Speed of Light (revisited). Permeability and Permittivity

Factual Questions
21

I think firstly what you see is not what you might surmise to be real. For example even in a theory with absolute time you could see a clock tick fatser or slower than the absolute time due to Doppler shift. In special relativity too the rate you see a clock tick is not necessarily the ‘observed’ rate as you have to factor in the non-transverse Doppler shift.

Constructing arbitary accelerated frames in special relativty is problematic, but you can set-up 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 non-accelerated 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 set-up 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 relativistically-correct 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

Is the speed of light infinite? No. Therefore it’s finite. A finite speed must have some measurable or calculable speed. We know what it happens to be in our universe.

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

This isn’t correct, or at best it’s highly misleading. It’s not that the universe gives a number and we shrug. It’s that the universe doesn’t give us any number. There is no number. There is no physical constant here. In the height v. width example above, it’s not the universe that gave us the number “2.54 cm/in”. That’s entirely a human-generated number driven by the artificial decision to measure two distances in different units for no reason.

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 4-d spacetime, and you rotate that stick, its length does not change. When you rotate a stick in 2-d or 3-d space, you change its angle (a unitless number). When you rotate a stick in 4-d spacetime, you change its [symbol]b[/symbol] (a unitless number, defined upthread, v/c). The math of rotations is a little bit different for spacetime than for 3-d space, as is the “Pythagorean theorem”-equivalent (with which one calculates distances between two points) but that’s no biggie. In both the 3-d and 4-d 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.*
[sub]*Get this on a t-shirt, somebody![/sub]

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

They see themselves going at 1 second per second, not infinity, just like everything else (to the extent that you can define anything meaningful in this ill-defined reference frame). However, all distances are shrunk to zero for them, and it doesn’t take any time to cover zero distance.

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. :slight_smile: )

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

That sounds like it might help for my posted problem and my discussions outside this message board. Any recommended ‘simplified’ resources I could check out?

30

Quite right. Physicists often fall into such strictly technical definitions they can’t really hear the question as it’s asked. And with other physicists seeing what their responses are they’ll tend to be even more technical to avoid being criticized by their peers.

OTOH, non physicists have to spend some time trying to understand what they are saying. As counter-intuitive 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

To be sure, there are some magic numbers in physics that demand further understanding, but if the question is not about units, then why would physicists (or anyone) argue about the speed of light? That is exactly about units, and can reach any number you wish by rescaling the units. There is some background on the nature of light and space and time required to understand what is going on, but once you say you don’t care about the units the number does not matter. The layperson can be told that there was a historical definition of 1 m and of 1 s and someone went ahead and used them to actually measure the speed of light.

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[sup]8[/sup] 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.

33

You got it!

34

Federal Law or more precisely Code of Federal Regulations.

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

That works, though. Pass your beam of light into a dielectric material, like water or glass or air. The light will then slow down.

38

Then why have physicists been arguing about the dimensionless fine structure constant for a century?

I believe you are saying that it’s a meaningless question, because of a lack of understanding of a deeper truth in physics.

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 non-academic 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. :slight_smile:

39

Physicists do, indeed, try to find ways to calculate the dimensionless constants from first principles. And ever-so-occasionally, 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 weak-force 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 sophisticated-enough 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

It was stated in this thread before I joined and many times in the thread linked by Riemann. However, there are common challenges one must face when explaining technical concepts in these fora. The biggest is that sometimes people do not bother to put in the work to understand long-form posts; to engage with the content and to ask targeted follow-up questions. Some drive-by commenters would rather skim for a sense that their preconceived notion is close to right, and then reply with that notion, even if it is incorrect. This is a generic problem, not directed at this thread or anyone in particular, but it happens a lot. When this happens, and if I am in that thread, I try to correct the incorrect statements so that the final record is as correct and useful as possible.

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 back-and-forth, 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).

As above, there is no generic “uninformed audience”. The background must be sussed out over the course of several exchanges with honest engagement on both sides, and with a little expectation on the layperson side that an answer that doesn’t make sense may not be wrong – it may just need some of that juicy iteration. Also, I’ll say in passing that the above quote (the point of which seems inapplicable here) assumes things about the educational training and non-academic writing expertise of other posters that may or may not be correct.