Why 186,282?

[Vanadium 50]

why is the value 1 or 186,000, it's a question of why it's "only" Mach 874,000 or 27,000x escape velocity or whatever. What parameters establish these ratios?

I don't think that is a terribly productive line of reasoning. What establishes these parameters? And what establishes the parameters that establish these parameters? And what establishes the parameters that....

It's turtles all the way down.

A question that does have an answer is "why is the speed of light
big' compared to everyday speeds?" and that actually has an answer. The velocity scale is ~$\sqrt{E/m}$. For chemical processes, E has a scale of an eV, and mass around a GeV. So we expect characteristic velocities of km/s. That's the speed of sound. That's the speed of neurons. That's the speed of the fastest animals. (All within a factor of a few)

We're powered by chemistry.

 

[DaveC426913]

Please read #13.

Thanks but I'm afraid post #13 is a bit inscrutable without prior in-thread context. It reads to me like a kind of shorthand, as if all along we'd been talking about ε0, μ0 and "the electromagnetic field and ... an electric part and a magnetic part" all along.

After all, this thread is labeled as "B", so I am kind of hoping at least the spirit of it can be communicated in Basic High School level concepts.

 

[russ_watters]

It's problematic, certainly. Imagine a rod that fits between here and Alpha Centauri. If you double the speed of light without changing $\alpha$ you have to change one or more of the constants $e$, $\hbar$ or $\epsilon_0$, and the consequence of that on the electrostatic force or the size of electron orbitals will double your calculation of the length of the rod. So it'll still take light 4.4 years each way, because really all you did was mess around with your unit system..[snip]. It's only if you change $\alpha$ that you get a change in the flight time of the light, because that messes around with the strength of electromagnetic forces.

Yes, that's what I was implying with that last bit. In my own words:

Because space and time are intertwined in our universe, 4.4 light years is a complete description of a position that does not allow changing distance without changing time(based on the ratio of c). A different ratio would be like changing the geometry of space-time but because C isn't just the speed of light, there are other implications to that regarding how the universe functions. Alternately it would be like changing the location of Alpha Centuari, which would also pose problems (halve the distance and the galaxy is now 8x as dense, for example).

(or, if you prefer, whatever you did was indistinguishable from messing around with your unit system).

I do. Because us laypeople don't intuitively understand space and time are connected so the idea that this is a unit conversion issue seems ludicrous to us (and I still don't believe it is, at least directly). I can change my car's speed from 30mph to 60mph by pushing down the accelerator. That's not a unit conversion, that's an actual change in speed. 300,000 x 2 = 600,000 ....change in speed or unit conversion? If that's m/s it's a change in speed but if I make it km/s it's a unit conversion? That makes no sense. 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.

 

[Dale]

After all, this thread is labeled as "B", so I am kind of hoping at least the spirit of it can be communicated in Basic High School level concepts.

It depends on the units is a Basic High School level answer.

 

[russ_watters]

I don't think that is a terribly productive line of reasoning. What establishes these parameters? And what establishes the parameters that establish these parameters? And what establishes the parameters that....

It's turtles all the way down.

I know that's a fun thing to say, and in many cases there is a tall tower of turtles, but it's not actually true that it's endless. Ultimately it leads to something fundamental - something that just "is". Moreover, "it's turtles all the way down" could be used as an excuse to decline to answer literally any question. It's more an insult to the questioner than it is a meaningful point. It's saying "I know you're not going to be satisfied with the answer and will just ask another question so I'm going to condescend instead of answering." It's no less wrong to say that to an adult who hasn't earned it than to a 6 year old kid who hasn't earned it yet. We know the 6 year old kid will, but the adult may not.

"Why is the speed of light what it is?" has useful answers, just as "Why is the speed of sound what it is?" has answers.

A question that does have an answer is "why is the speed of light
big' compared to everyday speeds?" and that actually has an answer. The velocity scale is ~$\sqrt{E/m}$. For chemical processes, E has a scale of an eV, and mass around a GeV. So we expect characteristic velocities of km/s. That's the speed of sound. That's the speed of neurons. That's the speed of the fastest animals. (All within a factor of a few)

We're powered by chemistry.

I think that answer works fine for biological processes, so it's a good part of the answer, but it doesn't work as well for things that rely on physics and not chemistry. Or rather, it's answering how physics processes drive chemical processes. So yeah, that'll prompt another questions: it doesn't answer what drives physics processes. Again, if the answer is just "the structure of the universe dictates it" and that's the last turtle, that's fine. Two turtles deep is not a long way to go.

 

[russ_watters]

It depends on the units is a Basic High School level answer.

I don't think it is. A high school student knows that 30km/hr x 2 = ?? is not a unit conversion problem.

 

[DaveC426913]

It depends on the units is a Basic High School level answer.

I'm sorry, but that just doesn't make sense (which, granted, may be my shortcoming).

I'm sincerely trying to reconcile what I'm being told (i.e. not merely being argumentative).

The speed of light was what it was when the dinosaurs were walking the Earth - before any units were invented. Photons didn't simply settle down and behave when we came along. There was something keeping them traversing the void at the same speed that has nothing to do with units.

Am I understanding correctly that:

• permittivity is merely an artefect of applying arbitrary units to c (as opposed to permittivity being a factor in its cause), and (more to the point)
• we really don't have any idea what keeps massless particles moving at the constant speed that they have

?

 

[Dale]

I'm sorry, but that just doesn't make sense (which, granted, may be my shortcoming).

The speed of light was what it was when the dinosaurs were walking the Earth - before any units were invented. Photons didn't simply settle down and behave when we came along. There was something keeping them traversing the void at the same speed that has nothing to do with units.

The question is specifically "why is $c$ 186,282 miles per second". That question simply cannot be answered without reference to the human inventions of miles and seconds. You can certainly apply the concept of miles and seconds to ancient distances and times, like the dinosaurs. The fact that they weren't invented at that moment in no way prevents us from using them today to discuss dinosaurs.

Once you fix the size of your units there are no remaining degrees of freedom to the value of $c$. Its value is determined. To get an answer that does not depend on units you need to ask a question that is dimensionless. Like the ratio of $c$ to the airspeed velocity of an unladen swallow (~30 million).

permittivity is merely an artefect of applying arbitrary units to c (as opposed to permittivity being a factor in its cause), and (more to the point)

The permittivity of free space is an artefact of some unit systems. Other unit systems do not even have such a thing. The relative permittivity of a material is a physical characteristic of that material.

we really don't have any idea what keeps massless particles moving at the constant speed that they have

We know exactly what it is. It is the fact that that speed is invariant that makes massless particles go at that speed. We don't know why there is a finite invariant speed, but given that fact it logically follows that massless objects travel at that speed and no other. But the size of that speed is not independently meaningful, only the fact that the invariant speed is finite. Every other physical statement will either be dependent on the units or a dimensionless comparison.

 

[Mister T]

I think when someone asks here, "Why is the speed of light what it is", what they are really asking is, "Why is the speed of light so slow compared to the enormous distances between stars (not to say galaxies), making it all but impossible to contemplate exploring even the nearest star systems?"

Then that's the same thing as asking why stars and galaxies are so far apart from each other compared to the distance between objects that are not as far apart. Like the distance between you and me.

 

[Baluncore]

It is the fact that that speed is invariant that makes massless particles go at that speed. We don't know why there is a finite invariant speed, but given that fact it logically follows that massless objects travel at that speed and no other.

It does not logically follow. That is an empirical observation that you believe will remain true. I want to know why it is true, and why there can never be a counter example.

 

[Vanadium 50]

Ultimately it leads to something fundamental - something that just "is".

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

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

There is no ε, there is no μ and there really isn't a c. These are not statements about nature; they are statements about us.

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

 

[Dale]

It does not logically follow. That is an empirical observation that you believe will remain true. I want to know why it is true, and why there can never be a counter example.

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 $v=c$.

 

[Baluncore]

It does logically follow. In a universe with a finite invariant speed the relationship between ...

Logically, but only if you define the universe to have a finite invariant speed.
My preferred universe, will one day be seen to be exceptional.

 

[russ_watters]

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

The question also specifically says it isn't about choice of units. It's right there in the OP.

Once you fix the size of your units there are no remaining degrees of freedom to the value of $c$. Its value is determined.

See, that is a different answer. What bothers me so much about this issue is that the answer has two parts and people keep giving the first part and omitting the second until pressed, and then seem confused about why only giving half the answer(which contradicts what they have been taught) isn't sufficient. I really don't get it.

 

[Averagesupernova]

This is like asking why pi is 3.1415.....
-
It's easy for us mere layperson's to wrap our heads around that, kind of....
-
I think a better approach is to ask what the universe might be like if C were different than it is. Just how far into the fabric of spacetime, matter, etc the speed of light is, is certainly not understood by myself. But I suspect from a philosophical viewpoint that if C were different, things would not look very much different to us from the way they look now. Think of measuring a rubber sheet with a rubber tape measure stretch them both and you get the same measurement.
-
A carpenter actually asked me once if I was using a rubber tape measure as I cut soffit material based on the numbers he called out to me. I simply replied that I suspected his tape was the rubber one.

 

[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.

 

[Mister T]

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.

 

[Mister T]

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.

 

[Mister T]

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.