Applications of Einstein’s General Relativity in everyday life

Hyperaxion October 24, 2020 4:41 am

General relativity is the theory proposed by the German physicist Albert Einstein that describes gravity and the relationship between time and space.

The concepts of time dilation and length contraction seem like elements of science fiction, but, in fact, they are recurrent in everyday life and used in devices such as hard drives, microwave ovens, MRI scanners, and GPS systems.

According to Albert Einstein, gravity is the curvature of the space-time fabric. While curvature in space-time affects how mass and energy (including light and matter particles) move, mass and energy affect how space-time curves.

As an example, consider the movement of the Moon around the Earth. The Moon follows the path in space curved by the Earth’s mass.

Interestingly, not only objects with mass are affected by the curvature of space-time. Light, which is a massless particle, is also affected by gravity.

The light follows a principle that establishes that it always travels the shortest path between any two points. In a flat space, the shortest path is a straight line.

However, when there is curvature, the trajectory is changed to a geodesic. In other words, the path of light is curved.

In an article called “On the Influence of Gravitation on the Propagation of Light”, published in the scientific journal Annalen der Physik, Albert Einstein predicted that a beam of light passing close to the Sun would be deflected because of the Sun’s gravitational field.

Imagine for a second that you already know the position of a star beforehand, and that position is “behind” the Sun. It would be impossible to observe the brightness of the star if the light traveled in a straight line.

But thanks to the curvature of space, the light would travel around the Sun and it would be possible to see such a star, even if it was directly behind the Sun.

(Credit: GSFC/NASA).

On May 29, 1919, there was a total solar eclipse. Astronomers from around the world gathered on the West African island of Príncipe and in the Brazilian city of Sobral to confirm Einstein’s prediction. This event was called the Eddington experiment.

They were able to confirm the theory of relativity – which radically changed the scientific concepts of the 20th century.

A century after the solar eclipse of May 29, 1919, the predictions of the theory of relativity continue to be proven: gravitational lenses, gravitational waves, and the image of a black hole’s event horizon at the center of the M87 galaxy.

The first image of a black hole’s event horizon, taken with the Event Horizon Telescope on April 10, 2019.
The first image of a black hole’s event horizon, taken with the Event Horizon Telescope on April 10, 2019. (Credit: Event Horizon Telescope collaboration et al).

Of course, all of these phenomena refer to objects in outer space: supermassive stars, black holes, galaxies, and clusters of galaxies, which may give the impression that relativity concerns only massive objects.

However, relativity has consequences in everyday life, as well as some applications.

The principle of relativity states that time and distance are not absolute: measurements of the same event yield different values ​​for different observers, and both are correct – everything is relative.

For example, a decade from a person’s perspective on Earth could be a few minutes for a person on a spaceship traveling close to the speed of light.

The twins' paradox, a mental experiment proposed by physicist Paul Langevin (1872-1946). In this paradox, two twins were separated: one was on Earth, and the other was sent on a long journey in a spaceship that moved at speeds close to the speed of light. On his return, the brother who remained on Earth had aged a few years more than his traveling brother. This would have happened due to time dilation.
The twins’ paradox, a mental experiment proposed by physicist Paul Langevin (1872-1946). In this paradox, two twins were separated: one was on Earth, and the other was sent on a long journey in a spaceship that moved at speeds close to the speed of light. On his return, the brother who remained on Earth had aged a few years more than his traveling brother. This would have happened due to time dilation.

If a person measures the length of a stationary train, and measures it again after the train begins to move, the person will notice that the moving train appears to be shorter.

These effects are, respectively, time dilation and length contraction.

Although we don’t have spaceships that travel close to the speed of light yet, we experience the effects of time dilation every day.

The Global Positioning System (GPS) works with 24 satellites orbiting the Earth, determining the position of the devices through the triangulation method.

The speed of these objects is approximately 14,000 kph (8,700 mph). Although it is only about a thousandth of the speed of light, these satellites end up experiencing time dilation.

The difference between satellite clocks and clocks here on Earth could lead to an error of 8 km (5 miles) per day in the position indicated by the GPS.

GPS satellites need to be corrected to compensate for the effects of relativity.
GPS satellites need to be corrected to compensate for the effects of relativity.

The devices are programmed to perform the necessary corrections with calculations based on Einstein’s relativity.

From the satellite’s perspective, time passes more slowly than on Earth, so the algorithm needs to compensate for this discrepancy.

Now, imagine a 10-meter-long train with 10 wagons, roughly speaking, the density of the train is 1 wagon per meter.

If the train starts moving, then according to relativity, for an external observer it will compress in the direction in which it moves. Also, the clocks inside the train will run more slowly.

Suppose that after compression the train is 5 meters long. This implies that the number of wagons per meter will increase, with 2 wagons per meter.

Obviously, the values ​​used here are only to facilitate the understanding of what is happening. In a real situation, the compression of the train is not visible, as well as the time dilation of the clocks.

An example of length contraction. For a stationary observer, the distance between the moving clouds appears to be less.
An example of length contraction. For a stationary observer, the distance between the moving clouds appears to be shorter. (Credit: Lumen Learning).

Although the length contraction is imperceptible for moving trains, it is thanks to it that electromagnetic objects work: hard drives, microwave ovens, MRI scanners, etc.

Relativity was taken into account even in those old tube televisions.

They were equipped with cathode-ray tubes, which accelerated and fired electrons against a coating that, when hit, emitted light.

But it was not as simple as firing a few electrons at a screen. The negatively charged electrons were directed to a very specific point on the screen using the positive charge of magnets.

The speed of the accelerated electrons reached around 30% of the speed of light and, therefore, it was necessary to make corrections due to the length contraction they suffered, otherwise the images formed on the screen would be incomprehensible.

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