104544596 revisiting the three polarizer paradox

7/30/2019 104544596 Revisiting the Three Polarizer Paradox

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Revisiting the Three-Polarizer ParadoxJ. Richter

public domain-photogtraph by Martin Hofer.

Original uploader was Rssel0815 at de.wikipedia

In 1972 I started working as an electronic engineer in the Telefunken antenna laboratories at

Allmersbach/Tal. In antenna theory ruled by the work of Samuel Silver1 we ignored any kind ofquantum physics. As far as I remember Silver never needed quantum models.

Those days our problems were side-lobes, reflections and of course cross-polarization 2. Cross-

polarization was the worst enemy for antenna designs. Those days the customer (the German Post

Office) needed a two channel communication for which the horizontal and vertical polarization was

used. Those days poor cross-polarization characteristics were quite uncommon. The specialists

knew how to avoid the asymmetries.

1 Microwave Antenna Theory andDesign - Samuel Silver(1949)

2 Reflector Antennas Revisited

Fig.1: One of the towers at the AEG-Telefunken antenna-lab, southern Germany
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The three-polarizer paradoxI remember to have studied the three-polarizer paradox which has been described in the web at

many locations. I borrowed the figure from a fine tutorial with the following short description 3:

If two polarizing films are aligned in the same direction light, from the first polarizerpasses through the second. If the polarizers are opposed at a 90o angle, the polarized light

transmitted from the first polarizer is absorbed by the second. If a third polarizer is

sandwiched between the two opposed polarizers at a 45o angle, some light gets through the

last polarizer. This is illustrated below using Dirac notation for both the photons and the

polarizers.

The quantum physical model starts with light waves from unpolarized sources. This of course is

very unusual for microwave antennas. The polarization state of the photons in light waves from

unpolarized sources is unknown as it is explained in various web-papers4, which also explain whathappens according to the standard quantum theory:

The model first suggests to remove the h character of the photon by absorption, but that is not

important. In fact we will start by eliminating the first polarizer.

When the v photon from the first vertical polarizer interacts with the middle polarizer

oriented in the skewed-vertical direction the h character of the photon is removed by

absorption and only the v character passes the middle polarizer. 5

All three absorbers absorb photons. This idea should be replaced by another model in which energy

is reflected to some other direction.

As mentioned, each of the three polarizers absorbs photons. Half of the photons from thelight bulb are absorbed by the first vertical polarizer because we can consider the

unpolarized light consisting of 50% photons in the v state, see eq 3. 6

...

Half of the v photons are absorbed by the second diagonal polarizer. 7

...

3 Matrix Mechanics Approach to Polarized Light by Frank Rioux, St. John's University/College of St. Benedict

4 Polarized Lightand Quantum Mechanics:5 Polarized Lightand Quantum Mechanics:

6 Polarized Lightand Quantum Mechanics:


Fig. 2: Three-polarizer Paradox setup
http://www.users.csbsju.edu/~frioux/polarize/740200jb.pdfhttp://www.users.csbsju.edu/~frioux/polarize/740200jb.pdfhttp://www.users.csbsju.edu/~frioux/polarize/740200jb.pdfhttp://www.users.csbsju.edu/~frioux/polarize/740200jb.pdfhttp://www.users.csbsju.edu/~frioux/polarize/740200jb.pdfhttp://www.users.csbsju.edu/~frioux/polarize/740200jb.pdfhttp://www.users.csbsju.edu/~frioux/polarize/740200jb.pdfhttp://www.users.csbsju.edu/~frioux/polarize/740200jb.pdfhttp://www.users.csbsju.edu/~frioux/polarize/740200jb.pdfhttp://www.users.csbsju.edu/~frioux/polarize/740200jb.pdfhttp://www.users.csbsju.edu/~frioux/polarize/740200jb.pdfhttp://www.users.csbsju.edu/~frioux/polarize/740200jb.pdfhttp://www.users.csbsju.edu/~frioux/polarize/740200jb.pdfhttp://www.users.csbsju.edu/~frioux/polarize/740200jb.pdfhttp://www.users.csbsju.edu/~frioux/polarize/740200jb.pdfhttp://www.users.csbsju.edu/~frioux/polarize/740200jb.pdf


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Finally, half of the v photons passing the middle polarizer are absorbed by the third

horizontal polarizer because the probability that a v photon will be found in the h state

passing through the third polarizer is sin2 (45) = .8

So each inserted polarizer halves the energy.

Without the first polarizer the receiver horn receives of the input energy in the Three- (or to be

more precise the Two-) polarizer Paradox setup, which will now be discussed in detail.

http://www.users.csbsju.edu/~frioux/polarize/740200jb.pdfhttp://www.users.csbsju.edu/~frioux/polarize/740200jb.pdfhttp://www.users.csbsju.edu/~frioux/polarize/740200jb.pdfhttp://www.users.csbsju.edu/~frioux/polarize/740200jb.pdf


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A microwave model without quantum physicsI remember to have derived a microwave model, which was considered to be a functioning

model for wave-functions without quantum physics9. The following documentation will

simplify the text by removing all comments and details into footnotes, which are not needed

for the mechanisms.

In a web-presentation there is a short demonstration of the microwave model of the three-polarizer

paradox: Polarization of Light and Microwaves (Quantum Physics).

In the demonstration it is explained that the phenomenon can not be adequately explained by

classical physics. I wasn't convinced that this was true and setup a proof for this particular

microwave model without quantum physics.

I am fully aware that the theoretical models should be confirmed by tests, and I remember how

often I derived some electronic circuit which behaved differently from what I had been conceived.

In the end all designs should be checked for their validity.

Unfortunately however I do not have the time to validate the idea and that's why it is written downfor later generations to dig up the solutions and fill up the gaps in the concepts.

The microwave setup

The link consists of the horn antennas at approximately 30-40 GHz10.

The polarizers are simple breadboards with copper stripes.

In the final setup the transmitter antenna is vertically polarized and the receiver horizontally

polarized.

The first polarizer grid is not needed as the transmitter feed produces a genuine vertically polarizedwave, which (hopefully) may be approximated as a plane wave.

The central diagonal11polarizer is placed between the transmitter feed and the third polarizer, which

is horizontally polarized12.

The antenna theory

The diagonal polarizer

The plane wave coming from the transmitter antenna hits the diagonal 45-polarizer. Let us assume

the energy of the arriving wave is A (Watt).

For symmetrical reasons 50% of the energy will be passed by this diagonal polarizer and the other

50% will be converted to currents in the metallic structure 13.

Now 50% of the incoming wave's energy will induce a current in the metallic stripes. These currents

will be causing a reflecting of electromagnetic energy back towards the transmitter14:

9 Fundamentals of the wave theory have been presented in Feynman's lecture -The Vega Science Trust -Richard

Feynman Video

10 The wavelength may be estimated from the wavepipe's dimensions.

11 with a 45-degree orientation

12 In fact this polarizer may also be eliminated in an ideal setup. The receiver antenna itself is already horizontally

polarized and should not respond to vertically polarized waves.13 This of course requires to use an ideal grid of very thin metallic conductors. No dissipation is to be assumed in the

system and no absorption of energy will occur.

14 The energy may even be bundled to have a small gain over the isotropic level, but of course there may also be some
http://www.youtube.com/watch?v=ZudziPffS9Ehttp://vega.org.uk/video/programme/46http://vega.org.uk/video/programme/46http://vega.org.uk/video/programme/46http://vega.org.uk/video/programme/46http://vega.org.uk/video/programme/46http://vega.org.uk/video/programme/46http://vega.org.uk/video/programme/46http://vega.org.uk/video/programme/46http://vega.org.uk/video/programme/46http://vega.org.uk/video/programme/46http://vega.org.uk/video/programme/46http://vega.org.uk/video/programme/46http://vega.org.uk/video/programme/46http://vega.org.uk/video/programme/46http://vega.org.uk/video/programme/46http://www.youtube.com/watch?v=ZudziPffS9E


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50% of the incoming wave's energy is reflected/re-radiated towards the transmitter15.

50% will be passed by the diagonal polarizer in the direction of the horizontal polarizer and

the receiver horn.

The re-radiated energy is polarized in parallel of the metallic stripes of the diagonal polarizer grid.

The passed by radiation is perpendicular to the re-radiated vectors.

The horizontal polarizer

50% of the emitted energy A will now hit the horizontal polarizer, where again the energy will be

split up in components as it has been described in the previous section of the diagonal polarizer.

For symmetrical reasons 50% of the energy of these components will be passed as horizontally

polarized waves by this horizontal polarizer and the other 50% will be converted to currents in the

metallic structure16and result in vertically polarized waves.

From symmetry we may assume that:

50% of the incoming wave's energy is reflected in the direction of the diagonal polarizer

where some of it may be reflected at the grid.

50% will be passed by the horizontal polarizer as horizontally polarized waves in the

direction of the receiver horn. Normally this main wave is of the energy A.

The receiver Horn

The reflected components may be generated with unknown phases, which may interfere with the

directly passed waves. The receiver horn therefore receives of the energy A, which is exactly the

amount we have found in the quantum physic's model. We may call this the main component of the

arriving wave.

Now the receiver horn as well receives some of the reflected components, which may add or

subtract some energy to respectively from the main wave. This would deliver some additional

power, which for some frequencies might add up to a significant raise of the power balance.

It would be easy to calibrate the setup of the microwave link for the standard power balance without

any polarizers. The received power level is calibrated to A.

Then we insert the polarizers and check for the expected level of the received power A. This is

the level which is to be expected if the polarizers absorb the relevant energy components of the

quantum model.

If the received power is considerably higher than of the energy A we might expect this additional

energy to be re-radiated power components.

In a quantum physic's model of the energy A is lost by absorption. Although this might also be

practiced in a microwave model by using absorbing materials we would not be able to observe any

difference between the quantum physic's model and the microwave model without quantum

physics. The reflected components may prove that the 50%-50% distribution of both polarizations is

a unique quantum physic property which will be missing in the microwave model.

losses. Let us assume the gain of the re-radiating structures is 0dB.15 Ideally this energy may be dissipated in an isolator between the feed horn and the klystron.

16 This of course requires to use an ideal grid of very thin metallic conductors. No dissipation is to be assumed in the

system and no absorption of energy will occur.


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Superfluous EnergyIn fact the re-radiated energy cannot have been absorbed and must be showing up somewhere.

The 50%-energy with returns to the transmitter's feed horn may be absorbed in an isolator which

usually is mounted between the microwave source (klystron, Gunn diode, etc.) and the feed horn

17

.The 50%-energy which returns from the horizontal polarizer to the diagonal polarizer may be

bouncing several times between both horn antennas. There is no control of the phases and somehow

it will be compensated in other field components or end up at the receiver along with the main

wave.

SummaryIn a quantum physics model of the three-polarizer paradox the receiver horn receives exactly of

the input energy in the setup of the web-experiment Polarization of Light and Microwaves

(Quantum Physics).

In a microwave-model this calculated power balance also results in a median value of of the input

energy. In contrast to the quantum mechanics model however the energy level at the receiver may

be higher or lower depending on the energy which is re-radiated by the polarizers.

These reflected elements do not depend on statistics but on geometrical dimensions and will be

reproducibly constant in time for specific frequencies.

A setup with accurate power level measurements would be able to prove whether the microwave

setup depends on quantum physics or may be considered a normal geometrical antenna design

according to the works of Samuel Silver18.

17 Without an isolator these reflections might interfere with the microwave source or even contribute to another re-

radiated energy.

18 Microwave Antenna Theory andDesign - Samuel Silver
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Contents

The three-polarizer paradox.................................................................................................................2

A microwave model without quantum physics....................................................................................4

The microwave setup.......................................................................................................................4

The antenna theory...........................................................................................................................4

The diagonal polarizer.................................................................................................................4

The horizontal polarizer..............................................................................................................5

The receiver Horn.......................................................................................................................5

Superfluous Energy..............................................................................................................................6

Summary...............................................................................................................................................6

104544596 revisiting the three polarizer paradox

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