Speed measurement -- Limitations to "instantaneous" measurements?

[Paul Colby]

This has nothing to do with integration time or sampling rate. The device makes one reading.

Please review how ADC actually work. An ADC has a number in the spec called the aperture. This is the integration time for a sample. This is very much on topic.

 

[russ_watters]

Every measurement of weight I know of takes some integration time. Our theory of what weight means likely includes some notion of its time invariance. It still will take some integration time to measure it no matter how constant we think it is.

I've never heard of such a thing. Can you give an example of a weight measurement that utilizes a time measurement? Using what equation?

 

[Paul Colby]

The kitchen scale I ordered on Amazon used ADCs and a load cell. Reading a voltage is alway, always always a band limited finite integration time measurement.

 

[russ_watters]

The kitchen scale I ordered on Amazon used ADCs and a load cell. Reading a voltage is alway, always always a band limited finite integration time measurement.

What is the equation for that?

I'm trying to establish here if you even recognize if there are single and multi point measurements.

 

[Paul Colby]

Well, $f_p = \frac{1}{2\pi R C}$ R is always finite and C is never 0.

 

[russ_watters]

Well, $f_p = \frac{1}{2\pi R C}$ R is always finite and C is never 0.

I'm not familiar with that equation; can you describe what it does?Edit; wait, you said ADC; analog to digital conversion, using time intervals to deconstruct waveforms. I'm not accepting that; you've already made an assumption that you are measuring a time varying signal, regardless of if it is or isn't.

 

[Paul Colby]

You never studied circuit design? Personally, I suck at it but it comes up often. This is an expression, the frequency cut off of an R-C network. It came up recently in a discussion of the finite response time of a photo diode to a chopped light source in an other post. Response time is effectively an integration time in this context.

 

[russ_watters]

If you take a single measurement using a spring scale, you measure elongation and convert to force using the spring constant:
f=kx. There is no time interval involved in/inherent to the measurement. There's no clock on a spring scale.

A load cell uses a variable resistor in place of a spring, but the point is the same: R=V/I, with (delta) R being a proxy for F. Again, tere's no time parameters involved, but I don't know if voltage is measured instantaneously.

 

[Paul Colby]

I'm trying to establish here if you even recognize if there are single and multi point measurements.

I'm trying to figure out how one could ever not understand that a "single point" measurement you speak of is always an idealization.

 

[Paul Colby]

There is no time interval involved in/inherent to the measurement. There's no clock on a spring scale.

Wow, I can't read a scale in 0 time. I can't take a picture of it in 0 time either. I can't use lasers or ADCs or mirrors in 0 time, ever.

 

[Paul Colby]

R=V/I, with (delta)R being a proxy for F.

It takes time to read a load cell. My bet is they are slow.

 

[Paul Colby]

This discussion of weight measurement actually amusing. Some years ago I considered using high frequency weight measurements as a means of detecting high frequency gravitational waves (RF frequencies). One would have to make a load cell that could be read out in the MHz frequency range. Not a simple nor uninteresting problem.

 

[russ_watters]

Wow, I can't read a scale in 0 time. I can't take a picture of it in 0 time either. I can't use lasers or ADCs or mirrors in 0 time, ever.

No? How much time does it take? What's the equation for that? If I take twice as long to read a scale, does that mean I have twice the weight or half the weight?

Again, you are misconstruing how long it takes to make a measurement for the measurement itself being time dependent. That's why this matters: when a time parameter is part of a measurement, it affects the measurement differently from just a time delay in taking an instantaneous measurement.

Also, I guess I shouldn't have asked an open question: sure, you can express measurements by chopping up a continuous signal, but that doesn't mean individual measurements aren't discrete. I don't know how a digital voltmeter works, but an analog voltmeter uses magnetism to move a needle to a location; there is no time parameter involved in the reading.

 

[russ_watters]

This discussion of weight measurement actually amusing. Some years ago I considered using high frequency weight measurements as a means of detecting high frequency gravitational waves (RF frequencies). One would have to make a load cell that could be read out in the MHz frequency range. Not a simple nor uninteresting problem.

Taking a large number of readings in a small time doesn't make the readings have a time parameter. I'm betting it still read a lot of individual measurements that just said N. Not N/s

 

[Paul Colby]

Also, I guess I shouldn't have asked an open question: sure, you can express measurements by chopping up a continuous signal, but that doesn't mean individual measurements aren't discrete. I don't know how a digital voltmeter works, but an analog voltmeter uses magnetism to move a needle to a location; there is no time parameter involved in the reading.

It's worth reviewing how they work. A mechanical meter integrates over its response time which is a function of inertia, spring constants and resistance. You can't read them at 100MHz cause they average out the variations on these time scales. It's silly to think of them as instantaneous.

 

[russ_watters]

It's worth reviewing how they work. A mechanical meter integrates over its response time which is a function of inertia, spring constants and resistance. You can't read them at 100MHz cause they average out the variations on these time scales. It's silly to think of them as instantaneous.

This is simply not correct. There is no t2-t1 like in a traditional velocity measurement: (x2-x1)/(t2-t1)

In your example, (x1,t1) and (x1000,t1000) are each separate instantaneous measurements. (x1,t1) does not change if you decline to later take (x1000,t1000)

 

[Paul Colby]

This is simply not correct. There is no t2-t1 like in a traditional velocity measurement: (x2-x1)/(t2-t1)

How is this relevant? Just because it doesn't fit your narrow view of the subject? Write out the response of a harmonic oscillator (good model for a meter movement) and solve the equation for a general driving force. The meter position will be the integral of the system green function times the driving force over time. This is a time average no matter how you confuse the matter.

 

[russ_watters]

How is this relevant? Just because it doesn't fit your narrow view of the subject?

It's relevant because it is the subject we are discussing. You seem to want to discuss a different subject, and that's the problem. This is the first I've seen you acknowledge you are talking about a different subject!

 

[Paul Colby]

It's relevant because it is the subject we are discussing. You seem to want to discuss a different subject, and that's the problem. This is the first I've seen you acknowledge you are talking about a different subject!

OP asked about instantaneous measurement. How is the meter movement not relevant. My point is measurement is always band limited, it always involves some finite integration time to produce a sample. How this is this a different topic?

 

[russ_watters]

OP asked about instantaneous measurement. How is the meter movement not relevant. My point is measurement is always band limited, it always involves some finite integration time to produce a sample. How this is this a different topic?

Instantaneous is t2-t1=0 or rather that there is no t2. You are talking about t1, t2, t3, t4...etc. As you correctly point out, they are different things (except of course yours contains mine/theOP's).

And not for nothing, but the OP didn't mention measurement.

 

[Paul Colby]

Taking a large number of readings in a small time doesn't make the readings have a time parameter. I'm betting it still read a lot of individual measurements that just said N. Not N/s

It does, but only in the sense that sample rate can't exceed the time for a single datum or sample.

 

[Paul Colby]

Instantaneous is t2-t1=0 or rather that there is no t2. You are talking about t1, t2, t3, t4...etc. As you correctly point out, they are different things (except of course yours contains mine/theOP's).

And not for nothing, but the OP didn't mention measurement.

You seem to be make up what I'm talking about. Give an example where a single sample is performed in exactly 0 time.

 

[Paul Colby]

And not for nothing, but the OP didn't mention measurement.

Nor the measurement of energy, or weight or ... It was a pretty open-ended question. None of these things you've introduced are off topic and are certainly relevant. The difference between quantifiable and measurable was what I commented on. Instantaneous velocity is quantifiable in my view, but as a theoretical construct. The measurement of such things are very much on topic and very much limited to finite time scales.

 

[Paul Colby]

I'm not accepting that; you've already made an assumption that you are measuring a time varying signal, regardless of if it is or isn't.

Selection of a measurement method always makes a host of assumptions. The fact is ones expectations drives the supposed time dependence the measurement method selected will be sensitive to. As I've tried to stress, this involves inferences, guesses and assumptions one must make up front. These are based on models and cost. For example, measurement of weight may well have the implicit ASSUMPTION that the weight is not varying at frequencies above a 100MHz. This ASSUMPTION then justify the experimentalist adopting a method limited by integration time to say 10Hz rather than say 100MHz, 1GHz or higher. These kind of limitations are always present in any real measurement or experiment. They certainly can't be eliminated as you have been implying and they are certainly always present.

 

[russ_watters]

You seem to be make up what I'm talking about. Give an example where a single sample is performed in exactly 0 time.

I've never made such a claim. I don't think I'm making up what you are talking about, I think you aren't following what this thread is about, so you are confused about what I'm saying, and why your responses are largely off topic - I think you just don't understand what an instantaneous data point is, measurement or otherwise. Here's my summary of what the thread has been about, from the question the OP asked, to its children and tangents:

1. Instantaneous events/data points/properties
2. A progression of instantaneous events/data points/properties
3. The integration of a progression of instantaneous events/data points/properties
4. Signal/processing delay in measuring instantaneous events/data points/properties
5. Noise in a progression of measured instantaneous events/data points/properties

4&5 are not necessarily related to 1-3, but the collection can be viewed in the contexts of:

(a) Reality
(b) Measurement of reality
(c) Modeling of reality

The OP wanted to know about #1 in the context of (a): does "instantaneous" exist in reality. A number of examples/arguments were invoked using the rest. You appear to be primarily arguing that 1 doesn't exist because of problems with (b), and you invoked examples/arguments involving 2-5. Ironically, there's an obvious logical contradiction there, in that 2 & 3 require/use 1, so if 1 didn't exist, neither would 2 & 3. And 4 and 5 can be in part filtered out using 1-3.

The differences and relationships between these can be important (and not just for discussion in the thread), but 4 & 5, which you put a lot of emphasis on, are tangential at best. Specific to your post above: how long it takes for a person or electronic device to detect, make sense of and record a measurement has nothing whatsoever to do with whether what is being measured is an instantaneous event/data point or not. If the device is measuring/recording one data point, with or without a time stamp, it's an instantaneous measurement/single-point in time event/property. If it's measuring two data points, each with a time stamp, and then dividing the difference in data points by the elapsed time, then it's measuring a time rate of change. If it's multiplying by elapsed time, it's measuring a time integrated process.

Examples:
5N -> instantaneous force
25C at 11:00 am -> instantaneous temperature
Chicago at 5:00 pm on Monday -> instantaneous position
10 kW -> instantaneous rate of energy transfer
25C at 11:00 am to 30C at 12:00 pm = 5C/hr - > time rate of change process
10 kW for an hour = 10 kWh -> time-integrated power use (energy)

See the difference?

 

[Paul Colby]

As I've said repeatedly, the instantaneous velocity is quantified in that it's assigned a real number value at each instant of time in theory. It's assumed to have this value within a model. Measurement of the value, extracting a number from data, never involves a solitary instantaneous value except as idealizations where the integration or averaging time is neglected by assumption or simple omission. Measuring devices all have finite bandwidths or finite integration times. They AVERAGE values over some finite time period. An actual measurement is never ever instantaneous in the OP sense.

I also think you've simply ignored the example of the meter movement I gave in #52. The needle position is not the instantaneous value as you've claimed, but rather it's a time average of the instantaneous values integrated and weighted by the response function of the meter movement.

 

[russ_watters]

As I've said repeatedly, the instantaneous velocity is quantified in that it's assigned a real number value at each instant of time in theory. It's assumed to have this value within a model.

Thanks for clarifying. For the rest, I don't see any further value in going over the same things another time.

I also think you've simply ignored the example of the meter movement I gave in #52. The needle position is not the instantaneous value as you've claimed, but rather it's a time average of the instantaneous values integrated and weighted by the response function of the meter movement.

I understand what you are saying - I understand a moving needle has a mass and friction which cause lag and damping on its motion - but that isn't the topic being discussed, so I ignored it. Sorry, but I'm not interested in trying anymore.

 

[gmax137]

Can you give an example of something that happens instantly?

Instantaneous is a useful approximation where one timescale (the snapping of a string) can be neglected relative to another (a 20 foot drop) for the sake of analysis.

How about when you toss a ball upwards? At the top of it's trajectory the velocity is up, then zero, then down. The time at zero velocity is "instantaneous," that is, the ball has zero velocity but only for a zero duration time interval. I don't think this is an "analysis" artifact or approximation, it is a necessary consequence of an object changing direction. Unless we actually live in a simulator-type universe where there is an imperceptible clock "cycle time."

 

[berkeman]

How about when you toss a ball upwards? At the top of it's trajectory the velocity is up, then zero, then down. The time at zero velocity is "instantaneous," that is, the ball has zero velocity but only for a zero duration time interval.

The vertical velocity is changing linearly with time (smoothly decreasing), so your "instantaneous" comment applies to any exact velocity anywhere in its profile. There is nothing all that special about when the vertical velocity goes through zero while linearly decreasing, IMO...

https://webassign.net/question_assets/buelemphys1/chapter04/section04dash7.pdf

 

[gmax137]

The vertical velocity is changing linearly with time (smoothly decreasing), so your "instantaneous" comment applies to any exact velocity anywhere in its profile.

Yes, I know that. We could just as easily say, "the velocity as the ball passes through 10 feet elevation." It is just more concrete to point to the top of the trajectory; it is a point on the path we can all agree to. Plus a zero velocity implies the notion of "standing still" and "standing still for 0 seconds" sort of emphasizes the seeming paradox.

In my mind these questions are similar to what the mathematicians do in Real Analysis - looking deeply into the infinite number of points between any two numbers. The spooky continuum.

 

[Paul Colby]

How about when you toss a ball upwards? At the top of it's trajectory the velocity is up, then zero, then down. The time at zero velocity is "instantaneous," that is, the ball has zero velocity but only for a zero duration time interval.

Yep, there is absolutely no question that in a model based on classical mechanics, the instantaneous value of the ball velocity has a definite value at each time in its trajectory. Questions of does this model somehow "exist" is outside the realm of physics and almost laughable when more complete models are considered. I can't even understand what people really mean by "exist" in this context and I often expect they don't either really.

I personally think it's both interesting and germane to address limitations of actual measurements aimed at obtaining estimates of instantaneous values. The OP's question was shove the measurement time scale to an instant of time. Specifically he asked about limitation to the ability to count rapidly. I suggest it is never possible since some finite integration time is alway required for any actual measuring device to obtain a given sample. The phenomena is quite general and is evident not only in time dependent measurements but also space. It's equally hard to measure something at an exact point. The smaller the volume of concern the shorter the wavelength of the probe required, the higher the energy. Energy is never ever infinite independent of all other issues.

 

[sepcurio]

There is a semantic issue here also. The dictionary definition of the noun "instant" can refer to a point in time. The adjective "instantaneous" usually describes something that happens, "Done occurring or acting without any perceptible duration of time..." However, the word "instant" is also an adjective with a meaning similar to the adjective "instantaneous". And just to muss things up even more, the word "instantaneous" can be used to characterize an attribute of a point in time (to characterize an attribute of an "instant") such as "instantaneous velocity".

I think this is one of the reasons why there was so much difficulty in discussing this topic (on top of the intrinsic conundrums the topic possesses).

 

[Paul Colby]

There is a semantic issue here also.

Your point is well taken. It's also why I need to be clear in case I haven't already. When I claim a measurement or measuring device integrates over a finite time period I mean its readout, a sample, is a weighted sum of all values of the observable of interest over some non-zero time interval. The weighting factor is the response function of the measurement device. To extract a value at a given instant requires assumptions be made about the behavior of the observable in this time interval. For example, the weight of a brick is assumed to not be varying in this time interval. While this is very likely the case, this is still very much an assumption supplied by theory and not the actual measurement. Now, all measuring devices have a non-zero response functions over some given time interval which depends on its design. This time interval can't be reduced to exactly zero as a matter of principle. Which principle exactly will depend on the sensor so it's a mushy question at best.

Sorry to belabor this point but I think it's quite relevant. Too often people formulate questions assuming physical limits are always possible or attainable and therefore "exit". In the case of measurement and experiments, they most surely are not. Good experimental work is quite careful to explain what the limits of the measurements are.

 

[homerwho]

Sorry if I have been quiet I have been thinking of all the input I have received.

 

[Saw]

I was reflecting about this in the context of calculus (see here) and I have read this thread with utmost interest.

I fully agree with Paul Colby's point that all measurements need time (certainly speed measurements but his point seems to be all measurements and that looks also reasonable). A measurement instrument is a physical thing that interacts with physical things and that always requires a time period. During this time, the relevant property of the object may have changed, so you cannot guarantee that what you have measured is its instantaneous value.

This does not mean that the observed phenomenon does not have such instantaneous "property". For example if you kick a ball far away enough from any gravity source and it moves by inertia across vacuum, it will acquire a "state of motion" that is constant, so the same at every interval, no matter how small, even at a null interval or instant. But when you get your hands dirty with measurements, you cannot guarantee that that is the case.

PS: Another argument, by the way: otherwise we would not have SR. If a measurement instrument, which must be separated from the measured object by some distance, could detect things instantaneously, it could also be re-converted for capturing information instantaneously, in violation of SR...