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Color

Color

“Mere color, unspoiled by meaning, and unallied with definite form, can speak to the soul in a thousand different ways.” 

- Oscar Wilde

Generated using AI

For a normally sighted person, color is everywhere. Colors can be pleasantly subdued, enhancing relaxation, or loud and calling to us from advertising billboards or magazines. Color entices us to eat, consume, or at least buy. Color likely has helped us to survive as a species. Our (known) contacts with the world and the universe are by way of our five senses. Persons with a normally functioning visual system obtain what is probably the largest amount of information about the world surrounding them from vision, and color experiences are an important outcome of this flow of information. In the past several thousand years, color has blossomed into much more than just a survival and communications tool. We have learned to derive aesthetic pleasure from it by way of crafts, design, and art.

A fabric is dyed with red dye; when painting, we use various colored pigments or draw with various colored crayons or ink pens. The rainbow has four colors, or is it six or seven? In a mirror, we see the colors of objects appearing slightly duller and deeper than in the original. On a winter day toward evening, shadows look deeply blue. We are told that color illustrations in an art book are printed just with four pigments and that all colors on a display screen are “made” from red, blue, and green light-emitting phosphor compounds. To cope with these confusingly varied sources of color, we just disregard them in our everyday languages. An apple is red, the traffic light is red, the rose as seen reflected in a mirror is red, the bar in the bar graph on a tablet display is red, and the paint on the brush is red. All of these varied experiences have something in common: redness. We simply attach the perceived phenomenon to the object without bothering about the source or thinking about the nature of color.

We normally experience color as a result of the interaction between light, materials, and our visual apparatus, eye, and brain. However, there are also means of having color experiences in the dark like pressing against the eyeballs or hitting the temples moderately hard. There are two sets of facts that complicate understanding of the phenomenon of color firstly, many different stimuli can result in an essentially identical color experience and secondly a particular stimulus can result in many different color experiences, usually as the result of changes in illumination and/or surrounding stimuli. The same situation applies to vision in general.



The best definition of color that we can have is " Color: Attribute of visual perception consisting of any combination of chromatic and achromatic content. This attribute can be described by chromatic color names such as yellow or brown, red, pink, green, blue, purple, etc., or by achromatic color names such as white, gray, black, etc., and qualified by bright, dim, light, dark, etc., or by combinations of such names."


Understanding Light

Light consists of a certain range of electromagnetic radiation, which is a convenient name for the as-yet not fully explained phenomenon of energy transport through space. Electromagnetic radiation, depending on its energy content, has different names: X-rays capable of passing through our bodies and, on prolonged exposure, causing serious harm, ultraviolet (UV) radiation that can tan or burn our skin, light that we employ to gain visual information about the world around us, infrared radiation that we experience on our skin as warmth or heat, information transmission waves for radio and television, or electricity transmitted and used as a convenient source of energy. Electromagnetic radiation travels at high speed (the speed of light, about 300,000 km/s). The human eye, our visual sensory organ, is sensitive to a narrow band of electromagnetic radiation, the visible spectrum.

The Electromagnetic Spectrum. (a) This diagram shows the wavelength and frequency ranges of electromagnetic radiation. The visible portion of the electromagnetic spectrum is the narrow region with wavelengths between about 400 and 700 nm. (b) When white light is passed through a prism, it is split into light of different wavelengths, whose colors correspond to the visible spectrum.
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Ways of producing light 

Incandescence 

Light is normally produced by a glowing body in a process called incandescence; for example, the sun, a burning wax candle, or an electrically heated tungsten metal coil in a light bulb, but there are other modes of generation. Incandescence is the shedding of electromagnetic radiation by a very hot material, resulting in light that can give rise to color experiences. Our dominant example of an incandescent body is the sun, where the energy is produced by what is known as nuclear fusion. The nature of incandescence as produced on Earth is most easily observed in the work of a blacksmith. An iron rod, placed in an intense coal fire, as it heats up when it reaches about 525°C will begin to give off a dull reddish glow. When viewing it in the dark, we recognize it as the source of reddish light. As the temperature of the metal increases so does the intensity of the emitted light and its energy content. Simultaneously, reddishness diminishes and the object becomes “white hot.” With further increase in temperature, it eventually assumes a bluish-white appearance. Energy is absorbed by the the iron rod from the fire and emitted in visible form by the glowing metal. The imparted energy can have many sources: thermonuclear in case of the sun; electrical in case of a light bulb; and chemical in case of burning coal. All elements can, in proper conditions, be made to show incandescence, as can many inorganic molecules. Organic molecules (those containing carbon), are usually destroyed before they show incandescence, with incandescence produced by their decomposition products (say, in case of candle wax). The nature of the emitted energy depends on the form of the incandescent material: gaseous substances and many chemical elements emit energy in one or more distinct bands; incandescent liquids and solids tend to emit energy across broad spectrum bands.

Energy absorption and incandescence are explained using the atomic model of matter. Atoms consist of protons and neutrons in the nucleus, surrounded by electrons in shells. When an atom absorbs energy, its outermost electrons get excited to higher energy levels. These excited electrons eventually fall back to lower levels, releasing energy as electromagnetic radiation. If the emitted energy has a wavelength between 400 and 700 nm, it is visible light. Significant radiation emission, or incandescence, occurs when an object's temperature reaches about 525°C.

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Blackbody radiation

A blackbody is an idealized material that is a perfect absorber and emitter of energy across all wavelengths. It absorbs all incident radiation, regardless of frequency or angle of incidence, and re-emits energy perfectly based on its temperature. The theoretical emission spectrum of a blackbody can be calculated using Planck's law, which describes the intensity of radiation emitted by a blackbody as a function of wavelength for a given temperature.

Real materials often exhibit emission spectra similar to a blackbody, and this similarity allows scientists to use the concept of blackbody temperature, expressed in Kelvin, to describe the emission behavior of light sources. Even if a light source’s emission spectrum is not exactly like that of a blackbody, its color temperature can still be correlated to the temperature of a blackbody that emits light of a similar color. This is known as the correlated color temperature (CCT).

In practical terms, consider the example of a blacksmith heating an iron rod. As the rod heats up in a coal fire, it begins to glow red at around 525°C (798 K). This reddish glow intensifies and changes color as the temperature increases, moving towards white and eventually bluish-white as it reaches higher temperatures. This color change corresponds to the shifting emission spectrum of the iron, which approximates that of a blackbody at different temperatures.

Low-burning coal, with a blackbody-like spectrum at around 1800 K, emits primarily in the reddish-orange part of the visible spectrum. Incandescent light bulbs, typically operating at about 2500 K, have an emission spectrum that is also close to that of a blackbody. However, these bulbs are inefficient because most of their emitted energy is in the infrared region, which we perceive as heat rather than visible light. This inefficiency is why incandescent bulbs become very hot during operation.

In contrast, fluorescent lamps are more energy-efficient. They emit most of their energy in the visible spectrum, resulting in less wasted heat. The most energy-efficient fluorescent lamps, known as triband lamps, emit light in three specific bands around 440 nm (blue), 540 nm (green), and 610 nm (red). These wavelengths align with the peak sensitivities of the human visual system, making these lamps more efficient in terms of visible light output compared to other types of fluorescent lamps that emit across a broader spectrum.

The appearance of certain materials can change significantly depending on the spectral power distribution of the light under which they are viewed. For example, a material might look different under incandescent lighting compared to daylight. Blackbodies at temperatures of 2500 K and higher emit light that, to the human eye, appears colorless or "white" due to our adaptation to daylight. This neutral white light is perceived when objects with high reflectance functions are illuminated, making them appear white. Various light sources with different spectral power distributions can still result in light that appears white, as long as the light has a similar effect on our visual perception as daylight.

Thus, the concept of a blackbody provides a foundational understanding of how different materials emit and absorb energy. It also helps explain the color changes observed in heated objects and the efficiency differences between various types of light sources.

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Luminescence

Light can be created by processes not based on the absorption of energy, known as luminescence. There are three main types of luminescence:

  1. Electroluminescence: This occurs when electrons, influenced by an electric field, collide with particles of matter, resulting in the emission of light. Examples include sparks, arcs of light, lightning, certain lasers, and gas discharges.                                                      


  2. Chemiluminescence: This is the production of light from chemical reactions, typically oxidations, at low temperatures. Natural chemiluminescence, also called bioluminescence, is seen in glowworms, fireflies, some deep-sea fish, decaying wood, and putrefying meat. Commercial examples include glowing liquid-filled plastic tubes.           


      

  3. Photoluminescence: This appears in two forms, fluorescence and phosphorescence.

    • Fluorescence: Certain molecules absorb near-UV or visible light and re-emit it as visible light of a higher wavelength. Fluorescent whitening agents in detergents, for example, absorb UV radiation (300-380 nm) and emit visible light (400-480 nm), giving materials a very white appearance. Fluorescent dyes absorb and emit visible light, such as a fluorescent red dye that absorbs light from 450-550 nm and emits it at 600-700 nm. Fluorescent minerals and light tubes are also examples of fluorescence. Fluorescent light tubes have an interior coating of fluorescing phosphor compounds and contain a small amount of mercury. When excited by an electric field, mercury emits near-UV energy, which is absorbed by the phosphor compounds and re-emitted as visible light. Fluorescence stops when the energy source is interrupted.
    • Phosphorescence: Some substances can store absorbed energy and continue to emit light for some time after the exciting energy is stopped. This is different from fluorescence, where light emission stops immediately once the energy source is removed, like Glow-in-the-dark materials that continue to emit light after being "charged" by exposure to light.                                                                              

These luminescence processes provide diverse ways to produce light, each with unique applications and properties.


Absorption, reflection, scattering, and transmission

Light undergoes numerous transformations from creation to oblivion. When photons interact with atoms or molecules, they lose energy and are re-emitted at lower energy levels, often as infrared radiation, resulting in a loss of visible light and an increase in perceived heat. An ideal blackbody is the most efficient absorber and emitter of energy across a wide range, but real objects absorb selectively, reflecting or scattering some photons. Reflection occurs when photons bounce off a smooth surface at the same angle, while scattering happens when photons hit rough surfaces or fine particles, spreading light in many directions.

Scattering is common in natural phenomena and materials like textile fibers, water droplets in clouds, fog, smog, dust, milk, and bird feathers. The blue sky results from the scattering of shorter light wavelengths by small atmospheric particles, while clouds appear white due to the equal scattering of all wavelengths. Near sunset, the sky turns red as particles scatter shorter wavelengths, leaving longer wavelengths to dominate.

No material perfectly reflects or scatters light, but some, like pure barium sulfate and metallic mirrors, come close. Most colors we see result from a combination of wavelength-specific absorption and scattering, known as object colors, depicted by spectral reflectance curves.

Transmission is the passage of light through a transparent material, like water. If the material lacks absorbing substances, the transmitted light's spectral distribution remains unchanged. When absorbing materials like dyes are present, some light is absorbed, and the rest is transmitted, with the amount depending on the material and layer thickness. The Beer-Lambert-Bouguer law describes the absorption and transmission of light by dissolved substances.



Refraction 

Refraction denotes the change in direction of light as it passes from one medium to another, such as from air to water or glass. This occurs because light changes speed when entering a different medium, bending according to the laws of refraction. Refraction is fundamental to phenomena like rainbows and image formation in cameras and eyes. In both, lenses control the refraction to focus light and form clear images. The degree of refraction depends on the optical densities of the media and the energy level (wavelength) of the photons, with higher energy photons bending more sharply.

A practical application of refraction is the use of glass prisms to separate light into its component wavelengths. When a beam of white light passes through a prism, it disperses into a spectrum of colors, visible when projected onto a white surface. Each color corresponds to a specific wavelength: blue (400-490 nm), green (490-570 nm), yellow (570-590 nm), orange (590-630 nm), and red (630-700 nm). This separation of colors can be reversed to recombine the light into white light.

The most dramatic natural example of refraction is a rainbow, where sunlight is refracted and dispersed by water droplets in the atmosphere. Refraction also causes the sparkling "fire" seen in cut crystals, diamonds, and other gemstones. However, refraction in lenses can lead to chromatic aberration, a problem where different wavelengths focus at different points, causing blurred or colored edges in images. Lenses must be corrected for this to achieve clear focus across all colors.


Interference 

Puddles of water with bright multicolored bands near car repair shops or gas stations after rain, as well as the shimmering colors on butterfly wings or peacock feathers, are examples of iridescence. Unlike the scattering effect seen in blue jays, iridescent colors change in hue and intensity based on the viewing angle due to a phenomenon called interference.

Interference occurs when light waves split into separate parts that later recombine. Think of it as two synchronized swimmers: if they move perfectly together (in phase), their splash is bigger; if they move oppositely (out of phase), their splash cancels out. Similarly, light waves in phase amplify the light, while out-of-phase waves reduce the light. A common source of interference is a thin transparent film, such as oil on water or a soap bubble. The thickness of the film determines whether the reflected light waves are in or out of phase. When in phase, light of different wavelengths reflects at corresponding angles, producing pure, strong colors that change with the viewing angle. In thin films with varying thickness, like oil on water, multiple colors appear due to varying path lengths of the reflected light.

This phenomenon also occurs in nature. The wings of butterflies and feathers of birds like peacocks and hummingbirds have microscopic structures that create thin-film interference. These structures split and reflect light at different angles, resulting in vibrant, shimmering colors that change as the light or observer's position changes. Iridescence in these structures is often due to layers of chitin or keratin, creating multiple thin films that produce striking visual effects. Interference is also seen in everyday life. The colors in soap bubbles are due to thin-film interference. The varying thickness of the soap film creates a spectrum of colors that shift as the bubble moves. Similarly, anti-reflective coatings on glasses and camera lenses use destructive interference to reduce glare by causing specific wavelengths of light to cancel each other out.



Diffraction

Diffraction is a phenomenon that combines scattering and interference of light waves. When a light wave encounters the edge of a solid object, such as a razor blade, its behavior depends on the sharpness of the edge and the wavelength of the light. The wave might pass unimpeded, get scattered, or be absorbed, reflected, or refracted by the material at the edge. When there are multiple edges, like fine lines etched into a glass or metal plate, the scattered waves can interfere with each other—waves in phase will reinforce, while out-of-phase waves will cancel each other out.

To understand diffraction, think of it like water waves encountering a barrier with multiple gaps. As the water waves pass through the gaps, they spread out and interact with each other. Where the peaks of the waves meet, they reinforce each other, creating larger waves; where the peaks meet the troughs, they cancel each other out. This creates a pattern of waves that can be seen in the water, similar to how light waves create patterns of light and dark bands when they diffract.

This effect is particularly noticeable with a grating, an assembly of many fine edges. When daylight strikes a grating, the interference of scattered waves produces a display of spectral colors viewed from different angles. A common example is the surface of a compact disk, which shows colors due to the diffraction of light by the tiny grooves on its surface, although the effect is imperfect due to irregularities and curvature.

Diffraction gratings are widely used in optical equipment to separate polychromatic light into its individual components. Certain natural structures also cause diffraction. For instance, the wings of some insects have microstructures that act as diffraction gratings, creating vibrant colors. Liquid crystal molecules can also act as diffraction gratings; their arrangement depends on temperature, making them useful in temperature indicators. The vivid colors of opal gemstones are another example of diffraction effects in nature, resulting from the microscopic arrangement of silica spheres within the stone.


Molecular Orbitals

So far, we've discussed physical sources of color stimuli like refraction and interference, and the behavior of excited electrons in atoms and molecules. Electrons in atoms are arranged in orbits around the nucleus, and when electrons from two atoms pair up, they form a chemical bond, creating a molecule. In some molecules, electrons move freely across larger areas, giving rise to color.

For example, sapphire is mainly aluminum oxide. Pure aluminum oxide, or corundum, is colorless, but sapphires contain impurities like iron and titanium. An electron transfer between these impurities results in electron excitation under absorbed energy from visible photons (550 to 700 nm). The energy is then released in the infrared range, making the sapphire appear deep blue by reflecting light from 400 to 550 nm.

Dyes and organic pigments also show this behavior. These molecules have alternating single and double bonds, known as conjugated bonds, which absorb visible light, making the substances appear colored. These molecules are called chromophores. Auxochromes are side groups that can accept or donate electrons, enhancing the color.

Natural substances like blood and chlorophyll get their color from conjugated bond systems, and most modern colorants are synthetic, with around 8,000 having commercial significance. Fluorescent colorants absorb near-UV or short-wave visible light and emit visible energy, making them both absorbers and emitters of visible light.


Electrical conductors and semiconductor 

In conductors and semiconductors, electrons can travel throughout the material. In copper wire, for instance, electrons can move from one end to the other, creating an electric current when an electric field is applied. Metals have a plasma frequency; wavelengths higher than this frequency are reflected, while lower frequencies pass through, making some metals like chrome good reflectors of visible light. Copper, with a plasma frequency in the visible range, appears reddish.

Semiconductors like silicon, boron, arsenic, and indium have a gap in their energy absorption behavior, leading to the absorption of specific energy bands and the generation of color. Cinnabar (mercury sulfide) and cadmium sulfide are examples of colored semiconductors. Doping semiconductors with impurities can produce color in devices like LEDs.

The understanding of color stimuli is extensive but not fundamental due to limitations in quantum theory. However, this knowledge allows for creating synthetic substances with specific absorption and emission behaviors, such as lasers. Lasers, which produce coherent light beams, were first made using ruby. Now, lasers of any visible wavelength can be created, with applications in manufacturing, medicine, measurement, and entertainment.

Despite the complexities, the causes of most color phenomena are well understood. All color perceptions result from photons of specific wavelengths reaching our eyes, where their energy is transformed into responses by our brain and body.




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A Realist view of logic and physics

 Realism: A Journey through Logic and Physics

“I know three things will never be believed - the true, the probable, and the logical.”

- John Steinbeck 

 



In a time scale of the sun's age we we can confidently say that we have not made the world, compared with the changes achieved by animals and plants. Yet we have created a new kind of artifact which promises in time to work changes in our corner of the world as great as those worked by our predecessors, the oxygen-producing plants or the islanding building corals. These new products, which are decidedly of our own making, are our myths, our ideas, especially our scientific theories: theories about the world we live in. 

I suggest that we may look upon these myths, these ideas, and theories as some of the most characteristic products of human activity ( as said by Karl Popper).  They are organs evolving outside our skins per se these are exosomatic artifacts. 

Thus we may count among these characteristics products especially what is call " human knowledge" where we take the word 'knowledge' in the objective or impersonal sense, in which it may be contained in a book, stored in a library, or in the internet. 

" Knowledge produced by a person is analogous to honey produced by bees". Bees produce, store, and consume honey, but typically, a bee does not just eat the honey it has produced. Drones, which don't make any honey, also consume it, and bees can lose their stored honey to bears or beekeepers. Interestingly, worker bees need to consume honey, often made by other bees to maintain their ability to produce honey.

This concept largely applies, with minor differences, to oxygen-producing plants and theory-producing humans. Like bees with honey, we are both producers and consumers of theories. We must consume others' theories and occasionally our own to continue generating theories. Here, 'to consume' primarily means 'to digest,' similar to bees. However, it extends further: consuming theories involves critiquing, altering, and often dismantling them to make way for better ones. These processes are essential for the advancement of our knowledge.

Humans produce not only scientific theories but also a variety of other ideas, such as religious or poetic myths and friction. What distinguishes a scientific theory from a work of fiction? It's not just that theories might be true while fictional stories are not, though truth and falsehood are relevant. The key difference is that theories and stories are embedded in different critical traditions. They are judged by distinct traditional standards, despite having some commonalities. 

A scientific theory is characterized by its purpose as a solution to a scientific problem. This problem may have emerged from previous critical discussions of tentative theories or may have been discovered by the theory's author within the realm of scientific problems and solutions. However, this is not the whole picture. The scientific tradition, until recently, has been defined by what can be termed scientific realism. This means it was driven by the idea of finding true solutions to its problems that correspond to the facts. This regulative ideal of seeking theories that match facts is what makes the scientific tradition a realist one. It differentiates between the realm of our theories and the realm of facts to which these theories pertain. Furthermore, the natural sciences, with their critical methods of problem-solving, and some social sciences like history and economics, have long represented our best efforts in problem-solving and fact-finding. By fact-finding, I mean discovering statements or theories that correspond to facts. Thus, these sciences generally contain the best statements and theories from the standpoint of truth, providing the best descriptions of the world of facts, or what we call 'reality'.



Emergence from reduction

Physics and chemistry, which deal with physical things and states, are closely related. Chemistry’s inapplicability at extreme temperatures suggests it may be reducible to physics—a significant scientific achievement, fostering unity and understanding. Assuming chemistry is fully reduced to physics, we might hope to similarly reduce biology to physics. However, living organisms differ fundamentally from non-living things, making this reduction more challenging. While progress in understanding the origin of life and creating primitive organisms may occur, true reduction requires more than control over processes. It demands theoretical integration, comprehending the new field through the principles of the old one.

The reduction of chemistry to physics, seemingly progressing well, can be seen as a prime example of a true scientific reduction that meets all the criteria for a robust scientific explanation. A 'good' or 'scientific' reduction is a process through which we gain significant insights: we come to understand and explain the theories of the field being reduced (chemistry in this case) and we also learn about the capabilities of the theories from the reducing field (physics in this instance).

I term "bad reduction" or "ad hoc reduction" as the method of reducing concepts through mere linguistic maneuvers. For instance, physicalism, which proposes the ad hoc existence of physiological states to explain behavior previously explained by mental states (without such ad hoc postulation), is an example. Another example is the linguistic device of claiming to describe a physiological state when stating that one understands the Schrödinger equation. This second type of reduction, or misuse of Ockham's razor, is problematic because it obscures the real issue. As Imre Lakatos vividly describes, it is a "degenerating problem shift" that can hinder either a good reduction or the study of emergence, or both.



Thought process and understanding

Supporting the emergent nature of theories or knowledge in an objective sense. I'll mention a few arguments against the naive and popular view that theories can be reduced to the mental states of those who create or understand them. (We won't discuss whether these mental states can, in turn, be reduced to physical states.) The notion that a theory in its objective or logical sense can be reduced to the mental states of those who hold it is typically framed as the theory simply being a thought. However, this is a fundamental mistake: it fails to distinguish between two meanings of the word 'thought'. Subjectively, 'thought' refers to a mental experience or process. But two mental experiences or processes, while possibly causally related, cannot be logically related. 

For example, if I say that certain ideas of the Buddha align with those of Schopenhauer or contradict those of Nietzsche, I'm not referring to the mental thought processes of these individuals or their interactions. Conversely, if I say Nietzsche was influenced by Schopenhauer's ideas, I mean that Nietzsche's thought processes were causally affected by his reading of Schopenhauer. Therefore, we have two distinct realms: the realm of thought processes and the realm of the products of thought processes. The former may be causally related, while the latter are logically related. The incompatibility of certain theories is a logical fact, independent of whether anyone has recognized or understood this incompatibility. These objective logical relationships define the entities I call theories or knowledge in the objective sense. 

This distinction is evident when considering that the creators of theories often do not fully understand them. For instance, it could be argued that Erwin Schrödinger did not fully understand his own equation until Max Born provided a statistical interpretation; or that Kepler did not fully comprehend his own area law, which he reportedly disliked. Understanding a theory is akin to an infinite task, suggesting that a theory is never completely understood, although some may grasp certain theories very well. 

Understanding a theory is similar to understanding a human personality: we may predict a person's behavior in various situations but cannot fully understand all their possible responses due to the infinite variety of potential situations. Similarly, a full understanding of a theory would require grasping all its logical consequences, which are infinite. Thus, no one, not even its creator, can fully comprehend all the possibilities within a theory, highlighting that theories, in their logical sense, are objective entities that we can study and attempt to understand. It is no more paradoxical to say that theories or ideas are our creations yet not fully understood by us than to say that our children are our creations yet not fully understood by us, or that honey is a product of bees yet not fully understood by any bee.



Realism and physics

In modern physics, subjectivism has become integral in two key areas: Boltzmann's theory of entropy (the arrow of time) and Heisenberg's uncertainty principle, which define a minimum limit on the observer's influence over the observed object. Einstein also introduced subjectivity when he included the observer in various thought experiments aimed at elucidating relativity, but he subsequently removed the observer from this domain over time.

The Heisenberg formula for energy is independent of both wave mechanics and Heisenberg's matrix mechanics. It also does not rely on commutation relations. Surprisingly, it does not stem from the revolutionary quantum mechanics of 1925-1926 but directly derives from Planck's earlier quantum postulate from 1900.

The interpretation proposed here suggests viewing Heisenberg's uncertainty principles as statistical scatter relations rather than indicators of the precision of measurements or limits to our knowledge. In this view, the principles don't speak directly to the precision of measurements but rather to the limits of homogeneity in quantum-physical states, indirectly addressing predictability. 

For instance, the formula Δ𝑝⋅Δ𝑞 ≈ ℎ implies that upon determining the coordinate 𝑥 of a system, such as an electron, the momentum 𝑝 will scatter upon repetition of the experiment. This assertion can be tested by conducting a series of experiments with a fixed shutter opening Δ𝑥, measuring the momentum 𝑝​ in each case. If the measured momenta scatter as predicted, the formula survives the test. Notably, these experiments require measuring 𝑝 with a precision greater than Δ𝑝, as otherwise, speaking of Δ𝑝 ​ as the scatter of 𝑝 ​ wouldn't make sense. Such experiments are routinely conducted in physical laboratories, challenging the interpretation of Heisenberg's indeterminacy principle. While Heisenberg acknowledged the possibility of such measurements, he deemed attaching meaning to them a matter of personal belief or taste, leading to their disregard as meaningless. 

However, they serve a specific purpose: testing the formulae themselves as scatter relations. This perspective argues against accepting Heisenberg's or Bohr's subjectivist interpretation of quantum mechanics, suggesting instead that quantum mechanics is a statistical theory suited to solving statistical problems, such as spectral intensities. As such, there's no philosophical need to defend its non-causal character.

There's no reason to doubt the realism and objectivity of physics. In modern physics, the observer's role remains similar to that in classical physics – primarily testing theories. This process involves evaluating competing and auxiliary theories, highlighting that we are not so much observers as thinkers.




Realism in logic

Logic, in essence, can be seen as the theory of deduction or derivability. It involves transmitting truth from premises to conclusions, as seen in proofs, and transmitting falsity from conclusions back to premises, as seen in disproofs or rebuttals. In critical discussions, logic is frequently used to challenge assertions by demonstrating their falsehood. If a conclusion is shown to be false, and the inference is assumed to be valid, it follows that at least one premise must be false. Thus, criticism becomes a vital methodological tool. Rejecting criticism by dismissing the logic used undermines the effectiveness of critical discussion. Logic serves two main purposes: in demonstrative sciences like mathematics, it's primarily used for proofs, while in empirical sciences, it's predominantly employed for critical analysis to uncover falsity. Although applied mathematics plays a role in empirical sciences, its significance is somewhat questionable in various aspects.

The rationalist view is characterized by its realist perspective on logic. Firstly, it associates logic with the methodology of the natural sciences, which the rationalist view considers to be grounded in realism. Secondly, it emphasizes logical inference as a process of transmitting truth or retransmitting falsity, thus highlighting the importance of truth in logical reasoning.



Theories of Truth

There are three main theories of truth. The oldest, the correspondence theory, posits that truth corresponds to the facts or accurately describes them, as Tarski emphasized. The coherence theory views truth as coherence with existing knowledge, while the pragmatic theory defines truth in terms of its practical utility or usefulness.

The coherence theory encompasses various interpretations, two of which are notable. The first posits truth as coherence with our beliefs, implying that a statement is true if it aligns with our existing beliefs. However, this approach raises concerns about integrating beliefs into logic due to potential logical constraints conflicting with individual beliefs. The second version suggests that an uncertain statement should be deemed true if it aligns with previously accepted statements, fostering a highly conservative approach to knowledge preservation. Contrastingly, the pragmatic utility theory focuses on the utility of theories in natural sciences, particularly physics. It suggests that a physical theory should be accepted as true if it proves pragmatically useful and successful in tests and applications.



Questions and interpretations???

Eliminating verbal or definitional questions, considering them as pseudo-questions. Questions like "What is life?", "What is matter?", "What is mind?", or "What is logic?" are viewed as unfruitful. They advocate discarding the question "What is truth?" for two main reasons. First, they reject essentialism, and second, they advise against discussing the meaning of words, likening it to a game that philosophers are addicted to but which they consider unimportant.





Incorporating the concept of verisimilitude or approximation to truth into logic enhances its realism by enabling discussion of how one theory aligns better with real-world facts than another. From a realist perspective, logic serves as the tool for criticism rather than proof in our quest for true and highly informative theories. Criticism becomes the primary instrument for advancing our knowledge about the factual world, aiming to promote the growth of our understanding by refining and improving upon existing theories.





This article is inspired from the works of Sir Karl Popper, Wolfgang Yourgrau, Allen D Breck




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- J John Paul

Look into the spectrum - Spectroscopy

 Look into the spectrum

through spectroscopy
"What we are nowadays hearing of the language of spectra is a true 'music of the spheres' in order and harmony that becomes ever more perfect despite the manifold variety. All integral laws of spectral lines and of atomic theory spring originally from the quantum theory. It is the mysterious organon on which Nature plays her music of the spectra, and according to the rhythm of which she regulates the structure of the atoms and nuclei."
- Arnold Sommerfeld, Atombau und Spektrallinien

Imagine you have a magical pair of glasses that allow you to see things in a whole new light—literally! Spectroscopy is like those glasses but for scientists. Instead of helping you see hidden worlds, spectroscopy helps scientists see hidden details about the stuff around us by using light beyond the power of our naked eye to comprehend. You know how when you look at a rainbow, you see all those different colors? Well, light is made up of lots of different colors (wavelength), and each color has its own special "fingerprint" that can tell us about what it's made of. Spectroscopy is like taking a close look at those fingerprints to figure out what's in the things around us. Together, they form a symphony of energy, each wavelength playing its part in the cosmic melody of existence. Within the Electromagnetic Spectrum lies the key to understanding the universe and unlocking its infinite wonders.


1. A picture of sunlight at a particular (random) angle. Due to the angle and some imperfections in the mobile camera, the sunlight splits into different colors which is the essence of spectroscopy.
2. Splitting of light in a diffracting grating which splits the light in a more organized manner. The diffracting grating is an important tool in spectroscopy. Which gives us a goos spectrum of white light. 
3.  The sunlight is reflected by a diamond-like crystal which produces a unique color. This is not essentially a useful way to understand spectroscopy but understanding the physics behind it is useful to understand spectroscopy. 
(Images taken by John and are not edited or color corrected)

A spectrum refers to a range or continuum of something, typically ordered by some characteristic quality. In physics, the electromagnetic spectrum encompasses the range of all possible frequencies of electromagnetic radiation, including visible light, radio waves, microwaves, infrared, ultraviolet, X-rays, and gamma rays. The visible light spectrum, for instance, includes all the colors of light that can be seen by the human eye, from red to violet.

The nature of the electromagnetic spectrum is that it is always in a state of interaction with matter. Actually, we can confirm the presence of spectrum only through interaction with matter. We can use this interacting nature of the electromagnetic spectrum to look out for what is around us and understand nature. This technique which is used to study the spectrum is called Spectroscopy. Through spectroscopic techniques, people can analyze how light is absorbed, emitted, or scattered by substances, allowing them to infer characteristics such as composition, structure, and behavior.

Figure elucidating the interaction of the electromagnetic wave with the matter in a technical way
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Spectroscopy enables us to explore and understand the spectrum by examining how different materials interact with electromagnetic radiation. By analyzing the patterns and characteristics of the spectrum, spectroscopy provides valuable insights into the nature of matter and its interactions with light. Thus, spectroscopy and spectrum are intimately linked, with spectroscopy serving as the primary tool for studying and interpreting the spectrum


Note on spectrum

The concept of the electromagnetic spectrum has evolved over centuries, beginning with Isaac Newton's experiments on visible light in the 17th century and progressing through subsequent discoveries by scientists such as Thomas Young and Augustin-Jean Fresnel, who revealed light's wave nature. James Clerk Maxwell's equations in the 19th century provided a theoretical framework for understanding electromagnetic radiation, while the study of spectroscopy, pioneered by Joseph von Fraunhofer and Gustav Kirchhoff, shed light on the interaction between light and matter. The 20th and 21st centuries saw advancements in technology enabling the exploration of regions beyond the visible spectrum, leading to the discovery and utilization of radio waves, microwaves, infrared radiation, ultraviolet radiation, X-rays, and gamma rays. Today, the electromagnetic spectrum encompasses a wide range of frequencies or wavelengths, each playing a crucial role in scientific research, technology development, and everyday applications, driving innovation and deepening our understanding of the universe.

The theoretical framework of spectra

The theoretical framework of the electromagnetic spectrum is based on the principles of electromagnetism and quantum mechanics. Electromagnetism provides a fundamental understanding of how electric and magnetic fields interact and propagate through space. These equations describe how electromagnetic waves, including light, propagate at the speed of light and carry energy and momentum. Quantum mechanics further refined our understanding of the electromagnetic spectrum by introducing the concept of quantized energy levels. According to quantum mechanics, energy is not continuously distributed but exists in discrete packets or quanta. This concept explains phenomena such as the discrete spectral lines observed in spectroscopy, where atoms and molecules absorb or emit light at specific frequencies corresponding to the energy differences between their quantized energy levels.

How the electromagnetic spectrum is produced?

The electromagnetic spectrum is produced by the emission, absorption, and scattering of electromagnetic radiation by matter, ranging from subatomic particles to astronomical objects.

Emission: Atoms, molecules, and other particles can emit electromagnetic radiation when they undergo transitions between energy levels. For example, when an electron in an atom moves from a higher energy level to a lower one, it emits a photon of electromagnetic radiation. The frequency (or wavelength) of the emitted radiation depends on the energy difference between the initial and final energy levels, according to the equation  ΔE=hν, where  ΔE is energy, ℎ h is Planck's constant, and ν is frequency. This emitted radiation contributes to the electromagnetic spectrum.

Different ways of obtaining electromagnetic spectra in a lab. 

Absorption: Conversely, matter can absorb electromagnetic radiation when it interacts with photons. If the energy of a photon matches the energy needed to promote an electron from a lower energy level to a higher one, the photon will be absorbed, and the electron will transition to a higher energy level. The absorbed radiation is typically in specific frequency ranges corresponding to the energy differences between the atomic or molecular energy levels involved. This absorption leads to dark absorption lines in the electromagnetic spectrum, where certain frequencies of light are missing due to absorption by specific substances.

Scattering: When electromagnetic radiation interacts with particles or surfaces, it can be scattered in different directions. The scattered radiation contributes to the overall electromagnetic spectrum, often with no distinct pattern. However, certain types of scattering, such as Rayleigh scattering, are wavelength-dependent and can result in phenomena like the blue color of the sky.

Synchrotron Radiation: In some cases, highly energetic particles moving through magnetic fields, such as those in synchrotron accelerators or astrophysical environments, can emit synchrotron radiation. This radiation spans a wide range of frequencies and contributes to the electromagnetic spectrum.

These processes result in a continuous range of frequencies or wavelengths, from radio waves to gamma rays, that make up the electromagnetic spectrum.

Emission spectra of various elements in the periodic table in the visible region.  This means that these elements when heated produce a light that contains this spectrum. If you see the emission spectra of Tungsten (W) and Neon (Ne) you can see the presence of a complete spectrum i.e. all the visible colors are visible, This is the reason these materials are used in lighting applications.  
Source : THE Elements A Visual Exploration of Every Known Atom in the Universe. Photographs by Theodore Gray and Nick Mann


What is spectroscopy?

Spectroscopy is a scientific technique used to study the interaction between matter and electromagnetic radiation. It involves analyzing how materials absorb, emit, or scatter light at different wavelengths or frequencies. By examining the unique patterns of light absorbed or emitted by a substance, spectroscopy provides valuable information about its composition, structure, and properties. Some common spectroscopic methods include infrared spectroscopy, ultraviolet-visible spectroscopy, nuclear magnetic resonance spectroscopy, and mass spectrometry. 

In spectroscopy, several fundamental equations are essential for describing the interaction between electromagnetic radiation and matter. 
  • The Beer-Lambert Law establishes a relationship between the absorbance of light by a sample and the concentration of the absorbing species, defined by the molar absorptivity, concentration, and path length of the sample. 
  • The Planck-Einstein Relation relates the energy of a photon to its frequency or wavelength, providing a basis for understanding the quantized nature of electromagnetic radiation. 
  • The Rydberg Formula describes the wavelengths of spectral lines emitted or absorbed by hydrogen-like atoms, aiding in the analysis of atomic spectra.
Additionally, the Schrödinger Equation in quantum mechanics is crucial for determining the allowed energy levels and wavefunctions of electrons in atoms and molecules, providing a theoretical framework for interpreting spectroscopic transitions.


Let's become a spectroscopist

First, Using a CD as a diffraction grating to split white light and analyze it is a simple yet effective way to demonstrate spectroscopy. CDs, with their closely spaced tracks of pits and lands, act as diffraction gratings when illuminated with white light. When white light is directed onto the surface of a CD, the grooves on the CD surface diffract the light, causing it to spread out into its component colors. This process is similar to how a prism splits white light into a rainbow of colors. Each color in the spectrum corresponds to a specific wavelength of light. By observing the pattern of colors produced by the diffracted light from the CD, one can analyze the spectrum of the light source. This spectrum reveals information about the composition of the light source, as different materials emit or absorb light at specific wavelengths.


1. The spectrum of white light was obtained using the above-mentioned way. 
2. The spectrum of green led. As you can see green LED is partially composed of red and blue lights other than green light which is evident by comparing the spectra with the graph in 7.
3. The spectra of red LED. As you can see it is partially composed of yellow light i.e. the red light for the LED splits into red and yellow-orange colors. 
4. The spectrum of blue LED. As you can see the blue LED spectra split into indigo and violet. 
5. The clear spectrum of which light.
6. The graph showing the composition of different LEDs and compare it with white light and a distant astronomical object (DOI:10.3762/bjoc.12.170)
(1-5 are taken using a mobile camera and they are un-edited images)

Second, In this experiment, various concentrations of a colored liquid are prepared, with each solution having a different level of light absorption due to the presence of colored molecules. To perform the experiment, a light source, such as a smartphone flashlight, is directed through each solution. The color picker app is then used to measure the intensity of light transmitted through the liquid. By comparing the intensity of the transmitted light for each concentration, one can determine the absorbance of the liquid at specific wavelengths. According to the Beer-Lambert Law, absorbance is directly proportional to the concentration of the absorbing species and the path length of the sample. Therefore, as the concentration of the colored molecules in the liquid increases, so does the absorbance of the solution. By plotting the absorbance values against the concentration of the colored liquid, a linear relationship should be observed, confirming the validity of the Beer-Lambert Law.

UV/VIS absorbance spectrum of sucrose solutions over 10 mm path length. As you can see for higher conc. the absorption is high. It is because there are more number of molecules when the concentration is higher so the incident light will interact with more molecules hence the absorption is greater. 
Source: doi: 10.3390/s8010010 Cantilever Micro-rheometer for the Characterization of Sugar Solutions



Beginner course in analyzing spectra

UV spectroscopy, also known as ultraviolet-visible (UV-Vis) spectroscopy, is a technique used to measure the absorption of ultraviolet and visible light by molecules in solution. UV-Vis spectroscopy relies on the fact that molecules absorb light at specific wavelengths corresponding to transitions of electrons between different energy levels. The absorption of light causes the electrons to move to higher energy levels, which results in a decrease in the intensity of the transmitted light. The absorption spectrum obtained shows peaks and troughs corresponding to the wavelengths at which the molecule absorbs light.

The raw UV spectra of tea samples in the wavelength range of 400–2498 nm are plotted in Figure.   

Visible and near-infrared spectra of tea samples. 
(From the article "Nondestructive monitoring of polyphenols and caffeine during green tea processing using UVVis-NIR spectroscopy")
Source: DOI:10.1002/fsn3.1861

The absorption peaks at 480 nm and 670 nm were located in the visible region of the spectra (400–800 nm). It proved that the tea leaves mostly absorb light in the visible spectral range (blue-violet (455–492 nm) and red (622–770 nm)) while green light absorption (500–560 nm) is too low, so this is the reason the tea leaves look green.

The absorption spectra of water showers that the water doesn't have any absorption peaks in the visible light region so the water is transparent to visible light.


Absorption spectra of Water for a wide range of incident electromagnetic waves.


Nuclear Magnetic Resonance (NMR) spectroscopy is a powerful technique for studying molecule structure and dynamics. It exploits the magnetic properties of atomic nuclei, revealing details about their arrangement and chemical environment. By subjecting samples to radiofrequency radiation in a strong magnetic field, NMR spectroscopy generates spectra with peaks corresponding to specific nuclei types. This information aids in identifying compounds and understanding molecular interactions.

When peanuts are used as adulterants, there is an additional risk of potential health hazard to consumers due to allergy-induced anaphylaxis. Peanuts can be used as an adulterant in powdered hazelnuts, almonds, and walnuts. The close inspection of NMR spectra of various powders can reveal the peanut as an adulterant in these products.  


H NMR spectra obtained by the two polar solvents (A: deuterated phosphate buffer/methanol-d4, B: methanol-d4) show an individual marker signal (Extraction A: singlet at 3.05 ppm, extraction B: singlet at 3.02 ppm), which could indicate the admixture of peanut. The highlighted region showed the difference between peanuts and other nuts. 
Source: Detection of Peanut Adulteration in Food Samples by NMR Spectroscopy. J. Agric. Food Chem.,• DOI: 10.1021/acs.jafc.0c01999

The above figure shows the variation of the peak at 3 ppm (Parts per million calibrated based on the frequency difference between the resonance of the sample and the reference compound) from which we can find this type of adulteration. 


The IR (Infrared) specifically Mid-infrared (MIR) spectra are informative fingerprints of molecular vibrations and rotations within compounds. This spectral region typically ranges from approximately 4000 to 400 cm^-1. In MIR spectroscopy, molecules absorb radiation in the mid-infrared range, causing characteristic peaks in the spectrum corresponding to specific functional groups and chemical bonds. These peaks provide valuable information about molecular structure, composition, and interactions.

The following figure shows the M-IR spectra of milk showing different nutrients and edible biological molecules present in it. If more water or any other chemical is added to it the resulting spectra will be different. 


Representative images of the mid-infrared spectrum of milk and the approximate putative region obtained with TQ Analyst software ver. 8.0 (Thermo Fisher Scientific, Madison, WI, USA).
Source: Recent Advances in the Determination of Milk Adulterants and Contaminants by Mid-Infrared Spectroscopy: Foods 2023, 12(15), 2917; https://doi.org/10.3390/foods12152917 


The famous and widely used diagnostic tool MRI in the medical field is also a type of spectroscopy. It reveals the inner structure of the human body. It is a non-invasive medical imaging technique used to visualize the anatomy and pathology. MRI relies on the interaction of hydrogen nuclei (protons) in water and fat molecules with a strong magnetic field and radiofrequency pulses. By measuring the signals emitted by these nuclei, detailed images of the spinal cord can be generated.

The following image shows the MRI image of a patient which shows the anatomy and pathology of the spine and its surrounding structures. 

Various orientations of spin were taken using an MRI.


X-ray crystallography is a powerful technique used to determine the three-dimensional structure of crystalline materials at the atomic level. X-ray crystallography relies on the interaction of X-rays with the electron density of atoms within a crystal lattice. When X-rays strike a crystal, they are diffracted by the regularly spaced atoms, producing a diffraction pattern of spots on a detector.

The following figure shows the x-ray peak of  Maltose and Cocaine. As both of them are physically indistinguishable the XRD pattern of the compounds can be used to detect the presence of cocaine. The following shows the different peaks of the two compounds. 


Simulated diffraction patterns of cocaine and maltose are displayed along with the peak positions of the International Centre for Diffraction Data (ICDD) standard. Two mixtures, 50% cocaine / 50% maltose and 10% cocaine / 90% maltose, show the qualitative differences in the XRD pattern as the components are varied. Qualitative identification is based on the presence of the unique diffraction lines for each substance, the "X-ray fingerprint." In addition, a quantitative determination can be made for each component by measuring its peak intensity and comparing it to the intensities measured from one or more samples of known concentration.
Source: FORENSIC ANALYSIS BY X-RAY DIFFRACTION: https://www.rigaku.com/applications/bytes/xrd/miniflex/1060214993


Concluding remarks: 

Using a CD as a diffraction grating for spectroscopy is a fun and educational experiment that can be easily performed at home or in a classroom setting. It provides a hands-on way to explore the properties of light and learn about the principles of spectroscopy. Additionally, it highlights the versatility of everyday materials in scientific experimentation and encourages curiosity and exploration in the field of optics and spectroscopy.

In summary, understanding spectroscopy is crucial for advancing scientific knowledge, developing new technologies, improving healthcare outcomes, and addressing global challenges. It enriches our understanding of the natural world and empowers us to innovate and make informed decisions in both scientific and everyday contexts.



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