Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Luke Pullsy on 08/12/2016 22:31:31
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Hello all. First post and all, so let's hope it is a good one!
As per the title: What limits the speed of light in a vacuum? Why does it have an arbitrary velocity?
Thanks!
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Worth reading up on Maxwell's equations, which explain how selfpropagation of an electromagnetic wave works at a constant speed - essentially because the properties of a vacuum can't change (there being nothing there to change).
Which rather questions your use of "arbitrary". If anything, the speed of light is the necessarily fixed quantity in the universe, and we choose arbitrary units of length and time to measure it. When I was a lad, c was around 186,000 miles per second, and now it's around 300,000,000 meters/second, and both the meter and the second have new definitions too. If you have a mind to, you can calculate it in millifurlongs per microfortnight, but it's a fixed quantity thanks to the total absence of stuff in a vacuum.
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I'm interested in the answer to this too.
Worth reading up on Maxwell's equations, which explain how selfpropagation of an electromagnetic wave works at a constant speed - essentially because the properties of a vacuum can't change (there being nothing there to change).
I don't have a great math/physics background, but after looking into Maxwell's equations, I see a formula that defines the speed of light in relation to the permittivity (electrical field resistance) and permeability (magnetic field resistance) of a vacuum.
So, why does a vacuum have the specific permittivity and permeability that it does?
(I know that the units of measurement for vacuum permittivity and vacuum permeability are arbitrary, but I'm asking why they don't have values which are not equal to their current values)
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You could base your entire physics on the permittivity and permeability of free space being any value you choose, say 1, and define all your other units from the speed of light, but you would end up with inconvenient units of time and length. Historically we chose the meter, kilogram and second to be convenient for engineering and commerical purposes and related to accessible mesoscopic natural quantities such as the length of a day, the circumference of the earth, and the density of water, that appeared to be adequately constant. The requirement for greater precision and reproducibility has led to the redefinition of base units but their magnitude hasn't changed and latecomers such as permittivity and permeability thus end up with the numbers we have.
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Right, but I'm not asking why the permittivity and permeability have the numbers they have, I'm asking why they are at the strengths that they are at.
Let me ask it this way:
Why are the permittivity and permeability of a vacuum non-zero and non-infinite?
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Worth reading up on Maxwell's equations, which explain how selfpropagation of an electromagnetic wave works at a constant speed - essentially because the properties of a vacuum can't change (there being nothing there to change).
That's not why the speed of light is invariant. I used to believe the same thing until I mentioned it who was more knowledgeable than I am who then explained it to me.
The fact is that nobody really knows why c is invariant. Maxwell's equations cannot be used to prove it either, the reason being that one must postulate that photons have zero proper mass when using Maxwell's equations. If the proper mass is non-zero then one can derive the appropriate version of Maxwell's equations using the Proca Lagrangian. So the invariance of the speed of light is theoretically equivalent to a zero proper mass for photons.
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But that presumes that Maxwell began with quantised photons, which he didn't. As I recall (from a lecture I attended 53 years ago!) the derivation of the equations for a selfpropagating wave is based on classical continuum electromagnetics only.
The broad philosophical statement is also surely axiomatic: if a wave can selfpropagate through a vacuum, its speed must be invariant because by definition its "medium" is invariant and isotropic.
Admittedly this doesn't explain why the apparent speed is independent of the speed of the source and observer, for which I defer to my learned friend Pete.
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The broad philosophical statement is also surely axiomatic: if a wave can selfpropagate through a vacuum, its speed must be invariant because by definition its "medium" is invariant and isotropic.
But that depends on Maxwell's equations being correct and the correctness depends on the second postulate, i.e. the invariance of the speed of light. In modern physics when one attempts to show that an EM wave is invariant one has to plug in the value of the proper mass of the photon. When one derives the wave equation which is invariant one is typically assuming that the proper mass is zero. When you look at Maxwell's equations you're almost always going to see them in the form where the proper mass is zero.
Admittedly this doesn't explain why the apparent speed is independent of the speed of the source and observer, for which I defer to my learned friend Pete.
Thank you my friend. I'm honored! :)
I have friends who's a renowned experts on this subject. I'll e-mail them and see how they explain all of this. After all, only a fool thinks that they can't be wrong. :)
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James Clerk Maxwell [1831-1879] was an Einstein/Newton-level genius who took a set of known experimental laws (Faraday's Law, Ampere's Law) and unified them into a symmetric coherent set of Equations known as Maxwell's Equations. Maxwell was one of the first to determine the speed of propagation of electromagnetic (EM) waves was the same as the speed of light - and hence to conclude that EM waves and visible light were really the same thing.
The constancy of c was only determined experimentally in 1887, when Maxwell was well dead, so it can't be germane to the equations. Indeed it isn't.
Unfortunately I can't reproduce partial differentials here, but http://maxwells-equations.com/equations/wave.php tells it like I remember it from my student days. You start with the experimental laws of induction and you end up with the second spatial differential of the E vector being a constant times the second time differential, an equality that is satisfied by a wave travelling at constant speed.
It is true that nowadays it is easier to teach physics from a relativistic standpoint, assuming from the outset that c is constant and working towards some very neat experimental results like Pound-Rebka, Haefle-Keating and pair production, but they don't answer the question of why c is constant and what value it should have, whereas Maxwell starts from very simple laboratory observations that magnetic field is proportional to current and induced voltage is proportional to the rate of change of field. Even in the absence of the normalising constants, these statements are all you need to derive the Maxwell equations and hence prove that c is a constant.
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To begin with, I consider the title of this thread to be somewhat misleading. In the vacuum of space, "there is nothing limiting the speed of light". While we see light speed slowed when passing through a material medium, in free space, no such interference is present. So in the vacuum of space, where light is permitted to travel at it's maximum velocity, it agrees with our predicted theory regarding the permittivity and permeability of free space.
Maybe the question should be: "Why does light have a maximum speed?"
The answer would of course be the answers both Pete and Alan have given.
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What exactly does in a vacuum mean? The speed of light is slowed in a medium. Does this imply that the vacuum is not a medium? Otherwise is it the perfect medium? Light has to travel at some finite speed otherwise, if the speed were infinite, it wouldn't interact with the universe and all would be darkness and devoid of information. This also raises the issue of the connection between the speed of light and the dilation of time.
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Light has to travel at some finite speed otherwise, if the speed were infinite, it wouldn't interact with the universe and all would be darkness and devoid of information.
That's an interesting comment, Jeffrey. As you can probably believe, I've made several attempts to visualise infinite speed, and to understand its implications; but I'd never really considered its interaction (or lack thereof) with the rest of the Universe. Perhaps you could say a bit more about this lack of interaction?
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How can a wavelength be defined when the particle covers an infinite distance in zero time. Not only is the particle present at every point along its path simultaneously but its energy will be zero. A zero energy particle by definition cannot interact.
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The vacuum is not a medium. The speed of light is calculable from first principles and directly measurable. What's the problem?
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The vacuum is not a medium. The speed of light is calculable from first principles and directly measurable. What's the problem?
That is the point. The vacuum ISN'T a medium.
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I'm currently working at a new concept and it says propagation of values of all fields happens at the same constant speed. Light waves travel straight and thus the forward speed is c. Particles with mass travel in a helix /6 spiral and thus the forward speed is reduced, but the internal field propagation is at the same constant speed c. Thus c limit becomes obvious for non zero mass particles. The c limit for light is the natural propagation speed of EM waves and is not a limit but the speed the propagation it is always happening. It feels natural for fields to travel at a certain speed rather than infinite. Infinite speed would be unimaginable and a universe like that wouldn't work. The value 3 10^8 m/s is because the conventions we use when defining dimensions. The only importat thing is that is constant and non infinite.
The reason why c is not variable is because the propagation environment and propagation mechanics don't change. Why would they ? There is no reason to change. Also the fundamental waves that compose other particles propagate the same way. In other words there is a single fundamental speed in the universe. Speeds below c are apparent. If you send a light beam through a channel with mirrors and it is goes in a zigzag pattern, it reaches the observer slower but the wave has traveled the same speed. The apparent speed is lower. Otherwise you would say look only c is constant. All other particles travel a various speeds. That is not the case in my opinion.
GR limits the particle speed justifying that to accelerate a particle to c you need infinite energy and sometimes people ask what would happen if you exceed this limit. Some even think that would mean going back in time. My model seems more natural to me. Exceeding c is clearly impossible and also there is no reason to thing of going back in time.
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How can a wavelength be defined when the particle covers an infinite distance in zero time. Not only is the particle present at every point along its path simultaneously but its energy will be zero. A zero energy particle by definition cannot interact.
Wouldn't a standing wave satisfy the requirement? It would have a finite wavelength.
Can you explain the relationship between infinite speed and energy needing to be zero for me?
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Standing waves can be thought as infinite speed or zero speed, I think, but only after they have been established. However to create it, the propagation goes from the source to the end where it gets reflected and comes back to interfere with the waves at the source and afterward that it becomes stationary. Basically the propagation is at the same constant speed and the infinite zero speed seems an illusion. That is how I understand it.
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propagation of values of all fields happens at the same constant speed. Light waves travel straight and thus the forward speed is c
Physicists think that gravitational waves also travel at c (in a vacuum, when measured in your lab).
How does this theory explain the reduced speed of light (and other particles) when a distant observer monitors events happening closer to a black hole?
Note: We have a section called "New Theories" which is the natural home, if you want to explore new theories...
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I haven't analyzed this process from my model poiny of view. One way can be the trajectory deviation of light by frame dragging. As it approaches the BH it is deviated until it gets into an orbit around it.
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Maxwell's equations, etc.
That's not why the speed of light is invariant. I used to believe the same thing until I mentioned it who was more knowledgeable than I am who then explained it to me.
The fact is that nobody really knows why c is invariant. Maxwell's equations cannot be used to prove it either, the reason being that one must postulate that photons have zero proper mass when using Maxwell's equations. If the proper mass is non-zero then one can derive the appropriate version of Maxwell's equations using the Proca Lagrangian. So the invariance of the speed of light is theoretically equivalent to a zero proper mass for photons.
I'm still not sure I understand this.
Imagine I invented a machine that can change the permittivity and permeability of the vacuum.
According to Maxwells equations, the calculated speed of light would change.
So the question is, would the actual speed of light change in response to my machine, or the equation just a description of a coincidence?
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Would be nice to hear from JP on how Maxwell thought about EM, I suspect he's pretty knowledgeable on that.
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Then again, it's a theory, and it still works as far as I know. It may change at some time, but I don't think so myself. 'c' is 'c' in all experiments I've read about. And I also think it gives the wrong idea discussing it as being 'limited'.. Saying that it is a constant is more correct, although I do call it a limit myself at times.