How was the speed of light measured to such high precision?

[Ibix]

I don't quite understand this. Let's say the light interacts with the mirror for 1e-10 of a second before it bounces back. How would we detect this by varying the position of the reflecting mirror?

Using my simple approach of bouncing a laser off a mirror: The speed of light is $c$. The distance to the mirror is $x$. The delay due to interacting with the mirror and or your sensor electronics is $T$, and does not depend on the location of the mirror. The round trip time is therefore $t=T+2x/c$. Measure $t$ for a range of $x$ and you will get a straight line with an intercept. The slope of the line is $2/c$ and the intercept is the delay. Job done.

As noted by Dale, $T$ is most likely immeasurably small.

 

[h1a8]

you have already been told several times that it is insignificant and is doesn't affect
our use of the current measurements in science and technology

you are making a mountain out of a molehill by pushing your pet idea of something that just isn't relevant

You still haven't provided any links to your so called bottleneck
you have been asked to do that several times as well

This is clearly wrong. No one here stated that it was insignificant. One person stated it wasn't a bottleneck but later stated he wasn't sure (believes it to be insignificant). Even if one did then you are still wrong (as you stated I been told several times and not once). If someone did state this then where's the proof?
I never claimed the bottleneck was significant or insignificant. I stated that we don't know. If you disagree then kindly provide proof that the bottleneck is insignificant.

Like I said, it's IMPOSSIBLE to know the bottleneck to a decent degree of precision without measuring the speed of light WITHOUT MIRRORS.

Planck time proves a bottleneck (even if insignificant).

 

[h1a8]

Using my simple approach of bouncing a laser off a mirror: The speed of light is $c$. The distance to the mirror is $x$. The delay due to interacting with the mirror and or your sensor electronics is $T$, and does not depend on the location of the mirror. The round trip time is therefore $t=T+2x/c$. Measure $t$ for a range of $x$ and you will get a straight line with an intercept. The slope of the line is $2/c$ and the intercept is the delay. Job done.

As noted by Dale, $T$ is most likely immeasurably small.

The problem is measuring x to a decent degree of precision. We can definitely measure t to an awesome degree of precision, but not distance without using circular reasoning. But for extremely large distances, x may not need to be precise. I have to think about it.

 

[Ibix]

The problem is measuring x to a decent degree of precision.

You don't measure $x$. That's how you define $x$. If $T$ is significant you will find that your definition of $\lim_{t\rightarrow 0}x$ is not zero.

Alternatively, set up two mirrors facing each other and inject pulses so that some bounce off the far mirror and return while some bounce off the far mirror, then the near mirror then the far mirror again before being detected. The first lot have one interaction while the second have three, so the flight time for the second lot minus twice the time for the first lot is $T$.

 

[PeroK]

I don't quite understand this. Let's say the light interacts with the mirror for 1e-10 of a second before it bounces back. How would we detect this by varying the position of the reflecting mirror?

You could try posting that in the Introductory Physics Homework thread.

 

[Dale]

It's impossible to know the bottleneck size unless you can measure the speed of light with great precision without it having to bounce off mirrors.

It is not true that that is the only way to estimate it. However, we can measure c without mirrors and have done and have found no significant difference.

I never claimed the bottleneck was significant or insignificant.

The term “bottleneck” refers to the rate limiting step of a process. So if there even is a delay at all then the fact that it is so small as to be immeasurable indicates that it is not the rate limiting step and therefore not a bottleneck. You cannot have an insignificant bottleneck.

 

[russ_watters]

No process is instant. Light interacting with matter to bounce the light back make take a process of x of a second. To assume their is no bottleneck is asinine.

What if the electronics are only recording the measurement and not creating the measurement? You should read the linked article on interferometry, because the best measurements are not like measuring distance with a stopwatch. Interferometry is closer to measuring it with a ruler. Signal and processing delay are not a factor.

 

[Herman Trivilino]

We can definitely measure t to an awesome degree of precision, but not distance without using circular reasoning.

It appears you don't want to listen to what we're telling you. When we measure distances all we are doing is comparing the lengths of different objects. We know a skyscraper is taller than a person, there is nothing circular about that.

Do you really think that you're right and the tens of thousands of metrologists spread all across the globe are wrong?

When you need a new roof on your house and measurements of lengths are used to determine the cost do you reject the contractor's estimates because he's using circular reasoning to bill you?

 

[h1a8]

What if the electronics are only recording the measurement and not creating the measurement? You should read the linked article on interferometry, because the best measurements are not like measuring distance with a stopwatch. Interferometry is closer to measuring it with a ruler. Signal and processing delay are not a factor.

I was referring to the delay of the beam interacting with the mirror. An interferometer already has the distances set. But what if the distances are off (using bouncing light to measure distances accurately is using circular reasoning).

It appears you don't want to listen to what we're telling you. When we measure distances all we are doing is comparing the lengths of different objects. We know a skyscraper is taller than a person, there is nothing circular about that.

Do you really think that you're right and the tens of thousands of metrologists spread all across the globe are wrong?

When you need a new roof on your house and measurements of lengths are used to determine the cost do you reject the contractor's estimates because he's using circular reasoning to bill you?

I don't understand. The theory was to calculate the delay by varying the distance. But the distance can be off a significant amount. t = T +2/c *x

It is not true that that is the only way to estimate it. However, we can measure c without mirrors and have done and have found no significant difference.

The term “bottleneck” refers to the rate limiting step of a process. So if there even is a delay at all then the fact that it is so small as to be immeasurable indicates that it is not the rate limiting step and therefore not a bottleneck. You cannot have an insignificant bottleneck.

I would like to know what other ways man measures light with the same degree of accuracy without using mirrors. I still don't see a way man determines the delay is insignificant without proof. The linear line method where the intercept is the delay is faulty if x, the distance, is not measured to a sufficient degree of accuracy. And man usually measures distance with great accuracy by bouncing light (which becomes circular).

 

[russ_watters]

An interferometer already has the distances set. But what if the distances are off (using bouncing light to measure distances accurately is using circular reasoning).

That isn't true. Did you not read the article? An interferometer isn't measuring against its own length, that would be as pointless as using a hunk of metal alone!

The inteferometer has one stationary and one movable mirror and the signal is tuned to create the interference pattern, enabling precise measurement of the wavelength. The locations of the mirrors at the start isn't important; what matters is how far you move the movable mirror, locating a starting and ending point. Here's another article with more detail:
https://www.renishaw.com/en/interferometry-explained--7854

I still don't see a way man determines the delay is insignificant without proof.

As they say, the proof is in the pudding. If the error was actually unknown and actually much larger than believed, then the things people do that require accurate measurements would not work.

 

[FactChecker]

Suppose there is a significant delay at a mirror. It can be determined. It would be a constant delay even if the distances were doubled, tripled, or even increased by orders of magnitude. That constant term could be easily calculated and adjusted for. It would be the constant term in a linear fit of results from different distances to the mirror.

 

[Dale]

The linear line method where the intercept is the delay is faulty if x, the distance, is not measured to a sufficient degree of accuracy. And man usually measures distance with great accuracy by bouncing light (which becomes circular).

We have been over this already. There is no circularity involved.

Pre-1983 the length of a meter was measured by counting wavelengths of the light from a particular light source, not “bouncing light”. Thus the measurements of the speed of light were non-circular, but the single greatest source of error was the extant standard for length. I.e. the bottleneck was the length standard and all other errors combined (including any mirrors) were about 1/6 of the error of the length standard.

As a result we changed the standard of length to the speed of light. This resulted in an immediate improvement in the precision of length measurements by a factor of 6. It also meant that the speed of light was no longer measured at all but was defined exactly.

So, once again, there is no circularity in the measurement of the speed of light. If you are “bouncing light” to measure distance then the speed of light is known exactly. If you are measuring the speed of light then you are using pre-1983 meters and so you are not “bouncing light“ to measure distance.

 

[Herman Trivilino]

I don't understand.

When the length of an object is measured it's always a comparison to another object's length. There are only three possibilities: Suppose you have two objects, the lengths of which are $A$ and $B$. Either $A>B, A=B,$ or $A<B$. Since there is no circularity in that process, your claim that measuring a length is circular is false.

 

[sophiecentaur]

The whole point about choice of a definition is repeatability. People on the planet Zog should be in a position to build up a measurement system, identical to what's used on Earth without needing to have the King's big toe available everywhere in order to start off.

For a satisfactory system of units, everything has to pivot about quantities that can be reproduced in any Lab, anywhere. So atoms of a well behaved element are great for defining time and that gives you distance. Numbers of similar atomic nuclei (again, something that is chemically stable etc etc) can define your Mass unit. The electronic charge is a great way to start on Electrical units.

We suffer from a history in which none of the above were available when units were first defined but now is now.

 

[sophiecentaur]

As they say, the proof is in the pudding. If the error was actually unknown and actually much larger than believed, then the things people do that require accurate measurements would not work.

The questioner may not be aware of the very common experimental method of finding and eliminating 'offsets' by repeating an experiment with different known values and subtracting the results. Unknown errors become known errors.

 

[Herman Trivilino]

So atoms of a well behaved element are great for defining time and that gives you distance.

It does give you distance because of course of a reproducible way of measuring the speed of a light beam in a vacuum.

 

[sophiecentaur]

If and when we ever get to chat with the Scientists on Planet Zog, it would be a serious ego trip to find they arrived at the same philosophy as us. Otoh, it could be a gobsmacking surprise when we find that it's all based on King Zog's toe!

 

[Baluncore]

There seems to be a bottleneck of understanding here, combined with a fear of mirrors.

A mirror for an EM wave can be made from a flat conductive sheet. The reflection is from the surface layer of conductive atoms. If the wave penetrated more than one atom deep it would suffer multiple internal reflections which would increase energy losses within the mirror.

We can know that the zone of reflection must be spread over a depth of less than λ/4, or we would see destructive interference of reflected light.

An incident magnetic field causes a perpendicular current to flow on a conductive surface. That re-generates a perpendicular magnetic field, now opposite to the incident field. Turning left twice is the same as going back the way you came, i² = –1, reflect on that. The incident and reversed fields cancel into the mirror, so the incident energy must be carried away from the mirror in a reflected wave.

Since the incident and induced fields cancel into the mirror, the time needed to reverse must be very close to zero, or the phases into the mirror would not cancel, and the mirror would be lossy, making an inefficient reflector of energy.

This all suggests that the time delay of a mirror is less than the time needed to travel the ionic radius of a conductive atom. We do not know where the effective reflective surface of a mirror is, until we look near the face of the mirror, at standing waves formed between the incident and reflected rays . But it is the reflective surface we are interested in, so there is no problem, and no delay.

 

[Vanadium 50]

ombined with a fear of mirrors

Catoptrophobia ?

 

[Baluncore]

Catoptrophobia ?

I get confused by Catoptrophobia, Spectrophobia and Eisoptrophobia.
https://en.wikipedia.org/wiki/Spectrophobia

I fear Sciophobia.

 

[DrClaude]

This thread has reached its end.

Thanks to all that have contributed.

Thread closed.