Top page ( quantum mechanics and Einstein relativity are wrong )

Quantum entanglement is meaningless.

Quantum computer, information are useless forever.

If you have already read the photon page, please proceed to the next section,

Bell inequality violation can be explained by classical electromagnetic waves!.

The photon particle is said to exist. But the *interference of a single photon with itself* can be explained only by the **wave nature** of the electromagnetic (E-M) waves, **NOT** by the photon particle.

*(Fig.1) Photon is particle or wave ?*

According to QED, a single photon must be a **point** particle.

But in various real experiments, they often use the classical electromagnetic waves such as left-, right-circularly, vertically, and horizontally polartized lights.

Though they clearly use the property **specific** to the classical lights, they **always** try to express them as a **photon** particle in some papers or something.

As shown in Fig.1, if the light is a **point particle**, how can it be polarized or interact with other particles ?

So the concept of photon "point" particle is **impossible**.

*(Fig.2) Entangled photon pair ?*

Entangled photon pair is often created by "parametric down-conversion".

In this process, a photon of wavelength λ enters some crystal, and is split into a pair of photons of wavelength 2λ.

So the total energy is conserved. (= their frequency becomes half ).

( If photon is a particle, it can be split so easily ?? )

One of the produced photon pair is horizontally polarized, and another is vertically polarized.

Though this photon pair is clearly **classical** electromagnetic **waves**, they always use the word of a "photon".

*(Fig.3) Photon "point" particle can interfere with each other ?*

Suprisingly, photon "point" particle can interfere with each other, according to their experiments.

In Fig.3 upper, due to the destructive interference between photons, they vanish !.

Conversely, in Fig.3 lower, due to the constructive interference, the number of photons (= amplitude ) has increased, they insist.

But as shown in Fig.3, these interferences prove that what they call "photon" is clearly **classical waves**.

*(Fig.4) Single photon detector shows photon is particle ? *

First, we **cannot** generate single photon directly.

By weakening coherent laser and seeing their electric current signal at photon detector, we only **estimate** their existence.

This detector **cannot** always detect photon ( < 60% ), when it enters, and due to dead time, **cannot discriminate** between a single and two photons.

Of course, as we cannot see directly a single photon, this photon's concept is only **speculation**.

Repeating **photoelectric** effect, photon detector increases electric current signals from a single photon.

Considering light loss in these processes, it is natural that we think photon detector can show current signal, when the light **intensity** is above some **threshold**.

*(Fig.5) Mach-Zehnder interferometer. *

In the Mach-Zehnder interferometer, when one photon is split into the two different paths at the beam splitter (= BS1 ), we can detect one photon **only in one of the two paths** at the same time (= Fig.5 ).

( This means that this single photon particle is NOT split into two, according to the *quantum mechanical interpretation*. )

*(Fig.6) Interference of a single photon. *

But the **interference** of electromagnetic waves from these **two** different paths is actually observed, though a single photon exists only in one of the two paths. It is amazing!

It is said that this strange phenomenon is caused by the *superposition* of one photon in the two different paths.

But is it really so?

This **"superposition" has NO reality**, because it is equal to "*many fantasy worlds*". (= world A and world B in this case. )

*(Fig.7) Photon = classical electromagnetic waves !*

For example, the first light intensity is

We suppose the photon detector can detect it when *the light intensity is 6* as a single photon.

So 10 is detected as one photon, not 2 photons (=12).

But the split photon (waves, 6 & 4) can *interfere with each other*.

And the 4 side is not detected, **only 6 side is detected as a photon**.

So we can explain the "strange" single photon interference by the *combination of the electromagnetic wave and detection threashold !*

For example, in case of the 50/50 beamsplitter ( BS1 ), if the E-M waves is split into 5 + 5, no photons can be detected. (This case is not recognized at all, so it can be ignored. )

We can recognize the photon existence **only when** we detect it as a photon.

50/50 beamsplitter divides **unpolarized** electromagnetic waves into about half on **average**.

Depending on the polarization and frequency of the light at the beamsplitter, this probability **changes**.

*(Fig.8) Beam splitter 2 ( BS2 ).*

After splitting at the beam splitter 1 (BS1), both the electromagnetic waves are split into almost half also by the beam splitter 2 ( BS2 ).

( For example, 6 → 3 + 3, 4 → 2 + 2 )

In this experiment, only one side reflection is supposed to reverse light phase at the beam splitter 2 (BS2), as shown above.

( The transmitted lights are not changed. )

So at the photon detector 1 (D1), the light **amplitude** is increased by constructive **inteference**, and can be recognized as a photon.

Because the light intensity at D1 **always** reaches "6" by the inteference.

(The light amplitude is a square root of the light intensity.).

*[ One photon "always" detected at D1 by the interference. ]*

On the other hand, at the D2 detector, the light amplitudes from the two paths cancel each other, so it can not be detected as a photon.

( The light intensity at D2 side does not reach "6". )

*[ At D2, no photon is detected by the interference. ]*

Of course, also when the first light "10" is split into 5 + 5 at the beam splitter 1, this result is the same as the above.

In this case the light intensity "5" is split into 2.5 + 2.5, so at D1 side,

And at D2 side,

In these cases, the total energies are conserved. ( 10 → 10 ).

As a result, we can explain all these phenomena by classical electromagnetic wave model.

*So they don't need the concept like "photon particles" at all. *

( See also Delayed choice experiment is real ?. )

*(Fig.9) Delayed choice experiment. *

In the delayed choice experiment, after a single photon has passed through the beam splitter 1 (= BS1 ), that single photon has entered into one of two paths.

Actually, by the photon detector, only one photon is detected ( for example, at D2 in the upper figure ).

What will happen, when we insert the beam splitter 2 (= BS2 ) **after** the photon has passed BS1 ?

Surprisingly, in this case, the electromagnetic waves **suddenly appear** in the two different paths, and interfere with themselves ! (= right panel of the upper figure. )

So we can choose the past event (= particle or wave ) from the future (= delayed choice ) !

Of course, in this **real** world, it is **impossible**.

So as I said above, the concept of a single photon itself is wrong.

( Unfortunately, ordinary people do not know about these strange things related to "photon" well . )

*(Fig.10) Photon spin is really " 1 " ? *

One photon is said to have "spin" ±1. *What in the world is the "photon spin 1"?*

The ordinary textbooks say that the photon spin ±1 correspond to the electromagnetic (E-M) waves with *left and right circular polarization*.

And the "*linear*" polarization corresponds to the *superposition* of these two states.

But this superposition state is **very strange and difficult to imagine**.

The quantum mechanics often uses a **mathematical trick** like this.

Then we can take this convenient word "superposition" in **every situation** arround us!

(e.g. when some things in different states are only mixed, when one thing is "vibrating" very fast, when one thing only keeps still....).

This means that the superposition itself is **meaningless**.

*(Fig.11) Fine-structure = "photon" spin 1 ?? *

To begin with, how this photon spin 1 was **discovered** ?

In 1910's, the fine structure of the hydrogen atom meant the relativistic energy difference between the 2S and 2P states of Bohr-Sommerfeld model.

But after the electron spin appeared, the **interpretation** of this fine structure was changed to the *spin-orbital interaction* ( = the energy difference between 2P_{1/2} and 2P_{3/2} of the hydrogen atom. See this page. )

"*Accidentally*" this value *coincided* with that of the Bohr-Sommerfeld model !

So the "unnecessary" transition ( = 2S ---> 1S) *needs to be forbidden* to explain the spectrum results of the hydrogen with electron spin.

Then the selection rule (2S --x--> 1S) was introduced, and they *made* the photon spin 1 which probably causes this selection rule.

This means that the photon spin 1 is only an **artificial thing.**

*(Fig.12) Point particle = photoelectric effect ?? *

It is said that the photoelectric effect needs the concept like "photon particle". But is it really so?

The electrons are always accompanied by the de Broglie's waves around them. And it synchronizes with the electron's momentum. So we must consider the de Broglie's waves rather than the **very small point-like electron** in case of the photoelectric effect or the Compton effect.

**Actually**, circularly or linearly polarized electromagnetic waves are emitted from exicited atoms in the experiments.

And Willis Lamb himself, who was great experimentalist dealing with the light, did **NOT** believe photon particle.

Recent interesting studies indicate that a single photon consists of **electromagnetic waves** ( in *both two slits* ) in the weak measurements.

(Science 2011, 332, 1170, S.Kocsis et al., Nature 2011, 474, 188, J.S.Lundeen et al.)

*(Fig.13) Frequency = photon particle is oscillating ? *

The ordinary textbooks often say that the *relation between the photoelectric effect and the wave's frequency* shows the particle's nature of the photon.

First, the **frequency itself is based on the electromagnetic wave nature !**

Second, when we *heat* the air or the water which give rise to "sound wave" or "wave", the *frequency* of each particle in those waves is increased.

So it is quite natural that the energy is related to the frequency.

( **Frequency, amplitude = wave nature !** )

In the Compton effects, if the light is a particle, its **velocity** would change instead of its frequency, when its momentum changes.

As I said above, the frequency itself is based on **wave** nature.

*(Fig.14) "Convenient" photon can pass through dark energy, matter, Higgs "uninjured"?*

As shown on this page, photon particle needs to have strange ability to go through very crowded space "uninjured" for very long time.

Redshift by expanding universe is thought to be caused by the **tired light**, in which the light loses energy while it is going through the space.

The shining duration from supernova is more elongated from farther stars.

You can imagine this reason from the difference between "marathon" and "100-meter race".

And the concept of photon particle is the **origin** of many-world interpretation and virtual photon, which violates relativity. ( See this page. )

*(Fig.15) Illusory superluminal action or entanglement is caused by the intentional misinterpretation of classical polarized light as a (illusory) photon particle*

The media and academia repeatedly spread **fake** news that quantum entanglement or spooky action indicates a **superluminal** link denying any realism, spawning many quantum mechanical fantasies such as parallel worlds.

This quantum entanglement or teleportation (= equal to entanglement ) cannot send any real information or do any work such as communication ( this 4th-paragraph, this 10-th-paragraph ), so the entanglement is a **meaningless** useless concept except for this.

Actually, the (illusory) quantum entanglement has **No** practical application, as seen in the still-useless (= forever ) quantum computer or quantum information.

If the misleading claim that the spooky entanglement could really send information faster than light is true, it clearly contradicts and **disproves** the current mainstream science where Einstein relativity prohibits any superluminal information ( this 6-7th-paragraphs, this p.4-6 ).

Then, why did physicists **mistakingly** start to say such an illusory and **contradictory** superlumial entanglement link may actually happen ?

In fact, this illusory quantum entanglement is just about "**measurement** of some states (= Not the act of sending real information )".

Physicists prepared two lights (or photons ) with some particular polarizations (= on this page, we use the case of two lights with the same parallel vertical-vertical or horizontal-horizonal polarization ), and they call these polarized lights "entanglement", which has **nothing** to do with the faster-than-light action.

When they measure one light (or photon ) as horizontally-polarized, this measurement instantly (= superluminal link ? No way ! ) determines the other light's polarization as horizontal ( this p.2-3rd paragraph ). ← That's all. Entanglement is Neither a superluminal link nor sending actual information ( this 2-4th paragraphs ).

In fact, the illusory superluminal quantum entanglement is caused by intentionally **misinterpreting** the ordinary **classical polarized light** wave as a *fictional indivisible photon* particle.

We explain this misinterpretation of entanglement and Bell or CHSH inequality violation based on the illusory photon pair here.

*(Fig.15') Superluminal nonlocal quantun entanglement vs. Quantum parallel-world theory with hidden variable compatible with Einstein relativity forbidding superluminal link.*

If the (useless) quantum entanglement or seeming superluminal spooky action is true, the quantum mechanics needs the fictional parallel worlds or many-world interpretation to avoid the clash with another mainstream science = Einstein relativity forbidding any superluminal actions ( this 5th-paragraph ).

↑ This is why the unrealistic parallel-world theory is accepted as the mainstream interpretation of quantum mechanics, as shown in the parallel-world quantum computers ( this 4th-paragraph ) which are unrealized forever.

↑ But even if physicists tend to choose (fantasy) many-world intepretation as the current mainstream physics, after all, the many-world interpretation **also needs** some **superluminal** spooky signal to determine which polarization or which world the distant entangled photon instantly chooses to explain the quantum superluminal entanglement, hence, it can**not** avoid contradicting another mainstream physics = Einstein relativity.

The (illusory) superluminal entanglement action is called "nonlocal", and the realistic action slower than light is called "local" or hidden variable theory.

*(Fig.16) The moment light (or photon )-A is measured as vertically-polarized, the photon-B also becomes vertically-polarized through (illusory) superluminal or instantaneous entanglement action ? ← This is wrong.*

In 1982, Alain Aspect showed that the Bell inequality (CHSH) was violated using the alleged entangled photons and claimed that it showed the existence of the faster-than-light entanglement link between two photons.

But in fact, this **false** cotradictory claim of the **faster**-than-light entanglement is caused by intentionally mistaking the ordinary divisible classical polarized light waves for the illusory indivisible photon particles (= illusory photons are red balls with fictitious polarizing arrows as shown in the upper figure )

In (illusory) superluminal quantum entanglement experiments, it is said that physicists used a pair of two polarized photons (= particle ? ), which were emitted from some special crystal or excited atoms.

Here we use the case where these two "alleged-entangled" photons are prepared to have the same **parallel** polarizations, when one photon A has vertical polarization (= V ), the other photon B also has vertical polarization, or when one photon A has horizontal polarization (= H ), the other photon B also has horizontal polarization.

Whether each photon has vertical or horizontal polarization is unknown and indistinguishable, until the measurement (= this condition is necessary for quantum entanglement ).

And when an observer measures one photon A as vertically-polarized, it **instantly** determines (= **superluminal** entanglement action !? No ! ) the distant other photon B as vertically-polarized ( this p.2 ), because these two photos A and B are prepared to have the same polarization in advance. ← This is the current ridiculous superluminal quantum entanglement logic, though physicists **never** show any detailed physical mechanism of this occult entanglement link. ← Science stops progressing due to fantasy quantum mechanics **forever**.

In fact, physicists use the ordinary classical electromagnetic wave and Maxwell electromagnetism as a fictitious quantum photon in entanglement experiments, so the occult superluminal quantum entanglement is impossible.

When physicists generate a pair of two alleged entangled polarized photons, they try to split one single (pump) photon into two daughter photons (= idler, signal ) with lower energy or frequencies by the method called "parametric down conversion" that just passes an incident photon (= just classical light wave or laser ) through the special crystals ( this p.4, this p.2-lower ). ← **No** magical superluminal entanglement

↑ First of all, it is impossible for a ball-like rigid photon particle (= if it existed ) to have the wave-like polarization or wave frequency, which is clearly the **wave** nature, Not a particle.

And the idea that an indivisible photon particle can split into **two** daughter entanged photons is self-**contradictory** and wrong.

In this parametric down-conversion process, they use the ordinary **classical** Maxwell electromagnetism where the incident **divisible** classical light wave's **electric** fields oscillate the atoms inside the crystal, and this atomic oscillation by the light electric field emits two electromagnetic waves, which process has **nothing** to do with a quantum indivisible photon (= but they **falsely** treat these newly-generated classical divisible electromagnetic light waves as indivisible fictitious quantum entangled photons, this p.5-6, this p.3-6 ).

Aspect used the excited calcium atoms moving in random directions as a source of entangled photons (= just classical light wave, this p.20 ), whose polarization points in the random directions satisfying one condition that these emitted paired photons (= or two lights ) have the polarizations parallel to each other.

Also in the down conversion entangled photon-pair source, whether each photon (= light wave ) has vertical or horizontal polarization is indistinguishable and unknown ( this p.6, this p.6-last ), hence, these unknown different polarizations are mixed and oriented in the random directions like non-polarized light.

↑ Illogical quantum mechanics wants to associate this "**classically mixed** light polarization state" with "unreal parallel-world superposition" of quantum entangled photons with different polarizations ( this p.5 ), under one condition that these two emitted photons (= lights ) have the same parallel polarizations, when they are measured.

↑ There is No (illusory) superluminal entanglement action between these (fictitious) photons (= just classical light wave ) here.

The ordinary divisible classical light wave can perfectly explain the experimental results or Bell inequality violation **without** such a fictional superluminal entanglement link.

*(Fig.17) Pass probability of a ( illusory unseen ) photon at a polarizing filter.*

According to the classical Malus' law, when the angle between the *polarization axis* of the electromagnetic light wave and the *polarizing filter* (= polarizer ) is **θ**, the classical divisible light **splits** into two weaker light waves at the polarizer where the *light intensity* passing the polarizer is I cos^{2}θ and the reflected light intensity is I sin^{2}θ (= of course, this rough probability estimation is different from the fact, considering the light loss ).

The point is this classical Malus' law is valid **only** in the **classical divisible** light wave, **Not** valid in the illusory indivisible photon particle.

But physicists tries to **falsely** apply this classical Malus' law also to the unseen illusory photon particle, which is why the **unrealistic** superluminal quantum entanglement idea is created ( this 9-11th paragraphs ).

*(Fig.18) Pass or reflect probability of a single photon at filter is false.*

Quantum mechanics **falsely** claims that even a illusory indivisible photon particle (= quantum particle of light ? ) satisfies the classical Malus' law ( in a little modified way, though, because the original Malus law is based on the **divided** classical light wave at the polarizer ).

They insist when a (unseen) photon particle with red arrow as the fictitious polarization hits the polarizing filter, this unseen photon can pass through this polarizer with the **probability** of cos^{2}θ where θ is the angle between polarizer's axis and the photon's polarization ( this-(4), this p,5-(11) ) **without** dividing each photon particle at each polarizer, which is **different** from the original Malus law.

And they insist the photon reflects off the polarizer with the probability of sin^{2}θ (= cos^{2}θ + sin^{2}θ = 1 ? this p.7 ) **without** dividing each photon particle.

The problem is that the single photon detector can**not** detect the very weak fragile photon (= just weak classical light wave ) with 100% detection efficiency due to the frequently lost photons and false dark count.

Usually, the photon detection probability or efficiency is far lower than 100% ( this p.8-9 ). The coincidence detection rate of two entangled photons is less than 20% ( this p.3-3, Fig.2, this p.3-Table.I, this Fig.2, Table I )

↑ This **low** photon (coincidence) detection probability at single-photon detectors causes the **illusion** such as faster-than-light spooky entanglement, which is called "detection loophole ( this p.3-2nd-paragraph, this p.4-left-lower )".

In order to eliminate the possibility of classical light wave, they need to achieve not only the high detection efficiency of each weak photon but also the extremely **high coincidence** detection rate of two paired photons, which is **impossible** in the photon entanglement experiments.

*(Fig.19) The probability of both ( fictitious classical ) photons passing their polarizing filters ?*

The fatal flaw of the (illusory) quantum entanglement is
physicists **falsely** try to compare the quantum photon entanglement experiments with the **unreal classical indivisible** photon particle (= Not real classical divisible light wave ), though such an indivisible classical photon particle does **Not** exist.

On this page, we use the case where two paired photons whose polarizations are parallel to each other are emitted in the opposite directions, and the photon A hits the polarizing filter A and the photon B hits the polarizing filter B.

Each photon passes or reflects from each filter it hits depending on the angle (= α or β in the upper figure ) between the photon's polarization and polarizing filter's axis.

The angle of each polarizing filter's axis can be freely changed in advance.

When the angle between the (fictitious classical) photon A's polarization and the polarizing filter A is **α**, the probability that the photon A *passes* through the filter A is **cos ^{2} α** ( ← (E cos α)

When the angle between the photon B's polarization and the filter B's axis is **β**, the probability of the photon's *passing* the polarizer is **cos ^{2} β**, and the reflection is sin

In this case, for example, the probability that **both** these (fictitious classical) photon particles **pass** their filters is ( **cos ^{2} α × cos^{2} β** ).

But this case **satisfies** the Bell inequality (= hence, no entanglement ) and is **different** from the experimental results, so physicists claim that (illusory) superluminal quantum photon's entanglement link is necessary, instead of adopting the real divisible classical light wave.

*(Fig.20) Experimental results. ( = proving fantasy faster-than-light entanglement ? ) = chance of both photons passing (and both photons reflecting from ) their filters is cos ^{2}θ where θ is the axis angle difference between two polarizing filters A and B. *

The actual probability of detecting two photons (= lights ) passing each polarzing filter is different from Fig.19 of two fictitious classical photons.

The probability that *both* of the two photons *pass* each filter is about **1/2 cos ^{2} (β - α)** (

Here, **θ = (β - α)** means the **angle difference between the axes of two polarizing filters A and B**.

The number of the coincidence count of two photons passing their filters seems to roughly obey the curve of **cos ^{2}θ** ( this p.4-Fig.3, this p.3-Fig.2 )

So physicists (**falsely**) claim that the quantum faster-than-light entanglement is real, **violating** the Bell inequality in some filter's angle θ. ← Nonsense.

Because if the probability of two (fictitious) photon particles A and B passing their polarizing filters A and B (= angle difference between two polarizers' axes is θ ) is cos^{2}θ, the following unrealistic interpretation is needed, when you use the indivisible photon particles.

When the photon A (whose polarization angle is different from the filter A axis by arbitrary α ) passes the filter A (= the photon A's polarization becomes parallel to the filter A's axis, after the photon A passes the filter-A ), the other photon B polarization **instantly** (= by superluminal entanglement !? ) **changes into the same angle as the distant filter A's axis **(= same as the passing photon A's polarization ), then the pobability of the entangled photon's B passing the filter B is cos^{2}θ (= instead of cos^{2}β ) where θ is angle difference between two distant plarizers' axes due to Malus law ( this p.2-right ).

The chance of the photon's A passing the polarizing filter A is supposed to be 50% due to the random light polarization setting (= under the condition that polarizations of two photons A and B are parallel to each other ), so the total probability of both photons A and B passing each filter becomes **1/2cos ^{2}θ = 1/2cos^{2}(β-α);** = 1/2 ( θ = 0, this p.41, this p.2-3 ).

In the same way, when two polarizers's axes point in the same direction ( θ = 0 ), the probabilities of two photons A and B are reflected by each polarizer is also **1/2cos ^{2}θ** = 1/2, because they ridiculously claim that when photon A is reflected by the filter A (= the reflected photon A's polarization becomes perpendicular to the filter A's axis ), the photon b's polarization instantly (= sueprluminal entanglement action !? ) becomes

The total probability of two photons A and B giving the same results (= pass-pass + reflect-reflect ) equals 1/2+1/2 = 1 = **cos ^{2}θ** ( θ = 0 ), which probabilities are allegedly given by the quantum superluminal entanglement theory connecting two distant particles with supernatural occult power.

But as I said, this **ridiculous** claim of superluminal entanglement is the result of the **misinterpretation** of the realistic divisible classical light wave as a fictitious indivisible photon particle.

*(Fig.21) Quantum entanglement is caused by faster-than-light "spooky" link ? ← Quantum mechanics is just pseudo-science lacking reality. *

Physicists unrealistically claim that when the photon A passes (or reflects from ) the polarization filter A, the photon A's polarization becomes parallel (or vertical ) to the filter A's axis, and it instantly makes the **distant** photon's B polarization the same as the photon's A polarization (= photons A,B polarizations instantly become the same parallel even after they pass their different filters far away from each other ) by the (**illusory**) fanster-than-light entanglement action.

As I said, if this fantasy superluminal quantum entanglement is right, the current mainstream science of Einstein relativity forbidding any faster-than-light transmission is wrong.

So the current mainstream physics based on (fantasy) quantum mechanics and Einstein relativity is **self-contradictory** and wrong.

*(Fig.21') Unreal photon particle is not divided ← Unreal superluminal entanglement occurs. Realistic light wave is divided. ← No spooky link needed.*

Illusory idea of superluminal entanglement is caused by physicists intentionally **mistaking** the realistic divisible classical light wave for an **illusory indivisible photon** rigid particle.

The indivisible photon particle is illusion, as seen in extremely lower photon detection efficiency and conincidence detection rate of two paired (entangled) photons (= a very weak photon easily splits into weaker light waves which can no longer be detected at the single photon detector, and disappears ).

If the photon is a realistic light wave, the passing photon A can be detected only when the polarized angle of the photon A is **near** the angle of the polarizing filter A's axis due to the detecting threshold.

For example, when the angle α between the photon A's polarization and the filter A's axis is about **π/4** or 45^{o} (= middle point), the photon A = **light wave** A is **divided** into the pass and reflect sides **equally** at the filter (= light intensities passing and reflecting from the filter A become the same cos^{2}π/4 = cos^{2}45^{o} = 1/2 of the original light intensity due to Malus law ) and detected on *neither* the pass *nor* reflect sides of the filter.

Because both the pass and reflect light intensities (= 1/2 × I ) become equally divided and **weaker** to the half of the original light intensity (= I ), which cannot reach the detection threshold (= Fig.21'') of a single-photon detector.

For example, we can suppose the single photon detector can detect the weak (split) light as a (fictitious) photon, only when its light intensity exceeds the photon detection threshold of 0.7 × I (= the photon detector's threshold can be artificially adjusted ) in which case, the equally-divided photon or light intensity = 0.5 × I cannot be detected by the single-photon detector as a (fictitious) photon.

When we cannot detect two prepared (entangled poalrized) photons A and B at the same time (= coincident detection ), this case is **NOT** counted as a entanglement result (= entanglement experiments see only the cases of detecting two photons A and B simultaneously, which two photon coincidence detection rates are extremely **low**, this p.4-left-lower ).

*(Fig.21'') Wave is equally divided = not reach detection threshold.*

When we detect two photons A,B at the same time at each single-photon detector, it is possible that those two photons (= just weak classical lights ) **originally** have the polarization angle **near** the polarizing filters they hit, in which case, most of those light waves whose polarization is near the filter's axis can pass each filter enough to **exceed** the photon's detection threshold.

When the angle between the photon (= or light ) polarization and the polarizing filter's axis is about 45^{o} or π/4 as shown in the upper figure, the photon (= or light wave ) intensity is almost equally divided into the pass and reflect sides of the filter (= the pass or reflect light intensity weakens to almost half of the original light intensity due to Malus law, Icos^{2}π/4 = 1/2 × I ), and this equally-divided photon (= light wave ) cannot be detected as a photon on either side of the polarizing filter due to Not reaching the detection threshold of the photon detector

This means that the "wave nature" of the **divisible** light causes the **false** idea that the (illusory) superluminal quantum entanglement is occurring.

On this page we use the two (entangled) photons (= light waves ) whose polarizations are **paralell** to each other (= which direction both these photons's polarizations point is random and uncertain until the measurement ).

If you want to use a pair of the vertically-polarized and horizontally-polarized photons as entangled particles, change cos^{2} θ into *sin ^{2} θ*, which meanings are the same as far as they satisfy Malus's law.

*(Fig.22) Directions (= axes ) of two distant polarizing filters A and B are the same or parallel to each other. ( θ = 0 degrees )*

Two photons (= or weak classical light waves ) with polarizations parallel to each other are emitted in the opposite directions and hit each polarizing filter (= photon A hits the polarizing filter A, and the photon B hits the polarizing filter B ), pass (or reflect off) the filter, depending on the angle between the light polarization and the polarizer's axis ( this p.3 ).

We arrange for these two photons or light waves to have the same parallel polarizations (= vertical-vertical, horizontal-horizontal, 45^{o}-45^{o}, 80^{o}-80^{o} ... polarizations. Which direction these two lights point is unknown until the mesurement ).

The light polarization directions are uncertain and randomly changed under the condition of two light wave polarizations always parallel to each other (= or the directions of two polarizing filters' axes are randomly changed under the condition of the angle difference between two polarizing filters' axes is always the constant. In the upper Fig.22 case, two polarizing filters' axis angles are the same parallel ).

This figure shows the case in which the angles ( = the directions of the arrows) of the axes of two polarizing filters A and B are **the same** ( = *0 degree*).

So in this case, when photon A *passes* through filter A, photon B **always** *passes* through filter B, ( = *cos ^{2} 0 = 1* ), which detection probability agrees with the experimental results (= of illusory sueprluminal entanglement according to quantum physicists ) even

So the fictional superluminal quantum entanglement is **unnecessary**.

The polarization directions of two photons are random, except for one condition that these two light polarizations are always parallel to each other.

When the light polarizations of these two photons point in the direction of ( ++ ) of the upper figure, most light intensities of both these photons (= divisible light wave ) A and B can pass through their polarization filters, and can be detected as the passing photons by exceeding the detection threshold of the single-photon detector ( this p.7-2nd-paragraph ).

When these photon polarizations point in the direction of the blue region of the polarization filters, neither photon A nor B can be detected, because the photon (= light ) is almost equally divided in the pass and reflect sides of the polarizing filter, and their light intensities cannot exceed the photon detection threshold of photodetector.

When the light polarizations of these two photons point in the direction of ( -- ) of the upper figure, most light intensities of both these photons (= divisible light wave ) A and B are reflected by their polazation filters, and can be detected as the reflected light (= photon ) by exceeding the detection threshold of the photodetector.

↑ As shown here, we can perfectly explain the experimental results (= Bell inequality violation ) using the ordinary **divisible** classical light wave even **without** relying on the contradictory superluminal entanglement action.

*(Fig.23) Most of both the divisible light waves A and B pass their polarizing filters ( ++ ), then, their passing light intensities remain strong enough to be detected as (fictitious) photons at the photodetector. ← Trick of fictional superluminal entanglement !*

When the polarization direction of the photons A ( this photon A's polarization direction is *the same* as the photon B, because these two photons' polarizations are prepared to be parallel to each other ) points toward ( ++ ) of Fig.22, **both** the photons A and B are likely to pass each filter, and are detected as "photon particles", because these light (intensity) can pass these filters *enough to be detected* at the photodetector (= Fig.23 ).

The pass light intensity is **I cos ^{2}α** ( or I cos

When the light polarization points to (++), this angle α (or β ) between the light polarization and the filter's axis is

*(Fig.24) Both classical light waves are split almost equally = not detected at a single-photon detector due to their equally-split light intensities not reaching the detection threshold.*

But when the polarization direction of the photon A( = the same as photon B polarization ) points toward the *blue* part of Fig.22, the transmitted (or reflected) light intensities are *below detection threshold* of a single-photon detector, because these lights are **divided almost equally** into pass and reflect sides of the polarization filters obeying the classical Malus' law.

For example, the pass light intensity is **I cos ^{2}α** and the reflect intensity is

When this angle α is near

In this case, both pass and reflect light intensities become *weaker* by being equally split into almost half of the original light intensity.

So **neither** photon A **nor** B can be detected as a "photon particle" by the detector (this case is *not* used or counted for the entanglement or calculating the detection efficiency, because both photons are undetectable ).

*(Fig.24') Both light waves (= intensities ) reflect ( - - ) from polarizers enough to be detected at the single photon detectors as (fictitious) photons.*

And when the polarization direction of the photon points toward the ( -- ) of Fig.22, *both the photons A and B are reflected* by the polarizing filters **enough** to be detected as "photon particles" due to their reflected light intensities exceeding the detection threshold.

For example, the *reflect* light intensity is **I sin ^{2}α**. when this angle α is near 90 degrees (= (--) part of Fig.22 ), the reflect light intensity becomes strong enough.

So in this case, the "illusion" of the entanglement of these paired photons are occurring (= if we consider the fictitious photons to be the realistic divisible light wave, this illusory superluminal entanglement link is

In Fig.22 case where the axes of two polarizing filters A and B point in the same direction (= θ = α - β = 0 ), the probabiliy of both the photon A and B giving the same results (= both photons passing their polarizers + both photons are reflected by their polarizers ) become cos^{2}θ = 1, as predicted by (illusory) photon's entanglement theory.

*(Fig.I) There are No such things as indivisible classical (or quantum ) photons. *

As shown in the upper Fig.I, physicists falsely assume that the (fictitious) indivisible classical photons pass or reflect off each polarizer obeying Malus' law, though Malus's law originally applies only to the realistic classical light wave Not a photon particle.

In this fictitiously indivisible classical photon case, when photon A passes the filter A, the photon B passes **or reflects**, even when the axis angle difference between the polarizing filter A and B is zero ( θ = 0 ).

So the results of photon A and photon B are NOT always the same even in θ = 0, which disagrees with the experimentally observed probability of cos^{2}θ

As a result, the illusory superluminal quantum entanglement action is caused by the false assumption of the illusory quantum or classical **indivisible photon particles**. ← Realistic classical light wave can perfectly explain the experimental results **without** needing the unrealistic entanglement.

This is the **trick** of the illusory superluminal quantum entanglement.

*(Fig.II) Illusory entangled photon particles can be replaced by realistic divisible classical light wave.*

In entangled photon pair, when the photon A passes the filter A, the photon B **always** passes the filter B due to the **unrealistic superluminal** spooky link which allegedly can change the distant photon's polarization instantly and superluminally with unknown **supernatural** power.

Instead of accepting this **unrealistic** ridiculous entanglement link idea, it is more natural to think a photon is just classical divisible electromagnetic waves detected as "photon", only when the classical light intensity after splitting exceeds the detection threshold of a single-photon detector.

*(Fig.25) Angle between polarizing filters A and B is θ = 90 degrees.*

Next, this figure shows the case in which the axis angle difference between the polarizing filters A and B is *90 degrees* (= two polarizers' axes are perpendicular to each other ).

The photon A and B polarizations are always the same, parallel to each other, as I said.

In this case, when the photon A **passes** through the filter A, the photon B is **always** **reflected** by the filter B ( = *cos ^{2} 90 = 0* ) according to the entanglement theory.

When the polarization of the photon A ( = the same direction as photon B's polarization ) points toward (+ -), the photon A passes the filter A, and the photon B is reflected by the filter B whose axis is perpendicular to the filter A (and both photons or lights can be detected as "photons" exceeding the detection threshold due to their light intensities not equally divided at the filter ).

*(Fig.25') Photon A passes, photon B reflects ( + - ).*

But the polarization of both photons points to the *blue* part of this figure (= both photons's polarizations are prepared to be parallel to each other ), *neither photon A nor B can be detected* as a "photon particle" due to their light intensities equally splitting and not reaching the photon detection threshold.

Because in this case, the divisible classical light waves (= intentionally mistaken for indivisible photons ) are "almost equally" divided into pass and reflect directions at the polarizing filters (= both pass and reflect light intensities weakens to the half of the original light intensities due to cos^{2}45^{o} = sin^{2}45^{o} = 1/2 ), which fail to reach the detection light intensity threshold of the photon detector.

*(Fig.26) Angle difference between two polarizing filters' axes A and B is θ = 45 degrees.*

This figure shows the case in which the axis angle difference between two polarizing filters A and B is *45 degrees*.

In this case , when the photon A *passes* through the filter A and is detected, the probability that the photon B *passes* the filter B is *50 percent* ( = *cos ^{2} 45^{o} = 1/2* ) according to the entanglement theory.

When the polarization of the photon A ( = photon B's polarization parallel to photon A ) points toward ( ++ ), *both* the photons A and B can *pass* each polarizing filter and be detected as "(illusory) photon particles" (= both photons or light waves **unequally split** into the pass and reflect sides, and the pass light intensity is stronger enough to be detected at the single photon detector by exceeding the detection threshold ).

When the photon polarizations point in the direction of ( +- ), most of the photon A (= divisible light wave ) *passes* the filter A and most of the photon B is *reflected* by the filter B and can be detected as "photons" by reaching the detection threshold.

So the probability that **both** the photons A and B **pass** each filter becomes **50 %** (= *cos ^{2} 45^{o} = 1/2* ) compatible with the experimental results without relying on the unrealistic superluminal entanglement.

*(Fig.26') Photon A pass, reflect, not detected regions.*

When the polarizations of two photons or light waves point in the directions of the *blue* parts (= both photons A and B are prepared to have the same parallel polarization ), *only one of the two photons A and B* can be detected as a photon, because **one of photon or light wave** tends to be almost equally split at the polarizing filter and have *weaker* transmitted (or reflected ) light intensity than the detection threshold at the photodetector.

If only one of two photons or lights can be detected, this case is *not used* as the correct experimental result.

Because *only when* we detect both the two photons *at the same time* (= coincidence ), we consider these photons to be in the *entangled* states.

(In the actual Bell test experiment using the photon pairs, the coincidence ( = entangled photon pairs ) detection rate is **very low** ( < 20% ). So the truly-loophole-free entanglement experiments are **impossible**. this p.3, this p.3-3, Fig.2 )

This example *violates* the Bell inequality due to the cos^{2} θ probability. But of course, the unrealistic phenomenon such as the faster-than-light entaglement action is not occurring here.

Here, let's calculate the **Bell inequality (CHSH type)**.

We add one more case in which the axis angle difference between the polarizing filters A and B is *30 degrees*.

*(Fig.27) Angle difference between two polarizing filters A and B is θ = 30 degrees.*

We think about the case when the angle difference between two polarization filters A and B axes is 30^{o}.

When two photons or classical light waves with polarizations parallel to each other hit each polarizing filter ( the photon A or light wave A hits the polarizing filter A, and the photon B or light wave B hits the polarizing filter B ), these classical light waves split into the pass and reflect sides depending on the filter's axis.

Only when the light intensity even after splitting at the polarizing filter remains strong enough, it can reach the detection threshold and be detected as "(fictitious) photon" at a single-photon detector.

When the polarizations of two light waves (or photons ) point to the red parts (+ +), **both** light waves A and B pass each polarizing filter enough to be detected as "photons (= split light intensity can reach the photon detection threshold )" obeying the classical Malus law.

When the polarizations of two light waves (or photons ) point to the purple parts (+ -), the light wave A *passes* and light wave B is *reflected* by each filter enough to be detected as "photons".

When the polarizations of two light waves point to the shaded parts (light blue), *only* one of light wave A (pass) or B (reflect) can be detected as a photon, because one of lights A and B is equally split at the polarizing filter, and its split weaker light intensity cannot reach the detection threshold of the photodetector. (= This case is *Not used* or counted in the entanglement experiments which see only two photons' coincidence detection, this p.13 )

As shown in this figure, *when* the photon A *passes* through the filter A and is detected, the probability that the photon B *passes* the filter B is *3/4*. ( = 45/(45+15) = *cos ^{2} 30 = 3/4* )

(In the case of

The light intensity and the photon detection threshold can be **artificially adjusted** to fit this (fictitious) entanglement theory of cos^{2}θ.

Next, we explain about the Bell inequality violation allegedly proving the (illusory) superluminal entanglement link simply.

*(Fig.28) Photon A hits filters A1 or A2. Photon B hits filters B1 or B2.*

Suppose, **photon A** bumps into two kinds of polarizing filters *A1 whose axis points to 0 degree* and *A2 whose axis points to 60 degrees*.

And **photon B** bumps into two filters *B1 whose axis points to 30 degrees* and *B2 whose axis points to 90 degrees*.

Fig.28 shows the axis directions in these four polarizing filters.

( Caution: The polarizing filters A1 and A2 are at the side of photon A, and the filters B1 and B2 are at photon B side.)

In this case, there are *16* patterns (= 2^{4}) in which photons (= light waves ) A and B pass (+) or are reflected (-) by the polarizing filters ( A1,A2,B1,B2 ), as follows,

where the sum of all these probabilities is *1* ( **P1 + P2 + P3 + .....+ P15 + P16 = 1** ).

Here we define as follows,

---------------------------------------------------------------------

< A1, B1 > = ( the probability that the signs of A1 and B1 are the *same*, **+ +** and **- -** ) - (the probability that the signs of A1 and B1 are *different*, **+ -** and **- +** )
= (P1+P2+P5+P6+P11+P12+P15+P16) - (P3+P4+P7+P8+P9+P10+P13+P14)

In the same way,

< A2, B1 > = ( the probability that the signs of A2 and B1 are the *same*, + + and - - ) - (the probability that the signs of A2 and B1 are *different*, + - and - +)
= (P1+P2+P7+P8+P9+P10+P15+P16) - (P3+P4+P5+P6+P11+P12+P13+P14)

< A2, B2 > = ( the probability that the signs of A2 and B2 are the *same*, + + and - - ) - (the probability that the signs of A2 and B2 are *different*, + - and - +)
= (P1+P3+P6+P8+P9+P11+P14+P16) - (P2+P4+P5+P7+P10+P12+P13+P15)

< A1, B2 > = ( the probability that the signs of A1 and B2 are the *same*, + + and - - ) - (the probability that the signs of A1 and B2 are *different*, + - and - +)
= (P1+P3+P5+P7+P10+P12+P14+P16) - (P2+P4+P6+P8+P9+P11+P13+P15)

---------------------------------------------------------------------

So we arrive at the following equation,

< A1, B1 > + < A2, B1 > + < A2, B2 > - < A1, B2 > = **2 ( K - L )**

K = P1+P2+P6+P8+P9+P11+P15+P16

L = P3+P4+P5+P7+P10+P12+P13+P14

Using the relation, **(K + L) = Σ P _{i} = 1**,

So the following inequality (**Bell inequality, CHSH type**) must be satisfied in the fictitious indivisible photon particles with idealistically No photon loss (= which is impossible ),

| < A1, B1 > + < A2, B1 > + < A2, B2 > - < A1, B2 > | = 2 | K - L | **≦ 2**

this p.2-3, this p.32-35, this p.20-21, this p.33-35, this p.12

For example, the probability that the results of the photons A (→ A1) and B (→ B1) are *the same* summing the cases of ( ++ = both photons A and B pass each polarizing filter ) and ( -- = both photons A and B are reflected from each polarizing filter ) is **cos ^{2} (A1-B1)**,

where (A1-B1) is the axis

And the probability that the results are *different* summing ( + - = photon A passes and photon B reflects from each polarizing filter ) and ( - + = photon A reflects and photon B pass each filter ) is **sin ^{2} (A1-B1)**.

So, < A1, B1 > of Bell inequality is ( this p.4-10, this p.3, this p.2-right )

*(Eq.1)*

where θ_{A1 - B1} means the angle of (A1 -B1) between two polarizing filters's axes A1 and B1.

In the case of Fig.28, each cosine value becomes

*(Eq.2)*

and

From Eq.2, the above Bell inequality (CHSH type) is,

*(Eq.3)*

**This violates** Bell inequality !

So physicists claim these two polarized photons A and B showed the faster-than-light quantum entanglement action, and we must give up any realities in quantum mechanics. ← ridiculous.

But as I said, this illusory superluminal quantum entanglement is caused by falsely treating the realistic divisible classical light wave (+ detection threshold trick at the single photon detector ) as a fictitious indivisible photon particle.

In conclusion, if the photon is a (fictitious) indivisible particle, the strange nonlocal phenomena such as the entanglement are actually occurring, and we **must** believe this fantasy faster-than-light transmission.

In other words, if the photon is a dividable electromagnetic wave, we **need not** consider this fantasy superluminal entanglement action.

You can easily judge which case (photon is a (fictitious) particle or realistic light **wave** ) is more natural.

In order to claim this unrealistic superluminal quantum entanglement link is true, physicists must detect two polarized photons simultaneouly with almost 100% coincidence detection rate, which is impossible ( this p.4-left-lower, this p.22, this p.3-3, Fig.2-3, this p.3-Table.I, this Fig.2, Table I ).

Physicists gave up using the fictitious photons and tried to conduct the illusory quantum entanglement experiments of high detection efficiency using two Beryllium ions (= Be+ ), arranging that when one Be+ ion's nuclear spin is up (or down ), the other Be+ ion spin is always up (or down, = so up-up or down-down = entanglement !? No! ), this p.2-3, this p.1-left ).

↑ This Be+ ion case also has **nothing** to do with (illusory) superluminal quantum entanglement link, physicsts just artificially **prepared** two Be ions with the same-directional nuclear spins using the classical electromagnetic field and laser light so that both Be+ ions have the nuclear spins point in the same direction (= both Be+ ions are prepared to be in the same hyperfine energy levels ), which nuclear spin directions are estimated by illuminating Be+ ions with another lights ( this p.2 ) without using polarizing filters.

In the low detection efficiency photon case, physicists tried to change the original Bell inequality or intentionally avoid measureing the photons reflected from the polarizers to avoid the unsolvable issue of the intrinsically-low photon conincidence detection efficiency loophole ( this p.4, this p.2-2nd-last paragraph, p.3-Table.I ).

↑ So the low detection efficiency problem (= low conincidence rate of counting both pass and reflect photons at each polarizing filter ) is Not solved, and they cannot exclude the classical light wave case.

As a result, the superluminal quantum entanglement is just **illusion** which can be naturally **replaced** by the realistic divisible classical light wave without the fantasy superluminal spooky action.

*Because, they are obstructing development of "real" science under their present stance .*

First, all researchers and news writers **should** make efforts to explain to **ordinary** people to make them understand easily, and should **NOT** confuse them ONLY by fascinating words "entanglement".

It cannot be helped that some top journal had spreaded **illusory** fields such as entanglement and quantum computer due to the time gap related to three-body helium. ( I understand their feelings well. )

But aiming at illusory ideas such as closing loopholes forever, means we admit only **unreality** and "Shut up and calculate !" forever, which **obstructs** the development of science.

*[ Bell inequality violation is "still" an illusion. ]*

In some website, we see the news about closing all local realistic ( fair sampling ) loophole.

But unfortunately, they did **NOT** close all loopholes by usual **CHSH**-type bell inequality.

As far as I see, different-type inequality allows **lower**-efficiency and some photon's **loss**.

And I cannot find all single (= not coincident ) events. ( They seem to use some **limited** single events, in inequality calculation. Is this really allowed ? )

Different from usual CHSH-type, this inequality relies ONLY on incomplete and **Not** enough informations = about a **half** of usual CHSH-type.

Anyway, this result **cannot** elimilate electromagnetic wave's local realistic model, as I explain above.

This different-type inequality experiment uses some light **rotator**, and NOT detect reflection from splitter.

In this method, our realistic electromagnetic wave model can give **much more** than 100 % efficiency (= their definition, coincident / single events ).

So this result cannot eliminate electromagnetic wave model.

( "Light rotator" uses **phase** change of a part of a photon, which means photon particle is just classical **waves**. )

*[ All three loopholes have NOT been closed "simultaneously". ]*

You may read some articles such as all loopholes have been closed, so Einstein is wrong.

But this experiment closed only ** one** loophole of "fair-sampling".

( The fair-sampling loophole is the only one left that hasn't been closed until now. )

So all three important loopholes of "detection", "locality" and "fair-sampling" loopholes have **NOT** been closed **simultaneously**.

This means **spooky** link has NOT been proved to be correct in any experiment.

I confirmed this fact in some site, but all webnews should explain this fact **more** clearly to ordinary people, I think.

"Freedom-of-choice" is important, because we can "**artificially**" choose the special situation which can violate Bell inequality.
**At least**, they should violate **usual** CHSH inequality, not only in very special inequality.

*[ Time gap causes various serious illusions and paradoxes. ]*

As I say, very complicated three-body helium couldn't be solved without **computers**.

Due to this time gap ( from 1920s to 1990s ), various **illusory** fields such as entanglement and quantum computers need to be created to **fill** this gap in physical world.

And serious **paradoxes** of special relativity have been **hidden** and eliminated from usual textbooks.

*(Fig.T-1) "1" and "4" photons can be really entangled at different times ?*

They claimed that recent experiment showed entangled "photons" that never coexisted in time.

But as I said many times, the **trick** of these kinds of experiments is they **always** use the word of "**photon**", NOT electromagnetic wave.

In Fig,T-1, entangled photon pair (= **1, 2** ) is generated at first BBO.

( One of them is horizontally polarized (= H ), and another is vertically polarized (= V). )

After detecting photon 1 state, another entangled pair of (= **3, 4** ) photons are generated.

Then, **mixing** photons 2 and 3, and they detect 2 and 3 photon states (= H or V **polarizations**. )

Of course, we cannot know which photon enters upper or lower detector, because they are mixed.

*(Fig.T-2) Entangled photon pair is generated at BBO ?*

Entangled photon pair is often created by "parametric down-conversion" at BBO.

In this process, a photon of wavelength λ enters some crystal, and is split into a pair of photons of wavelength 2λ.

So the total energy is conserved. (= their frequency becomes half ).

But as I said many times, if photon is a particle, it **cannot** be split so easily.

And "horizontally" or "vertically" polarized states mean they are just classical electromagnetic waves ( **NOT** a particle ).

How can a **point** particle of photon be **polarized** ?? It's **impossible**.

*(Fig.T-3) Pattern I photons ( 2, 3 ) = ( V, V ) → ( 1, 4 ) = ( H, H ).*

When we detect both photons "2" and "3" as vertically polarized (= V ) photons, both photons 1 and 4 are **automatically** horizontally polarized photons (= H ).

It is quite natural, because they generated photon pair, one of which is H, and another is V at BBO.

So they insist photons 1 and 4 are in the mysterious "entangled" states.

But as you feel, these results are **natural** things from the usual **classical** light's viewpoint.

Then why they insist these states are faster-than-lihgt **entanglement** ?

*(Fig.T-4) They suppose "virtual" classical "photon" pair, *

I don't think ordinary people understand why they consider these results as mysterious entanglement.

As I said in above section, these kinds of experiments assume, what we call, "**classical**" photons.

If classical photons really exists, they cannot be devided at beam spilitter, so they cannot always show the same polarization results at detector, even if their polarizations are in the same direction.

For example, in Fig,T-4, both filters A and B point in the same directions.

( And both photons A and B have the same polarization. )

In the entangled photons, when one of them passes the filter, another photon **always** passes the filter by **spooky** link.

But in classical photons, even when photon A passes the filter A, photon B does **NOT always** pass filter B, as shown in Fig,T-4 (= it **reflects** at the probability of sin^{2} α ).

If you have not read the sections above in this page, read them first.

*(Fig.T-5) Both waves pass their filters ( ++ ) enough to be detected.*

If we think classical "photon" as **illusion**, and use the concept of classical "**electromagnetic waves**", we can easily explain these kinds of experiments from the local **realistic** viewpoint.

First, when we can detect both "2" and "3" photons at detectors, it means both "2" and "3" photons, which have passed the beam splitter, have **strong** light intensities **enough** to be detected as a "photon".

( If their intensities are weak, we cannot detect them as a single photon below **threshold**, and they are neglected. )

So in this case, both "1" and "4" **also** have strong light intensities, which are polarized in the **specific** directions, and we can detect them as "entangled" states, at the single photon detector (= H and H in this case ), because they are more than detection **threshold**.

For example, if you can detect photon "2" as "V", it means photon 2 almost points towards "V" **before** it enters beam splitter.

Because if photon 2 points **between** "V" and "H" (= 45 degree ) in advance, it is **divided equally** into pass and reflect directions ( cos^{2} 45 = sin^{2} 45 = **1/2** ), and **cannot** reach detection threshold.

*(Fig.T-6) Pattern II.*

When we detect photons 2 and 3, as one is "V" and another is "H", it means one is H, another is V in 1 and 4 photons.

Again it is quite natural from the usual **classical** viewpoint.

"Bell state measurement" needs to detect **both** photons.

So if we can detect **only** one of 2 and 3 photons, their results are **NOT** used as experimental results. (= **trick** ! )

I'm sorry for experimentalists of entanglement, but if you spread "supernatural" phenomena such as faster-than-light entanglement, you should explain to ordinary people in **more detail** for them to understand your procedure well, I think.

Even in **2013** of **21th** century, various top journals continue "**Shut up and calculate !**" about "**spin**".

( For example, the role of spin in organic photovoltaics, or quantum many-body spin system in an optical lattice clock even in 2013. )

As shown on this page, it is **impossible** that very **weak** spin magnetic moment can cause the energy difference between singlet and triplet states.

And S states (= angular momentum zero ) in each energy levels are **impossible**, too.

Because outer electron **cannot** penetrate many inner electrons and nucleus.

*[ Doublet = spin or circular motion ? ]*

If the two electrons are entangled to the spin 0 state (spin up + spin down = spin 0), it is said that the magnetic moments are canceled out and become zero.

But this explanation is **wrong**. Because the two electrons are **apart** from each other by the repulsive Coulomb force. (If the two electrons having the opposite magnetic moments are completely sticking to each other, the sum of their magnetic moments becomes zero. But it is *impossible*.)

*[ Electron spin is real ? ]*

And the spinning fermions don't go back to their original configurations by the 2π rotation. (By the 4π rotation, they return.)

And if the electron spin is caused by the real spinning of the electron, the electron rotation speed becomes more than 100 times faster than the speed of light.

So the spin is only the "mathematical" thing, **not a "real" physical object**. (See also this page.)

So it is unnatural that we use this "mathematical" spinor for the "real" entanglement experiment (for example, like cosθ/2).

The original spin state may be changed by each experimental environment having some external magnetic fields. It is "artificial" manipulation

Bell inequality of spin 1/2 particles *often* appears in usual textbooks, though actual experiments treat *other things* such as photons.

Because this experiment with spin 1/2 particles is very **difficult**.

The important point is that the Bell inequality itself of spin 1/2 particle is "**unreal**" thing, which is a little different from that of photons.

We explain this reason later.

*[ Rydberg blockage. ]*

It is said that they succeeded in entanglement of neutral **atom-atom**.

But as far as I see, these kinds of entanglement use imaginary (two) photons to detect them.

So we can explain this phenomenon by usual **local** classical mechanics ( **NOT** fantasied nonlocal ), as I said in above section.

When two Rb atoms are trapped and very **close** to each other (= several **micrometers** ), the energy to excite **both** two atoms is a little bigger due to dipole-dipole interactions.

*[ Faster-than-light entanglement ? Really ?? ]*

So, they can excite only **one** of two atoms, and only this excited atom goes down to the lower hyperfine state (= red arrow ) by additional irradiation.

As a result, one of the two atoms is in the original upper hyperfine state, and another is the lower hyperfine state. (= 5s, upper and lower arrows. )

This state is an entanglement, they insist. But is it really so ?

To confirm these two hyperfine states, they use, what we call, (two) **photons**.

So at this moment, atom-atom entanglement is equal to photon- photon entanglement.

Furthermore, they just **artificially** make two atoms upper and lower hyperfine states, which is **NOT** related to entanglement.

*[ Faster-than-light entanglement ? Really ?? - part II. ]*

Basically, electron and hole, which are generated from each other, are correlated.

They often use very **vague** concept of "**spin**", this spin state can be measured by light **polarization**.

At this moment, spin-hole entanglement can be explained by **classical** lights, as I said above.

And spin has the **same** magnetic moment (= Bohr magneton ) as Bohr's orbit.

Or they insist the entanglement can be confirmed by measuring vague **noise** of thin insulator between them.

But as you see, the distance between electron and hole is so **short**, that we **cannot** confirm they are really **faster-than-light**.

Actually, these entanglement things are **NEVER** useful for our daily lives, though these kinds of experiments have been performed **extremely many** times.

These facts clearly **proved** the entanglement itself is just an **illusion**.

First we define the next **unit vector** using the polar coordinates as follows,

*(Eq.4)*

When the spin points to the direction of this unit vector, the spin operator can be expressed as

*(Eq.5)*

This is an inner product of vectors n and S.

So the spinor of the eigenfunction, which **points to the direction of n** is

*(Eq.6)*

And the spinor of the eigenfunction, which points in the **opposite** direction from n is

*(Eq.7)*

Suppose two spin 1/2 particles of the *opposite* spins are flying in the opposite directions.

The spin of the **particle A** is measured by **A**, while the spin of **particle B** is measured by **B**.

First, we suppose the direction of measurement A points to the unit vector **n** of Eq.4.

If the spin of the particle A is **+1/2** in the n direction at the measurement A, the particle B instantly becomes **- 1/2** in the n direction. (= *entanglement*.)

This means that *the instatnt* the particle A becomes **α** of Eq.6, the particle B becomes **β** of Eq.7.

Next we suppose the direction of **measurement B** is **z direction**.

(So the angle betweem measurements A and B is **θ**.)

According to Eq.7, the probability that the spin of the particle B becomes **-1/2** in the **z** direction is

*(Eq.8)*

When the particle A is **+1/2** at the measurement A and the particle B is **-1/2** at the measurement B, this case is named "**( + + )**".

Because they are usually *opposite* from each other.

And the probability that the spin of the particle B becomes **+1/2** in the **z** direction is

*(Eq.9)*

When the particle A is **+1/2** at the measurement A and the particle B is **+1/2** at the measurement B, this case is named "**( + - )**".

In the same way, when the particle A is **-1/2** at the measurement A, the particle A means **β** of Eq.7, and the particle B *instantly* becomes **α** of Eq.6.

So the probability that the spin of the particle B becomes **+1/2** in the **z** direction is

*(Eq.10)*

When the particle A is **-1/2** at the measurement A and the particle B is **+1/2** at the measurement B, this case is named "**( - - )**".

And the probability that the spin of the particle B becomes **-1/2** in the **z** direction is

*(Eq.11)*

When the particle A is **-1/2** at the measurement A and the particle B is **-1/2** at the measurement B, this case is named "**( - + )**".

So like the above photon case, the probability of ( + + ) and ( - - ) *minus* the probability of ( + - ) and ( - + ) is

*(Eq.12)*

where θ_{A1-B1} means the **angle between the measurements A1 and B1**.

Here we do the following four measurement (each particle has two). (Fig.29).

*(Fig.29) Particle A → measurement A1 or A2. Particle B → B1 or B2.*

So each cosine value can be calculated as (like Eq.12),

*(Eq.13)*

and

So the Bell inequality of the spin 1/2 particle is

*(Eq.14)*

**This violates Bell inequality !**

But we go back to Eq.6 and Eq.7 again.

According to Eq.6 and Eq.7, the spinor **can't return by one rotation** !

(It needs **two** rotations (= 720 degrees) for returning to its original form.)

So this spinor is *NOT* a real thing, either.

This means that Bell inequality *itself* of Eq.14 is **wrong** in the case of spin 1/2 particles.

As a result, it is *very difficult* to say that the "real" entanglement of spin 1/2 "real" particles is occurring.

( The *illusions* of Entanglements are caused by "unreal" particles such as photons and spin 1/2 particles.)

The many worlds interpretation(MWI) was proposed first by Hugh Everett [5].

And now the MWI is considered as the best interpretation of QM.

But many people including I think it is **only fantasy**.

In many-worlds, the collapse of the wavefunctions in superposition states is explained by the mechanism of quantum decoherence.

By decoherence, many-worlds claims to resolve all of the correlation paradoxes of quantum theory, such as the EPR paradox and the Schrödinger's cat.

(But I think "decoherence" is very **intentional** and a very **convenient** way to interpret.)

In MWI, there is no strange *observation-triggered* wavefunction collapse which the *Copenhagen* interpretation proposes.

(Surely, it is **unnatural** that we treat only "observer" as a "**special**" thing.)

*(Fig.30) All interpretations are unnatural ? → "Shut up and Calculate !"*

The most "real" interpretation of the quantum mechanics is the Bohmian mechanics (BM) ( De Broglie - Bohm theory or **pilot wave** ).

But strange to say, *the BM electron doesn't have the charge and spin 1/2*.

Because if the BM electron has the charge, it radiate energy as it is moving.

And the BM electron may be **faster** than the speed of light. See also this page.

On the other hand, in the **Bohr model**, when the orbital length is *a integer times* the de Broglie's wavelength, the electron's motion becomes **stable** not radiating the energy.

The BM obeys the probability density of the Schroedinger equation, so the electron's movement is much more complex than the Bohr's model.

And strange to say, the probability density near the point at infinity of the ground state hydrogen electron is *not* zero.

More important problem is that *all these interpretations are inconsistent with the relativistic quantum field theory(QFT)*.

All interpretations of QM are based on the Schroedinger equation(S.E.) which is acausal and "probabilistic".

But the nonrelativistic S.E. can't explain the relativistic effects including the fine structure (spin-orbital interactions)
.

As the atoms become heavier (which means the atomic nucleus charge becomes larger), the experimental results become more different from that of S.E., because the electon's speed becomes faster.
In S.E., *irrespective of the nucleus charge*, the electrons of any atoms are all static as electron clouds obeying the probability density.

So the **Schroedinger equation is incomplete in explaining the experimental results.**.

On the other hand, the Dirac equation (D.E.) which *satisfies the (relativistic) causality* can explain this relativistic effects.

Of course, D.E. is not "probabilistic".(= D.E. doesn't show the probability density.) So the causal Dirac equation can be said to be only a "mathematical" model.

So the relativistic QFT is inconsistent with all interpretations and the nonlocal phenomena such as the entanglement.

This means the *QM contains self-inconsistency*.

And according to "superposition" of the QM, the *Benzene*'s electrons are in the **many-world like superposition** state !

From the classical viewpoint, the Benzene's electrons are **only oscillating and moving**.

So the strange "superposition" state can be **replaced** by the classical movement "*naturally*".

How about the Bohr-Sommerfeld model ?

Sommerfeld developed the original Bohr model to the model which can explain the relativistic effect **completely**, (which result accidentally coincided with that of the Dirac hydrogen model).

Of course, the *Bohr-Sommerfeld model dosn't contain self-inconsistency at all*.

[1] A. Einstein, B. Podolsky, N. Rosen: "Can quantum-mechanical description of physical reality be considered complete?" Phys. Rev. 41, 777 (1935).

[2] J. Bell: "On the problem of hidden variables in quantum mechanics" Reviews of Modern Physics 38 #3, 447 (1966).

[3] A. Aspect, Dalibard, Roger: "Experimental test of Bell's inequalities using time-varying analyzers" Phys. Rev. Letters 49 #25, 1804 (1982).

[4] A. Aspect, P. Grangier, G. Roger: "Experimental realization of Einstein-Podolsky-Rosen-Bohm gedanken experiment; a new violation of Bell's inequalities" Phys. Rev. Letters 49 #2, 91 (1982).

[5] Hugh Everett: "Relative State Formulation of Quantum Mechanics" Reviews of Modern Physics 29 454 (1957).

Leggett Teleportation Cheshire cat (14/8/28) Delayed choice quantum eraser. Quantum computer (14/4/13).

2022/10/6 updated. Feel free to link to this site.