Light & Coherence part 2: Spatial Coherence (and the Double Slit Experiment)
Summary
TLDRThis video delves into the concept of spatial coherence, following up on the previous episode about temporal coherence and light's spectral properties. Using a pond analogy and numerical simulations, the presenter illustrates how waves become organized and spatially coherent over distance. The video explores the relationship between spatial coherence and geometry, explaining the formula for coherence area and applying it to the Sun and Antares, a star in the Scorpio constellation. It also touches on the historical misunderstandings in science communication, the double-slit experiment with white light, and the Fourier transform effect with multiple slits. The script concludes by pondering the classical versus quantum perspectives on light, setting the stage for further discussion in a future sequel.
Takeaways
- 📚 The video is a sequel focusing on spatial coherence, continuing from a previous episode about temporal coherence and its relation to the spectral properties of light.
- 🌌 The presenter uses a pond in Hilversum, Netherlands, named after Hendrik Antoon Lorentz, to illustrate spatial coherence by observing the behavior of waves in water.
- 🌊 Waves in the pond become more organized and linear as they move away from the chaotic splash zone, demonstrating how spatial coherence develops with distance from the source.
- 🔍 A numerical simulation by Nils Berglund is introduced to show in detail how waves develop over time and how spatial coherence grows with distance from multiple wave sources.
- 📉 The simulation highlights areas of strong wave amplitude separated by boundaries of low amplitude due to destructive interference, illustrating spatial coherence and decoherence.
- 📐 The spatial coherence of waves can be quantitatively understood through geometry, with the coherence area being related to the distance from the source, wavelength, and source diameter.
- 🌞 The formula for coherence area is applied to the Sun, revealing that its spatial coherence on Earth is quite small, comparable to the cross-section of a human hair.
- 🔬 Thomas Young's famous experiment on light and colors used sunlight and a pinhole to create a spatially coherent beam, despite common misconceptions about a double slit configuration.
- 🌈 A true double slit experiment with white light is demonstrated, showing how spatial coherence affects the interference pattern and the visibility of colors.
- 🌠 The video discusses the coherence area for stars like Antares, which is much larger than that of the Sun, emphasizing the uniformity of the field despite the star's immense size and distance.
- 🤔 The presenter reflects on the different perspectives on light between classical and quantum mechanics, questioning whether light itself is quantized or if only its interaction with matter is probabilistic.
Q & A
What is the main topic of the second video on coherence?
-The main topic of the second video is spatial coherence, explaining how it arises and its implications for the properties of light.
What is the significance of the pond named after Hendrik Antoon Lorentz in demonstrating spatial coherence?
-The pond, with its fountain and water jets, serves as a real-life example to illustrate how waves become spatially coherent as they move away from the source of disturbance.
How does the video script use the analogy of waves in a pond to explain spatial coherence?
-The script describes how waves in the pond near the fountain are chaotic, but as one moves away, the waves become more organized and linear, demonstrating the concept of spatial coherence.
What role does the numerical simulation play in the explanation of spatial coherence?
-The numerical simulation, created by Nils Berglund, provides a controlled environment to observe the development of waves over time and how spatial coherence grows with distance from the source.
How does the script relate temporal coherence to the frequency changes of waves?
-The script mentions that the frequency of waves changes with time in the direction of wave propagation, linking this phenomenon to temporal coherence, which was covered in a previous video.
What is the formula given in the script for calculating the area of coherence for waves in 3D space?
-The area of coherence is proportional to the distance from the source squared, the wavelength squared, and inversely proportional to the diameter of the source squared, applicable when the distance R is much larger than the size of the emitter.
How does the size of the emitter affect the area of coherence according to the formula?
-The area of coherence is inversely proportional to the diameter of the source squared, meaning that a smaller emitter results in a larger area of coherence.
What historical figure's work is discussed in the script, and how does it relate to the understanding of light?
-The script discusses Thomas Young and his experiments with light and colors. It highlights the historical misunderstanding around the double-slit experiment and emphasizes the wave nature of light.
How does the script use the double-slit experiment to demonstrate the effects of spatial coherence in light?
-The script describes an experiment with two slits and white light, showing how a light source with a larger area of coherence produces an interference pattern with colored lines due to different wavelengths going in and out of phase.
What is the significance of the star Antares in illustrating the concept of spatial coherence?
-Antares, being a massive star with a large area of coherence, demonstrates that even though it emits vast amounts of random emissions, the resulting field on Earth is almost uniform within a large area, showcasing the concept of spatial coherence.
How does the script differentiate between the classical and quantum mechanical perspectives on light?
-The script suggests that a classical mindset views light primarily as an electromagnetic phenomenon, while a quantum mechanical perspective focuses on the emission and absorption processes involving discrete energy transfers.
What is the script's stance on the quantization of light?
-The script questions whether experiments like the photoelectric effect and Compton scattering truly show that light is quantized into discrete energy packages or if they only demonstrate the probabilistic nature of electromagnetic radiation's interaction with matter.
Outlines
🌌 Introduction to Spatial Coherence
The script introduces the concept of spatial coherence, building upon a previous video on temporal coherence. It sets the stage for a discussion on spatial coherence's emergence and its implications for light properties. The presenter uses a real-life example of a pond named after Hendrik Antoon Lorentz to illustrate spatial coherence in waves. The pond's water, disturbed by a fountain, moves chaotically near the source but becomes more organized as one moves away, demonstrating spatial coherence. The video promises a sequel to further explore the topic, including numerical simulations to better understand wave development over time.
📚 Mathematical Insight into Spatial Coherence
The script delves into the mathematical characterization of spatial coherence, particularly for light in 3D space. It presents a formula that relates the coherence area to the distance from the source, wavelength, and source diameter. The explanation simplifies the formula's derivation, using an analogy of a flat round disk as a wave source. The relationship between phase shift, wavelength, distance from the source, and emitter size is discussed, leading to the conclusion that coherence area is influenced by these factors. The sun is used as an example to calculate coherence area, revealing it to be comparable to the cross-section of a human hair, with variations depending on wavelength and atmospheric conditions.
🔬 Historical Perspective on Light Coherence
This paragraph explores the historical context of light coherence experiments, focusing on Thomas Young's work. It corrects a common misconception about Young's double-slit experiment, clarifying that he initially used a single slit and a card that split the light, not a double slit. The script discusses how scientific communication often relies on metaphors rather than precise details, which can lead to confusion. It contrasts the traditional double-slit depiction with the original experiment's setup and emphasizes the importance of understanding the actual experimental conditions for a clearer grasp of scientific phenomena.
🧪 Practical Demonstrations of Spatial Coherence
The script describes practical demonstrations to illustrate the effects of spatial coherence in light, using a double-slit experiment with white light. It explains how changing the light source's proximity to the slits affects the resulting interference pattern. When using a light source with a small area of coherence, no pattern emerges due to the lack of phase relationships. However, with a source producing spatially coherent light, a clear pattern of colored lines appears, showcasing temporal decoherence. The experiment highlights the necessity of spatial coherence for accurate double-slit experiments and introduces the concept of a 'bunch-a-slits' experiment, which performs a Fourier transform on the light's temporal signal.
🌟 Coherence and the Wave-Particle Duality of Light
The final paragraph contemplates the vastness of stars like Antares and how their light, despite originating from a chaotic process, becomes spatially coherent over astronomical distances. It contrasts this with the small coherence area of the sun's light on Earth. The script then transitions to a discussion on the nature of light, highlighting the difference in perspectives between classical and quantum mechanics. It questions whether experiments like the photoelectric effect and Compton scattering truly demonstrate that light is quantized or merely show that interactions with matter are probabilistic. The paragraph concludes by anticipating further discussions on these topics in a future video.
Mindmap
Keywords
💡Coherence
💡Spatial Coherence
💡Temporal Coherence
💡Wavefront
💡Numerical Simulation
💡Destructive Interference
💡Area of Coherence
💡Wavelength
💡Double Slit Experiment
💡Fourier Transform
💡Quantum Mechanics
Highlights
Introduction to the concept of spatial coherence and its relation to the properties of light.
Explanation of how spatial coherence emerges from a chaotic wave source, illustrated with a pond analogy.
Introduction of Hendrik Antoon Lorentz and the use of a pond named after him to demonstrate spatial coherence.
Numerical simulation by Nils Berglund to visualize the development of waves over time and spatial coherence.
Discussion on how wave patterns become more organized and coherent as they move away from the source.
Quantitative understanding of spatial coherence through a formula relating coherence area to source geometry.
Derivation of the coherence area formula for light and its dependence on distance, wavelength, and source size.
Calculation of the sun's coherence area using the derived formula and its implications for light observation.
Historical account of Thomas Young's experiments with light and colors, and the misunderstandings surrounding his methods.
Clarification of the actual setup used by Young in his famous 'double slit' experiment, involving a single slit and a card.
Critique of the use of metaphors in science communication and their potential to cause confusion.
Demonstration of a true double slit experiment with white light and the importance of spatial coherence for the experiment.
Observation of temporal decoherence in the double slit experiment and its effect on the interference pattern.
Experiment with multiple slits performing a Fourier transform on the temporal signal of the light wave.
Calculation of the coherence area for light from Antares, a star in the Scorpio constellation, and its surprising uniformity.
Reflection on the different perspectives on light between classical and quantum mechanics, and the implications for understanding light.
Introduction of the concept of probabilistic interaction between electromagnetic radiation and matter, contrasting with the idea of quantized light.
Transcripts
Hey Everyone, This is my second video on
coherence. The previous episode was mostly about temporal coherence and how it is directly related
to the spectral properties of light. If you haven’ t seen it, it might be a good idea to watch that
one first, because the current video it really a sequel of part 1. Today, I will mainly talk
about spatial coherence, how it comes about and what it means for the properties of light. And,
I will also take a few side tracks. I found that I could not fit all the side tracks into this video,
so good news for those of you who like sequels: there will be a part 3.
I live in Hilversum, the Netherlands and close to my home there is this a long rectangular pond
that is named after Hendrik Antoon Lorentz, in my opinion one of the greatest Dutch
scientists ever. And this pond is just ideal to demonstrate real life spatial coherence.
The pond has a fountain in it, which consists of 3 water jets that generate a lot of splashes. And
so, in the vicinity of the fountain, every point on the surface moves rather chaotically. However,
if we move away from the actual splash zone, we observe that the waves gradually all start moving
in this same direction, away from the source and become ever more organized. Shh, go away.If we
consider a small enough part of the wavefront, we observe that the waves are almost linear. Which
means that all points in the direction transverse to wave propagation move in unison or in sync.
And so, if we consider a small enough area of the wavefront, we can say that the waves have
gradually become spatially coherent. If you look at the spacing between the waves you will still
observe that the frequency of the waves changes with time in the direction of wave propagation.
And this is related to temporal coherence, a phenomenon that was covered in the previous video.
What you observe in a general sense is that the region of spatial coherence gradually
expands when the waves move further away from the sources. Now, although, quite illustrative,
this pond is not ideal as a model, especially with birds and the wind contributing to the
total wave pattern. So let me take you the more controlled environment of numerical simulation.
The simulation that I’m about to show you here is made by Nils Berglund who runs a YouTube channel
in his name. On his channel, he regularly posts visualizations of all kinds of physical phenomena,
from chemical reactions to lasers solving mazes. And he very kindly accepted the challenge to do
this wave simulation, which allows us to look in more detail how waves develop in time.
Let’s go to the start of the simulation. It involves 15 randomly positioned wave sources that
each emit a longitudinal wave in one long burst. The sources have a slightly different emission
frequency and start at a random phase. As you can see, they emit waves in all directions and what we
observe is how, relatively close to the sources, the wave patterns are quite chaotic, a bit like
in the pond. But as the waves move away from the disorder, we see that things settle down pretty
quickly. And again, if we consider only a part of the wavefront, we can actually see how spatial
coherence grows with distance. But there is more: we can identify these areas where the waves are
relatively strong. These are separated by what appear to be boundaries where the amplitude is
low due to destructive interference. Now for the casual observer it may seem that the waves and the
wave energy is non-uniformly distributed in space. But that is actually not the case, because the
simulation basically only highlights potential energy and not so much the kinetic energy in
the waves. But what we do observe is that the waves from apparently randomly emitting sources
result in a wave pattern that gradually becomes spatially coherent some distance further away.
It also illustrates nicely the most important aspects of temporal and spatial decoherence.
But why do waves seem to add up to a fairly regular pattern when they move
away from the sources? Well, one important aspect is that as they move further away,
the wave propagation directions of different sources are lining up. And what you should realize
is that when waves of the same frequency but with a different phase are lined up,
they will result in one single regular wave of the same frequency. And so, all the initial
chaos related to just phase difference from the various wave sources gradually disappears
when we move further away. Now in this case, the linear addition of individual waves will
never show a 100% regular pattern, because the sources all emit at a different frequency and so
phase relationships are not constant in time and space. And that is why we observe these areas of
decoherence in both the direction of propagation as well as in the transverse direction.Let’s
see if we can understand quantitatively how spatial coherence in waves is related to geometry.
Spatial coherence of waves in 3D space, like for example light, can be characterized by
an area of coherence and it is interesting to see what defines this area. I’ll just start by
giving you a formula. You see that the coherence area is proportional to the distance from the
source squared, and the wavelength squared and inversely proportional to the diameter
of the source squared. I should add that this is a simplification which only applies if the
distance R is much larger than the size of the emitter. Now there is actually quite a lot to it
if you want to derive this formula property in the case of light, which I don’t want to do. However,
I think it would be good to give you some very general insight into this formula.
Imagine we have a source in the shape of a flat round disk emitting waves. And let’s
for now consider only those waves arriving from the extreme outside of this source which arrive
on a surface located somewhat further away. This surface is perpendicular to the axis pointing in
the direction of the source and we observe that these waves are in phase on this axis.
If we move some distance in the y-direction away from the central axis, the waves will
gradually get out of phase more and more until they are completely out of phase.
Now if we define Y as the distance over which the phase shift between these 2 waves is lower
than an acceptable value, say for example 60 degrees phase shift, we find that this
distance Y is proportional to the wavelength: so, the shorter the wavelength, the smaller
this distance Y. And this relationship between Y and wavelength is actually a linear one.The
same kind of relationship holds for the distance from the source: the longer the distance between
source and area, the larger the value of Y within which waves will still be considered
to be in phase. However, for the size of the emitter, it is exactly the opposite: the smaller
the distance between the outer boundaries of the emitter, the larger the value of Y.
And so, we can summarize that the distance Y is linearly proportional to the wavelength and
the distance from the source, and is inversely proportional to the size of the emitter. And that
means that the Area of coherence which is defined by Y as the radius of a circle, is proportional to
Y squared. Now if you compare this result with the formula I showed you, you may notice there
is one detail which is still a bit out of place and that is the one over pi. This is actually a
proportionality factor that arises if we derive this formula in a mathematically more rigorous
way, based on the exact geometric configuration of a round source and our coherence requirement.
Now as stated, this is a somewhat simplified representation, but nevertheless the resulting
formula is actually quite useful. So, let’s calculate the area of coherence for the sun using
this formula. I must remark that, technically speaking, on earth the constraint between
distance and size is not truly satisfied. You should also keep in mind that the sun
is spectrally very broad, so we have to choose a wavelength for which to do the calculation.
But when we fill in the values for the diameter of the sun, the distance between the sun and
earth and choose a value for Lamba in the center of the visible spectrum, say 500nm, we arrive at
an area of coherence of almost 900 square microns which is equivalent to an area with a diameter of
34 um. This area is comparable to the cross section of a human hair. Of course, this only
works if there are no clouds in the sky because in that case, the area of coherence will definitely
be smaller. And since wavelength is a parameter, for blue light with a shorter wavelength the area
of coherence it will be somewhat smaller and for red light it somewhat larger.It
is interesting to note that when Thomas Young wrote his paper about the theory of light and
colors in 1801, he did of course not have a laser or other really bright light sources available,
other than the sun. And so Young was more or less forced to use sunlight for his experiment. From
what I’ve read on the internet, he used a mirror to direct the sunlight through a tiny pinhole into
a darkened room, to create a bright beam of light. And with the knowledge you have just aquired about
the area of coherence of the sun, I think it should be fairly obvious to you what the function
of the pinhole is: it’s intended to make all the light entering the room spatially coherent.
When I tried to confirm that this is how he actually did it in the original paper, I could not
find any reference to a mirror or an aperture in the window. Or a double slit for that matter. Yes,
that is correct: Thomas Youngs’ famous double slit experiment actually did not involve a
double slit configuration. Instead, he placed a thin card in the beam that split it in half,
which caused the diffraction pattern. And this is how he could observe the separation of light
into different colors. Even a few years later in his 1803-1804 paper on the same subject,
there is no reference to a double slit configuration anywhere. However, six years
after the original experiment, Young published 2 books that contained a large collection
of lectures. And in volume 1, he did actually mention a configuration resembling a double slit.
The reason why I think this is interesting is because it illustrates how we communicate
about science. We don’t necessarily communicate facts. Most of the time we communicate metaphors
that represent the essence of an experiment and not necessarily the details of the actual
configuration. So somewhere in history, someone decided to name it the Thomas Young’s double slit
experiment and this then became synonymous with the phenomenon observed. Now, don’t get me wrong:
There is nothing like a good metaphor to explain difficult concepts to an audience of non-experts.
However, extending the use of metaphors beyond what they were intended for can become pretty
confusing. Take the double slit experiment for single electrons instead of photons. Here are a
few examples of how that experiment is depicted: see if you can spot the confusing aspect.
It’s not this cougar here, which might very well be a metaphor for something else too, who knows.
No, the confusing aspect is that all these visuals show narrow slits with a very substantial distance
between then. Which makes the experiment intrinsically mysterious: because how can a
particle small enough to pass through a narrow slit, pass through two widely spaced slits at
the same time?However, if we refer to the original experiment performed at Hitachi, the interference
was actually created by using an electron biprism. This device basically consists of
an extremely thin charged wire, with a thickness much smaller than a micron. When you look at this
configuration, the interference effect suddenly becomes much less mysterious because it is
basically about how the electron interacts with an object small enough as to demonstrate that the
electron has wave properties. And so, the metaphor of the double slit and the way it is presented
doesn’t necessarily help people understand. If anything it just adds to the confusion.Ah
well, all of this does not change the fact that actual double slits do a good job in demonstrating
the effects that Thomas Young observed. So, let’s do a true double slit experiment that illustrates
the effect of spatial coherence in light. And for this demonstration we will use white light. So
here are 2 slits etched in a layer of chromium on a glass slide and we are looking at them under a
microscope. They are quite small about 300 microns long and 5 microns wide. Why so small? Well,
because we really want to bring out the colors and the interference here in a lot of detail. I’ll
place a link to another video in the description about how you can record this type of images.
We will start out by looking at how the light through the slits develops when the area of
coherence is much smaller than the dimensions of the current double slit configuration. Basically,
this can be achieved by placing a white light LED very near to the slits. If we
now move away from the slits, we’ll observe how the light passing the slits is diffracted
and how this results in 2 blurry blobs that merge without any noticeable interference pattern. And
this is because the light does not contain any phase relationships on points in the slit area.
Not particularly fascinating right? Now, let’s replace the close-by positioned LED with a light
source that produces spatially coherent light. And this means that the area of coherence is much
larger than the total area of the 2 slits. So in this case there is a fixed phase relationship for
every wavelength at every point on the slits. And look what happens now if we do the same
experiment. Once light from the 2 beams starts to overlap, we observe this fascinating pattern of
colored lines developing, because of different wavelengths going in and out of phase.What
we observe in this pattern is actually temporal decoherence. In the center of the pattern,
all wavelengths are in phase with each other, because the distance to the two slits is equal
for every point on that line. But as we move away from the center, every wavelength has its
own interference periodicity and so the phase differences between the light originating from
the 2 different slits will be different for every wavelength. So this is the reason that
you need spatial coherence to do a proper double slit experiment. Pretty cool huh?
Want to see something even cooler? Here I’ve got a bunch of slits on which we can do the famous
bunch-a-slits experiment. Together these can actually perform a little math operation for us.
They can do a Fourier transforms on the temporal signal of the light wave passing the area of the
slits. Here you see how the transformation develops in space as we move away from the
grating. It results in a spectrum showing all frequencies present in the LED used for the
experiment. In other words, it’s a microscopically small spectrometer in one pattern. Previously we
calculated the area of coherence for light from the sun and found that the area is pretty small in
the visible range. But of course, for stars a bit further away, we can do the same thing. That is,
if we know their size and distance and that is for example the case for this particular star here in
the Scorpio constellation: The star is called Antares after the Greek god of war. And indeed,
Antares is not a friendly little neighborhood star. Depending on which source you consult,
Antares is about 600- 800 times larger than our sun. And I mean larger in diameter. If we were
to place this big boy in our own solar system, it’s physical boundaries would extend beyond
the orbit of the planet mars. It’s a monster, but fortunately for us, it’s also 550 light years away
from earth. Now, if we do the same calculation for the area of coherence of light Antares on earth,
we find a value of about 2.3 square meters. Now I want you to let this sink in for a second.
Here we have an object so massive it’s beyond human comprehension. Which emits unimaginable
amounts of random emissions every second. Yet by the time the radiation arrives on earth,
the sum of these individual contributions yields a field that is as good as uniform within an area
of several square meters. And you can measure this with methods similar to the double slit
experiment. Of course, as for the temporal field properties: it still contains a lot of frequencies
since the light emitted by Antares is spectrally also very broad. But just think about how you
could explain for example the phase relationship from a corpuscular perspective on light.
Also, keep in mind Antares is a huge star, relatively close by. Smaller,
further away stars can easily have an area of coherence the size of a square kilometer.
As you may have noticed, I’ve focused only on the wave behavior of light so far, in this video but
also in the previous one. And if you want, you can consider this a “classical” perspective. In
the previous video I made friends for life with the quantum mechanics community by stating that
the properties of light arise purely from wave behavior. And as much as I would elaborate on
this a bit further now, I don’t think it would be wise to do that near the end of a video that is
already too long. By the way, apart from the use of the word photon in video part 1, I did not make
a single reference to quantum mechanics. Because I think it is safe to say I don’t understand Quantum
Mechanics. I did take courses in the subject at university and I did pass the exams without a
problem. But somehow it never made sense to me at. I guess I just wasn’t smart enough.
There was one thing that struck me during the discussion. And that is
that at some fundamental level, we do not seem to agree on what exactly we mean with the word
“light”.If you’d ask someone like me with a classical mindset to describe light,
that person would probably mainly refer to the electromagnetic phenomenon. So, I would say
something like: we have a source that emits light. This light propagates in space, is scattered,
diffracted, reflected whatever and is then detected or absorbed, for example in your eye.
From this perspective, I’m referring to the electromagnetic radiation as light.
However, if you’d ask the same question to someone deeply involved in quantum mechanics,
the emphasis would not be on the radiation aspect. It would likely be more on the emission
and absorption processes and how these involve the transfer of discrete energy packages. So I guess,
from the viewpoint of someone in quantum mechanics, double slit experiments are only
marginally interesting at best. They would argue that the quantized interaction between radiation
and matter is proof that the radiation or the field itself must also quantized. And that this
proof is in many experiments, including the photoelectric effect and Compton scattering.
Now just to be clear, I’m not questioning the quantized nature of the interaction between
radiation and matter. But do these experiments truly show that the radiation which I refer to
as light, is quantized into discrete packages of energy? Or do they merely demonstrate that the
interaction of electromagnetic radiation with all matter is fundamentally probabilistic?
I have a feeling that we’ll have plenty to talk about in part 3. And maybe we
can even discover a suitable common metaphor.
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