Tag Archives: einstein

Gravitational Waves Discovered by LIGO

The world is abuzz with news that gravitational waves have been detected for the first time. This is a huge leap forward for scientists’ understanding of gravity! For all that we experience gravity every day as we (mostly) stay grounded on the Earth, figuring out exactly how it works has been a challenge.

Gravity draws things together, but how ? One of the most brilliant discoveries of Albert Einstein was realizing that objects with mass actually warp spacetime itself. If we imagine space as an enormous sheet, throwing a light object like a tennis ball onto it would only pull the sheet down a little, whereas a bowling ball would pull the sheet down significantly more. Everything with mass distorts the sheet though, affecting other objects on the sheet and even massless things like light as they pass through.


Seeing that gravity affected light was actually the first major proof of Einstein’s theory of general relativity. During an eclipse in 1919, light from a cluster of stars was seen to distort from its normal pattern as it passed close to the temporarily obscured Sun. But another consequence of Einstein’s work was the idea that the speed of light is a maximum speed for any particle or force, including gravitation, however it’s propagated. This implies that gravitational interactions can only happen so fast, and that if a huge gravitational event were to take place emitting a lot of gravitational energy, that energy would have a maximum speed to move through the universe.

What kind of huge gravitational event? Well, the strongest gravitational interactions we have been able to observe take place around black holes, whose mass causes gravitational forces that overcome even basic quantum mechanical ones that prevent matter from piling up on itself. So black holes are supermassive point objects, singularities with exceptionally strong gravity. And if two of them were to come together, their movement might create gravitational waves in spacetime itself that could be strong enough for us to detect.

The Laser Interferometer Gravitational-Wave Observatory (LIGO) has been looking for gravitational waves using light as a ruler to measure whether spacetime is being warped. LIGO compares the length of two 2.5 mile long tunnels, set at right angles to each other, which would warp in alternation if a gravitational wave were to pass through them. The precision needed to see even very strong gravitational waves is tremendous, as we know from the fact that we don’t just observe our living rooms getting bigger and smaller in response to cosmic events. LIGO has been searching for gravitational waves since 1992, and improving its precision since then. Finally this week, they announced a signal!


The gravitational waves detected come from two black holes merging, a billion light years from our planet. These black holes were enormous, 36 and 29 times the mass of our Sun. They merged into a black hole 62 times the mass of our Sun, converting three solar masses into energy as gravitational waves. It is these waves that the LIGO researchers managed to detect, corroborating their results at two separate facilities in Louisiana and Washington. The difference in lengths of the LIGO tunnels due to the gravitational waves was less than a millionth of the size of an atom, an astounding physical feat, and yet the LIGO collaboration is confident in its measurements to 99.9999%.

Validating a prediction made over a hundred years ago about the way mass warps spacetime is impressive enough, especially considering that gravity is still the least well understood of the four fundamental forces. But it’s also a beautiful new way to look at the stars, and at the massive universe beyond our planetary doorstep.

Moving Charge, Magnetism, and Inductors

Last time I talked about how magnetization arises from the alignment of spins, which is favorable in some materials due to the quantum mechanical exchange interaction. But, there is another way to generate a magnetic field: it turns out that moving charges (i.e. an electric current) create a magnetic field as well! This was first observed experimentally by Ørsted, who noticed a compass needle moving in response to current running through a coiled wire. It was then incorporated into Maxwell’s Equations, which attempted to provide a unified framework for observed electric and magnetic phenomena.

But while the evidence that a moving charge generates a magnetic field was clear, explaining the mechanism by which this happens took some time. The key insight actually came from Einstein, who saw Maxwell’s Equations and had a question: why is the speed of light independent of the reference frame? That is to say, we know that if we are in a car that is passing another car, our car appears to be going only a bit faster than the other car, even though an observer standing on the sidewalk would say that both cars were moving fairly fast. The observed speed depends on the frame of reference of the observer! And so in classical mechanics, the speed of an object and the speed of its reference frame can be added together to give the total object speed. Why should it be any different for something moving at the speed of light? Well, the answer to that question gets into special relativity, but consider the same question with a moving charge from two frames of reference:

  1. From the reference frame of the charge, an electrical field is induced by a static charge.
  2. From the reference frame of a static observer, a magnetic field is induced by a moving charge.

The implication is that electric and magnetic fields, and forces, are simply two facets of the same phenomena, which is now called electromagnetism.

In fact, the magnetic field of the earth, shown above, is due to moving charge in the form of molten iron in the outer core of the planet. The charge flow is maintained because magnetics fields induce current flow, just as current flow induces magnetic fields, forming a feedback loop. The earth’s magnetic field is not very large, but it is enough to enable measurement devices such as compasses, which have long been used for navigation. Some animals are also able to sense the earth’s magnetic field to directly use for navigation, including homing pigeons, sharks, and even smaller organisms such as bacteria. Many different biological sensors for magnetic field seem to have evolved independently, likely due to the significant survival advantages associated with reliable navigation.

But another place where the magnetic field induced by a moving charge arises is in electronics. Any wire with a current running through it will generate a magnetic field proportional to the size of that current. That means that nearby objects that respond to magnetism may experience magnetic forces, or even have electric currents induced in them. Coaxial cable, which has an inner wire carrying current encased in an insulator and a cylindrical outer conductor, confines the magnetic field to the insulating region of the wire. It was developed specifically to shield the magnetic field of the current-carrying wire, and to shield the wire itself from stray external magnetic fields.

And there is a basic circuit component that makes use of this phenomenon as well, the inductor. An inductor, as you can see above, consists of wire coiled in a loop, possibly with many coils and possibly with a material lodged inside the coils of wire. The current on the wires induces a magnetic field in the center of the loop. The forces from this magnetic field act against any change in electric current, using the energy stored in the magnetic field. Because inductors are sensitive to changes in current over time, they are very useful in processing time-dependent electronic signals. The magnetic field of one inductor can also be coupled to the coils of a second inductor, inducing a second current which may be larger or smaller depending on the relative sizes of the coils of the two inductors. This is how a transformer is made, a device which inductively transfers electrical signals and is central to power transmission from the power grid to individual homes and businesses.

As you can see from all these examples, there are a lot of technologically useful things to do with the interplay between electricity and magnetism! And the realization that they were intertwined was a huge step forward for physics.