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This page explains the principles of quantum mechanics without equations and formulas.

Since the 19th century it is known that light is waves. At the beginning of the 20th century it was confirmed that light is also particles,
separate pieces of something, they are called photons.

As the wave flies, it oscillates sideways. Some photons oscillate horizontally right – left – right – left – right – left. Some other photons oscillate vertically up – down – up – down – up – down. The direction of oscillation is called polarization. There are photons polarized horizontally, there are photons polarized vertically, there are photons polarized obliquely. The eye does not distinguish the polarization of photons. The eye only registers that a photon hit it and does not recognize how the photon was polarized, in which direction the photon was oscillating.

Light that is composed of photons oscillating in the same direction is called polarized light.
We meet polarized light e.g. when we watch reflection of light on polished furniture.
The light from reflection consists mostly of photons oscillating in one direction.

Photographs remove reflections by using polarizing filters. A polarizing filter looks like a lens that gets screwed on the camera, but is not convex like a lens, is flat and what it does with light is that it transmits only light oscillating in one direction. A photograph rotates the polarizing filter mounted on his camera and in so doing he watches the reflections intensify and diminish.

Let's now take a polarizing filter and let's rotate it so that it transmits light oscillating vertically. A photon with vertical polarization passes through the filter. A photon with horizontal polarization gets caught up by the filter and doesn't pass through. What happens with a photon that is polarized obliquely? When we send photons with oblique polarization through the filter we discover that some of them pass through while others get caught up. We cannot say in advance whether one specific photon passes through or gets caught up. We send one photon – it passes through. We send exactly the same photon – it doesn't pass through. There is no way to determine in advance what happens with an obliquely polarized photon on the polarizing filter.

Let's place a second polarizing filter after the first one and rotate it so that it transmits light oscillating horizontally. Now we have two polarizing filters one after the other, the first one polarizing vertically and the second one polarizing horizontally. Such a pair of filters does not transmit any light. A photon that passes through the first filter is set into vertical polarization by that passage. No matter whether it was polarized vertically or obliquely, after passing through the filter it is polarized vertically. There are neither horizontally nor obliquely polarized photons hitting the second filter so that nothing passes through it.

And now comes the magic – a third polarizing filter rotated so that it polarizes neither vertically nor horizontally but obliquely.
We place the third polarizing filter before the first polarizing filter – nothing passes through such a triad of polarizing filters.
We place the third polarizing filter after the second polarizing filter – nothing passes through such a triad of polarizing filters.
We place the third polarizing filter between the first and the second polarizing filter – and lo – whereas nothing passed through
the twosome of polarizing filters, some light passes through after adding the third barrier in between. How is it possible? Vertically polarized
photons hit the newly added obliquely polarizing filter. When they pass it, their polarization is set oblique. The horizontally polarizing filter
is then hit by obliquely polarized photons which have the possibility to pass through it.

Each atomic nucleus can decay. The more time we give to an atomic nucleus the higher is the probability that it decays during it.
Various atomic nuclei are variously prone to decay. When we want to express by a number the susceptibility to decay, we use a time measure
called half-life. E.g. the half-life of carbon ^{14}C is 5730 years. Why there is always written about half-life, why there is not
plainly stated “whole-life”? It is so because for no atomic nucleus we have guaranteed that it surely decays after sufficient time.
Half-life is the time after which the probability of decay is half.

When a piece of matter contains one million atoms ^{14}C, it will contain just one half a million atoms ^{14}C
after 5730 years because one half a million atoms ^{14}C decays during 5730 years.
One quarter of million atoms ^{14}C remain after next 5730 years,
one eighth of million atoms ^{14}C remain after next 5730 years,
one sixteenth of million atoms ^{14}C remain after next 5730 years, etc.
Can we predict which individual atoms ^{14}C decay and which don't? There is no rule for it, the number of possible combinations
is astronomical and all are equally good, there is no natural law favoring one of them.

In atomic nucleus, no mechanism is ticking and measuring a time for which the decay is scheduled.
When we detect that an atom ^{14}C is undecayed, it always pays that its half-life will be 5730 years,
no matter how recently the atom originated nor how many times nor when we have checked it before.
By detecting that an atom ^{14}C is undecayed we rejuvenated it perfectly and it has again 5730 years of half-life ahead.

A photosensitive material is a material that permanently changes when hit by light. A chemical reaction is caused when light falls on a photosensitive material. A photographic plate is a plate, which is coated by a film of a photosensitive material. A photographic plate is kept in the dark, in some controlled manner light is let to fall on it and then the plate is dipped into chemicals which stop the photosensitivity and visualize places that were changed by hits of light. Such a dip of a photographic plate into chemicals is called photographic development.

Let's arrange an experiment so that we place a photographic plate vertically and a thin barrier from an opaque material a small distance before it. Let there be two narrow vertical slits side by side in the opaque barrier, the distance between the slits is very small. A barrier that light passes through just two narrow slits side by side is called double slit.

When we shine light on the photographic plate through the double slit, what will we see on it after the photographic development? We would expect two vertical lines because light shined through two vertical slits. But light is waves. It bends right and left when passing a narrow vertical slit. The double slit becomes two sources of waves the origin of which is actually one source. The photographic plate is being hit by waves from both slits. On some places of the photographic plate the incident waves consolidate each other, on other places of the photographic plate the incident waves weaken each other. After photographic development we make out that light was hitting a vertical strip centered between the slits and other vertical strips by its sides.

What we find on the photographic plate when sending photons stepwise one by one? Exactly the same strips as when more photons are flying together.
Also one single photon creates a pair of sources of waves that affect each other and this affection determines the places the photon can hit.

We would expect a particle to pass just through one slit. The double slit experiment proves that a particle can be in more places simultaneously. And it applies for not only photons. The slits experiment shows the same also with electrons, atoms and even with molecules composed from more than one hundred atoms. Also a big molecule is a wave that passes through more slits simultaneously.

As heavier and hotter a piece of matter is, the less it shows its wave nature. As lighter and colder a piece of matter is, the more it shows its wave nature.
Electrons moving around a nucleus show their wave nature fully. An electron is spread around the nucleus, it is on one side and simultaneously on the other
side of the atom. When two molecules collide, a chemical reaction between them can happen. The positions of the electrons in the molecules and also the positions
of both the molecules are spread out, thus the chemical reaction happens and simultaneously does not happen.

The state when one physical quantity has more values simultaneously is called superposition. For example position, speed, polarization and other physical quantities can be in superposition. An atomic nucleus gets into a superposition of the states “undecayed” / “decayed”. As time progresses, the proportion of the state “undecayed” decreases and the proportion of the state “decayed” increases, exactly and non-randomly. A photon that hits a polarizing filter obliquely gets into a superposition of the states “didn't pass through” / “passed through”. The proportions of the states are exactly determined by the angle formed by the photon and the polarizing filter.

Pen's position in a superposition of three values (in the proportion of 60% : 30% : 10%). |

At a double slit, a photon gets into a superposition of the states
“caught by the barrier” / “passed through the double slit”. We can further differentiate the state “passed through the double slit”
say into “hit the central strip” / “hit another strip”. On the places that the photon can hit, the photosensitive material
gets into a superposition of the states “photochemical reaction did not happen” / “photochemical reaction happened”.
There is nothing random in it, the proportion of each state in the superposition is exactly given.

Superposition is in sharp contrast to our everyday experience of the world. Each time we observe some physical quantity, it is not in a superposition, it has only one value. This is because the very act of observing is an event that carves the physical reality. When we observe the physical reality, the superposition is curtailed. The physical quantities the values of which the observation does not reveal remain in the superposition. The superposition of the observed physical quantities collapses to one of the possibilities. This is called wave function collapse.

The physical reality is accurately described as a certain superposition. The uncertainty of position, speed and other physical quantities does not mean that the description of nature would be uncertain. It only means the superposition which can be described exactly. Knowing the initial superposition, it is possible to calculate how the physical reality will look in any time in the future, unless a wave function collapse happens. The wave function collapse nondeterministically chooses the observed option and reduces the superposition. Except the wave function collapse all quantum mechanics is deterministic.

When we know how the superposition looks, we can calculate probabilities of the observable options. The higher the proportion
of an option in the superposition the higher the probability that the option will be chosen by the wave function collapse.

We sent one thousand photons stepwise one by one through a double slit on a photographic plate. We found one hundred dots on the plate after the photographic development. The dots are distributed into strips, the most densely grouped in the central strip. Nine hundred photons did not pass through the double slit or did not manage to cause a photochemical reaction. One hundred photons caused those one hundred dots. The question is – can we sort the dots in chronological order from the oldest photon to the latest one? If chemical reactions on the plate did not interact with the environment during the time we were sending the photons, and if the difference in the age of the photochemical reactions does not manifest itself in the state of the molecules notably, we are looking at a superposition of different sequences of the photochemical reactions. One dot does not correspond with one photon, one dot is a superposition of the same photochemical reactions caused by different photons.

It is common to perform experiments in which a number of particles get in a superposition of different mutual swaps. One particle cannot be then assigned to just one of the particles as they were before the superposition.

If we wanted to trace back the history of some particle, we might find that we have to draw a branching genealogical tree
because of the superposition.

Polarization can be in superposition. An example is a photon that is polarized at once horizontally and with the same proportion vertically. Such a photon gets into a superposition of the states “didn't pass through” / “passed through” on an anyhow rotated polarizing filter and the proportions of the states “didn't pass through” / “passed through” are equal. In other words, this photon has the property “it passes through a polarizing filter with half the probability no matter how the polarizing filter is rotated”. Is it possible to distinguish this property by measuring?

When we can examine one photon only, we can learn very few about it by measuring. We have only one opportunity to put a somehow rotated polarizing filter in the path of the photon and to measure whether the photon passed or didn't pass through.

We can examine superposition by measuring when some source, some physical process, repeatedly generates identical particles for us. When we have a large number of identical photons,
we can let some amount of them hit a polarizing filter, calculate the probability from the number of passes, and do it again with the polarizing filter being rotated to several angles.
In this manner it is possible to distinguish also the property “it passes through a polarizing filter with half the probability no matter how the polarizing filter is rotated”
which can only be achieved by the superposition.

Consider two photons. The first photon is in the superposition of the states “polarized horizontally” / “polarized vertically”
and also the other photon is in the superposition of the states “polarized horizontally” / “polarized vertically”.
The existence of such two superpositions means the existence of one superposition of these four states:

- the first photon is polarized horizontally, the other photon is polarized horizontally
- the first photon is polarized horizontally, the other photon is polarized vertically
- the first photon is polarized vertically, the other photon is polarized horizontally
- the first photon is polarized vertically, the other photon is polarized vertically

- the right photon is polarized horizontally, the left photon is polarized vertically
- the right photon is polarized vertically, the left photon is polarized horizontally

We keep the left photon unobserved, put a vertically polarizing filter in the path of the right photon and observe whether the right photon passed the filter.
A wave function collapse happens, the superposition collapses to just one of these two states:

- the right photon was polarized horizontally, the left photon is polarized vertically
- the right photon was polarized vertically, the left photon is polarized horizontally

The equiproportional superposition of the horizontal polarization and the vertical polarization is identical to the equiproportional superposition of the oblique polarization and the perpendicular to it polarization. It is also identical to the equiproportional superposition of all possible polarization angles. So the pair of entangled photons can also be described as “the polarizations of two photons are in the superposition of all possible angles and perpendicular to each other.”

When one of the two entangled photons reaches us, we can decide what angle to rotate a polarizing filter placed in its path. By detecting whether our photon
didn't pass or passed through the polarizing filter we set the second, distant photon to the angle that we chose or to the angle perpendicular to it.
Somebody may examine the collapsed distant photon. To be able to uncover something about the angle that we chose, that person would have to know
whether the photon collapsed right in the angle that we chose or to the angle perpendicular to it.

We know from the theory of relativity that faster than light information transfer can place an effect before its cause. When the effect happens first and the cause happens afterwards, it may lead to a logically impossible situation. The emergence of logically impossible situations can simply be avoided by prohibiting any faster than light information transfer.

The ban on faster than light information transfer implies that it must not be possible to influence nor to predict the result of the wave function collapse of entangled particles. If there is a nonrandom factor behind the wave function collapse of entangled particles, then the consistency of causes and effects must be cared for at the level of this factor.

It is possible to come across the opinion that the nondeterminism which quantum mechanics speaks about is surely just a temporary inability of physicists to design a better, deterministic theory. We do not know in advance what all we are yet to discover, so how can we affirm definitely that nature is nondeterministic? Because of the relation between the wave function collapse of entangled particles and the causality we can affirm it, except we include a hypothetical deterministic inexplorable metaphysics into nature.

How does physics lead us to metaphysics? Let us assume that the wave function collapses of entangled particles are not random. Then it holds that the rules or some order according to which they happen must remain hidden from us when we are ready to use them to produce a logically impossible situation. We cannot handle them reliably by a law of physics, therefore it is possible to label them as metaphysics.

When somebody claims that he or she uses some paranormal ability, reproducibility is required as a proof. Every paranormal ability has failed such testing.
If, however, there is something more than randomness beyond the border of physics, then reproducibility is just what we cannot require from it.

We are sending single electrons through a double slit. They are hitting one central strip and other thinner strips spaced around the central one. This proves that one electron flies through both the slits and that the two flies interact. We add a device to record through which slit the electron flied. The adding of such device causes the electrons to hit elsewhere. The places they hit witness of flying through just one slit at the time.

When an electron touches the device then the position of the electron entangles with the state of the device. The position of the electron remains in the superposition of flying through both the slits, but this superposition is now a part of a larger superposition which contains also the state of the device and hence any interaction of the two flies after the double slit is prohibited.

When a superposition entangles with something else and the entanglement prevents interaction between parts of the superposition then such entanglement is called decoherence.

Over time, pieces of matter contact mutually and their states entangle. Their positions are in a superposition of different places in space, thus also the entanglement happens at different places and at different times. There may be parts of the superposition where the pieces of matter don't meet and no entanglement happens. Decoherence simplifies the situation by making parts of the superposition not being able to interact.

The entanglement of states spreads to more and more pieces of matter. Each piece of matter involved in the entanglement is likely to get in contact with other pieces of matter and involve them too. Then it is very improbable that all the involved pieces of matter ever form such a mutual position that allows parts of such a large superposition to interact.

Scientists who explore interactions between parts of superpositions are faced with decoherence. It happens to them that a particle, which may have originated for example in cosmic rays, in natural radioactive decay or in an electric discharge, flies in and its state entangles with the state which is being examined. The entanglement makes parts of the examined superposition not to interact.

Decoherence splits a superposition up into simpler parts that don't interact. The wave function collapse chooses from them. If assuming that the wave function collapse gives a random result, then it makes no sense to distinguish whether the wave function collapse happens at a conscious registration of the result by an observer, or at the decoherence, or at any time in between. Decoherence is therefore confused with the wave function collapse.

Let's have two detectors and in the middle of them an apparatus. At a pre-agreed time, the apparatus sends a pair of photons to the detectors, one photon to each detector. The polarizations of the photons of the pair are not determined but they are mutually perpendicular. Both the detectors do the same. After the photons split and embark on their journey, each one detector throws a dice with the labels “0º”, “30º”, “60º”, “90º”, “120º” and “150º”. According to the result of the dice roll, the detector rotates a polarizing filter to the given angle. Then the photon either passes or doesn't pass through the polarizing filter, which gets recorded together with the angle of the filter. This procedure is repeated many times with other and other pairs of photons, creating a record like this:

90º | didn't pass through |

120º | didn't pass through |

30º | passed through |

90º | didn't pass through |

0º | passed through |

150º | passed through |

60º | passed through |

30º | didn't pass through |

... |

When we take the records from both the detectors and compare them, an interesting thing shows up:

- Each time the polarizing filters were set to the same angle, one photon of the pair passed through and the second one didn't pass through.
- Each time the polarizing filters were set perpendicular to each other, either both the photons passed through or both the photons didn't pass through.

The remaining cases, in which the polarizing filters formed an oblique angle, will help us. All possible combinations of the results “passed through” / “didn't pass through” of both the photons occur here. However, we can classify them into just two results: Either “one photon passed through and the second photon didn't” or “both the photons passed through or both didn't”. The more parallel the polarizing filters are, the more frequent is the result “one photon passed through and the second photon didn't”. The more perpendicular the polarizing filters are, the more frequent is the result “both the photons passed through or both didn't”.

If the photons did not know about each other when they were hitting the polarizing filters, then the frequency of the results would vary in direct proportion to the angle between the two polarizing filters. Whatever hidden variables the photons might carry, the randomness of the settings of the angles of the polarizing filters averages all out.

The probability that a photon passes through a polarizing filter is not in direct proportion to the angle between the photon's polarization and the filter. When the photon's polarization is rather parallel with the filter, the probability of passing through is higher than the direct proportion. When the photon's polarization is rather perpendicular to the filter, the probability of passing through is lower than the direct proportion. We didn't need to know it until now.

Quantum mechanics says that as soon as one photon of the pair hits a polarizing filter, the second photon also gets the corresponding polarization, which determines the probability of passing through the second polarizing filter. It doesn't matter which photon of the pair is the first to hit a polarizing filter, whether one detector is the first or the other detector is the first, the probability of the observed results is the same. When the polarizing filters are rather parallel, quantum mechanics predicts that the result “one photon passed through and the second photon didn't” will be more frequent than the direct proportion. Likewise, when the polarizing filters are rather perpendicular, quantum mechanics predicts that the result “both the photons passed through or both didn't” will be more frequent than the direct proportion.

Thus, the faster than light arrangement is a measurable phenomenon. Experiments have agreed with quantum mechanics. When you hear about experiments which demonstrated the violation of Bell's
inequalities, this is what they are.

The state of a particle can be a complex superposition. When we make an observation on the particle, we get to know something about it but much more information is destroyed by the collapse. It is impossible to take the particle and produce its copy. The state cannot be copied but we can move it from the particle to another particle so that no information about the state can be obtained from the original particle and the other particle has it now. Teleportation moves the state through a pair of entangled particles.

We have a particle with a state and we want to teleport this state to a distant target station. We use two additional particles, mutually entangled, one of them is with us and the other is in the target station. So altogether the teleportation works with three particles. Two particles are with us – one of them has the state we want to teleport and the other is entangled with the third particle in the target station. We perform an observation of the our two particles in the manner that both get observed by one collapse. This observation gives us information about the pair of particles as a whole without giving us any information about the state of the teleported particle itself. The state gets moved to the unobserved particle in the target station.

It is necessary to perform yet another simple transformation on the state of the particle in the target station to be the same as the original state of the teleported particle. The result of the our observation is needed. We have to deliver the information what the observed result was to the target station. Not knowing this information it is not possible to arrange any measurement of the particle in the target station that would reveal anything about the teleported state.

The first teleportation was accomplished in 1997. Experiments were successfully repeated many times, including teleportations across a distance of several
kilometers.

What kind of an article about quantum mechanics would this be without mentioning Heisenberg's uncertainty principle? In the philosophical literature, Heisenberg's uncertainty principle is sometimes even used as a synonym for quantum mechanics. So let's finally see what Heisenberg's uncertainty principle is:

Some physical properties, such as position and velocity, cannot be accurately determined simultaneously. Is it strange? An illustrative explanation exists: Whenever we want to measure some object, we must jog it by some particle. The particle has its own wavelength, therefore where it bounces from the collision does not allow us to determine the exact position of the collision nor where exactly the measured object came from.

Before the invention of quantum mechanics, physicists took it that nature is deterministic. And, at first sight, also Heisenberg's uncertainty principle does not appear to question determinism yet. It seems to say only: We don't know exactly which state matter is in, and never get to know it fully by affecting matter with matter. Every measurement disturbs the measured object. At the microscopic level, the behavior of nature cannot be predicted.

Such assertions remind of quantum mechanics, yet a deterministically understood uncertainty is not quantum mechanics. The disturbance of the measured object very strongly reminds of the wave function collapse, but it is not it. A superficial understanding of Heisenberg's uncertainty principle offers an incorrect deterministic interpretation of terms and statements which resound around quantum mechanics.

Heisenberg's uncertainty principle is important for some particular physical tasks. If we want to grasp the basic principles and philosophical implications of quantum mechanics, we do not need to know it.

pavel.bilek@quantum-mechanics.info

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