Spacetime the final frontier! At least, this is what the producers of Star Trek and Brian Greene would like us to believe.
Space and time form the very fabric of the world, an arena of reality upon which all events both human and non-human play out. Professor Greene of Columbia University devotes his book to a study of this fundamental concept from various viewpoints and in the process teaches us some things about Newtonian physics, quantum mechanics, cosmology and string theory.
Though invisible, Newton and other early scientists regarded space as an almost physical medium, a substance that allowed, for example, light to propagate from one place to another. Space was to light as water was to a wave. This notion was dispelled by the Michelson-Morley experiment.
If space were a medium, a so-called ether, then it should be possible to deduce Earth's motion through it. Unlike a boat in water, however, one cannot simply reach overboard to feel the current. If ether exists, Earth's motion through it is more difficult to sense.
Detecting ether can be achieved by observing light. One's measurement of the speed of light should depend on whether one is moving with the ether or against it or in some other direction. This is true of water waves; they pass by you more quickly if you row against the current.
In the nineteenth century, Michelson and Morley performed an experiment to detect Earth's motion through a possible ether but found a null result: The speed of light did not change during the year-long period in which the Earth moves around the Sun. One's measurement of the speed of light is independent of how fast or in which direction one is moving. Ether does not exist.
In Einstein's special theory of relativity, time is united with space and it becomes impossible to separate the two. Measurements of lengths and time intervals are observer-dependent: Suppose two supernovae events take place in different parts of the universe. Then, two observers moving at extreme speeds with respect to one another do not measure the same distance between the supernovae nor do they measure the same amount of time that has elapsed between the two explosions. Events that are seen to be simultaneous in one inertial reference frame are seen not to happen at the same time in another frame. Time (and also distance) is relative. These effects are not noticeable if one observer is moving relatively slowly with respect to the other, but if their relative speed approaches that of light, the effect is pronounced.
In Einstein's general relativity, the notion of a cosmic fabric returns. However, it does not involve just space. General relativity builds on special relativity. As such, time and space are united into one entity: spacetime; and spacetime is regarded as a dynamic medium that can stretch and bend. Massive bodies such as planets and stars create significant warping of spacetime. When other objects move through such a curved medium, they no longer travel at constant speeds in fixed directions; in other words, they accelerate. And this acceleration is what we attribute to gravity. From Einstein's viewpoint, gravity arises from the curvature of a dynamic spacetime.
Special relativity destroyed the concept of ether. General relativity resurrected it.
Brian Greene analyzes all these issues using both standard arguments, origin examples, various insights and illuminating analogies. The historical development is also presented going back even as far as Plato and Aristotle but mostly focusing on what has been discovered since Newton.
The Fabric of the Cosmos is not an easy book to understand. To appreciate it, one should have a level of understanding commensurate to that of an undergraduate physics major. Given this, it is hard to fathom how the book has made it on the New York Time's best seller list. Of course, having had a first best seller The Elegant Universe by the same author on the list certainly helped.
Occasionally, the discussion in the book borders on philosophy. At one point, Greene even asks, "What is reality?" Another example is when he tries to address fundamental questions about time: Does it have a beginning? Does it always flow forward? Can one travel back in time or fast-forward into the future?
The list of topics that Greene covers is enormous. Besides the topics mentioned already, there are discussions about cosmology, dark matter, particle physics, Nature's symmetries, unification of forces, the Big Bang and inflation, string theory, M-theory and braneworlds, hidden dimensions and black holes. No wonder the book is 500 pages long. In this review, we discuss three issues.
How does one then determine the direction of time in physics? One way is to use the second law of thermodynamics. It says that the entropy of the universe almost always increases with time.
Entropy is a measure of the probability that something might happen. Hence, the second law simply says that the universe evolves to what is more probable. This certainly seems reasonable.
When an egg is dropped and spatters on the floor, it makes a mess. Before being destroyed, the egg was in a very ordered state its organic molecules had been carefully arranged so that, under the right conditions, a life form would begin to develop. Eggs are a very unlikely arrangements of molecules. To drive home the point, it is doubtful that you find them on the Moon, on Mars or on Mercury. Eggs have achieved their rare state through the use of a lot of work and energy by another low-entropy individual: a chicken.
On the other hand, the mess on the floor is a more probable state for the molecules of the egg. They are randomly arranged with little concern for placement. There are also many possible arrangements, almost infinitely many messes that can be made. In contrast, the arrangement of molecules in an egg is quite unique.
So the above process, the smashing of an egg, exemplifies the second law of thermodynamics. One has gone from an unlikely situation to a more likely one.
If you think that you've never known about the second law of thermodynamics, think again. Through your experiences, you have used the law to judge the direction of time. Given two movies, one in which an egg falls off a table and splatters and one in which the splatter is tossed upward and converges miraculously into an egg, you will immediately recognize that the second movie is being run backwards. Although not perfect because it is not fundamental and may be violated for small systems and for extremely short moments, the second law allows one to assign a direction to time.
We shall now discuss two issues in quantum mechanics: decoherence and entanglement. Quantum mechanics introduces confusion and complications concerning the nature of spacetime.
It turns out that at the microscopic level, say at the scale of a molecule or smaller, nature is probabilistic. In a world governed by classical mechanics, objects have definite positions and velocities. In quantum mechanics, this is not the case. For example, the position of an electron in an atom is determined only probabilistically. It might be that there is a 25% chance that the electron is within 0.5 Angströms of the nucleus, a 50% chance that it is at a distance from 0.5 to 1.5 Angströms, and a 25% chance that it is beyond 1.5 Angströms. These probabilities are encoded in what is known as the wave function. Quantum mechanics provides a precise way of computing the wave function and the associated probabilities.
The probabilistic nature of the universe significantly manifests itself only at small distances. In the macroscopic world that humans are used to, there is still uncertainty but it is so small as to be not noticeable. Quantum mechanics also reproduces almost perfectly the results of classical mechanics for macroscopic objects. This is known as the correspondence principle.
The notion of quantum probability is difficult for most of us to comprehend because we do not directly observe atoms, nuclei, elementary particles and other microscopic entities. When the microscopic is connected to the macroscopic, paradoxical situations seem to arise. Two of these are Schröndinger's Cat and the Einstein-Podolsky-Rosen (EPR) paradox.
Electrons can spin in only two ways, clockwise or counterclockwise, each with one fundamental unit of spinning. This is a quantum mechanical effect. A football may spin in any amount depending on how much a quarterback snaps his wrist. No so for an electron. The amount that it rotates is quantized to a fixed quantity.
The spin of an electron is easily detected with appropriate equipment. Such a device reports whether the electron spins clockwise or counterclockwise.
The quantum mechanical wave function determines the probability of an electron's spin. In many elementary processes that produce an electron, there is a 50% chance that it spins clockwise and 50% chance that is spins counterclockwise.
An unusual feature of the quantum world is that various possibilities (that are determined probabilistically) coexist simultaneously. For example, consider the electron's spin. When an electron is produced, it is not generated with a definite spin. Rather, it is produced in an ambiguous situation in regard to its spin. This ambiguous state, which represents 50% clockwise and 50% counterclockwise rotation, persists until something interacts with the electron to change its wave function.
If a device measures the spin of the electron to be clockwise, then at that instance, we know that it spins clockwise with 100% probability. However, just before the measurement is made, there was still a 50% probability of achieving either spin motion. The sudden change in probability is the result of a rapid modification of the wave function. Such a sudden transformation is called the collapse of the wave function. In the above example, the collapse is due to the detection process itself.
What is being said here is that probabilities are intrinsic in quantum mechanics. Quantum mechanics is not simply classical mechanics with probabilities imposed. Here are three versions of a scene in a movie that clarify what is going on.
Movie Scene Version 1: Two people, Mary and John, meet at Lebanon, Kansas, which is close to the geographical center of the United States. They have in their possession two tee shirts. One has "clockwise" written on it and the other has "counterclockwise" on it. Mary, who will travel to New York, has been told to wear the clockwise shirt. John, who is heading to San Francisco, will wear the counterclockwise shirt. When they arrive at their respective airports, their parents meet them and compliment them on their nice tee shirts.
The scene is similar to what happens in classical mechanics. The actors follow a script; there is determinism and no uncertainty.
if you sense that something about it cannot be correct,
if you feel uneasy and uncomfortable, you are not alone.
Einstein had the same sentiments.
Movie Scene Version 2: Mary and John, meet at Lebanon as in Version 1 above, but this time they flip a coin to decide who wears the clockwise tee-shirt. When Mary wins, she puts on the shirt and then flies to New York.
The above is again analogous to a situation in classical mechanics. However, this time there is uncertainty due to the flip of the coin. The actors really do not know which shirt they will wear in the movie until they view the coin.
Movie Scene Version 3: Mary and John meet as in Versions 1 and 2. They travel from Lebanon to New York and San Francisco. In the movie, it is not shown who wears which tee shirt. But just as they are about to meet their parents, the scene switches to a dark room where a coin is flipped. When heads come up, Mary's parents see her wearing the clockwise shirt. John's parents in San Francisco see him in the counterclockwise shirt.
In this surrealistic scene, Mary does not know which shirt she is wearing until the secret coin flip is performed. Version 3 is the one most similar to what transpires in quantum mechanics.
In one rendition of Schröndinger's cat, an animal is placed in a box and the lid is closed. Inside the box is a vial of deadly poison. In the experiment, an electron is generated in an uncertain spin state that is 50%-chance clockwise and 50%-chance counterclockwise. A detector inside the box will trigger the emission of the poison only if the spin is clockwise. As the electron enters the box through a small hole and heads towards a detector, there is a 50% chance that the cat will die.
To be sure of the outcome, we must open the lid. Some scientists claim (and it is often stated in books) that, until the lid is opened, the cat exists in a quantum mechanical state of being 50% dead and 50% alive. They argued that only by observing the cat do we collapse its wave function and determine the poor animal's fate. It seems absurd that a cat could be suspended in such an uncertain state. This paradox has been used to argue that quantum mechanics is incomplete as a theory.
However, no paradox arises. When the electron strikes the detector, its wave function is thoroughly transformed. The "collapse" takes place. From this point onward, the spin has been determined to be either clockwise or counterclockwise with certainty. If the cat dies, it has been dead for some time before the scientists lift the lid. Indeed, if they wait days before looking into the box, they will observe decay and smell a stench.
In terms of the analogies above, we are in movie version 3 up until the electron strikes the detector. After that, the situation is best described by version 2.
Although it is possible to construct states in which a microscopic entity such as an electron is "suspended in uncertainty" among two or more possibilities, it is virtually impossible to construct the analogous thing for macroscopic objects. There is essentially no way to create a quantum state of a cat in which it is 50% dead and 50% alive. The process in which virtual certainty arises in going from the microscopic to the macroscopic is called quantum decoherence.
Movie Scene Version 3 is designed to illustrate how the probabilistic nature of quantum mechanics cannot be eliminated until an observation, measurement or interaction takes place. It is often incorrectly stated that human involvement is needed at this stage. This is not the case a detector, electron or photon will do. Indeed, any object that interacts with the entity in consideration can cause a change or collapse of the wave function.
Physicists have studied the decay of a particle that emits two electrons in opposite directions such that their spins are correlated to be unknown but opposite. These electrons can travel macroscopic distances before machines measure their spin. It is always found that if the spin of one electron is clockwise then the spin of the other is counterclockwise. Some scientists find this paradoxical violating both quantum decoherence and the special theory of relativity.
Imagine waiting until the electrons are several light years apart before applying the spin detectors. Through the detection of the spin of one electron, one instantly gains knowledge of the spin of the other distant electron. For this reason, it might appear that special relativity is violated. This is not the case. Indeed, in movie version 1, when Mary's parents see her in New York, they instantly know which shirt John is wearing, yet information has not traveled faster than the speed of light.
The reason why special relativity is not violated in the above cases is that a correlation has been established at an earlier moment. In the case of movie version 2, this took place when Mary and John were at Lebanon, Kansas. In the case of the electrons, it took place at the time they were created through the decay of the particle. These earlier events are casually connected to the detection events of the parents observing the shirts and of the machines measuring the spins. Hence, there is no inconsistency. For an application of this idea that one day might save the world, click here.
The struggle that some scientists have with the Einstein-Podolsky-Rosen paradox arises because of the additional conceptual difficulties associated with quantum mechanics. Until one of the electron's spin is detected, the situation is suspended in uncertainty: 50% probability for one state and 50% probability for another state. The entanglement of the wave functions of the two electrons persists over macroscopic distances, and the collapse of the wave function and quantum decoherence is only achieved after one of the two electrons is detected.
Version 3 illustrates the mind-boggling situation. Who is wearing which shirt is not determined until a parent sees a child. If the coin had turned up tails, Mary would have been wearing the counterclockwise shirt. Indeed, it the affair is repeated, sometimes John is wearing the clockwise shirt and sometimes the counterclockwise one. The situation is completely uncertainty at the time the airplanes arrive, and in no way was determined when the two departed from Kansas. In a movie, one can quickly call a break and have the actors change their clothes. In the quantum world, this happens automatically and instantly.
Some scientists, who have not fully embraced the implications of quantum mechanics, have argued that the universe involves some "hidden variables" that allow everything to be explained classically but probabilistically. They would like to argue that the "dice" are really thrown at the time of the correlation event and not at the time of the measurement. For them, movies unfold only in versions of type 1 and 2. However, other physicists have been able to construct experiments to rule out the existence of hidden variables. In the quantum world, surrealistic-like movie scenes like the one in version 3 actually do take place.
General relativity resurrected it.
There is a big difference between a probabilistic classical universe and a quantum universe. In the former, probabilities obey certain, well-known, logical rules of mathematics. In the latter, the wave functions are combined first subject to interference effects, and then the probabilities are extracted. For this reason, the rules governing probabilities in quantum mechanics are not always the same as in standard probability theory.
If you find the above discussion about quantum mechanics to be counterintuitive, if you sense that something about it cannot be correct, if you feel uneasy and uncomfortable, you are not alone. Einstein had the same sentiments. However, many of Einstein's thoughts about quantum mechanics were shown to be wrong by other great physicists. The problem here that we simply lack experience with the very strange quantum mechanical universe.
Many of the topics in The Fabric of the Cosmos are discussed in Jupiter Scientific's book The Bible According to Einstein such as (1) the birth of the Universe and the Big Bang: Genesis I: The Planck Epoch and Genesis II: The Big Bang, (2) Inflation: Genesis V: Inflation, (3) superstrings: Chapter V: Superstring Speculation: Truth or Superstition? of Moments in Modern Science, (4) Einstein's life and ideas: Einstein, (5) dark matter: Chapter IV: Dark Matter of Moments in Modern Science, (6) quarks: Chapter IV: The Recent Developments of History of Elementary Particles, (7) electroweak symmetry breaking and the Higgs field: Chapter VIII: The Mystery of Fundamental Mass of Moments in Modern Science, (8) classical physics, (9) special relativity, (10) general relativity and (11) quantum mechanics.
Jupiter Scientific's myriad webpages presents reports and information that overlap with the following subjects in Greene's book: (1) history and age of the universe, (2) Inflation and developments in cosmology, (3) recent measurements of the cosmic microwave background radiation, (4) dark matter,(5) dark matter (radio conversation), (6) accelerating universe, (7) special relativity, (8) important unsolved problems in science, (9) general relativity, (10) string theory, (11) particle physics, (12) quantum mechanics, (13) the Michelson-Morley experiment, (14) a book review of Hawking's A Brief History of Time, and (15) a book review of Smolin's Life of the Cosmos.
The Fabric of the Cosmos is available through the internet at Amazon.com. Jupiter Scientific participates in Amazon.com's Associates Program.