An illustration of the Ptolemaic geocentric system by Portuguese cosmographer and cartographer Bartolomeu Velho, 1568 (Bibliothèque Nationale, Paris)
During the many thousand years that human beings have been looking up at the stars, our concept of what the Universe looks like has changed dramatically. At one time, the magi and sages of the world believed that the Universe consisted of a flat Earth (or a square one, a zigarrut, etc.) surrounded by the Sun, the Moon, and the stars. Over time, ancient astronomers became aware that some stars did not move like the rest, and began to understand that these too were planets.
In time, we also began to understand that the Earth was indeed round, and came up with rationalized explanations for the behavior of other celestial bodies. And by classical antiquity, scientists had formulated ideas on how the motion of the planets occurred, and how all the heavenly orbs fit together. This gave rise to the Geocentric model of the universe, a now-defunct model that explained how the Sun, Moon, and firmament circled around our planet.
Albert Einstein during a lecture in Vienna in 1921.
Credit: National Library of Austria/F Schmutzer/Public Domain
One of the benefits of being an astrophysicist is your weekly email from someone who claims to have “proven Einstein wrong”. These either contain no mathematical equations and use phrases such as “it is obvious that..”, or they are page after page of complex equations with dozens of scientific terms used in non-traditional ways. They all get deleted pretty quickly, not because astrophysicists are too indoctrinated in established theories, but because none of them acknowledge how theories get replaced.
For example, in the late 1700s there was a theory of heat known as caloric. The basic idea of caloric was that it was a fluid that existed within materials. This fluid was self-repellant, meaning it would try to spread out as evenly as possible. We couldn’t observe this fluid directly, but the more caloric a material has the greater its temperature.
Ice-calorimeter from Antoine Lavoisier’s 1789 Elements of Chemistry. (Public Domain)
From this theory you get several predictions that actually work. Since you can’t create or destroy caloric, heat (energy) is conserved. If you put a cold object next to a hot object, the caloric in the hot object will spread out to the cold object until they reach the same temperature. When air expands, the caloric is spread out more thinly, thus the temperature drops. When air is compressed there is more caloric per volume, and the temperature rises.
We now know there is no “heat fluid” known as caloric. Heat is a property of the motion (kinetic energy) of atoms or molecules in a material. So in physics we’ve dropped the caloric model in terms of kinetic theory. You could say we now know that the caloric model is completely wrong.
Except it isn’t. At least no more wrong than it ever was.
The basic assumption of a “heat fluid” doesn’t match reality, but the model makes predictions that are correct. In fact the caloric model works as well today as it did in the late 1700s. We don’t use it anymore because we have newer models that work better. Kinetic theory makes all the predictions caloric does and more. Kinetic theory even explains how the thermal energy of a material can be approximated as a fluid.
This is a key aspect of scientific theories. If you want to replace a robust scientific theory with a new one, the new theory must be able to do more than the old one. When you replace the old theory you now understand the limits of that theory and how to move beyond it.
In some cases even when an old theory is supplanted we continue to use it. Such an example can be seen in Newton’s law of gravity. When Newton proposed his theory of universal gravity in the 1600s, he described gravity as a force of attraction between all masses. This allowed for the correct prediction of the motion of the planets, the discovery of Neptune, the basic relation between a star’s mass and its temperature, and on and on. Newtonian gravity was and is a robust scientific theory.
Then in the early 1900s Einstein proposed a different model known as general relativity. The basic premise of this theory is that gravity is due to the curvature of space and time by masses. Even though Einstein’s gravity model is radically different from Newton’s, the mathematics of the theory shows that Newton’s equations are approximate solutions to Einstein’s equations. Everything Newton’s gravity predicts, Einstein’s does as well. But Einstein also allows us to correctly model black holes, the big bang, the precession of Mercury’s orbit, time dilation, and more, all of which have been experimentally validated.
So Einstein trumps Newton. But Einstein’s theory is much more difficult to work with than Newton’s, so often we just use Newton’s equations to calculate things. For example, the motion of satellites, or exoplanets. If we don’t need the precision of Einstein’s theory, we simply use Newton to get an answer that is “good enough.” We may have proven Newton’s theory “wrong”, but the theory is still as useful and accurate as it ever was.
Unfortunately, many budding Einsteins don’t understand this.
Binary waves from black holes. Image Credit: K. Thorne (Caltech) , T. Carnahan (NASA GSFC)
To begin with, Einstein’s gravity will never be proven wrong by a theory. It will be proven wrong by experimental evidence showing that the predictions of general relativity don’t work. Einstein’s theory didn’t supplant Newton’s until we had experimental evidence that agreed with Einstein and didn’t agree with Newton. So unless you have experimental evidence that clearly contradicts general relativity, claims of “disproving Einstein” will fall on deaf ears.
The other way to trump Einstein would be to develop a theory that clearly shows how Einstein’s theory is an approximation of your new theory, or how the experimental tests general relativity has passed are also passed by your theory. Ideally, your new theory will also make new predictions that can be tested in a reasonable way. If you can do that, and can present your ideas clearly, you will be listened to. String theory and entropic gravity are examples of models that try to do just that.
But even if someone succeeds in creating a theory better than Einstein’s (and someone almost certainly will), Einstein’s theory will still be as valid as it ever was. Einstein won’t have been proven wrong, we’ll simply understand the limits of his theory.
Cardinal Bellarmine had written in 1615 that the Copernican system could not be defended without "a true physical demonstration that the sun does not circle the earth but the earth circles the sun". Galileo considered his theory of the tides to provide the required physical proof of the motion of the earth. This theory was so important to him that he originally intended to entitle his Dialogue on the Two Chief World Systems the Dialogue on the Ebb and Flow of the Sea.
For Galileo, the tides were caused by the sloshing back and forth of water in the seas as a point on the Earth's surface sped up and slowed down because of the Earth's rotation on its axis and revolution around the Sun. He circulated his first account of the tides in 1616, addressed to Cardinal Orsini. His theory gave the first insight into the importance of the shapes of ocean basins in the size and timing of tides; he correctly accounted, for instance, for the negligible tides halfway along the Adriatic Sea compared to those at the ends. As a general account of the cause of tides, however, his theory was a failure.
If this theory were correct, there would be only one high tide per day. Galileo and his contemporaries were aware of this inadequacy because there are two daily high tides at Venice instead of one, about twelve hours apart. Galileo dismissed this anomaly as the result of several secondary causes including the shape of the sea, its depth, and other factors. Against the assertion that Galileo was deceptive in making these arguments, Albert Einstein expressed the opinion that Galileo developed his "fascinating arguments" and accepted them uncritically out of a desire for physical proof of the motion of the Earth. Galileo dismissed the idea, held by his contemporary Johannes Kepler, that the moon caused the tides. He also refused to accept Kepler's elliptical orbits of the planets, considering the circle the "perfect" shape for planetary orbits.Cardinal Bellarmine had written in 1615 that the Copernican system could not be defended without "a true physical demonstration that the sun does not circle the earth but the earth circles the sun". Galileo considered his theory of the tides to provide the required physical proof of the motion of the earth. This theory was so important to him that he originally intended to entitle his Dialogue on the Two Chief World Systems the Dialogue on the Ebb and Flow of the Sea.
For Galileo, the tides were caused by the sloshing back and forth of water in the seas as a point on the Earth's surface sped up and slowed down because of the Earth's rotation on its axis and revolution around the Sun. He circulated his first account of the tides in 1616, addressed to Cardinal Orsini. His theory gave the first insight into the importance of the shapes of ocean basins in the size and timing of tides; he correctly accounted, for instance, for the negligible tides halfway along the Adriatic Sea compared to those at the ends. As a general account of the cause of tides, however, his theory was a failure.
If this theory were correct, there would be only one high tide per day. Galileo and his contemporaries were aware of this inadequacy because there are two daily high tides at Venice instead of one, about twelve hours apart. Galileo dismissed this anomaly as the result of several secondary causes including the shape of the sea, its depth, and other factors. Against the assertion that Galileo was deceptive in making these arguments, Albert Einstein expressed the opinion that Galileo developed his "fascinating arguments" and accepted them uncritically out of a desire for physical proof of the motion of the Earth. Galileo dismissed the idea, held by his contemporary Johannes Kepler, that the moon caused the tides. He also refused to accept Kepler's elliptical orbits of the planets, considering the circle the "perfect" shape for planetary orbits.
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It’s too bad that they missed Black Friday, but you’ll at least be able to get a few gifts for that astronomy enthusiast friend of yours for Christmas (or even for yourself!). The auction house Christie’s will be putting on the block 160 pieces from Edward Tufte’s rare book collection December 2nd in New York City.
Among the works are original 1st edition copies of such books as Isaac Newton’s Opticks (1704), and Galileo Galilee’s Sidereus nuncius (1610) which is better known in English as The Starry Messenger. Galileo famously reported some of his early telescopic observations in this book, discovering the moons of Jupiter and craters and mountains on the Moon. There will also be a copy of René Descartes’ Principia philosophiae (1644) and various works by other famous astronomers, philosophers and scientists.
Edward Tufte is a Professor Emeritus of Political Science, Statistics, and Computer Science at Yale University. According to his bio on their site, “His research concerns statistical evidence and scientific visualization.” Looking through the Christie’s catalog, his interests in science history and visualization are well-represented, and the collection is quite impressive.
Of course, all of these items come at a price, rare and famous as they are. Would you expect anything less from such a notable auction house? Opticks is billed to sell for $30,000 – $40,000, Principia philosophiae for $6,000 – $8,000 and Siderius nuncius – the most expensive of the entire lot – is valued at between $600,000-$800,000 (all amounts in US Dollars). Here are a few other items for sale, accompanied by their expected fetching price:
– John Snow – On the Mode of Communication of Cholera (1849) $10,000 – $15,000 This is an important book that revolutionized our understanding of disease transmission. Steven Johnson’s book Ghost Map is based on this work, and is a fascinating read.
– Euclid – Elements $400 – $600 A 1589 copy of this important mathematical work that underlies our understanding of physics and math today. Euclid was born around 300 BC, and the oldest fragment of the Elements only dates to 100 AD.
– Thomas Hobbes – Leviathan, or The Matter, Forme, & Power of a Common-Wealth(1651). $15,000 – $20,000 A very influential work in the history of political philosophy and social contract theory. You may recognize this quote from chapter 12 of the book, “…and the life of man, solitary, poor, nasty, brutish and short.”
– Christiaan Huygens – Systema Saturnium (1659) $25,000 – $35,000 This is a digest of Huygens’ observations of the Saturnian system, and contains one of the first drawings of the Orion nebula.
– Edmund Halley – A description of the passage of the shadow of the moon, over England, in the total eclipse of the sun, on the 22nd day of April 1715 in the morning. (1715) $15,000 – $20,000 An illustrated broadside of Halley’s prediction of the shadow cast by the lunar eclipse on April 22nd, 1715. There are a few other works from Halley for sale as well.
I suggest sifting through the catalog – there are a lot of detailed photos and descriptions of the books for sale, many of them rare gems from the history of philosophy and astronomy and science.
Tufte is also selling a piece of his own artwork for $50,000 – $70,000 titled, Pioneer Space Plaque: A Cosmic Prank (2010). A digital print that uses animation electronics, it is a redesign – and parody – of the original plaques that still fly aboard the Pioneer 10 and 11 probes. For a picture, visit the auction page.
When we raise an apple up to a height of one meter, we perform approximately one joule of work. So what is a joule?
Joule is the unit of energy used by the International Standard of Units (SI). It is defined as the amount of work done on a body by a one Newton force that moves the body over a distance of one meter. Wait a minute … is it a unit of energy or a unit of work?
Actually, it is a unit of both because the two are interrelated. Energy is just the ability of a body to do work. Conversely, work done on a body changes the energy of the body. Let’s go back to the apple example mentioned earlier to elaborate.
An apple is a favorite example to illustrate a one joule of work when using the definition given earlier (i.e., the amount of work done ….) because an apple weighs approximately one Newton. Thus, you’d have to exert a one Newton upward force to counteract its one Newton weight. Once you’ve lifted it up to a height of one meter, you would have performed one joule of work on it.
Now, how does energy fit into the picture? As you perform work on the apple, the energy of the apple (in this case, its potential energy) changes. At the top, the apple would have gained about one joule of potential energy.
Also, when the apple is one meter above its original position, say the floor, gravity would have gained the ability to do work on it. This ability, when measured in joules, is equivalent to one joule.
Meaning, when you release the apple, the force of gravity, which is simply just the weight of the body and equivalent to one Newton, would be able to perform one joule of work on it when the apple drops down from a height of one meter.
Mathematically, 1 joule = 1 Newton ⋅ meter. However, writing it as Newton ⋅ meter is discouraged since it can be easily confused with the unit of torque.
Particle physics experiments deal with large amounts of energies. That is why it is also known as high energy physics. If you liked our answer to the question, “What is a Joule?”, you might want to read the following articles from Universe Today:
The gravity formula that most people remember, or think of, is the equation which captures Newton’s law of universal gravitation, which says that the gravitational force between two objects is proportional to the mass of each, and inversely proportional to the distance between them. It is usually written like this (G is the gravitational constant):
F = Gm1m2/r2
Another, common, gravity formula is the one you learned in school: the acceleration due to the gravity of the Earth, on a test mass. This is, by convention, written as g, and is easily derived from the gravity formula above (M is the mass of the Earth, and r its radius):
g = GM/r2
In 1915, Einstein published his general theory of relativity, which not only solved a many-decades-long mystery concerning the observed motion of the planet Mercury (the mystery of why Uranus’ orbit did not match that predicted from applying Newton’s law was solved by the discovery of Neptune, but no hypothetical planet could explain why Mercury’s orbit didn’t), but also made a prediction that was tested just a few years’ later (deflection of light near the Sun). Einstein’s theory contains many gravity formulae, most of which are difficult to write down using only simple HTML scripts (so I’m not going to try).
The Earth is not a perfect sphere – the distance from surface to center is smaller at the poles than the equator, for example – and it is rotating (which means that the force on an object includes the centripetal acceleration due to this rotation). For people who need accurate formulae for gravity, both on the Earth’s surface and above it, there is a set of international gravity formulae which define what is called theoretical gravity, or normal gravity, g0. This corrects for the variation in g due to latitude (and so both the force due to the Earth’s rotation, and its non-spherical shape).
Astronomy Cast’s episode Gravity gives you much more on not just one gravity formula, but several; and Gravitational Waves is good too. Be sure to check them out!
There is not one, not two, not even three gravity equations, but many!
The one most people know describes Newton’s universal law of gravitation:
F = Gm1m2/r2,
where F is the force due to gravity, between two masses (m1 and m2), which are a distance r apart; G is the gravitational constant.
From this is it straightforward to derive another, common, gravity equation, that which gives the acceleration due to gravity, g, here on the surface of the Earth:
g = GM/r2,
Where M is the mass of the Earth, r the radius of the Earth (or distance between the center of the Earth and you, standing on its surface), and G is the gravitational constant.
With its publication in the early years of the last century, Einstein’s theory of general relativity (GR) became a much more accurate theory of gravity (the theory has been tested extensively, and has passed all tests, with flying colors, to date). In GR, the gravity equation usually refers to Einstein’s field equations (EFE), which are not at all straight-forward to write, let alone explain (so I’m going to write them … but not explain them!):
G?? = 8?G/c4 T??
G (without the subscripts) is the gravitational constant, and c is the speed of light.
where a is the acceleration a star feels, due to gravity under MOND (MOdified Newtonian Dynamics), an alternative theory of gravity, M is the mass of a galaxy, r the distance between the star in the outskirts of that galaxy and its center, G the gravitational constant, and a0 a new constant.
