observation experiment and physical theory

Observation is a purposeful perception of a phenomenon without interfering with it: an astronomer records a star's position and does not affect its motion. Experiment is observation under controlled conditions, where the researcher sets the values of the independent variable (for example, the length of a pendulum) and measures the system's response. The key difference is intervention and reproducibility: an experiment can be repeated under the same conditions, while passive observation depends on what nature provides.

A physical theory is a system of concepts, laws, and equations that connects many results and predicts new ones. A theory is not derived from experience mechanically: it is built as a model, and its consequences are tested by experiment. A confirmed prediction strengthens the theory; a refuted one forces it to be refined or replaced. This closes the cycle: observation $\to$ hypothesis $\to$ experiment $\to$ theory $\to$ new predictions.

A student hangs a mass on a string and, for five different lengths $L$, measures the time of ten complete oscillations. The student chooses both the length $L$ and the initial displacement. Is this work an observation or an experiment? Justify your answer.

Observations show that a metal rod lengthens when heated. Formulate a testable hypothesis about the relation between the elongation and the temperature change, and describe an experiment that could falsify it.

In 1919, during a solar eclipse, the apparent displacement of star positions near the Sun's disk was measured. The measurement itself is a passive recording of light. Why is it nevertheless called a test of a theory rather than a simple observation?

Self-study plan (30–40 minutes; work in a simulation if you cannot fix the support rigidly).

1. Observation (5 min). Start a pendulum simulation (for example, Pendulum Lab) or use a safe pendulum made of a string and a small load at the edge of a table. Change nothing: describe in your notebook what you see and record only qualitative features (the period is roughly constant, the amplitude slowly decreases).
2. Hypothesis (5 min). Write down the model $T = 2\pi\sqrt{L/g}$ and its falsification condition: if the graph of $T^2$ versus $L$ is not linear within uncertainty, the model is wrong.
3. Experiment (15 min). Choose five values of the length $L$ (for example, from $0{,}20$ to $0{,}60$ m). For each one measure the time $t$ of ten complete oscillations, compute $T = t/10$, repeat the measurement three times, and average.
4. Analysis (10 min). Plot $T^2$ against $L$. Check whether the line passes through the origin, and compare the slope with $4\pi^2/g \approx 4{,}02\ \text{s}^2/\text{m}$.
5. Reflection (5 min). State which step was observation, which was experiment, and which was a test of a theoretical consequence.

Safety: with a real pendulum, fix the support so that it cannot fall, and do not use heavy or damaged loads; if in doubt, work only in the simulation.

Show how passive observation differs from an experiment with a controlled variable, and indicate the place of theory in the closed cycle of inquiry.

Block diagram (boxes and arrows). On the left, a box labelled observation (no intervention) with an example: a star, a pendulum at rest. An arrow leads down to a box labelled hypothesis: a testable statement, for example $\Delta L / L_0 = \alpha \Delta T$. From it an arrow goes to a box labelled experiment: set the independent variable, measure the response, repeat. This box has two outgoing arrows labelled supported (into a box labelled theory: model and predictions) and falsified (back to the hypothesis box as a dashed loop). From the theory box an arrow returns to observation, labelled new predictions. At the bottom, a dashed frame lists three criteria of distinction: presence of intervention, reproducibility, and a falsification condition fixed in advance.

A player releases the ball from $2.10\ \mathrm{m}$ above the floor with speed $7.0\ \mathrm{m/s}$ at $50^\circ$ to the horizontal. A phone films at $240\ \mathrm{frames/s}$, that is one frame every $4.2\ \mathrm{ms}$. Marking the centre of the ball on each frame gives its coordinates with an uncertainty of about $\pm 0.02\ \mathrm{m}$. The team checks whether the path of the ball matches the parabola $y = y_0 + v_y t - \tfrac12 g t^2$ with $g = 9.8\ \mathrm{m/s^2}$.

This shows the whole cycle of the physical method: a hypothesis (the ball is a point mass in free fall), a prediction taken from theory (the same parabola $y(t)$ for every throw), a measurement with a stated uncertainty, and a comparison. Filming alone is an observation, because nothing is changed in the throw; the numerical check of the parabola is the experiment part, and the theory of projectile motion supplies a prediction that can fail and therefore can be tested.

A car travels at $50\ \mathrm{km/h} = 13.9\ \mathrm{m/s}$ on dry asphalt ($\mu \approx 0.7$). Theory gives the braking distance $s = v^2/(2\mu g) = (13.9)^2/(2\cdot 0.7\cdot 9.8) \approx 14\ \mathrm{m}$. On a closed track the driver brakes fully and a phone records the deceleration: the measured distance is $16\ \mathrm{m}$ and the largest deceleration is $6.4\ \mathrm{m/s^2}$ instead of the predicted $6.9\ \mathrm{m/s^2}$. A reaction time of $0.9\ \mathrm{s}$ adds another $12.5\ \mathrm{m}$ before the brakes act at all.

The theory of uniformly decelerated motion together with the law of dry friction gives the formula $s = v^2/(2\mu g)$, and the experiment tests it with concrete numbers. The gap between $14\ \mathrm{m}$ and $16\ \mathrm{m}$ is data, not a failure: it points to worn tyres and to a $\mu$ smaller than the one used in the model. That is how a theory is corrected rather than discarded.

At normal pressure $101\ \mathrm{kPa}$ water boils at $100\ ^\circ\mathrm{C}$. In a pressure cooker the pressure inside rises to about $180\ \mathrm{kPa}$ and a kitchen thermometer reads $117\ ^\circ\mathrm{C}$; potatoes that need $20\ \mathrm{min}$ in an open pan are soft after $6\ \mathrm{min}$. At an altitude of $2240\ \mathrm{m}$ (Mexico City, about $77\ \mathrm{kPa}$) the same pan boils water at $93\ ^\circ\mathrm{C}$ and the potatoes take $30\ \mathrm{min}$.

An observation — water boils at a different temperature in the mountains — becomes an experiment when the pressure is changed on purpose in a sealed pot and the temperature is measured with a thermometer. The theory of saturated vapour pressure and of the equilibrium between liquid and vapour explains why the boiling temperature tracks the pressure, and it gives a numerical prediction (about $120\ ^\circ\mathrm{C}$ at $200\ \mathrm{kPa}$) that the thermometer reading can confirm or refute.