# How does the unbreakable speed of light controversy works?

by Psinter
Tags: controversy, light, speed, unbreakable
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PF Gold
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 Quote by Psinter 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
 Sci Advisor P: 2,462 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.
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## How does the unbreakable speed of light controversy works?

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.
P: 51
 Quote by tiny-tim 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 ). 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.
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 Quote by Psinter 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 ). 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.
 P: 132 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.
 PF Gold P: 5,551 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_o...ole_in_physics And 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
 P: 51 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.
P: 46
 Quote by Psinter 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 physic 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. http://www.physicsforums.com/showthread.php?t=582233
 P: 104 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 travelling faster than light. But in some moving reference frames it will appear travelling 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.
 Sci Advisor P: 2,462 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.
PF Gold
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 Quote by K^2 Square root of a negative value is undefined.
I'm sure you meant imaginary, based on the rest of your post.
 P: 3,793 There is a generic transformation equation (see http://en.wikipedia.org/wiki/Lorentz...h_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.
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 Quote by yuiop 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?
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 Quote by Austin0 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 (At,Ax,Ay,Az), with At usually written as φ, and the other coordinates written as the three-dimensional vector A, thus: (φ,A)
E is then -φ - (1/√(εoµo))∂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 εo and µo whose product has the dimensions of time2/distance2

in other words, 1/√(εoµo) is a speed!
we want maxwell's equations to apply, with the same εo and µo, 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
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 Quote by tiny-tim maxwell's equations include two constants εo and µo whose product has the dimensions of time2/distance2 … in other words, 1/√(εoµo) 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/√(εoµo)=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
 Mentor P: 10,729 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.

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