I can understand that velocity of light is a universal constant. I can see that from a constant “wavelength to period” ratio even when the frequency of light changes. But I do not understand why the relative velocity of light should also be constant and not exceed the velocity of light.

Isn’t that an assumption by Einstein? What is the logic underlying Einstein’s conclusion?

The Dutch astronomer De Sitter showed that the velocity of light does not depend on the velocity of the source of light. This is similar to the fact that the velocity of sound does not depend on the velocity of the source of sound.

Sound is a disturbance in a physical medium. Similarly, we may look at light as a disturbance in a physical medium. That physical medium is not aether, but space itself. Space has definite physical properties, such as, permittivity and permeability. The only difference is that space does not consist of mass. Instead space consists of a more fundamental substance called “field”.

When there is no sound, its medium of air may be considered to have a frequency of zero. Similarly, when there is no light (electromagnetic wave), the medium of space may be considered to have a frequency of zero. It is the postulate of Disturbance Theory that

#### Space is the theoretical state of electromagnetic field at zero frequency.

We cannot compare the velocity of the disturbance in a physical medium (sound) to the velocity of the physical medium (air) itself. This is like comparing apples to oranges. When a plane is moving at supersonic speed in air and sound is moving as a disturbance in air, that does not mean that air itself is moving at supersonic speed.

Air as a medium is flexible. That is how it allows sound wave to move through it. Similarly, space has to be flexible to allow light wave to move through it. We cannot assume space to be rigid, just like we cannot assume air to be rigid.

When a source of sound is moving relative to air, it only changes the frequency of sound and not the speed of sound. Similarly, when a source of light is moving relative to space, it only changes the frequency of light and not the speed of light.

What happens when the source of sound is moving at the speed of sound? The frequency of sound would increase until it collapses into rigidity because sound cannot advance any faster. The medium of air would appear inflexible and rigid to the source of sound. Similarly, when a source of light moves in space at the speed of light, the medium of space would appear inflexible and rigid to the source of light.

**We recognize this rigid condition of space as the Euclidean space.**

So, when we assume space to be totally rigid as Euclid does, it is as if we are looking at it relative to a source of light moving at the speed of light. However we don’t observe that directly. We only know that we become aware of objects when light reflects or scatters off them.

**Could it be that high frequency electromagnetic waves collapse into mass that makes up the objects?**

This conjecture is in line with the Disturbance Theory, but it is yet to be demonstrated.

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This article establishes an uncanny parallel between sound and light waves. We know that the velocity of sound can be exceeded both in relative and actual sense. So, what made Einstein assert that the velocity of light could not be exceeded even in a relative sense?

To answer this question we look at Section V of Einstein’s Book “Relativity: The Special and General Theory”. In this section Einstein establishes the Principle of Relativity (in the restricted sense).

Einstein takes up the case where a railway carriage is undergoing uniform translation without rotation. Using this example Einstein shows that the mechanical laws hold good for uniform translatory motion of Galilean co-ordinate system. This co-ordinate system applies to bodies with mass changing their position in space with time. It is valid for Newtonian mechanics.

Einstein then makes the assumption that all natural laws shall hold good for uniform translatory motion of Galilean co-ordinate system. But the natural laws of electrodynamic and optics move beyond classical mechanics.

We know now that light is a disturbance in electromagnetic field. The electromagnetic field is more basic than mass and it is devoid of inertia. It is the concept of frequency that is more applicable to electromagnetic field than the concept of velocity because we cannot use the concept of rigid space for light. The Galilean co-ordinate system assumes space to be rigid.

Therefore, Einstein’s principle of relativity when restricted to uniform translatory motion of Galilean co-ordinate system, does not apply to light.

**Therefore, the conclusion that the velocity of light cannot be exceeded, even relatively, comes under question.**

The theory of relativity needs to be reviewed thoroughly because the assumption that Einstein made has now come under question.

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## Comments

You are making some good progress on this. However, I do not understand your question, “But I do not understand why the relative velocity of light should also be constant and not exceed the velocity of light.” You’ve answered it in the text following the question.

I was pointing out the difference between “velocity” and “relative velocity”. I totally agree that the velocity of light is a universal constant because it depends on the physical properties of space.

But does that logic extend to the perception of relative velocity always being “c”? It will depend on the viewpoint one takes. This gets into subjectivity.

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Of course, I see what you mean and that is a very interesting question. Possibly the paradox gives a clue as to where the weakness in our thought experiment lies. Overall, your exploration into the properties of “massless” spacetime seems a productive vector to put your energy. Also the transition moment of “energy” to “mass” and vice versa. Wouldn’t it be fun to be able to visit CERN and ask those blokes a few questions?

I find that The Doppler Effect defines relativity much better than Lorentz transformation.

https://vinaire.me/2016/01/11/velocity-in-space/

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Einstein assumes space to be rigid like mass. All his computations using the Lorentz transformation are based on that assumption.

In my opinion space is flexible and that is how it allows light to propagate through it. Space appears rigid only at very high frequencies as those inside the nucleus of an atom.

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Maybe a clue lies in the word “exceed.” c is a constant property of spacetime when the medium is constant. Maybe we need to remember to include time when making references to motion.

What is the relative velocity when two sound waves cross each other in opposite directions?

Is it same as the velocity of sound or twice the velocity of sound?

Quite right! Of course subjectively, the relative speed of the wave fronts must be twice the speed, however, is that what we are being taught? And how do the massless properties of electromagnetic radiation counterintuitively affect our understanding?

In my opinion the two wavefronts of light passing each other in opposite directions will have the relative velocity of ‘2c’ when you look at it from a viewpoint outside the universe. I don’t think that violates the principle of relativity.

It violated the principle of relativity for Einstein because he didn’t interpret speed of light as “wavelength to period ratio”, which always remains constant regardless of frequency.

The correct frame of reference for light is frequency and not inertia. The inertial frame of reference applies only to mass and not to light.

Einstein’s error is to apply the inertial frame of reference to light.

Classical mechanics deals with the interaction between mass (collapsed high frequency) and spatial (zero frequency) fields.

Electrodynamics deals with the interaction between electromagnetic (finite frequency) and spatial (zero frequency) fields.

SR (special relativity) seems to be looking at the interaction between electromagnetic (finite frequency) and mass (collapsed high frequency) fields,

But SR is looking at this interaction using a mass (collapsed high frequency) coordinate system, and not through the spatial (zero frequency) coordinate system.

In my opinion, it is more accurate to use spatial (zero frequency) coordinate system as the basic reference rather than the mass (“infinite” frequency) coordinate system.

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Space should be used as the basis of relativity and not mass and light as used by Einstein..

This helps, doesn’t it?

What helps is viewing space as a field of zero frequency. Compared to this,

(1) Energy is “space with a frequency”

(2) Mass is “space with so high a frequency that it has collapsed”.

You can get an idea of (2) above when an object is moving through air at the speed of sound. The disturbance in air is also moving at the speed of sound. Then the frequency of the disturbance in front of the object will be totally squished and will collapse.

The medium of air will appear as rigid to the moving object. It won’t stop the object because the object can push through that rigidity..

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From the viewpoint of space the distance between two objects cannot be measured.

From the viewpoint of mass we measure the distance using rigid rods.

From the viewpoint of light we measure the distance using the “wavelength to period” ratio “c”. Here distance and time will appear in a constant ratio.

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The theorem of the addition of velocities does not apply to light, because space is not rigid in this case. Instead of absolute distance and time (velocity) we should be looking at flexible distance and time (frequency).

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I do not think that space between planets is rigid at all. The rigidity of space shall depend on the frequency of the disturbance that is traveling through space. Rigid space shall correspond to electromagnetic frequencies in upper Gamma Range

Euclidean space is rigid. It refers primarily to space between connected solids, All space close to the surface of our planet is treated as rigid. But I would not consider the space between earth and a plane flying at 50,000 feet to be entirely rigid.

Lorenz transformation equations treat the space between two coordinate systems in uniform motion relative to each other as rigid. I do not trust the math here for that reason.

That means I do not trust the math formulas of the Theory of Relativity.

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I would use wavelength and frequency to measure intersteller space rather than distance and velocity.

Professor Michel Alcubierrre has already been where you’re trying to go.

Alcubierre correctly noticed that while the speed of light was fixed in the medium, the speed of the medium was not. (This is as you have tried to point out, above with your allusions to the speed of sound in air compared to the velocity of the air molecules.)

Alcubierre used his idea to formulate a method of faster-than-light travel which ends up looking a lot like a surfer on a surf-board.

From the surfer’s point of view he’s standing relatively motionless on the board but is being propelled to a velocity that is dictated only by the velocity of the wave he is riding. Similarly with space, if you could expand space behind you, you would be pushed forward.

Yes, space pushes. That’s explained by general relativity.

So space being expanded behind you can push you forward while the space you are sitting in shows no relative motion about you, just like the observation of the surfer on the board. This allows you to be propelled to high velocities while never feeling any effect of acceleration.

NASA has built a (non-functioning) model based based on the Alcubierre principle with the hope it will inspire future youth to become the engineers and physicists that will make the drive a reality.