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.
“We talk about energy and we know that there are various forms of energy (PE, KE …) and you can do work with it, and it has to be conserved, and energy and matter are interchangeable, etc. But what is energy?”
Energy is something that touches all aspects of our lives. Yet if you try defining it, you’ll wind up tying yourself in knots. It’s not something we can isolate in a laboratory, but rather is a property inherent to all matter, antimatter, and radiation particles. It can only be defined relative to other particles, rather than absolutely. The definition we use in physics, that it’s the ability to do work, is over 300 years old and is rather circular.
A little over a century ago, the esteemed physicist Henri Poincaré noted the following, “science is built up of facts, as a house is built of stones; but an accumulation of facts is no more a science than a heap of stones is a house.” We speak all the time of what energy can do, how it’s used, where it appears and in what quantities, and how to accomplish a myriad of tasks with it. But a fundamental, universal definition?
Our Sun Is Lighter Than Ever, And The Problem Is Getting Worse
“As time goes on, the amount of mass lost by the Sun will increase, particularly as it enters the giant phase of its life. But even at this relatively steady rate, the growth of helium in the Sun’s core means that we will heat up here on planet Earth. After about 1-to-2 billion years, the Sun will be burning hot enough that Earth’s oceans will boil away entirely, making liquid water impossible on the surface of our planet. As the Sun gets lighter and lighter, it will counterintuitively get hotter and hotter. Our planet has already used up approximately three-quarters of the time we have where Earth is habitable. As the Sun continues to lose mass, humanity and all life on Earth approaches its inevitable fate. Let’s make these last billion-or-so years count.”
As the Sun burns through its nuclear fuel, it loses mass in not one, but two ways. Sure, in its core, it’s fusing hydrogen in a chain reaction into helium, with the reduction in mass corresponding to a gain in energy: the energy that powers the Sun and gives life to all the planets. But it also blows off particles, including electrons, protons, and atomic nuclei, in a phenomenon called the solar wind. Even though more massive stars burn hotter and brighter than less massive ones, the Sun, perhaps paradoxically, will increase in temperature and luminosity as it loses mass to these two processes. The Sun is getting lighter and lighter, and the problem of its increasing energy output will eventually destroy all life on Earth.
You might have seen animations like this that show an electron undergoing a transition from a lower energy to a higher energy state and vice versa like so:
There is something really important about this image that one must understand clearly.
The diagram represents the transition in energy of an electron BUT this does not mean that the electron
is magically jumping from one position and respawning at another
The electron’s position is NOT doing this i
If you want to know about the probability of finding an electron around the nucleus at a certain energy level, you look at its wavefunction and not at the energy diagram.
Here is the wavefunction of a hydrogen atom and each stationary state defines a specific energy
level of the atom.
This might not sound like a big deal but one might be surprised to know that there are a lot of people who think that the electron is magically transported from energy level to another which most certainly is not true.
Ask Ethan: Can A Laser Really Rip Apart Empty Space?
“Science Magazine recently reported that Chinese physicists will start building a 100-petawatt(!!!) laser this year. Can you please explain how they plan to achieve this, and what unique phenomenon this will help physicists explore? Such as, what exactly is “breaking the vacuum?"”
As we strive for the greatest frontiers in physics, that always means pushing the limits. To that extra digit closer to absolute zero, the extra factor in high energy particles, the extra depth into the distant Universe. Or, in the case of laser physics, to that extra intensity: power focused into an extremely narrow space. There are three things you need to up that to the maximum amount possible:
-the most extreme amount of energy, -in the shortest-span of a pulse, -focused on the narrowest area possible.
If you can make it all the way up to a high enough energy, you should be able to rip electron/positron pairs out of the quantum vacuum (empty space) itself. Colloquially, people have started calling this “breaking the quantum vacuum,” but in reality, nothing gets broken.
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.
No, Melting Quarks Will Never Work As An Energy Source
“In order to create a particle with a heavy quark (strange, charm, bottom, etc.) in it, you have to collide other particles together at extremely high energies: enough to make equal amounts of matter and antimatter. Assuming you then make the two baryons you need (two charmed or two bottomed baryons, for instance), you must then have them interact under the right conditions — fast and energetic, but not too fast or too energetic — to cause that fusion reaction. And then, at last, you get that ~3-4% energy gain out.
But it cost you over 100% to make these particles in the first place! They’re also incredibly unstable, meaning they’ll decay to lighter particles on incredibly short timescales: a nanosecond or less. And, finally, when they do decay, you get 100% of your energy back, in the form of new particles and their kinetic energies. In other words, you don’t get any net energy out; you simply get out what you put in, but in a lot of different, hard-to-harness ways.”
Nuclear fusion is often hailed as the future of energy, as it converts more mass into energy via Einstein’s E = mc^2 than any other reaction we’ve ever produced in large quantities. But even though the fusion of hydrogen into helium causes such a large energy release, it’s still less than 1% of the mass you begin with. On the other hand, a new set of simulations involving a recently discovered particle indicates that, by fusing charmed baryons with one another, you can produce a doubly-charmed baryon and get up to 4% of your mass converted into energy. While many are touting this as a potential game-changer, the reality is much more sobering. Nuclear fusion is promising not just for the large yield, but because its reactants are abundant and stable, because the energy outputted is easy to harness, and the reaction is controllable. “Melting quarks” offer none of these, and as such, will never work as an energy source.
In this amazing work by the Fluids group at University of Twente, a drop’s response to a focused laser pulse has been analyzed in slow motion. The drop reacts to the energy imparted by the laser in many different ways, such as
vaporization or even plasma generation.
We will believe in the newton’s law of motion and for a particle whose force is dependent only on its position it states that:
Now let’s take a closer look at this:
On the LHS you have something that is dependent on x and t, but irrespective of all that dependency, this quantity ( mx’’ – F(x) ) is ALWAYS 0.
Therefore we can define a quantity (or function) called Energy which is invariant with time i.e:
This implies that if you take any system doing any sort of crazy motion, there is always this quantity that will always remain constant with respect to time irrespective of all that craziness. That quantity is Energy !
“On Earth, we’re currently burning more than ten billion tonnes of fossil fuels per year worldwide, supplying some 80% of our energy needs through those methods. Unfortunately, air-and-water pollution, along with vast atmospheric changes, have arisen from this. Renewable sources of energy are one potential (although, arguably only a partial) solution, but nuclear power — if it can be done safely — could solve our fossil fuel problem today, with current technology alone. With the amount of fuel it presently takes to power the world, the cost of doing nothing is not only far too high, but will be borne by humanity for generations to come.”
Arguably the greatest advance of humanity
and the cause of the greatest increase in our quality of life — in the past few centuries has been the widespread availability of electrical energy. It powers our homes, our industries, our automobiles, our places of business and more. Our world runs on energy, with the world using upwards of 155,000 TeraWatt-hours annually. That’s a huge amount of energy, and it requires a huge amount of fuel. But must it? If we were to power the world entirely with coal, oil, or natural gas, it would take billions of tonnes of fuel each year to make it happen. If we switched to nuclear, those “billions” drop to thousands. And if we could switch to nuclear fusion or even antimatter, the amount of fuel plummets even further. Looking at the numbers, it makes no sense not to switch. Is it only our fears of nuclear disaster that prevents us from using our current technology to better the world for humanity for generations to come?