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#1




Speed of Light (revisited). Permeability and Permittivity
I started a thread on this a log time ago asking why is the speed of light the value that it is. Unfortunately that thread degraded into a discussion of units that amounted to "it's the speed it is in the units we measure it in" which doesn't really answer the question.
I found out that the speed of electromagnetic wave is inversely proportional to the magnetic permeability and electric permittivity of a vacuum. OK, that makes sense and I thought I understood how permability works it is the ability of a magnetic field to be formed in a vacuum (excuse my layman explanation and correct me if I'm wrong) but I don't understand permittivity. It is in effect the capacitence of a material right? How can a vacuum "store" electrical charge?
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When I was a boy, a mere lad, A FAERIE APPEARED UNTO ME AND TOLD ME I WOULD BE BOTH POPE AND KING! But … I am a bastard. And a pretender. Richard Hariss 
#2




It's not the vacuum storing charge; it's how much electric field a charge produces. That's one of the things that determines how strong a capacitor will be, but capacitors aren't the only thing it's relevant for.

#3




Particles like electrons and protons, not an empty vacuum, carry electric charge, but surrounding a charged particle is an electric field, even if the particle is sitting in a vacuum. (One may ask interesting questions about how two particles separated by a vacuum can actually exert a force on each other...)

#4




In God's physics book, space and time are measured in the same units, the speed of light is equal to one, and the equations of physics never have the speed of light in them. We didn't understand that when we started choosing units, so we are stuck with a number for the speed of light that is very large in our units and seems arbitrary, but the value is just a feature of the arbitrary units we chose.
God's physics book says the vacuum electric permittivity and the vacuum magnetic permeability are reciprocals of each other, so when you multiply them together you get one. Now we are back to the situation that you mentioned was the outcome of a previous thread. I assert, however, that it really does answer the question. 


#5




So is it fair (though simplistic) to say vacuum permittivity is a measure of how far an electric charge extends out in a vacuum?

#6




There's a thread asking a similar question here:
https://boards.straightdope.com/sdmb...d.php?t=876002 In which may I direct you to Francis Vaughan's at post #36, which I thinks is a very clear explanation that may help you to understand what it means to say it's "just the units": https://boards.straightdope.com/sdmb...6&postcount=36 Also, the finetuning problem is an unresolved question in physics somewhat similar to what your asking, why does our universe have the parameters that it does? But if you read about that, you'll see that for similar reasons it only makes sense to ask such a question about dimensionless physical constants, such as mass ratios, where there are no arbitrary units. Last edited by Riemann; 10232019 at 12:21 AM. 
#7




Not at all, since it extends infinitely far, though the strength drops off (inversesquare law). Also you probably meant "electric field" instead of "electric charge"; charged particles like electrons are really small.

#8




Speed of light and relativity (tangentially related)
I saw this recent thread and thought I might be permitted to ‘check my math’ before responding to a poster on a different board who’s not understanding the SoL, time dilation and relativity.
I’m using the familiar example of the ‘superfast car with its headlights on’ that manages a speed of 0.999c, racing against a parallel light beam. The ‘course’ is a straight line over one light day distance. Probably dozens of examples like this scattered over the internet that might help, but I’d prefer it if it’s in my own words. From the perspective of the race official at the starting line, both the car’s headlight and the light beam go forward and reach the halfway point at the same time (twelve hours), with the car itself only slightly behind. Similarly, he observes the race finishing a further twelve hours later, with the light beam and headlight arriving at the same time and the car a short way behind. He notes the car’s clock appears to be a little slow though. From the perspective of the race driver, his headlights (and the light beam) rush off ahead at a speed of 1.0c relative to him. Once he’s nearly at half way, he sees both headlight and light beam ‘arrive’ at the finishing line, even though only twelve hours have passed on his clock. The race driver reaches the finish line a short time after one full day according to his own clock. Where my math is needing the finetuning is in getting an idea of the relative times showing on the race official’s clock according to the race driver at the halfway point. If it’s clearer to use a different course length in order to emphasise the differences, I’m ok with that. What would be superhelpful would be some kind of animated cartoon version of this, if anyone’s seen anything like that? Apologies for a slight derailment, but I felt the topic was close enough (and with sufficiently expert posters around) to chance my arm. Thanks. 
#9




Your problem (one car sitting still, another passing it at a substantial fraction of the speed of light) is completely symmetric, so you should be able to work it out from that (they both experience "time dilation" where the moving clock appears to tick slower).
Similarly, a stationary electric charge is moving in a different frame of reference, so one observer will detect a magnetic field where the other does not. 


#10




For all of those saying it's about the units (yet again) miss the whole point of the question. The correct answer is, as I pointed out in post #1, it is the inverse of the geometric mean of the vacuum permeability and permittivity. It's about the velocity and not how we measure it. That's a tautology  it's speed is 299792458 m/s because it goes 299792458 meters every second does NOT answer why that particular speed whereas if you say that it is that particular speed because as an electromagnetic wave the speed is depends on how easily magnetic and electric fields can form in a vacuum, well now that seems obvious.

#11




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In your second question about permeability and permittivity are you asking if those properties are limitations on the speed of light that cause it to be the particular speed we measure it as? Do you mean something like the speed of light is the fastest an EM wave can propogate because of those properties? I think you have to reword your questions some way that doesn't sound like "why is the speed of light what it is?" If I'm not reading you at all then please forgive me, just trying to help. 
#12




You could say that it's the inverse of the geometric mean of the electric and magnetic constants, but that's just because those constants are the inverses of each other.

#13




I'll echo TriPolar.
The "it's just the units thing" is a foundational piece of the answer, and I think it isn't clear whether that piece is mutually agreed yet. To rehash Chronos's example from the thread linked to by Riemann: If we thought height and width were fundamentally different types of measurements, we might measure them in different units like centimeters for height and inches for width, and in that world, the constant c = 2.54 cm/in would show up all over physics. But obviously height and width are two dimensions in a single space, and treating them differently is clumsy and artificial. The exact same thing is true of space and time. We treat them differently, so the constant c = 3x10^{8} m/s shows up all over physics. But less obviously space and time are two dimensions in a single spacetime, and treating them differently is clumsy and artificial. In the first example, why is the number "2.54"? It's because one billionth of the distance between the north pole and equator (the height standard) is 2.54 times bigger than one twelfth the length of a typical adult male's foot (the width standard). Clearly arbitrary. In the second example, why is the number "3x10^{8}"? It's because one ten millionth of the distance between the north pole and equator (the space standard) is 3x10^{8} times bigger than the time it takes the earth to complete 1/86400 of a rotation (the time standard). Clearly arbitrary. In the first example, I compared height with width, and you're okay with that. In the second example, I compared spatial distance with temporal distance. Are you okay with that? There equivalence as two different directions in a single space (or spacetime) is as fundamental as height v. width. This needs to be established before the values of permittivity and permeability can be directly discussed. 
#14




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We have this length here called a meter. We also have this duration of time called a second. The reason the speed of light is 299792458 m/s is because it travels 299792458 of these distance during this duration of time. But why that distance over that time? Why not 100000 m/s? Because that would be different units. Different example: Suppose I ask why the Bugatti Veyron has a top speed of 267.856 mph. I'm looking for the engineering reason but y'all are saying it's all about the units. That's the top speed because it's intantaneous velocity has a maximum of 267.856 mph. No, I say, what is the physics/engineering where that is it's particular top speed. Why does it go that fast but no faster. You sigh and look over your glasses at me. Well you could say it goes 431.072 km/h but that's because kilometers are different units than miles. I persist. No, what is it about the engine, aerodynamics, tires, road surface, etc. where it's top speed is 267.856 mph. Why can't it go 300 mph? Because those would be different units. So I'll take TriPolar's advice and ask it a different way. What would I have to change in the universe: permeability, permittivity, fine structure constant, magnetic monopoles, making McRibs permanent, etc. that would cause the speed of light to change independent of units  like changing this constant 4% would cause light to slow 7% from where it is now. 


#15




I think there's a bit of miscommunication here.
If I'm reading the OP right, the question is not one of units, it's why fundamental constants take the particular values they do. That is, it doesn't matter to the OP if c is 3*10^8 m/s or 51.6 quatloos per whatsit but why is it that particular value at all? Why isn't it 4*10^8 m/s with the 'same' meter and second as now (if these units can even have a meaningful definition in such a universe)? Could such a universe even support life as we know it? This is more of a philosophical question than a scientific one (see: Anthropic Principle) and there's been a lot of thought put into it but no satisfactory answers. Last edited by Great Antibob; 10232019 at 04:39 PM. 
#16




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And this may be wrong, but it's the only way I can conceive of this stuff, but the speed of light just "is", and everything else works because that's the speed it is. Last edited by TriPolar; 10232019 at 04:43 PM. 
#17




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It remains true that the primary answer to the OP's question is "it's just the units". Last edited by Riemann; 10232019 at 05:27 PM. 
#18




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A tangent, in case it is new and/or helpful: Electric fields and magnetic fields are not really different things. They are two ways of looking at one thing, electromagnetic fields. If you have an electric charge (say an electron) and you are moving relative to it, that electric charge creates both electric and magnetic fields. Mathematically, we talk about the electromagnetic field (or potential), a single beast, but humans have chosen to also give names to different aspects of this beast. In particular, the piece that shows up when you are stationary relative to the charge is the "electric" field and the piece that shows up when you are moving relative to the charge is the "magnetic" field (plus still a piece that looks a like an electric field). If you start with basic electrostatics and you do nothing else except introduce Special Relativity (i.e., the very concept that says that time and space are two directions in a single spacetime), then voila, you have magnetism. Magnetism is not a separate thing. It is an emergent phenomenon that happens when there is relative motion between electric charges and observers.* With this in mind, it is clear that physical constants that relate to the notatallfundamentally distinct E and M will be related. In the cgs (or Gaussiancgs) unit system, there is no such thing as permittivity or permeability constants. Coulomb's law reads F=q_{1}q_{2}/r^{2} and the Lorentz force reads F=q(v/c x B). No misleading constants hither and yonder. Electric fields and magnetic fields are measured in the same units. If one jams in historical choices for some units like electric charge, then those choices need to be canceled out elsewhere in the math. This is why permittivity and permeability show up in SI units and why they are reciprocals of one another. The fact that c also shows up in SI units reflects the other piece of historical gummingup, namely that special relativity was not considered when choosing units for measuring distances (spatial and temporal). Another aside: In F = q(v/c x B), notice the quantity "v/c". Physicists give this ratio a different symbol often: b (beta). This is because b is the fundamental quantity, free from human artifacts. When b=0, you are moving through time at 1 second per second. When b=1, you are moving through space at 1 second per second. (Notice that I've used "second" as the fundamental distance unit here.) When b is between 0 and 1, you are moving through space and time. Trying to have permittivity and permeability change to influence how c comes out is the tail wagging the dog. Distances in space and distances in time are the same type of thing, full stop, and if you choose to measure them in different units, then you automatically introduce arbitrary, nonfundamental choices that lead to physical constants like c, e_{0}, and m_{0}. The presence of all these constants is not fundamental. They overspecify the system. If you change one, you must change others to compensate or the math breaks. Much better is to rationalize the unit system (as is done regularly, just not in SI) to remove the "false" constants. _{* Purely classical picture here. Quantum mechanics would be an irrelevant distraction.} 
#19




A related question that may (or may not) shed some light on the OP's question.
Is the speed of light constant in an accelerating frame? If I take a tube that bounces light back and forth, and flashes at either end when it reaches it, will I, or will an observer, see those flashing lights slow down, as I am accelerating? If I take an atomic clock and put it under my feet, (in a gravity field, like on Earth) it will tick slower than if I lift it over my head. Would the same hold true for my light tubes? Last edited by k9bfriender; 10232019 at 06:13 PM. 


#20




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#21




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Constructing arbitary accelerated frames in special relativty is problematic, but you can setup a reasonable coordinates for an observer undergoing constant linear (proper) acceleration, called Rindler coordinates. That's not to say Rindler coordinates are on a equal footing as nonaccelerated Lorentz coordinates, for example Rindler coordinates fail to cover the whole of spacetime. In Rindler coordinates the coordiante speed of light depends on the distance from the observer along their axis of acceleration and the acceleration of the observer. However it is worth noting that if your goal is to setup reasonable coordinates for the same observer where the coordinate speed of light is constant you could also do that. 
#22




It's perhaps worth mentioning that James Clerk Maxwell was a hipster: Electromagnetism was relativistic before relativity was cool. Maxwell managed, without even having a clue about relativity, to construct a complete and relativisticallycorrect theory of electromagnetism, and Einstein's work didn't require any changes at all to that theory. In fact, it was by studying the relativistic nature of Maxwell's equations that Einstein was inspired to develop the theory of relativity for everything else.

#23




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ASAIK, this speed does not arise from any other set of values. Neither do other critical dimensioned constants like G or h, for that matter. There just are. Why? I don't know. Third base. I understand that "they just are" is an unsatisfying answer. It's a major reason why many physicists believe that we haven't yet gotten to the bottom of what makes the universe go. But asking the same question in different words will get you the same answer. The speed of light is the speed of light because that's the answer the universe gives us. I could be all wet in saying this, to be sure, and our physics folk will correct me. But I think the communications gap here is simply that they want to explain physics to you and you want to hear an answer that's not there. 
#24




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When we say that time and space can be measured in the same units, that's declaring that humans do of course have a choice to introduce the complication of using different units. But as far as the math behind the physics is concerned, they must be the same under the hood, regardless of human choices. There is no ratio here. Let's look at rotations in our height v. width example. I have a stick that that is horizontal, and the distance between its two ends is 10 inches. If we insist on measuring height in centimeters, though, what happens if I rotate the stick vertically? Now the distance between its two ends is 25.4 centimeters. But we know the length of the stick didn't change because we know how rotation works. But if we insist on the different units, then we need to bake in some conversion factor between distances (lengths) measured in these two orientations. And if we rotate the stick at an angle between 0 and 90 degrees from horizontal, calculating the length of the stick is even more messy, since we have to measure the "width" part and "height" part separately and then combine them with an appropriate conversion. This is all intrinsic to how geometry works, and we would never dream of introducing this complication. The same exact thing holds for spacetime. It's intrinsic to the geometry of spacetime that distances in time and distances in space are the same thing. If you have a spacetime "stick" measuring distances between two points in 4d spacetime, and you rotate that stick, its length does not change. When you rotate a stick in 2d or 3d space, you change its angle (a unitless number). When you rotate a stick in 4d spacetime, you change its b (a unitless number, defined upthread, v/c). The math of rotations is a little bit different for spacetime than for 3d space, as is the "Pythagorean theorem"equivalent (with which one calculates distances between two points) but that's no biggie. In both the 3d and 4d cases, all directions are fundamentally equivalent. This is a bedrock of modern physics. Any  any  numerical value that purports to distinguish between space distance and time distance is 100% human introduced. Trying to deviate from this equivalence in the math violates how the universe works experimentally. If this remains an unsatisfying answer, the next step is probably to look into special relativity and some of the introductory thought experiments (and real experiments) there. Those experimental results require what is said above. There is no c.* _{*Get this on a tshirt, somebody!} 


#25




Yes. At least from the photon's reference frame.
If photons don't experience time, if a trip across the universe is as instantaneous to them as a trip past a proton, then their speed is effectively infinite. They are going the fastest possible speed, infinity. 
#26




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If we avoid the mathematical pitfalls of v=c and instead take the limit v>c, then the above interpretation is sound. Time "perceived" by any object is always one second per second, no matter how close to c it gets relative to an outside observer. To that outside observer, the moving object appears to moving through time very slowly. But that is importantly not what the object experiences. It experiences the normal flow of time, although the distance to its destination is very short, so it doesn't take long to get there. (This contradicts some of the statements in your link. This post is right, and the link is wrong. ) 
#27




That said, it is sometimes meaningful to compare the time experienced by an observer, compared to to the distance between two points as measured in the reference frame where they're simultaneous. The ratio of the two is called the "proper velocity", and even though it's a bastardized mix of reference frames, it makes some calculations a lot simpler.

#28




Our experts here are trying to answer a physics problem. But that's not truly what the OP asked. That was a people problem.
The layperson sees 299792458 m/s and asks, as Saint Cad explicitly did, "Why not 100000 m/s?" This is an eminently reasonable question from a layperson and, to my understanding, has a eminently reasonable answer. Because. Note that this is not a question about units. The ratio of proton to electron mass, 1836.15267343, is dimensionless, but a layperson can reasonably ask: why not 1932.8790347? That answer, again to my understanding, is because. From everything I've read we don't know why, nor can we derive these numbers from first principles. Nor are the values of no interest to physicists. Major names in the field have been arguing about the dimensionless fine structure constant, 0.0072973525693, both why it is that number and whether it is really a constant, for 100 years. "Why that number?" is a primal human question. The answer may be "I don't know" or "because" or "when we find out we'll know something really deep" but as a people question, the answer is not a physics lecture. If, conversely, the answer is "we know but we can't express it in lay terms because it's buried under grad school physics that doesn't have English equivalents," then that can also be said, perhaps more usefully than trying to say it in English. The answer may be "that's a meaningless question." But none of these direct answers have appeared. I think that's why the sides keep talking past one another in these threads. One side hears a different question than the other is asking. Frustration is the result. That does not imply that the answers given are worthless or that the time and effort put into them is not appreciated. Sometimes the physics is exactly the right response. Other times, and I think this is one, a different type of answer may also help. 
#29




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#30




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OTOH, non physicists have to spend some time trying to understand what they are saying. As counterintuitive as it may seem to the layman, the speed of light seems to be a fixed finite number, but it is a constant which is something different. We are applying the numbers and the units. In so many ways relativity makes no sense and I could never do the math to understand it very well, but it is clear to me if the measurement of the speed of light is always the same despite other conditions then it is other measurements which will be variable based on the conditions. I have no idea how that works, but fighting the concept won't help. 
#31




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#32




It may not be clear from the answers, but I truly do understand what you are saying. And I appreciate the frustration. The question "Why did the universe chose this particular number?" can be asked about many things in physics. It does not, however, apply to c.
Why are there 2.54 centimeters in an inch? Why not 3.1? Why not 6.2? I invite folks to seriously think about this question for a moment, at least long enough to realize that it makes no sense to expect nature to provide the number "2.54". This is a key point. The number 2.54 is there because someone chose this thing to be a standard centimeter and someone chose that thing to be a standard inch. But they measure the same thing, so converting between them is an artifice. If you agree that "2.54" is not a matter of physics but of history, then (given how special relativity works) you must agree that there being 3x10^{8} meters in 1 second is also not a matter of physics but of history. Someone chose this thing to define the meter and that thing to define the second, unaware that underneath it all they were measuring the same thing (i.e., distances in spacetime) and this conversion between them is an artifice. This is not easy to wrap one's mind around. But it's not a cop out. Last edited by Pasta; 10242019 at 06:39 PM. 
#33




#34




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#35




Now I'm really frustrated, not with the answers per se but with the fact that it is c that is built into the fabric of the university. I was so happy when I thought I had the answer that c was based on how magnetic & electric fields work in a vacuum, like cause and effect, and I could change those constants and change the speed of light.

#36




You change the speed of light to change those constants.

#37




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#38




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Which is fine. And that answer can be derived, so to speak, from the answers you've been giving. But perhaps you should give some thought to stating that outright and then spend the time explaining why that's true instead of leaving it as an exercise to the reader, which, for the lay reader, I believe it is. As I said earlier, I am not in any way belittling your time and effort here. But I'm a nonacademic writer and my expertise is probably a closer fit to seeing what sense an uninformed audience can make of an answer than someone who has absorbed the knowledge fully. I don't know what university that is, but pm me with the name so I can bet on them in their next football game. 
#39




Physicists do, indeed, try to find ways to calculate the dimensionless constants from first principles. And eversooccasionally, we do succeed in calculating one of them. Whenever that happens, it's a good sign that whoever managed it is on to something big. I think that the last time it happened was with the mass ratios of the weakforce gauge bosons, which turns out to be related to some other known properties of the weak force. Which, yeah, most laymen won't have any understanding of at all, but it was pretty exciting for physicists.
Personally, I've the suspicion that, with sophisticatedenough theories, we'll eventually be able to calculate values for all of them, or maybe all but one. But I really can't back up that suspicion, and opinions will vary considerably on that point. 


#40




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It is also important to recognize that there is not a generic layperson. A technical answer must make some initial assumptions about the reader's baseline knowledge, and the possible range is huge. So, there are initial answers, and then there is a (potentially long) iteration to fill in the holes or dive into a technicality. This requires that the participants are willing to engage in this backandforth, aiming for mutual understanding. When this happens, the threads are a lot of fun for all (and I wish I had time lately to post more often, because it is fun). Quote:

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