Why 186,282?

[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##.

 

[Mister T]

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.

 

[Mister T]

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.

 

[Mister T]

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.