Proof of the Constancy of the Speed of Light

[gabemaiberger]

 

[jacks]

Well I'm convinced!

 

[Ophiolite]

Well I'm convinced!

He had me at the large font!

 

[Occams Barber]

He had me at the large font!

It's a good job Dad isn't around to see this. One look at this evidence and he'd be forced to admit that it totally destroys his 'different state past' theory.

OB

 

[Kaon]

Classically.

 

[sjastro]

Excellent; good to see the SF being used as a source of education.
Not wishing to nitpick but perhaps you should have specified this is as the constancy of the speed of light in free space in the absence of charges and currents.
This will explain why Maxwell's first equation takes on the form ▽.E = 0 instead of the more familiar ▽.E = ρ/ε₀, and the fourth equation ▽ x B = (μ₀ε₀)∂E/∂t instead of ▽ x B = μ₀j + (μ₀ε₀)∂E/∂t

 

[gabemaiberger]

Excellent; good to see the SF being used as a source of education.
Not wishing to nitpick but perhaps you should have specified this is as the constancy of the speed of light in free space in the absence of charges and currents.
This will explain why Maxwell's first equation takes on the form ▽.E = 0 instead of the more familiar ▽.E = ρ/ε₀.

Thanks for reminding me.

 

[Contenders Edge]

If you ever hope to make a believer out of anyone about the constancy of the speed of light, how about demonstrating the proof in a way that we can all understand and then we can have a discussion about whether or not it is really proof or just speculation and theory.

 

[gabemaiberger]

If you ever hope to make a believer out of anyone about the constancy of the speed of light, how about demonstrating the proof in a way that we can all understand and then we can have a discussion about whether or not it is really proof or just speculation and theory.

Mathematics is not speculation. It can be proven from its basic axioms: TOC of Theorem List - Metamath Proof Explorer. If you are confused about divergence and curl, I recommend the following video explaining them:

. Maxwell's Equations have failed attempts at falsification through experimentation enough times to be accepted. You can even fail to falsify them yourself using a power supply, a straight copper wire, iron filings, and a digital multimeter.

 

[gabemaiberger]

If you ever hope to make a believer out of anyone about the constancy of the speed of light, how about demonstrating the proof in a way that we can all understand and then we can have a discussion about whether or not it is really proof or just speculation and theory.

A theory is not a guess. A theory is a concatenation of multiple hypotheses. A hypothesis (in a scientific context) is a proposed explanation for a phenomenon that is testable, repeatable, falsifiable, and parsimonious (Occam's Razor). If the explanation is not testable, repeatable, falsifiable, or parsimonious, then it is not a scientific hypothesis.

 

[gabemaiberger]

If you ever hope to make a believer out of anyone about the constancy of the speed of light, how about demonstrating the proof in a way that we can all understand and then we can have a discussion about whether or not it is really proof or just speculation and theory.

The proof I gave is derived from Maxwell's Equations. These equations describe the behavior of electromagnetism. First, I derived the electromagnetic wave equation from Maxwell's Equations. Then, I took the second-order partial derivative of the solution to the electromagnetic wave equation with respect to x and the second-order partial derivative of the solution to the electromagnetic wave equation with respect to t. Finally, I substituted the two second-order partial derivatives back into the original electromagnetic wave equation and cancelled duplicate terms to get c.

 

[Belk]

If you ever hope to make a believer out of anyone about the constancy of the speed of light, how about demonstrating the proof in a way that we can all understand and then we can have a discussion about whether or not it is really proof or just speculation and theory.

Because some things can not be simplified down so everyone can understand it?

 

[Kaon]

.

 

[Contenders Edge]

Because some things can not be simplified down so everyone can understand it?

And in such cases, you will fail to convince anyone of what you are hoping to convince them of because what you are presenting them will not make any sense unless your evidence can be presented in such a way as to make sense to everyone, and not just to a handful of elitists.

 

[Contenders Edge]

Mathematics is not speculation. It can be proven from its basic axioms: TOC of Theorem List - Metamath Proof Explorer. If you are confused about divergence and curl, I recommend the following video explaining them:

. Maxwell's Equations have failed attempts at falsification through experimentation enough times to be accepted. You can even fail to falsify them yourself using a power supply, a straight copper wire, iron filings, and a digital multimeter.

Mathematics is not what is being debated on this thread. It is your claim and alleged proof that the speed of light is constant and cannot be manipulated. You presented your proof in mathematical equations that most people on this thread and in this forum will not understand and won't mean anything to them unless they understand the formulas.

If we can all understand you formulas and what they mean, then you will be better able to present your case.

 

[Contenders Edge]

A theory is not a guess. A theory is a concatenation of multiple hypotheses. A hypothesis (in a scientific context) is a proposed explanation for a phenomenon that is testable, repeatable, falsifiable, and parsimonious (Occam's Razor). If the explanation is not testable, repeatable, falsifiable, or parsimonious, then it is not a scientific hypothesis.

So, in other words, a theory consists of multiple explanations whose validity can only be determined by repeatable and falsifiable tests. But that still does not make it a fact.

 

[Contenders Edge]

The proof I gave is derived from Maxwell's Equations. These equations describe the behavior of electromagnetism. First, I derived the electromagnetic wave equation from Maxwell's Equations. Then, I took the second-order partial derivative of the solution to the electromagnetic wave equation with respect to x and the second-order partial derivative of the solution to the electromagnetic wave equation with respect to t. Finally, I substituted the two second-order partial derivatives back into the original electromagnetic wave equation and cancelled duplicate terms to get c.

I assume that the behavior of electromagnetism described in Maxwell's equations are the foundation upon which your belief in the constancy of the speed of light rests. But when you say that you "derived" "substituted" and "cancelled", it may lead some to think that you manipulated the formula in order to produce a favored outcome.

 

[Kaon]

Mathematics is not what is being debated on this thread. It is your claim and alleged proof that the speed of light is constant and cannot be manipulated. You presented your proof in mathematical equations that most people on this thread and in this forum will not understand and won't mean anything to them unless they understand the formulas.

If we can all understand you formulas and what they mean, then you will be better able to present your case.

The equations E and B are solutions to a set of conditions called the Wave Equation - which says the changes in time for the wave function (WF) is proportional to the changes in space for the WF.

The speed of light in a vacuum, for classical phenomena (i.e. non quantum) is considered a constant because of the boundary conditions (constraints) of the Wave finction. We find (through those solutions to the Wave equation) that the speed of light evolves out of the math as a costant and maximum of c ~ 300,000,000 m/s, dependent on magnetic and electric permeability.

Special relativity attempts to juxtaposition general relativity and quantum mechanics. This is where the speed of light c as a constant and maximum begins to break down, and where SR and even basic QM loses some of its substance.

The equations in the OP are evolved from Maxwell's equations for electromagnetic phenomena.

1. The divergence of the fields of a charged particle is equal to the CHARGE (not zero). Think of the electric field as a ball with lines coming out of it. If you measure the volume the lines permeate at a certain radius, it will give you the CHARGE expected in that space.

2. The divergence of the magnetic field is *alegedly* zero. This means the magnetic field curls in spirals as opposed to diverging in straight lines. If you have seen representations of magnetic fields, you can understand why it curls. This also suggests there are no magnetic monopolies (like there exists electric monopoles), but this is also alleged because of the math (if the divergence of a vector is zero, then there exists a vector potential for which the curl of the vector is nonzero; if the curl of a vector is zero, there exists a scalar potential for which the divergence is nonzero. The math tends to explain the physics more.

3. A change in electric field gives a magnetic field

4. A change in magnetic field gives an electric field.

Electrodynamics can be thoroughly proven in the lab, but there are still issues with classical electroydynamics. Depending on your method of information transfer, c can be greater or smaller than the vacuum value.

Entanglement, for example, categorically must exchange information faster than the speed of light (superlunimar).

 

[Michael]

I assume that the behavior of electromagnetism described in Maxwell's equations are the foundation upon which your belief in the constancy of the speed of light rests. But when you say that you "derived" "substituted" and "cancelled", it may lead some to think that you manipulated the formula in order to produce a favored outcome.

I don't think that he necessarily manipulated Maxwell's formulas to produce a favored outcome, but he certainly did make a few important "assumptions" as he made various substitutions/simplifications to Maxwell's equations, as sjastro rightly pointed out:

Excellent; good to see the SF being used as a source of education.
Not wishing to nitpick but perhaps you should have specified this is as the constancy of the speed of light in free space in the absence of charges and currents.
This will explain why Maxwell's first equation takes on the form ▽.E = 0 instead of the more familiar ▽.E = ρ/ε₀, and the fourth equation ▽ x B = (μ₀ε₀)∂E/∂t instead of ▽ x B = μ₀j + (μ₀ε₀)∂E/∂t

In other words, his mathematical 'proof' is only valid in a specific set of circumstances, specifically it only applies to the speed of light in free empty space where no charges or currents are present.

If one assumes a different set of conditions, like the speed of light through a dense material, or in the presence of charges or powerful currents, the speed of light will vary based on those different conditions.

It's a valid mathematical proof about the speed of light in the very simplified instance of empty space. The real "space" as it exists in reality however is full of charged plasma particles and currents. His proof is therefore a bit limited, and applies to oversimplified scenarios, but it's still mathematically valid in the specific conditions that sjastro listed. You and sjastro are correct that gabemaiberger should have included some type of verbal explanation, particularly in the instance instances where he actually deviated from (simplified) Maxwell's actual formulas.

 

[Michael]

Mathematics is not speculation.

Mathematics itself is not necessarily speculative, but the moment it's used in 'physics' to develop "models', it usually is very speculative. For instance, SUSY theory involves a lot of math, but it's also quite speculative, in fact a lot those mathematical models were falsified at LHC. Likewise, the Hubble constant as it's derived from SN1A events doesn't match the same constant as it's derived from Planck data. There's a problem somewhere but it's not necessarily a problem with the math.