This One Puzzle Brought Physicists From Special To General Relativity
“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.
What were the key steps, and how did they help revolutionize our view of the Universe? The history is rich and spectacular, and holds a lesson for those on the frontiers of physics today.
This One Thought Experiment Shows Why Special Relativity Isn’t The Full Story
“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.
If you considered that, you’d immediately realize how special relativity was insufficient for describing our Universe! Come learn how to reason it out for yourself today!
Ask Ethan: Where Is The Center Of The Universe?
“I am wondering how there isn’t a center of the universe and how the cosmic background radiation is [equally] far away everywhere we look. It seems to me that when the universe expands… there should be a place where it started expanding.”
Ah, the old center of the Universe question. If the Big Bang happened a long time ago, and we see galaxies moving away from us faster and faster the farther away they are, then where did the Big Bang happen? Where did the expansion start?
It seems like such a simple question, but it turns out this is the wrong question to be asking. The way space and the expanding Universe works is very different from the picture most of us have in our heads, which is much more like an explosion than like an expansion. Yet there’s a very large suite of evidence that points us away from an explosion.
Instead of asking *where* the Big Bang occurred, we should be asking *when* the Big Bang occurred. It makes a lot more sense when you think about it in those terms. Come and find out why.
General Relativity Rules: Einstein Victorious In Unprecedented Gravitational Redshift Test
“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.
Did Einstein’s predictions for gravitational redshift come out right? You bet they did: 5-sigma, baby! Come get the full, amazing story here!
Ask Ethan: Can We Really Get A Universe From Nothing?
“One concept bothers me. Perhaps you can help. I see it in used many places, but never really explained. “A universe from Nothing” and the concept of negative gravity. As I learned my Newtonian physics, you could put the zero point of the gravitational potential anywhere, only differences mattered. However Newtonian physics never deals with situations where matter is created… Can you help solidify this for me, preferably on [a] conceptual level, maybe with a little calculation detail?”
You’ve very likely heard two counterintuitive things about the Universe before. One of them is that the Universe arose from nothing, and this defies our intuition about how it’s impossible to get something from nothing. The second is that we have four fundamental forces in the Universe: gravity, electromagnetism, and the strong and weak nuclear forces. So how, then, do we account for the fact that the Universe’s expansion is accelerating? Isn’t this clearly evidence for a fifth force, one with negative gravity?
Guess what? These two counterintuitive aspects of reality are related. If you understand them both, you’re one step closer to making sense of the Universe.
Ask Ethan: Why Do Gravitational Waves Travel Exactly At The Speed Of Light?
We know that the speed of electromagnetic radiation can be derived from Maxwell’s equation[s] in a vacuum. What equations (similar to Maxwell’s – perhaps?) offer a mathematical proof that Gravity Waves must travel [at the] speed of light?
If you were to somehow make the Sun disappear, you would still see its emitted light for 8 minutes and 20 seconds: the amount of time it takes light to travel from the Sun to the Earth across 150,000,000 km of space. But what about gravitation? Would the Earth continue to orbit where the Sun was for that same 8 minutes and 20 seconds, or would it fly off in a straight line immediately?
There are two ways to look at this puzzle: theoretically and experimentally/observationally. From a theoretical point of view, this represents one of the most profound differences from Newton’s gravitation to Einstein’s, and demonstrates what a revolutionary leap General Relativity was. Observationally, we only had indirect measurements until 2017, where we determined the speed of gravity and the speed of light were equal to 15 significant digits!
Gravitational waves do travel at the speed of light, which equals the speed of gravity to a better precision than ever. Here’s how we know.
What Is The Smallest Possible Distance In The Universe?
“At present, there is no way to predict what’s going to happen on distance scales that are smaller than about 10-35 meters, nor on timescales that are smaller than about 10-43 seconds. These values are set by the fundamental constants that govern our Universe. In the context of General Relativity and quantum physics, we can go no farther than these limits without getting nonsense out of our equations in return for our troubles.
It may yet be the case that a quantum theory of gravity will reveal properties of our Universe beyond these limits, or that some fundamental paradigm shifts concerning the nature of space and time could show us a new path forward. If we base our calculations on what we know today, however, there’s no way to go below the Planck scale in terms of distance or time. There may be a revolution coming on this front, but the signposts have yet to show us where it will occur.”
If you went down to smaller and smaller distance scales, you might imagine that you’ll start to see the Universe more clearly and in higher resolution. You’ll be able to hone in on the fundamental properties of nature, and glean more information the deeper you go. This is true, but only up to a point. Beyond that, you start running into the inescapable quantum rules that govern the Universe, and that means there’s a fundamental scale at which our best laws of physics cannot be trusted any longer.
That scale is the Planck scale, and for distances, it corresponds to about 10^-35 meters. It really is a problem for physics, and it’s high time you understood why.
This Is How, 100 Years Ago, A Solar Eclipse Proved Einstein Right And Newton Wrong
“Today, May 29, 2019, marks the 100th anniversary of the day, the event, and the expedition that validated Einstein’s General Relativity as humanity’s leading theory of how gravitation works. Newton’s laws are still incredibly useful, but only as an approximation to Einstein’s theory with a limited range of validity.
General Relativity, meanwhile, has gone on to successfully predict everything from frame-dragging to gravitational waves, and still has yet to encounter an observation that conflicts with its predictions. Today marks a full century of General Relativity’s demonstrated validity, with not even a hint of how it might someday break down. Although we certainly don’t know everything about the Universe, including what a quantum theory of gravity might actually be like, today is a day for celebrating what we do know. 100 years after our first critical test, our best theory of gravity still shows no signs of slowing down.”
Happy 100th anniversary to the critical observations that demonstrated Einstein was right and Newton was wrong when it came to gravitation. There’s an incredible story to how this all occurred, and you won’t want to miss a drop of what it all means.
It took one of the longest solar eclipses in modern history for us to get there, but oh, was it worth it. Come find out why and how for yourself.
This Is Why Einstein Knew That Gravity Must Bend Light
“This is the basis of Einstein’s equivalence principle: the idea that an observer cannot distinguish between an acceleration caused by gravitational or inertial (thrust) effects. In the extreme case, jumping off of a building, in the absence of air resistance, would feel the same as being completely weightless.
The astronauts aboard the International Space Station, for example, experience complete weightlessness, even though the Earth is accelerating them towards its center with about 90% of the force we experience here on its surface. Einstein later referred to this realization, which struck him in 1911, as his happiest thought. It was this idea that would lead him, after four years of further development, to publish the General theory of Relativity.”
Imagine that you were inside a closed-off elevator, and that light came in through a tiny hole from the outside. If your elevator were accelerating, you’d see that light follow a curved, bent trajectory, as your changing motion would cause the path that light took to appear that way. But from inside the elevator, you have no way of knowing whether that acceleration was due to thrust, which is an inertial effect, or gravitation. An elevator accelerating at a constant 9.8 m/s^2 from a firing thruster would be indistinguishable from one stationary on Earth’s surface, where the acceleration due to gravity is 9.8 m/s^2. If they’re indistinguishable, then gravity must bend light, the same way any other acceleration does.
This is why, nearly a century ago, Einstein never doubted what the results of the experiment that tested his theory for the first time would be. Come learn why Einstein knew that gravity must bend light!
Ask Ethan: Why Don’t Gravitational Waves Get Weaker Like The Gravitational Force Does?
“You have stated:
1) The strength of gravity varies with the square of the distance.
2) The strength of gravity waves, as detected by LIGO, varies directly with the distance.
So the question is, how can those two be the same thing?”
Here’s a puzzling fact for you: if you get ten times as far away from a source of gravitational waves, how much less would you expect the signal to be in your gravitational wave detector? For light, brightness falls off as the inverse of the distance squared: it would be 1/100th as bright. For the gravitational force, it also falls off as the inverse of distance squared: 1/100th the force. But for gravitational waves, the signal strength only drops as the inverse of the distance; the signal would be 1/10th the original strength.
Why is this? Believe it or not, it’s mandated by physics! Come find out the deep truth behind why on this special* edition of Ask Ethan!
(* – special because I had to derive this myself; nobody gives the full explanation anywhere I can find!)