Einstein had a mind that leapt nimbly from one new idea to the next. His powerful sense of intuition steered him to a safe landing and a new discovery. These leaps make his scientific essays miniature works of art. They are simple and graceful, but reveal a mind dancing among the deepest ideas. One example … Read more
Imagine trying to run if every faster stride made your legs heavier and even sprinting speeds turned them into lead weights. Increasing a body’s speed requires some kind of push or force. Increasing the speed of heavier bodies requires stronger and harder pushes. If a body’s mass approaches infinity, then further increases in speed would … Read more
Energy is the “amount of motion”. Suppose that two identical cars are racing down a road; the faster car has more energy. Suppose that a truck and a small car are travelling side by side along the road and at the same speed; the truck is heavier and therefore has more energy. It is harder … Read more
A few months after Einstein published his first paper on relativity in 1905, he sent in a sort of extended footnote to the same journal. His theory had an odd little consequence. It seemed so strange that he phrased the note’s title as a question: “Does Mass Depend on Energy?” To leaf through the next … Read more
The most famous of the problems prominent in the early controver- sies over relativity was the twin paradox. It is easy to state but exposes some very deep issues, and so hundreds of papers have been written about it over the decades. Now that the dust has settled, it is clear that the paradox does … Read more
Both the majority and minority interpretations agree that measure- ments show that one ship is longer and shorter than the other, or that the car is longer and shorter than the garage, depending on which set of rulers and clocks is used. That is, they agree that appearances are symmetric. They also agree that there … Read more
An illustration will help bring these points home. According to Einstein, length contraction will permit us to house the six-metre Jaguar in a three-metre garage, as mentioned above. By driving at 85 per cent of the speed of light, the car will contract by some 50 per cent. We can drive the car into the … Read more
How can one spaceship be shorter and longer than the other? Is there a contradiction? The short answer is no. For a contradiction, opposite properties must belong to one thing at the same time, but this is not the case. The different spaceships have different times. Consider how the lengths of moving bodies are measured. … Read more
Among physicists, the word “symmetry” means “sameness across differ- ence”. The prefixes “sym” and “syn” mean “same”, so “symphony” means “many musicians making the same sound” and “synchrony” means “same time”. “Metry” comes from the Greek word for “measure” (as in “metric”) and here means “size” or “shape”. Thus a face has a symmetry when … Read more
The young Einstein was a rebel, moving from job to job and scrambling to find a secure job. The great father figure in physics at that time was the famous Dutchman Hendrik Lorentz. A generation older than Einstein, and a picture of prosperous, upper-middle-class respectability, Lorentz had played a major role in the discovery of … Read more