Speed and Distance...

[TillEulenspiegel]

Not adding anything intelligent but I thought it funny...A 2x4 isn't.

 

[rppa]

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

A light bulb. I think I know what you're saying (Brian that is; I'm not talking to myself). You're envisioning a lab where they say "OK, I measure the Cesium frequency as 1.23456 GHZ and the clock as 1.23457 GHz. Adjust the clock. OK, now I measure the Cesium frequency as 1.23456 GHz and the clock as 1.23456 GHz. It's calibrated." I agree that would require our frequency measurement device to be itself calibrated, and would therefore be circular.

But I don't think that's what's going on. I think they adjust a stable microwave source until it resonates with the Cesium. The Cesium itself is the measurement device, and it tells us when we get the frequency right. The only external measurement we need is the ability to determine that the resonance is happening. No frequency measurement has happened yet.

Then when we have the microwave matching the Cesium, we can count oscillations. A certain number of those becomes our standard second. That's the first time in this process that a unit of time enters into anything we're doing.

Now, you bring up something interesting and mysterious. When NIST makes their announcements that they've just made a new clock 1000 times more accurate than the previous one ... how do they KNOW? How can you know your clock is accurate to one part in whatever if you have no other clock to compare it to? I have no idea, but I'm guessing it involves cesium resonances again.

 

[Atlas]

Now, you bring up something interesting and mysterious. When NIST makes their announcements that they've just made a new clock 1000 times more accurate than the previous one ... how do they KNOW? How can you know your clock is accurate to one part in whatever if you have no other clock to compare it to? I have no idea, but I'm guessing it involves cesium resonances again.

Apparently this was discussed in the November 18, 2004 issue of Science. I was reading a short review of the article in mit technology review.(Free subscription required I think.) I'm not sure what they mean about the strontium ion clock. It sounds less accurate than cesium but perhaps some advantage concerning light calibration. Here is the review of the Science article.
<blockquote> Light Clock Promises Finer Time

December 3, 2004


Making the most of time requires that time be well defined. And in order to be precise, a definition of time must involve something that happens very quickly.

The current definition of a second is the duration of 9,192,631,770 oscillations of cesium atoms excited by microwaves. Today's cesium atomic clocks are accurate to within one million billionth of a second, or 1 second in 30 million years.

This is precise enough for a cluster of orbiting satellites to calculate the position of a stationary object to within a millimeter. For moving objects like cars and planes, however, the accuracy is a few meters, which is not enough to allow a global positioning system to, for instance, automatically land a plane.

Researchers from the National Physical Laboratory in England have made a prototype atomic clock that divides time into slices based on optical radiation, or lightwaves, rather than microwave radiation.

Lightwaves are smaller and faster than microwaves, and so divide time into much finer slices, which makes for higher accuracy. Such clocks could eventually improve global positioning systems, make space exploration more accurate, and more accurately test the laws of physics.

The researchers' strontium ion clock prototype is accurate to 3.4 million billionths of a second, which is about three times less accurate than the best cesium clocks, but is potentially precise enough that it would be limited by the current definition of the second, according to the researchers. Given a redefined second, optical clocks could be a thousand times more accurate than the best clocks of today.

Such a clock would not lose a second over the lifetime of the universe.

The researchers' optical clock could be used for global positioning system ground stations in five years and on satellites in 10 years, according to the researchers. </blockquote>(edit: After reading that strontium ion paragragh again, it seems to say that right now the prototype is less accurate than cesium, but as they develop it, it will require the redefinition of the second to exploit its increased accuracy potential.

 

[Rocky]

Now, you bring up something interesting and mysterious. When NIST makes their announcements that they've just made a new clock 1000 times more accurate than the previous one ... how do they KNOW? How can you know your clock is accurate to one part in whatever if you have no other clock to compare it to? I have no idea, but I'm guessing it involves cesium resonances again.

It has to do with known sources of instability and error.

a Cesium clock actually uses several million atoms of Cesium. The measured frequency is an average of that group. If a single atom could be measured (like with a mercury clock) it would remove much of the uncertainty.

Another of the major issues is, at a certain point, it becomes impossible to set a second clock to the first since the errors of transferring the time are greater than the uncertainty of the clocks. Also you can't move either clock since doing so will induce relativity "errors".

 

[Atlas]

Another of the major issues is, at a certain point, it becomes impossible to set a second clock to the first since the errors of transferring the time are greater than the uncertainty of the clocks. My article catagorized the error involved as a change from 1 second in 30 million years to less than a second over the lifetime of the universe, but I hadn't thought about the implication that you suddenly have to guess exactly when the second hand is on 12 in order to set the more accurate clock. Funny.

Also you can't move either clock since doing so will induce relativity "errors". That's kind of a funny upshot of the whole thing too.

 

[Rocky]

September 2002 Scientific American was all about time and clocks. Lots of really good stuff.

 

[Ziggurat]

The researchers' strontium ion clock prototype is accurate to 3.4 million billionths of a second, which is about three times less accurate than the best cesium clocks, but is potentially precise enough that it would be limited by the current definition of the second, according to the researchers. Given a redefined second, optical clocks could be a thousand times more accurate than the best clocks of today.
...
(edit: After reading that strontium ion paragragh again, it seems to say that right now the prototype is less accurate than cesium, but as they develop it, it will require the redefinition of the second to exploit its increased accuracy potential.

Part of the confusion here is that in science, accuracy and precision are not the same thing. Here's a bit of a metaphor for the distinction: let's say you've got two people playing darts, player A and player B. When player A throws darts at the dart board, they fall all over the board, but the average position is always around the bullseye. This player is accurate but not precise. When player B throws darts at the board, they all land in a very tight bunch, but the bunch is always to the left side of the bullseye. This player is precise but not accurate. For a clock, the precision is limited by the shortest "tick" of the clock. Make that shorter, and the clock is more precise, but it may not help your accuracy.

 

[Atlas]

Part of the confusion here is that in science, accuracy and precision are not the same thing. Here's a bit of a metaphor for the distinction: let's say you've got two people playing darts, player A and player B. When player A throws darts at the dart board, they fall all over the board, but the average position is always around the bullseye. This player is accurate but not precise. When player B throws darts at the board, they all land in a very tight bunch, but the bunch is always to the left side of the bullseye. This player is precise but not accurate. For a clock, the precision is limited by the shortest "tick" of the clock. Make that shorter, and the clock is more precise, but it may not help your accuracy.

Good point and good example.

 

[Brian]

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.

I have to admit, I don't really get it. The first thing that popped into my head when reading about a length of film and a pile of prints made from the film was static and dynamic time. Which has nothing at all to do with what we were talking about.

 

[Brian]

A light bulb. I think I know what you're saying (Brian that is; I'm not talking to myself). You're envisioning a lab where they say "OK, I measure the Cesium frequency as 1.23456 GHZ and the clock as 1.23457 GHz. Adjust the clock. OK, now I measure the Cesium frequency as 1.23456 GHz and the clock as 1.23456 GHz. It's calibrated." I agree that would require our frequency measurement device to be itself calibrated, and would therefore be circular.

Where I was when I started thinking about this, I don't think I had anything this precise in mind. I started with: all units of measure depend on other units (not true, it seems), then you need to use seconds to measure how long a second is (not I true, it seems).
When I asked how the clock was calibrated, I still assumed you needed a second to define a second. I figgured if you're going to use a clock to measure Cesium in cycles per second, how do you tell the clock how long a second is. This has been cleared up for me.

 

[epepke]

I have to admit, I don't really get it. The first thing that popped into my head when reading about a length of film and a pile of prints made from the film was static and dynamic time. Which has nothing at all to do with what we were talking about.

You're right; it has nothing at all to do. But as usual, there are many ways to become confused. Concepts like static and dynamic are unimportant here and in fact are confusing. All that is important is that the stack of prints has a thickness which can be seen as a spatial dimension. Have you got that part?

 

[Brian]

You're right; it has nothing at all to do. But as usual, there are many ways to become confused. Concepts like static and dynamic are unimportant here and in fact are confusing. All that is important is that the stack of prints has a thickness which can be seen as a spatial dimension. Have you got that part?

Sort of. A block of wood could substitute for the pile of prints though? For this example, what is it about it being film with images on it that makes it different?
Let me go off on a limb. Let's say the film is of a car driving down a street. The right most period is where the car is, each line is a photo in the stack.

.
..
...
....
.....

Something to do with that?

 

[rppa]

Sort of. A block of wood could substitute for the pile of prints though?

Where does the relation between size and time come into a block of wood?

For this example, what is it about it being film with images on it that makes it different? Let me go off on a limb. Let's say the film is of a car driving down a street. The right most period is where the car is, each line is a photo in the stack.

I don't know what you mean by "each line is a photo in the stack", but I think the idea was just to say that there's a direct relationship between size (of stack) and time. You can say that one inch corresponds to a minute (or whatever the conversion factor was). You can look at a 6" stack and say that represents six minutes of time. You can use a ruler to measure length (in time) of the film.

 

[epepke]

Sort of. A block of wood could substitute for the pile of prints though? For this example, what is it about it being film with images on it that makes it different?
Let me go off on a limb. Let's say the film is of a car driving down a street. The right most period is where the car is, each line is a photo in the stack.

.
..
...
....
.....

Something to do with that?

Yes. That's pretty good. That's why I like these discussions; everytime I engage in one I learn another way of looking at it.

So in your list, there's a series of lines of dots. I don't know what it measures going down on your screen. On my screen, it's about 3/4 of an inch. (I just measured using my pinky finger.) So, 3/4 inch = 4 whavevers, assuming that a whatever is the time distance between each row of dots and the subsequent one.

Are we agreed on this?

 

[Brian]

Yes. That's pretty good. That's why I like these discussions; everytime I engage in one I learn another way of looking at it.

So in your list, there's a series of lines of dots. I don't know what it measures going down on your screen. On my screen, it's about 3/4 of an inch. (I just measured using my pinky finger.) So, 3/4 inch = 4 whavevers, assuming that a whatever is the time distance between each row of dots and the subsequent one.

Are we agreed on this?

Yes, I'm with you. One question, does time distance mean the same thing as unit of time? Like a second or a half second ?

 

[Atlas]

Yes, I'm with you. One question, does time distance mean the same thing as unit of time? Like a second or a half second ?

Since you've made this a kind of barstool conversation, I'll chime in and wait for a correction.

Generally a time distance measurement is thought of as a distance measure. "That star is more than 20 light years away."

A light second is 186,000 miles.

A light nanosecond is about a foot.

But I think it's thought of as a distance measure as a matter of convention. As long as everyone is conversent with what's being measured there is no real ambiguity in discussing it as a time phenomenon.

If a car zooms past at exactly sixty miles per hour (88 feet per second) and you're measuring with a stop watch how fast it covers the 264 foot track... You'll shout out "That's 3 seconds."

In a similar fashion, if everyone knows you're talking about light speed, you can hold up a foot ruler and say, "That's approximately a nanosecond."

 

[epepke]

Yes, I'm with you.

Good. So in your diagram, which let's say describes 10 second of motion of a car,

.
..
...
....

ten seconds is about half a vertical inch. (I'm using a different computer now.) So, 20 seconds = 1 inch. But that's an arbitrary conversion, based on my monitor.

One question, does time distance mean the same thing as unit of time? Like a second or a half second ?

Time (and distance) are measured in units, but it's a little more complex than that.

Take your 2 by 4. It has a length. The length is a physical property of the 2 by 4. It is the same whether you measure it in inches or centimeters, but you'll get different numbers. This, I think, is fairly obvious. You can compare lengths of 2 by 4s or cut a second 2 by 4 to the length of another without using a tape measure or yardstick.

So let's talk about units. You would probably use the same tape measure for your 2 by 4 whether it's horizontal or upright. You'd be measuring in the same units either way. This is a natural way of using units. Note that it doesn't matter whether you use inches or centimeters, so long as it's the same.

Sometimes this is not the case. Consider an airplane in the US. The altitude of the airplane is measured in feet. The horizontal distance is measured in statute miles. That's not so natural a way of using units, but it's OK in this case because of the way an airplane works. Commercial airliners, at least, fly mostly horizontally and usually only tilt up or down by a few degrees. So it isn't really important to consider altitude and horizontal distance the same kind of thing.

Now, for this to be a useful metaphor, we have to simplify it. Imagine it's an airplane on another planet (which magically happens also to use miles and feet). Imagine that the pilots on this planet really don't see that vertical distance and horizontal distance are the same sort of thing. They understand horizontal distance, and they understand vertical distance, but they just don't connect the two. Maybe they are on a planet with much higher gravity and the sky is always uniformly gray, so they didn't evolve the ability, or they can't tip their heads and can only see a single horizontal line, or something. It doesn't matter why. Imagine, also, that they don't think about time so much. Maybe they're like the Prophets in Voyager who just don't grok it, or they're precogs, or their brains use reversible computing and go at random rates. Again, it doesn't matter why. Also imagine that their airplanes always go nearly horizontal (maybe the high gravity).

They could still say some things about the motion of their airplanes. If the plane is climbing 100 ft for every mile it flies, they could say that it's climbing at a rate of 100 ft/mile. They could also measure the angle of their planes with a plumb bob inside them, and they'd know that the behavior of the plumb bob was related to the rate of climb or descent.

That would be the important number to them. The commercial airliners would go at 20 ft/mile. High-performance stunt planes would go at 150 ft/mile. There might be top-secret projects for fighters that can go at 200 ft/mile.

But then somebody gets an insight. Maybe this altitude thing is just another dimension, at right angles to the two horizontal spatial dimensions that they already know about. And then this slit-eyed monster starts to wonder what is a natural way of converting from feet to miles that doesn't depend on what kind of airplane that you can afford. It knows about the plumb bob. It reasons that, if the plumb bob were at a 45 degree angle, then the plane would be traversing the same amount of vertical distance as horizontal distance. And, at that rate, 5280 ft = 1 mile.

We are in a similar situation as these creatures. We understand three dimensions as the same. Maybe it's because some of our ancestors lived in trees, or because it's easy to build tall things, or because we can lie down. In any event, though we have a distinction between horizontal and vertical, it's minor, and we can overcome it easily. However, our brains have a strong distinction between space and time. Time is, to us, like the vertical dimension is to those creatures. But we can follow the same logic, and at the 45 degree angle, the conversion factor is not 5280 ft/mile. It's c. Of course, c may be in different units, like about 186,000 miles/second, or about 300,000,000 meters/second, but it's the same quantity.

This is a completely good metaphor for understanding up until 1905. It's still a mostly good metaphor, and in spacetime diagrams, the 45 degree angle is still used to represent c.

It's slightly wrong, because the creatures could conceivably think of planes that had 55 degree angles, which does not carry over to time. But that's that Minkowski stuff, and I'll save it for later.

I will say one thing. People talk about c as the speed of light in a total vacuum. That's kind of backward, but it's historical. c is a basic property of the universe. The real question is why does light go at c, which we perceive as a speed, in a total vacuum? But that's for later, too.

 

[Ziggurat]

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

No, it's a certain number of cycles defines a second, not the other way around. So seconds don't depend on anything spatial. C is also now defined as an absolute number, and likewise does not depend on meters. Rather, meters are defined by the combination of c (again, an absolute number now) and seconds, which we get from cycles which do NOT depend on c or meters. It's a one-way flow, not a circle.

 

[Brian]

Time is, to us, like the vertical dimension is to those creatures. But we can follow the same logic, and at the 45 degree angle, the conversion factor is not 5280 ft/mile. It's c. Of course, c may be in different units, like about 186,000 miles/second, or about 300,000,000 meters/second, but it's the same quantity.

Sorry it took awhile to reply, I'm not losing interest, I'm trying to wait untill I have time to read closely and try to digest it.
Can I summarize everything up to and including the first sentence I quoted as "due to some limitation of human perception time as a dimension is not even close to being as intuitive as length, width and height"?
I get the 5280 ft/mile and 45 degrees. Why this =c I don't understand.

Does the 45 degree angle have anything to do with the car travelling diagonally down and to the right in the stack of prints from the film?
.
..
...
....
That thing.

hmmm. That stack of prints would look different from the cross section than it would looking at it from the top. From the top it would look like the farther the car was from the left the farther away from the top it would look.
That have anything to do with it, or have I exited left field and begun walking around the parking lot?

edited to add: View from the top?

. . . .

 

[epepke]

Sorry it took awhile to reply, I'm not losing interest, I'm trying to wait untill I have time to read closely and try to digest it.

It's quite all right, in fact it's better.

Can I summarize everything up to and including the first sentence I quoted as "due to some limitation of human perception time as a dimension is not even close to being as intuitive as length, width and height"?

Yes.

I get the 5280 ft/mile and 45 degrees. Why this =c I don't understand.

c is just a name for the ratio that this is. Those people on the other planet might call their ratio q or something. When comparing feet to miles, the number comes out to be 5280 ft/mile. If they measured in kilometers versus cubits, the number would be different, but they'd still call the ratio q.

Does the 45 degree angle have anything to do with the car travelling diagonally down and to the right in the stack of prints from the film?

Yes. But we haven't gotten into that Minkowski thing yet, which complicates it somewhat.

hmmm. That stack of prints would look different from the cross section than it would looking at it from the top. From the top it would look like the farther the car was from the left the farther away from the top it would look.
That have anything to do with it, or have I exited left field and begun walking around the parking lot?

That's good insight, but you may be getting ahead a bit. It's essentially the same insight that's behind Special Relativity. In such a picture (which is deliberately simplified and doesn't have all the nuances of time, mind you), what you see is dependent on your relationship to the stack of prints. We can ignore the perspective projection and foreshortening now; I'm sure as a carpenter you're familiar with isolinear or orthographic diagrams such that the length of a beam parallel to another is the same no matter it the drawing depicts it as closer or farther away.

But still, if you happen to be looking along the path of the car, you won't see the car as moving; you'll see other things around the car as changing. Which is also what happens in a real car, or an airplane, because they fly smoother (sometimes, anyway). In an airplane, if you don't look out the windows, you might get the impression that the airplane is not moving.

Yet I think this is getting ahead.