Category: relativity

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!

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This Is Why Black Holes Must Spin At Almost The Speed Of Light

“Realistically, we can’t measure the frame-dragging of space itself. But we can measure the frame-dragging effects on matter that exist within that space, and for black holes, that means looking at the accretion disks and accretion flows around these black holes. Perhaps paradoxically, the smallest mass black holes, which have the smallest event horizons, actually have the largest amounts of spatial curvature near their horizons.

You might think, therefore, that they’d make the best laboratories for testing these frame dragging effects. But nature surprised us on that front: a supermassive black hole at the center of galaxy NGC 1365 has had the radiation emitted from the volume outside of it detected and measured, revealing its speed. Even at these large distances, the material spins at 84% the speed of light. If you insist that angular momentum be conserved, it couldn’t have turned out any other way.”

Have you ever wondered how black holes, ranging from a few times our Sun’s mass up to billions of times as massive, can spin so rapidly? Most black holes, as far as we can tell, are spinning very close to the speed of light: the ultimate speed limit of the Universe. Yet most stars, like our Sun, rotate extremely slowly: just once over a period of many days (or even longer).

So how does a slowly-rotating star, which goes supernova and forms a black hole, give rise to an object spinning near the cosmic speed limit? Find out today.

How To Prove Einstein’s Relativity In The Palm Of Your Hand

“If you ever doubted relativity, it’s hard to fault you: the theory itself seems so counterintuitive, and its effects are thoroughly outside the realm of our everyday experience. But there is an experimental test you can perform right at home, cheaply and with just a single day’s efforts, that allow you see the effects for yourself.

You can build a cloud chamber, and if you do, you will see those muons. If you installed a magnetic field, you’d see those muon tracks curve according to their charge-to-mass ratio: you’d immediately know they weren’t electrons. On rare occasion, you’d even see a muon decaying in mid-air. And, finally, if you measured their energies, you’d find that they were moving ultra-relativistically, at 99.999%+ the speed of light. If not for relativity, you wouldn’t see a single muon at all.

Time dilation and length contraction are real, and the fact that muons survive, from cosmic ray showers all the way down to Earth, prove it beyond a shadow of a doubt.”

Hold out the palm of your hand and turn it upwards to face the sky. Congratulations: right now, approximately 1 muon per second is passing through your hand! You might not be a very sensitive particle detector, but you can build one, in the form of a cloud chamber, for less than $100 with off-the-shelf materials. If you did, you’d be able to see these muons individually. With a little extra work, and a bit of physics, you can prove to yourself that without Einstein’s relativity, these muons wouldn’t exist!

And yet, they’re real, you can observe them yourself, and they can help you prove the truth of relativity itself. Come find out how to do it for yourself!

Ask Ethan: What’s It Like When You Fall Into A Black Hole?

“[W]hat is it like to be/fall inside a rotating black hole? This is not observable, but calculable… I have talked with various people who have done these calculations, but I am getting old and keep forgetting things.”

I get a lot of questions that people submit for Ask Ethan, but only rarely do they come to me from other scientists who tower above me in the field. This week’s question, from Event Horizon Telescope scientist extraordinaire Heino Falcke, asks me to help him visualize what it would look like if you fell into a black hole. Not just any black hole, mind you, but a realistic, rotating black hole. There’s really only one person on Earth who understands this well enough: Andrew Hamilton, who has devoted the last 15 years of his life to figuring out what it looks like and what it means when this actually happens.

So what did I do? I went and met Andrew, interviewed him, read his papers, and used his simulations to give everyone the best answer I could. I hope you love it, and I hope (even moreso) that I got it right!

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!

Could All Our Scientific Knowledge Come Tumbling Down Like A House Of Cards?

“Now, think about what would be required to do today to tear down one of our leading scientific theories. It’s not as complicated as you might imagine: all it would take is a single observation of any phenomenon that contradicted the Big Bang’s predictions. Within the context of General Relativity, if you could find a theoretical consequence of the Big Bang that didn’t match up with our observations, we’d truly be in store for a revolution.

But here’s the important part: that won’t mean that everything about the Big Bang is wrong. General Relativity didn’t mean everything about Newtonian gravity was wrong; it simply exposed the limit of where and how Newtonian gravity was successful. It will still be accurate to describe the Universe as having originated from a hot, dense, expanding state; it will still be accurate to describe our observable Universe as being many billions of years old (but not infinite in age); it will still be accurate to talk about the first stars and galaxies, the first neutral atoms, and the first stable atomic nuclei.”

There are a great many people out there who absolutely cannot wait for the day where one of our greatest scientific theories is demonstrated to be wrong. Where an experiment or observation comes in that cannot be reconciled with our leading ideas of how the Universe works. At last, perhaps an unintuitive part of our existence, like relativity or quantum mechanics, might be replaced with something that’s a closer approximation of our actual reality. But that won’t invalidate what we already know; it will merely extend it. 

Scientific revolutions aren’t what most people think, but they are going to come, eventually. Here’s what the revolution will actually look like.

Could All Our Scientific Knowledge Come Tumbling Down Like A House Of Cards?

“Now, think about what would be required to do today to tear down one of our leading scientific theories. It’s not as complicated as you might imagine: all it would take is a single observation of any phenomenon that contradicted the Big Bang’s predictions. Within the context of General Relativity, if you could find a theoretical consequence of the Big Bang that didn’t match up with our observations, we’d truly be in store for a revolution.

But here’s the important part: that won’t mean that everything about the Big Bang is wrong. General Relativity didn’t mean everything about Newtonian gravity was wrong; it simply exposed the limit of where and how Newtonian gravity was successful. It will still be accurate to describe the Universe as having originated from a hot, dense, expanding state; it will still be accurate to describe our observable Universe as being many billions of years old (but not infinite in age); it will still be accurate to talk about the first stars and galaxies, the first neutral atoms, and the first stable atomic nuclei.”

There are a great many people out there who absolutely cannot wait for the day where one of our greatest scientific theories is demonstrated to be wrong. Where an experiment or observation comes in that cannot be reconciled with our leading ideas of how the Universe works. At last, perhaps an unintuitive part of our existence, like relativity or quantum mechanics, might be replaced with something that’s a closer approximation of our actual reality. But that won’t invalidate what we already know; it will merely extend it. 

Scientific revolutions aren’t what most people think, but they are going to come, eventually. Here’s what the revolution will actually look like.

How Far Could A Human Travel In A Constantly-Accelerating Rocket Ship?

“Imagine that we could constantly accelerate at the same rate as Earth’s gravitational pull, 9.8 m/s2, indefinitely. While you’d initially speed up, you’ll rapidly approach the speed of light.

Owing to Einstein’s Special Relativity, time will dilate and lengths will contract. As you continue to accelerate, the distances and travel times to faraway destinations will plummet.

At the halfway mark, simply reverse your thrust to accelerate in the opposite direction for the remaining journey.

If you wanted to travel to a star that was 100 light-years away, you might think it would take you at least 100 years to get there. That might be true from the perspective of someone who remains on Earth, but for an astronaut who journeyed there at close to the speed of light, Einstein’s Special Relativity tells you that it would take far less than a century of travel. In fact, if you could accelerate at a constant rate, you could pretty much reach anywhere you wanted within 15 billion light-years of us within a human lifetime.

I even went and did the math for you here. Don’t be afraid to see how far a human could travel if we had the dream technology to get us there!