Kinkajou : So tell us how the quantum world affects the visible real world.
Erasmus : Quantum effects are most visible at very high energy levels, such as exist in the stellar environment. Astronomers deal with quantum effects in stellar realm often.
Planets increase in size as they get the mass till the point they are approximately 1.7 times the mass of Jupiter (540 earth masses). At this size adding further mass causes gravity to compress the mass of the planet, causing the planet to shrink in size. Planets reach a maximum size at approximately 70 Jupiter masses.
At approximately 75 Jupiter masses, planets become stars. At this point, energy generated by nuclear fusion reactions within the star cause the diameter of the stellar body to increase.
Heat from fusion reactions creates thermal mediated pressure effects which cause the stellar body to expand. So planets are at their most dense at just below the critical size at which they are able to initiate and sustain fusion reactions.
This last fact generates yet another constraint, because the energy radiation of a sphere suspended in a vacuum obeys a law known as the Stefan-Boltzmann Equation:
L = C R2 T4 (Total luminosity of a hot sphere)
Here L is the luminosity of the star, C is a constant1, R is the radius of the star in meters, and T is the surface temperature of the star in K°. Note how swiftly the energy radiated by a star rises with T: doubling the temperature causes its energy output to increase by 16 times.
Erasmus : In short stars begin to shine and to radiate energy.
In quantum mechanical theory, electrons are normally constrained to occupy energy and momentum states that exist in specific quantised values. This is relevant to electrons that are constrained within a single atom.
However, within the stellar environment gravitational pressure forces the atoms to shrink. Eventually a point is reached or a single electron overlaps a number of atomic nuclei. At this point there exists only one single quantum state of low energy level across an increasing number of atomic nuclei, as gravitational pressure aggressively increases.
The other electron is prohibited on quantum mechanical grounds from overlapping the existing electron. Gather electrons are pushed into high energy states. As the states fill as well electrons are pushed progressively into higher and higher energy quantum states.
Eventually, the electrons within the depth of the star gain energy levels equivalent to 100,000 electron volts (note the normal electron energy is equivalent to approximately nine electron volts in orbit around a hydrogen proton).
Electrons as a gas and Star Size
Erasmus : Today electrons are regarded as essentially wave phenomena. However they do have discrete mass and momentum and at times act as if they are particles. This particle aspect is useful to us in examining behaviour of electrons within the stellar environment.
If you regard electron as a gas particle, this amount of energy is equivalent to approximately a temperature of 1 billion° Kelvin.
These energy levels are sufficient to rip the electrons away from the atomic nucleus. They are then free to wander throughout the star much like a gas.
Physicists call this unusual state of matter: “electron- degenerate” matter. At this point a star of perhaps a quarter of solar mass (equivalent to approximately 80,000 earth masses), is packed into a volume not much more than double earth radius. Stars with this profile are common.
Astronomically they are described as white dwarfs, because they are very small very hot and tend to radiate white light energy.
The motion of the atomic nuclei is almost unaffected by the change in our electron accompaniment. We believe that the electron naked nuclei travel much like lead shot bullets through a gas. Protons and neutrons making atomic nuclei have their own quantum states, which are substantially higher than those of electrons.
Astronomic Body radiation Energy
Key factor controlling the activity the electron gas is the mass of the white dwarf star which determines its gravitational field. Temperature change is essentially irrelevant in the internal activity of the electron degenerate matter. Normal gases increase in volume when they are heated. However, electron degenerate matter behaves more as an exotic incredibly dense liquid than as a gas.
Liquids do not change much in volume in a heated they only get hotter. Hence electron degenerate matter is much more difficult to compress than normal matter or gases, even though at times it appears to have some of the properties and general structure of a gas.
Erasmus : However, a threshold is soon reached. In 1931 a 21-year-old theoretical astrophysicist called Subrahmanyan Chandrasekhar published a number of papers on electron degenerate matter.
The calculations in his papers calculated the critical point at which electron degenerate matter fails to sustain itself against the force of gravity. Calculations relate to Einstein’s theory of relativity in that as electrons become hotter and travel faster than in two approach speed limits as constrained by relativity, namely the speed of light (“c”).
His calculations predicted the white dwarf above the critical mass above approximately 1.4 times the mass of our sun, would catastrophically collapse.
This came to be known as Chandrasekhar's Limit. While treated with disdain by the astronomical community. It was a fact that astronomers had discovered no white dwarf stars with the mass above 1.4 solar masses.
As the radius of the sun decreases, new gravitational theory predicts the force of gravity is proportional to the inverse of the radius squared, (1/r2). Hence, halving the radius of the sun quadruples a gravitational field at surface, creating a collapse situation.
Chandrasekhar's Limit describes as the fate that awaits those stars with the mass above 1.4 times the mass of our sun. Above this size, electron degenerate pressure cannot support the core of the sun against further collapse.
Rapidly increasing density forces the star to compact resulting in the formation of structures such as a neutron star, a black hole or possibly even a quark star.
The situation is a little bit more complicated this. Main sequence stars up to approximately eight solar masses, do shared mass as a result of their heat and particle radiation.
They will often shed sufficient mass to form a white dwarf star having a mass below Chandrasekhar’s Limit. The effects of heat and particle radiation modify the evolution of the effects of the nuclear and gravitational reactions that control a stars fate.
For very massive, low-metallicity stars, it is also possible that instabilities will destroy the star completely.) During the collapse, neutrons are formed by the capture of electrons by protons in the process of electron capture, leading to the emission of neutrinos.
The decrease in gravitational potential energy of the collapsing core releases a large amount of energy which is on the order of 1046 joules (100 foes). Most of this energy is carried away by the emitted neutrinos. This process is believed to be responsible for supernovae of types Ib, Ic, and II.
Stars within the main sequence remain in hydrostatic equilibrium between inward gravity and outward heat/radiative pressures. Red giant stars lose mass at a high rate and are not in hydrostatic equilibrium but on a process of physical evolution.
A white dwarf may well not be fusing anything within its core and may only be radiating energy. The stars such as the sun the process of evolution continues until the superficial superheated gas layers are lost in the stellar core becomes exposed for white dwarf stars.
Paradoxically, as the core increases in size the wife dwarf becomes denser. Thus the smaller a white dwarf is in diameter the larger as its mass.
White dwarf stars are intrinsically very faint because are so small and having consumed their nuclear fuel, their luminosity deteriorates rapidly as they cool down. Again note the Stefan-Boltzmann Equation:
L = C R2 T4 (Total luminosity of a hot sphere)
Star Stability and Size
Erasmus : The tight interrelation of temperature, pressure, mass, and rate of nuclear burning means that a star of a given mass and age can only achieve hydrostatic equilibrium at one set of values. That is, every star in our galaxy of the same mass and age as the Sun also has the same diameter, temperature, and energy output.
There is no other way for everything to balance. If one generates a very hard-core astrophysics graph known as a Hertzsprung - Russell diagram (H-R diagram for short), the relationship between a star's mass and its other properties becomes clearer.
The main sequence exists precisely because of the inflexible nature of hydrostatic equilibrium. Stars with very low masses (as little as 7.5% that of the Sun) lie at the lower right of the H-R diagram.
They must lie at the lower right. This part of the H-R diagram corresponds to extremely low luminosity – as little as a ten thousandth that of the Sun – and low surface temperature, equivalent to the dull orange-yellow glow of molten metal.
These stars do not have enough mass to create the pressure necessary to make the nuclear burning in their cores go any faster. High-mass stars (upwards of 40 solar masses) reside at the upper left, as they must.
Contrary to the low-mass stars, their immense masses and high central pressures give rise to giants that can be 160,000 times more luminous than the Sun, and so hot that they give off more energy in the ultraviolet than they do as visible light.
The Sun lies almost exactly halfway between these extremes, and thus it is neither extremely dim nor extremely bright as stars go. It shines with a bright yellowish-white colour.
The Collapse of High Mass Stars
Erasmus : The one-to-one nature between mass and hydrostatic equilibrium means that as you vary the mass of a star, all you can do is slide along a single, predetermined track with respect to all its other physical properties. This track is exactly the main sequence.
But now that I've said that, a second look at the H-R diagram reveals that there is a smattering of stars well off the main sequence: they are concentrated in "islands" at the upper right and lower left.
Since the stars at the upper right are very luminous yet nonetheless have cool, reddish surfaces, astronomers call them red giants. Similarly, since the stars at the lower left are very dim yet also white-hot, they are called white dwarfs.
We have met the white dwarfs already, in a theoretical way. Now let's see where the real ones come from.
Astronomers traditionally classify main-sequence stars with letters, like so:
O - 30,000 to 40,000 K°
B - 10,800 to 30,000 K°
A - 7240 to 10,800 K°
F - 6000 to 7240 K°
G - 5150 to 6000 K°
K - 3920 to 5150 K°
M - 2700 to 3920 K°
Within each class, numbers from 0 to 9 provide subclasses, with zero being the highest subclass (highest temperature). The Sun is classified as a G2 star.
Star Sizes Limits
Kinkajou : So let’s move on old dog. Let’s have a look at what tech is needed for human race to migrate into space.
Erasmus : “The potential for faster than light communications are very exciting”. A solution seems to teeter at the edge of your awareness. This is one idea that I feel that I should almost be able to work out for myself.”
Erasmus: The trouble of course is that you get that impression after reading analogies for the original quantum experiments in books. While these are useful learning tools, they are not reality. Reality requires a more complex understanding. You learn rapidly that what you have “learned” is not true, (only sort of “true”), in a manner of speaking.
Quantum mechanics may offer us a way to bypass the theoretical limitations on the maximum speed of a photon: the speed of light. It could allow essentially instantaneous communications over any distance. If the human race ever wishes to embrace space, it will desperately need some form of faster than light communications.
There are a number of points of view about the possibility of creating Quantum radio communications. Obviously, via the concept of entanglement, paired photons or other particles can acquire their properties as if they were paired.
If the photons are widely separated, this entanglement occurs effectively at faster than light. It is as if the space, between the two particles, does not really exist.
Recent work suggests that perhaps even time does not exist in this alternate dimension of entangled matter.
However, some information theorists hold that it would be impossible to use this property to communicate. They state: Say that firstly the properties of one group of particles were all determined.
Then the experiment is conducted on a second group of particles or photons. The no communication theory (based on Quantum statistics), says statistically, Observer B Bob cannot tell the difference between what Observer A did and a random measurement (or whether Observer A did anything at all).
Kinkajou : That’s mind expanding and confusing. So where does that leave us?
Erasmus : I think the current state of play is that quantum informatics research has generated the ability to transfer qubits of information. “I think it’s difficult to say what we will one day be able to accomplish.
I would sum up the arguments for and against the Quantum radio communication concept as this: “And yet they entangle”. Something happens. The issue is whether we can work out a clever way to exploit this.
Erasmus : If faster than light communications are possible, the possibility is based on the concept of quantum entanglement.
Kinkajou : But surely there are even more possibilities growing out of our understanding of quantum mechanics.
A plethora of opportunities Travelling Sideshow: physics
Erasmus: yes! Quantum tunnelling, quantum computing and quantum cryptography offer us many parts to the future. Even more exciting the possibility of FTL or superluminal travel. Perhaps one day the Stargate of fiction may be the Stargate reality.
Can macroscopic objects such as people or transport machinery access this alternate dimension and survive? Only research, persistence and time can give an answer.
We are already exploiting quantum mechanical effects, even in such superficially simple systems such as solar voltaic electricity generation. Even though we do understand some of these effects, further understanding can well increase efficiency and energy yields, changing commercial realities of solar voltaic electricity production.
New methods of imaging, seemingly at a distance can change the way we view and explore the world. Imagine studying lunar structures with entangled particles, and viewing the results by viewing their entangled twins not the exploring particles themselves. Weird!
I think we have summarised much of the science underlying as well as the cutting-edge of our understanding of the quantum mechanical world.
I’ll finish off by describing what we know about the electron today. Once thought of to be little particle in orbit around a small dense nucleus, now we believe them to be wave functions with perhaps some particle aspects. They no longer elementary particle but an agglomeration of elementary particles.