B Why 186,282?

[Dale]

Section 2.2.1 states they are units. I agree. But that does not preclude them from also being dimensions.

Quoting from section 2.2.3: "Each of the seven base quantities used in the SI is regarded as having its own dimension."

Taking the example of time, table 2 shows the base quantity as having a name "time" and a typical symbol "t". The corresponding base unit is graphically separated and separately listed as having a different name "second" and symbol "s". Table 3 lists the base quantity as having a name "time" and a typical symbol "t" and a symbol for dimension "T". The dimension symbol "T" is always associated with the quantity name "time". Never once is the dimension symbol "T" associated with the base unit "second".

Anyway, I am done with this tangent. It seems to me like you are going out of your way to misunderstand this, but it is your choice.

 

[Nugatory]

It’s like the photons give out at 186,282 and say “I just can’t go any faster”. No… there must be some physical reason the speed of light only goes 186,282, and not faster, such as 188,476?

Light moving through space is an electromagnetic wave, and the speed of any wave is determined by the balance between whatever pushes the crests down and the troughs up and the force that opposes this motion. (This is of course a hand-wavey explanation, but a better one will involve a college-level textbook and some partial differential equations). In the case of light these are the interacting electrical and magnetic fields (sorry, that’s another college-level textbook) and if you work through the math it will turn out that the natural speed of electromagnetic waves in a vacuum is $c$ (which will of course be a different number depending on which units you’ve chosen).

Historical note: this calculation was first done by Maxwell around 1863; when he realized that the natural speed of electromagnetic waves was equal to the then-measured speed of light he made the inspired conjecture that this was because light IS electromagnetic radiation.

Footnote: Photons have absolutely nothing to do with it. Light is not photons moving from light source to light destination, photons are something completely different, they don’t even move the way you’re thinking.

 

[russ_watters]

Busy day....

It's a specific issue with $c$ because $c$ is inextricably entangled in the definition of distance and time....
Changing it changes other quantities in such a way that no measurements change...

That's why analogising to car speeds fails. I can accelerate without changing fundamental constants. I can't change 𝑐 without changing something else fundamental.

Thanks. That is the point I'm after, and IMO the real answer to the OP's question. The speed of light (or more specifically C) is different than other speeds so when someone asks about changing it, the real answer is 'you are not allowed to change it because it is baked-into the structure of the universe'.

The answer 'it's a unit conversion' is a consequence of the real answer and an unnecessary/confusing distraction from it. You cannot give the second answer and expect it to be understood unless you provide the first answer. Especially when you are answering at B level to people who don't already know the real answer.

 

[russ_watters]

It wasn’t a question about increasing or decreasing the speed of light. It was a question about why it is the value that it is. Not about changing the value. A question about the size of a value is not the same as a question about a relative change in a value.

Not true. 'Why is it this value' is the same as 'why isn't it a different value' (higher or lower) -- and the OP did say "whatever speed it is" and "and not faster, such as 188,476". However, I still don't think that should affect the answer: 'It's the value it is in that set of units because it is baked into the structure of the universe and isn't allowed to be changed.' IMO the "unit conversion" answer is confusing or unnecessary except as a not particularly important footnote to the real answer.

I gave that answer immediately also, even though it was not asked.

Ehh, unclear. What you said was: "Physically, what is important about 𝑐 is that it is invariant. Its numerical value is only an artifact of the choice of units." What's missing from that is why it's invariant. Is it invariant merely because it's convenient for us to define it as such?

Even worse, you flipped-over/pulled out of context the prior quote by the OP to mean the opposite of what he intended it to mean. The OP was acknowledging the existence of unit conversions and saying he wasn't talking about unit conversions. Basically: 'I understand that 100 kph is 62 mph via unit conversion but what if I increase to 200 kph, an actual change in the speed?' And you basically responded with 'yep, it's about unit conversions.'

Or another way: the OP demonstrated he knows about unit conversions, so an answer trying to teach unit conversions doesn't address the thing that he's missing in his understanding of the issue: why something that is clearly (to a high school educated mind) not an issue of unit conversions really is.

A question about changing $c$ I would answer as I did in post 61. Such a question is incomplete. You must also specify what else changes.

Yes, that's why I think post #61(albeit a bit short) is a much much better answer than post #4.

 

[russ_watters]

Maybe, but those discussions serve not only for the OPs, but for a wider group of people. E.g. for me

For my part I want to emphasize that truly my participation here is not intended to be argumentative, it's that I think there is a real communication problem between experts and laypeople. In effect I'm trying to bridge a language barrier.

 

[russ_watters]

All dimensions are units, but not all units are dimensions. The radian is an example of a dimensionless unit.

I guess I'm not following or there is something I don't understand about those definitions. Is "length" a unit or is "feet" a unit (or both)? Here's what I'm seeing:

"Dimensions are physical quantities that can be measured, whereas units are arbitrary names that correlate to particular dimensions to make it relative (e.g., a dimension is length, whereas a meter is a relative unit that describes length)"

https://www.sciencedirect.com/topics/engineering/units-and-dimension

That appears to me to say that "length" is a dimension and "feet" is a unit and they are not interchangeable terms/concepts. Same goes for "dimensionless" -- what you are saying is the opposite of what I'm seeing:

https://www.nature.com/articles/s41467-022-35084-w

[what comes after appears to hinge on this issue so I'll put it on hold.]

[edit] I've been replying as I'm reading and it appears the discussion covered this already. I think we're past it.

 

[russ_watters]

Neither did I. For me it was 2nd year undergrad. But to be fair the comment made by @Dale was simply that "It is the fact that that speed is invariant that makes massless particles go at that speed".

One could argue that that's a high school-level comment made in response to a query. It was only when pressed for validity that he went into what could be called a non-high school response.

That makes sense to me. We learn things in high school and then later in college learn the deeper reasons for why those things are said.

All of that is fine. Sometimes a question by a B-level person does not have a B-level(high school) answer. If that's the case it's fine to stretch to a higher level while clearly specifying the part that isn't B-level, and that's the gap I'm trying to bridge. But in this case we had people saying it was a B-level answer when it really wasn't:

-Supposed B-Level Answer: It's just a unit conversion issue.
-B-level person: What? It clearly isn't.
-Follow-up: Oh, right, it's really these I-level reasons that conspire to make it look like a unit conversion issue.

 

[russ_watters]

Not really. The very existence of each of those quantities depends on the system of units. You can make them disappear entirely simply by choosing different units. That is why I had to specify “SI” above. This includes $c$.

The wiki article on the fine structure constant says it is dimensionless and therefore is not dependent on the chosen system of units:
https://en.wikipedia.org/wiki/Fine-structure_constant

Be that as it may, @DaveC426913 I've seen the issue of dimensionless constants debated here at a higher level that what I can lift. It's enough for me to recognize that the speed of light is baked into the structure of the universe and leave it at that. Especially because I haven't formally studied the issue beyond that.

 

[Dale]

Are any of these values taken from nature

Only the dimensionless fine structure constant. All the others reflect the units in one way or another.

The wiki article on the fine structure constant says it is dimensionless and therefore is not dependent on the chosen system of units

That is correct. The part you quoted was referencing the other (dimensionful) constants.

Not true. 'Why is it this value' is the same as 'why isn't it a different value' (higher or lower) -- and the OP did say "whatever speed it is" and "and not faster, such as 188,476".

Well, we disagree on that point. I read those as two substantively different questions and answer them accordingly. To me a question about a value and a change in a value are different, and I answer them differently.

the answer: 'It's the value it is in that set of units because it is baked into the structure of the universe and isn't allowed to be changed.'

I disagree that this is the answer to either question. The value of $c$ isn’t baked into the structure of the universe. It is the value of the fine structure constant that is baked into the structure of the universe. Only the fact that $c$ (the invariant speed) is finite is baked into the structure of the universe, not its value.

What's missing from that is why it's invariant.

We don’t know why it is invariant. We have no theory that would answer that. As far as we can tell it is a fundamental fact of the universe that is not based on other principles.

As a summary of my personal perspective here: in my opinion a question about the value of $c$ is a dimensionful question that cannot be divorced from the units. A question about a change in the value of $c$ is a dimensionless question that is incomplete and needs to be referred to the fine structure constant. A question about $c$ being finite and invariant is a foundational question about the causal structure of spacetime. I answer them differently because I think they are different.

 

[russ_watters]

Well, we disagree on that point. I read those as two substantively different questions and answer them accordingly. To me a question about a value and a change in a value are different, and I answer them differently.

I can't reconcile that with the OP. The OP gave a different (change in) value. But whatever, moving on for now:

I disagree that this is the answer to either question. The value of $c$ isn’t baked into the structure of the universe. It is the value of the fine structure constant that is baked into the structure of the universe. Only the fact that $c$ (the invariant speed) is finite is baked into the structure of the universe, not its value.

So the fine structure constant is baked into the structure of the universe, the fine structure constant helps determine C but that doesn't mean C is baked into the structure of the universe? That seems like a circle that should close but doesn't.

We don’t know why it is invariant. We have no theory that would answer that. As far as we can tell it is a fundamental fact of the universe that is not based on other principles.

At least that part sounds fine based on the prior answer: "baked into the structure of the universe". It seems like it should follow that "is invariant" means "has to be this speed" based on the previous statements. But I do get that "invariant speed" doesn't quite answer "that particular speed". It just seems like both have the same answer ("baked into the structure of the universe/fine structure constant").

As a summary of my personal perspective here: in my opinion a question about the value of $c$ is a dimensionful question that cannot be divorced from the units. A question about a change in the value of $c$ is a dimensionless question that is incomplete and needs to be referred to the fine structure constant. A question about $c$ being finite and invariant is a foundational question about the causal structure of spacetime. I answer them differently because I think they are different.

I think all of that is fine and this disconnect may come down to the disagreement in the top of the post: different interpretations of the question the OP was asking. I will say this though: laypeople on PF often ask wrong questions, and we get a lot of wrong questions asked repeatedly, including this one. IMO, what has happened here(frequently) is that many of the answers answered the right question without explaining why the question that was asked was the wrong question.

 

[strangerep]

We don’t know why [the universal limiting relative speed, commonly denoted as $c$] is invariant. We have no theory that would answer that. As far as we can tell it is a fundamental fact of the universe that is not based on other principles.

The 1-postulate (group theoretic) derivations of SR do answer that. They show that it (or more precisely, the $\lambda_v$ constant I mentioned earlier) is a mathematical consequence of the Relativity Principle (given also spatial isotropy and some Lie group technicalities).

[I feel a thread-move to the relativity forum approaching...]

 

[Dale]

The 1-postulate (group theoretic) derivations of SR do answer that. They show that it (or more precisely, the $\lambda_v$ constant I mentioned earlier) is a mathematical consequence of the Relativity Principle (given also spatial isotropy and some Lie group technicalities).

[I feel a thread-move to the relativity forum approaching...]

No, they do not. The one postulate derivations are also consistent with the Galilean transform.

I know you had mentioned $\lambda_v$ earlier. I had earlier mentioned multiple times (posts 43, 47, 109) that I am specifically talking about a finite invariant speed, $c$.

 

[Herman Trivilino]

So the fine structure constant is baked into the structure of the universe, the fine structure constant helps determine C but that doesn't mean C is baked into the structure of the universe? That seems like a circle that should close but doesn't.

It's not the value of $c$. It's the ratio of the value of $c$ to those other constants that's "baked", or in other words, is fundamental to the structure of the universe.

 

[Herman Trivilino]

It seems to me like you are going out of your way to misunderstand this, but it is your choice.

No, I'm not. After doing a bit of reading of Arnold B. Arons; who apparently misspoke, or I misheard, or I remember incorrectly from, a few decades ago, I stand corrected.

 

[Herman Trivilino]

That appears to me to say that "length" is a dimension and "feet" is a unit and they are not interchangeable terms/concepts. Same goes for "dimensionless" -- what you are saying is the opposite of what I'm seeing:

Yeah, sorry about that. I was mistaken. See Post #114.

 

[edfriedmanis65]

TL;DR Summary: Why this speed

Is there an explanation for why the speed of light tops out at 186,282 miles per second? Of course that number depends on our definition of miles and seconds. If a mile was 3000 feet then c would be a different number.

But whatever speed it is…. Why that speed? In other words… there is something tangible that limits c to a top limit of some speed. Again, why 186,282? Why is it not 231,655? If it were then that would be the speed beyond which we could not speed.

It’s like the photons give out at 186,282 and say “I just can’t go any faster”. No… there must be some physical reason the speed of light only goes 186,282, and not faster, such as 188,476?

Tex

Empty space has some characteristics; permeability and permittivity. Multiply them, find the square root and invert that number; its the speed of light. Those two numbers define the speed of light. if they were different, the speed would be different.

 

[PeroK]

Empty space has some characteristics; permeability and permittivity. Multiply them, find the square root and invert that number; its the speed of light. Those two numbers define the speed of light. if they were different, the speed would be different.

The modern SI approach is to define the second and then define the metre in terms of the distance light travels, in vacuum, in a given time:

https://en.wikipedia.org/wiki/Metre

 

[Ibix]

Empty space has some characteristics; permeability and permittivity.

...which you need to measure using some unit system, or explicitly define as the basis of your unit system. Track back through your unit system and you'll find the assumptions that lead to the particular number for $c$. Furthermore, as already discussed on this thread, changing those values cannot be done in isolation. Depending on what else you vary, such a change may just be mucking around with units - which gets us back to "$c$ is just defined to be the value it has, directly or indirectly".

 

[Agent Smith]

An interesting question. With mass we can use ratios (e.g. the ratio between the mass of a proton and an electron is 1436, unitless) to get our hands on a number that'll make universal sense (I'm talking about ET ). With speed we have just 1 number viz. c (the speed of light); for all other "objects" the speed is variable and so we can't use them to compute a constant ratio. One of the defining properties of light is its speed, constant at c and there's no other like it.

What about Planck units? Are these universal in any sense?

 

[pbuk]

What about Planck units? Are these universal in any sense?

Perhaps in some sense, but in other senses no. For instance do we take the reduced Planck constant (as is now the convention) or not (as Planck did)? Do we use the Coulomb charge (as is the convention but depends on experimental measurement of the fine structure constant) or the electron charge (which is a real physical quantity), or even the down quark charge (my own idea, being more fundamental than the electron charge)?

There is an illuminating PF Insight on this, although note that it is nearly 10 years old and so predates the overhaul of the SI unit system in 2019.

 

[sophiecentaur]

TL;DR Summary: Why this speed

Is there an explanation for why the speed of light tops out at 186,282 miles per second?

Yes. There is an explanation but, to follow it in depth, you need to take a course in advanced Electromagnetic Theory. There is no short cut to this one; you just have to accept what you're told and believe that Science is 'right' in this respect