herself. But, since the particles are in a singlet state, she knows that and so if she measures her particle's spin to be σ {\displaystyle \sigma } , she can predict that Bob's particle ( β {\displaystyle \beta } ) will have spin − σ {\displaystyle -\sigma } . All this follows from standard quantum mechanics, and there
7920-455: The wave function is to generate the velocity field for the particles. These velocities are such that the probability distribution for the particle remains consistent with the predictions of the orthodox quantum mechanics. According to the de Broglie–Bohm theory, interaction with the environment during a measurement procedure separates the wave packets in configuration space, which is where apparent wave function collapse comes from, even though there
8010-420: The wave function, on the order of once every hundred million years. Though collapse is extremely rare, the sheer number of particles in a measurement system means that the probability of a collapse occurring somewhere in the system is high. Since the entire measurement system is entangled (by quantum entanglement), the collapse of a single particle initiates the collapse of the entire measurement apparatus. Because
8100-565: Was published in an English translation in 2021 as Helgoland: Making Sense of the Quantum Revolution . Relational quantum mechanics arose from a comparison of the quandaries posed by the interpretations of quantum mechanics with those resulting from Lorentz transformations prior to the development of special relativity . Rovelli suggested that just as pre-relativistic interpretations of Lorentz's equations were complicated by incorrectly assuming an observer-independent time exists,
#718281