Quantum mechanics is the theory that we use to describe the microscopic world. The microscopic world is the realm of atoms, photons, nuclei, electrons, neutrons, and a whole host of other subatomic particles. These particles are the “building blocks” of our universe, in the sense that everything that is observable in the macroscopic world that we can see and feel around us is the result of the presence and interactions of these elementary particles.
Quantum mechanics is also an inherently probabilistic theory, in that there exists uncertainty at the most fundamental level when we try to measure any value, or observable, of a system. This is unlike classical and relativistic theories, where everything exists with precise and definite values, and the time evolution of a system can theoretically be determined as far into the future as we want. This is not the case in quantum mechanics; we can only define probabilities to the future behaviour of a system. Despite its seemingly limited nature, quantum mechanics has been extremely successful at explaining and illuminating the microscopic world, which classical Newtonian mechanical theory is unsuccessful at explaining.
First, a little history. The initial seed that was to later grow into the quantum theory that we have today was Max Planck’s postulate that energy is quantised, or comes in discrete packages, as opposed to existing in an infinitely continuous series of states. He put forward this postulate in order to explain the phenomena of blackbody radiation. He postulated that an electromagnetic wave can only interact with matter in integer multiples of h, where is the frequency of the wave, and h is a quantity known as Planck’s constant. Planck’s constant has a value of h = 1.05457 10-34 Js, which is an extremely small number, and it is because the value of Planck’s constant is so small that we don’t ordinarily notice any of the behaviour associated with quantum mechanics in the macroscopic world around us. Only by probing the microscopic world do we encounter the strange and mystifying behaviour of sub-atomic particles.
In 1905, Albert Einstein used the idea of quantised states to explain the photoelectric effect. He explained the observed frequency dependence of the emitted particles by postulating that light energy too comes in tiny discrete bits, or quanta. These discrete light packets, or photons, also come in integer multiples of h, with here being the frequency of the light.
A paradigm shift was beginning. In 1913 Neils Bohr was able to explain the observed spectral lines of a hydrogen atom by quantising the atom. He postulated that atoms could only exists in states of discrete energy, and that any interaction between a hydrogen atom and any surrounding radiation could only happen as integer multiples of h. For example, the hydrogen atom can only be raised to the first excited energy state from its ground state if it absorbs exactly one times h. Likewise it can only be raised to it’s second excited state from it’s ground state if it absorbs exactly two times h, and so on. Bohr’s quantisation of the hydrogen atom successfully explained the problems that the classical model could not.
In 1924, Louis De Broglie showed that matter itself had wavelike properties. He derived the equation, = h/p, that related a particle’s momentum with an associated wavelength. This equation tells us that all matter has wavelike properties, and must in some cases be thought of as existing as a wave, rather than as a discrete particle.
The explanations put forward by these scientists successfully explained many outstanding problems, and only by assuming quantised states. However these explanations were not based on any underlying theory, with the idea of quantisation seeming to be arbitrarily postulated. A more rigorous theory was needed, and soon emerged, extending and developing the work of Planck, Einstein, Bohr, De Broglie, and others. This theory came to be known as quantum mechanics.
In 1927, Werner Heisenberg developed his uncertainty principle, which states that you cannot know both the momentum and position of a particle at the same time with absolute certainty. The uncertainty principle gives us a limit to our knowledge of a system, and tells us that we can never determine exactly the future behaviour of a system, because we can never exactly determine it’s present state! In more mathematical terms, we can never determine two related observables simultaneously. We can only say that something might happen with some probability, but never with certainty.
The Schrodinger equation is another fundamental part of quantum mechanics. This wave equation, which Schrodinger derived in 1925, tells us the evolution of a quantum mechanical system in time. The full equation is:
[-/2m2 + V(r)](r,t) = i(r,t)/t
This equation is a classical equation in the sense that it does not take into account special relativity. It has the classical kinetic energy term on the left, rather than the relativistic term for kinetic energy. Paul Dirac was to derive a relativistic version of the Schrodinger equation in 1928.
In 1925 the concept of spin was introduced by Ralph Kronig. Spin is the intrinsic angular momentum that a microscopic particle possesses, although the concept of spin is a bit different from what it means in classical mechanics. In classical mechanics, an objects angular momentum is due to its rotation around its central axis, or around an extended axis.
Spin angular momentum in quantum mechanics does not arise from a particle actually spinning like a top, rather it is an intrinsic property of a particle, like its mass. An important thing to note is that spin is quantised. It can only have discrete values. For example, protons, neutrons and electrons are all “spin half” particles, that is, they have spin values that are one half , where = h/2, and h = Planck’s constant. A hypothetical particle that will play a large part in the conflict between general relativity and quantum mechanics is the graviton. This as yet undetected particle is a spin two particle, meaning two times .
Let’s look at what quantum mechanics has to say about the fundamental forces. We have known since Newton’s time what forces are. A force can basically be defined as something that causes the state of an object to change; whether it is a change in the object’s motion, temperature, electrical charge, or potential energy; a force is responsible. However Newtonian mechanics does not specify any mechanism by which force is transferred, except in the most basic sense. It tells us that when an object is in contact with another you have some force between them. Newton’s laws tell you what the effect of a force is, and how to calculate the magnitude of a force, but they do not have much to say about what actually happens at the microscopic level when forces act - the actual mechanism by which a force acts.
Quantum mechanics gives us that mechanism. It has been determined after much smashing of particles together that forces are the result of the exchange of force particles that transfer force from one object to another. Every interaction in the known universe can be explained by the exchange and effect of force particles. A wonderful discovery relating to forces has been that all interactions between objects can be reduced to the work of four fundamental forces. Those fundamental forces are: The strong nuclear force, the weak nuclear force, the electromagnetic force, and gravity. And each of these four forces has associated force particles that are responsible for the force.
The strong nuclear force is the force that holds together protons and neutrons in an atomic nucleus. More specifically, the strong force can be thought of as having two aspects, one which holds together the quarks within protons and neutrons, and the other that holds protons and neutrons together in a nucleus, known as the fundamental strong force and the residual strong force respectively. The fundamental strong force arises due to the interactions of eight different types of force particles called gluons. The residual strong force is due to the interactions of mesons. The strong nuclear force is a very short range force, not usually having any influence further than the radius of a proton or neutron.
The weak nuclear force is responsible for things like radioactive beta decay, which is when a neutron turns into a proton, with an electron and an anti-neutrino being emitted in the process. The force particles responsible for this force are called W and Z bosons. The weak nuclear force is also a very short range force, only acting over distances not bigger than an atomic nucleus. This force is about one billion times weaker than the strong force.
The electromagnetic force is the force that acts between electrically charged particles. This includes all electric and magnetic forces which arise from the motion of charged particles, and also from stationary electric charges. This force is responsible for most of the phenomena we see around us, such as light, friction, and the structure of elements and molecules. This force can be both attractive and repulsive. The force particle responsible for electromagnetic interactions is the photon.
When we say that the interactions of forces are due to the exchange of force particles, this means that force particles are emitted from their “parent” particles, and these force particles then interact on another particle, and this interaction results in a force. To use the electromagnetic force as an example, we can think of an electromagnetic field consisting of huge cloud of photons that are emitted from a charged particle. When two charged particles exert force on one another, they shoot photons out between themselves. Classically this looks like two electromagnetic fields interacting.
The fourth fundamental force is Gravity. It is the attraction that all masses have for each other. It is the weakest of the four forces, approximately 1036 times weaker than the electromagnetic force, but it is always attractive, and has the longest range of all the forces. Consistency would indicate that a force particle must also exist for the force of gravity, and has been dubbed the graviton. Since the other three forces have been successfully explained by assuming force particles, it makes sense that gravity would also be the result of some particle exchange. So the graviton was postulated, with the expectation that a quantum gravity theory would quickly pop out, one that is consistent with general relativity.
However this was not to be. Conflicts and inconsistencies soon arose due to the fundamental differences between relativity and quantum mechanics, which will be elaborated on in later pages.
One fundamental difference is that general relativity says that spacetime is warped due to the presence of masses, and the force of gravity is not the result of any particle, but due to the curvature of spacetime. For example, a planet circling the sun appears to be in orbit due to the gravitational force exerted by the sun, but general relativity tells us that the planet’s orbit is due to its passage through curved space. It is attempting to take the straightest path through curved geometry. Thus no force particle is needed in general relativity. The nature of spacetime will be explained in the general relativity section of this website.
An interesting thing happens when we try to probe the microscopic world at greater and greater levels of magnification; space becomes more and more turbulent, or frothy. Space loses its “smoothness” in that quantum indeterminancy becomes more and more prominent. The Heisenberg uncertainty principle gives us a limit as to how much we can know about a system. The more we try to pin down space and time, the greater the indeterminancy in the system grows, in that the values a system can take grow larger and larger – the values can fluctuate wildly. As we zoom in on space and time, we find that quantum fluctuations start to turn space and time into a violent and energetic proto-stuff, or as the physicist John Wheeler calls it, “quantum foam”. Einstein’s smooth spacetime soon becomes a hyperactive froth where concepts such as up-down, left-right, before-after, cease to have any meaning. When we try to examine the gravitational field, we find that the quantum fluctuations distort and warp space and time so much that it is simply impossible to think of space and time as smooth. The weakness of gravity and the miniscule size of Planck’s constant combine to give us a value to where these fluctuations take place, known as the Planck length, which is roughly 10-35 metres in length. In this realm of existence, the geometry of spacetime is smashed up and destroyed by the Heisenberg uncertainty principle.
In quantum mechanics time is thought to have a fixed, non-dynamic structure as opposed to relativity. Time exists as an absolute quantity, like in Newtonian mechanics; it is the background on which quantum mechanical interactions take place. However just as there is a limit in our measurements of space due to the Heisenberg uncertainty principle, so is there a limit when we try to measure time. The smallest unit of time that has any meaning in quantum mechanics is known as Planck time, which has a value of: 5.391 10-44 seconds. This is the length of time it would take a photon travelling at the speed of light to travel one Planck length. Also, when we try to examine the origin of the universe, we cannot determine or measure any difference between the actual moment the universe came into existence and one Planck time unit after.
With the concepts and ideas introduced in the general relativity section and quantum mechanics section, we are now ready to examine the conflict between the two theories more closely, and look at the possible solutions.
REFERENCES NEEDED STILL AND PROBABLY REWRITE SOME BITS