Quantum Mechanics is Really “Relational” And Not An “Objective Collapse Theory”
Different observers can describe the same system in fundamentally different ways, yet quantum mechanics ensures that predictions made from these different perspectives never yield contradictory results.
In my personal experience, I have encountered many people who mistakenly conflate quantum mechanics with an objective collapse theory. Often, it is specifically conflated with a theory where particles spread out as waves until the first observer “observes” them, causing them to “collapse” into particles. This “collapse” is described as an absolute event, meaning it happens for all possible observers: the first observer “collapses” it by observation, and the second merely reveals what was already there.
It is important to emphasize that not only is quantum mechanics not an objective collapse theory, but it is impossible for such a theory to exactly match the predictions of quantum mechanics. Some of these theories may approximate the predictions closely enough that any deviations are currently beyond our ability to measure, making them difficult to rule out. However, they still ultimately make different predictions and are distinct theories. The point is not that objective collapse theories are necessarily wrong, but that they are fundamentally different from quantum mechanics as it is currently formulated.
The reason is that in quantum mechanics, the reduction of the state vector (sometimes called the “collapse of the wave function,” though I personally find that term misleading) is perspective-dependent, similar to how velocity is relative in Galilean relativity. It is not an absolute event. To claim it is absolute would require introducing additional mathematics to define when and how such an event occurs.
For example, Ghirardi–Rimini–Weber theory ties collapse to spontaneous events with an increasing probability over time, while Diósi–Penrose theory links it to the strength of the gravitational field. In standard quantum mechanics, however, there is no absolute moment when the state vector collapses; it is entirely relative to the observer’s frame of reference.
This relativity is where Wigner’s friend paradox arises. If an electron is in a superposition of states and Wigner’s friend measures it, from the friend’s perspective, the state vector has collapsed. Yet, from Wigner’s perspective, it hasn’t because he has not yet measured it. Despite popular mysticism surrounding this “paradox,” it doesn’t reveal anything profound about consciousness — it merely shows that the reduction of the state vector is perspective-dependent. It is no more mysterious than the relativity of velocity in Galilean relativity, and it’s not a paradox in the true sense, as it presents no contradiction.
A common misconception is that the state vector’s reduction occurs as an absolute event when the first observer interacts with the system. For instance, I often hear that the solution to Wigner’s friend paradox is that reduction occurs absolutely when the friend measures the particle, and Wigner’s uncertainty is simply due to his ignorance of the result. Similar claims are made about Schrödinger’s cat, suggesting that a definite outcome exists before a human opens the box because the cat or the Geiger counter already caused the collapse.
This interpretation is incorrect. It represents an objective collapse theory, not quantum mechanics, and leads to different predictions. A system in a superposition of states can exhibit interference effects, while a system with a definite state cannot. This distinction is experimentally testable.
Consider a qubit placed in a superposition of states using a Hadamard gate. Measuring it will yield a 50% probability of finding it as either 0 or 1. However, this is not equivalent to having a definite value but being unknown in a 50%/50% probability distribution. The difference is that in the latter case, interference effects cannot occur, while in the former, they can.
Suppose you have many qubits initially set to 0. If half are placed in a superposition using a Hadamard gate, and the other half are randomly flipped by a pseudorandom number generator with a 50% chance, both groups will show a 50% distribution of 0s and 1s upon measurement. Yet, these groups can be distinguished experimentally. Applying another Hadamard gate to both groups results in different outcomes. The qubits flipped by the pseudorandom generator remain in a 50%/50% distribution, while the qubits initially placed in a superposition will return to their original 0 state due to interference, yielding a 100% probability of 0.
Thus, stating a qubit is in a superposition means more than its outcome being random; it implies that interference effects can occur, distinguishing it from classical randomness. In fact, interference is the hallmark of quantum mechanics. Entanglement, often viewed as mysterious, is merely statistical correlation between particles, and Bell inequality violations show interference across such correlated systems.
This distinction matters because claiming that a system is no longer in a superposition has measurable consequences. Take the double-slit experiment: if you measure which slit the particle goes through, you reduce the state vector, collapsing the particle’s position into a definite state. Without superposition, the particle cannot interfere with itself, so instead of an interference pattern, you observe a diffraction pattern.
This isn’t just an abstract philosophical point; it has real, testable consequences. Saying that the cat in Schrödinger’s box has a definite state before opening the box is equivalent to claiming the system cannot exhibit interference effects, which can in principle be experimentally verified (difficult in practice). Asserting that the “first observer” causes a global collapse requires a precise definition of what constitutes an observer. Is it a human, a cat, or a Geiger counter? Without this definition, the theory is vague and inconsistent. Moreover, drawing an arbitrary line between observers inherently introduces a threshold beyond which interference cannot occur — a threshold that doesn’t exist in quantum mechanics, making it a different theory altogether.
Misunderstandings about collapse often arise from the double-slit experiment. For example, suppose Alice measures which slit particles pass through while Bob does not. Alice reduces the state vector, so no interference pattern forms on her screen. Bob did not measure the which-way information and thus could not reduce the state vector. Yet, it would be silly for Bob, knowing Alice is measuring the which-way information, to predict that there must be an interference pattern on the screen. He would also predict that it should not show an interference pattern. People falsely conclude from this that Bob must assume Alice’s measurement of the which-way information causes an absolute reduction of the state vector — that, from Bob’s perspective, the particle has a definite value, and he is simply ignorant of it since Alice measured it and not himself.
This misconception stems from the mistaken belief that the only way particles can lose their ability to interfere with themselves is if the state vector is reduced, giving them a definite value. In reality, particles in quantum mechanics can also lose their ability to interfere with themselves under a second condition: when they become entangled with another system.
If a particle becomes entangled with another, meaning it forms a statistical correlation with another system, it is no longer valid in quantum mechanics to describe the particles individually with separate state vectors. Instead, they must be described collectively. To derive the probabilities for individual particles, you must perform a partial trace to “trace out” the systems you are not interested in, leaving a reduced density matrix for the subsystem you care about.
When you perform the partial trace, the reduced density matrix resembles a probabilistic density matrix that cannot exhibit interference effects — its coherence terms are reduced to zero. In other words, once two particles become entangled, interference effects only apply to the particles taken together, not separately. If the particles are considered individually, they cannot exhibit interference effects.
For example, consider two entangled particles that can exhibit interference effects when taken together. If one of those particles becomes entangled with a third particle, you will find that the original two particles now have a reduced density matrix with zero coherence terms. Only when all three particles are taken together can interference effects be observed.
This illustrates why scaling up interference effects is difficult. If a particle accidentally interacts with particles in the environment, interference effects can only be observed for the particle and the environmental particles together. The “environment” typically refers to particles outside the experiment that you cannot control. While it is theoretically possible to observe interference effects by isolating and measuring those environmental particles, in practice, this is impossible. The environmental particle will likely interact with others, spreading entanglement across countless particles, making it impossible to recover the interference effects. This process, known as decoherence, is one of the key challenges in building quantum computers, which must be extremely well-isolated to preserve observable interference effects.
A measuring device is designed to become correlated with what it measures. If an electron has an upward spin, you expect a measuring device to display an upward spin. The point of a measuring device is to establish a correlation between the display and the measured property. Without such a correlation, it would not function as a proper measuring device.
Since entanglement is merely statistical correlation between systems, a measuring device becomes entangled with the system it measures. This includes the observer’s sensory apparatus, such as their eyes. From Bob’s perspective, knowing Alice is measuring the particle but unaware of her result, he would describe Alice and the particle as entangled.
This is not strange or mystical; it simply means Alice and the particle are statistically correlated. Assuming Alice is mentally sound and her equipment functions correctly, the result she sees should correlate perfectly with the actual particle state. The detector’s display, Alice’s sensory perception, and her brain state should all be in agreement. If an electron has an upward spin, the detector should display it, and Alice should believe that outcome.
Thus, Bob would describe Alice as entangled with the particle, meaning interference effects apply only to Alice and the particle taken collectively, not separately. Since it is only the particle that passes through the slits, not Alice and the particle together, Bob would not expect to observe an interference pattern. This isn’t because Alice’s measurement caused an absolute reduction of the state vector but because the particle became entangled with another system. Both Alice and Bob agree that no interference pattern will be observed, but for different reasons.
In principle, Alice and the particle could still exhibit interference effects if isolated together, though practically this is impossible for something as complex as a human. However, one can imagine replacing Alice with simpler systems that can record the state of a particle — such as a Geiger counter, a cat, or even a single particle. The question then becomes: how simple can a system be before it no longer qualifies as a measuring device? Each of these, from complex to simple, can record the state of a system onto itself.
This highlights a problem with objective collapse models. They posit that reduction occurs absolutely for all observers under specific conditions. But what are those conditions? If every interaction down to a single particle counts as a measurement, absolute reduction would occur upon any particle interaction, meaning interference effects could never occur — clearly inconsistent with observations. If reduction only occurs for complex systems, such as mechanical devices like Geiger counters, interference should not be observable beyond that threshold. If it only occurs for conscious observers, one would conclude that systems can still exhibit interference effects until observed by a mammal with a brain.
David Deutsch pointed this out in his paper “Quantum Theory as a Universal Physical Theory”, noting that if absolute reduction occurs upon the first observation, interference effects cannot scale beyond interaction with a “sense organ.” This could be tested experimentally.
In quantum mechanics, all operations are unitary, meaning they are, in principle, reversible until the state vector is reduced, which is a non-reversible process. Imagine a simple mammal’s sensory organ is well-documented at the quantum level. One could design an opposite analogue to reverse its interaction with the particle. If the state vector is only reduced relative to a specific perspective, measuring the outcome after reversing the interaction should yield the initial state. This is because the experimenter, akin to Wigner’s friend, would describe the mammal’s sensory organ interacting with the particle as still being in a superposition from their perspective.
If the state vector is reduced in an absolute sense when interacting with a sense organ, we would expect a different outcome. The interaction with the sense organ would cause the particle to no longer be in a superposition of states, and any attempt to reverse the interaction would fail, producing different results.
Hence, any claim that “observers” or “measuring devices” play a special role leading to an absolute reduction of the state vector would, in principle, result in different predictions than quantum mechanics. The point at which these predictions deviate would depend on how “observer” or “measuring device” is defined.—Deutsch, instead, tries to argue that the state vector is never reduced at all, but in my opinion, this approach introduces more confusion than clarity. It’s simpler to state that the reduction of the state vector is relative, not absolute, rather than asserting it should never be reduced.
For such an objective collapse model to be coherent, you would need a rigorous mathematical description of when this absolute reduction occurs, as the specific definition influences actual predicted outcomes. That’s why theories like GRW theory and Diósi–Penrose (DP) theory, mentioned earlier, are distinct from quantum mechanics — they provide different mathematical rules for when absolute reduction happens.
Until there is evidence of deviations from quantum theory’s predictions, it seems more in line with Occam’s razor to avoid proposing deviations altogether. In other words, treat the reduction of the state vector as relative rather than absolute, eliminating the need to assign a special role to observers, measuring devices, or thresholds for interference effects.
Saying that the reduction is relative means it depends on a chosen coordinate system. Whenever two physical systems interact, a coordinate system is needed to describe the outcome, with its origin tied to a physical system. For example, you can describe a train’s velocity relative to a person or even a rock. In this context, “perspective” refers to describing a property (such as velocity) relative to another system, as it is not an absolute property.
If, during an interaction, the origin of the coordinate system is one of the interacting objects, the state vector would be reduced from that “perspective.” Conversely, if the origin is external to the interaction, the two particles would be described as entangled.
Recall the earlier example of distinguishing pseudorandomly distributed qubits from qubits in a superposition of states based on their ability to exhibit interference effects. Quantum key distribution (QKD) relies on a similar principle. The sender transmits qubits, some randomly in superposition and others not. From an eavesdropper’s perspective, observing the qubits reduces their state vector, preventing them from exhibiting interference effects. The recipient can detect this by applying a second Hadamard gate, just as we distinguished between pseudorandom qubits and those in superposition.
The sender randomizes qubits to prevent the eavesdropper from reliably determining when to apply a Hadamard gate. If all qubits were sent in superposition, the eavesdropper could apply a Hadamard gate, read the qubit value, then use a second Hadamard gate to restore it to superposition before passing it to the recipient undetected. Randomizing the qubits ensures the eavesdropper doesn’t know when to apply a Hadamard gate. When qubits not in superposition have a Hadamard gate applied, they are placed into superposition, altering the data’s statistical distribution.
There’s a partial misconception that QKD relies on the eavesdropper “collapsing the wave function” (reducing the state vector absolutely) when observing the qubits. While this is correct from the eavesdropper’s perspective, it’s not how the sender and recipient would explain the loss of interference. From their perspective, the qubits become entangled with the environment (which includes the eavesdropper), leading to decoherence.
From the eavesdropper’s perspective, the reduction is irreversible. But what if a second eavesdropper, unaware of the first’s measurement outcome, attempted to reverse the process? In principle, the process could be reversed because the system remains in a superposition relative to the second eavesdropper. However, since the superposition involves both the first eavesdropper and the qubits, the second eavesdropper would need to apply an operation to both.
If successful, this operation would not only restore the qubits to their initial state but also revert the first eavesdropper’s brain state to its prior condition, erasing their knowledge of the qubits. Thus, even if the second eavesdropper could reverse the interaction, the first eavesdropper’s knowledge would be lost, defeating the purpose of eavesdropping.
These subtleties in quantum mechanics are often lost when people interpret it as an objective collapse theory, where the first observer (whatever “observer” means) causes an absolute reduction of the state vector, resulting in the particle no longer being in a superposition for all observers.
This interpretation is incorrect — not only because it requires modifying quantum mechanics mathematically, making it a distinct theory, but also because it conceals how profoundly relative quantum theory is. This relativity differs from that of general or special relativity, which is why relational quantum mechanics uses the term “relational” instead of “relativistic.” The term “relativistic” already refers to quantum mechanics incorporating special relativity (i.e., quantum field theory).
Quantum theory is relative in a unique sense: different observers can describe the same system in fundamentally different ways, yet quantum mechanics ensures that predictions made from these different perspectives never yield contradictory results.
