## What If – Yao Zhecheng

What if the universe we live in has a different Planck constant? What if high-temperature superconductors are discovered? What if we can store the power of lightening for everyday use?

This week’s fact of the week will seek to provide an answer to those fascinating “what if” questions in physics.

What if Planck constant was 6.63 X 1030, how would this change the world?

These issues are very tricky. Again, the only thing that makes physical sense is to change *dimensionless* quantities. For instance, change the fine structure constant alpha. The reason for that is that we could work in natural Planck units where h = 1, c = 1, G = 1. All of physics can be expressed that way, and there it doesn’t make sense to ask what will happen when h changes value!

You would first have to say how the other constants, like the lightspeed, the mass of the electron and so on would alter. But let us assume that we keep the lightspeed and the mass of the electron constant. In that case, you’ve just re-defined the units “second” and “meter”, and kept the universe the way it is.

The reason is that the planck constant gives you a definition of what means 1 J s = 1 kg ms-1: it says essentially that 1 kg ms-1, is  times the spin angular momentum of an electron.

Lightspeed essentially says that 1 m s-1 = 1/(3.00 X 108) = 3.34 X 10-9 times the velocity of light.

The electron mass essentially says that 1 kg = 1/(9.109 X 10-31) = 1.098 X 1030 times the mass of an electron.

Let’s define the new units kg’, m’ and s’

If we say now that Planck’s constant equals 6.63 x 1030, then this means that 1 kg’ m’2 s’-1   times the spin angular momentum of an electron.

Keeping lightspeed, it means that 1 m’ s’-1 = 1/(3.00 X 108) = 3.34 X 10-9  the speed of light.

Keeping the electron mass means that 1 kg’ = 1/(9.109 X 10-31) = 1.098 X 1030  times the mass of an electron.

Now, you can say that you want to KEEP 1 kg = 1 kg’, 1m = 1m’ and 1s = 1s’. However, each unit is defined in a particular way, as a certain number of times a physical quantity. By keeping the mass of the electron, we’ve used the mass of the electron as our definition of the unit kg.

The lightspeed is just a definition of the ratio of the unit of length over the unit of time: if we keep it numerically the same, both units are now in fixed relation. In the same way, the planck constant relates the combination of the unit of mass, of length (square) and of time so that it is a certain number times the angular momentum of the electron. All this means that if we change that number, we’ve just changed the unit of length (and, because of the fixed ratio (lightspeed!), the unit of time).

In fact, 1 kg = 1 kg’, and 1m’ = (6.6 X 10-34)/(6.63 X 1030) = 10-64 m and 1s’ = 10-64 s.

When Planck’s constant becomes very big, then all physical laws will tend to become quantum laws. In such a case we would have a world exclusively governed by quantum physics, with everything proceeding through quantum jumps.

If the electromagnetic force becomes greater, then the strong force will no longer have that sufficient energy to bind nucleons together and our world will collapse into protons and neutrons.

A high-temperature superconductor levitating above a magnet

Diagram of the Meissner effect. Magnetic field lines, represented as arrows, are excluded from a superconductor when it is below its critical temperature.

What if high T super-conductors are discovered? Sadly right now we do not have all those magnificent technology available to realize its full potential. Even the unobtainium of electronics-super high T superconductors are discovered accidentally these days, they may not have applications beyond the boundaries of labs in a few decades to follow.

Superconductors are not perfect—they are far from what we expect them to be. Though you can manipulate to create the bizarre anti-gravitational effect via causing diamagnetic materials to float in air and even straight out of Earth, the energy you spend to hold the superconductor in position will be exactly the same as you use a rocket to propel it up into cloud. Currently developed high T superconductors are all defected either for their brittleness or the inability to hold much charge and their superconductivity is highly sensitive to external electric and magnetic field, they must be well protected and cooled in liquid nitrogen. And these limitations will hamper our effort to try to utilize the superconductors as a effective electric cell to store electricity in excess and many industrial applications may only be a smoke in the air.

The Meissner effect was given a phenomenological explanation by the brothers Fritz and Heinz London, who showed that the electromagnetic free energy in a superconductor is minimized provided. where H is the magnetic field and λ is the London penetration depth.
This equation, which is known as the London equation, predicts that the magnetic field in a superconductor decays exponentially from whatever value it possesses at the surface.
A superconductor with little or no magnetic field within it is said to be in the Meissner state. The Meissner state breaks down when the applied magnetic field is too large. Superconductors can be divided into two classes according to how this breakdown occurs. In Type I superconductors, superconductivity is abruptly destroyed when the strength of the applied field rises above a critical value Hc. Depending on the geometry of the sample, one may obtain an intermediate state[8] consisting of a baroque pattern[9] of regions of normal material carrying a magnetic field mixed with regions of superconducting material containing no field. In Type II superconductors, raising the applied field past a critical value Hc1 leads to a mixed state (also known as the vortex state) in which an increasing amount of magnetic flux penetrates the material, but there remains no resistance to the flow of electric current as long as the current is not too large. At a second critical field strength Hc2, superconductivity is destroyed.

In a weak applied field, a superconductor “expels” nearly all magnetic flux. It does this by setting up electric currents near its surface. The magnetic field of these surface currents cancels the applied magnetic field within the bulk of the superconductor. As the field expulsion, or cancellation, does not change with time, the currents producing this effect (called persistent currents) do not decay with time. Therefore the conductivity can be
thought of as infinite: a superconductor.

Superconductors in the Meissner state exhibit perfect diamagnetism, or superdiamagnetism, meaning that the total magnetic field is very close to zero deep inside them (many penetration depths from the surface). This means that their magnetic susceptibility, χv = −1.

Since the late 1980s there have been several attempts to investigate the possibility of harvesting energy from lightning. While a single bolt of lightning carries a relatively large amount of energy, this energy is concentrated in a small location and is passed during an extremely short period of time (milliseconds); therefore, extremely high electrical power is involved. It has been proposed that the energy contained in lightning be used to generate hydrogen from water, or to harness the energy from rapid heating of water due to lightning.

A technology capable of harvesting lightning energy would need to be able to capture rapidly the high power involved in a lightning bolt. Several schemes have been proposed, but the high energy involved in each lightning bolt render lightning power harvesting from ground based rods impractical. According to Northeastern University physicists Stephen Reucroft and John Swain, a lightning bolt carries a few million joules of energy, enough to power a 100-watt bulb for 5.5 hours. Additionally, lightning is sporadic, and therefore energy would have to be collected and stored; it is difficult to convert high-voltage electrical power to the lower-voltage power that can be stored.

In the summer of 2007, an alternative energy company called Alternate Energy Holdings, Inc. (AEHI) tested a method for capturing the energy in lightning bolts. The design for the system had been purchased from an Illinois inventor named Steve LeRoy, who had reportedly been able to power a 60-watt light bulb for 20 minutes using the energy captured from a small flash of artificial lightning. The method involved a tower, a means of shunting off a large portion of the incoming energy, and a capacitor to store the rest. According to Donald Gillispie, CEO of AEHI, they “couldn’t make it work,” although “given enough time and money, you could probably scale this thing up… it’s not black magic; it’s truly math and science, and it could happen.”

According to Dr. Martin A. Uman, co-director of the Lightning Research Laboratory at the University of Florida and a leading authority on lightning, a single lightning strike, while fast and bright, contains very little energy, and dozens of lighting towers like those used in the system tested by AEHI would be needed to operate five 100-watt light bulbs for the course of a year. When interviewed by The New York Times, he stated that the energy in a thunderstorm is comparable to that of an atomic bomb, but trying to harvest the energy of lightning from the ground is “hopeless”.

A relatively easy method is the direct harvesting of atmospheric charge before it turns into lightning. At a small scale, it was done a few times with the most known example being Benjamin Franklin’s experiment with his kite. However, to collect reasonable amounts of energy very large constructions are required, and it is relatively hard to utilize the resulting extremely high voltage with reasonable efficiency.