Table of Contents

Speed of light

My questions at HN and Physics forum

Some comments

  1. I commented at Hacker News and I got lynched. I guess I questioned some people’s faith.
  2. I asked the same question at Physics forum. The same thing. It is really hard to understand why these people get so defensive. It really looks like they are the defenders of faith.
  3. But I’m not questioning their faith. I’m just trying to understand.
  4. This speed of lignt fetish must be a serious business in physics. The cult of the speed of light.
  5. There were interesting answers:

You’re asking how to make a Star Trek transporter — destroy the object in one place while recording its complete state of being, transmit the information to another place, and use it to reconstruct the object. I’m pretty sure that quantum mechanics makes this impossible, but that might be a philosophical question still and not 100% accepted physics. –
The Photon

  1. No. I’m not asking that. They’ve corrupted physics into trash pulp scifi.
  2. Another answer:

You’re already doing it! Since there is no absolute reference frame, there exists a reference frame where you are moving at 99% of the speed of light right now.

  1. Classic GR answer.

My answer

  1. When I asked the question I also thought that this was a Einstein question, a general relativity question. But after reading some comments I realized that this was a simple orbit question.
  2. These people are living in a fictional universe where Kepler’s Rule is not valid. This is not our universe.
  3. So the question is about accelerating a spaceship with astronauts to the speed of light.
  4. To do this we fire our rocket from earth and place our ship into an orbit around the earth.
  5. I said I want to compute this in practice not in a thought experiment in someone’s science fictional universe where Kepler’s Rule is not valid.
  6. Kepler’s Rule is valid here in this universe.
  7. If we use our thrusters in the direction we are moving we would increase our radius and our period will increase proportionately meaning that we will slow down.
  8. In order to increase our speed we need to fire our thrusters in the opposite direction of our motion. This reduces our radius and reduces our period. We pick up speed.
  9. Since we want to increase our speed we need to fire our thrusters in the opposite direction.
  10. Here I need to do some calculations. As earthlings how fast can we move even if we reduce our orbit to almost zero radius?
  11. But the important thing to realize is that this problem has nothing to do with general relativity.
  12. These people assume inertial motion following Newton on a straight line. There is no such motion in this world. All motion is orbital motion. Natural motion is circular motion. Circular motion does not have acceleration. Newton intentionally confused orbital motion with Huygens’ centrifugal motion.

Acceleration

  1. Is light accelerating non-stop
  2. Continuous acceleration
  3. But this does not seem to make sense

Wavelength and frequency

Yes, light has both wavelength and frequency. These are key characteristics of electromagnetic waves, including visible light.

  • Wavelength (\( \lambda \)): This is the distance between two consecutive peaks (or troughs) of the wave. It is usually measured in meters (m), nanometers (nm), or other units depending on the scale. For visible light, the wavelength ranges from about 400 nm (violet) to 700 nm (red).
  • Frequency (\( f \)): This refers to the number of wave cycles that pass a given point per second. It is measured in hertz (Hz), where 1 Hz equals one cycle per second. The frequency is inversely proportional to the wavelength.

The relationship between wavelength, frequency, and the speed of light is given by the equation:

\[ c = \lambda \cdot f \]

Where:

  • \( c \) is the speed of light in a vacuum (\( 3.00 \times 10^8 \) m/s).
  • \( \lambda \) is the wavelength.
  • \( f \) is the frequency.

In a Medium:

When light enters a medium (e.g., glass or water), its speed changes, but its frequency remains constant. The wavelength, however, adjusts according to the change in speed.

Thus, both wavelength and frequency are essential to describing the nature of light waves.

Error

The speed of light has been measured many times throughout history, and each measurement improved in accuracy as technology advanced. Before it became a defined constant, the speed of light (\( c \)) was experimentally measured with some degree of uncertainty or error. Here are key milestones and the associated errors:

1. Ole Rømer (1676)

  • Method: Observing the motion of Jupiter’s moons.
  • Estimated Speed: Around \( 2.14 \times 10^8 \) m/s.
  • Error: His result was about 30% lower than the true value. At the time, his calculation was considered groundbreaking, but it had significant inaccuracies due to the lack of precise tools.

2. Hippolyte Fizeau (1849)

  • Method: A rotating toothed wheel and a beam of light reflected by a distant mirror.
  • Estimated Speed: \( 3.13 \times 10^8 \) m/s.
  • Error: About 4% higher than the true value.

3. Léon Foucault (1862)

  • Method: A rotating mirror method to reflect light across a known distance.
  • Estimated Speed: \( 2.98 \times 10^8 \) m/s.
  • Error: This was within about 0.6% of the modern value, a significant improvement over previous methods.

4. Albert A. Michelson (1879-1931)

  • Method: Improved versions of Foucault’s rotating mirror technique.
  • Final Estimated Speed (1931): \( 2.99796 \times 10^8 \) m/s.
  • Error: Michelson’s measurements were incredibly accurate, with an error of about 0.002%. His work led to the most accurate pre-defined value of the speed of light.

Modern Definition (1983)

In 1983, the speed of light was defined as exactly \( 299,792,458 \) m/s by the International Committee for Weights and Measures. This definition was based on the fact that the speed of light in a vacuum is a constant and independent of any system of measurement, allowing the meter to be redefined in terms of the time it takes light to travel.

Summary of Errors in Earlier Measurements:

  • 1676 (Rømer): ~30% error.
  • 1849 (Fizeau): ~4% error.
  • 1862 (Foucault): ~0.6% error.
  • 1931 (Michelson): ~0.002% error.

As technology improved, the measurement errors became extremely small, and the value became more precise until it was eventually fixed by definition.

Only light can move with the speed of light

Yes, it is accurate to say that only light (and other massless particles) can move at the speed of light in a vacuum. This statement is a consequence of Einstein’s theory of relativity and applies to massless entities like photons (the particles that make up light).

Here’s why:

1. Massless Particles

  • Photons: Light is made up of photons, which are massless particles. According to special relativity, any particle that is massless must travel at the speed of light (\( c \)) in a vacuum.
  • Other massless particles, such as gravitons (if they exist, as they are hypothetical at this point), would also travel at the speed of light.

2. Massive Particles

  • Objects with mass (e.g., electrons, protons, or cars) can never reach the speed of light. As their velocity increases, their relativistic mass (or energy) increases, requiring more and more energy to accelerate further. To reach the speed of light, an object with mass would need infinite energy, which is impossible.

3. The Speed Limit

  • The speed of light acts as a cosmic speed limit for all matter and information. Anything that has mass can approach the speed of light but can never reach or exceed it.
  • Similarly, no information or object can be transmitted or moved faster than the speed of light in a vacuum, as this would violate causality and fundamental principles of relativity.

Exceptions:

  • In a medium (e.g., water or glass), light slows down due to interactions with the material, but photons are still the fastest-moving entities in that medium. Sometimes particles like electrons can move faster than light in the same medium, leading to phenomena like Cherenkov radiation (the optical “shockwave” produced when a particle moves faster than light does in that medium).

In summary, only light (photons) and other massless particles can move at the speed of light in a vacuum. All objects or particles with mass are restricted to speeds below this limit.

Notes

  1. I question the constancy of the speed of light in principle.
  2. The principle is that motion is change so like everything else it must change
  3. If something is not changing it is a perpetual motion machine but in this world perpetuality does not exist whatever is must change
  4. If something is moving it must change
  5. So what is constant is not change but change of change. In the case of motion accelerütion is constant
  6. Since light cannot accelerate, that is, increase its speed it must slow down
  7. “When light enters a medium?…”
  8. This must mean that light must move in a medium. They used to call this medium “ether”.
  9. Then ether must exist
  10. So if ether existed was it denser than glass? I guess glass is denser than water
  11. How does speed change but frequency remains same?

[chatgpt]

I read this sentence: “When light enters a medium (e.g., glass or water), its speed changes, but its frequency remains constant.” I’m familiar with the debate about the existence of the “luminiferous ether”. Ether was defined as the medium for light to travel in. Assume that ether exists. If ether existed, was it more or less dense than water and glass?

If we imagine that a luminiferous ether exists as the medium through which light travels in vacuum, then by comparison with water or glass it would have to be extremely “light”—that is, far less dense.

In materials like water or glass, light appears to slow down because of interactions with the medium’s atoms. These media have a high density of particles, which in modern terms leads to a higher refractive index (about 1.33 for water and 1.5 for many types of glass) compared to vacuum (which has a refractive index of 1). If the ether were the underlying medium in which light travels at its maximum speed (c ≈ 3×10⁸ m/s), it would need to be very different from ordinary matter. Specifically, it would have to be so tenuous that its effective density is negligible compared to that of water or glass.

Historical theories of the ether even postulated that it had properties unlike conventional materials—it was thought to be extremely rigid (to support the very high speed of light) yet incredibly low in density. This combination would allow electromagnetic waves to propagate at speed c without the kind of interactions (and consequent slowing) seen in denser substances like water or glass.

So, under the assumption that an ether exists as the medium for light, it would be much less dense than water or glass.

Got it. But being rigid without being dense seems contradictory to me. Maybe this is why they assumed that ether “had properties unlike conventional materials.” Can you comment on this (apparent?) contradiction?

Yes, the idea of ether being both extremely rigid and almost massless does seem contradictory when judged by ordinary material properties. This was one of the major conceptual difficulties with ether theories.

In classical physics, rigidity is usually associated with high density and strong intermolecular forces—think of a diamond, for example. But ether was supposed to transmit light waves at an incredibly high speed, which, in wave mechanics, generally requires a medium with very high stiffness. For example, sound waves travel faster in solids than in gases because solids are more rigid. If this analogy applied to ether, it should have been more rigid than steel to allow light to travel at 3×10⁸ m/s.

At the same time, ether was supposed to be undetectable in terms of resistance or drag on moving objects (e.g., Earth moving through it). If it were dense like air or water, one would expect measurable friction or turbulence, but none was observed. This led physicists to propose that ether was not made of conventional particles with mass but was instead a unique kind of substance that pervaded all space without impeding motion.

This contradiction—needing ether to be rigid for wave propagation but also imperceptible in interactions—was one of the main reasons ether theory struggled. When Einstein’s special relativity eliminated the need for a medium by explaining light as an electromagnetic wave in empty space, the paradox of ether’s supposed properties disappeared.

So, your intuition is correct: the rigidity-without-density idea was unnatural based on conventional materials, which is why ether was assumed to have special, almost paradoxical properties.

When we look at water waves we observe that waves do not move “in” water but waves are water. Similarly, what objection may you have against saying that light itself is the ether? This sounds like the explanation of light in modern physics as being fluctuations of a field. What are your comments on this?

That’s an insightful observation! The idea that light is the ether, rather than something moving through it, would indeed remove the need for a separate, undetectable medium. This is strikingly similar to how modern physics treats light—not as a disturbance in a material medium, but as self-sustaining fluctuations of an electromagnetic field.

### Possible Objections in the Classical Context
If we go back to classical physics and try to say “light itself is the ether,” some objections might arise:

  1. Wave Transmission vs. Medium Identity
    In classical wave theory, a wave typically requires a medium that has distinct properties from the wave itself. For example, water waves are made of water, but the water itself is distinct from the wave’s motion—it exists even without waves. If light were the ether, would that mean ether doesn’t exist where there is no light? Classical physics would struggle with this idea, since ether was thought to be a continuous background filling all space, regardless of whether light was present.
  2. Mechanical Interpretation of Waves
    Ether was historically conceived as a mechanical medium, something akin to air or water. If light were the ether itself, then what was “waving”? In modern terms, an electromagnetic wave is a variation in electric and magnetic fields, not a physical displacement of particles in a medium. But classical physicists expected waves to be in something—just as sound waves are in air and water waves are in water.
  3. The Need for a Medium to Justify Maxwell’s Equations
    When Maxwell formulated his equations, the assumption was that the ether provided a background structure allowing electric and magnetic fields to oscillate. If light were the ether, classical physicists might have asked: What determines its properties? Why does it have the particular speed c? The classical mindset assumed that the speed of a wave depends on the properties of the medium, so ether was needed to “explain” the speed of light.

### How Modern Physics Resolves This
Your intuition that modern physics replaces the ether with a field is exactly right. In quantum field theory (QFT) and relativity:

  • Light is not a disturbance in a medium but a fundamental excitation of the electromagnetic field.
  • The field exists everywhere, even in vacuum, and does not need a separate medium to “carry” waves.
  • Light’s speed is not explained by an underlying medium but is set by the structure of spacetime itself.

Effectively, modern physics says that what classical physicists were searching for in the ether (a background structure enabling light to propagate) is actually the fabric of spacetime and the electromagnetic field itself.

### Conclusion
If we say light is the ether, we would have to redefine ether not as a mechanical medium but as something more like a field. This is very close to modern physics, but it would have been difficult for 19th-century physicists to accept because they expected all waves to be in something. The genius of Einstein’s relativity was in recognizing that no such medium was necessary—only the field itself.

Great explanation. But it seems like this issue requires a clear definition of the concept of field in physics. But it seems to me that field in physics is eqiuvocal. And when physicists resort to equivocation there must be some things that they don’t understand clearly. But, that’s a different topic. You answered my question about suppozed density of ether.

That’s a sharp observation! The concept of a field in physics does seem to shift depending on context—sometimes it’s a set of numbers assigned to points in space (like a classical gravitational field), other times it’s a more abstract entity that can have quantum excitations (like in QFT). When a concept carries multiple meanings, it often signals an area where deeper understanding is still evolving.

Physicists have refined the concept of fields over time, but your point suggests a deeper philosophical issue: *Does the field *exist as a physical entity, or is it just a useful mathematical description?** That’s a topic worth exploring, but as you said, it’s a separate discussion.

Glad I could clarify the density question!

Created: 2025-02-23 Sun 19:20

Validate