In 1887 Heinrich Hertz observed a phenomena known now as the photoelectric effect. Hertz saw that when electromagnetic radiation was shone onto a piece of metal it emitted electrons. Einstein furthered the understanding of this phenomena with 3 key observations. The first was that Photo-electrons would only be emitted if the frequency of the EM radiation was above a certain frequency that he called the fundamental frequency, the second was that if the frequency of the wavelength was above the fundamental frequency then emission of photo-electrons was instantaneous and intensity is independent of this.
The final observation is that the kinetic energy of the photo-electrons is also independent of intensity but actually seemed to depend on how far over the fundamental frequency the incident radiation is. Using the wave model for EM radiation these observations do not make sense since threshold frequency shouldn't exist, the electrons in the metal should absorb all the energy over time and eventually have enough energy to escape the surface of the metal however it appears as though the energy is exchanged in a one-to-one ratio and so that would mean energy is being transferred
Since the late 19th century scientists have been aware that classical physics has limitations when it comes to gaining an understanding of the microscopic world, and thus Quantum Theory was born. The word quantum itself comes from the word 'Quantize' to give something a value and or create discrete data from a world of madness, in our case the world of the very tiny details that, though small, define our universe as a whole.
So where did it all start?
It all began with Max Planck and black-body radiation in 1894. Black-body radiation is the thermal electromagnetic radiation within or surrounding a body in thermodynamic equilibrium with its environment, or emitted by a black body. This lead to the development of Planck's Law which began a revolutionary shift in the way physicists view the universe and everything within it, big and small in order to find out how it all works. Planck however suggested that quantization was purely a mathematical construct, without any material, fundamental and observable basis.
Electrons getting "knocked off" a sheet of metal by photons - making photoelectrons
Black-Body radiation
Bohr and Einstein in discussion
In 1905, Einstein took the idea of quantization to a new level by suggesting that it's not just a mathematical construct, but a material reality in which the energy in a beam of light actually occurs in individual packets or "discrete quanta," called photons. The energy of a single photon is given by frequency multiplied by Planck's Constant - E=hf.
Early 20th Century - Bohr Vs Einstein
The Bohr-Einstein debates began in 1905 when Bohr was skeptical about the photon, as he believed it rendered the choice for a mathematical solution arbitrary. This went on for the next 20 years until he eventually embraced the concept. In turn, Einstein took a while to accept Bohr's model of the Hydrogen atom - which is the model we still use today in many fields.
The quantum revolution, lead at large by Bohr and Einstein was the shift in our understanding of physics that dominated the 20th century. The theories and discoveries that came to light during and after the period include but aren't limited to; wave-particle duality, the uncertainty principle and the Dirac equation.
The main points of disagreement between Bohr and Einstein were arguably (and surprisingly so) quite philosophical. In the context of how to interpret quantum mechanics, both had very different ideas. An example of this would be how each would respond to Schrodinger's cat thought experiment.
The situation is as so: A cat is inside a closed box, a radioactive gun (that has the probability of 50% to emit lethal radiation) is pointed at the box (which can pierce through the box and hit the cat which will then be dead).
The question asked is: You open the box and you see the cat either to be dead or alive. What the cat was just before you opened it? After you open it, why is it in only one state?
Now Einstein would answer that if we find the cat dead, then it was dead before opening the box, and if it was alive then it would be alive before opening the box. This makes sense in the world we understand, because surely how can the answer be anything else?
Well as you'd expect, Bohr would disagree. His answer would've been that regardless of the state you found the cat it, just before opening the box the cat is both dead AND alive. The explanation behind this is that the cat chooses to be dead after you see it, and some other equal number of times it chooses to be alive. But before observing, it is both. In order to understand this, you have to ignore what makes sense fundamentally about life and death not being simultaneous processes and the fact that you can't choose which state to be in.
This in itself, stands for all of quantum mechanics. The idea that more or less everything relies on probability is a concept that Einstein despised because if there isn't an exact science to explain things, if our process of prediction and experimentation in deemed invalid, then how can we be sure about anything, ever?
These are the fundamental issues with understanding quantum mechanics, you must be able to break out the standardized, logical and linear way of thinking - because sometimes, if not a lot of the time, it really doesn't make any sense!