A misconception that can exist, in Quantum Mechanics.

First of all, I need to admit that I did not study Quantum Mechanics. I did study Physics, however, and have had numerous discussions with people, who either:

  • Studied Quantum Mechanics independently, Or
  • Studied Quantum Mechanics formally.

And those discussions have made me aware of a misconception that can exist, about how the wave-function of particles lead to measurement, but which will certainly not exist, for people who have studied the subject formally.

I have already made a posting, about The Myth Of Wave-Particle Duality, in which I highlighted what I see as an absurdity, in how the wave-function of particles is commonly defined. And, having written that, I should also point out, that the common sense which QM applies, not to treat Complex Eigenvalues as representing real properties of a particle, fails to spill over, to Complex Probabilities.

Even though the wave function of certain particles can be taken to exist factually, attempts to measure it as belonging to one particle will cause it to collapse. However, the way some people may visualize it, would be, that the wave-function continues to exist, simply because the Universe seems to be filled with waves, that continue to exist. And this is an especially possible misinterpretation of QM when the particle in question is a photon, just because low-energy photons, that lead to long and obvious wavelengths – i.e., radio waves and light from lasers – are so commonplace.

What happens with these obvious waves is that, most of the time, a large number of photons contribute to those waves, in such a way that each photon is being absorbed, in order for the actual wave to have been measured. And, when the photon is absorbed, as I have written elsewhere, it has also been ‘witnessed’, so that it is no longer in a superposed state. And, because one photon has been absorbed, it has also ceased to exist.

Even the way photons ‘work’ changes drastically, when individual photons have been measured. Modern physics is capable of measuring individual photons. When this happens, the detection of one photon either took place or did not. This can also loosely be described as ‘a click’, in contrast with ‘a wavelike phenomenon’, even if a more sophisticated method has been used, than methods that produce audible clicks. And it continues to be true for the low-energy photons, of which there will typically be a greater number, as it was with high-energy photons, that Historical Technologies such as a Geiger Counter were able to detect. This digital existence of single photons, when measured as such, is universal.

I suppose that a valid question which the reader may next ask could be, ‘How would this apply to Quantum Computing, which factually performs computations, based on wave-functions?’ And, there are basically two types of answers which I can think of. The actual Quantum Computer is a tiny device, that can work with individual photons, But:

  • When Scientists measure the output of a Quantum Computer, they may be using a larger number of actual Quantum Computers, all performing exactly the same computation, but in such a way that the combined light intensity is high enough to be measured directly at any instant in time, Or
  • They may be amplifying the photon which one Quantum Computing core actually outputs, so that one output photon leads to a more macroscopic phenomenon, through which Scientists can read the result of a Quantum Computation, Or
  • The optics of a single Quantum Computing core can cause numerous photons to perform the same computation.

Either way, even though the state within the Quantum Computer was defined in terms of QBits, what gets measured as output, is no longer so. Therefore, the Quantum Algorithm needs to be programmed in such a way, that the ability either to measure a photon or not to, will still lead to a successful experiment.

What I do know additionally is, that if the photon output by a Quantum Computer has been amplified, let’s say by a laser-like device, any superposition of the wave-function of the original photon has been collapsed, because, when lasers are used as light amplifiers, they also witness the Quantum State of the initial photon. (:1) At that point, the Quantum Computation has definitely ended.


 

 

One of the more remarkable observations I seem to have made about QM is, that ordinary refraction or reflection of light, such as by metallic surfaces or glass, does not seem to witness the photons. Anecdotally, the reader may present himself to his washroom mirror in the morning, secure in the knowledge that the mirror did not witness what the reader sees.  ;-) This form of light can continue in some superposed state. The reason I’ve concluded this, is the large number of experiments which Scientists carry out, and then write about, and which still seem to succeed, in spite of the fact that the Scientist’s apparatus has refracted or reflected the light used.

Now, whether the Scientist actually noticed, that he was refracting or reflecting the light, is a separate question. I suppose that if the experiment failed, the next thing the Scientist will naturally do, is search for why…

(Updated 7/12/2020, 14h55… )

Continue reading A misconception that can exist, in Quantum Mechanics.

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