How does the unbreakable speed of light controversy works?

[Psinter]

So I've had many wonders about the whole unbreakable speed of light and what an army of scientists at CERN did. I already know they said it was a broken fiber optic cable or something else which caused that, but let's assume that what they were saying was true, then my questions arises:


Does Einstein actually wrote an equation or formula that states that nothing can travel faster than the speed of light? If so, what is that formula? Is it a mathematical model?


If something were to travel faster than the speed of light, in what would that affect us? I mean, the media says it would be horrible because a lot of experiments would be invalidated (but don't specify what kind or which experiments)

Which theories, theorems, experiments or whatever would be affected by this?

Are there other theories than the theory of relativity (which btw I have no idea what it is... sorry for my lack of knowledge)?

Are there or there have been other scientists that oppose or have opposed Einstein? If there are or have been, who are they?

I have no idea where this whole unbreakable speed comes from so I don't really understand the controversy behind it (I'm like in the void). All the media do is to make super compressed resumes which miss a lot of details and in the end its as if I hadn't read anything at all. I would like to learn more about it, but I don't know where to start, so I thought I'd start here asking these questions. This might be the most stupid post ever considering the other highly intelligent posts here, but I have to try (start with something).

 

[tiny-tim]

I have no idea where this whole unbreakable speed comes from so I don't really understand the controversy behind it …

there's no controversy, don't be silly

the equations and the experiments are perfectly clear … one way of putting it is that things get heavier as they move faster, resulting in it being impossible to cross the speed of light

there are plenty of pages on this forum and on the internet which explain this in varying levels of detail​

 

[K^2]

There is plenty of confusion due to things like tunneling, warp drive, and wormholes, some of which can be mistaken for controversy. But yes, it's all pretty clear cut once you sort the details.

 

[phinds]

The universal speed limit is NOT based on light, but rather photons are just one kind of thing that have to obey the speed limit. ANY massless object has to obey it, and objects with mass cannot attain it. The idea that the speed limit is BASED on light is a misconception.

 

[Psinter]

there's no controversy, don't be silly

the equations and the experiments are perfectly clear … one way of putting it is that things get heavier as they move faster, resulting in it being impossible to cross the speed of light

there are plenty of pages on this forum and on the internet which explain this in varying levels of detail​

My bad then if its not controversy, anyway what you say is what everyone says, they talk about equations but where are they? Where are the so clear equations? I'm going crazy here. Can you give me one equation that could lead me or is it really that much complicated that one equation cannot possibly lead me to understand why matter cannot travel faster than the speed of light?

While searching on this spaghetti of information on the speed of light I found something about Maxwell Equations (but that is Maxwell, not Einstein at all :uhh:). Am I on the right path? Should I keep looking for Maxwell?

Thanks phinds, at least I learned a superficial of what is a massless particle while searching.

 

[Mentz114]

My bad then if its not controversy, anyway what you say is what everyone says, they talk about equations but where are they? Where are the so clear equations? I'm going crazy here. Can you give me one equation that could lead me or is it really that much complicated that one equation cannot possibly lead me to understand why matter cannot travel faster than the speed of light?

While searching on this spaghetti of information on the speed of light I found something about Maxwell Equations (but that is Maxwell, not Einstein at all :uhh:). Am I on the right path? Should I keep looking for Maxwell?

Thanks phinds, at least I learned a superficial of what is a massless particle while searching.

If you want equations, look for the Lorentz transformation.

 

[Michael C]

Here's an equation for you:

$E = \gamma mc^{2}$

In this equation, $E$ is the energy of an object, $\gamma$ is the Lorentz factor, $m$ is the object's mass and $c$ is the speed of light. You need to know that the Lorentz factor is defined as:

$\gamma = \frac{1}{\sqrt{1 - v^{2}/c^{2}}}$

where $v$ is the velocity of the object. As the velocity of the object gets nearer to $c$, the Lorentz factor approaches infinity: you would need an infinite amount of energy to accelerate a massive object to the speed of light.

 

[Naty1]

When Maxwell formulated his equations for electromagnetic waves it was realized they did not have frame of reference...people did not know what to make of that!...so scientists began to try to figure out what was going on and began by hypothesizing an 'ether'...that could explain the apparently 'fixed speed' which Maxwell's equations suggested...

well, as a lot of scientists struggled trying to experimentally verify 'ether' ... along comes Einstein and realizes, wait, electromagnetic waves are light..., the speed of light IS constant,ether is not necessary, it's space and time that are variable,...so everybody will measure the same fixed speed of light...and of course light is just visible electromagnetic radiation.

So in the following original paper, Einstein cleverly 'updated' Newtonian physics, where everything is simultaneous, that is, stuff happens instantaneously, by realzing stuff is 'fast', but not instantaneous...so watch in the paper where he sticks in 'c' representing the speed of light...right in the first pages under 'Simultaneity'...THAT, in my opinion is the revolution...[different observers do NOT see everything 'simulateously' ] ok, read here: maybe it's clearer than what I said above

[edit: no equations, maybe see below first, then read all the interpretations above.]

http://en.wikipedia.org/wiki/Speed_of_light#Fundamental_role_in_physicsAnd here is Einstein's original paper:

On the electrodynamics of Moving bodies...If you know derivatives it's easy...

C:\Users\Owner\Documents\PHYSICS\RELATIVITY black holes,Gravity\On the Electrodynamics of Moving Bodies.mht

 

[Psinter]

Wow, nice. Thank you very much guys. You see, where I come from, most people who talk about the speed of light doesn't provide details of anything. Not the ones that agree that nothing can travel faster, neither the ones who say there are things that can travel faster. It is a huge lack of information and I didn't know who should I believe so I wrote that it was "controversy", but I was wrong, everything is indeed well documented.

Lorentz Transformation clears a lot of doubts I had. Now I see everything a million times clearer (considering I didn't even knew the formulas ) and understand what's going on.

@Naty1, Thanks for the paper, I found it on google by its name. Also, your explanation was more than clear and very detailed (at least for me), thanks.

 

[Tantalos]

If something were to travel faster than the speed of light, in what would that affect us? I mean, the media says it would be horrible because a lot of experiments would be invalidated (but don't specify what kind or which experiments)

Which theories, theorems, experiments or whatever would be affected by this?

Are there or there have been other scientists that oppose or have opposed Einstein? If there are or have been, who are they?

None experiment would be invalidated, the physics laws will still remain the same. Maybe some theories explaining them would change .

The speed of light creates no controversy. Time dilatation does, see f. eg. https://www.physicsforums.com/showthread.php?t=582233

 

[georgir]

The formulas don't directly tell us "FTL is impossible".

They do tell us that a FTL point of view will result in imaginary numbers for lengths and time intervals though, which so far have no reasonable interpretation. Most people interpret that as meaning a FTL point of view is impossible.

They also tell us that for any two points on a FTL trajectory, or in other words two space-like separated events, there exist some reference frames in which one happens before the other, and then other reference frames in which their order is reversed. And even a reference frame in which they happen simultaneously.
This indeterminacy of their order doesn't match well with the idea that one causes or affects the other. It is assumed that causality only works within lightcones, and space-like separated events can not be causally related. So such events can not be from the worldline of "a thing that travels".

An example for exactly this kind of "not quite a thing that travels" is looking at the intersection point of a gilloutine's two edges. With a small angle between the edges and a large (but still far under c) velocity this intersection point is traveling faster than light. But in some moving reference frames it will appear traveling in the other direction, or in one frame it will even seem like the edges are parallel and touch simultaneously everywhere, so the intersection point is not even defined.

 

[K^2]

Actually, no, they don't. Taking a formula with a square root and substituting a negative value for argument does not yield imaginary result. Square root of a negative value is undefined. It's true that it's often possible to take it as a shortcut, but you need to look at the actual equation in hand, and consider whether the equation has imaginary roots.

Because there is an actual singularity at v=c in the Lorentz transforms, you cannot extend them into v>c by simply assuming imaginary roots exist. Certainly, you will come up with a self-consistent algebra, but it has nothing to do with physics.

The only time the v>c imaginary substitution sort of works is with Schwarzschild Metric, and only because the singularity at event horizon is a metric singularity. With a different metric describing the same geometry, you can avoid that singularity all together, allowing for a physically-meaningful continuation. In special Relativity, there is no equivalent. Singularity in Lorentz transforms is a true singularity, and cannot be extended past.

 

[ghwellsjr]

Square root of a negative value is undefined.

I'm sure you meant imaginary, based on the rest of your post.

 

[yuiop]

There is a generic transformation equation (see http://en.wikipedia.org/wiki/Lorent...rmation_matrices_consistent_with_group_axioms) that only stipulates that the laws of physics are the same in all reference frames. It has a parameter k that relates to the maximum possible speed in the system. If we set the maximum speed to infinite we obtain the Galilean transformation and if we set the maximum speed to the speed of light we get the Relativity transformation. Whatever this maximum speed is, it is the same in all reference frames. Maxwell's equations suggest that the speed of light is frame independent so this makes the speed of light a good candidate for the maximum possible speed. If the maximum possible speed was infinite or greater than the speed of light then the speed of light would not be independent of the speed of the source. Experiments have been carried out that confirm that the speed of light is independent of the speed of the source so this rules out speeds faster than the speed of light.

 

[Austin0]

Maxwell's equations suggest that the speed of light is frame independent so this makes the speed of light a good candidate for the maximum possible speed. .

Hi could you explain in easy or non mathematical terms how the equations suggest the invariance??
DO they indicate that the results require interactions between particles to take place at c or something like that , perhaps?
Thanks

 

[tiny-tim]

Hi could you explain in easy or non mathematical terms how the equations suggest the invariance??

maxwell's equations are generated by a 4-dimensional potential (A_t,A_x,A_y,A_z), with A_t usually written as φ, and the other coordinates written as the three-dimensional vector A, thus: (φ,A)

E is then -∇φ - (1/√(ε_oµ_o))∂A/∂t (so it's generally non-conservative, but it becomes the familiar conservative E = -∇φ if A = 0)

and B is simply ∇ x A​

if you know what wedge products (exterior products) are, then ∂ Λ (φ,A) = (E;B), and ∂ Λ ∂ Λ is automatically 0, and maxwell's four equations are just two equations, the geometric equation ∂ Λ (E;B) = 0 and the physical equation ∂ Λ *(E;B) = (ρ,J), but if you don't, just read on …

(i won't write out maxwell's equations here, but …)

maxwell's equations include two constants ε_o and µ_o whose product has the dimensions of time²/distance² …

in other words, 1/√(ε_oµ_o) is a speed!

we want maxwell's equations to apply, with the same ε_o and µ_o, in all inertial frames of reference (like Newton's laws and all other basic laws), and for that to happen, this speed must be the same in all inertial frames of reference​

 

[Austin0]

maxwell's equations include two constants ε_o and µ_o whose product has the dimensions of time²/distance² …

in other words, 1/√(ε_oµ_o) is a speed!

Thanks t-t Sadly I still have confusion.
Maxwell's equations were empirically derived purely from the study of charged particles and did not need or include the speed of light per se, correct?
So in that context. what did the speed derived from the product of the electric and magnetic constants apply to? Change in field potentials at distant locations in response to the motion of particles in other locations?
Other?

1/√(ε_oµ_o)=c
I read that c can be derived from the equations through a different approach but they didn't go into the method.

Thanks for your response

 

[jtbell]

All waves, of whatever type, satisfy a differential wave equation which relates the space and time variations of whatever is doing the "waving." This equation has the same form for all types of waves, the only difference being the name of the variable that represents the quantity that is "waving." This equation includes the speed of the wave as a constant whose value depends on the type of wave. (Google the term to see what the equation looks like, in general)

Starting from Maxwell's equations, we can derive differential wave equations for the electric and magnetic fields. In the spot where we expect to find the speed of the wave, both of these wave equations have the combination $1/\sqrt{\mu_0 \epsilon_0}$, which tells us the speed of electromagnetic waves.

 

[Austin0]

All waves, of whatever type, satisfy a differential wave equation which relates the space and time variations of whatever is doing the "waving." This equation has the same form for all types of waves, the only difference being the name of the variable that represents the quantity that is "waving." This equation includes the speed of the wave as a constant whose value depends on the type of wave. (Google the term to see what the equation looks like, in general)

Starting from Maxwell's equations, we can derive differential wave equations for the electric and magnetic fields. In the spot where we expect to find the speed of the wave, both of these wave equations have the combination $1/\sqrt{\mu_0 \epsilon_0}$, which tells us the speed of electromagnetic waves.

SO then the electric field is changing in response to electric waves propagating from charged particles at c and likewise the magnetic field?
Thanks for the help

 

[PhilDSP]

Maxwell's equations were empirically derived purely from the study of charged particles and did not need or include the speed of light per se, correct?

It's probably more accurate to say that Maxwell's equations were derived on the basis of a theory that accounted for the empirical results of the study of charged particles (Faraday's and to a lesser extent Ampere's experiments)

From the experimental determination of $\epsilon_0$ and $\mu_0$ and his brilliant linking idea of displacement current (which was then and is still not measurable) he determined that the displacement current traveled at approximately the same speed as light and then proposed that light was in fact the periodic variation of the displacement current (which can be considered the periodic variation of E and B fields)

SO then the electric field is changing in response to electric waves propagating from charged particles at c and likewise the magnetic field?

The electric waves consist of the variations of the electric field (propagating from charged particles at velocity c in a vacuum). But the fundamental question to which there was great controversy is whether the velocity c (or the equations themselves) are still valid if the local charge that you are using to measure the E and B fields is moving either with respect to the emitting charge, or to an electromagnetic medium possessing physical attributes such as momentum.

 

[elfmotat]

SO then the electric field is changing in response to electric waves propagating from charged particles at c and likewise the magnetic field?
Thanks for the help

No. EM waves don't require charges, nor would a uniformly moving charge create an EM wave. What's actually going on is that a changing electric field produces a changing magnetic field, and vice versa. An EM wave is just E and B fields continuously changing and producing each other.

 

[Austin0]

No. EM waves don't require charges, nor would a uniformly moving charge create an EM wave. What's actually going on is that a changing electric field produces a changing magnetic field, and vice versa. An EM wave is just E and B fields continuously changing and producing each other.

I understand what you are saying here but you seem to be referring specifically to photons.
I was not interested in that, but wanted to know how the speed derived from the product of the electric and magnetic constants related to other elements of electrodynamic interactions.
If a moving charge is introduced into a static field I would assume that the whole field would not respond instantaneously. That the various changes; flux,potential, whatever [my understanding of the subject is maddeningly sparse] would propagate from that point ,is this not correct??
How do these propagate and at what speed?
From what I am reading it sounds like the speed was already in the math before Maxwell even made the realization of light as being electromagnetic waves.
Thanks

 

[Austin0]

From the experimental determination of $\epsilon_0$ and $\mu_0$ and his brilliant linking idea of displacement current (which was then and is still not measurable) he determined that the displacement current traveled at approximately the same speed as light and then proposed that light was in fact the periodic variation of the displacement current (which can be considered the periodic variation of E and B fields)



The electric waves consist of the variations of the electric field (propagating from charged particles at velocity c in a vacuum). But the fundamental question to which there was great controversy is whether the velocity c (or the equations themselves) are still valid if the local charge that you are using to measure the E and B fields is moving either with respect to the emitting charge, or to an electromagnetic medium possessing physical attributes such as momentum.

SO this does sound like there is propagation of field fluctuations from charged particles that are not photon emissions [unless virtual photons ;-) ,,] but propagate at the speed of c

Is this correct?? Is this from the $\epsilon\mu$(∂E/∂t) term in the fourth equation?
Thanks for your help

 

[PhilDSP]

What's actually going on is that a changing electric field produces a changing magnetic field, and vice versa. An EM wave is just E and B fields continuously changing and producing each other.

That's actually a faux pas. If you think about the fact that the wave equation for the E field is fully independent but of the exact same form as the wave equation for the B field that should become clear. There is no casual dependence between the E and B fields as Jefimenko has proven:

http://en.wikipedia.org/wiki/Jefimenko's_equations

 

[PhilDSP]

SO this does sound like there is propagation of field fluctuations from charged particles that are not photon emissions [unless virtual photons ;-) ,,] but propagate at the speed of c

Is this correct?? Is this from the $\epsilon\mu$(∂E/∂t) term in the fourth equation?
Thanks for your help

According to the theory developed by Maxwell, yes, whenever a charge moves there must be an accompanying displacement current or polarization reaction. It seems reasonable to model that using virtual photons. It's only when a photon is emitted (typically from accelerated charges) though, that such a disturbance will be self propagating (as a traveling wave).

Note that $\epsilon_0$ and $\mu_0$ (constants) apply only in a vacuum. So within a vacuum, displacement current (and EM waves as a special type of displacement current) moves at c. Within media they become not constants but either scalars or tensors depending on the nature of the media.

 

[Austin0]

That's actually a faux pas. If you think about the fact that the wave equation for the E field is fully independent but of the exact same form as the wave equation for the B field that should become clear. There is no casual dependence between the E and B fields as Jefimenko has proven:

http://en.wikipedia.org/wiki/Jefimenko's_equations

Thanks for the link. Certainly seems logical that an electron intrinsically produces both fields.

Am I right in assuming the causal dependence was inferred from the phenomenon of inductance ?

I always had a problem understanding how, if the two aspects were mutually creative, a photons fields were out of phase. One's magnitude increasing while the other's was decreasing?

 

[Austin0]

According to the theory developed by Maxwell, yes, whenever a charge moves there must be an accompanying displacement current or polarization reaction. It seems reasonable to model that using virtual photons. It's only when a photon is emitted (typically from accelerated charges) though, that such a disturbance will be self propagating (as a traveling wave).

Note that $\epsilon_0$ and $\mu_0$ (constants) apply only in a vacuum. So within a vacuum, displacement current (and EM waves as a special type of displacement current) moves at c. Within media they become not constants but either scalars or tensors depending on the nature of the media.

I really want to thank you. I have posted previous queries about this question with no joy.
I had also investigated both the Maxwell equations and the constants but never recognized that the product of a measure of resistance to flux, and a measure of force could reduce to a simple unqualified speed.

$\epsilon_0$ and $\mu_0$ yes I was just too lazy to add the subscript.

Actually the concept of virtual photons in this context seems to be as clunky and unlikely as a corpuscular static ether. So I prefer the original conceptualization of spreading waves as opposed to wave packets with the limits of localization.
thanks again for your lucid explication.