B No vacuum anywhere vs the measurement of "c"

[Dangoe]

TL;DR Summary

Question: We defined the second and hence the meter by the speed of light in vacuum "c", but there isn’t anywhere a real vacuum possible in the universe never (see Wikipedia). How and where was c measured then?

Hi to the community!

Glad to be able to ask 1-2 questions here so signed up. As an interested layman with some autodidactic efforts, still can’t see how this happened or got to the value:

Question: We defined the second and hence the meter by the speed of light in vacuum, but there isn’t anywhere a real vacuum possible in the universe (see Wikipedia). How and where was c measured then?

Would appreciate any comprehensive answers!

Regards,
Dangoe

 

[hutchphd]

Welcome.
Here's the deal. If you make a claim like " but there isn’t anywhere a real vacuum possible in the universe" then you need to document that and (see Wikipedia) is insufficient.
You need to up your game a bit if you wish serious discussion.

 

[Vanadium 50]

The index of refraction in the space between galaxies is about 1.000 000 000 000 000 000 000 000 000 2. Why should I worry about that?

 

[fresh_42]

My Wikipedia pages say, the pressure on the moon is about $0.000000001$ Pascal, and we have achieved a vacuum pressure below $0.0000000000000001$ Pascal. And the moon has a mean free path of about $10000$ km.

 

[Dangoe]

Welcome.
Here's the deal. If you make a claim like " but there isn’t anywhere a real vacuum possible in the universe" then you need to document that and (see Wikipedia) is insufficient.
You need to up your game a bit if you wish serious discussion.

Thanks for your reply hutchphd,

Of course you are absolutely right

Welcome.
Here's the deal. If you make a claim like " but there isn’t anywhere a real vacuum possible in the universe" then you need to document that and (see Wikipedia) is insufficient.
You need to up your game a bit if you wish serious discussion.

Thanks for your reply hutchphd,

Of course you are absolutely right, I just skipped that because so obvious presumably. Anyway, here we go: “Im bekannten Universum gibt es kein vollständiges Vakuum, und es ist mit bekannten technischen Mitteln auch nicht erzeugbar.” (https://de.wikipedia.org/wiki/Vakuum) =~ In the known universe there is no complete vacuum, and it is not producible with known technical means.

 

[Dangoe]

Sorry I have some issues with my device (iPad), keeps ghosting my keyboard, tried again maybe overlapping answers - I switch to another one now.

 

[Dangoe]

The index of refraction in the space between galaxies is about 1.000 000 000 000 000 000 000 000 000 2. Why should I worry about that?

Hi Vanadium 50,
Thanks for this number. How did you get it, and how being so sure?
Regards,
Dangoe

 

[Dale]

Summary: Question: We defined the second and hence the meter by the speed of light in vacuum "c", but there isn’t anywhere a real vacuum possible

The question isn’t if a vacuum meets some unobtainable ideal of a “real vacuum”. What matters is if the light interacts with matter.

There is a theorem called the optical extinction theorem that can be used to know if light of a specific wavelength traveling through a specific actual vacuum has interacted with matter.

While there are experiments and astronomical observations that are subject to criticism under the extinction theorem, there are many that are not. The requisite levels of vacuum for easily accessible sources are in fact achievable.

 

[Dangoe]

My Wikipedia pages say, the pressure on the moon is about $0.000000001$ Pascal, and we have achieved a vacuum pressure below $0.0000000000000001$ Pascal. And the moon has a mean free path of about $10000$ km.

Thanks fresh_42, but both not a vacuum anyway. Maybe enough you say? Regards, Dangoe

 

[Vanadium 50]

How did you get it

Looked up the density of gas in the IGM.

 

[hutchphd]

Of course you are absolutely right, I just skipped that because so obvious presumably.

The other motivator for me was that there are almost never real absolutes. (@Dale invocation's of the optical theorem notwithstanding !) But a number without an uncertainty usually lacks standing.

 

[Dangoe]

The question isn’t if a vacuum meets some unobtainable ideal of a “real vacuum”. What matters is if the light interacts with matter.

There is a theorem called the optical extinction theorem that can be used to know if light of a specific wavelength traveling through a specific actual vacuum has interacted with matter.

While there are experiments and astronomical observations that are subject to criticism under the extinction theorem, there are many that are not. The requisite levels of vacuum for easily accessible sources are in fact achievable.

Ah, ok, thanks Dale!

I am going to follow your path "optical extinction theorem" to understand it better. I still can't believe we got c in a "vacuum" just like that, implying the second, meter and etcetera...

Regards,
Dangoe

 

[Dale]

I am going to follow your path "optical extinction theorem" to understand it better.

A good resource is this page:

https://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html

It lists a lot of experiments on special relativity and indicates which ones are subject to criticism under the extinction theorem and which are not.

I still can't believe we got c in a "vacuum" just like that, implying the second, meter and etcetera...

Why not?

When scientists describe c as “the speed of light in vacuum”, there never was any implication by them that it was some sort of unobtainable ideal of vacuum. That is just something that you added.

When scientists refer to the speed of light in vacuum, they just mean that the light isn’t interacting with matter. The extinction theorem quantifies that.

What is so unbelievable about that?

 

[Dangoe]

While I haven't read about the extinction theorem for me "in vacuum" means in vacuum. Not complicated, what to not understand what I find unbelievable about.

 

[phinds]

While I haven't read about the extinction theorem for me "in vacuum" means in vacuum. Not complicated, what to not understand what I find unbelievable about.

You seem to be more interested in promoting, and insisting upon, your point of view than you are in learning about science. As should be clear from reading the responses, YOU are the only one proposing that there is a requirement for some perfect vacuum in order for the physics to make sense.

 

[Dangoe]

I was just chatting before reading and learning more. Thanks again for the hint above. And yes, makes sense when clear, not before. Until later.

 

[Dale]

for me "in vacuum" means in vacuum

Yes, and it is measured in vacuum. An unrealizable stringent connotation to those words is not implied.

Not complicated, what to not understand what I find unbelievable about.

I understand your original confusion. What I don’t understand is why you found the clear answer unbelievable.

You are interpreting “in vacuum” with a meaning that is not intended by scientists. Why is that unbelievable? People miscommunicate in this fashion all the time. The listener hearing a word with a different meaning than the speaker intended. It is a daily experience for me. How can the idea that this has happened here be “unbelievable”? Have you really never had this experience before?

 

[sophiecentaur]

Maybe enough you say?

The phrase "near enough for Jazz" applies everywhere in Science. We know nothing with absolute accuracy but that doesn't prevent us from coming up with models that predict with useful accuracy. An example of this is the mass of a photon which is specified, not as zero but as less than a given value. Here, that value is quoted as possibly 3X10^-27eV but not zero.

 

[Drakkith]

There's a fairly simple procedure that would allay most doubts. Fill a chamber with high-pressure air and then measure the speed of light through that chamber. Next, reduce the air pressure and measure the speed of light through the chamber again. Then reduce the air pressure again and redo the measurement. Repeat until you can't get the pressure down any further or you reach the limits of precision with your experimental setup.

Now graph the calculated speed vs the air pressure. You'll find that it approaches a certain value as the pressure is reduced. This value also happens to closely match that calculated using measurements of the fine structure constant and many other methods.

How and where was c measured then?

See here for more info: https://en.wikipedia.org/wiki/Speed_of_light#Measurement
There have been many measurements of the speed of light throughout the last 100+ years, far too many to list individually. One could say that every single instance of telecommunications via satellites is a test, as are communications with space probes and rovers.

 

[Vanadium 50]

Well, there aren't any frictionless planes, stretchless ropes, perfect spheres, etc. either.At some point you have to ask "does the fact that this isn't ideal make any difference?"

Vacuum imperfections makes a difference of a part in 10²⁴. which is under a microsecond over the entire history of the universe. If that's really a problem, I don't know what to say.

It is also worth pointing out that a physical realization of a seconds standard - i.e. a clock - it a hundred million times worse. That is, if `I build two identical clocks as well as I can, over the life of the universe, they will drift apart by around a minute.

 

[berkeman]

Well, there aren't any frictionless planes

Obviously you've never seen me try to ice skate...

 

[malawi_glenn]

There are no infinite precision time- or position measurments. Since 1983 c is a defined quantity.

 

[Vanadium 50]

I think the OP's objection is "how can it be a defined quantity if the physical realization of the definition is imperfect in the 25th decimal place?"

This is essentisally the same question as "How can π have more than 25 digits if we can't make a bigger circle out of atoms?"

 

[fresh_42]

I guess the OP was surprised by the fact that meters and seconds are defined by some odd numbers with ten digits. If that involves the speed of light in a vacuum, the question is: Can we measure the speed of light up to ten digits without being able to create a perfect vacuum?

The answer is yes, and we can produce even better vacua than are necessary to obtain such precision. I further assume that this answer is satisfactory since it is a B-level thread. Measurement is never completely accurate, which is why those odd numbers were finally fixed in the definition of meters and seconds.

 

[Vanadium 50]

I guess the OP was surprised by the fact that meters and seconds are defined by some odd numbers with ten digits.

I don't think so. He starts with

Summary: Question: We defined the second and hence the meter by the speed of light in vacuum "c", but there isn’t anywhere a real vacuum possible

Based on what he writes, the objection seems to be that an ideal vacuum can't be realized. And there's nothing special about this - the ideal anything can't be realized. That's why we call it "ideal".

 

[fresh_42]

And there's nothing special about this - the ideal anything can't be realized.

Thank you! Nobody believes me when I tell them that there is no such thing like a circle.

 

[sophiecentaur]

Thank you! Nobody believes me when I tell them that there is no such thing like a circle.

Geometrical figures are all abstract and axiomatic. Saying there's 'no such thing' is bound to get you a hostile reaction. People tend not to get the distinction between maths and the real world.

 

[pinball1970]

Thank you! Nobody believes me when I tell them that there is no such thing like a circle.

A platonic one?

You mean in the real world though yes?

OOPS! EDIT. @sophiecentaur already answered

 

[jbriggs444]

It is important to get from the formal definition to a practical realization of the definition. The BIPM has something to say about that.

While the definition for the metre refers to light traveling in vacuum, in most cases the realization of the length unit is performed under atmospheric pressure. Then the exact value of the influence of the air on the speed of light is of major importance. Therefore, a distinction has to be made between c, the speed of light in vacuum and c′, the speed of light in general. Under atmospheric pressure, the air refractive index reduces the speed of light (c′ = c/n) with a relative effect of the order of $3 \times 10^{–4}$ corresponding to 300 µm per metre of measured length. Moreover, in the case of modulated light it is important to consider the group refractive index of air ng instead of the (phase-) refractive index, n. For example, for green light (λ  520 nm) ng – n is approximately $10^{–5}$ , i.e. considering n instead of ng causes an additional error of 10 µm per metre. This difference is significant and comparable in size to the variation of the phase refractive index of air over the entire range of visible light: n(380 nm) – n(780 nm) = $9 × 10^{–6}$ . Thus, determination of the exact speed of light to use in equation (1) is a significant consideration in realizing the metre through primary methods.

 

[hutchphd]

Don't abstractions exist?

Call the philosophy squad...

 

[pinball1970]

Don't abstractions exist?

Call the philosophy squad...

in what sense?

 

[jbriggs444]

in what sense?

Smell. A good abstraction smells like a musty book. A bad abstraction will clear the room almost as fast as a bad pun.

 

[sophiecentaur]

Smell. A good abstraction smells like a musty book. A bad abstraction will clear the room almost as fast as a bad pun.

As they say "He who smelt it dealt it". Calls for an abstractor fan, perhaps.

 

[malawi_glenn]

Student: -"Imaginary numbers do not exists"
*Teacher writes "i²=-1" on the blackboard*
Teacher -"there it is"

 

[Dangoe]

Thank you guys, you showed almost everything possible to understand better. Am so happy I signed up. I can't ask professors so sticking to asking in a forum, here is one of the best I was told. And indeed is, thanks a lot.

Wasn't reading here in between but read a part of Dale's suggestions.
@Dale: Of course missunderstandings are common by different definitions (interpretations) of words for example. Appreciating you understanding my initial confusion. Still having a hard time to accept the given language though.

From the link:

"Measured c = 299,792,458.8 0.2 metre/s, with 1.2 metre uncertainty due to realization of the Kr metre standard used."
Source: https://math.ucr.edu/home/baez/phys...ments.html#Measurements_of_the_Speed_of_Light

Those measures are obviously showing uncertainties there. Still haven't got into the papers there, no context available otherwise. Anyway probably enough.

And back to the vacuum:

The Ewald–Oseen extinction theorem says that the light emitted by the atoms has a component traveling at the speed of light in vacuum, which exactly cancels out ("extinguishes") the original light wave."
Source: https://en.wikipedia.org/wiki/Ewald–Oseen_extinction_theorem#Overview

This as an example, couldn't understand how this all really works, have to review it more in depth. Looks to me like a circular reasoning somehow or so until now. Have to learn much more...

Nevertheless I consider my question as answered, very well answered. Thanks for any contribution from the community. May get back to some details soon.
Dangoe

 

[hutchphd]

Let me try a little. The speed of light in vacuum is well defined within our concept of physics. It is a number appears over and over and therefore for practical purposes it behooves us to accurately measure (or otherwise adjudicate) its value relative to the other fundamental quantities. It does not matter that we cannot measure it directly and exactly (exactly is a meaningless concept) It matters only that we can measure it well enough for our purposes. And, by the way, it makes much more practical sense to use that value to define, using an atomic clock, the length unit than to store an oxidizing piece of metal in vault. Nothing is exact and inviolate
The fact that there are no perfect realizations of "light in a vacuum"in no way voids the concept, although you seem greatly worried.

/

 

[PeterDonis]

We defined the second and hence the meter by the speed of light in vacuum

No, we didn't. SI units define the second in terms of a hyperfine transition in cesium atoms. The SI meter is then defined so that the speed of light in vacuum (which is really a misnomer, a better term would be "the finite invariant speed aka unit conversion factor between time and distance that relativity theory tells us must exist") has a fixed value. However, that definition is just a unit definition and does not depend on making any measurements involving light in vacuum. So the fact that in practice we cannot achieve a 100% vacuum is irrelevant.

 

[Vanadium 50]

then to store an oxidizing piece of metal in vault

And flaking. Don't forget flaking.

 

[Dale]

Still having a hard time to accept the given language though.

Well, in a sense you don’t have to accept it. You can use “vacuum” to mean the unobtainable ideal vacuum you think of. You just need to understand that other people use it differently. That way you can understand what they say (even if you wouldn’t say it that way) and you can clarify how you mean the term (so that they can understand what you say).

That said, it is easier to just use a word the way others use it.

Those measures are obviously showing uncertainties there.

Yes, that was before the modern definition of the meter, so at that time there was indeed still some experimental uncertainty in $c$ using SI units.

 

[Dangoe]

Thanks for the further explanations as well, clarifying it even more.

I feel this is all rather trivial than rocket science but for me very informative. Being authentic I imagine or at least hope other interested people at a similar level may find this thread helpful as well. I feel much better now for sure trying to understand things like this was itching me (even blocking somehow) and now it's gone.

I don't want just to swallow other people's or textbooks' facts, I want to understand them, way more fun, and ... okay, leaving that at this point.

Let me try to summarize in my own words the lessons learned: (subject to the next post)
After that some thoughts on some quotes I have in my mind as well.
Dangoe

 

[Dangoe]

Summarizing more or less in short:

"We measured c historically by the reference meter stored in Paris until we could achieve very fine-tuned measurements in a vacuum better than needed [here the point - seems not to hurt] while getting more precise clocks (atomic clocks, Cäsium-based, even future improvements ongoing today) for the second, better say for time measurements.

And while a speed or a velocity is described by distance per time and while c is the upper maximal limit adding any to the same like a natural constant which we got to measure so accurately with the given means and several technics, we're able to somehow reverse engineer it, setting the meter close to the old one - to the old second as well - relying on the more and more precise time measurement abilities to fine-tune s and then setting c once as defined.

And Tadaaa we got a unit definition fixing c, m, and s. Good enough for our purposes, like very good.
The speed of light in a vacuum or which media ever is always the same with corrections to a given media.

As we can't define distances without c we are only left with more precise time measurements to be able to accomplish that. Because c is fixed by reality - a constant, we can rely on it to figure out a distance by finetuning the time by a good clock (Ca).

Nah, even if described without major flaws this still feels a bit shaky or because of my issues or real issues lurking - the latter way less probable. ;)

There I have a fallback. Again the initial measurements with whatever means are crucial. Leading to my opening: Where and how was it measured? And therein again the vacuum question, okay less important than I thought. So sorry - that happens while writing. Let me see you tomorrow again, maybe write a better summary. >or I got a point (of course not). I imagine most of that is kind of off-topic to reply to. But I can't summarize my actual current understanding without encompassing much more, sorry. I can probably do better like breaking down long sentences into smaller ones. Am not running away, this is it, for now, the next try may be better.

Dangoe

 

[Dangoe]

I think I need some time off, driving me crazy and consuming way too much of my time off. Coming back, until then!

 

[Dale]

Where and how was it measured?

Where and how was what measured?

 

[Dangoe]

Where and how was what measured?

c
I mean it wasn't guessed in the first place, so measured somehow - we had the uncertainties lately in the historical context. Things are still hidden from me behind a paper wall, I can ask my local uni or just pay access or try zlib, anyway at one point they were measuring, getting better, and only then we have got the unit definitions. This didn't fall from the sky.

 

[jbriggs444]

I mean it wasn't guessed in the first place, so measured somehow - we had the uncertainties lately in the historical context. Things are still hidden from me behind a paper wall, I can ask my local uni or just pay access or try zlib, anyway at one point they were measuring, getting better, and only then we have got the unit definitions. This didn't fall from the sky.

I think about it a bit differently.

We try to measure things in the most accurate way possible. If we measure distance, we use the most accurate distance measuring tools we can make. If we want to measure time, we use the most accurate clocks we can build.

But measurement by itself is not enough. We want to be able to compare my measurement over here against your measurement over there. We need standards. Standard units. Comparisons. Reliable, repeatable, traceable comparisons. [There is a term for this: "metrology"].

We want a consistent repeatable standard against which we can all compare our meter sticks.
We want a consistent repeatable standard against which we can all compare our wrist watches.
We want a consistent repeatable standard against which we can compare our standard lab weights.

If the most consistently repeatable (not necessarily the most accurate) way we have of establishing a standard distance is to examine two scratches on a particular metal bar supported in a particular way then that is what we will use for a standard of distance. And we did for a while.

If the most consistently repeatable way we have of establishing a standard time is as a fraction of the duration of a tropical year then that is what we will use for a standard of time. And we did for a short while.

We can judge consistency and repeatability by doing repeated comparisons and seeing that they come out the same way every time within some tolerances. We can get statistics on how rough the tolerances are.

But technology moves on. If a distance measuring apparatus based on interferometry turns out to deliver more accurate comparisons than a bar with scratches while still maintaining consistency and reliability then we will change our standard definition for distance units accordingly.

But we also do not want to tie our definition to one exactingly precise description of a specific measuring device. So we do not define our standard in terms of a "Hewlett-Packard 5710-A dual column gas chromatograph with flame analyzation detectors". Instead, we word the standard in vendor-neutral terms involving physical laws according to our well-verified understanding of how the universe works. [There is a certain amount of distaste for anchoring definitions to physical artifacts when well verified physical laws are available instead].

This, even though the whole point of the definition is to be able to realize the definition by building a device to perform reliable, repeatable, consistent measurements that match, within reason, what a hypothetical ideal device would measure.

 

[Dangoe]

@jbriggs444: You are basically explaining why we invented units and why a Rolex is better than a sundial. I mostly agree, except at the end:

...physical laws according to our well-verified understanding of how the universe works.

That's relative. From overwhelmingly good to not at all. We are not in a Hollywood movie.

 

[jbriggs444]

@jbriggs444: You are basically explaining why we invented units and why a Rolex is better than a sundial. I mostly agree, except at the end:That's relative. From overwhelmingly good to not at all. We are not in a Hollywood movie.

If you want to claim that our understanding of the universe is wrong, you are in the wrong forum. Our unit definitions are on solid ground. Very solid.

If you want to claim that our understanding is as ludicrous as Hollywood physics... Politeness requires that I shut up now.

 

[hutchphd]

I mean it wasn't guessed in the first place, so measured somehow - we had the uncertainties lately in the historical context.

It was initially guessed to be infinite (I would document this but why should I bother?) Then it was measured (most notably perhaps by Romer)
This is my last respoinse, because I prefer thoughtful people If nobody responds to you, that may be a clue.

 

[hmmm27]

I mean it wasn't guessed in the first place, so measured somehow - we had the uncertainties lately in the historical context. Things are still hidden from me behind a paper wall, I can ask my local uni or just pay access or try zlib, anyway at one point they were measuring, getting better, and only then we have got the unit definitions. This didn't fall from the sky.

Have you tried Wikipedia ? or YouTube, for that matter.

 

[PeterDonis]

We are not in a Hollywood movie.

Exactly. Which means you should not be making off the cuff claims that you cannot back up.

The OP question has been sufficiently addressed. Thread closed.