Speed and Distance...

[69dodge]

I drive somewhere at 100 km/h. How fast do I have to drive back to average 200 km/h for the round trip?

201 km/h?

If you drive for the same time at two different speeds, you can just average the speeds. But if you travel the same distance, you spend less time at the faster speed, so it counts less, and your average speed is therefore closer to the slower speed.

 

[69dodge]

Originally posted by Brian
Hmmm. Still seems to rely on cycles per second.

Not sure what you mean.

The clock adjusts its oscillator's frequency to maximize the absorption of the microwaves by the cesium. Then, a second is defined to be 9 192 631 770 cycles of the oscillator when it's running at that frequency.

We don't have to know how long a second is before we start. The clock tells us how long a second is.

c depends on meters and meters depend on seconds and seconds depend on c...

c is the speed of light. The microwaves in a cesium clock are light, basically. But, the length of a second doesn't depend on how fast the light travels; it depends on what color it is. Ok, not literally color---microwaves are invisible---but you get the idea. Visible light comes in various frequencies, which show up as different colors, and microwaves come in various frequencies too. Cesium atoms like to absorb microwaves of a certain frequency. So the clock tries out microwaves of different frequencies, and when it finds the one that results in the greatest absorption by the cesium, it locks onto it. Then it just counts out 9 billion cycles or so (whatever the exact number is), and calls that one second.

Once we know how long a second is, we can divide it into 299 792 458 parts and use some other piece of equipment to measure how far light travels in that small fraction of a second. Then we call that distance one meter.

 

[Brian]

Not sure what you mean.

The clock adjusts its oscillator's frequency to maximize the absorption of the microwaves by the cesium. Then, a second is defined to be 9 192 631 770 cycles of the oscillator when it's running at that frequency.

We don't have to know how long a second is before we start. The clock tells us how long a second is.c is the speed of light. The microwaves in a cesium clock are light, basically. But, the length of a second doesn't depend on how fast the light travels; it depends on what color it is. Ok, not literally color---microwaves are invisible---but you get the idea. Visible light comes in various frequencies, which show up as different colors, and microwaves come in various frequencies too. Cesium atoms like to absorb microwaves of a certain frequency. So the clock tries out microwaves of different frequencies, and when it finds the one that results in the greatest absorption by the cesium, it locks onto it. Then it just counts out 9 billion cycles or so (whatever the exact number is), and calls that one second.

Once we know how long a second is, we can divide it into 299 792 458 parts and use some other piece of equipment to measure how far light travels in that small fraction of a second. Then we call that distance one meter.

How is the clock calibrated? How is frequency determined?
And to get damn freaky, how is color determined?
The first question is the most important, I think.

Christ, by what rule does the clock "adjusts its oscillator's frequency to maximize the absorption of the microwaves by the cesium"?
GIGO?

I'm curious. I see a serpent eating its tail.

 

[Vim Razz]

I see a serpent eating its tail.

Exactly. You have three interdependant values. If you know any two you can calculate the third.

If you only know one, then that tells you nothing about the other two.

Any number of methods can be used to measure the values you need. After that, it's just a mater of making sure that everybody's counting with the same units. (so that my foot is the same as your foot, as opposed to our individual feet.)

 

[Hellbound]

Hmmm. Still seems to rely on cycles per second.
c depends on meters and meters depend on seconds and seconds depend on c...

Actually, it's all based on physical light, but it's defined int hose terms.

I think you're confusing yourself by mixing up the basis with the definition.

If we look into reality, we can figure how many cycles a certain atom performs in an arbitrary time. We call that time a second. In other words, a second is howevermany cycles of the Cesium atom, as others stated. It doesn't matter what we base it on, as long as it's constant. Any arbitrary length of time is fine. However, the actual vibrations of the atom are not dependant on seconds, or on any other unit of time. One simply counts cycles.

Likewise, c is not based on meters, it's simply measured in meters. We can, again, use the second. the distance light travels in a specificed fraction of a second is one meter. We don't even have to use the second...it's just easier to write. We could just as easily and accurately define a meter as the distance travelled by light in the time it takes for (9 192 631 770/299 792 458) cycles of a Cesium atom.

The problem is you seem to be thinking that meters and seconds define light or vibration. They don't, they simply label them. ANY arbitrary unit would work, as long as there is an external reference. Think of our units as variables in algebra...we use meter to represent a certain physical distance that light travels in a set amount of time. We use second to equate to a certain number of cycles of a particular atom. The meter or second are dependent on physical items for their basis, at which point they can them be defined in terms of each other much more easily than deriving all of them from physical attributes.

Now, some crossover is necessary due to the nature of things. Speed, the measurement, is directly dependant upon both distance and time. However, speed, the physical property of light, is the smae no matter what. It will be equivalent, with appropriate conversion factors, no matter what arbitrary units one measures it in.

To go even farther, it doesn't matter if the units rely on each other, because the physical properties do not. We could measure distance in Puppy-sized Milkbone Brand Dog Biscuit Lengths and time in Eyeblinks...as long as the units are standardized and accurate the physics (the laws and theories and such) will work out exactly the same. The only things that would change would be the numbers (which would be identical with a conversion factor, much like metric-english) and the names for the units.

I can't expalin it any better, and others I'm sure have said the same thing. However, it's simply not really an area that matters. It's like choosing the name for your puppy. Youc an call it Spot, Rover, Killer, Fluffy, Furrball, George, or Patty, and it's still a puppy. Whatever the name, the physical reality that name represents does not change.

 

[CurtC]

Brian, I suspect you're being intentionally obtuse here. There are two physical constants that are taken as absolutes: the frequency of a Cesium atom, and the speed of light. One second is defined as a certain number of cycles of the Cesium atom's oscillation.

One meter is defined as how far light will travel, in a vaccuum, in that one second. So the meter is derived from those two constants.

Now that a meter and a second are nailed down, you can derive other measurements, such as speed. Of course, if you try to derive the speed of light this way, you'll just find that "c=c". Is that your idea of circular? Any system of measurements must have identities where if you try to derive the quantities of the basic units, you'll come up with "base unit = base unit". OK?

If you're asking how the clock is calibrated, that's a different issue. The second is defined as 9192631770 cycles of Cesium. You could imagine a world where you just count those cycles, but for practical reasons we set up an oscillator to mimic it. Metrologists can explain the various ways that they can assure the oscillator is within X ppm of the real answer, but that seems to be beside your point of the units being curcularly referenced, which I hope is clear by now that they're not.

 

[epepke]

Hmmm. Still seems to rely on cycles per second.
c depends on meters and meters depend on seconds and seconds depend on c...

c depends on the structure of flat Minkowski spacetime in this universe. One meter north/south is the same as one meter east/west. When the meter stick is turned not into other directions in space but into time, it's one light-meter, which is a bit less than three nanoseconds.

 

[Rocky]

got a lucky break not going end-o

No kidding. I walked away thanks to lots of safety gear and a VERY low center of gravity.

 

[rppa]

Originally posted by Brian
The clock adjusts its oscillator's frequency to maximize the absorption of the microwaves by the cesium. Then, a second is defined to be 9 192 631 770 cycles of the oscillator when it's running at that frequency.
We don't have to know how long a second is before we start.

How is the clock calibrated? How is frequency determined?

I'm confused as to why you don't think the above description answers your question.

The clock is adjusted until it matches the cesium oscillations. All we know is "it matches". We haven't assigned it a number. We just know it matches our standard.

Just like when the length standard used to be a physical artifact. If we cut something to be that same length, we haven't used a length measuring device. We haven't had to define an inch or a meter before doing the matching and cutting. We just lined it up and cut.

Same thing if we used a balance scale. Suppose I have a lump of lead which I call "1 standard groo" and I use it on one pan of a scale to calibrate other 1 groo lumps of lead. Would you ask, "but how do you know how much 1 groo is?" I don't. I call this lump of lead a groo, and everything that matches it is also a groo.

And the same thing here. I don't a priori have a number assigned to my cesium atom. I match the clock to it. Now I have a clock whose property is "rate is same as cesium atom", whatever that rate may be. Once it's running at that rate, I define the second to be so many standard ticks.

 

[Atlas]

We knew the approximate length of time a second was by convention. We had divided a day into hours and hours into minutes and minutes into seconds.

It makes sense that once we figured out how long a cesium occillation was we knew that it would be 9 billion+ occillations and calibrated our devices with our previous arbitrary standard in mind but to new exacting specifications.

 

[Brian]

Brian, I suspect you're being intentionally obtuse here. There are two physical constants that are taken as absolutes: the frequency of a Cesium atom, and the speed of light. One second is defined as a certain number of cycles of the Cesium atom's oscillation.

One meter is defined as how far light will travel, in a vaccuum, in that one second. So the meter is derived from those two constants.

Now that a meter and a second are nailed down, you can derive other measurements, such as speed. Of course, if you try to derive the speed of light this way, you'll just find that "c=c". Is that your idea of circular? Any system of measurements must have identities where if you try to derive the quantities of the basic units, you'll come up with "base unit = base unit". OK?

If you're asking how the clock is calibrated, that's a different issue. The second is defined as 9192631770 cycles of Cesium. You could imagine a world where you just count those cycles, but for practical reasons we set up an oscillator to mimic it. Metrologists can explain the various ways that they can assure the oscillator is within X ppm of the real answer, but that seems to be beside your point of the units being curcularly referenced, which I hope is clear by now that they're not.

I want to start here, I'm not skipping the Huntsmans answer. Just to be clear, I'm not being intentionaly obtuse. I'm not trying to be difficult. I've been thinking of randomly slapping a few more smileys in my posts so that no one will get the idea I'm being confrontational.

I've seen the Sears Tower, I've been in an airplane, so I do know for a fact that these measurements work.

By reading this and the posts above and below I think I get it. You don't need to measure the cycles of Cesium in cycles per second. Just count them 1,2,3,4,5.... and when you hit 9,192,631,770 you call it a second by convention.

 

[Brian]

c depends on the structure of flat Minkowski spacetime in this universe. One meter north/south is the same as one meter east/west. When the meter stick is turned not into other directions in space but into time, it's one light-meter, which is a bit less than three nanoseconds.

This one I'll just call it at way over my head and leave it at that.

 

[CurtC]

The clock is adjusted until it matches the cesium oscillations. All we know is "it matches". We haven't assigned it a number. We just know it matches our standard.

Just like when the length standard used to be a physical artifact. If we cut something to be that same length, we haven't used a length measuring device. We haven't had to define an inch or a meter before doing the matching and cutting. We just lined it up and cut.

The question about calibration has to do with how closely you know a secondary standard matches the primary. In your meter-bar example, that second bar won't be exactly the same length as the primary standard, so someone needs to figure out what the error tolerance is. Then if you have a ternary standard based on the secondary, the errors will add. This field of study is called metrology - it's what the people at the National Institute of Standards and Technology do (in the US).

With the Cesium clock, this oscillator/counter is the secondary standard. The primary is the Cesium atoms themselves. So someone has to characterize how closely the clock's oscillator matches the Cesium atoms, and the error for them is typically one second every few hundred thousand years. NIST has some better ones.

By the way, I work for a company that makes Cesium clocks.

 

[epepke]

This one I'll just call it at way over my head and leave it at that.

I don't believe that it's over your head. Work with me.

The universe has four dimensions. Three dimensions of space and one of time. Because we move so slowly, we think they're fundamentally different things, but they aren't. c is simply a number that compares time to space. According to c, a nanosecond in time is the same overall "distance" as a bit more than a foot is a spatial distance.

 

[TeaBag420]

I don't believe that it's over your head. Work with me.

The universe has four dimensions. Three dimensions of space and one of time. Because we move so slowly, we think they're fundamentally different things, but they aren't. c is simply a number that compares time to space. According to c, a nanosecond in time is the same overall "distance" as a bit more than a foot is a spatial distance.

I suspect that more qualified people than I will explain to you why you're wrong. Nonetheless, you're looking very lovely today.

 

[Brian]

I don't believe that it's over your head. Work with me.

The universe has four dimensions. Three dimensions of space and one of time. Because we move so slowly, we think they're fundamentally different things, but they aren't. c is simply a number that compares time to space. According to c, a nanosecond in time is the same overall "distance" as a bit more than a foot is a spatial distance.

My curiosity is equal to my lack of education. (and my laziness)
What is a dimension? I know length, width and height. I worked as carpenter. I never stopped to think what that means.
A solid definition would be a good place to start. Like how can I look at a 2 by 4 and see time.
And...
"Because we move so slowly, we think they're fundamentally different things, but they aren't. "
Slowly compared to what?

Again, I'm not trying to beg an agument here. I'd start this topic off with the guy on the bar stool next to me.

 

[TeaBag420]

Brian, I suspect you're being intentionally obtuse here. There are two physical constants that are taken as absolutes: the frequency of a Cesium atom, and the speed of light. One second is defined as a certain number of cycles of the Cesium atom's oscillation.

One meter is defined as how far light will travel, in a vaccuum, in that one second

Because we are magnanimous, we shall offer you an opportunity to rephrase. Should you require a wire coathanger, one will be provided upon request. Nonetheless, you look very lovely today.

Bonus points for correcting the spelling.

 

[Ziggurat]

My curiosity is equal to my lack of education. (and my laziness)
What is a dimension? I know length, width and height. I worked as carpenter. I never stopped to think what that means.
A solid definition would be a good place to start. Like how can I look at a 2 by 4 and see time.

You convert between length and time by using c (~3x10^8 meters/second), which is an absolute quantity. To convert length to time, divide by c. To convert time to length, multiply by c. Example: 1 meter /c is approximately 3.3x10^-9 seconds (a rather short time interval).

And...
"Because we move so slowly, we think they're fundamentally different things, but they aren't. "
Slowly compared to what?

Slowly compared to the speed of light.

 

[rppa]

The question about calibration has to do with how closely you know a secondary standard matches the primary. In your meter-bar example, that second bar won't be exactly the same length as the primary standard, so someone needs to figure out what the error tolerance is. Then if you have a ternary standard based on the secondary, the errors will add. This field of study is called metrology - it's what the people at the National Institute of Standards and Technology do (in the US).

With the Cesium clock, this oscillator/counter is the secondary standard. The primary is the Cesium atoms themselves. So someone has to characterize how closely the clock's oscillator matches the Cesium atoms, and the error for them is typically one second every few hundred thousand years. NIST has some better ones.

By the way, I work for a company that makes Cesium clocks.

OK, granting all that. How does that make the Cesium standard "circular"? You're saying that secondary and tertiary standards are less repeatable than the primary standard.

But the primary standards for time (Cesium) does not depend in any way on the primary standard for distance (light travel). So where's the circle?

 

[epepke]

My curiosity is equal to my lack of education. (and my laziness)
What is a dimension? I know length, width and height. I worked as carpenter. I never stopped to think what that means.
A solid definition would be a good place to start. Like how can I look at a 2 by 4 and see time.

I can't give you a definition. That would be jumping the gun at this point. I can give you a metaphor.

A 2 by 4 is probably not the easiest of examples. So let's take a movie.

At any one time, a movie is entirely 2-dimensional. It's projected onto a flat screen. Of course, the screen has a little depth, but that isn't important here. A movie also moves through time.

Now, take that movie and print each frame of the movie on a sheet of paper. You will now have a stack of paper, a 3-dimensional object. The width and height of the movie are expressed in the same units, inches, if you like. The depth of the movie is expressed in time. A one-minute movie would result in a stack of paper one minute in depth.

You could also measure the depth of a one-minute movie with a scale. I think it would come out to about 10 inches. So, you could come up with a scaling factor: 1 minute = 10 inches.

In this case, the scaling factor depends on arbitrary values, such as the number of frames per second and the thickness of each sheet of paper. When dealing with actual time, though, the scaling factor is built into the universe. It's c. It seems to be a constant, everywhere we look, even when looking at distant galaxies (what we see is also far back in time). The value doesn't change. The numbers we use to represent c may change. Just as you can measure the length of a 2 by 4 in inches, centimeters, feet, yards, etc. and the numbers will be different, but the length itself does not change.

Now, I'm leaving out a lot of things about spacetime that are important (such as that Minkowski thing), but at this point, to talk about them would be jumping the gun.

To make a complete system of measurement, all you really need is c and another unit. The other unit can be completely arbitrary, but it should also be a constant.

By reading this and the posts above and below I think I get it. You don't need to measure the cycles of Cesium in cycles per second. Just count them 1,2,3,4,5.... and when you hit 9,192,631,770 you call it a second by convention.

Exactly. We could take the second as our second unit. For convenience, we might want to have scales to measure distances. From c, we get that a nanosecond in time comes out to a little more than a foot in space. That's the system I usually use for visualization purposes. I call the distance measurement a "bigfoot." I like this, because the units are easy to understand and also because, in this case, the number used for c is 1, which is easier to remember than 299,792,458, which is what it would be in the metric system.

Again, I'm not trying to beg an agument here. I'd start this topic off with the guy on the bar stool next to me.

I appreciate the opportunity to go through the intellectual exercise of trying to traverse subjects in an elementary fashion. Every time I do this, I get more insight.