4 ms·

You are raising a couple of great questions! There are a handful of extra (disjoint) pieces of information that I think are important to this conversation. You

You are raising a couple of great questions! There are a handful of extra (disjoint) pieces of information that I think are important to this conversation. You might be aware of some of them, but I will enumerate them just in case. The "speed of light" c is much more fundamental than simply the speed of EM waves in vacuum. While humanity first learnt of this constant in classical EM, in modern physics its roots are much deeper. Here are a few equivalent "definitions" of c that do not involve EM: - c is the speed at which massless particles travel in any reference frame (from special relativity) - c is the maximal speed at which information can propagate (vaguer, but present in relativity, quantum, and QFT) - if a given force fields (for whatever force) has the form ~charge/distance^2, then the carriers of that force field will propagate at the speed c (both EM and gravity) As you can see, c is much more important than mere EM. Thus, it is important to start with c, not with μ0 and ε0, because c appears in parts of physics that do not know of μ0 and ε0 (e.g. theory of gravity). But let us get back to μ0 and ε0. I will focus on ε0 first. This constant lets us relate an amount of charge to the force that charge will create. Historically, we have ended up with measurement style in which we measure force in Newtons and charge in Coulombs. But this is just an engineering prescription. In that particular prescription we need ε0 to have units and a specific clumsy value, because of the historical clumsy choice of Newtons and Coulombs. You can see how Coulomb is indeed arbitrarily defined here https://en.wikipedia.org/wiki/Coulomb https://en.wikipedia.org/wiki/Coulomb If instead we had defined a charge unit (or a current unit) from first principles, we would not have needed this extra ε0 to fix our silly choice of units. An example of a first-principles less-arbitrary choice of unit of charge is the Franklin https://en.wikipedia.org/wiki/Statcoulomb https://en.wikipedia.org/wiki/Statcoulomb Thus both ε0 and μ0 are present just because at some point in history we decided to use Coulombs to measure charge, etc. Similar to how Na, Avogadro's number, is just an arbitrary fixed number of atoms, that we use so that our textbooks do not have to say "use 10^20 atoms of this compound". Na is not a fundamental constant either. However, there are systems of units in which ε0 and μ0 are simpler. The cgs system of units is a great example. Check out the values of ε0 and μ0 in that system https://en.wikipedia.org/wiki/Centimetre%E2%80%93gram%E2%80%93second_system_of_units https://en.wikipedia.org/wiki/Centimetre%E2%80%93gram%E2%80%... Lastly, while we can dispense of ε0 and μ0 simply by picking a better system of units for our measuring devices, we can not do that for c and α. As already mentioned, "c" is the speed at which information propagates (which is important for fundamental notions like locality and causality), while α is related to the ratio between fundamental forces. By the way, in cgs units α does not contain μ0. In conclusion: at the end you have two reasons to say that c and α are more fundamental than ε0 and μ0: - you can not remove c and α from your equations simply by changing the units of measurement (well, you can set c=1, but this is another can of worms unrelated to this discussion) - c appears in fields unrelated to EM, while ε0 and μ0 are only in EM

hilbert42 6y ago
I'll reply to this soon (I'm short of time and neglecting other stuff).
hilbert42 6y ago
FYI, first read this new HN news post: https://news.ycombinator.com/item?id=24950863 https://news.ycombinator.com/item?id=24950863 First, I agree with your comments and I'll get to them shortly, but I'd like to begin by mentioning how these posts came about, as it has a bearing on what many of us say in response to HN stories, this includes myself. I'll start by saying many of the comments here are excellent in that they're considered and thought provoking (HN attracts a high quality crowd). Nevertheless, from my experience, ad hoc or impromptu internet discussions about QM are often perilous affairs for those of us who dare to respond. Almost nothing equals QM's ability to draw a crowd to comment when some controversial finding is made that may have the potential to alter QM theory. Unfortunately, sometimes confusion arises from the fact that many of us come to the subject from different directions and with different levels of skill. Comments here are no exception. This HN thread, the second of two about the same story, began from a popular press report pitched to a broad cross-section of readers who are assumed to have some scientific knowledge, that is they're already familiar with the basic concepts of the subject. The same would also be assumed for HN readers. Few of them will be true experts in said matter but some will be and that will significantly influence the posts. My initial comment to the first story was a quick throwaway-like response pitched at the level of the article (or that's what I'd initially intended anyway). In hindsight, I should have expressed it more carefully as there's always someone who'll pick up a loose comment. That isn't a criticism as one want's comment and feedback but the discussion is tighter if we express ourselves more precisely. The trouble is I'm not particularly good at doing that. The other problem is that when one has readers who have wide-ranging skills where do you draw the line in assumed knowledge? There's little point defining everything that's involved before discussing the issue or the majority of readers won't bother to continue. I'm not much good at judging that either. Probably the best thing to do is not to bother and just pitch one's comments at the level one's most comfortable at doing, as raattgift has done with his comments. That way, readers will find comments pitched to their own level. As I see it, this is a particular problem when discussing QM. Let's face it, for many of us this topic is difficult even at mid-level let alone the extremes, unfortunately it's easy for QM topics to slide into the extreme category seeming without effort. For instance, in the post to which you replied I found it difficult to explain in simple terms the nature of the static magnetic field for two reasons. The first is that the underlying physics is very difficult to comprehend in day-to-day terms and is best explained by mathematics which itself is complex; and second, that whilst I do have some understanding of the physics, I don't understand the principles to the extent that I should. Whilst there are those who've a much more in-depth understanding of this physics than do, I'd also hazard to suggest that no one fully understands this physics well (this further complexes the problem of trying to provide understandable analogies). I've no time here to give you my reasons but I'd be happy to do so in another post if anyone wants me to. Now to your points: The "speed of light" c is much more fundamental than simply the speed of EM waves in vacuum. While humanity first learnt of this constant in classical EM, in modern physics its roots are much deeper. I totally agree. I made those longwinded points above for the very reason that it's hard to discuss QM at one level without sliding into a deeper meaning. By referring to the relationship between c, μ0 and ε0 alone without mentioning relativity specifically meant that I was effectively still using the classical electrodynamics approach. Here's the confusion: I quoted those equations specifically as they're widely used nowadays and they normally would not be contentious; moreover, they're even a notch up on the classical Maxwell/Heaviside mathematical statement of electrodynamics given that they're quantum mechanical expressions in that α and h are involved. Essentially, I've stated the quantum view but not the relativistic quantum one. Unfortunately, this sort of misstatement reigns supreme everywhere. Nevertheless, it's understandable and it's hard to avoid as the next level up in 'precision' has to involve relativity and this then complicates matters considerably as the equations and mathematics get considerably more complex (so does the understanding thereof). You can see what I mean in my post to the new HN story I've linked to above. In his video, Derek Muller makes the point that we cannot know the 'true' speed of light due to the 'clock' problem. That's to say that if we measure the speed of light in a vacuum, then owing to the fact that we need two directions to do so, c could actually be 299,792,458 m/s in one direction and instantaneous in the other and we would not know the fact. He points to the fact that Einstein set the premise upon which he based relativity only by convention (Einstein Synchronisation Convention), which is that c is the same in both [all] directions. He then points to the equation in Einstein's paper that sets that convention 2AB/(t'A- tA) = c where A and B are the paths. My point is twofold, the first is that the way we define things in physics often leads to a problem and this extends to their mathematical descriptions, and the second is that the complexity of those definitions sets our level of understanding of them. At a superficial level, we have one understanding; at a more complex level, we have a deeper and more nuanced understanding. That is stating the obvious but to keep things simple it is not often stated in the textbooks. In mechanics, we don't often start out by saying 'learn F=ma' and yet in the same sentence also say 'it'd be better if you learned it from a Lagrangian perspective' but then add 'that as this is just another interpretation of Newtonian approximation, then you'd really be better off learning relativity'. Right, it just doesn't work that way for good reason but by not doing so can lead to later confusion. I reckon it's especially a problem with QM and relativity (I cite my own case in that I should have been taught Lagrangian mechanics much earlier than I was). Muller's raising the issue of Einstein Synchronisation Convention with respect to c points again to the matter that I initially raised, which is that c, μ0 and ε0 are somehow interlocked irrespective of the importance of c (and I'm not down-rating c by saying that). Similarly, that is if the equation c = 1/(μ0 ε0)^0.5, which is a quantum relationship, is to hold true then either the Einstein Synchronisation Convention was hardly worth the effort of stating it in the first instance, as QM would be wrong, or that QM is wrong and there's something fundamentally wrong with our interpretation of μ0 ε0. QED! (Yeah, I know, QM came later so he had to state it, but you get my point.) The fact that Muller does not mention that if c were instantaneous in one direction then the values of μ0 and ε0 in that direction would also have to be different to our understood values, is I reckon a failing. If true then it would make a complete monkey out of our understanding of QM. If direction asymmetry of this sort were actually a fact in vacuum space then our whole understanding of the quantum vacuum, zero point energy, etc. would be total nonsense. Again, this illustrates the complexity of the matter and the dangers of oversimplifying things. Here, it seems apt to quote Einstein on the matter: "Everything must be made as simple as possible. But not simpler." I also need to discuss your other points including gravity, etc. and especially the cgs/MKS matter so I'll post that separately as soon as I get a chance. (I'm afraid of again exceeding HN's maximum allowable post space as I did with the earlier post (I had to shorten it to fit and some of my meaning was lost in the process).)

hilbert42 6y ago

I'll reply to this soon (I'm short of time and neglecting other stuff).

hilbert42 6y ago

FYI, first read this new HN news post: https://news.ycombinator.com/item?id=24950863 https://news.ycombinator.com/item?id=24950863 First, I agree with your comments and I'll get to them shortly, but I'd like to begin by mentioning how these posts came about, as it has a bearing on what many of us say in response to HN stories, this includes myself. I'll start by saying many of the comments here are excellent in that they're considered and thought provoking (HN attracts a high quality crowd). Nevertheless, from my experience, ad hoc or impromptu internet discussions about QM are often perilous affairs for those of us who dare to respond. Almost nothing equals QM's ability to draw a crowd to comment when some controversial finding is made that may have the potential to alter QM theory. Unfortunately, sometimes confusion arises from the fact that many of us come to the subject from different directions and with different levels of skill. Comments here are no exception. This HN thread, the second of two about the same story, began from a popular press report pitched to a broad cross-section of readers who are assumed to have some scientific knowledge, that is they're already familiar with the basic concepts of the subject. The same would also be assumed for HN readers. Few of them will be true experts in said matter but some will be and that will significantly influence the posts. My initial comment to the first story was a quick throwaway-like response pitched at the level of the article (or that's what I'd initially intended anyway). In hindsight, I should have expressed it more carefully as there's always someone who'll pick up a loose comment. That isn't a criticism as one want's comment and feedback but the discussion is tighter if we express ourselves more precisely. The trouble is I'm not particularly good at doing that. The other problem is that when one has readers who have wide-ranging skills where do you draw the line in assumed knowledge? There's little point defining everything that's involved before discussing the issue or the majority of readers won't bother to continue. I'm not much good at judging that either. Probably the best thing to do is not to bother and just pitch one's comments at the level one's most comfortable at doing, as raattgift has done with his comments. That way, readers will find comments pitched to their own level. As I see it, this is a particular problem when discussing QM. Let's face it, for many of us this topic is difficult even at mid-level let alone the extremes, unfortunately it's easy for QM topics to slide into the extreme category seeming without effort. For instance, in the post to which you replied I found it difficult to explain in simple terms the nature of the static magnetic field for two reasons. The first is that the underlying physics is very difficult to comprehend in day-to-day terms and is best explained by mathematics which itself is complex; and second, that whilst I do have some understanding of the physics, I don't understand the principles to the extent that I should. Whilst there are those who've a much more in-depth understanding of this physics than do, I'd also hazard to suggest that no one fully understands this physics well (this further complexes the problem of trying to provide understandable analogies). I've no time here to give you my reasons but I'd be happy to do so in another post if anyone wants me to. Now to your points: The "speed of light" c is much more fundamental than simply the speed of EM waves in vacuum. While humanity first learnt of this constant in classical EM, in modern physics its roots are much deeper. I totally agree. I made those longwinded points above for the very reason that it's hard to discuss QM at one level without sliding into a deeper meaning. By referring to the relationship between c, μ0 and ε0 alone without mentioning relativity specifically meant that I was effectively still using the classical electrodynamics approach. Here's the confusion: I quoted those equations specifically as they're widely used nowadays and they normally would not be contentious; moreover, they're even a notch up on the classical Maxwell/Heaviside mathematical statement of electrodynamics given that they're quantum mechanical expressions in that α and h are involved. Essentially, I've stated the quantum view but not the relativistic quantum one. Unfortunately, this sort of misstatement reigns supreme everywhere. Nevertheless, it's understandable and it's hard to avoid as the next level up in 'precision' has to involve relativity and this then complicates matters considerably as the equations and mathematics get considerably more complex (so does the understanding thereof). You can see what I mean in my post to the new HN story I've linked to above. In his video, Derek Muller makes the point that we cannot know the 'true' speed of light due to the 'clock' problem. That's to say that if we measure the speed of light in a vacuum, then owing to the fact that we need two directions to do so, c could actually be 299,792,458 m/s in one direction and instantaneous in the other and we would not know the fact. He points to the fact that Einstein set the premise upon which he based relativity only by convention (Einstein Synchronisation Convention), which is that c is the same in both [all] directions. He then points to the equation in Einstein's paper that sets that convention 2AB/(t'A- tA) = c where A and B are the paths. My point is twofold, the first is that the way we define things in physics often leads to a problem and this extends to their mathematical descriptions, and the second is that the complexity of those definitions sets our level of understanding of them. At a superficial level, we have one understanding; at a more complex level, we have a deeper and more nuanced understanding. That is stating the obvious but to keep things simple it is not often stated in the textbooks. In mechanics, we don't often start out by saying 'learn F=ma' and yet in the same sentence also say 'it'd be better if you learned it from a Lagrangian perspective' but then add 'that as this is just another interpretation of Newtonian approximation, then you'd really be better off learning relativity'. Right, it just doesn't work that way for good reason but by not doing so can lead to later confusion. I reckon it's especially a problem with QM and relativity (I cite my own case in that I should have been taught Lagrangian mechanics much earlier than I was). Muller's raising the issue of Einstein Synchronisation Convention with respect to c points again to the matter that I initially raised, which is that c, μ0 and ε0 are somehow interlocked irrespective of the importance of c (and I'm not down-rating c by saying that). Similarly, that is if the equation c = 1/(μ0 ε0)^0.5, which is a quantum relationship, is to hold true then either the Einstein Synchronisation Convention was hardly worth the effort of stating it in the first instance, as QM would be wrong, or that QM is wrong and there's something fundamentally wrong with our interpretation of μ0 ε0. QED! (Yeah, I know, QM came later so he had to state it, but you get my point.) The fact that Muller does not mention that if c were instantaneous in one direction then the values of μ0 and ε0 in that direction would also have to be different to our understood values, is I reckon a failing. If true then it would make a complete monkey out of our understanding of QM. If direction asymmetry of this sort were actually a fact in vacuum space then our whole understanding of the quantum vacuum, zero point energy, etc. would be total nonsense. Again, this illustrates the complexity of the matter and the dangers of oversimplifying things. Here, it seems apt to quote Einstein on the matter: "Everything must be made as simple as possible. But not simpler." I also need to discuss your other points including gravity, etc. and especially the cgs/MKS matter so I'll post that separately as soon as I get a chance. (I'm afraid of again exceeding HN's maximum allowable post space as I did with the earlier post (I had to shorten it to fit and some of my meaning was lost in the process).)