The usual explanation given to understand why high energies are required to probe very small distances is that we need the de Broglie wavelength of the probe to be comparable/smaller than the length scale we are interested in probing.
$$\lambda = \frac{h}{p}$$
Small distance means using small $\lambda$ and therefore higher momentum implying higher energies. This is quite intuitive to understand given the analogy with light waves.
However, it is often shown that macroscopic objects like dust particles have tiny de Broglie wavelengths, less than a fermi or so (for ex. Complement $A_I$ of Cohen-Tannoudji Quantum Mechanics Vol 1).
My question is if $\lambda$ being small is the only criterion then what prevents classical/macroscopic objects with such tiny $\lambda$ from being used as probes? Is there a practical restriction to this or am I missing something conceptual? On the face of it, the question seems pretty absurd but I am unable to think of a clear answer and couldn't find an explanation addressing this particular issue.
Here are a few points that I have in mind about the question:
- $\lambda$ is fixed by $p$ and reaching a certain $p$ requires less energy if $m$ is higher. So it is energetically favorable to use particles of higher mass as probes.
- Macroscopic particles with tiny de Broglie wavelengths are not quantum (i.e. it has well-defined positions and momenta, the uncertainties being negligible), unlike an electron with the same de Broglie wavelength. Does this imply having wave characteristics is a necessity for probing small distances?
- If wave characteristics are necessary then forgetting about classical particles, suppose that there existed a very heavy elementary particle. It will show quantum behavior. Then can it be used to probe smaller distances using lesser energies?
