[Bored chemist]

What's the outcome predicted by your mathematical model in following experiments?

Exactly the same as the observation- or we would have changed the theory.

That's my point; the model works.

[hamdani yusuf (OP)]

What's the outcome predicted by your mathematical model in following experiments?

Exactly the same as the observation- or we would have changed the theory.

That's my point; the model works.

What are the results of the observation?
What are the results of the calculation?
Are they really the same?
Can you predict the outcomes before performing the experiments, based on the mathematical models alone?
Let's start with the simplest cases, such as single wire diffraction. Let the width of the wire 0.1 mm, wavelength of laser beam 500 nm, distance to a screen 5 m. What the diffraction pattern would look like?

Then tilt the wire 45 degree, top end of the wire is closer to the screen, while bottom end is closer to laser pointer. What the new diffraction pattern would look like?

Science should not be based on blind faith. If we can't proof or demonstrate that something is true, we shouldn't be convinced that it is true. If we can't proof or demonstrate that two things are equal, we shouldn't be convinced that they are equal.

[alancalverd]

The result from weighing the elephant can be used to predict if a particular helicopter can be used to lift it.

But it doesn't tell you what an elephant is, or what it will do next.

[alancalverd]

Can you predict the outcomes before performing the experiments, based on the mathematical models alone?
Let's start with the simplest cases, such as single wire diffraction. Let the width of the wire 0.1 mm, wavelength of laser beam 500 nm, distance to a screen 5 m. What the diffraction pattern would look like?

Yes. You can use Babinet's principle to predict it from the slit experiment, and IIRC from my schooldays, it works.

[Bored chemist]

Science should not be based on blind faith.

Which do you think happened first?
The experiment, or the model?

[hamdani yusuf (OP)]

But it doesn't tell you what an elephant is, or what it will do next.

That would need a more complex mathematical model and instrumentation. Although it's not an impossible task.
Nothing in my experiments is as complex as elephant nervous system. Some simple mathematical models should be enough.

[hamdani yusuf (OP)]

Yes. You can use Babinet's principle to predict it from the slit experiment, and IIRC from my schooldays, it works.

Is Babinet principle derived from the mathematical models, or is it an additional postulate? 

[hamdani yusuf (OP)]

Science should not be based on blind faith.

Which do you think happened first?
The experiment, or the model?

Like many other memes, scientific theories evolve through random mutation and natural selection. Scientists imagine/propose new assumptions or modification of existing theories as hypotheses. Experiments are then used to select compatible hypotheses which will survive to face further tests. Internal selection by the scientists themselves before publications may make the mutations look less random.
A good mathematical model can be extrapolated to explain new experiments haven't been done before.

[hamdani yusuf (OP)]

Geoff Pynn (Northern Illinois University) gets you started on the critical thinking journey. He tells you what critical thinking is, what an argument is, and what the difference between a deductive and an ampliative argument is.

Critical thinking is essential in doing a good scientific research.

[Bored chemist]

Critical thinking is essential in doing a good scientific research

Science should not be based on blind faith.

Which do you think happened first?
The experiment, or the model?

Like many other memes, scientific theories evolve through random mutation and natural selection. Scientists imagine/propose new assumptions or modification of existing theories as hypotheses. Experiments are then used to select compatible hypotheses which will survive to face further tests. Internal selection by the scientists themselves before publications may make the mutations look less random.
A good mathematical model can be extrapolated to explain new experiments haven't been done before.

It isn't clear that you answered the question.

Do you understand that science is largely driven by experiments?
Do you realise that anyone who looked through a fine woven silk cloth saw diffraction patterns?
Do you really think that there was a mathematical model of diffraction before there was an observation of it?

[hamdani yusuf (OP)]

Do you understand that science is largely driven by experiments?
Do you realise that anyone who looked through a fine woven silk cloth saw diffraction patterns?
Do you really think that there was a mathematical model of diffraction before there was an observation of it?

AFAIK, scientific progress usually started by observation of surprising phenomena, which produced unexpected result when being analyzed using incumbent theory. The scientists then proposed cempeting hypotheses plausible to explain the observation. They then device some experiments to rule out incorrect hypotheses. It's possible that more than one hypotheses can pass the test because they produce similar result for that particular experimental setup. We just need to device other experiments to amplify the differences to finally get the best hypothesis to be selected as accepted theory.

Seeing thing is much easier than explaining it. People has looked at the stars and found planets since ancient time. But the mathematical model for their movement wasn't clearly resolved until Newton's work.
It's not easy to show diffraction pattern using natural light sources. It takes dedicated work to produce clear and unambiguous results. Invention of mass produced laser pointer which are easy to obtain has changed the situation. Now virtually anyone can do the experiment at home.

It's possible to create a mathematical model to describe a phenomena for a limited condition. Galileo used parabolic equation to describe cannon ball trajectory, which is acceptable for most purposes they were dealing with. But for the situation where curvature of the earth is no longer negligible, we need a better mathematical model.

[hamdani yusuf (OP)]

In most physics textbook I read, explanation for diffraction is derived from Huygens' principle.
https://en.wikipedia.org/wiki/Diffraction_from_slits#Single_slit

As an example, an exact equation can now be derived for the intensity of the diffraction pattern as a function of angle in the case of single-slit diffraction.

A mathematical representation of Huygens' principle can be used to start an equation.

https://en.wikipedia.org/wiki/Huygens%E2%80%93Fresnel_principle

Modern physics interpretations
Not all experts agree that the Huygens' principle is an accurate microscopic representation of reality. For instance, Melvin Schwartz argued that "Huygens' principle actually does give the right answer but for the wrong reasons".[1]

This can be reflected in the following facts:

The microscopic mechanics to create photons and of emission, in general, is essentially acceleration of electrons.[1]
The original analysis of Huygens [10] included amplitudes only it does not include neither phases, neither waves propagating at different speeds (due to diffraction within continuous media) and therefore does not take into account interference.
The Huygens analysis also does not include polarization for light which imply a vector potential, where instead sound waves can be described with a scalar potential and there is no unique and natural translation between the two.[11]
In the Huygens description there is no explanation of why we choose only the forward going i.e. Retarded wave or forward envelope of wave fronts, versus the backward propagating advanced wave i.e. backward envelope.[11]
In the Fresnel approximation there is a concept of non-local behavior due to the sum of spherical waves with different phases that comes from the different points of the wave front, and non local theories are subject of many debates (e.g. not being Lorentz covariant) and of active research.
The Fresnel approximation can be interpreted in a quantum probabilistic manner but is unclear how much this sum of states (i.e. wavelets on the wavefront) is a complete list of states that are meaningful physically or represents more of an approximation on a generic basis like in the linear combination of atomic orbitals (LCAO) method.
The Huygens' principle is essentially compatible with quantum field theory in the far field approximation, considering effective fields in the center of scattering, considering small perturbations, and in the same sense that quantum optics is compatible with classical optics, other interpretations are subject of debates and active research.

The Feynman model where every point in an imaginary wave front as large as the room is generating a wavelet, shall also be interpreted in these approximations [12] and in a probabilistic context, in this context remote points can only contribute minimally to the overall probability amplitude.

Quantum field theory does not include any microscopic model for photon creation and the concept of single photon is also put under scrutiny on a theoretical level.

What's unclear for me though, are equations used in photon model derived from Huygen's principle? Or is it the other way around? If we are to be consistent with the meaning of the word principle, the Huygen's principle should be the basis of reasoning, or the starting assumption, and not derived from other assumptions. But I've seen cases where consistency is not always be complied with.

[alancalverd]

But it doesn't tell you what an elephant is, or what it will do next.

That would need a more complex mathematical model and instrumentation. Although it's not an impossible task.
Nothing in my experiments is as complex as elephant nervous system. Some simple mathematical models should be enough.

No amount of modelling or instrumentation will tell you what an elephant is. You can use them to extrapolate what an elephant is likely to do next, or interpolate whether it meets the criteria we have assigned to living, dead, grey, mammal, etc., but what it is, is determined by arbitrary human categorisation of things that look and behave similarly. There isn't even a rigid scientific definition of "species" - it's just a convenient box in which to look for large grey animals with prehensile noses. Not that we have a consistent definition of animal....   

[alancalverd]

In most physics textbook I read, explanation for diffraction is derived from Huygens' principle.

It's a very good predictive model, not an explanation. That is because it is dependent on a wave and wavelet synthesis of the propagation of light, which is all very well but doesn't consist with the particles you need to model photonuclear phenomena like pair annihilation gamma radiation, or even film photography!

[alancalverd]

the Huygen's principle should be the basis of reasoning, or the starting assumption

It's a starting axiom for wavelet analysis and synthesis, and works pretty well for all sorts of waves. But it simply doesn't explain quantum phenomena.

[hamdani yusuf (OP)]

No amount of modelling or instrumentation will tell you what an elephant is. You can use them to extrapolate what an elephant is likely to do next, or interpolate whether it meets the criteria we have assigned to living, dead, grey, mammal, etc., but what it is, is determined by arbitrary human categorisation of things that look and behave similarly. There isn't even a rigid scientific definition of "species" - it's just a convenient box in which to look for large grey animals with prehensile noses. Not that we have a consistent definition of animal....   

Human minds are a form of model to represent some part of objective reality. Their finiteness inevitably causes imprecision, which leaves some uncertainty. Arbitrary things can be agreed through convention.

[hamdani yusuf (OP)]

In most physics textbook I read, explanation for diffraction is derived from Huygens' principle.

It's a very good predictive model, not an explanation. That is because it is dependent on a wave and wavelet synthesis of the propagation of light, which is all very well but doesn't consist with the particles you need to model photonuclear phenomena like pair annihilation gamma radiation, or even film photography!

Why you need particle model to explain photonuclear phenomena like pair annihilation gamma radiation, or even film photography?

[hamdani yusuf (OP)]

the Huygen's principle should be the basis of reasoning, or the starting assumption

It's a starting axiom for wavelet analysis and synthesis, and works pretty well for all sorts of waves. But it simply doesn't explain quantum phenomena.

I've mentioned that classical wave model isn't adequate to explain quantum phenomena. But it doesn't rule out non-classical wave models. And I've also mentioned that I'll discuss them in new theory section, not here.

[Bored chemist]

Do you understand that science is largely driven by experiments?
Do you realise that anyone who looked through a fine woven silk cloth saw diffraction patterns?
Do you really think that there was a mathematical model of diffraction before there was an observation of it?

AFAIK, scientific progress usually started by observation of surprising phenomena, which produced unexpected result when being analyzed using incumbent theory. The scientists then proposed cempeting hypotheses plausible to explain the observation. They then device some experiments to rule out incorrect hypotheses. It's possible that more than one hypotheses can pass the test because they produce similar result for that particular experimental setup. We just need to device other experiments to amplify the differences to finally get the best hypothesis to be selected as accepted theory.

Seeing thing is much easier than explaining it. People has looked at the stars and found planets since ancient time. But the mathematical model for their movement wasn't clearly resolved until Newton's work.
It's not easy to show diffraction pattern using natural light sources. It takes dedicated work to produce clear and unambiguous results. Invention of mass produced laser pointer which are easy to obtain has changed the situation. Now virtually anyone can do the experiment at home.

It's possible to create a mathematical model to describe a phenomena for a limited condition. Galileo used parabolic equation to describe cannon ball trajectory, which is acceptable for most purposes they were dealing with. But for the situation where curvature of the earth is no longer negligible, we need a better mathematical model.

OK, so you now recognise that the observations came first (thousands of years earlier) and the models came second.
So, the next question is, do you think that when people like Thomas Young,  Joseph von Fraunhofer and Christiaan Huygens came up with theories, they didn't actually test them against experimental observation?

[hamdani yusuf (OP)]

OK, so you now recognise that the observations came first (thousands of years earlier) and the models came second.
So, the next question is, do you think that when people like Thomas Young,  Joseph von Fraunhofer and Christiaan Huygens came up with theories, they didn't actually test them against experimental observation?

They clearly didn't test their model against all possible experimental setups. They seems to use simplest setups only.
Have you seen any literature describing single slit or double slit experiment where the light source is not at normal angle to the aperture?
It's like Galileo's parabolic trajectory which only work when the effect of earth curvature is negligible.