Can anything be measured with a single measurement?

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In summary, the first step of measuring height is placing the end of a tape measure against the floor, and finding where the top of your head is against the tape. If you leave out the first step, the second step is useless.
  • #1
Jeff Root
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If I want to measure my height, I need to find not only
the location of the top of my head, but also the location
of the bottom of my feet. The difference is my height.

I make those measurements by placing the end of a tape
measure against the floor, and then find where the top of
my head is against the tape. If I leave out the first
step, the second step is useless.

Does that first step constitute a measurement?

If not, what is it?

Whatever it is, are all measurements like that? Every
measurement consists of (at least) those same two steps?

If I want to measure some property of a photon-- say the
simplest property that has a quantitative value, not just
existence versus nonexistence-- are there (at least) two
steps, like two measurements?

When I measure my height, the two steps necessarily take
place in different locations. Do they also necessarily
take place at different times, in my reference frame?
(You can assume that my head and my feet are not moving
relative to each other.)

How about when measuring a photon?

-- Jeff, in Minneapolis
 
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  • #2
Jeff Root said:
Whatever it is, are all measurements like that? Every
measurement consists of (at least) those same two steps?
What do you do when you measure your weight? (or, since we are talking physics, your mass :smile:)

Edit:
And...
Jeff Root said:
I make those measurements by placing the end of a tape measure against the floor, and then find where the top of my head is against the tape. If I leave out the first step, the second step is useless.

Does that first step constitute a measurement? (my bolding)
If that first step is a measurement, what was the result of it? (in e.g. centimeters or inches)
 
  • #3
This relates to Heisenbergs uncertainty principle.

What it comes down to is observation. In order to observe something, you have to interact with it, and that interaction thus changes it's "natural state". Some changes are noticable, most are not, but either way that object technically isn't the same as before you saw it.
 
  • #4
Jeff Root said:
Does that first step constitute a measurement?

If not, what is it?
It is equipment setup.

The first step does not measure the location of your feet.

Jeff Root said:
Whatever it is, are all measurements like that? Every
measurement consists of (at least) those same two steps?
I cannot think of any measurement that does not require some equipment setup.

Jeff Root said:
When I measure my height, the two steps necessarily take
place in different locations. Do they also necessarily
take place at different times, in my reference frame?
In fact, a measurement of length takes place simultaneously by definition.
 
  • #5
DennisN said:
What do you do when you measure your weight?
I have two bathroom scales: An old one with a spring and rotating
dial, and a new electronic one that seems to have some kind of
force sensor that I really have no idea how it works. When I use
the old one, I adjust the dial to zero, then I step on the platform
and wait a second or two for the dial to rotate under the indicator.
When I use the new scale I first step on it to turn it on, then step
off. The reading falls to 30 pounds for a moment, then to zero.
Then I step back on and hold very still while I watch the numbers
jump around for a couple of seconds until the thing decides how
much force I am putting on it, and the number locks in, so I don't
have to hold still any longer.

So the old scale I set to zero manually, because it always seems
to be slightly out of adjustment, and the new scale sets itself to
zero automatically the first time I step off of it, because that is
how it was designed to work. That would seem to correspond to
putting the end of the tape measure at the floor.

DennisN said:
(or, since we are talking physics, your mass :smile:)
A physician's "balance beam scale" balances my weight against
the weight of standard masses that slide along a scale. When I
move the masses so the two sides are in balance, the positions
of the masses on the scale indicate my mass. Complicated
enough that the "first step" may be hiding in there somewhere.
It is calibrated at the factory, though, and that seems likely to
be the "first step".

DennisN said:
If that first step is a measurement, what was the result of it?
(in e.g. centimeters or inches)
Usually zero centimeters, and zero inches.

-- Jeff, in Minneapolis
 
  • #6
Jeff Root said:
Usually zero centimeters, and zero inches.
Zero centimeters/inches... in relation to what? (I am not trying to be annoying, I promise :wink:, I'm trying to make an example of what @Dale said in post #4 above)
 
  • #7
Dale said:
It is equipment setup.

The first step does not measure the location of your feet.
If the top of my head is at 265 cm, it would probably be important to
note that the bottoms of my feet are at 100 cm. That sounds like a
measurement to me.

Dale said:
In fact, a measurement of length takes place simultaneously by
definition.
If I measure the distance I drive by noting that I start at mile marker
#100 and end at mile marker #130, is that "simultaneously"?

When someone measures the distance of a galaxy in the Hubble
ultra deep field in terms of the distance the light travelled, is that
"simultaneously"?

-- Jeff, in Minneapolis
 
  • #8
DennisN said:
Zero centimeters/inches... in relation to what?
I think the zero measurement is the relation between the location
of the end of the tape measure and the location of the bottoms of
my feet. It doesn't have to be zero, as I implied in my last post.

DennisN said:
(I am not trying to be annoying, I promise :wink:,
No way. Keep at me. I can be wrong more often than I'm right,
yet still make progress.

-- Jeff, in Minneapolis
 
  • #9
Jeff Root said:
I think the zero measurement is the relation between the location
of the end of the tape measure and the location of the bottoms of my feet.
But your intention in your original post was to measure your height, not measure the distance between the end of the tape measure and the bottoms of your feet.
 
  • #10
What I am trying to point out is that you are not making a measurement by setting the bottom of your feet to be 0 (origo). You are making a definition (or what Dale called above "equipment setup", or it could also be called "preparation").
 
  • #11
DennisN said:
But your intention in your original post was to measure your height,
not measure the distance between the end of the tape measure and
the bottoms of your feet.
Yes, the location of the bottoms of my feet is the first measurement,
and the location of the top of my head is the second. If I don't make
the first measurement-- that is, if I don't know where the bottoms of
my feet are in relation to the markings on the tape measure-- then
the measurement of the location of the top of my head doesn't tell
me anything about my height.

-- Jeff, in Minneapolis
 
  • #12
Jeff Root said:
If the top of my head is at 265 cm, it would probably be important to
note that the bottoms of my feet are at 100 cm. That sounds like a
measurement to me.
That would be a third step. One to set up the equipment (poorly) and two measurements. The extra measurement is not necessary in principle, but only because you set up your equipment poorly.

Jeff Root said:
If I measure the distance I drive by noting that I start at mile marker #100 and end at mile marker #130, is that "simultaneously"?
Suppose you started with the rear of your car at mile #100 and ended with the front of your car at mile #130. Is your car therefore 30 miles long? If not, why not?
 
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  • #13
DennisN said:
What I am trying to point out is that you are not making a
measurement by setting the bottom of your feet to be 0 (origo).
You are making a definition (or what Dale called above
"equipment setup", or it could also be called "preparation").
Can you say what is being defined?

Is there any difference between this setup step and measurement
of the starting point?

-- Jeff, in Minneapolis
 
  • #14
Dale said:
Jeff Root said:
If the top of my head is at 265 cm, it would probably be important to
note that the bottoms of my feet are at 100 cm. That sounds like a
measurement to me.
That would be a third step. One to set up the equipment (poorly)
and two measurements. The extra measurement is not necessary
in principle, but only because you set up your equipment poorly.
I don't see that anything is set up poorly.

When measuring a length, you need to know where to start measuring
and where to stop. You don't necessarily start at zero. Even if you do,
that value of zero is a measurement.

Dale said:
Jeff Root said:
If I measure the distance I drive by noting that I start at mile marker
#100 and end at mile marker #130, is that "simultaneously"?
Suppose you started with the rear of your car at mile #100 and
ended with the front of your car at mile #130. Is your car 30 miles
long? If not, why not?
Not, because I knew the car moved relative to the mile markers.
If I didn't know the car moved, then I would think it was 30 miles long.
I need information in addition to the start and end distances in order
to determine whether the car moved relative to the markers. If the
information was quantitative and sufficiently precise, I could calculate
the length of the car from the start and end positions. That could be
practical if the distance was 30 feet instead of 30 miles.

-- Jeff, in Minneapolis
 
  • #15
Jeff Root said:
that value of zero is a measurement.
That is where we disagree. The setting of the zero point is not a measurement, it is part of the equipment setup. In my opinion you define the zero point by your setup, you don’t measure it.

Jeff Root said:
Not, because I knew the car moved relative to the mile markers.
Exactly. A measurement of distance must be simultaneous because otherwise the length of moving objects will not be valid. The use of the mile markers is a perfectly legitimate means of measuring the length of objects provided it is done simultaneously.

Jeff Root said:
I need information in addition to the start and end distances in order
to determine whether the car moved relative to the markers
The information you need is that the measurement was simultaneous. If so then it is OK if the car is moving.
 
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  • #16
Jeff, you seem to be arguing a position and not asking a question. That position, as stated, seems to be logically inconsistent: if all measurements are really two measurements, so are those two measurements, so they are really four measurements, and then eight, and then...

The way out of this is to say all measurements that I am interested in are really relations between two measurements. But that's a statement on interest, not of anything fundamental.
 
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  • #17
Jeff Root said:
Is there any difference between this setup step and measurement
of the starting point?

yes...
Because you are not making a measurement as to where the bottom of your foot is or where the top of your head is.
All you are doing is locating those 2 points. Then you are making a measurement between those two point
to find out how far apart they are. There is just one measurement being madeDave
 
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  • #18
Jeff Root said:
When I measure my height, the two steps necessarily take
place in different locations. Do they also necessarily
take place at different times, in my reference frame?

If you are doing it alone you would need to be present at both events (what you are calling two steps). Since you can't outrun a light beam, the events have to be separated in time, also.

When you subtract the two readings on your height-measuring device you get the height, likewise when you subtract the two clock-readings you get the time that elapses between the same two events used to establish the height.
 
  • #19
Dale said:
Jeff Root said:
that value of zero is a measurement.
That is where we disagree. The setting of the zero point is not a
measurement, it is part of the equipment setup. In my opinion you
define the zero point by your setup, you don’t measure it.
I don't see the difference. It looks exactly like a measurement.

My warehouse got in a delivery of boxes of various sizes that are
now stacked up against the wall. They need to be moved to places
they will fit. The wall is marked in 1-foot increments, starting
1 foot above the floor, going up to the ceiling. I see a box way
up in the stack that has its top at the 18-foot line. How tall
is that box?

A second measurement is needed to determine the box's height.
I see the bottom of the box at the 15-foot line. 18 minus 15
is 3, so I know, by subtracting the second measurement from the
first, that the box is 3 feet tall. I did not make the two
measurements simultaneously, but that isn't a problem because
I could see the box didn't move relative to the marks on the
wall between the times I took the measurements.

Another box has its top at the 5-foot line. How tall is it?
The box is sitting on the floor, so its bottom is at the 0-foot
line. 5 minus 0 is 5, so I know, by subtracting the second
measurement from the first, that the box is 5 feet tall. This
calculation was particularly easy because one measurement
happened to have a value of zero.

For something as simple as boxes, we don't usually need to think
about it. Measuring photons might require more thought.

Dale said:
A measurement of distance must be simultaneous because
otherwise the length of moving objects will not be valid. The use
of the mile markers is a perfectly legitimate means of measuring
the length of objects provided it is done simultaneously.
No need for the measurements to be simultaneous if other
information is available.

A freight train is moving past my warehouse at a constant speed
of 20 feet per second, according to my laser speed gun. I can't
see either the front or back of the train for most of the time
it is going past me, but the gun is right beside the track, and
it got good measurements off of the ends of the cars. The front
of the train went past me at 2 PM, and the rear end went past me
at 2:05 PM. It took 300 seconds for the train to go by. 300
seconds times 20 feet per second is 6000 feet. The train is
more than a mile long!

Dale said:
The information you need is that the measurement was
simultaneous. If so then it is OK if the car is moving.
That is fine for many ordinary situations, but there are lots of
situations where the measurements cannot be simultaneous, and
the thing being measured is moving relative to the yardstick.
Trying to measure photons might be such a situation.

-- Jeff, in Minneapolis
 
  • #20
Vanadium 50 said:
That position, as stated, seems to be logically inconsistent:
if all measurements are really two measurements, so are those
two measurements, so they are really four measurements, and
then eight, and then...

The way out of this is to say all measurements that I am
interested in are really relations between two measurements.
But that's a statement on interest, not of anything fundamental.
I think the example I began the thread with is accurate.
Measuring my height, or any length, requires two measurements:
The location of the starting point and the location of the
ending point.

Very often I measure the length of something with a ruler by
positionong the starting point at an inch mark, then reading the
value at the ending point. Then I subtract the smaller number
from the larger. I do that when it is inconvenient to position
the starting point at the zero index on the ruler.

But it is the same thing when I do position the starting point at
the zero index, or when I just slap the ruler down on the object
without positioning it, and read the value of the starting point
from the ruler. In all three cases I am measuring the starting
point and the ending point in order to get a single measurement
of the object's length.

Whether I joggle the ruler around to get a mark on it to line up
with the starting point, or read the starting value from the ruler
by interpolating between index marks, the result is a measurement,
and two such measurements are required to measure the object's
length. It is most convenient if one of the measurements has a
value of zero. Then even I can do the arithmetic in my head.

-- Jeff, in Minneapolis
 
  • #21
davenn said:
Jeff Root said:
Is there any difference between this setup step and measurement
of the starting point?
yes...
Because you are not making a measurement as to where the
bottom of your foot is or where the top of your head is.
All you are doing is locating those 2 points. Then you are
making a measurement between those two point to find out
how far apart they are. There is just one measurement
being made
Locating a point and associating it with a value is a measurement.
That is done twice to measure a thing's length.

I most certainly am making a measurement as to where the bottom
of my foot is. I need to use the same care positioning the end
of the tape measure at the bottoms of my feet as I use in reading
the value at the top of my head. If the bottoms of my feet are
not at the end of the tape measure, then I need to subtract the
smaller number from the larger. Usually the smaller number is
zero, so I don't have to do anything.

-- Jeff, in Minneapolis
 
  • #22
Jeff Root said:
I don't see the difference. It looks exactly like a measurement.


No need for the measurements to be simultaneous if other
information is available.

A freight train is moving past my warehouse at a constant speed
of 20 feet per second, according to my laser speed gun. I can't
see either the front or back of the train for most of the time
it is going past me, but the gun is right beside the track, and
it got good measurements off of the ends of the cars. The front
of the train went past me at 2 PM, and the rear end went past me
at 2:05 PM. It took 300 seconds for the train to go by. 300
seconds times 20 feet per second is 6000 feet. The train is
more than a mile long!

Your measurement process here implicitly assumes that length is the difference between simultaneous measurements of position of the front and the back of the train. That's what you have calculated:

1) The back of the train passed at 2:05pm.

2) The front of the train you calculated to be at a position 6000ft further on at 2.05pm.

You then took the (calculated) simultaneous positions of the front and the back of the train (at 2:05pm) to determine its length.

You could also look at it this way. From 2:00pm until 2:05pm, the front of the train was in various places and the rear of the train was in various places. To get its length, you needed to know where the front and the rear were at the same time. It didn't actually matter what time you chose, but you had to do enough measurements and calculations to work out where the front and the end were at the same time.

What you didn't do, and couldn't do, was calculate the position of the front of train at some time (2.02pm, say) and the position of the rear at some other time. In fact, therefore, your measurement process for length conforms to the definition:

The length of an object is the difference between simultaneous measurements of position of the front and rear.

That's what you calculated.
 
  • #23
Jeff Root said:
I don't see the difference. It looks exactly like a measurement.
Then you get to the illogical problem identified by @Vanadium 50. That is a complete refutation for your stated claim.

If what I am calling device setup is a measurement and if each measurement requires two measurements then the device setup requires two measurements and so on recursively. You immediately wind up with an infinite number of measurements. So at some point, to make any measurement you must have some measurement which is not itself formed from two measurements, thereby refuting the claim that all measurements require two measurements.

Your position on this is logically untenable.

Jeff Root said:
No need for the measurements to be simultaneous if other
information is available.
The definition of length is that the distance is measured simultaneously. (This becomes critical in understanding length contraction in relativity, but it is true even classically). If you have other information, specifically the velocity, then you can determine and correct the error introduced by a non simultaneous measurement. You can also show that that error goes to zero as v goes to zero. But the definition remains that the measurements must be simultaneous, for the reason shown by the non-simultaneous 30 mile long car length.

Jeff Root said:
there are lots of
situations where the measurements cannot be simultaneous, and
the thing being measured is moving relative to the yardstick.
Then it is not a valid measurement of length. This is precisely the 30 mile long car measurement. The car was moving relative to the yardstick and the measurements were not simultaneous. Hence the car was “measured” 30 miles long.
 
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  • #24
PeroK said:
Jeff Root said:
I don't see the difference. It looks exactly like a measurement.

No need for the measurements to be simultaneous if other
information is available.

A freight train is moving past my warehouse at a constant speed
of 20 feet per second, according to my laser speed gun. I can't
see either the front or back of the train for most of the time
it is going past me, but the gun is right beside the track, and
it got good measurements off of the ends of the cars. The front
of the train went past me at 2 PM, and the rear end went past me
at 2:05 PM. It took 300 seconds for the train to go by. 300
seconds times 20 feet per second is 6000 feet. The train is
more than a mile long!
Your measurement process here implicitly assumes that length is
the difference between simultaneous measurements of position of
the front and the back of the train. That's what you have
calculated:

1) The back of the train passed at 2:05pm.

2) The front of the train you calculated to be at a position
6000ft further on at 2.05pm.

You then took the (calculated) simultaneous positions of the
front and the back of the train (at 2:05pm) to determine its
length.

You could also look at it this way. From 2:00pm until 2:05pm,
the front of the train was in various places and the rear of the
train was in various places. To get its length, you needed to
know where the front and the rear were at the same time. It
didn't actually matter what time you chose, but you had to do
enough measurements and calculations to work out where the
front and the end were at the same time.

What you didn't do, and couldn't do, was calculate the position
of the front of train at some time (2.02pm, say) and the position
of the rear at some other time. In fact, therefore, your
measurement process for length conforms to the definition:

The length of an object is the difference between simultaneous
measurements of position of the front and rear.

That's what you calculated.
Sort of.

You are right that I calculated the front of the train to be at
a position 6000 feet further on at 2:05 PM, the time at which I
measured the position of the rear of the train. And from that
calculation I correctly got the length of the train as 6000 feet.

However, unknown to me at the time, at about 2:03 PM the engine
and first 15 cars came uncoupled from the rest of the very long
train, and accelerated away. The front of the train was more
than two miles away from me at 2:05, not 6000 feet. The rest of
the cars continued down the track at constant speed, helped out
by a pusher engine, so I didn't notice anything was wrong.

At any rate, I didn't measure the position of the front of the
train simultaneous with my measurement of the position of the
rear, but I got a correct length anyhow. If I had measured the
position of the front of the train at 2:05, I would have got
the length way wrong.

A few minutes later the two parts came back together. :-)

PeroK said:
What you didn't do, and couldn't do, was calculate the position
of the front of train at some time (2.02pm, say) and the position
of the rear at some other time.
But I did.

At 2:02 PM, the front of the train was 2400 feet away, and at
2:05 PM, the rear of the train was zero feet away.

I could calculate the position of the front of the train any
time after it passed me at 2 PM, for as long as it maintained
constant speed. Since I started measuring the speed at 1:58 PM,
I can correctly calculate the the position during that interval
while it was approaching me. (Since my special-purpose speed
gun doesn't display distance, I couldn't do that calculation
until after the front of the train reached me.) Because the
front of the train decoupled at about 2:03, any calculation by
me regarding its position after that would have been wrong, but
I can say where it would have been had it not decoupled, for
any time as long as I was still measuring the train's speed.

Although I calculated where the front of the train should have
been at the moment the back of the train passed me, I measured
its position at a different time. I measured the speed of the
part of the train passing me continuously.

-- Jeff, in Minneapolis
 
  • #25
Dale said:
Jeff Root said:
I don't see the difference. It looks exactly like a measurement.
Then you get to the illogical problem identified by @Vanadium 50.
That is a complete refutation for your stated claim.

If what I am calling device setup is a measurement and if each
measurement requires two measurements then the device setup
requires two measurements and so on recursively. You immediately
wind up with an infinite number of measurements. So at some
point, to make any measurement you must have some measurement
which is not itself formed from two measurements, thereby
refuting the claim that all measurements require two
measurements.

Your position on this is logically untenable.
It works for quantum mechanics.

Please notice, though, that my claim has been that measurments
of length appear to require two measurements, but neither of
those measurements is a measurement of length. Typically they
are measurements of location.

I have then asked-- not claimed-- whether all measurments
work in this same way.

We have not yet begun to discuss here whether a measurment of
location requires two measurements.

Dale said:
Jeff Root said:
No need for the measurements to be simultaneous if other
information is available.
The definition of length is that the distance is measured
simultaneously. (This becomes critical in understanding length
contraction in relativity, but it is true even classically).
If you have other information, specifically the velocity, then
you can determine and correct the error introduced by a non
simultaneous measurement. You can also show that that error
goes to zero as v goes to zero. But the definition remains
that the measurements must be simultaneous, for the reason
shown by the non-simultaneous 30 mile long car length.
When I measure the length of something that is NOT moving
(which I do a lot), I hardly ever measure both the starting
point and the ending point simultaneously. Almost always
I line up an index mark on my ruler with a feature on the
thing I am measuring that serves as the starting point, then
try to hold the thing and the ruler still relative to each
other while I look away from that starting point and over
at the ending point to measure it. Typically that takes a
couple of seconds. I'll then look back at the starting
point again to be sure it hasn't moved, which also takes
a couple of seconds.

If the starting and ending points are close enough together,
maybe a centimeter or less, I may be able to focus on both
of them simultaneously. Otherwise it is virtually always
one at a time. Some sort of mirror or prism device could
make it possible to observe farther-separated points
simultaneously, perhaps superimposed.

Of course, it doesn't matter if there is no relative motion
between the measurements. The problem is when things move.
But it isn't unusual to measure things in motion, and my
difficulty in measuring non-moving things simultaneously
likely also applies to measurements of moving things.

My example of measuring the length of a train I think shows
conclusively that measuring something in motion can be done
without simultaneously measuring the starting and ending
points, though it also requires constantly measuring speed.

Dale said:
Jeff Root said:
there are lots of
situations where the measurements cannot be simultaneous, and
the thing being measured is moving relative to the yardstick.
Then it is not a valid measurement of length. This is precisely
the 30 mile long car measurement. The car was moving relative to
the yardstick and the measurements were not simultaneous. Hence
the car was “measured” 30 miles long.
I knew the car was not 30 miles long, because I knew the car
was moving. 30 miles is a terribly long distance for that kind
of measurement. As I said, 30 feet is more reasonable. More
like measurements actually made in the real world.

You can only get a length of 30 miles for the car if you are
trying to make a strawman argument. Use realistic values for
the speeds and distances involved, and you can probably get
nearly as accurate measurements of the length of a moving
car taken a couple of seconds apart as you could get with a
nonmoving car.

-- Jeff, in Minneapolis
 
  • #26
Jeff Root said:
Sort of.

You are right that I calculated the front of the train to be at
a position 6000 feet further on at 2:05 PM, the time at which I
measured the position of the rear of the train. And from that
calculation I correctly got the length of the train as 6000 feet.

However, unknown to me at the time, at about 2:03 PM the engine
and first 15 cars came uncoupled from the rest of the very long
train, and accelerated away. The front of the train was more
than two miles away from me at 2:05, not 6000 feet. The rest of
the cars continued down the track at constant speed, helped out
by a pusher engine, so I didn't notice anything was wrong.

At any rate, I didn't measure the position of the front of the
train simultaneous with my measurement of the position of the
rear, but I got a correct length anyhow. If I had measured the
position of the front of the train at 2:05, I would have got
the length way wrong.

A few minutes later the two parts came back together. :-)


But I did.

At 2:02 PM, the front of the train was 2400 feet away, and at
2:05 PM, the rear of the train was zero feet away.

I could calculate the position of the front of the train any
time after it passed me at 2 PM, for as long as it maintained
constant speed. Since I started measuring the speed at 1:58 PM,
I can correctly calculate the the position during that interval
while it was approaching me. (Since my special-purpose speed
gun doesn't display distance, I couldn't do that calculation
until after the front of the train reached me.) Because the
front of the train decoupled at about 2:03, any calculation by
me regarding its position after that would have been wrong, but
I can say where it would have been had it not decoupled, for
any time as long as I was still measuring the train's speed.

Although I calculated where the front of the train should have
been at the moment the back of the train passed me, I measured
its position at a different time. I measured the speed of the
part of the train passing me continuously.

-- Jeff, in Minneapolis

To be honest, Jeff, that's all mixed up thinking. If an object is breaking apart and reforming then it doesn't have a fixed length. In these cases, you don't know whether the train is still a train at 2.05pm! Or, whether it's an assorted collection of independent carriages.

And, in fact, these considerations would move you towards the measurement process where you have observers all along the line with synchronised watches. And you make sure that the train remains a train of fixed length.

Your process, which is a valid measurement process under some assumptions, does have the drawback that you didn't actually check that the train was of fixed length (not stretching or contracting). Your process, in fact, is only valid for a rigid body. Which is a fair enough assumption.

But, if you tried to apply that process to an object of variable length (the time-dependent length of a piece of elastic, say), then it wouldn't work. I.e. if the elsatic has one length at 2pm and another length at 2.05pm, then you cannot get the length of the elastic at any particular time from asynchronous measurements of its ends.
 
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  • #27
Jeff Root said:
I have then asked-- not claimed-- whether all measurments
work in this same way.
Ok. The answer to that is clearly “no” as pointed out by @Vanadium 50.

Since your actual question is answered and since the rest of the discussion is highly repetitive and going nowhere, it is time to close the thread.
 
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1. Can any physical quantity be measured with a single measurement?

It depends on the physical quantity and the accuracy of the measurement. Some physical quantities, such as length or mass, can be measured with a single measurement. However, other quantities, such as temperature or time, may require multiple measurements to accurately determine their value.

2. Is it possible to obtain an accurate measurement with just one instrument?

In most cases, it is not possible to obtain an accurate measurement with just one instrument. Different instruments have different levels of precision and accuracy, and using multiple instruments can help to reduce errors and improve the accuracy of the measurement.

3. Can a single measurement be used to determine the uncertainty of a quantity?

No, a single measurement cannot determine the uncertainty of a quantity. Uncertainty is a measure of the possible range of values for a quantity, and it is determined by taking multiple measurements and calculating the standard deviation.

4. How can a single measurement be affected by human error?

Human error can affect a single measurement in several ways. It could be due to incorrect use of the instrument, misreading the measurement, or not properly accounting for external factors that may influence the measurement.

5. Are there any limitations to using a single measurement to make conclusions?

Yes, there are limitations to using a single measurement to make conclusions. A single measurement may not accurately represent the true value of a quantity, and it may also not account for variations or fluctuations in the measured quantity. Therefore, it is important to take multiple measurements and analyze the data to draw accurate conclusions.

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