What does E = mc^2 mean? What are the consequences?

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

Not bad for something that seems so simple and innocent!

Science Modeling: Example, Climate models

Because this was an election year, I think there was an increased interest among many about climate change, and whether or not humans have any impact on climate and global warming. For full disclosure, I am a PhD physicist and know several experts on climate science, and there is no question in my mind that humans have something, and likely most, to do with climate change...the multiple, independent studies and evidence for this is too great, and experts who study this don't even question whether this is still a question.

But what the vast majority of non-scientists do not understand and tend to ask me, is how in the world can any scientist make a prediction about what could happen 100 years in the future? Especially when weather forecasts on the evening news cannot even get the weather correct one week from now? A valid, and important, question. The answer is very sophisticated climate models and computer simulations.

"Huh??" is a typical reaction when someone hears this for the first time. Computer simulations involve taking a mathematical model, and in this case, for a global climate system, the sets of mathematical equations relevant to the system are crazy hard to solve...nonlinear, partial differential equations for a huge number of different phenomena, all interacting with each other to lead to what we observe in nature. So difficult is the math that no one can possibly solve these with pencil and paper, and worse yet no one can possibly run these crazy hard equations through time by hand. But with powerful, crazy fast computers that can do trillions of calculations per second (i.e. supercomputing systems), one can code up the equations and figure out solutions to them. The result is a prediction over time of what the world may look like given an initial set of conditions to start the calculations.

How does a scientist have any confidence that results spewing from the computer are at all realistic? How do we know if anything about the simulation is believable or reliable? Well, one can look at past climates and events that affected climate, and put those conditions into the computer model and simulation. Run the simulations for past events and conditions, and compare the simulated predictions to real data and results that are measured - if the real data and simulated results overlap, then one has some confidence that the simulation is working properly. Do this for a large number of past events, and if all of them are showing good overlap with actual data, then confidence grows.

One can then make predictions with the simulations, even for past data and climates. One can change the parameter values for all sorts of things, leaving others fixed in value, to see if the changed values can make significant changes in climate by themselves. When one does this with natural parameters one does not get the increases in temperatures that are measured over the past century (especially since the 1970s). However, when one changes the greenhouse gas parameters, that alone creates the increase in temperatures we observe. Computer simulations are one avenue to show that human contributions to increased greenhouse gases has caused the increase in global temperatures.

For an excellent example of all this in action, check our the TED talk by Gavin Schmidt. He shows the process of making the models, and shows predictions for the future, having gone through the calibration and verification process described above.