Quantum Reality: Beyond the New Physics

by Nick Herbert

Left to itself, the total energy contained in an ordinary wave never changes; likewise the total probability contained in an...

The law of the conservation of energy is a familiar concept: energy can neither be created nor destroyed—only en...

Because of the way that waves add, four energy units show up at the interference site—two energy units have appeared out of nowhere! The process of in-phase (constructive) interference leads to a local energy surplus: more energy comes out than goes in.

Two units of energy go into the interference site; zero units come out—two energy units have vanished into thin air! The process of out-of-phase (destructive) wave addition leads to a local energy deficit: more energy goes in than comes out.

RANDOM PHASE WAVE ADDITION

Two units in; two units out. For random superposition of waves, energy is exactly conserved.

we check the accounts carefully we find that no energy is gained or lost overall: energy missing from the d regions exactly matches the energy excesses in the c regions. Although it redistributes wave energy in an inequitable way, wave interference, like every other physical process, obeys the law of (total) energy conservation.

When ordinary waves superpose with definite phases, energies do not add everywhere. When these same waves superpose with random phases, energies add everywhere.

When quantum waves superpose with definite phases, probabilities do not add everywhere. When quantum waves add with random phases, probabilities add everywhere. In Chapter 8 we will see that some physicists believe that the qualitative difference between random and coherent wave addition has important consequences for where one should draw the boundary line between quantum and ordinary reality.

FOURIER’S ...

Fourier’s theorem, the key to the new wave language, is the foundation stone of all wave-based sciences including communications theory, modern optics, sound reproduction, oceanography, and quantum theory.

Fourier’s theorem states that any wave can be written as a unique sum of sine waves.

The sine wave is a kind of undulatory archetype; its curvy profile is what most people have in mind when they visualize a wave.

Physicists like these waveforms because when they put a sine wave into any linear system, a similar sine wave always comes out. Linear systems change a sine wave’s amplitude and phase but they never change its sinusoidal shape.

Mathematicians like sine waves because no matter how many times they differentiate them, the result is always more sine waves.

The gist of Fourier’s important discovery is that sine waves form a universal alphabet in terms of which any wave can be written.

Just as a wave can be broken up into sine waves, so the same wave can be put together out of sine waves, an operation called “Fourier synthesis.” Fourier’s theorem tells us how to build any imaginable wave out of sine waves.

MUSIC SYNTHESIS

An impulse wave is an infinitely narrow spike of sound.

NEWTON’S PRISMS

Recently Fourier techniques have proliferated due to development of computer programs which rapidly analyze complex waveforms into their sine wave components.

THE SYNTHESIZER THEOREM

almost any waveform family will work as the basic alphabet of a wave language.

synthesizer theorem—

The synthesizer theorem says that as far as providing a basic alphabet for waves is concerned, there’s nothing special about Fourier’s sine waves.

a wave, in short, has no intrinsic parts.

WAVEFORM FAMILIES

personal

impulse wave family.

The spatial sine wave family

The temporal sine wave family

The spherical harmonic waveform family

According to the synthesizer theorem, a wave w can be written in a waveform alphabet drawn from an infinite number of waveform families.

There is one family to which it is closest in a certain sense, and one family from which it is most distant

The number of waveforms into which a prism splits a wave is called that wave’s spectral width, or sometimes bandwidth.

The size of this bandwidth bears an inverse relation to how closely wave w “resembles” the prism waveform which is analyzing

among all the waveform families in the world, there is one family (family M) whose prism gives the largest possible bandwidth when it’s used to analyze wave w. The members of family M resemble w the least. I call this prism—the prism that splits wave w the most—its conjugate prism.

Just as every wave belongs to a unique waveform family, so every waveform family possesses a conjugate family whose members are its polar opposites.

SPECTRAL AREA CODE

the spectral area code when applied to waves of quantumstuff leads immediately to the Heisenberg uncertainty principle.

Now due to semantic backformation more and more textbooks on ordinary wave theory refer to this natural limitation on mutual spectral widths as the uncertainty principle despite the fact that in its application to ordinary waves it has nothing to do with uncertainty.

quantum theory represents the unmeasured world as a wave identical in its behavior to ordinary waves, but interpreted in a decidedly non-ordinary manner. This

EPILOGUE: A FAMILY OF SPHERICAL WAVES

Whenever a sphere vibrates, certain nodal circles appear where the sphere stands still. On one side of the nodal circle, the sphere’s surface is moving in; on the other side of this boundary, the sphere is moving out.

all nodal circles are lines of definite latitude or longitude.

spherical harmonics possess personal names which are discrete.

fact that some waveform families have discrete names means, when applied to quantum waves, that certain physical attributes must be quantized.

Despite different notions about what they’re doing (indicative of physicists’ confusion about what quantum theory actually means), both theorists will come up with the same result.

From Berkeley to Gorky, quantum physicists predict quantum facts in exactly the same way.

Quantum theory by design only predicts the results of measurements; it does not tell us what goes on in between measurements.