There are certain truths that dictate the way we view the world. The earth is round. It rotates around the sun. The sun rises in the morning and sets in the evening. Gravity keeps us firmly on the ground. Or does it? Last week the New York Times published this fascinating article - “A scientist takes on gravity.” We asked our physics tutors to comment and got four just as fascinating articles back. Here’s the first one. Take a read and tell us what you think.
A new theory on the gravitational force proposed recently by a renowned physicist, Erik Verlinde of the University of Amsterdam, has caused quite a stir in the physics community and has even caught the attention of the media (see for example the New York Times article). Verlinde’s paper, titled ”On the Origin of Gravity and the Laws of Newton”, can also be accessed online.
To understand what the fuss is all about, some background is necessary.
As far as we know, there are only four forces in the universe: the gravitational force, the electromagnetic force (which, as its name indicates, accounts for both the electric and the magnetic forces) and two forces that operate only in atomic nuclei, the so-called strong and weak nuclear forces. Gravity is of course the most familiar of the four and was the first one for which an explicit formula was obtained (the universal law of gravitation, worked out by Newton over four hundred years ago).
In 1915, Einstein presented a new description of gravity that is more fundamental (and more beautiful) than Newton’s theory. In this theory, called general relativity, the gravitational force arises through the curvature of spacetime. Objects are not really pulled by a gravitational force as Newton had suggested, they instead simply move through curved spacetime and it is the bending of that spacetime that affects the motion of objects, which is what we then observe as a gravitational force. To understand this, consider the surface of a trampoline. If we make a baseball roll on this surface, it will move in a straight line. Now imagine that someone stands in the middle of the trampoline. The surface of the trampoline is now bent down by the weight of the person. If we now push a baseball on this surface not directly at the person but in some other direction, the path will not be a straight line but will curve due to the bending of the surface. In fact, if you push the baseball just in the right direction and at the right speed, it could roll around the person and come back to its initial position! If there was no friction, it could keep doing that forever, although in real life friction will cause it to spiral down until it hits the person. In general relativity, any object bends space and time around it, which affects the motion of other objects. For example, you could replace the person standing on the trampoline by the Earth, the baseball by the Moon and the surface of the trampoline
by space and time and you would get the General Relativity explanation of why the Moon orbits the Earth!
Although Newton had not understood the real nature of the force of gravity, it does not mean that his universal law of gravitation is useless! It is in fact an extremely good approximation to Einstein’s equations and in almost all practical applications Newton’s law of gravity is precise enough. Indeed, it’s Newton’s theory that was used to send men to the Moon. On the other hand, Einstein’s General Relativity allows the global positioning system (GPS) to be as accurate as it is.
Some strange properties of gravity started to be noticed in the 1970s through the study of black holes. For reasons we can’t go into in this blog entry, it was proposed that black holes have an entropy, a concept familiar to you if you have learned about thermodynamics. This came as a surprise. In thermodynamics, entropy is a measure of the disorder of a system. For example, imagine holding a stack of playing cards with the cards initially ordered (ace to king of hearts, ace to king of diamonds, ace to king of diamonds and ace to king of clubs). This is a state of low entropy because it is well ordered.
Now you shuffle the deck of cards. It is very unlikely (but not impossible!) that after having shuffled for a while, you will get back exactly the same order you started with. It is also very unlikely that all the first 26 cards will be black and the next 26 will be red, which is also a state that has a lot of order. What is much more likely is that the colors and suits will be pretty much completely mixed and there will be no order in the values of the cards (for example it is unlikely that there will be ten consecutive cards with the values 1 to 10, in that order). We then say that the disorder of the playing cards has increased due to the shuffling and therefore the entropy has increased. If you have done some thermodynamics, you know that entropy in that case is associated to arrangements of atoms and molecules, which therefore play the role of the playing cards in our example.
Then Stephen Hawking discovered that black holes have a temperature and emit radiation. In other words, black holes have all the properties of a thermodynamical system. In 1995, Ted Jacobson of the University of Maryland showed that Einstein’s theory of general relativity can be cast in a form that shows that entropy and temperature can be assigned to gravity itself (and not just to black holes)! But if this is the case, what is the equivalent of the playing cards in the case of gravity? In other words, what are the things that can be shuffled around to measure the entropy? Nobody knows for sure although there are some tentative ideas floating around in two very active areas of theoretical physics, superstring theory and loop quantum gravity (see for example the books Three Roads to Quantum Gravity by Lee Smolin, The Elegant Universe, and The Fabric of the Cosmos, both by Brian Greene).
We are finally in a position to understand the proposal of Verlinde. We need one last analogy. Imagine a very fine string resting on a surface and which is attached to one extremity while the other one is loose. Let’s imagine that you can move and shake the surface on which the string is resting; it’s on the surface of a book, for example. Now you shake the book violently and look at the result. It is very unlikely that the string will end up being completely straight because that’s a low entropy configuration. It’s much more likely that the
string will be curled to some extent.
Let’s say that the string is plunged into a liquid at some temperature. Then the molecules in the liquid will be hitting the string from all directions in a rather chaotic manner. Now we come to the main point. If you pull the string to its maximum length and then let it go, it is initially in a state of low entropy. And now you watch what happens. The molecular collisions will tend to make the entropy of the string increase, which means that the string will slowly bend in a random pattern that has a higher entropy. Now imagine that you pull again the string to its maximum length and this time you don’t let it go. You will then feel a force that pulls the string to a state of higher entropy (which corresponds to the string curled up). This is what is referred to as an ”entropic force”. And the higher the temperature of the liquid is, the stronger the force will be because the collisions with the molecules of the liquid will be more violent. Note that the force that you feel on the string is not a force produced by the string itself, it is really due to the collisions from the the molecules with the string. If we do not know about the molecules and the way they interact with the string, we can still write down equations describing the force exerted by the string on our fingers, but the equations we have thus obtained do not describe a real, fundamental force! The actual force at play is the force between the molecules and the string that plays a role during the collisions.
Verlinde’s proposal is that what we see as the force of gravity is actually an entropic force! It is important to understand that he does not identify what is the equivalent of the molecules in our string example.There must be some microscopic entities associated to gravity that plays that role, but it is definitely not ordinary matter because gravity is felt in empty space! It is something completely new, possibly something that makes up space and time themselves.
In other words, ”atoms” of space and time! Verlinde does not need, however, to identify these entities precisely in his theory. His basic idea is that, as two masses get closer to one another, the entropy associated to gravity increases (this is the basic idea, he obviously makes it more precise in his work). So that, as when the string gets pulled to a curled position because it is a state of higher entropy, two masses are pulled toward one another. For example, if you drop a penny from a certain height, the penny has less ”gravitational entropy” if it is at a lower height, and the tendency of physical systems to increase entropy will pull the penny down, which is we see as a gravitational force!
This is a completely new way to think of gravity. Indeed, in this approach gravity is not a fundamental force of nature, like the force pulling the string to curl up was just a consequence of the collisions with the molecules of the liquid and not a fundamental force (by the way, when Verlinde says in the NY Times article that he does not think that gravity exists, what he means is that he does not think that gravity as a fundamental force exists, not that objects are not attracted to one another!).
In addition, it begs the obvious question: what are the fundamental entities responsible for the entropy?
As mentioned earlier, nobody knows for sure!
Verlinde’s idea is still only a proposal and not all physicists think that it is a viable theory. In addition, there is no way yet to test experimentally if this is correct and it might prove impossible to do so, which would not make it useful as a physical theory. On the other hand, it could represent the first step in a completely new approach to gravity and lead to a more fundamental understanding of nature.
Dr Patrick L. has been with Tutor.com since 2008 and tutors physics. Read more comments on this New York Times article by other Tutor.com tutors.
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