“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.
“But there’s no retconning history; Einstein wasn’t right after all. While our Universe might actually have a non-zero cosmological constant, it isn’t there to stabilize our Universe. Rather, our Universe isn’t stable at all; it’s expanding from an initially hot, dense, and uniform state into the cold, sparse, and galaxy-rich cosmos we see today.
Einstein missed all of that because he insisted on a static Universe, and invented the cosmological constant to achieve that goal. Take it away, and you get a Universe that’s very much like the one we have today. The cosmological constant that affects our Universe serves to break the balance between the expansion and the other forms of matter-and-energy; it causes distant galaxies to accelerate away from us, pushing the Universe apart. Had Einstein predicted that, it would have been mind-boggling. Instead, he forced the equations to fit his (incorrect) assumptions, and missed the expanding Universe.”
When Einstein first set forth his General theory of Relativity, it included a term that no one had ever heard of before: a cosmological constant. Einstein had realized that a static Universe, the one he thought he lived in, was unstable. Gravitation would cause matter to collapse, and so something had to counteract that. His solution was to concoct a cosmological constant, something that he called his “greatest blunder” after the expanding Universe was confirmed.
“In order to get different observers to agree on how gravitation works, there can be no such thing as absolute space, absolute time, or a signal that propagates at infinite speed. Instead, space and time must both be relative for different observers, and signals can only propagate at speeds that exactly equal the speed of light (if the propagating particle is massless) or at speeds that are blow the speed of light (if the particle has mass).
In order for this to work out, though, there has to be an additional effect to cancel out the problem of a non-zero tangential acceleration, which is induced by a finite speed of gravity. This phenomenon, known as gravitational aberration, is almost exactly cancelled by the fact that General Relativity also has velocity-dependent interactions. As the Earth moves through space, for example, it feels the force from the Sun change as it changes its position, the same way a boat traveling through the ocean will come down in a different position as it gets lifted up and lowered again by a passing wave.”
According to Newtonian gravity, space and time are absolute, and the gravitational force between any two objects is defined by the distance between them. In relativity, though, different observers don’t agree on distances, which means they won’t agree on forces, accelerations, or other properties of motion from a relativistic perspective. And yet, if you use Newton’s law of gravitation to compute the orbits of Solar System objects, it gets the right answer. If you instead tried to use Newton’s laws but allowed planets to be attracted to where the Sun was in the past, you’d get the wrong answer! Does this mean that the speed of gravity is infinite?
Hardly, but you have to dive deep into relativity to understand what else is up. Thankfully, we’ve done this, and you can enjoy the answer for yourself! Here’s why the speed of gravity must equal the speed of light.
“With an average speed of 47.36 km/s, Mercury moves very slow compared to the speed of light: at 0.0158% the speed of light in a vacuum. However, it moves at this speed relentlessly, every moment of every day of every year of every century. While the effects of Special Relativity might be small on typical experimental timescales, we’ve been watching the planets move for centuries.
Einstein never thought about this; he never thought to calculate the Special Relativistic effects of Mercury’s rapid motion around the Sun, and how that might impact the precession of its perihelion. But another contemporary scientist, Henri Poincaré, decided to do the calculation for himself. When he factored in length contraction and time dilation both, he found that it led to approximately another 7-to-10 arc-seconds of orbital precession per century.“
Special Relativity was easy enough to discover in a certain sense: the Lorentz transformations, Maxwell’s equations, and the Michelson-Morley experiments had been around for decades before Einstein came along. But to go from Special Relativity to General Relativity, incorporating gravitation and the equations governing motion into the same framework, was a herculean effort. However, it was the simple identification and investigation of one puzzle, the orbit of Mercury around the Sun, that brought about Einstein’s new theory of gravity: General Relativity.
“In Einstein’s initial formulation of General Relativity way back in 1916, he mentioned the gravitational redshift (and blueshift) of light as a necessary consequence of his new theory, and the third classical test, after the precession of Mercury’s perihelion (already known at the time) and the deflection of starlight by a gravitational source (discovered during a total solar eclipse in 1919).
Although a thought experiment is an extremely powerful tool, practical experiments didn’t catch up until 1959, where the Pound-Rebka experiment finally measured a gravitational redshift/blueshift directly. Yet just by invoking the idea that energy must be conserved, and a basic understanding of particle physics and gravitational fields, we can learn that light must change its frequency in a gravitational field.”
If a photon flies through space towards Earth, it must gain energy and become bluer in nature as it approaches Earth’s surface. This idea, of a gravitational redshift or blueshift, dictates how a photon must change in energy in the presence of a gravitational field. Yet this effect, which only exists in General Relativity, could have been predicted as soon as special relativity was discovered by one simple thought experiment: to consider a particle-antiparticle pair dropped from high above the surface of the Earth, but to let the annihilation occur at varying locations.
This Is Why Time Has To Be A Dimension
“But even two different objects with the same exact three-dimensional spatial coordinates might not overlap. The reason is easy to understand if you start thinking about the chair you’re sitting in right now. It can definitely have its location accurately described by those three spatial coordinates familiar to us: x, y, and z. This chair, however, is occupied by you right now, at this exact moment in time, as opposed to yesterday, an hour ago, next week, or ten years from now.
In order to completely describe an event in spacetime, you need to know more than just where it occurs, but also when it occurs. In addition to x, y, and z, you also need a time coordinate: t. Although this might seem obvious, it didn’t play a large role in physics until the development of Einstein’s relativity, when physicists started thinking about the issue of simultaneity.”
When you describe where you are in the Universe, you typically think of the coordinates you’d need to give to describe your location. This includes an x, y, and z-direction: the three spatial coordinates corresponding to where we live in our three spatial dimensions. But this doesn’t fully tell you everything you’d need to know, because your location is defined not only by your spatial location but when you’re located there: you need a time coordinate, too. If we take a deep look into the relationship between space and time, first put forth by Einstein over a century ago, we’d find that it isn’t even enough to put in an additional coordinate. Time is more than a separate value; it’s every bit as much a dimension as any of the three spatial dimensions.
The 5 Lessons Everyone Should Learn From Einstein’s Most Famous Equation: E = mc^2
“3.) Einstein’s E = mc2 is responsible for why the Sun (like any star) shines. Inside the core of our Sun, where the temperatures rise over a critical temperature of 4,000,000 K (up to nearly four times as large), the nuclear reactions powering our star take place. Protons are fused together under such extreme conditions that they can form a deuteron — a bound state of a proton and neutron — while emitting a positron and a neutrino to conserve energy.
Additional protons and deuterons can then bombard the newly formed particle, fusing these nuclei in a chain reaction until helium-4, with two protons and two neutrons, is created. This process occurs naturally in all main-sequence stars, and is where the Sun gets its energy from.”
Even if you don’t know any physics at all, there’s a good chance that there’s at least one equation you know of: Einstein’s E = mc^2. It tells us that energy and mass are equivalent quantities, and that c^2 (the speed of light squared) is the constant that enables you to convert from one to the other. Along for the ride, we learn some amazing things, including that mass is not conserved, that bound objects have less mass than the same objects when they’re not bound, and that you can spontaneously create matter/antimatter pairs if you have enough available energy under the right conditions.
“The most interesting part of this result is that it clearly demonstrates the purely General Relativistic effect of gravitational redshift. The observations of S0-2 showcase an exact agreement with Einstein’s predictions, within the measurement uncertainties. When Einstein first conceived of General Relativity, he did so conceptually: with the idea that acceleration and gravitation were indistinguishable to an observer.
With the validation of Einstein’s predictions for the orbit of this star around the galactic center’s black hole, scientists have affirmed the equivalence principle, thereby ruling out or constraining alternative theories of gravity that violate this cornerstone of Einsteinian gravity. Gravitational redshifts have never been measured in environments where gravity is this strong, marking another first and another victory for Einstein. Even in the strongest environment ever probed, the predictions of General Relativity have yet to lead us astray.”
If you want to test Einstein’s General Relativity, you’ll want to look for an effect that it predicts that’s unique, and you’ll want to look for it in the strongest-field regime possible. Well, there’s a black hole at the center of our galaxy with 4 million times the mass of the Sun, and there’s a star (S0-2) that passes closer to it, during closest approach, than any other. In May of 2018, it made this closest approach, coming within 18 billion km (about twice the diameter of Neptune’s orbit) of the black hole, and zipping around at 2.7% the speed of light.