Understanding wave particle duality

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Wave-particle duality suggests that particles can exhibit both wave and particle characteristics depending on observation. The discussion connects this concept to Einstein's E=mc², proposing that unobserved particles exist in a state of equilibrium between energy and mass. When observed, this balance collapses, resulting in either a wave or a particle manifestation. It is emphasized that while E=mc² represents mass-energy equivalence, wave-particle duality is a distinct quantum phenomenon. The de Broglie relationship is highlighted as a fundamental equation illustrating this duality.
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I haven't studied physics, but I've had this thought in my head lately and I want to get it out. I'm hoping someone here can either help me understand this or set me straight if I'm on the wrong track.

I've been mulling over wave particle duality in my head, and I realized that Einstein sort of showed us a duality as well in E=mc2.

Basically, I'm wondering if while no one is really observing a particle it is present in an equilibrium of energy and mass potential, so it is a wave and a particle at the same time, but when you try to observe it via its mass the energy is converted to mass temporarily, so that the wave form collapses. Conversely if we had a way to observe the particle by its energy, then the mass would be converted to energy and temporarily the particle would disappear - leaving us with a wave.

I'm thinking its balanced between energy and mass normally, but if you check one side of the duality then you force all of the potential energy to that side of the duality and end up with a wave or a particle.

Does that make any sense at all? Are wave/particle duality and E=mc2 related? Am I totally thinking in the wrong direction?
 
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I would just point out that wave-particle duality applies not only to massive particles but also massless particles like photons. But both can be described by the more general equation E=(p2c2+m2c4)1/2. (From which you can derive the limiting form E=mc2).

In my opinion, E=mc2 reflects mass-energy equivalence, which is a relativistic phenomenon, while wave-particle duality is a quantum phenomenon, so you're free to read as deeply into both of them as you'd like, but it's important to keep them straight.

BTW, I think the equation that best reflects wave-particle duality on a basic level is de Broglie's relationship p=h/λ.
 
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Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?

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