# Quantum Mystery #1 - Complementarity Principle

• zekise
In summary: No, because closing slit A would change the delay for a photon that was detection at point D on the screen (since it now has to travel the longer path through slit A). And that would change the pattern of hits on the screen, indicating that it has taken a different path.
zekise
Quantum Mystery #1 - Complimentarity Principle

Hi all - Making sense of the standard double-pinhole experiment is
not easy for the layman! In order for me to better understand complimentarity, an experiment is proposed. What is wrong with this thought experiment? Please view (you may need to scroll horizontally):

http://www.geocities.com/zekise/QuantumMystery-1.htm

The Photon Delay device is just a series of mirrors that reflect the
beam and elongates the path, causing the photon to arrive with a delay.

A single photon is sent to the half mirror and then the full mirror. An
interference pattern should be statistically detected at D, and
visibility of the pattern is V = 1. Assume we record the time t that it takes the photon to travel the path (the difference in the time of emission and absorption).

If t = t_1 (t_1 is measured by replacing M_h by M_f), then we know the
photon has taken path 1. If t = t_2 (t_2 is measured by removing
M_h), then we know the photon has taken path 2. Therefore, the
which-way information is known sharply, and K = 1. This would

Question - What is the value of t (when V = 1)? What is wrong with the picture?

TIA -Zak

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Same problem as in the classical double slit experiment, just replace your mirrors by slits and ask the same questions:
If I close slit A, I detect a photon on the screen, therefore I know the which slit the photon passed through;
If I close slit B, same stuff.
Now, if I open the 2 slits, which slit the photon passes through?

Nothing contradicts the complementary principle in this experiment. Your assumption that you can detect the "which path" by measuring the delay of the photon arriving at the detector when the 2 mirrors are present is simply wrong as this delay has nothing to compare with the delay when only one mirror is present.

Seratend.

Yes, it is quite like the double slit experiment with both slits open and the photons one-by-one building up an interference pattern on the screen.

You have two possible paths for a photon to one point on the screen. One path through one slit is longer than the other path through the other slit when a photon is detected at any other point on the screen other than the middle. The photon is traveling at the speed of light, so it would seem obvious as to which path the photon took if you time the emission and detection of a single photon.

But something must be wrong with this picture too, as the two possible paths are interfering with each other and there is no single path for the photon.

The answer must be that something about the time which must not be telling us which path is which. The time when there are interference effects building up on the screen must have a different value from those two possible paths when only one slit is open. But why is it different? I keep meaning to find out.

caribou said:
The time when there are interference effects building up on the screen must have a different value from those two possible paths when only one slit is open. But why is it different? I keep meaning to find out.

Just go back to the double slit experiment. And ask the 2 questions:

1) at what time the event "a photon hit the screen when the 2 slits are open" occur ?

2) at what time the event "a photon hit the screen when one slit is open" occur ?

(After the event "emission of a photon at time t=0)

And finaly, do these 2 events types define a path for the photon?

Seratend.

I am not sure if I understand seratend -

Are you saying that t (time with double slits open) is nondeterministic and t_2 <= t <= t_1 ?

If let's say t = t_1 half the events, or t = t_2 the other half of events, then I suppose it could be concluded that we have knowledge of which-way information.

Question: What is the value of t (if the experiment was conducted)?

zekise said:
If let's say t = t_1 half the events, or t = t_2 the other half of events, then I suppose it could be concluded that we have knowledge of which-way information.

How can you conclude that? It has only a meaning (relatively to you) if each photon has a "classical path". If it is the case, closing one slit should not change the interference pattern (you should get holes in the spatial distribution of the hits in the screen).

In other words, if I say "all the photons detected on the top of screen “passes” through the slit A when the two slits are open". Do you believe that it is the case? I think no. Your statement is of the same sort: As long as you are not able to define exactly what a quantum path for a single photon is for you, concluding that 2 events (the emission of a photon and the detection of a photon) identify this undefined path is totally irrelevant (i.e. you can say what you want). Thereafter, claiming that this experiment contradicts the HUP is completely nonsense.

Seratend.

P.S. Quickly for the timing of the double slits (has been a long time I have studied this topic): we recover, for the wave function, mainly the same results as with the classical em waves because the free propagator of the wave function (of the SE) is the same as the free propagator of em waves (helmotz equation).
Therefore, for each position on the screen and photon, we may have 2 possible delays if we neglect the size of the slits and these delays are analogue to a classical particle going through one of the slits (but please do not say that the photons has gone through a given slit! this just a timing not a path).

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seratend said:
Just go back to the double slit experiment. And ask the 2 questions:

1) at what time the event "a photon hit the screen when the 2 slits are open" occur ?

2) at what time the event "a photon hit the screen when one slit is open" occur ?

(After the event "emission of a photon at time t=0)

And finaly, do these 2 events types define a path for the photon?

I suspect we get a speed and time from emission and detection of the particle which comes the interference of the longer paths that go through the slits that makes it seem as if the particle had taken the shorter paths through the screen with the slits.

It's a sum-over-histories without the most direct paths, just the paths to either side of the most direct paths creating an effect as if there were direct paths. And the time and speed are very similar to what we'd expect from these nonexistent direct paths.

## 1. What is the Complementarity Principle in quantum mechanics?

The Complementarity Principle is a fundamental concept in quantum mechanics that states that certain properties of a particle, such as its position and momentum, cannot be observed simultaneously with precision. This means that the more accurately we know one property, the less accurately we can know the other.

## 2. How does the Complementarity Principle relate to the famous double-slit experiment?

In the double-slit experiment, particles of light or matter are fired through two parallel slits and create an interference pattern on a screen behind them. This experiment demonstrates the Complementarity Principle by showing that particles can exhibit both wave-like and particle-like behavior, depending on how they are observed.

## 3. Why is the Complementarity Principle important in understanding the nature of reality?

The Complementarity Principle challenges our traditional understanding of reality, which is based on classical physics and the ability to measure properties of particles with precision. It highlights the limitations of our perception and forces us to rethink our understanding of the physical world.

## 4. Can the Complementarity Principle be violated?

No, the Complementarity Principle is a fundamental law of quantum mechanics and has been extensively tested and verified through experiments. It is a key aspect of the Copenhagen interpretation of quantum mechanics, which is the most widely accepted interpretation among physicists.

## 5. How does the Complementarity Principle impact technology and practical applications?

The Complementarity Principle has led to the development of technologies such as electron microscopes and particle accelerators, which allow us to observe and manipulate particles at the quantum level. It also plays a crucial role in technologies such as quantum computing and cryptography, which rely on the principles of quantum mechanics to function.

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