Why Is the Speed of Light Constant?

The speed of light is not constant in all circumstances. It varies depending on the medium through which light travels. In a vacuum, however, the speed of light is exactly 299,792,458 m/s. In air, which has a refractive index of approximately 1.0003, the speed of light is about 299,700 km/s—roughly 90 km/s slower than in a vacuum.

The speed of light in a vacuum is designated by the symbol c and is considered a universal constant. Its value is the same regardless of the frame of reference of the observer. Unlike ordinary low-speed problems involving Galilean relativity, one cannot simply add or subtract velocities from c.

Light is a form of electromagnetic radiation. The Scottish mathematical physicist James Clerk Maxwell described the behaviour of electromagnetic waves through his famous Maxwell equations, which provided a mathematical framework linking the concepts of electric and magnetic fields.

In doing so, Maxwell showed that the speed of electromagnetic waves in a vacuum is determined by two fundamental constants: the electric constant, ε0, and the magnetic constant, μ0. They are related to the speed of light by the equation:

c=1/(ε0μ0)0.5

Thus, the speed of light is not an arbitrary value. It emerges from the fundamental properties of electric and magnetic fields in a vacuum.

Could the universe exist without gravity? If so, what would it look like?

Hypothetically, one could imagine a universe without gravity, although it would look radically different from anything we experience or could easily conceive of.

For one thing, without gravity there would be no gravitational clumping of matter. We could therefore forget about planets, stars, stellar clusters, galaxies, galactic clusters, and the vast cosmic structures that emerge from gravity drawing matter together.

That said, not everything would necessarily disappear. Atoms could still exist because atomic nuclei are held together primarily by the strong nuclear force, while the electromagnetic force binds electrons to those nuclei. The weak nuclear force would still play its usual role in certain particle interactions and radioactive processes.

Beyond that, things become highly speculative. Without gravity, there would be no familiar mechanism for assembling matter into the large-scale structures we see throughout our universe. Instead, one might imagine something more akin to an enormous, diffuse particle soup, governed by the remaining fundamental forces.

The question of how such a universe would expand is considerably more complicated. Removing gravity would not automatically mean that the universe would expand without resistance or inevitably end in a Big Rip. Cosmic expansion depends on the underlying laws governing spacetime and on the universe’s energy content, including dark energy. If gravity as described by general relativity simply did not exist, we would need an alternative theory to tell us how spacetime itself behaves.

So, yes, a gravity-free universe can be imagined—but once gravity is removed, virtually every feature of the cosmos that we take for granted becomes radically different. The resulting universe might still contain particles, atoms, and electromagnetic interactions, but it would lack the gravitational architecture that transforms matter into the stars, galaxies, and cosmic structures we know.

Do all planets revolve around the Sun at the same speed?

No, they don’t. The closer a planet is to the Sun, the stronger the gravitational force acting on it. For a planet to remain in a stable, approximately circular orbit, its orbital speed must therefore be greater at smaller orbital radii. In other words, the closer the planet is to the Sun, the faster it must move.

For a circular orbit, the orbital speed is given by

v=(GM/r)0.5

where:

• G is the universal gravitational constant,

• M is the mass of the Sun, and

• r is the orbital radius, measured from the Sun’s center.

Thus, as r decreases, v increases.

Notice something interesting: the planet’s mass does not appear in the equation. Therefore, for a given orbital radius around the Sun, the required circular orbital speed is independent of the planet’s mass.

It is worth being careful with the idea that the higher velocity provides “greater inertia” to resist the Sun’s gravitational pull. In modern physics, inertia is not a force that resists gravity. Rather, the planet’s tangential velocity causes it to continually fall toward the Sun while its forward motion carries it past the point toward which it is falling. The result is an orbit.

The equation above can be derived by equating Newton’s law of universal gravitation with the expression for centripetal force:

GMm/r2=mv2/r

The planet’s mass m cancels, leaving

v=(GM/r)0.5

This relationship is also closely connected to Kepler’s Third Law, which describes the relationship between a planet’s orbital period and its orbital radius.

Of course, real planetary orbits are elliptical rather than perfectly circular. Consequently, a planet’s orbital speed is not constant throughout its orbit: it moves faster when it is closer to the Sun and slower when it is farther away.

Can we perfectly predict the position of a planet in the solar system using Newtonian mechanics alone?

All measurements in science carry with them some degree of error. In addition, every scientific model contains built-in assumptions that allow it to approximate reality remarkably well, but those approximations are not reality itself.

In Praise of the Big Bang

The story of the universe begins with one of the most remarkable ideas in modern science: the Big Bang Theory. According to the theory, the universe as we know it emerged from an extremely hot, dense state often described, in simplified terms, as a singularity. It is important, however, not to imagine this as an explosion occurring at some particular point in empty space. The Big Bang was not an explosion into space; rather, space itself began expanding.

The expression “Big Bang” was actually coined by the English astronomer Fred Hoyle, and he did not intend it as a compliment. Hoyle was a strong supporter of the competing Steady State Theory, which proposed that the universe had always existed and maintained roughly the same overall appearance as it expanded. He used “Big Bang” somewhat derisively during a radio broadcast, but the name eventually stuck.

The modern picture is very different from Hoyle’s Steady State universe. Today, the best estimate places the age of the universe at approximately 13.8 billion years. In its earliest moments, the universe was unimaginably hot and dense, and the familiar forces of nature were not yet separated in the way we experience them today. As the universe expanded and cooled, the fundamental forces gradually separated. Gravity was the first to separate from the other fundamental interactions.

One of the most important developments in our understanding of this earliest period came from the idea of cosmic inflation, particularly associated with physicist Alan Guth. Inflation proposes that, during an extraordinarily brief interval shortly after the beginning, the universe underwent an enormous burst of expansion. The idea helps explain several otherwise puzzling features of the universe, including its remarkable large-scale uniformity and near-flatness.

Long before modern cosmology had the observational evidence to support the Big Bang, however, the basic idea had been anticipated by a remarkable Belgian priest and physicist, Georges Lemaître. Lemaître proposed that the universe was expanding and developed an early version of what became the Big Bang model. He imagined the universe beginning from what he called a primordial “primeval atom.” His ideas represented a radical departure from the traditional picture of a static, eternal cosmos.

Lemaître's theoretical work was complemented by the mathematics of the Russian physicist and mathematician Alexander Friedmann, who showed that Einstein's equations of General Relativity naturally allowed for a universe that could expand or contract. Einstein himself initially resisted this possibility because he believed the universe was static. To make his equations produce a static universe, he introduced what became known as the cosmological constant.

Einstein later referred to the cosmological constant as his “greatest mistake.” Ironically, the story has taken a remarkable turn. Modern observations suggest that something very much like a cosmological constant—or, more generally, dark energy—may actually be responsible for the accelerated expansion of the universe. What Einstein considered a mistake may have been a remarkably prescient addition to his equations.

The observational evidence for an expanding universe emerged dramatically in the work of Edwin Hubble. Working primarily with observations from the Mount Wilson Observatory, Hubble studied distant galaxies and discovered that their light was generally shifted toward the red end of the spectrum. This redshift indicated that many galaxies were receding from us. More importantly, Hubble found a relationship between a galaxy's distance and the apparent speed with which it was receding. The farther away a galaxy was, the faster it appeared to be moving away.

This became known as Hubble's Law and provided powerful evidence that the universe is expanding.

But how could Hubble determine the distances to those distant galaxies in the first place? One important answer involved Cepheid variable stars. Cepheids have a predictable relationship between their period of variation and their intrinsic brightness. This makes them valuable “standard candles”: by comparing how bright they actually are with how bright they appear, astronomers can estimate their distances. Cepheids therefore became a crucial rung on the astronomical distance ladder and played an important role in establishing the scale of the universe.

Another major piece of the Big Bang puzzle came from the discovery of cosmic background radiation, or CBR. This faint radiation permeates the universe and is often described as the echo or afterglow of the Big Bang. It represents light released when the young universe had cooled sufficiently for atoms to form and radiation to travel freely through space.

In 1965, Arno Penzias and Robert Wilson accidentally discovered this pervasive background radiation while working with a sensitive microwave antenna. Their observation provided spectacular evidence in favor of the Big Bang model and against the Steady State Theory. The discovery ultimately earned them the Nobel Prize in Physics.

The Big Bang model also predicts that, during the first few minutes of cosmic history, the universe underwent a period of nucleosynthesis. As the universe cooled, fundamental particles combined to form protons and neutrons—the particles collectively known as nucleons. These then participated in the formation of the light atomic nuclei, principally hydrogen and helium. The predicted abundance of these light elements became another important piece of evidence supporting the Big Bang.

The theoretical foundations of this early universe were developed further by Ralph Alpher, working with George Gamow. Their calculations helped establish how the early universe could produce the light elements we observe today. Gamow was one of the great scientific minds of the twentieth century and also possessed a remarkable talent for communicating complex scientific ideas to the public.

The observational and theoretical successes of the Big Bang gradually undermined the Steady State model. The Steady State Theory had proposed an eternal universe in which new matter was continuously created as the universe expanded, preserving its overall appearance. The discovery of the cosmic background radiation, together with other observations, made the Steady State increasingly difficult to defend.

The Big Bang also challenged one of the long-standing assumptions about the universe: the idea that it was unchanging on the largest scales. The universe was no longer viewed as an eternal, static arena. It had a history. It evolved.

Two important cosmological principles, however, remain fundamental to our description of the large-scale universe: homogeneity and isotropy. Homogeneity means that, on sufficiently large scales, matter is distributed relatively uniformly. Isotropy means that the universe looks broadly the same in every direction. Together these ideas form the basis of the cosmological principle.

The story of the Big Bang has also required physicists to confront some profound questions about the very beginning. Our current theories cannot reliably describe the universe all the way back to the mathematical singularity. The earliest time at which our present laws of physics can be reasonably applied is generally taken to be around the Planck time, approximately 10⁻⁴³ seconds after the beginning. Before that point, we expect that a theory combining quantum mechanics and gravity will be necessary.

And so the Big Bang story continues to move beyond what we can directly observe.

Modern cosmology tells us that the universe contains far more than the ordinary matter from which stars, planets, and people are made. Observations indicate that most of the universe consists of mysterious components that we still do not fully understand. Dark energy appears to be driving the accelerating expansion of the universe, while dark matter provides additional gravitational influence that cannot be explained by visible matter alone.

The ultimate fate of the universe depends, among other things, on its overall matter and energy content and the resulting critical density. In older descriptions of cosmology, an important parameter called Omega was used to compare the density of the universe with the critical density. An Omega value greater than one corresponds to a closed universe, while a value less than one corresponds to an open universe. Modern observations, however, indicate that the universe is extremely close to spatially flat, largely because dark energy must be included in the cosmic energy budget.

The question of why the universe contains matter at all introduces another great mystery. According to the simplest expectations, the Big Bang should have produced matter and antimatter in nearly equal quantities. Yet our universe is overwhelmingly dominated by matter. This discrepancy is known as the matter–antimatter asymmetry, or baryon asymmetry. Understanding why matter won out over antimatter remains one of the major unanswered questions in physics.

As our ability to observe the universe improved, scientists launched increasingly sophisticated spacecraft to study the cosmic background radiation. One particularly important mission was NASA's Wilkinson Microwave Anisotropy Probe (WMAP), launched in 2001. WMAP mapped tiny variations in the cosmic microwave background with extraordinary precision, providing important information about the age, composition, geometry, and evolution of the universe.

These observations have transformed the Big Bang from a speculative idea into the foundation of modern cosmology.

The story has even inspired physicists to explore theories that go beyond the traditional Big Bang picture. In M-theory, for example, fundamental objects can exist as higher-dimensional entities known as branes, short for membranes. Some speculative models propose that our universe could have originated through a collision between branes in a higher-dimensional space. Such ideas remain theoretical, but they demonstrate how far physicists are willing to go in trying to understand the ultimate origin of the cosmos.

The history of the Big Bang has also been brought to a wide public audience by scientists and science writers such as Simon Singh, whose work has helped explain difficult scientific ideas and their historical development to general readers. Another influential popularizer was physicist Steven Weinberg, whose celebrated book The First Three Minutes provided a compelling account of what physics can tell us about the earliest moments of the universe.

What began as a controversial idea—that the universe had a beginning and has been evolving ever since—has therefore become one of the central frameworks of modern science. From Lemaître's primeval atom, through Friedmann's equations and Hubble's observations, to Penzias and Wilson's discovery of the cosmic background radiation and the detailed maps produced by modern spacecraft, the evidence has steadily strengthened our picture of an expanding, evolving universe.

Yet the Big Bang does not represent the end of the story. In many ways, it is the beginning of the questions.

What happened before the earliest moment we can describe? Why is there more matter than antimatter? What exactly are dark matter and dark energy? Why does the universe have the physical constants and laws that it does? And ultimately, why is there a universe at all?

The remarkable thing about cosmology is that the more we learn about the beginning of the universe, the more profound the remaining mysteries become

Why is Physics so badly taught?

 Why is physics so badly taught? It is an excellent question—and one that teachers and educators have been wrestling with for a very long time.

There are, of course, many reasons why students can struggle to learn physics, but several recurring problems stand out.

Perhaps the most fundamental is that we often do not spend enough time making sure students genuinely understand the key concepts—the “Big Ideas”—before moving on to problem solving. Too frequently, instruction moves almost immediately from introducing a concept to plugging numbers into equations. Students may learn how to obtain an answer without ever developing a meaningful understanding of what the answer represents or why the underlying physics works.

A related problem is the overuse of simplistic or inappropriate analogies. Analogies can be extremely useful teaching tools, but only when their limitations are made clear. A poor analogy may help students develop an initial intuition, but it can create significant misconceptions later when they encounter more complex situations. What begins as a useful shortcut can ultimately become an obstacle to deeper understanding.

Another issue is the way physics is sometimes taught as if it were simply applied mathematics. Many physics teachers come to the subject with strong backgrounds in mathematics, and there is nothing wrong with that. Mathematics is an essential language of physics. However, physics is much more than manipulating equations. It is about understanding the physical world, identifying relationships, making predictions, interpreting evidence, constructing models, and recognizing when those models no longer apply. When physics becomes little more than mathematical manipulation, students can become very good at solving equations while remaining surprisingly weak at understanding the physical phenomena those equations describe.

This is one reason laboratory work and demonstrations are so important. Students need opportunities to see, touch, measure, and experience the phenomena they are studying. A well-designed demonstration or laboratory investigation can consolidate a Big Idea at a visual and hands-on level in a way that a textbook or lecture often cannot. Physics should not exist solely on the page or the whiteboard; students need opportunities to encounter it in the real world.

There is also a broader curricular problem, particularly in North American physics courses: we often emphasize breadth at the expense of depth. Teachers are expected to cover an enormous amount of material, and there is constant pressure to “get through the curriculum.” In the rush to check off every topic, we can sacrifice the deeper analysis and discussion that allow students to develop genuine conceptual understanding. Students may encounter dozens of topics but master very few of them. Sometimes, teaching less material more deeply would produce far better physicists.

Another factor is that instructional methodology is often not sufficiently diverse. There is no single teaching approach that works equally well for every student or every concept. Effective physics instruction should draw upon a variety of teacher- and student-oriented strategies: direct instruction, questioning, discussion, demonstrations, laboratory investigations, collaborative problem solving, simulations, individual reflection, and opportunities for students to explain their thinking. These approaches need to be combined thoughtfully according to the concept being taught and the diverse mosaic of students sitting in the classroom.

Finally, we place far too much emphasis on formula memorization. Formulas are certainly important, but memorizing an equation is not the same thing as understanding the physics behind it. Students need to know where a formula comes from, what physical relationships it represents, when it can be applied, and—perhaps most importantly—when it cannot. Every physical equation rests on assumptions and conditions that limit its applicability. If students understand those assumptions, they can recognize when a model is appropriate and when they need to look for something more sophisticated.

Ultimately, the problem is not that physics is inherently too difficult for students. Rather, we sometimes teach it in ways that obscure what makes the subject so fascinating. Physics is about understanding how the world works. Mathematics is one of the tools we use to express that understanding, but it is not the understanding itself.

If we want students to become better at physics, we need to give them time to develop the Big Ideas, experience the phenomena firsthand, question their assumptions, explore the limitations of models, and explain their reasoning. We need to move beyond simply asking, “What formula do I use?” and toward the much more important questions: What is happening? Why is it happening? How do we know? And under what conditions does our explanation work?

That, ultimately, is the physics we should be teaching.

Science vs Scientism

Pure science is not an ideology; it is a method for examining claims through empirical investigation and drawing conclusions that can be tested and, ideally, used to make predictions. It relies on mathematics and statistics to analyze evidence, quantify uncertainty, and identify relationships that can then open new avenues of inquiry. In this respect, science has been extraordinarily successful.

That success, however, does not make scientists immune to the weaknesses of human institutions. The philosopher Paul Feyerabend argued that when practitioners of science become dogmatic or overly political in their outlook, the practice of science can itself become vulnerable to groupthink. When contrary evidence is dismissed rather than investigated, and when credentials and institutional authority become more important than the strength of an argument, scientific inquiry can begin to drift away from its methodological ideals.

The danger is that a community devoted to challenging assumptions can gradually become protective of its own assumptions. Consensus, professional status, and institutional power can begin to substitute for evidence. At its worst, this can produce a kind of secular priesthood—an intellectual hierarchy whose authority is derived less from the continuing scrutiny of its claims than from the credentials and prestige of its members.

When that happens, scientific methodology risks being subordinated to predetermined conclusions. The result is stagnant thinking, diminished intellectual curiosity, and a reluctance to pursue evidence that might challenge the prevailing view.

The irony is that this is precisely what science, at its best, is designed to prevent. Its greatest strength lies not in the authority of scientists, but in the willingness to subject claims to evidence, criticism, replication, and revision. Science remains most powerful when no conclusion is considered sacred—not even the conclusions reached by scientists themselves.

Physics Reading List

Books I recommend

1. The Elegant Universe – Brian Greene - excellent introduction into the fundamentals of Modern Physics.

2. Hyperspace – Michio Kaku - wonderful take on extra-dimensions by a strong narrator.
3. The Ideas of Physics – Ernest Hutten - an oldie but a goldie – discusses key ideas that shaped the discipline.
4. Fearful Symmetry – A. Zee - Looks at the Beauty in Physics.
5. Physics of Immortality – Frank Tipler - a bit over the top but highly entertaining nevertheless.
6. Theories of Everything – John Barrow - Low key but well written.
7. Feynman Lecture Series – Richard Feynman - A struggle for the lay person but if you can get through a third of it your effort will be rewarded.
8. The Trouble with Physics – Lee Smolin - an important critique of the group think that has encroached on the discipline.
9. Physics – Douglas Giancoli - Doesn’t matter what the edition is its treatment of classical physics is praiseworthy.
10. The Flying circus of Physics – Jearl Walker – Challenging problems that force one to really think deep.
11. Relativity Simply Explained – Martin Gardiner – Its title says it all.
12. The First Three Minutes – Steven Weinberg- Still one of the best treatments of the Big Bang.
13. The Constants of Nature – John Barrow – Delves into the details of these definitive constants that so encapsulate our universe.
14. Thirty Years that Shook Physics: The Story of Quantum Theory – Gamow is a great storyteller and he didn’t disappoint with this useful read.
15. 50 Physics Ideas – Joanne Baker – Lots of fun and really easy to read.

Why does time slow down the faster you move?

 My Answer on Quora.

It doesn’t slow down at least in the sense that this question is worded. This is a misconception. Lets look a bit more at the bigger picture that comes from Einstein’s Special Theory of Relativity (1905).

Time is a relative concept. There is no such thing as absolute time in the broader scope of non-Galilean relativity. The measurement of time is specific to the frame of reference of the person making the measurement. Within the same frame of reference all observers agree on the same time measurement. However if one frame of reference is moving with respect to the other then there will be a disagreement in how much time has elapsed between events.

You see the only ‘absolute’ here is that the laws of physics hold across all frames of reference. The speed of light in a vacuum as measured by all is the SAME. We call it c. One cannot add or subtract onto c. It is what it is. There is no such thing as c + v or c-v (which Galilean relativity argues for).

Which means that something has to give. Actually several entities do, including absolute time and absolute length. The relative motion of one frame of reference to the other has to be taken into account and it is corrected for by invoking the Lorentz or Gamma factor.

where v = speed of the one frame of reference relative to the other.

For example if Bob boards a space ship and travels at a constant speed v relative to his Earthbound cousin Ann. Bob will experience what is called proper time (a poorly worded term). Ann will be the benefactor of relativistic or measured time. Both measurements of time are correct within their specific frame of reference.

Now the two times are related by the Gamma factor as shown below:

where delta t prime = measured time and delta t is proper time. Gamma is included in this equation and is always greater than or equal to 1. As v approaches c gamma tends to infinity so that the discrepancy between measured time and proper time ramps up considerably. We don’t see this as much in the day-to-day as v is so small compared to c. However the phenomenon is real….we call it TIME DILATION.

Consequently for Ann it will seem that Bob’s clock is running VERY slow. However from Bob’s perspective life is normal and there is nothing wrong with his clock. He will likely argue that Ann’s clock is running too fast. Both are correct in their own frame of reference.

Worth noting is that there is an additional assumption built into this analysis. Both frames of reference are not-accelerating. That is they are Inertial. For accelerating Frames of reference we need to bring in ideas from Einstein’s Theory of General Relativity (1915).

The Mathematical model for Special Relativity in a nutshell

 Special Relativity is predicated on two postulates.

1. All uniform motion is relative and the laws of physics apply equally to all frames of reference.
2. The speed of light is c in a vacuum across all frames of reference.

The necessity of these two paradigms forces a relaxation of absolute time, space, momentum, kinetic energy and simultaneity.

Time Dilation can be understood by a pythagorean analysis of vectors that produces a relation whereby proper time is a multiplied by the Lorentz Factor to obtain relativistic time.

The former is determined by an observer who is at rest relative to the event. The latter sees the event occurring in different places in space.

Relativistic time will always be greater than or equal to measured times with the discrepancy between the two becoming more extreme as velocity tends to c (speed of light).

What are Emprical Laws? How are Newton's Laws Emprical?

 My answer on Quora

These are phenomena that at their very core are driven by the nature of what the universe is at its fundamental level and can only be elucidated through experimentation (not deductive rationalism). They could indeed be otherwise if the nature of the physical universe and its key constants were different. We can probe deeper with mathematics to explain the ‘how’ but the ‘why’ is a different beast altogether.

Newton’s Three Laws of motion emerge as special cases of a broader physics model that rests on a deeper physical base empirically in the MODERN framework. CLASSICALLY without the benefits of Quantum Mechanics and Relativity (both Special and General) we treat them as Empirical.

How were Newton and Huygen's ideas on the nature of light different?

(My answer on Quora)

Both Isaac Newton and Christiaan Huygens were brilliant minds. Where they primarily clashed was on the fundamental nature of light.

Isaac Newton source: World News, Economics and Analysis Based on Bible Prophecy

Christiaan Huygens source: ThoughtCo

Newton believed that light was made up of tint particles called corpuscles that could account for such phenomena as Reflection, Refraction and Rectilinear Propagation.

Huygens favored a wave model where each wave front consisted of wavelets that were the source for the next wave front that propagated forward. Light rays represented the direction of wave propagation.

He believed that all of the properties of light including diffraction could be explained with such a model.

Source: Olympus Science

Huygens Principle and Interference source: Physics Stack Exchange

The deadlock existed until the very early 19th century when Thomas Young carried out his famous Double Slit Experiment. Young was able to produce the characteristic wave interference pattern(alternating bands of maxima and minima) that is the definitive signature for wave like behavior.

Young’s Double Slit Experiment yields definite Interference Pattern source: lumenlearning.com

This implied that in the world of classical physics Huygens was correct - Light is a wave.

In the world of modern physics we now know that light has both a particle and wave nature and exhibits what we called Wave-Particle Duality. Light particles (photons) are however very different to Newton’s original Corpuscles or Billiard balls. 

What does Gibbs Free Energy measure?

 (My answer on Quora).

Gibb’s Free Energy (delta G) measures the maximum amount of reversible work that can be extracted from a system. The caveat though is that the system has to be at constant temperature and pressure (or volume). It must also be a closed system (that is one that does not exchange matter although it can exchange heat and work)

Gibb’s Energy (also known as available energy) is given by the symbol G and is named after the American chemist Josiah Gibbs. The unit of G (like all energies) is Joules (J).

When a system is in chemical equilibrium G is minimized. Delta G becomes zero which implies that no spontaneous energy can be extracted from the system at this pressure and temperature.

Photon Scattering

(Based on my Quora Answer)

A photon is a particle and it doesn’t have mass. It does however have momentum (p).

Source: Hyperphysics

This is shown in the diagram above of Compton Scattering. The collision of the photon with an electron at rest increases the wavelength of the scattered photon and provides the electron with momentum (shown with relativistic correction). Photons have energy that is proportional to its frequency. This energy of a photon can be calculated by multiplying the frequency (v…Greek symbol nu) by Planck’s constant (h).

The momentum of a photon can be calculated by dividing this Energy by c (speed of light in a vacuum).

Remember photons travel at c in a vacuum. Nothing that can travel at c has mass.

In modern physics you don’t need mass to have momentum. In classical physics you do.

Why does the magnitude of acceleration remain constant?

Asked on Quora. My answer.

This happens when the net force is constant (read about Newton’s Second Law of Motion). A free falling object, that is one being impacted by the force of gravity only, is subject to a constant net force that is equal to the weight of the object. (mg). Since the gravity field (g) is roughly uniform close to the Earth’s surface this results in a constant net force and therefore a non-changing acceleration.

In uniform circular motion the magnitude of the acceleration also stays constant if the Centripetal force (another net force) has constant magnitude. However the direction of the acceleration will change though as the net force is perpendicular to the direction of motion of the object which forces a change in velocity but not speed.

Science v Scientism

 Pure Science itself isn’t inherently an ideology. It a method of examining claims through empirical investigation and then drawing conclusion that have predictive value. It uses the framework of mathematics and statistics to analyze the evidence thereby opening up further avenues of investigation to test deeper claims. In this regard it has been very successful.

Having said that though Paul Feyerabend has a point when the practitioners of science become dogmatic and political in their outlook to the point that they transform the practice of science into a milieu dominated by groupthink, the willful neglect of contrary evidence and the elevation of the power dynamic of credentialism.

This invariably results in stagnant thinking, the formation of a closed secretarian priesthood/authority and the sacrifice of the rigorous scientific methodology to preordained conclusions.

The further venture of science into realms which are less quantifiable or indeed falsifiable (eg. morality and metaphysics) further challenges the scope of science’s applicability. A realism that seems lost to those who with each passing moment are intent in transforming science into the ideology of scientism.

Why do gases float? Don't they have gravity?

 (Asked in Quora. My answer)

All gases have weight. Weight is the force of gravity acting on an object and is equal to the mass of the object multiplied by the strength of the gravitational field at the specific point in space.

If you created an imaginary open pathway (or vacuum tunnel) a gas on Earth would be pulled towards the center of the Earth and would travel as such. However such an open pathway only exists in theory. In reality there is material in the way of the gas that is usually more dense than the gas. The material exerts a normal force upwards which pushes the gas backward until it reaches a stable balanced position that we call floating.

We also call this force the buoyancy force and it counteracts the downward pull of the gases weight.

Less dense gases are pushed upward by the buoyancy force provided by the more dense gases below them. These lighter gases will eventually settle in an equilibrium position where the weight pulling down is equal to the buoyancy force pushing up.

Balloons filled with the light gas Helium demonstrate this phenomenon clearly by rising to a level in the atmosphere where the density of gas around then is more rarefied and therefore comparable with the density of the Helium gas itself.

What do Feynman diagrams relate to?

(My answer in Quora).

Feynman Diagrams are very useful visual tools (book keeping devices) that have application in understanding the understanding of particles and antiparticles against the critical back drop of time. They are largely employed in the area of Quantum Field Theory as they offer a mechanism of simplifying a complex system into one that is simpler and easier to understand.

Here is an example of a Feynman Diagram

Particles are shown moving forward in time. Antiparticles are indicated by a backward motion in time.(Source: Physics forum)

In this diagram an electron (e negative) interacts with a positron (e positive), The positron is an antiparticle of the electron so it is shown moving backwards. The two particles annihilate each other producing a photo. The photon is indicated by the -sine wave. This in turn becomes a muon-antimuon pair shown by the Greek letters mu negative and mu plus respectively. Again the antiparticle is shown moving backwards in time.

The interesting story about Feynman diagrams is that they were initially resisted by the physics community who preferred equations/graphs to represent the interactions. To his credit Richard Feynman sold the diagrams to the community where they initially known as Feynman-Dyson diagrams (after Freeman Dyson who made a significant contribution to perturbation theory).

Fun fact…Feynman was not the first person to use these diagrams . The accolade for that for goes to the Swiss Physicist Ernst Stueckelberg. Nobel Laureate Murray Gell-Mann regularly referred to these diagrams as Stueckelberg diagrams in honour of their earlier development.

Key methodology followed when drawing a Feynman diagram

1. Electrons are represented with a straight line in the initial state pointing to a vertex. In the final state they point away from the vertex. Positrons as mentioned earlier are depicted going the other way around.
2. Virtual particles are shown with wavy lines.
3. Exchange particles (such as W + Bosons) are shown with Squiggly lines.
4. Time is shown as going from left to right or bottom to top (depending on the diagram)
5. Gluons - particles that mediate the strong nuclear force are shown as spirals.

The diagrams can take on various complexities that can be analyzed using quantum probability calculations.

source: Research gate.

Below is an example showing how Feynman diagrams are applied in Quantum Field Theory.

Source: IB Physics - Particle Physics/

Further reading

https://arxiv.org/pdf/1602.04182.pdf