Established physics · Quantum Foundations Bridge · Q1 of 3
Superposition and interference
Quantum alternatives combine as amplitudes before we calculate probabilities.
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Picture it
Send one photon at a time toward two openings, with a screen beyond them. Each detection makes one local spot. After many repetitions, bright and dark bands appear when the two alternatives remain coherent. The pattern belongs to the statistics of many events; each event is still a single detection.
What a superposition says
A quantum state can combine alternatives such as two routes through an apparatus. An amplitude is a number with both size and phase. A useful picture is an arrow: its length gives size and its direction gives phase. These arrows describe a calculation, not little physical arrows attached to a flying particle.
Why two openings can give less
Where indistinguishable alternatives can lead to the same detector event, their amplitudes add. Arrows pointing together reinforce; arrows pointing oppositely can cancel. Cancellation makes a dark region even though either opening alone could contribute events there. Adding ordinary positive probabilities alone cannot produce that cancellation.
When the pattern changes
If a path becomes correlated with a distinguishable record in another system, interference between those alternatives is reduced or lost when that record is ignored. No person has to inspect the record. The relevant change is a physical interaction that makes the alternatives distinguishable.
Keep the physical claim small
The same amplitude rule covers photons, electrons, and other quantum systems. Superposition does not require the claim that a particle follows two ordinary classical trajectories. A wavefunction is a mathematical state description; the interference evidence does not by itself settle its interpretation.
One careful technical level
For two coherent alternatives ending in the same outcome, P = |a₁ + a₂|². The extra interference term depends on their relative phase. For the ideal balanced, lossless two-output interferometer below, P(A) = (1 + cos φ)/2 and P(B) = (1 − cos φ)/2. They always add to one. This is a simple two-output apparatus, not a numerical double-slit screen calculation.
Work one example
At one chosen screen position, let the two path amplitudes be +0.3 and −0.3. Together they give amplitude zero, hence probability density zero there. Separately they would contribute 0.09 each in the same units. The rest of the detection distribution changes too; probabilities over the complete set of outcomes must remain normalized.
Read the demonstration
In the balanced two-output example: phase 0° gives A = 100%, B = 0%; phase 90° gives 50%, 50%; phase 180° gives 0%, 100%. Changing phase redistributes probability, while the total stays 100%.
Keep this: Add coherent amplitudes first. Take their squared magnitude second. Phase is what lets alternatives reinforce or cancel.
Check your understanding
What must be combined before calculating a probability for indistinguishable routes?
- The amplitudes
- The already-squared probabilities
- The number of observers
Answer and explanation
The amplitudes
Amplitudes carry phase. Adding them before squaring preserves interference.
Two contributions to one outcome are +0.3 and −0.3. What is their combined probability density?
- 0.18
- 0
- 0.6
Answer and explanation
0
The amplitudes cancel: |0.3 − 0.3|² = 0.
Which change can remove interference even if nobody reads a detector?
- A physical interaction records which route
- Closing the laboratory door
- Giving the photon a name
Answer and explanation
A physical interaction records which route
A distinguishable path record changes the physical correlations; consciousness is unnecessary.
Does an interference pattern establish two ordinary classical trajectories for each particle?
- Yes, that is the definition
- No; it establishes phase-dependent quantum statistics
- Only for electrons
Answer and explanation
No; it establishes phase-dependent quantum statistics
Interference tests amplitude predictions. It does not independently pick an interpretation of the state.