How Can Scientists Measure Something They Cannot See Directly?
1. The challenge
Many of the most important objects in science—atoms, nuclei, and subatomic particles—are far too small to observe with the naked eye. Even with advanced instruments, they often cannot be measured directly.
In this experiment, you use probability and geometry to estimate the size of an object without measuring it directly.
By repeatedly tossing a coin into an area that contains “invisible” circles, you can analyze how often a collision occurs and use that information to estimate the approximate size of the object.
This method reproduces, in a simplified way, the logic behind some historic experiments in physics.
2. Importance in the real world
A large portion of scientific knowledge is obtained through indirect measurements.
For example:
- Physicists discovered the atomic nucleus by analyzing how particles bounced off thin metal foils.
- Astronomers calculate the size of planets and stars by observing their motion or the light they emit.
- Geologists estimate the age of Earth by measuring the radioactive decay of certain elements.
In all these cases, scientists cannot manipulate the object they study directly.
Instead, they analyze its effects.
3. Mental model of the experiment
Imagine that the circles drawn on the cardboard represent atomic nuclei.
Each coin toss works like a particle passing through the material. Two outcomes are possible:
- Collision: the coin touches one of the circles.
- No collision: the coin lands in empty space.
If you repeat the experiment many times, you can calculate the probability of collision.
That probability allows you to estimate the size of the circles—even if you never measure them directly.
This is the same principle used in many physics experiments: studying how particles interact to deduce the structure of matter.
4. Common misconception
“If something cannot be seen, it cannot be measured.”
Science shows exactly the opposite.
In reality, many things we cannot see can still be measured by analyzing their effects, such as:
- Gravity
- Magnetic fields
- Subatomic particles
- The internal structure of atoms
This experiment shows how data and statistics can reveal invisible properties.
5. Expanding the challenge
The challenge proposes investigating how astronomers measure enormous objects such as planets or stars.
Surprisingly, they often use principles similar to those in this experiment: they observe indirect effects and apply mathematical models. Some examples include:
Planetary transits
When a planet passes in front of a star, it blocks a small fraction of its light. By measuring that decrease, astronomers can calculate the size of the planet.
Stellar parallax
When a star is observed from different points along Earth’s orbit, it appears to shift slightly in position. This tiny displacement allows scientists to calculate its distance.
Spectroscopy
By analyzing the light emitted by stars, scientists can determine their temperature, chemical composition, and even their velocity.
In this way, just like in this experiment, science learns to measure things that it cannot touch or see directly.
6. Scientific microhistory
In 1909, the physicist Ernest Rutherford carried out one of the most famous experiments in the history of science.
In his laboratory, he fired tiny particles at an extremely thin sheet of gold.
Most of the particles passed straight through the metal without deflection, but some bounced back at unexpected angles. This result was astonishing: it meant that inside the atom there must be a very small and very dense region.
From this experiment, Rutherford proposed the existence of the atomic nucleus.
No one could see it directly, but the trajectories of the particles revealed its presence.
It was one of the first clear demonstrations that science can discover invisible structures by studying their effects.
7. Final question
If scientists can deduce the size of an atomic nucleus or the distance to a star using only indirect clues…
How many other things in the universe might still be waiting to be discovered in the same way?
