Why 186,282?

[russ_watters]

Yes, but that is not what was asked. What was asked is why is your cars speed 100 kph and not 103 kph. You cannot answer that without reference to SI units. They are part of the question.

No, that's the same nonsense. It's attaching a "why" to the speed increase that still doesn't depend on units. If I increase the power of my car by 27% I'll get a 3% increase in speed regardless of the units I choose to measure it in. Again, we're talking about a real change in speed not a change from 100 mph to 103 kDph.

Yes, other questions about dimensionless quantities could have been asked. But again, the important thing about $c$ is its invariance, not its size.

Right - so again, that is the answer, not this non sequitur about units.

 

[russ_watters]

Feet, miles, and kilometers are all units with dimensions of length.

I'm glad we agree on this. So my question is: if you change a value without changing the units, how can that be an issue of choice of units? If I press the accelerator of my car and 30 mph x 2 = 60 mph, how is that an issue of my choice of units?

 

[Ibix]

if you change a value without changing the units, how can that be an issue of choice of units?

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 - you literally do nothing more than decide that the scales on all your rulers are wrong by exactly the same factor you changed $c$ by. This is explicit in the SI, and better hidden in other unit systems.

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.

That's also why ratios to quantities like escape velocity fail. You will find that your change to $c$ changed something (most probably your measure of the radius of the Earth, but it does depend how you choose to mess with other constants) so that the escape velocity changed by the same factor as $c$ and the ratio is constant.

The only way to have an actual physical change is to change $\alpha$ (edit: the fine structure constant), but whether that changes $c$ or not still depends on your unit system. In modern SI it would not change $c$ (because that's a defined constant) but metre rules would be a different length. In "rod in a box in Paris" old school SI metre rules would stay the same but $c$ would change. So you can't get away from unit changes even then.

 

[pines-demon]

You all gotta love how PF can get hot on a simple question. We are already at three pages and still we do not know if OP is getting anything from what we already said because OP is not responding.

 

[Dale]

No, that's the same nonsense. It's attaching a "why" to the speed increase that still doesn't depend on units. If I increase the power of my car by 27% I'll get a 3% increase in speed regardless of the units I choose to measure it in. Again, we're talking about a real change in speed not a change from 100 mph to 103 kDph.

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.

Right - so again, that is the answer, not this non sequitur about units.

I gave that answer immediately also, even though it was not asked. But the answer about units is not a non sequitur (is a sequitur?) to the question about the size of $c$.

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.

 

[weirdoguy]

We are already at three pages and still we do not know if OP is getting anything from what we already said because OP is not responding.

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

 

[tech99]

I think I am right in saying that Maxwell noticed that the electric attraction between two stationary charges is the same as the magnetic repulsion when their relative speed is that of light. Maybe someone can correct me.

 

[pines-demon]

I think I am right in saying that Maxwell noticed that the electric attraction between two stationary charges is the same as the magnetic repulsion when their relative speed is that of light. Maybe someone can correct me.

Is that even true (putting aside that you cannot bring a mass to $c$)?

Edit: looking at the magnetic field of a moving charge, the magnetic field has a factor $(1-v^2/c^2)$ in the numerator, so it may go to zero when $v\to c$. I would also like a confirmation that Maxwell came up with this idea.

 

[DaveC426913]

The only way to have an actual physical change is to change $\alpha$,

Great. What is $\alpha$ ?

As far as I dan determine, this is the first and only time it has been cited in this thread.

(Now do you see what we mean when we wonder if you physicists are so comfortable with the subject that you are talking right over the heads of Basic High School?)

 

[Mister T]

What is the difference between a dimension and a unit then, if any? (and a "quantity"?)

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

And? I don't know where you are going with this.

You were responding to this ...

You cannot ask about the value of a dimensionful quantity independent of the units.

You responded, speaking about doubling a speed, and I responded to that saying you were talking about a dimensionless factor of 2. That's not a dimensionful quantity.

 

[Mister T]

Feet, miles, and kilometers are all units with dimensions of length.

You can say it that way. But length is a quantity that has dimensions of feet, miles, or kilometers.

 

[Ibix]

Great. What is $\alpha$ ?

The fine structure constant, mentioned several times in this thread. I thought I'd said alpha was the symbol for it somewhere, but apparently not. Sorry. I've edited in a clarification.

 

[weirdoguy]

The fine structure constant, mentioned several times in this thread

And if someone does not know what that is, and participate in the discussion, I would assume one would check that in google, and we have three alpha symbols right away:

 

[Mister T]

And if someone does not know what that is, and participate in the discussion, I would assume one would check that in google, and we have three alpha symbols right away:

Well, to be fair, they would have had to google $\alpha$, not "fine structure constant" to find out what was meant by $\alpha$.

 

[Dale]

But length is a quantity that has dimensions ... kilometers.

Not in the SI. See the SI brochure section 2.2.1 and SI brochure section 2.2.3. The meter is a unit, not a dimension. The dimensions are named after the base quantity, not the corresponding base unit.

 

[Dale]

I gave my layperson's opinion with the lame analogy with the rubber tape measure. I am implying that you cannot change the speed of light without changing spacetime and matter (if that were even possible ) in such a way as to make our measuring tools come back and give us the same number we had before we tweaked the fabric of our universe. Again, if this were actually possible. Think about it, no matter how we observe it, it's always the same.

In SI units $$\alpha = \frac{e^2}{2 \epsilon_0 h c}$$ So if you change $c$ then at least one of these other quantities must also change. You cannot have $c$ change in isolation.

So suppose $c$ doubles and $h$ halves. Then there would be no effect on physics at all. The universe before would be the same as the universe after. This is the type of thing that the SI committee could decide to do arbitrarily.

Suppose instead that $c$ doubles and $\alpha$ halves. That would be a very different universe. The electromagnetic interaction would be weaker compared to other interactions. Chemical reactions would provide less energy compared to the mass energy. Etc. The SI committee could not do this.

 

[pines-demon]

In SI units $$\alpha = \frac{e^2}{2 \epsilon_0 h c}$$ So if you change $c$ then at least one of these other quantities must also change. You cannot have $c$ change in isolation.

I was wondering where the $4\pi$ went and where the 2 came from. Using $h$ instead of $\hbar$ should be forbidden by now…

 

[DaveC426913]

In SI units $$\alpha = \frac{e^2}{2 \epsilon_0 h c}$$ So if you change $c$ then at least one of these other quantities must also change. You cannot have $c$ change in isolation.

So suppose $c$ doubles and $h$ halves. Then there would be no effect on physics at all. The universe before would be the same as the universe after. This is the type of thing that the SI committee could decide to do arbitrarily.

Suppose instead that $c$ doubles and $\alpha$ halves. That would be a very different universe. The electromagnetic interaction would be weaker compared to other interactions. Chemical reactions would provide less energy compared to the mass energy. Etc. The SI committee could not do this.

It sounds like you're saying that 𝛼 (the fine structure constant) - being a constant - cannot change (I mean, obviously). But is it an observed quantity? Not derived?

If c is dependent on it then it seems the answer to the question of the thread is "the reason c is what it is is because the fine structure constant fixes it". The obvious next question being: "Why is the FSC what is?" and this we do not know; we simply know that it is.(I know at least one member has been trying to get that across)

Is this a fair summary? if so, that is an answer I personally can live with.

 

[Mister T]

If c is dependent on it then it seems the answer to the question of the thread is "the reason c is what it is is because the fine structure constant fixes it".

Not quite. The fine structure constant fixes the relationship that $c$ has with the values of those other constants.

Edit: Fixed typo.

 

[Dale]

But the question is: it is an observed quantity? Not derived?

Yes, it is an experimentally observed quantity. There is no way to derive it in modern theories.

 

[DaveC426913]

Not quite. The fine structure fixes the relationship that $c$ has with the values of those other constants.

Sure. But ultimately, those other constants are constants of nature - they are observed - are they not? I mean, independent of our theories - they're more than just balancing numbers that make the equations work.

 

[Dale]

Sure. But ultimately, those other constants are constants of nature - they are observed - are they not? I mean, independent of our theories - they're more than just balancing numbers that make the equations work.

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 $c$.

 

[Mister T]

Sure. But ultimately, those other constants are constants of nature - they are observed - are they not? I mean, independent of our theories - they're more than just balancing numbers that make the equations work.

The same argument that applies to the value of $c$ applies also to the value of those other constants.

 

[DaveC426913]

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 $c$.

This whole thing is beginning to sound like a tautology. It's turtles all the way down.

Are any of these values taken from nature, as opposed to a self-referential (what did Ibix call it?) spiral of metrology?

 

[Mister T]

I did not learn that in high school.

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.

 

[Mister T]

Not in the SI. See the SI brochure section 2.2.1 and SI brochure section 2.2.3.

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

The meter is a unit, not a dimension.

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

The dimensions are named after the base quantity, not the corresponding base unit.

I agree. In Post #69 you seem to be assigning dimensions to units, whereas I interpret the above quote to mean that dimensions are assigned to quantities.

 

[Ibix]

Are any of these values taken from nature, as opposed to a self-referential (what did Ibix call it?) spiral of metrology?

$\alpha$ has no units - it is a bare number. So it is the only way out of the metrology mess. If you change it you change something real; if you change only dimensionful constants then you just change your unit system.

Changing $\alpha$ does not necessarily change $c$, but it has the effects one usually attributes to $c$. If I build a rod and fire a light pulse along it, changing $\alpha$ will change how long it takes the pulse to fly the length of the rod.

 

[tech99]

Is that even true (putting aside that you cannot bring a mass to $c$)?

Edit: looking at the magnetic field of a moving charge, the magnetic field has a factor $(1-v^2/c^2)$ in the numerator, so it may go to zero when $v\to c$. I would also like a confirmation that Maxwell came up with this idea.

Maxwell noticed that emu and esu units of the cgs system used at that time are related by a constant, which he thought might be c. And it was. He tried to set up an experiment to balance the forces of electric attraction between fixed charges and the magnetic force between currents and he obtained a value for c of 288,000 km/sec. Method of Making a Direct Comparison of Electrostatic with Electromagnetic Force, with a note on the EM Theory of Light, 1868.
An interesting book about Maxwell and his train of thinking is "The Man who changed Everything", by Basil Mahon.

 

[jbriggs444]

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

"Having" a dimension is not the same as "being" a dimension. The meter ("m") has the dimension of length ("L"). See the table here.

Unless one is trying to chop word salad, I regard such fine points as being of limited utility. You can use the language to pass a test but it won't help much when running an experiment.

 

[Mister T]

"Having" a dimension is not the same as "being" a dimension.

Right. Length has the dimension of meter.

The meter is a dimension.

The meter is a unit.

 

[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.