What do I mean by quantum weirdness? Its the observation of things that cannot be explained with the classical laws of physics and need to be explained or are the results of quantum mechanics that seem odd, strange or just plain weird. Maybe quantum bizarre would be better word. What effects or thing do I mean that are quantum weird? Here are some examples:

Schrodinger's cat This is the most famous cat in physics. Also apparently Schrodinger owned a cat when he thought of his thought experiment in 1935 I think. This is the paradox that can arise when one applies quantum mechanics to macroscopic sized objects in which we can not observe. The paradox is that the state that describes the cat quantum mechanically has to have the cat both alive and dead at the same time. This is because Schrodinger equation is linear so the most general solution is a linear combination of all the solutions. This is also known as superposition. It leads to a just weird situation.

Image without detecting light Another article on the same experiment is here. This is a recent experiment using entangled photons. Entanglement can led to many weird quantum effect. Basically using entangled photons physicists were able to make a photograph of an object where the entangled photons never were involved in the illumination or reflection from the object whose picture was taken. The photons didn't see the object or have anything to do with the object yet they could be used to make a picture. Of course the picture was of a cat. This is just plain weird. Einstein called entanglement "spooky".

Quantum computing Where in a qubit does the calculation take place in a quantum computer? This has to do with superposition.

The uncertainty_principle can lead to many odd effects.

Wave particle duality.is just plain weird. How a particle can both be a wave and a particle.

You can probably think of other weird quantum effects, or in quantum mechanics things are different. This quantum weird is something that all students of physics talk about partially because it is just plain weird. Some people learn about quantum weirdness in reading about science in newspapers or other popular media. Recently a meeting was held to help educate science journalists about quantum mechanics and some of its weirdness. One of my favorite blogs Backreaction has a post about this meeting because blog author helped organize the meeting.

One of the problems with quantum mechanics is that physicists don't really understand what quantum mechanics is trying to tell us. Quantum mechanics has many interpretations. The equations of quantum mechanics are well known its just what do they mean? Some blog discussions about this are very illuminating on this subject. One is in the blog quantum frontiers posted here. This is written by John Preskill a physics prof at Caltech. Another is posted by Sean Carroll here.entitled "The Most Embarrassing Graph in Modern Physics". The graph mentioned is about a poll taken at a meeting showing that physicists can't agree on which interpretation of quantum mechanics is correct. As is usual the comment sections of the posts are very educational.. I have also talked about the problems with quantum mechanics here. This is one of my earlier posts and might be poorly written.

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