Einstein's Baby: How Has Relativity Held Up Over Time?

Einstein's theories on Relativity were revolutionary and hugely influential. A century later, and experiments are still being conducted to test them.

Einstein's Baby: How Has Relativity Held Up Over Time?
The path of S2 as it passes very close to Sagittarius A* ESO/M. Kornmesser

Albert Einstein (1879 - 1955) is what you might call a "household name", and for a good reason. Thanks to the immense contributions he made to multiple fields of science over the course of his lifetime, the very name Einstein has become synonymous with genius.

The image of the white-haired scientist with the quirky attitude, that's because of him too. Even those who are not well-versed in physics, cosmology or quantum mechanics are likely to recognize the term Relativity (or the elegant equation E=mc²).

RELATED: EINSTEIN'S THEORY OF GENERAL RELATIVITY HOLDS UP FOR NOW

This theory, which revolutionized our understanding of the Universe, is arguably Einstein's most profound and enduring contribution. And even though Relativity was proposed over a century ago, it is still being tested and verified to this day. But first, a little background...

What is perhaps less known is the fact that Einstein did not coin the term Relativity. The credit for that goes to Galileo Galilee (1564-1642) who proposed the concept (aka. Galilean Invariance) as a way of arguing for the heliocentric model of the universe.

Galileo's ship

As part of his promotion of the heliocentric model, Galileo argued that the laws of motion are the same in all inertial frames. This came to be known as Galilean Relativity (or Invariance), which is summarized as follows:

“[A]ny two observers moving at constant speed and direction with respect to one another will obtain the same results for all mechanical experiments.”

He first described this principle in his 1632 treatise Dialogue Concerning the Two Chief World Systems, which was his defense of Copernicus' heliocentric model. To illustrate, he used an example of a ship traveling at a constant speed on smooth water.

To an observer below the deck, Galileo reasoned, it would not be clear whether the ship was moving or stationary. Furthermore, if the person on the deck were to drop a ball on their foot, it would appear to be falling straight down (when in fact, it would be traveling forward with the ship as it fell).

This argument was a way of showing how the Earth could be moving through space (i.e. orbiting the Sun), but observers standing on its surface would not be immediately aware of it.

Similarly, Galileo is also said to have conducted experiments with falling bodies where he dropped balls of different mass from the Leaning Tower of Pisa.

While this story is thought to be apocryphal, Galileo did observe that objects with different masses would falltowards the groundat the same speed when released from an elevated point.

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This was contrary to the conventional (Aristotelian) thinking that the speed with which an object fell was dependent on its mass. Galileo also added that objects would retain their velocity unless an external force impedes that velocity.

These observations would go on to inspire British polymath Isaac Newton, who would beautifully summarize these observations in a single system that would remain an accepted convention for centuries (thereafter known as Newtonian physics).

Newton's apple

During the late 17th century, Sir Isaac Newton (1642 - 1726/27) would use this principle and Galileo's observations about gravity to develop his Three Laws of Motion and his Law of Universal Gravitation. The Three Laws state that:

  1. A body at rest will remain at rest, and a body in motion will remain in motion, unless acted on by an external, unbalanced force. This is otherwise referred to as the law of inertia.
  2. Force equals mass times acceleration, expressed mathematically as f(t) = m ⋅ a(t) - where f is force, t is time, m is mass, and a is acceleration.
  3. For every action in nature there exists an equal and opposite reaction - e.g. if object A exerts a force on object B, then object B also exerts an equal force on object A.

Newton's Three Laws effectively extended the force of gravity beyond Earth and argued that the same force that causes an apple to fall from a tree also causes the Moon to orbit the Earth, and the planets to orbit the Sun.

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Universal Gravitation, meanwhile, tells us that each body in the Universe attracts other bodies with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

Mathematically, this is expressed as F = G m1m2/r², where F is the gravitational force between two objects, m1 and m2 are the masses of the objects, r is the distance between them, and G is the gravitational constant.

These theories invariably contained two conclusions about the nature of space and time. One, that an inertial frame is a reference point to an "absolute space". Second, that all inertial frames share a universal time. In other words, time and space are absolute and separate.

It was not until the late-19th/early-20th century that Newtonian physics would run into any serious problems. Thanks to numerous discoveries made in the realm of atomic and subatomic physics, the very nature of matter & energy and time & space came to be questioned.

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In the end, it was a theoretical physicist living in Switzerland (and working at a patent office) who would offer a theory that would prove to be revolutionary. This was none other than Albert Einstein, whose theory of Relativity came in two parts.

The first, his theory of Special Relativity, addressed electromagnetism and the behavior of light (with respect to space and time). The second, General Relativity, addressed gravitational fields (with respect to space and time).

Special Relativity

In 1905, Einstein experienced what he called his annus mirabilis ("miracle year") in which he published multiple groundbreaking papers while working at the patent office in Bern, Switzerland.

Prior to this, scientists had been grappling with the inconsistencies that existed between Newtonian physics and the laws governing electromagnetism (part of the emerging field of quantum mechanics).

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These were characterized by work of 19th/20th physicists James Clerk Maxwell (1831-1879) and Hendrik Antoon Lorentz (1853-1928) - specifically, Maxwell's equations and the Lorentz force law.

Maxwell's equations are a set of differential equations that provides a mathematical model for how electricity, magnetism, and related phenomena behave. In essence, they express how fluctuating electric and magnetic fields propagate at a constant speed (c) in a vacuum.

The Lorentz force, on the other hand, describes the electromagnetic force on a charged particle as it moves through an electric and magnetic field. While these fields of research accurately described how electrical and magnetic waves behaved, they were not consistent with Newtonian physics - which was still predominant at the time.

These inconsistencies were especially apparent when it came to how light traveled from one point or another. By the 19th century, scientists had managed to calculate the speed of light based on experiments using electromagnetic waves.

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This led to the realization that light was, in fact, an electromagnetic wave and behaved similarly. Unfortunately, this presented a number of theoretical problems. Like any other type of wave (ex. sound), the phenomena would need a medium in order to propagate.

By the opening by the 20th century, the scientific consensus was that light traveled through a moving medium in space and was therefore dragged along by that medium. In order to explain this, scientists postulated that space was filled with a mysterious "luminiferous aether".

In short, this meant that the speed of the light - 299,792,458 m/s (300,000 km/s; 186,000 mps) - was the sum of its speed through the aether plus the speed of that aether. In other words, the speed of light (as measured) was not absolute and depended on the medium it used to propagate.

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A consequence of this was that either the aether itself would be dragged by moving matter, or transported with it. Unfortunately, this was not consistent with experimental results and presented numerous theoretical problems.

For instance, the Fizeau Water Tube Experiment (1851) measured the speed of light as it traveled through water. If the current theory of light propagation was correct, the experiment would have shown a noticeable reduction in speed.

And while the results showed that light traveling through a medium was subject to drag, the effect was not nearly as much as expected. Other experiments produced had similar results, such as Fresnel’s partial aether-drag hypothesis and the experiments of Sir George Stokes.

This left scientists scratching their heads. In 1905, Einstein addressed these inconsistencies of this with his seminal paper, "On the Electrodynamics of Moving Bodies" ("Zur Elektrodynamik bewegter Körper").

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In it, Einstein argued that the speed of light (c) in a vacuum is constant, regardless of the inertial reference frame of the source or the observer. This came to be known as Einstein’s Theory of Special Relativity, which is often summarized by the simple equation E=mc² (where E is energy, m is mass, and c is the speed of light).

This theory would overturn centuries of scientific orthodoxy and be groundbreaking because of its simplicity, and how it resolved the inconsistencies between electromagnetism and classical mechanics.

For one, it reconciled Maxwell’s equations for electricity and magnetism with the laws of Newtonian mechanics. It also simplified the math by doing away with extraneous explanations and making the existence of an aether unnecessary.

Einstein's theory also introduced the idea that as an object approached the speed of light, major changes occured with regard  to space-time. This includes time dilation, where the perception of time for the observer slows down the closer they get to c.  

All of this would serve to turn classical mechanics on its head. Whereas conventional thinking held that matter and energy are separate, Einstein's theory essentially suggested that the two were both expressions of the same reality.

In other words, one cannot move through space without also moving through time. 

General Relativity

Between 1907 and 1915, Einstein began to consider how his theory of Special Relativity could be applied to gravity fields. This was another stumbling block for modern scientists, who were beginning to notice that Newton's Law of Universal Gravitation had limits.

Here too, inconsistencies were noted thanks to breakthroughs in the field of electromagnetism. For example, in 1865, James Clerk Maxwell published his major work, "A dynamical theory of the electromagnetic field".

At the end of this paper, he made the following comments about gravitation:

"After tracing to the action of the surrounding medium both the magnetic and the electric attractions and repulsions, and finding them to depend on the inverse square of the distance, we are naturally led to inquire whether the attraction of gravitation, which follows the same law of the distance, is not also traceable to the action of a surrounding medium."

However, Maxwell acknowledged that this raised a paradox. Basically, the attraction of similar bodies would mean that the energy of the surrounding medium would decrease in the presence of these mediums. Without finding a cause for gravitation, Maxwell admitted that he was unable to resolve this.

In 1900 and 1905, Lorentz and mathematician Henri Poincaré theorized that gravitation could be related to the propagation of light, which echoed what Einstein would eventually argue with his Theory of General Relativity.

In 1907, Einstein published the first in a series of articles that would seek to resolve these issues. Titled "On the Relativity Principle and the Conclusions Drawn from It", Einstein addressed how the rule of special relativity might also apply to acceleration.

It was in this paper that Einstein proposed the Equivalence Principle, which states that gravitational mass is identical to inertial mass. To illustrate, he explained that the acceleration of bodies towards the center of the Earth at a rate of 1 g (g = 9.81 m/s2) is equivalent to the acceleration of an inertially moving body that would be observed on a rocket in free space being accelerated at a rate of 1g.  Thus, free fall is actually inertia and the observer experiences no gravitational field as a result.

In this respect, Einstein argued that space and time - which classic physics also maintained were separate - were two expressions of the same thing.

By 1911, Einstein expanded on his 1907 paper with a new paper titled “On the Influence of Gravitation on the Propagation of Light". In this, he predicted that an object that was accelerating away from a source of gravitation would experience time faster than one that was sitting still in an unchanging gravitational field.

This phenomenon is known as gravitational time dilation, where the perception of time differs depending on the observer's distance from a gravitational mass or position within a gravitational field.

In the same article, he predicted the bending of light in a gravitational field, and gravitational redshift (aka. Doppler shift). The former is a consequence of the equivalence principle, where the passage of light is affected by the curvature of space-time and its deflection is dependent on the mass of the body involved.

The latter concerns light leaving a massive body (like a distant star or galaxy) which is then shifted towards the red end of the spectrum due to losing energy in order to escape gravitational fields (more on that below).

These arguments were especially influential because (unlike what Einstein argued in 1907) they could be verified by astronomical observations. Einstein would go on to write several more papers in the coming years expanding on his theories of gravitation, and by 1915, they began to be accepted.

Since that time, General Relativity has been confirmed through multiple experiments and become central to modern astrophysics. It would play a role in developing the theories of black holes, cosmic expansion, dark energy and other aspects of modern cosmology.

How has Relativity been tested (and confirmed)?

Short answer: Nine ways from Sunday!

Long Answer: Read on...

Both Special Relativity (SR) and General Relativity (GR) have been tested repeatedly over the course of the past century and have been confirmed again and again. 

In fact, even before Einstein proposed his theory of SR, there was an experimental basis for it (which is what ultimately led him to develop his theory). What's more, it didn't take long before scientists were adopting his theories to make further breakthroughs.

But it was really only in the decades since Relativity was proposed that Einstein's theories have been so thoroughly vetted and tested. In fact, much of what astronomers have learned about our Universe since Einstein proposed SR and GR have reinforced his theories.

Mercury's precession of perihelion

For starters, GR resolved a problem that astronomers had been trying to solve since 1859, which was the curious nature of Mercury's orbit. For centuries, astronomers relied on Newtonian mechanics to calculate the orbit of Mercury around the Sun.

While these mechanics could account for the eccentricity of the planet's orbit, they could not explain why the point where Mercury' reached perihelion (the farthest point in its orbit) shifted around the Sun over time.

This issue was known as Mercury's "precession of perihelion", which did not make sense according to classical physics since, according to Newton, the point of perihelion in any two-body system was fixed.

A number of solutions were proposed, but they tended to introduce more problems than they solved. However, Einstein's theory of GR - where gravitation is mediated by the curvature of spacetime - agreed with the observed amount of perihelion shift.

That was one of the first, but definitely not the last, predictions made by Einstein that would be borne out. Here are a few more...

Black holes and gravitational waves

One of the predictions of GR is that a sufficiently compact mass could deform spacetime to the point that within its outer boundary (aka. the event horizon) time would cease and the laws of physics would become indistinguishable from each other.

A consequence of this is that the gravitational strength would actually exceed the speed of light, making this compact mass the ideal "black body" - meaning that no electromagnetic radiation (including light) could escape it.

While scientists had theorized about such masses before, the first to propose the existence of "black holes" as a solution of GR was Karl Schwarzschild. In 1916, he calculated the radius that a mass would need to achieve to become a black hole (thereafter known as the Schwarzchild Radius).

For decades, black holes would remain a scientific curiosity. But by the 1960s, often referred to as the "The Golden Age of General Relativity", research into GR and cosmological phenomena began to demonstrate the influence of black holes.

By the 1970s, astronomers discovered that a radio source at the center of the Milky Way (Sagittarius A*) also had a bright and very compact component to it. Combined with subsequent observations of the surrounding environment, this led to the theory that Sag A* was, in fact, a Supermassive Black Hole (SMBH).

Since then, astronomers have observed that most massive galaxies have similarly active cores that cause them to shine brightly in the radio, infrared, x-ray, and gamma-ray wavelengths. Some have even been found to have jets of superheated material coming from their cores that extend for millions of light-years.

In 2016, scientists from the Laser Interferometer Gravitational wave Observatory (LIGO) announced that they had made the first-ever detection of gravitational waves. Originally predicted by GR, this phenomenon is essentially ripples in space-time that are caused by cataclysmic events.

These include events like binary black holes or neutron star mergers, black holes merging with neutron stars, or collisions between other compact objects. Since 2016, multiple gravitational wave events have been detected.

On April 10th, 2019, the collaborative scientific project known as The Event Horizon Telescope (EHT) announced the first-ever direct image of the event horizon surrounding a SMBH - located at the core of Messier 87.

Cosmological constant and dark energy

Another consequence of the field equations for Relativity was the Universe either had to be in a state of expansion or a state of contraction. Curiously enough, this did not sit well with Einstein, who preferred to believe the Universe was static and stable.

To address this, Einstein conceived of a force that would "hold back gravity", thus ensuring that the Universe did not collapse in on itself. He called this force the "cosmological constant", which was represented scientifically by the character Lamba (Λ).

However, in 1929, American astronomer Edwin Hubble resolved the issue thanks to his discovery of neighboring galaxies. After measuring their redshift, he discovered that the majority of galaxies in the Universe were moving away from our own.

In short, the Universe was in a state of expansion, the rate of which came to be known as the Hubble Constant. Einstein graciously accepted the discovery and claimed that the Cosmological Constant had been "the biggest mistake" of his career.

By the 1990s, however, astronomers were able to conduct observations that looked farther and farther out into the cosmos (and consequently farther back in time). These observations appeared to reveal that the rate at which the Universe was expanding was actually increasing.

According to the current theory, from the earliest observable period of the Universe (ca. one billion years after the Big Bang) to about ten billion years after the Big Bang, the Universe was dominated by gravity and expanded more slowly.

But as of four billion years ago, the large-scale structures in the Universe were far enough apart that dark energy became the dominant force and everything started to move apart faster. Einstein's mysterious force that "held back gravity" had been found!

Experimental evidence for Relativity

Since 1905, hundreds of experiments of incredible range and diversity have been conducted that have confirmed SR. This included multiple experiments that confirmed that light was isotropic (i.e. has the same properties when measured in every direction).

These include the Michelson-Morley Experiment (MMX) in 1887, which was intended to measure the speed of light in perpendicular directions using an interferometer - a device where two sources of light are merged to create an interference pattern.

The purpose of this was to detect the relative motion of matter (in this case, the Earth) through the “luminiferous aether”. The experiment was a failure since it showed that there was no significant difference between the speed of light in the direction of Earth's orbit and the speed of light at right angles.

Similar experiments were conducted throughout the early 20th century using different apparatuses and instruments of increasing sensitivity, but all produced the same (null) result.

By the latter half of the 20th century, experiments were conducted using lasers to measure the isotropy of light. These experiments involved measuring the one-way and round-trip speed of light and using both stationary and moving objects.

Once again, these experiments obtained null results, which is consistent with SR. Compared to experiments that could not confirm the presence or influence of an "aether", Einstein's solution remains the most elegant and comprehensive to date.

In terms of General Relativity (GR), extensive observation campaigns have been conducted that show its predicted effects at work. For example, in 2017, a team of European astronomers demonstrated how twenty years of observing Sagittarius A* - the Supermassive Black Hole (SMBH) at the center of our galaxy - confirmed predictions made by Einstein and GR.

Using data from the European Southern Observatory's Very Large Telescope (VLT) in Chile, and other telescopes, they monitored three stars that orbit Sagittarius A* and noted its effect on their eccentricity.

What they found was that one of the stars (S2) follows a particularly elliptical orbit around the SMBH which it takes 15.6 years to complete. At its closest, it gets to within 120 times the distance between the Sun and the Earth (120 AU). These deviations in orbit were consistent with GR.

Gravitational lensing and redshift

Shortly after Einstein proposed his theory of how space-time behaves in the presence of a gravitational field, an opportunity arose to test it. In 1919, astronomers knew that a total solar eclipse would occur on May 29th, which presented an opportunity.

Einstein and German astronomer Erwin Finlay-Freundlich urged scientists from around the world to test GR by measuring the deflection of light during this event.

Sir Arthur Eddington, a British astronomer and science communicator who was adept at explaining concepts like Relativity, took up the challenge and mounted an expedition to the island of Principe (off the coast of Equatorial Guinea, Africa).

During the eclipse, the Sun's rays were obscured by the presence of the Moon, making the stars around it  visible. Eddington took pictures of these stars and confirmed that the path of their light was shifted due to the gravitational influence of the Sun.

On Nov. 7th, 1919, The Times published the results of his campaign under the headline: “Revolution in Science – New Theory of the Universe – Newtonian Ideas Overthrown”.

This effect, where the passage of light is influenced by a large object, gave rise to the method known as "gravitational lensing". This involves relying on the presence of a large celestial object (stars, galaxies, galaxy clusters, black holes, etc.) to observe objects beyond them.

In fact, astronomers have found that when there is a near-perfect alignment between a light source, a gravitational lens, and an observer, the light becomes deformed into a ring - which is now referred to as the "Einstein ring".

Einstein's Baby: How Has Relativity Held Up Over Time?
Hubble image of an "Einstein Ring". Source: ESA/Hubble & NASA

This effect has been regularly observed by astronomers, especially with the deployment of space telescopes like Hubble. A good example of this took place in 2018, where a team of international scientists used a galaxy cluster to view the farthest individual star ever observed (named Icarus, located 9 billion light-years away).

Another line of evidence that confirms General Relativity is the way the electromagnetic radiation is stretched out by the presence of a gravitational field.  This is the aforementioned phenomenon known as "redshift", where the influence of a gravitational field causes the wavelength of light to become longer.

In other words, light emanating from a distant celestial object (a star, galaxy or galaxy cluster) is shifted towards the red end of the spectrum. The extent of the redshift is then used to calculate how massive the gravitational field affecting it is.

Redshift is also widely used to measure the rate at which the Universe is expanding since light from distant galaxies becomes stretched by the intervening space between the light source and the observer.

However, it has also been used as a method for testing GR; in particular, when observing how light behaves in the presence of a black hole. A good example of this also involved observations made of a star orbiting Sagittarius A*.

The team responsible was made up of members of the GRAVITY collaboration, which used the VLT to monitor S2 as it passed in front of the black hole – which took place in May of 2018. At the closest point in its orbit, the star was within 20 billion km (12.4 billion mi) of the SMBH and moving at almost three percent of the speed of light.

Consistent with GR, the team observed a gravitational redshift that intensified the closer S2 got to Sagittarius A*. The very strong gravitational field of the black hole stretched the wavelength of the star’s light and caused it to shift towards the red end of the spectrum.

When Einstein began his career as a theoretical physicist, he was entering a world on the verge of revolution. The old conventions were being questioned due to inconsistencies with new discoveries that presented all kinds of problems.

When he passed away, Einstein left behind a legacy that was virtually unparalleled in the history of science. He offered synthesis to old and new theories and created a new understanding of how space-time, matter, and energy interact.

On top of that, he pioneered breakthroughs that would lead to many more revolutions in science. Today, over one hundred years later, his theories are still holding up and continue to inform our understanding of the Universe.

Further Reading:

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