Why is the wave-like nature of matter not observed every day for macroscopic objects?

To answer this question, we first need to understand the concept of the de Broglie wavelength. The de Broglie wavelength is the wavelength associated with a particle that exhibits both wave-like and particle-like properties. The French physicist Louis de Broglie proposed that any particle, not just light, can have both wave-like and particle-like characteristics. The de Broglie wavelength (\(λ\)) of a particle is given by the formula: \(λ = \frac{h}{mv}\) where: - \(h\) is the Planck's constant (\(h ≈ 6.63 × 10^{-34} Js\)) - \(m\) is the mass of the particle - \(v\) is the velocity of the particle

Now that we understand the de Broglie wavelength, let's apply it to macroscopic objects. The wavelength (\(λ\)) of an object depends on its mass (\(m\)) and velocity (\(v\)). For everyday macroscopic objects, such as cars, baseballs, or humans, their masses are relatively large compared to the tiny particles at the quantum level (e.g., electrons, protons). Despite what seems like varying velocities for these objects in our lives, when compared to the velocity of light, their velocities are still relatively small.

When we plug the mass and velocity of macroscopic objects into the de Broglie wavelength formula, we find that their wavelengths are extremely small compared to those of light. Since wavelength determines the observed wave-like behavior, smaller wavelengths result in less noticeable wave-like properties. For example, let's take a baseball with a mass of 0.145 kg and a speed of 40 m/s: \(λ = \frac{h}{mv} ≈ \frac{6.63 × 10^{-34} Js}{0.145 kg × 40 m/s} ≈ 1.14 × 10^{-34} m\) As we can see from the calculation, the wavelength of a baseball is exceedingly small and much smaller than the wavelength of light (which is in the order of \(10^{-7} m\)). This would be equivalent to looking for a tiny wave in a vast ocean.

In our day-to-day lives, we're more familiar with observing objects as particles rather than waves, mainly because the wave-like properties of macroscopic objects are not easily detectable due to their minuscule wavelengths. The wave-like nature is still present, but it is incredibly difficult to observe with our unaided senses or even with most scientific instruments. To summarize, the main reason we don't observe the wave-like nature of macroscopic objects in our daily lives is that their wavelengths—related to their mass and velocity—are too small compared to that of light or other familiar wave phenomena, which dwarfs their wave-like properties and makes them practically imperceptible to us.