## Ask Ethan: If Einstein Is Right And E = mc², Where Does Mass Get Its Energy From?

“My question is, in the equation E = mc², where does the energy in the "m” come from?“

It’s still hard, more than 100 years after Einstein demonstrated its truth, to wrap our heads around the idea that energy and mass are equivalent. There are many forms of energy that can all be converted into one another, and mass is just another one of them. You can create particles with mass if you have enough available energy, and if you set up the right conditions to destroy mass, such as in a nuclear reaction or an antimatter annihilation, you can turn mass back into pure energy.

But what about the question of where that energy responsible for creating the “m” of rest mass comes from? It might be a tempting answer to assume that it’s the Higgs, since we all heard last decade about how the Higgs gives mass to the Universe. But for the matter we know of, predominantly made of protons, neutrons, and electrons, the Higgs is responsible only for about 1% of the mass in the Universe.

The rest of it? Well, it’s a little more complicated than that, but science has got you covered. Find out where mass gets its energy from on this week’s Ask Ethan!

## This Is Why Neutrinos Are The Standard Model’s Greatest Puzzle

“But this is where the big puzzle comes in: if neutrinos and antineutrinos have mass, then it should be possible to turn a left-handed neutrino into a right-handed particle simply by either slowing the neutrino down or speeding yourself up. If you curl your fingers around your left thumb and point your thumb towards you, your fingers curl clockwise around your thumb. If you point your left thumb away from you, though, your fingers appear to curl counterclockwise instead.

In other words, we can change the perceived spin of a neutrino or antineutrino simply by changing our motion relative to it. Since all neutrinos are left-handed and all antineutrinos are right-handed, does this mean that you can transform a left-handed neutrino into a right-handed antineutrino simply by changing your perspective? Or does this mean that left-handed anti-neutrinos and right-handed neutrinos exist, but are beyond our current detection capabilities?”

Every fermion in the Standard Model has a number of properties inherent to it. Mass, charge, baryon number, lepton number, lepton family number, etc. All the fermions that exist in the Standard Model have non-zero masses, even the neutrino, and all of them can have their intrinsic angular momentum go in any direction… except the neutrino. Unlike all the other fermions, we’ve only ever seen left-handed neutrinos and right-handed antineutrinos. But if we’re clever enough, we can design an experiment that will reverse the perceived spin of these neutrinos.

What will we see then? Believe it or not, the answer could unlock the mystery of why our Universe is filled with matter and not anti-matter. Let’s do what we can to solve this puzzle; the entire Universe may be at stake!

## Ask Ethan: Where Does A Proton’s Mass Come From?

“What’s happening inside protons? Why does [its] mass so greatly exceed the combined masses of its constituent quarks and gluons?”

The whole is equal to the sum of its parts. That’s one of the first rules you learn, and it’s true about almost everything in the Universe. If you were to break a human being down into our constituent components, the cells in our body would add up to our entire selves. Same for the molecules in our cells and the atoms in our molecules.

But when you get down to atomic nuclei, something funny happens: the individual protons and neutrons are about 1% heavier than the atoms as a whole. That’s a clue as to what’s happening, but it cannot prepare us for the most mind-boggling fact: the quarks that make up the proton are only 0.2% of the proton’s actual mass!

Why is this? And, if it’s not from the quarks that make it up, where does the proton’s mass come from? We know, both theoretically and experimentally, and now you can know, too!

## Could The Milky Way Be More Massive Than Andromeda?

“The Milky Way is home to the Sun, our Solar System, and hundreds of billions of stars beyond that. Yet unlike all the other galaxies out there — in our Local Group and in the Universe beyond — we have no good way to view our own galaxy from our position within it. As a result, the full extent of our galaxy, including its total size, mass, matter content, and number of stars, remains mysterious to modern astronomers.

We’ve long looked at the galaxies surrounding our local neighborhood in space and compared ourselves to them. Although there may be more than 60 galaxies present within the Local Group, two of them dominate in every way imaginable: ourselves and Andromeda. We are the two largest, most massive galaxies around, with more stars than all the others combined. But which one is bigger? Long thought to be Andromeda, we’re now finding out the Milky Way might have a chance at being number one.”

It’s 2019, and we still don’t know how massive the Milky Way is, or even whether we’re the most massive galaxy in the Local Group or not. It’s a lot like measuring your eye color: looking out at everyone else, it’s easy to see what color their eyes are. But if you didn’t have a reflection, photograph, or the observations of others, how would you know your own eye color? Well, being trapped within the Milky Way makes measurements notoriously difficult, and we’re only now figuring out how to overcome that obstacle.

It’s not only possible, but even likely that the Milky Way, despite having fewer stars occupying less volume than Andromeda’s, is the most massive galaxy in the Local Group. Come get the full story.

## Ask Ethan: How Do Massless Particles Experience Gravity?

“Given the equation for gravity between two masses, and the fact that photons are massless, how is it possible for a mass (like a star or a black hole) to exert influence on said photon?”

You know the law of universal gravitation: you put in what any two masses are, how far apart they are from each other, and the gravitational constant of the Universe, and you can immediately know what the force is between any two objects. Set one of the masses to zero, and the force goes to zero. So why is it, then, that if you take the ultimate particle with no mass, a photon, and pass it close by a mass, its path does bend? Why do massless particles experience gravity?

To understand why, you should think about what happens if you and I start at the same place near a mass, but I’m stationary and you’re moving. How far away is that mass? What’s the “r” that goes into Newton’s equation? And who’s right: me or you?

The answer is that we both need to be right, and Newton won’t get us there. Come get the real story on gravity, and learn why, in the end, massless particles feel it, too!

## At Last, Physicists Understand Where Matter’s Mass Comes From

“The way quarks bind into protons is fundamentally different from all the other forces and interactions we know of. Instead of the force getting stronger when objects get closer — like the gravitational, electric or magnetic forces — the attractive force goes down to zero when quarks get arbitrarily close. And instead of the force getting weaker when objects get farther away, the force pulling quarks back together gets stronger the farther away they get.

This property of the strong nuclear force is known as asymptotic freedom, and the particles that mediate this force are known as gluons. Somehow, the energy binding the proton together, the other 99.8% of the proton’s mass, comes from these gluons.”

Matter seems pretty straightforward to understand. Take whatever system you want to understand, break it up into its constituents, and see how they bind together. You’d assume, for good reason, that the whole would equal the sum of its parts. Split apart a cell into its molecules, and the molecules add up to the same mass as the cell. Split up molecules into atoms, or atoms into nuclei and electrons, and the masses remain equal. But go inside an atomic nucleus, to the quarks and gluons, and suddenly you find that over 99% of the mass is missing. The discovery of QCD, our theory of the strong interactions, provided a solution to the puzzle, but for decades, calculating the masses in a predictive way was impossible. Thanks to supercomputer advances, though, and the technique of Lattice QCD, we’re finally beginning to truly understand where the mass of matter comes from.

Come get the scoop, and then tune in to a live-blog of a public lecture at 7 PM ET / 4 PM PT today to get the even deeper story!

## Ask Ethan: If Mass Curves Spacetime, How Does It Un-Curve Again?

“We are taught that mass warps spacetime, and the curvature of spacetime around mass explains gravity – so that an object in orbit around Earth, for example, is actually going in a straight line through curved spacetime. Ok, that makes sense, but when mass (like the Earth) moves through spacetime and bends it, why does spacetime not stay bent? What mechanism un-warps that area of spacetime as the mass moves on?”

You’ve very likely heard that according to Einstein, matter tells spacetime how to curve, and that curved spacetime tells matter how to move. This is true, but then why doesn’t spacetime remain curved when a mass that was once there is no longer present? Does something cause space to snap back to its prior, un-bent position? As it turns out, we need to think pretty hard about General Relativity to get this right in the first place at all. It isn’t just the locations and magnitudes of masses that determine how objects move through space, but a series of subtle effects that must all be added together to get it right. When we do, we find out that uncurving this space actually results in gravitational radiation: ripples in space that have been observed and confirmed.

The deciding results are actually decades old, and were indirect evidence for gravitational waves long before LIGO. Come get the answer today!

## In A Quantum Universe, Even Mass Is Uncertain

“It’s one of the most remarkable and counterintuitive results of the quantum Universe, that every unstable particle that you make has an inherent uncertainty to the most seemingly fundamental property of all: mass. You can know what the average mass of a typical particle of any particular type, and you can measure its width, which is directly related to its mean lifetime through the Heisenberg uncertainty principle. But every time you create one new particle, there’s no way to know what its actual mass will be; all you can do is calculate the probabilities of having a varieties of masses. In order to know for sure, all you can do is measure what comes out and reconstruct what actually existed. Quantum uncertainty, first seen for position and momentum, can now be convincingly stated to extend all the way to the rest energy of a fundamental particle. In a quantum Universe, even mass itself isn’t set in stone.”

There are a few properties you can say intrinsically belong to a particle: things like mass, spin, electric charge, and certain other quantum numbers. If your particle is completely stable for all eternity, there’s no reason to question any of this. But if a particle you create, even a fundamental one, has an inherent instability and can decay, all of a sudden Heisenberg comes in to mess everything up! Suddenly, the fact that you have an uncertain lifetime means you have that pesky energy-time uncertainty, and the energy of your particle is intrinsically uncertain, too. Because E = mc^2, that means your mass is uncertain, too. And the shorter-lived your particle is, on average, the more uncertain your mass is. This means when you make a top quark, for example, it could have a mass of 165 GeV, 170 GeV, 175 GeV, 180 GeV, or anywhere in between those values. (Including some values outside of that range!)

In a quantum Universe, even mass is uncertain. Here’s the fundamental physics story of how that came to be, both theoretically and experimentally.

## The Three Meanings Of E=mc^2, Einstein’s Most Famous Equation

“Even masses at rest have an energy inherent to them. You’ve learned about all types of energies, including mechanical energy, chemical energy, electrical energy, as well as kinetic energy. These are all energies inherent to moving or reacting objects, and these forms of energy can be used to do work, such as run an engine, power a light bulb, or grind grain into flour. But even plain, old, regular mass at rest has energy inherent to it: a tremendous amount of energy. This carries with it a tremendous implication: that gravitation, which works between any two masses in the Universe in Newton’s picture, should also work based off of energy, which is equivalent to mass via E = mc^2.”

When it comes to equations, few can lay claim to being ‘the most famous one’ of all time, but right up there is Einstein’s greatest and simplest: E = mc^2. Yet it doesn’t simply state that mass and energy are equivalent, or that the relationship between them is given by the constant c^2. Sure, it says those things, but there’s also a vital physical meaning behind them. Understanding E = mc^2 has led to a variety of tremendous discoveries and breakthroughs, from nuclear power to the creation of new particles in particle accelerators. It even led directly to discovering that Newtonian gravity was theoretically unsound, ushering in the era of General Relativity, as well as the fact that any theory of gravity needs to include a gravitational redshift/blueshift.

How did it all come about? Find out the three meanings of Einstein’s most famous equation, and what it means for our Universe.

## Ask Ethan: Do Black Holes Grow Faster Than They Evaporate?

“Wondering why black holes wouldn’t be growing faster than they can evaporate due to [Hawking] radiation. If particle pairs are erupting everywhere in space, including inside [black hole] event horizons, and not all of them are annihilating one another shortly thereafter, why doesn’t a [black hole] slowly swell due to surviving particles that don’t get annihilated?”

So, you’ve got a black hole in the Universe, and you want to know what happens next. The space around it is curved due to the presence of the central mass, with greater curvature occurring closer to the center. There’s an event horizon, a location from which light cannot escape. And there’s the quantum nature of the Universe, which means that the zero-point-energy of empty space has a positive value: it’s greater than zero. Put them together, and you get some interesting consequences. One of these is Hawking radiation, where radiation is created and moves away from the black hole’s center. It occurs at a specific rate that’s dependent on the black hole’s mass. But another is black hole growth from the mass and energy that falls through the event horizon, causing that black hole to grow. At the present time, realistic black holes are all growing faster than they’re decaying, but that won’t be the case for always.

Eventually, all black holes will decay away. Come find out the story on when evaporation will win out on this week’s Ask Ethan!