B Why 186,282?

[Dale]

The question also specifically says it isn't about choice of units

It can’t not be. That is the error. You cannot ask about the value of a dimensionful quantity independent of the units.

 

[russ_watters]

But we are at the "it is" and people don't like it.

There is no "space" and "time". There is only "spacetime".

No we're not. Those are two different answers, not the same answer. Go back and look through the first few posts in the thread. There are a couple that discuss how c is fundamental to the way spacetime works and then....unit systems. And just as bad: "it's defined to be that"(it was of course measured before it was defined).

Again, I think professional physicists are skipping steps in the explanation because they are so fundamental to them that they are missing the question that is being asked or the level needed for the answer (thinking they are answering at the high school level when they are answering at the halfway through undergrad level).

For historic reasons, we measure space in meters and time in seconds, and the number that links the two is c. It is exactly analogous to measuring land distances in miles and altitudes in feet: "where does the 5280 come from?"

But as I said, people don't like this answer.

So, My understanding is that feet, miles, km etc are units and distance, time and speed are dimensions. Miles and feet are both different units of the same dimension (distance/length). Is that not true? d=s/t isn't converting units it is converting dimensions, right?

20 mph x 2 = 40 mph is doubling a dimension?

20 mph * 1.6 km/mi = 32 km/hr is converting units?

 

[strangerep]

If the answer is really 'that's an invalid speed' and '"the speed of light" really is just happens to be "C"' and 'C is so baked-in to the fabric of the universe that you can't change it so any attempt leads to a unit conversion', that's an answer that makes sense to someone like me. I think maybe physicists may be so far past the rest of the answer in their thought process that it's something you don't think to include.

I've written about that "something" multiple times on PF, and @Ibix already alluded to it in post #3 of this thread. The short version is that the Principle of Relativity (without the Light Postulate) implies the existence of a universal constant (which I've previously called $\lambda_v$) with dimensions of inverse velocity squared. The possibility $\lambda_v = 0$ corresponds to Galilean Relativity, while $\lambda_v \ne 0$ corresponds to Special Relativity (and people then define $c^2 := 1/\lambda_v$). The mathematical analysis exposes many physical phenomena implied by the existence of such a universal invariant constant, but doesn't yield the value of $\lambda_v$ in terms of familiar units -- that must be measured empirically.

[Edit: @Baluncore: this is also the closest we can (currently) get to answering your post #45.]

Here are links to some of my previous posts on this subject...

https://www.physicsforums.com/threa...-1-spacetime-only.1000831/page-2#post-6468652
Post #44.

https://www.physicsforums.com/threads/linearity-of-the-lorentz-transformations.975920/#post-6219004
Post #6.

https://www.physicsforums.com/threads/derivation-of-the-lorentz-transformations.974098/
Post #26.

https://www.physicsforums.com/threa...tulate-or-an-assumption.1052965/#post-6903963
Posts #37 and #39.

 

[Herman Trivilino]

I want to know why it is true, and why there can never be a counter example.

It's true because the alternative is empirically false. Of course there may some day be a counter example. But we don't have one today and we may never have one.

 

[russ_watters]

It does logically follow. In a universe with a finite invariant speed $c$ the relationship between mass, energy, and momentum is $m^2 c^2=E^2/c^2-p^2$. The relationship between velocity, energy, and momentum is $\vec v=\vec p c^2/E$. Set $m=0$ then solve the first to get $E=p c$. Then substitute into the second to get $v=c$.

I did not learn that in high school.

 

[DaveC426913]

The question is specifically "why is $c$ 186,282 miles per second".

You stopped reading too soon ...

"Of course that number depends on our definition of miles and seconds."

As @russ_watters also pointed out, the OP clearly recognizes that units are arbitrary. Therefore we can infer that they are not literally asking why, specifically, 186,282.

The problem is it is difficult for a layperson without the terminology to formulate the question a different way, except to simply declare "and I don't mean the numbers or the arbitrary units".

 

[russ_watters]

It can’t not be. That is the error. You cannot ask about the value of a dimensionful quantity independent of the units.

Nonsense. I can double the speed of my car and the fact that I have doubled the speed of my car does not depend on the units I have chosen to express the speed in. I don't even have to include units in the equation.

 

[DaveC426913]

Again, I think professional physicists are skipping steps in the explanation because they are so fundamental to them that they are missing the question that is being asked or the level needed for the answer (thinking they are answering at the high school level when they are answering at the halfway through undergrad level).

This.


A cheetah tops out at a certain speed regardless of how we choose to quantify that speed - whether it be km/h or furlongs per fortnight. The reason the cheetah tops out is due to a bunch of causative physiological factors that limit its muscle-movement, etc.

Hopefully, nobody here is going to tell us that the cheetah tops out at 60mph merely because we have arbitrarily chosen miles and hours as our units.

 

[Herman Trivilino]

So, My understanding is that feet, miles, km etc are units and distance, time and speed are dimensions.

No. Feet, miles, and kilometers are both dimensions and units. (The radian is an example of something that's a unit but not a dimension. In other words it's a dimensionless unit).

Distance, speed, and time are quantities.

 

[Herman Trivilino]

Nonsense. I can double the speed of my car and the fact that I have doubled the speed of my car does not depend on the units I have chosen to express the speed in. I don't even have to include units in the equation.

But here you are talking about a dimensionless factor of 2.

 

[Dale]

I think a better approach is to ask what the universe might be like if C were different than it is

This approach is good, but incompletely specified. $c$ cannot change in isolation. So you also have to specify what else changes. If the dimensionless fine structure constant also changes then the physics would be different. If only another dimensionful constant changes then the physics would be exactly the same.

 

[weirdoguy]

I did not learn that in high school.

Well, I did.

 

[Averagesupernova]

I can watch two cheetahs running and watch one approach and then pass the other, knowing which one is moving faster without knowing or caring about units or dimensions.

 

[Averagesupernova]

This approach is good, but incompletely specified. $c$ cannot change in isolation. So you also have to specify what else changes. If the dimensionless fine structure constant also changes then the physics would be different. If only another dimensionful constant changes then the physics would be exactly the same.

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.

 

[Dale]

Nonsense. I can double the speed of my car and the fact that I have doubled the speed of my car does not depend on the units I have chosen to express the speed in. I don't even have to include units in the equation.

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.

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

 

[russ_watters]

Well, I did.

Seriously? You learned both the basics of relativity and Maxwell's equations in high school? I didn't, even through two semesters of physics and EE (for engineers) in college.

 

[russ_watters]

No. Feet, miles, and kilometers are both dimensions and units. (The radian is an example of something that's a unit but not a dimension. In other words it's a dimensionless unit).

Distance, speed, and time are quantities.

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

But here you are talking about a dimensionless factor of 2.

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

 

[Dale]

You stopped reading too soon

You started reading too late. See post 4.

 

[Dale]

No. Feet, miles, and kilometers are both dimensions and units.

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

 

[Averagesupernova]

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

No. Feet, miles, and kilometers are both dimensions and units. (The radian is an example of something that's a unit but not a dimension. In other words it's a dimensionless unit).

This makes sense to me.

 

[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?)

 

[Herman Trivilino]

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.

 

[Herman Trivilino]

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:

 

[Herman Trivilino]

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.

 

[Herman Trivilino]

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 $c$.

 

[Herman Trivilino]

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?

 

[Herman Trivilino]

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.

 

[Herman Trivilino]

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.

 

[Herman Trivilino]

"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.