B Why Does the Speed of Light Max Out at 186,282 Miles Per Second?

[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.