No Medium Required For Propagation
19 Jul 2005 14:52:19 UTC
Topic 189567
(moderation:
I was wondering if anyone could, in a sentence or three (or with a reference), help me to understand why combining the principle of relativity with the invariance of the speed of light leads one to conclude that no medium is required for light to propagate? (Neither space, nor time, nor space-time is a medium?)
Is there actually a causal relationship, then, between the speed of light and the permittivity of free space? If “c” defines the permittivity of free space (as it's said), then what defines “c”?
Which would be considered more fundamental – the constant “c” (speed of light in vacuum), or the constant “epsilon_0” (permittivity of free space), or the constant “alpha” (fine structure)? Are they equally fundamental?
No Medium Required For Propagation
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I look forward to what the physicists will provide as an answer, but a decidely non-scientific response: if you mean by medium some kind of 'stuff' that has substance (as opposed to the vacuum which does not), then motion of the medium (relative to the observer) would have to result in a varying speed of light (much as an airplane traveling at 175 knots into a 50 knot headwind only makes 125 knots over the ground). Conversely, an unvarying speed would be hard to explain if light was actually moving 'through' something.
From a semantic or philosophical point of view you could say that space-time is a medium, but what is generally being referred to is some other kind of 'stuff' that resides in space-time through which light moves.
(Of course, if you start to think about what a vacuum is in regards to this you can get yourself all rolled up into logical knots. I don't pretend to understand very much of what physicists mean when they say that all of space is permeated by a Higgs field with a non-zero value, etc....)
RE: was wondering if
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Relativity says that light propagates along null paths ie (t2-t1)^2*c^2-(x2-x1)^2==0. This means that the speed v=(x2-x1)/(t2-t1) allways equals plus or minus c.
the permittivity times the permeability equals the inverse of the speed of light squared in a media.
this one
I don't understand the question. The values of c is usually considered a fundamental constant. Which values and which consants you use depends on the problem you are working on.
Alpha is usually considered a derived constant see
and this one
Thank you, hm. I do feel a
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Thank you, hm. I do feel a bit 'all rolled up into logical knots,' for exactly the reasons you point out.
I think I'm learning that much of this is counterintuitive, and that analogies used to explain certain things can't always be applied the same way in a broader sense.
And thanks (again!), for your help, Mark. As for my question about the constants, it didn't make sense to me that “c” should define “epsilon_0”. It makes more sense to me that “permittivity” would set the limit for “c”, but now I understand how the invariance of “c” must be a more fundamental aspect.
That empty space is full of virtual particles, and that there's (at least mathematical) structure to it such that it inflates, warps, and contracts – these points are still sticklers for me...
The invariance of the speed
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The invariance of the speed of light is baked into the geometry of space-time. This does not disprove the existence of ether. But rather provides an explaination of results of the Michelson-Morley experiment. The ether theory could not do so. For this and other reasons the either theory fell out of favor. Now electro-magnetic fields are considered a thing in their own right.
Michelson-Morley
The values of permittivity, permeability and c in a vacuum are a reflection of the units used ie meter, second, coulomb & ampere. Change one of units and you change the value of one or more of the constants. It is possible by changing the units to make all of the values equal to one. This is done when definig Plank length, time & mass; Newton’s gravitational constant, Plank's constant and the speed of light are scaled to equal one.
What confused me about the 3rd question was the inclusion of alpha. Alpha is a true constant which does not depend on the units used.
RE: What confused me about
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I mentioned alpha to give a respondent a bit more to work with (didn't mean to add confusion, sorry!). And so the 'problem I am working on' would be phrased as an attempt to understand the nature of physical constants on an abstract level where there is some kind of hierarchy to “fundamental”. To me it seems that a constant which is derived is somehow less fundamental than one which is invariant. But isn't alpha also invariant?
You could take alpha to be
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You could take alpha to be fundamental. Then use it together with c & h to define the charge of an electron. This would change the unit of charge from coulomb to name_of_your_choice_here.
I think you are for looking for something deeper than just playing around with units. Alpha and c are a good place to start. I can't help you with any other canidates nearly as good.
Chipper Q, I'm not sure if
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Chipper Q,
I'm not sure if I'm answering quite the question you were asking, but here goes:
First, why do we get light waves at all? Without going through the technical details of Maxwell's equations for the electric and magnetic fields, I'll say qualitatively what they mean: Electric fields point out from (or into) charges (depending on the sign), and magnetic fields curl around currents (moving charges). Those are the main things you notice in a lab (which is full of matter), and historically they were the first to be discovered. If that was the whole story, you wouldn't see much away from matter (charges and currents).
But electric fields also curl around magnetic fields that are changing with time, and magnetic fields curl around electric fields that are changing with time. Those effects were harder to detect, especially the latter which is very weak. So if you set up electric and magnetic fields just the right way relative to each other, and oscillating with time, they can propagate off in some direction and sustain themselves even in vacuum (no charges or currents present) by curling around each other. That's an electromagnetic wave, a.k.a. light. Because you get this mutual curling even in the absence of matter, it doesn't rely on a medium to exist and can be perfectly happy in vacuum (although it does change the speed of propagation).
The definition of units has a lot of semantics in it. (That's more or less the meaning, after all...)
Most physicists would say that alpha is a more fundamental number than c or something; indeed, that dimensionless numbers are more fundamental than any numbers with dimensions. Really what we measure are dimensionless numbers. When I say it is fifty yards to the street corner, what I mean is that the ratio of that distance to the standardized stride of some long-dead English king is fifty. That ratio would not change if I measured both lengths in inches, furlongs, or whatever.
Dimensions, or units, let us distinguish between things that cannot be compared without reference to some other factor. Like I can't define a distance as a time without using some outside information: I can say that my house is four hours from Philadelphia if I use my average driving speed as a conversion. But if I used light speed as a conversion, I would say that Philadelphia is a millisecond away. Contrast this to saying Philly is two hundred miles away - at first that looks just as arbitrary, but really I am saying the ratio of that distance to that English king's stride is 350,000. And that ratio doesn't change no matter what units I use, and I don't need to bring anyone or anything into it except me and the English king.
I hope this helps more than it confuses-
Ben
I can't thank you enough, Ben
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I can't thank you enough, Ben -
I was finding it impossible to understand how light required no medium, and that it was somehow self-regenerating.
As you were explaining this part, I was thinking, “yes, I'm most familiar with these effects when I energize and de-energize the coils in a relay, solenoid, or motor, and I know it as 'electromotive force and counter-electromotive force'.” So when you said -
- it was like a light went on in my head! No medium required. And it's furthermore apparent when any media are present.
Your remarks about alpha are also helpful. Since the time of my original post, I've been trying to gain a better understanding of Planck units (from Wikipedia's page, Planck units) - the section on “Planck units and the invariant scaling of nature” states that the only quantities we ultimately measure are dimensionless ones, as you said...
I would like to add to the “nice guy” accolades you've earned in so many other threads: Your effort here reflects credit upon yourself, the forum, and the scientific community.
Sincerely and gratefully,
Chip