1.5. Observations and Measurements

In this section, we will discuss the concepts of observation and measurement, addressing them in both classical and quantum mechanics.

1.5.1. Observations

In both classical and quantum mechanics, observations represent measurable properties of physical systems. These properties include variables such as mass, position, momentum, and energy. Measurements are conducted through specific experiments to obtain the actual values of these properties. In both cases, observation results are expressed as real numbers.

In classical mechanics, observations are typically conducted with minimal or no impact on the system’s internal state. In contrast, in quantum mechanics, observations interact with states in a more complex manner. Due to the nature of quantum systems, significant effects on the system can occur during observation.

Here is a comparative table of Classical Mechanics vs. Quantum Mechanics:

Property	Classical Mechanics	Quantum Mechanics
Measurement Process	Generally less invasive	Measurement process can disrupt and is invasive
Degree of Intervention	Minimal intervention or none	Measurement device must be at the same scale as the system
Determinability of Results	Results are definitively determinable	Results rely on predefined probabilities
Output	Real numbers	Real numbers

1.5.2. Measurement

In quantum mechanics, during measurement, the “sharp edge” of the measuring device must be on the same scale as the system being measured. This means that the quantum measurement process can disturb the system’s state. This phenomenon can be likened to the “bull in a china shop” analogy; a bull inspecting china inevitably alters its condition. Thus, the post-measurement state will differ from the pre-measurement state.

Large-scale analogies help to understand the challenges of the quantum measurement process but do not fully capture its intricacies. When comparing classical and quantum measurements, several key points emerge:

1. Classical Measurement Process: In classical physics, measurement processes are generally less invasive and can be carried out with minimal or no change to the system’s state. If a state change occurs, it is typically predictable and deterministic. That is, measurements conducted under the same conditions will always yield the same results. For example, when measuring an object’s mass, the same value is obtained under the same conditions.
2. Quantum Measurement Process: In quantum mechanics, the measurement of similarly prepared systems may yield different results. These variations stem from the nature of the system’s quantum state and are expressed in terms of known, predefined probabilities. In other words, measuring a quantum system involves the likelihood of obtaining a particular result. For example, when measuring the spin state of a quantum particle, different outcomes (such as “spin up” or “spin down”) may be observed.
3. Outputs and Determinism: Both classical and quantum measurement processes yield real numbers. However, classical measurement is deterministic, meaning it consistently produces the same results under identical initial conditions. This implies that similar systems yield similar results.

In quantum mechanics, however, measurements of similarly prepared systems can yield different results due to probability distributions inherent in quantum states. Thus, a measurement includes the probability of achieving a specific outcome, determined by a predefined distribution.

The Stern-Gerlach experiment exemplifies the issues outlined in points (1) and (3). This experiment, used to probe the internal structure and quantum states of atoms, illustrates the fundamental principles of quantum mechanics. The experiment demonstrates that measurements associated with certain quantum states yield results with a more complex, probabilistic structure compared to classical thought.

Furthermore, the outcomes of the Stern-Gerlach experiment are also relevant to the concept of the “qubit.” A qubit, the quantum equivalent of a bit in classical digital computing, is one of the fundamental building blocks of quantum computers. The computational power of quantum computers arises from the superposition and entanglement properties of qubits, opening the door to revolutionary advancements in quantum computing.

Below is a comparative table outlining the differences in measurement between classical and quantum mechanics.

Property	Classical Mechanics	Quantum Mechanics
Intervention	Generally less invasive	Invasive and may alter the state
State Change	Minimal or no change	Post-measurement state differs
Results	Real numbers	Real numbers, but probabilistic
Probability	Not predetermined	Expressed in predefined probabilities
Measurement Process	Deterministic measurement processes	Probabilistic measurement processes
Determinism	Same results under identical initial conditions	Different results under identical initial conditions
Measurement Device Scale	Device scale independent of the system	Device must be at the same scale as the system
Example Experiment	Mass measurement	Stern-Gerlach experiment