electrons - The Dual Nature of Matter

I can't seem to understand the dual nature of matter completely.

If electrons have a wave nature, then if two electrons were to collide, wouldn't they undergo interference and form an electron wave of larger or smaller amplitude? Does that mean the electrons merge and turn into a "bigger" electron?

Then again, this would mean that the electrons would have a phase difference, so what determines the phase of matter?

Also, if we were to consider two photons colliding, would they also undergo interference and form a "bigger" photon?

Why don't normal everyday objects undergo interference? Just because the wavelength (according to the de Broglie equation) of something is small doesn't mean that it doesn't undergo interference (take for example gamma rays which have a very small wavelength but are the most powerful form of radiation).

Answer

First one needs to understand that electrons, and nature in general, are what they are - neither waves nor particles. Whether they exhibit wave like or particle like behaviour depends on the experiments we do. An electron microscope, for instance, uses interference between many electrons to create an image of the object.

For a long time people doubted the ability of matter to change properties depending on what WE, the observer, did, but Alain Aspect and others showed that the result of an interference experiment does depend on our choice to measure interference, even of we set things up so that the choice is made after all the photons have travelled past the mirrors/slits in question.

For quantum mechanical waves, except in interesting topological circumstances, phases are usually unobservable. The amplitudes may be multiplied by any phase without affecting the outcome of the experiment, which is determined by the (real) squares of the amplitudes. The phases are certainly necessary for the description of waves, but it is not right to say 'the phase of matter'. There is also nothing 'bigger', because as a state/ensemble evolves the total of all amplitudes squared is conserved - this is the law that probabilities always sum to 1. If you want to think of intensity, as in the number density of photons in a beam, this might be changed by various means, but remember that you are then talking about many photons. If you integrate the interference pattern, the expected total intensity does not change from what it was.

Everyday objects do undergo interference, but on such large scales that we cannot separate the effects from the complex world around us, the quantum state of which defies description. Some people doubt this, but all evidence indicates that the world really is a quantum one.