Speed measurement -- Limitations to "instantaneous" measurements?

[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...

 

[sophiecentaur]

No, radar guns measure speed from doppler shift of reflected radio waves. They are single-point/instantaneous measurements.

. . . . plus a number of other similar comments. But this is not true.The information that can be gleaned from an observation is always subject to Noise. The more 'instantaneous' the measurement, the wider the bandwidth of the measuring instrument and so the more noise energy will affect the result. So a 'good' instantaneous measurement is progressively harder and harder to achieve.
We initially learned our Differential Calculus in the ivory tower of Pure Mathematics (even if we didn't know it). Later, if we were lucky, we found that the basics of taking limiting cases of smaller and smaller intervals had to involve caveats about a function being continuous and differentiable before the simple dy/dx can be looked on as valid. QM excludes this condition so we are left with a system that just works but don't look too hard at it.

This thread has a parallel in all the other threads that deal with Zeno's Paradox etc.. Only Professors of Very Hard Sums are qualified to deal with the bottom line of this and many of those guys can't find their back pocket with both hands.

 

[Stephen Tashi]

Most quantities I can think of are actually inferred from measurements.

In this digital age, we could even say that most quantities are inferred from voltages!

 

[Paul Colby]

In this digital age, we could even say that most quantities are inferred from voltages!

Well, voltage without some corresponding current can't be measured either. Even an FET has some current flowing into the gate to effect or change the drain-source impedance. If I were making grand generalizations (and I am) signals are power. Taken with the measurement device's integration time this makes a measurement an amount of energy. Nothing in experimental science comes with 0 energy cost ever as far as I can tell.

 

[PeroK]

QM excludes this condition so we are left with a system that just works but don't look too hard at it.

I think you'll find that describes classical mechanics rather than QM!

 

[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. 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."

The ball's velocity passes through 0 in theory. The ball has a position only in some theory. Now, the OPs question used the word 'quantifiable' which I read as measurable. After using the "quantifiable" word the OP went on to ask about counting faster. Sure sounded like they were asking about limitations to the measurement of a theoretical concept.

 

[gmax137]

The ball's velocity passes through 0 in theory. The ball has a position only in some theory.

I have no idea what this means. The ball exists independent of anyone's theories. I must be missing your point.

 

[Paul Colby]

I have no idea what this means. The ball exists independent of anyone's theories. I must be missing your point.

Well, a real ball may be treated (modeled) as an ideal rigid solid in classical mechanics, as an elastic solid supporting internal vibrations, or a collection of atoms, QM, LQF etc. The number of atoms in the ball is not really fixed since air molecules might adhere to the surface and then release, so there is a thermodynamic component to the center of mass. The center of mass is certainly a theoretical construct in and of itself. My point is the velocity of the ball and it's position don't exist other than in a model.

 

[gmax137]

My point is the velocity of the ball and it's position don't exist other than in a model.

You and I are just going to disagree on that.

 

[sophiecentaur]

I think you'll find that describes classical mechanics rather than QM!

It does but there is a lower scale limit to which Classical Mechanics applies. The word "instant' only really applies to idealised mathematical functions. But we're talking angels on a pinhead here.

 

[Paul Colby]

You and I are just going to disagree on that.

Fair enough. I will close with my choice of the words "don't exist" #77 is a really poor one. A better choice closer to my intended meaning is "aren't defined."

 

[ericlreite]

Can you give an example of something that happens instantly?

an application of mass would create instantaneous universal repercussions...??

 

[ericlreite]

Say this mass "evaporated" from a close dimensional universe

Just sayin'

into ours, would the effects be instantaneous?

Speed (relative to something) is quantifiable in math terms. What else is there? If you mean can we measure speed to infinite precision then certainly not.

ok, we can all manipulate mathematical variables, agreed. Does that not mean we can give T a value of plus or minus nothing or infinity?

 

[Paul Colby]

into ours, would the effects be instantaneous?

Wouldn't that violate conservation of energy in this universe? There is much data and theory in this universe that currently would rule this out. I haven't seen the data from any other universe. Perhaps a reference?

 

[sophiecentaur]

into ours, would the effects be instantaneous?

That would go against the basics of Relativity, surely? I don't see why the idea is attractive enough to pursue.

 

[PeteLindsey]

Quantum entanglement can cause an event in two places to happen instantaneously. As an example an entangled photon at point (a) gets measured binding its state to the measurement, the same state will be bound to the other entangled photon at point (b).

 

[sophiecentaur]

Quantum entanglement can cause an event in two places to happen instantaneously. As an example an entangled photon at point (a) gets measured binding its state to the measurement, the same state will be bound to the other entangled photon at point (b).

I know about QE but trying to apply the OP to this example is problematic. Where would "ds/dt" be quantifiable. I think it's outside the scope of the thread. (Beyond my pay grade at least)

 

[DennisN]

Quantum entanglement can cause an event in two places to happen instantaneously.

No, that is not quite an established fact. What is established is that when entangled systems, e.g. two particles, are measured at two different locations the measurements are shown to have a special, strong correlation when the sequences of measurements afterwards are compared.

Entanglement does not say that the measurement of one entangled particle instantly causes the other entangled particle to acquire a state (e.g. wave function collapse). And the underlying mechanism - if there is any - for entanglement is unknown at this time.