# Why does the wave-particle duality become unnoticeable with more mass? [duplicate]

According to the formula $λ=h/mv$ for the De Broglie wavelength, as the mass increases, it becomes a greater coefficient to multiply the velocity by, and the larger number in the denominator makes the wavelength so small that it can't be detected for high mass objects. My physics teacher used this reasoning to explain how even large macroscopic objects may have their own wave functions, but are so small we can't really detect them.

However, aren't all larger objects made of smaller ones? Like how molecules are made of atoms, and atoms are made of the elementary particles, and etc. Since this is the case, why can't we apply the λ=h/mv formula to all the particles that make up the atoms and molecules that are inside of say, a baseball, and average find the average of those waves? Since on average, half of those waves should be constructive, and the other half destructive, shouldn't the average of all the waves of the particles that make up the larger object be the true wavelength of the object? This obviously isn't the case though, since a baseball doesn't exhibit wave-like behavior.

What's the flaw in my reasoning? Why don't high-mass objects behave like I expect them to? I tried to read the Wikipedia page on the wave-particle duality, but I still haven't been able to come to a conclusion.

## marked as duplicate by ACuriousMind♦ quantum-mechanics StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Jul 26 '17 at 8:43

• What you are saying would be true for a collection of non-interacting atoms/molecules. A baseball (or any other macroscopic object) is not one of those. All constituents are bound in a lattice and therefore interact to varying degrees with every other constituent. – probably_someone Jul 26 '17 at 4:40
• So when particles are bound with other particles, they lose their individual wave functions and can only be expressed as one package? Why does this happen? I learned that atoms are mostly empty space, so even if they bond to other atoms, shouldn't they retain their individuality? – Peter Mei Jul 26 '17 at 4:52

There exist wave equations , second degree differential equations which have as solutions sinusoidal functions. These functions can model perfectly water waves, sound waves, and even light waves. What is modeled as waving is the amplitude of the transfer of energy in water waves, acoustic waves, and light waves.

The energy "waves", i.e. if one sits at an (x,y,z) and an acoustic wave passes, the appropriate detector will go up and down at the frequency of the passing wave. Appropriate means that its dimensions are commensurate with the wavelength of the passing energy transferring wave.

In quantum mechanics similar differential wave equations give solutions that model the particle experiment results, wave solutions, sinusoidal ones, that is why they are called wavefunctions. BUT, and it is a huge "but" what is "waving" is not the energy of the particles. It is the probability of finding the particle at (x,y,z) at time t, that changes in in wave pattern, a sinusoidal pattern.

This becomes clear watching single electrons going through the double slit.

Starting at the top frame, each electron manisfests into a dot, that looks random, what you might expect if you threw balls at double slits, the balls scattering randomly at the edges. But going down in frames and accumulating many electrons, an interference pattern appears. The accumulation of measurements gives a probability distribution for the experiment " electron hitting double slits" , a quantum mechanical experiment, with a given energy of electrons and distances and widths of slits connected with the quantum mechanical wavelength. BUT it has nothing to do with energy , it is how probable it is to see an electron hitting the screen at (x,y).

At the particle level, ensembles of particles interact with each other and have a wavefunction which is a solutions of the quantum mechanical problem, but it is again on probability distributions. The solutions are coherent, i.e. the phases are known and what is called a density matrix "sums" all the individual wavefunctions.As the distances between atoms and molecules grows going into bulk matter the coherence of the solutions is lost, and one goes into the classical physics regime.

Coherence is necessary for any interference effects, wave effects to show up, both classically and quantum mechanically. A baseball can be described by a quantum mechanical density matrix , but the coherence is lost, the matrix has only diagonal elements. In quantum mechanical terms it means that the probability of a baseball to appear in a spot different than the classical calculation is zero. Large molecules have been seen to interfere.