Category: special 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.

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!

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!

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!

Ask Ethan: How Does A Photon Experience The Universe?

“Relativity says all inertial frames of reference are equally valid and true. From a photon’s point of view the entire cosmos is flattened into a two-dimensional timeless plane. Imagine I place an apple on my desk, then a while later replace it with a banana. How does the photon perceive my desk to be, when it’s all flattened into a plane without any sense of time?”

At rest, everything looks like you expect: clocks run at the same rate everywhere you look, distances are exactly as they appear, and material objects possess the color you know them to intrinsically possess. Close to the speed of light, however, all of that changes. Clocks run slower as objects move closer to the speed of light relative to you. Distances appear contracted along the direction of relative motion, including for physical objects and the fields they generate. And colors appear either redshifted or blueshifted, depending on how quickly an object moves either away from your or towards you, respectively. These effects get more and more severe the closer objects move, relative to you, to the speed of light.

But what if you reached the speed of light? What would the Universe look like from a photon’s (or any massless particle’s) point of view? The answer is most definitely not what you expect! Find out on this edition of Ask Ethan.

How Come Cosmic Inflation Doesn’t Break The Speed Of Light?

“In an inflationary Universe, any two particles, beyond a tiny fraction of a second, will see the other one recede from them at speeds appearing to be faster-than-light. But the reason for this isn’t because the particles themselves are moving, but rather because the space between them is expanding. Once the particles are no longer at the same location in both space and time, they can start to experience the general relativistic effects of an expanding Universe, which — during inflation — quickly dominates the special relativistic effects of their individual motions. It’s only when we forget about general relativity and the expansion of space, and instead attribute the entirety of a distant particle’s motion to special relativity, that we trick ourselves into believing it travels faster-than-light. The Universe itself, however, is not static. Realizing that is easy. Understanding how that works is the hard part.”

It’s true that nothing can move faster than the cosmic speed limit, the speed of light, and that no two particles can move faster than light relative to one another. So how, then, do you explain the fact that during inflation, two particles that begin a subatomic distance away from one another are, after just a tiny fraction of a second, are then billions of light years apart? The answer is because special relativity only applies, strictly, to particles that occupy the same location as one another in both space and time. If they’re separated, then the Universe is under no obligation to be static, and space is free to expand and/or contract. You cannot figure your apparent motion with special relativity alone, but need to factor in the effects of general relativity as well. And that’s where things get really weird.

If you can understand it, however, the notion of how objects appear to recede faster than light suddenly starts to make sense. Come learn how inflation doesn’t break the speed of light after all!

Comments of the Week #171: From light’s speed to proving Einstein right

“Science, just to be extremely clear, does not rely on one experiment to settle the matter, and then never perform the experiment again. No; we are constantly checking our results, gathering more data to improved precision, and looking for flaws in our predictions at the 10% level, then 1%, then 0.1%, then 0.01%, etc.

The story of scientific investigation is a story of ever-increasing precision and ever decreasing uncertainty, and one that I value and will keep telling, no matter what some (or many, or even most, sometimes) of the commenters here or elsewhere say. The scientific truth is too important, even if (and when) public opinion is against it. It’s why I’m here, and it’s what I’ve been doing — somewhat successfully, mind you — for over nine years now. In fact, when January rolls around, that will mark 10 years since the inception of Starts With A Bang. That we’re all here, thinking about the Universe and how it all works, is something worth celebrating, even when it’s difficult.”

Some of you caught me at the Star Trek Las Vegas convention this year, where thousands of Star Trek fans gathered and a tremendous time was had by practically everyone. But even while away and traveling, the science doesn’t stop, and I couldn’t help myself from sharing another dose of bonus science with you all.

Check out our comments of the week and enjoy!

Ask Ethan: Does Light Always Move At The Same Speed?

“Does light always move at the same speed? If it is slowed down by something, will is stay slower after it is no longer being slowed down? Will [it] speed back up to the speed of light?”

Throughout the entire Universe, there’s a fundamental law that governs the motions of all particles: Einstein’s relativity. It states that all particles with mass can never attain the speed of light, no matter how much energy you put into it. Additionally, all massless particles only move at the speed of light, no matter what you do to either them or to the device/person observing them. No matter what reference frame you’re in, the speed of light in a vacuum is a constant. But light isn’t always in a vacuum!  From air to quartz to acrylic to glass to many other media, light can pass through transparent material, and when it does, it slows down. Not only that, but light of different energy slows down by different amounts. In what ways is the speed of light always the same, and in what ways can it change?

And most importantly, what do the known properties of light mean for the rest of the Universe? Find out on this edition of Ask Ethan!

The coolest physics thing that I know keeps changing over time. But here is one that is extremely fascinating ( and also exaggerated for the effect ; but true! ):

Person living at the top of a skyscraper experiences time faster than one at the bottom

It is a known fact that the higher you are in the earth’s ** atmosphere, the lesser the effect of gravity is.

But the lesser the effect of gravity is, the faster the time ticks.

image

By how much you ask? Even if you live on the top floor of the Burj Khalifa  your entire life, you would have aged more only by a few milliseconds than your friends at the bottom. 

( Sure, doesn’t seem like much, but hell would break loose if we don’t consider this on the bigger scale of things )

This is known as Gravitational time dilation and is at the foundations of General Theory of Relativity. (More about this in an upcoming post)

Have a great day and thanks for asking!

EDIT: ** Lets just say hypothetically the earth is not spinning( just to ignore special relativistic effects) and we are looking at only the effects of height.

The coolest thing that I know keeps changing over time. But here is one thing that is extremely fascinating ( and also exaggerated for the effect ; but true! ):

Person living at the top of a skyscraper experiences time faster than one at the bottom

It is a known fact that the higher you are in the earth’s atmosphere, the lesser the effect of gravity is.

But the lesser the effect of gravity is, the faster the time ticks.

image

By how much you ask? Even if you live on the top floor of the Burj Khalifa  your entire life, you would have aged more only by a few milliseconds than your friends at the bottom.

This is known as Gravitational time dilation and is at the foundations of General Theory of Relativity. (More about this in an upcoming post)

Have a great day!