Hypothesis Disproved

A linear polarizer which I had ordered on-line recently arrived, and I did a promised experiment today, to test a hypothesis.

Hypothesis:

In This earlier posting and This earlier posting, I had proposed what amounts to two hypotheses combined:

  1. That photons may be circularly-polarized as one of their fundamental states, specifically left-handedly or right-handedly, so that other states of light can emerge from those states, eventually also due to a superposition of these two, intrinsic states.
  2. That quantum superposition can generally be collapsed, after which it will not resume as such, but after which witnessing of the resulting state may still take place.

The second hypothesis was meant as a synonym, for stating that:

  • Quantum-Mechanics is to take a form, in which certain states of particles are primary, while others are secondary, so that the secondary states can only form from the superposition of the primary states, while the reverse does not follow. This paraphrasing of the second hypothesis was further meant as a motivation to test, whether the particle-nature of matter and energy are in fact primary – hence, the circularly-polarized photons – and not the wave-nature.

Equipment used in the experiment:

A circular polarizer: A complex component, which has the logical operations of filtering light first, so that only light whose wave-function is plane-polarized along one axis is transmitted, and then secondly, to circularly-polarize the resulting light, so that its wave-functions along any two axes will be phase-shifted 90⁰ with respect to time. This was meant as a source for a primary state of light, polarized in an unknown direction out of two possible directions, since the retail store that sold me this circular polarizer, also did not label, whether it would produce left-handed or right-handed light. It’s to serve as a sufficiently-reliable source of circularly-polarized light.

A linear polarizer: A technically simpler component, which simply transmits light whose wave-function is plane-polarized along one axis, while absorbing light, whose wave-function is perpendicular to the plane transmitted. This was meant as an alternative, secondary state of light, formed as the superposition of left-handed and right-handed, circularly-polarized light.

A light-source: To consist of a mundane room-lighting fixture, which is assumed to generate randomly-polarized light.

Comments:

  1. The matter will be regarded as trivial, that when stating ‘the wave function’, I am referring to ‘the electrostatic wave-function’, which is assumed to be perpendicular to the magnetic wave-function, while also being in-phase with it at all times.
  2. The question will be ignored, whether the circular polarizer itself physically consists of two distinct layers, that perform its logical operations one-by-one, or whether it is of some other design, that accomplishes the same logical operations in some other way.

Procedure:

Control:

Light from the light-source will first be passed through the linear polarizer, and then through the circular polarizer, to confirm that two axes of plane-polarized light, when perpendicular, will lead to near-zero overall transmission, while when they are parallel, will lead to maximum transmission, which will also be used as the notional reference, corresponding to ‘50% transmission’.

Test-Case:

Light from the light-source will first be passed through the circular polarizer, the output of which is somehow to correspond to photons polarized in one circular direction, after which it will be passed to the linear polarizer.

Expected Result:

Because according to the hypotheses, the circularly-polarized light corresponds to an intrinsic state, which will no longer become superposed with the opposite state, the second component, the linear polarizer in the test-case, should not be able to output linearly- or plane-polarized light, because to do so should require the availability of both left- and right-handed photons. But, the linear polarizer will only receive a full amplitude of one or the other.

Real results:

Control:

The control case performed as expected.

Test-Case:

In the test-case, regardless of what orientation was chosen between the two polarizers, light emerged from the last, with constant brightness corresponding to ‘50% transmission’.

Conclusion:

While the principal is to be upheld, that circularly-polarized light may be one system for stating polarization, out of which plane-polarized light can emerge, eventually through quantum superposition, the reverse also seems to be possible.

However, this does not seem to favor an intrinsic state, as belonging to classical concepts of a particle, because the wave-function can be manipulated, regardless of the eventual existence of particles. And so this result further seems to suggest that wave-particle duality is plausible.

(Further Observations as of 02/24/2018 : )

Continue reading Hypothesis Disproved

Quantum Superposition, Quantum Entanglement

There is some ambiguity, with how I see other sources defining “quantum superposition”. From what I can extract, If there is a quantity of particles, whose combined wave-function is of a mixed nature between two other wave-functions, and if single particles are thought to emerge from that quantity, it can happen that the state of each particle is unknown, with a probability function between the two, mixed states. In that case, the particle can be superposed, as if having properties belonging to both states.

I think that some public writing fails to distinguish between the quantum superposition, and a possible, simple mixing of the properties of particles, whose states may be distinct.

(Edited 02/21/2018 :

In any case, if a particle is superposed, then one category of phenomena which may follow, is that its state may be “witnessed”, at which point it is no longer superposed. But while its state is superposed, without collapsing this superposition, its superposed states can have an effect on whether it can be witnessed or not. Specifically, if the wave-functions of the two states cancel out, then the presence of the particle cannot be detected, and therefore, its state can also not be witnessed. )

(As of 02/21/2018 :

As a result of a recent experiment, I’m learning to modify my vocabulary to some extent. As I now have it, the collapse of superposition of states is not always possible. But, a state can nevertheless be witnessed as belonging to one out of two entangled photons, in which case it will either be equal or opposite, depending on the case, to the corresponding state of the other particle, of that entangled pair of particles.

Whether this state is defined by the superposition of a separate pair of states, may not be relevant, to whether it can be witnessed.

My experiment did not involve entanglement. But, I’m inferring ideas from it anyway, and this would be a hypothetical example:

  1. A type of entanglement is possible, that affects linear polarization.
  2. A type of entanglement is possible, that affects circular polarization.

Example (1) should lead to matching, while example (2) should lead to opposite states. More specifically, Example (1) should lead to an inversion along an arbitrary axis.

I should add a detail which most people already know:

  • When a particle is witnessed as having a defined state, that state also changes.

End of Edit, 02/21/2018. )

I think that some experiments with entangled particles have as their basis, to use such cancellation, to reduce the rate at which some particles are witnessed in one beam, in an attempt to communicate this event to a second beam, whose particles should be entangled with the particles of the first beam.

The only part of this that really interests me for the moment, is the fact that light could be plane-polarized, and that at the same time, its photons could be in some superposed state. If a Polarizing Mirror next tries to extract light from that beam, which is polarized perpendicularly to the original direction, then the wave-function of this sought direction would be zero – even if this is due to cancellation. And then, not only would the amplitude of the derived beam be zero, but the state of the particles in the original beam, would also not be witnessed.

This would be, because a polarizing mirror actually ‘does something’, when a photon has the selected combination of properties. In contrast, if the linear polarizer is a Gel-Block, it ‘does something’, when photons have the opposite of the selected combination of properties – it absorbs them. Thus, for a gel-block not to witness the particles, it needs to be oriented parallel to the direction of polarization of the original beam.

Dirk

 

The Myth of Wave / Particle Duality

This posting describes some of the History, which many people may be bypassing, in their appreciation of Quantum Mechanics.

About until the 1920s, ‘light’ was largely thought to consist of waves. But a problem with that was, how to explain, why light can travel through apparently empty space. After all, the light that reaches us from distant stars is not fundamentally different, from light that originates on Planet Earth. And until the 1920s, it was believed that there exists a mysterious “Aether“, which transmitted light through space.

A basic premise of wave-propagation, such as in the case of sound-waves, is that there must first be some sort of medium, to conduct the waves, which in the case of sound may be air. But the need for the existence of a medium, also explains why there is no sound in space.

But during the 1920s, the existence of an aether was disproved. Decisively. And so another explanation was needed, of what constitutes light. And the thought seemed more logical, that particles can easily travel through empty space – hence, photons. Even though this was not actually the first form in which photons were theorized.

But then obviously, this raises questions, about how these particles are supposed to relate to waves, where waves were at first easier to observe.

I think that the way many people today are presented, what Quantum-Mechanics consists of, is just, “Wave / Particle Duality”. But then what many students believe – and what I once believed myself – is, that Quantum Mechanics holds some sort of secret key, as to how Matter and Energy might simultaneously consist of particles and waves. And in reality, QM holds no such decisive, secret answers. The only real secret which QM may hold, is a detail that could be embarrassing to the present way in which QM works.

Continue reading The Myth of Wave / Particle Duality

About Why the output of a Laser is so Wavelike

The subject of wave-particle duality continues to mystify commoners, while the ultimate explanation given by experts, who need to be schooled in Quantum-Mechanics for years, before they are exposed to these secrets, seem to defy some common-sense reasoning. More specifically, the way in which Quantum-Mechanics mainly explains it, is that the wave-phenomena, specifically those that take place in a vacuum, only exist as being secondary to the existence of particles. We think we can see many examples in our practical world, where waves ‘seem real’.

One such example is the beam of light output by a Laser, that is both monochromatic and coherent, that is highly parallel, and that only seems to make its wave-nature obvious. It is this ultra-high consistency of the wave-nature of a Laser-beam, that also makes it useful for creating holograms – aside from the fact that the beams output from these devices have many more uses today.

But in a way that might disappoint some skeptical thinkers, this nature of the light output from a Laser is actually predicted by Quantum-Mechanics, and fails to provide a contradiction to it. And I will explain why.

Quantum Mechanics is largely built around the Heisenberg Uncertainty Principle, although Heisenberg did not dare to assign complex numbers to his probability clouds yet. Those probability clouds are supposed to represent the superposed states of a particle, with the additional detail that they can be phase-shifted according to understanding today, which means that they seem to conserve a two-component number – i.e. a complex number.

What the uncertainty principle seems to state, is that the precision with which the position of a particle can be known, is inversely proportional to the precision with which its momentum-vector can be known, and vice-versa.

Photons are understood to have momentum vectors, even though when the photon-energy is low, such as for visible light, that momentum-vector also has low magnitudes. But the momentum-vector of a photon is supposed to follow entirely from the direction-vector it is traveling with, as well as being inversely proportional in magnitude, to its wavelength. The energy of the photon is also inversely proportional to its wavelength.

Because of the nature of the light output by a Laser, all the variables needed to know the momentum-vector of its photons are known – and are exactly equal. So the precision of their momentum-vectors is actually zero – i.e. their momentum vectors should have a variance of zero, based on the fact that they are parallel and fully monochromatic.

And so it would only seem to follow from the Uncertainty Principle, that the variance with which their position-vectors should be knowable, should be off-the-scale. By that logic, the position-vector of any one photon in the beam, cannot be knowable.

And so we seem to obtain a beam of light, only the wave-nature of which is knowable.

Dirk