Tag Archives: einstein

Why Can't We Travel Faster Than Light?

James writes: I know light is the fastest thing in the universe, but why can’t anything else go that fast? Is it just that we haven’t built a ship fast enough yet?

James, I am no physicist. I believe I understand the reason for “lightspeed” being the cosmic speed limit, but I could be wrong. Here goes my best shot:

The hard part, to me, is why light travels at a constant velocity – and why that velocity is 299,792,458 meters per second (in a vacuum; going through air or other media slows it down). I have no idea why light travels at exactly that speed, instead of going faster or slower. But Albert Einstein’s famous relativity equation – E=mc² – explains why we cannot build a ship that goes that fast.

In the relativity equation, “E” stands for the energy of an object. The “m” on the right side of the equation is the object’s mass. And “c” means “constant”: the velocity of light. In math, a constant is a value that does not change. Variables are properties that can change. “E” is a variable, because the energy an object has can change. For example, if a karate master moves his fist very slowly towards a wooden board, he might push it out of the way, but the board will not break. But if the karate master throws a fast punch at the board, his fist will break through it easily. Why? Because his fist had much more energy when it was moving fast. Energy increases with speed; this is why cars (and passengers) are damaged a lot worse if they crash at high speeds than if they crash when moving slowly.

An equation is a statement that both sides are equal, like 3+2=5. The left side equals the right side. If we add to the left side, we must add the same value to the right side for the equation to be true: 3+2+1=5+1. Einstein’s relativity equation states that an object’s energy is equal to its mass multiplied by the square of a constant, “c”. The constant does not change, so if “E” changes, “m” must also change. In effect, an object moving very quickly becomes more massive.

More mass means that it takes more energy to accelerate. This is why a Ferrari can accelerate faster than a dump truck, even if the dump truck has more power. So if we build a starship and move it faster and faster, its mass will begin to increase. The more massive it is, the more energy it takes to make it go faster. As we approach the speed of light, the mass becomes so great that it would take an infinite amount of energy to make it go as fast as light. Since we do not have an infinite amount of energy, we cannot reach lightspeed.

That is as much as I understand about your question, James. I hope it helps. If there are any physicists in the audience who can explain it better, or correct any mistakes I have made, I will appreciate it.

Stay curious, my friends!

If You Fell Through a Black Hole, Where Would You Go?

Black holes are definitely some of the most mysterious things in the universe. A hole that looks the same from all sides is quite a puzzle!

If I were to go up into the attic and saw a circular hole around me, I would fall down into the living room. Likewise, if there were a hole in my living room floor, I might keep falling down into the basement. This is easy to imagine. It is not too much harder to picture gravity reversing, so that I would fall up from the basement through the hole in the living room floor, ending up back on the couch where I started. In each of the three places I had been – the living room, the attic, and the basement – I could look through (or fall through) a hole to another space.

Before I start talking about black holes, I should say that everything we know about them is based on math. Until 1971, there was no observed evidence that they even existed. Today, there are many known black holes, but we will never see one of them directly, so all our knowledge of black holes is based on measurements of things happening in space that cannot be explained without the math model of a black hole. Most of my readers are not math professors, so you may be wondering what I mean by “math model”. If I tell you that I am thinking of an object that is 5 cm long, 5 cm wide, and 5 cm tall, you could guess that it is a cube. But what if it is a sphere? All you really know is how big it is. Now, if I tell you that the object has six square sides, you know it is a cube. You can picture it in your mind. There is no real cube, but your image of it is based on numbers I gave you. The cube in your mind is a math model.

Remember the holes in my ceiling and floor? Now imagine a hole in the middle of empty space. It is not a hole in a wall or anything else; it is a hole in space. You might be able to see the hole if you got close enough, but you would not be able to see through it. If you moved in a big circle around the hole, it would look the same from any angle! If you were to throw an object – like a marshmallow – through a hole in a wall, you could look over the wall (or through the hole) and see the marshmallow on the other side. But if you threw a marshmallow into a black hole, there is no other side. It is gone forever!

How can this be? About 250 years ago, a scientist named John Michell imagined a thing nobody had thought of before.

(Scientists of his time already knew that objects had to reach a certain speed to escape the gravity of any planet or star; this speed is called the “escape velocity”. The more massive a planet or star is, the faster an object has to move to escape out into space. This is why a rocket can get to the moon, but a bullet from a gun cannot. It is not fast enough. A rocket fast enough to escape the Earth’s gravity would still not be able to escape the Sun, because the Sun is so much more massive than the Earth. You would need a much faster rocket. On the other hand, if you have seen pictures of the Apollo missions to the Moon, the rocket they used to get off the Moon was not very fast at all. It didn’t have to be; the Moon is much less massive than the Earth, so its gravity is much weaker.)

John Michell imagined a star so massive that even light would not have enough speed to escape its gravity. If the light from the star could not escape out into space, then nobody would be able to see it! John Michell called his imaginary star a “dark star”. Later scientists, including Albert Einstein and Karl Schwarzschild, made math models of dark stars to describe the behavior of light and of objects that got close to them. It was a scary but fascinating idea! In 1964, a journalist named Ann Ewing wrote a report about these math models. The report was called “Black Holes In Space”. Since then, people have been calling them “black holes”.

Even though many scientists made lots of math models of black holes, nobody had ever seen one. They are, after all, invisible! Between 1971 and 1973, a team of astronomers watched a giant star far out in space. It behaved unlike any other star. By 1973, they knew from their measurements that the star had a black hole next to it, just like you knew (after getting enough information) that the object I was describing was a cube. The star system fit the math model: it could only be a black hole!

That first observed black hole is called Cygnus X-1. Since then, we have observed many other black holes. Although they are invisible, we know they are black holes from observing what happens around them. If it fits the math model, it must be a black hole.

So what is the answer to the question we started with? If you fell into a black hole, where would you go? By now, you know that black holes are not really holes at all. They are objects with such strong gravity that nothing, not even light, can escape them, which is why they are perfectly dark. Because its gravity is so strong, anything that falls into a black hole is crushed into zero volume. Since one of the properties of matter is that it takes up space, objects falling into a black hole would really not even be objects anymore. The center of a black hole is called a “singularity”, and the math model for a singularity seems to break the rules for what we know about the universe.

Black holes may always be one of the universe’s mysteries!

Einstein and da Vinci

This morning on the way to school, my son asked me, “Dad, was Einstein the new da Vinci?” Mind you, this is at about ten to seven in the morning and my second cup of coffee is still in the travel mug. But the boy wants to know; what can I do?

“OK, let’s see: Einstein and da Vinci, each one a transcendental genius, each a household name. Both names are used ad nauseam by marketers of educational products.”

“What’s ad nauseam?”

“”With disgusting persistence. They were both intensely curious men; Einstein said so himself on numerous occasions, and Leonardo’s notes and sketches are proof that he was interested in pretty much everything. They were both mathematicians. So much for similarities. Einstein was much more famous in his own time than Leonardo was, probably because of communications technology like newspapers and radio. Einstein’s theory of relativity had an immediate, major, and permanent effect on the world: it was the beginning of the Nuclear Age. Leonardo had plenty of great ideas for inventions – the helicopter, the battle tank, solar power – but the technology to make them real was centuries in the future. He was too far ahead of his time. In the end, he changed the world of art, but not science, really.”

“What if Leonardo had been born at the same time as Einstein?”

“You know, that’s a really smart question. I don’t know. No doubt da Vinci was into everything while Einstein was pretty focused on math and science – the math part of science, anyway. But his education and da Vinci’s were very different. Einstein did well in school, in spite of what people think, but he thought schools were too much like student factories when they should be places where learning is fun. Leonardo probably had more fun with his education because he didn’t go to school at all; he learned whatever caught his interest from people around him. Later he studied painting from a really great painter named Verrocchio. If da Vinci had been born in Einstein’s day, he might not have been allowed to study art, or he might have been punished for getting distracted in class or doodling during a lecture. There would be no Mona Lisa. On the other hand, if Einstein had been born in the 15th century, the math he ended up using to work out his own ideas – Newton’s math – would still have been in the future, so somebody else would have probably become famous in the 20th century for relativity.”

“I’m glad Einstein and da Vinci were born when they were.”

“Me too.”

A Few Einstein Quotes

“Imagination is more important than knowledge.”

“It is a miracle that curiosity survives formal education.”

“I never teach my pupils. I only attempt to provide the conditions in which they can learn.”

In Einstein’s day, formal education consisted mostly of rote and recital. Independent thinking was, as a rule, not encouraged. We have come a long way since then! Educational doctrine has come round to mirror exactly Einstein’s point of view; all professional educators today learn that they are – primarily – facilitators of learning, not sources of knowledge. A large base of knowledge is a good thing, but in this age of information technology, we are seldom more than the push of a button away from the facts we need to process. Anyone can access data; knowing how to interpret it is another matter. Using it to gain further knowledge is at another level completely. Those higher levels are accessed by minds engaged through curiosity. As a father of students, and teacher of my neighbors’ children, I am glad that curiosity has taken its place in the formal education of the new generations.