Relativity and Energy: How E = mc^2 leads to numerous other features of Nature!

In my classes, when we are going through the usual classical physics portions of energy and work, I also throw in a couple days of modern theories of energy, including special relativity and some basic quantum mechanical ideas. After we see one way of deriving E = mc^2, and Einstein's energy equation in special relativity, I want to make a point that this is a truly large breakthrough in our thinking of the physical world. I like to use E = mc^2 as a stepping stone to better understand the following:

The discovery of E = mc2 basically sets up the discovery of quantum  mechanics, and the weirdness we see with particles.

            Energy = matter, is effectively what this tells us.

These are two forms of the same stuff, like steam (energy) and ice (matter)  are two forms of the same H2O molecule.

     Whatever properties energy (waves) can have, then matter (particles)  has those properties.

     Whatever properties matter (particles) can have, then energy (waves)  has those properties.

Examples:

If waves have wavelengths, then so must particles

If particles have momentum, then so must waves (light/photons)

If matter is affected by gravity, then so must waves (light/photons)

This equation also re-defines conservation of mass and conservation of energy. In nuclear reactions, conservation of mass is violated, since products weigh less than reactants.

         Conservation of mass-energy is now more correct!

• This equation changed the course of history, as we entered the age of nuclear power and weapons.

• It allows us to understand how stars form and 'burn,' and their life cycles

• It allows us to understand how heavier elements are formed through thermonuclear fusion (nucleosynthesis; we are made of star dust!!)

• It allows us to understand how the universe can form from a burst of pure energy (Big Bang), as we have phase transitions from energy to matter or vice versa.

• The unification of space and time allows us to understand what causes gravity (warps in space-time)

• It allows us to understand how to make particle accelerators and explore the basic question, "What are we made of?"
• It led to the prediction of antimatter 

• It allows us to think in terms of multiple dimensions, giving rise to things like string theories

• It allows us to begin to understand radioactive processes, and nuclear physics

• The theory of photons allowed Einstein to understand photoelectricity (solar energy), for which he won the Nobel Prize

• This also helped lead to his discovery of 'stimulated emission,' the process that makes lasers possible

• It predicts 'matter waves' or the wave-particle duality, which is the heart and soul of quantum mechanics