# I Speed measurement -- Limitations to "instantaneous" measurements?

#### homerwho

Summary
Is instantaneous something that is quantifiable?
Is instantaneous limited to our in ability to continue to count time faster.

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#### phinds

Gold Member
Summary: Is instantaneous something that is quantifiable?

Is instantaneous limited to our in ability to continue to count time faster.
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.

#### berkeman

Mentor
Summary: Is instantaneous something that is quantifiable?]]

Is instantaneous limited to our in ability to continue to count time faster.
Kind of. There are digital and analog methods to measure "speed".

As you know, speed is the distance covered in some amount of time. So a simple description of speed in a discrete sense is:

$$\frac{\delta x}{\delta t}$$

or using differential calculus,

$$\frac{dx(t)}{dt}$$

So from the perspective of discrete measurements or approximations using differential calculus, yes, the value depends on the minimum time interval you can measure.

And using a more "analog" measurement like a speedometer, you are relying on analog "low pass filtering" to smooth the measurements. So again you are limited a bit by the sampling interval and the lowpass function that you are using.

Does that make sense?

#### homerwho

Yes it makes sense. Can assumptions be made on a change that it happened instantly?

#### berkeman

Mentor
Can you give an example of something that happens instantly?

#### homerwho

Transfer of energy? Just guessing.

#### PeroK

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Yes it makes sense. Can assumptions be made on a change that it happened instantly?
There are lots of scenarios where we assume that something happens instantly. For example, an object may be suspended by a string, which is cut and the object falls. You would normally treat that as a situation where at some instant the nett force on the object goes from zero to the full force of gravity.

But, then you think about it and the cutting of the string takes a finite time. And perhaps before the string is fully cut there is a short time when the string is still providing some upward force but the object is starting to fall. A more sophisticated model would have a short initial phase where the nett force on the object gradually increases from zero to the full force of gravity. I.e. it's not really an instantaneous change, just very close to instantaneous.

There are lots of examples like this where changes happen very quickly but are in general not truly instantaneous.

#### Paul Colby

Gold Member
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.

#### sepcurio

This has many concepts associated with it. "Instantaneous" implies two events happening at the same time, which is the concept of simultaneity. The comparison of simultaneous events in different frames of reference is what launched Einstein's Special Theory of Relativity -- what is simultaneous in one frame of reference is not simultaneous in another.

But instantaneous also implies cause and effect -- something happens that causes something else to happen "instantly." Under the Standard Model, everything in the universe acts on the quantum level via the fundamental interactions, which are mediated by gauge bosons. Since those interactions can't take place any faster than the speed of light, it means that time must elapse between any cause and effect. So no, nothing is instantaneous.

However, in Classical physics there are many things that, for all practical purposes, can be considered to happen instantaneously. But when you are talking about motion and measuring speed, it doesn't matter if it's within the realm of classical and quantum physics -- motion requires time, otherwise the matter that "moves" would be in two places at the same time.

There is also the more philosophical concept of memory and comparison. When motion is measured, there has to be some memory (not necessarily biological) of where is "was" and a comparison of that to where it "is."

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#### sophiecentaur

Gold Member
Maths is not 'real' and only applies in some cases. At school, we were introduced to Differential Calculus (don't switch off!) and to the idea of the limiting value of the slope of a curve. Δx/Δt is the ratio of a small increment in distance over a (also small) increment in time. Maths assumes ('believes') that you can make Δt as small as you like and the answer will get close and closer to the instantaneous value of speed. Not all relationships are like that and you can get teeth on a ratchet or Energy levels in Quantum Mechanics with discrete steps between them so you cannot always get an instantaneous speed - but results can be near enough and there is always the problem of uncertainty and 'noise' which limit the resolvable step size.

#### sepcurio

Maths is not 'real' and only applies in some cases.
Yes, the physics of velocity is bound by the physical laws relating to spacetime as humans currently understand them. Math is purely conceptual, so it is not bound by those same limits. The measurement of speed (the OP's original question), and perhaps the measurement of any physical phenomenon, is the joining or alignment of the physics of spacetime with conceptual math. So both the physical and the conceptual must be bound by those limits to make that joining feasible in a definite manner.

Things that can't be measured definitely, like quantum states, still require an alignment of the physical with the conceptual, but in the case of QM, the math is limited to probabilities in order to facilitate that joining of the physical and conceptual.

#### russ_watters

Mentor
This has many concepts associated with it. "Instantaneous" implies two events happening at the same time...

However, in Classical physics there are many things that, for all practical purposes, can be considered to happen instantaneously.
I don't agree with that definition. I'd say "instantaneous" means "happens in zero time". And I'd say that based on that definition, all events are instantaneous by definition of the word "event".
There is also the more philosophical concept of memory and comparison. When motion is measured, there has to be some memory (not necessarily biological) of where is "was" and a comparison of that to where it "is."
No, speed is often measured over a time duration, but not always. And the units it is expressed in do not require/imply it needs to be.

#### Paul Colby

Gold Member
When reading the OP and replies I get the feeling people are equating quantifiable with measurable. These are not at all the same in my mind. For example, weak gravitational waves produced by vibrating solids are quantifiable in the sense GR may be used to compute them and their effects on radiation and mater. This is a far cry from being able to measure them. Velocity of the center of mass of an object is quantified even if the measurement of such is always of limited precision.

#### russ_watters

Mentor
When reading the OP and replies I get the feeling people are equating quantifiable with measurable...

Velocity of the center of mass of an object is quantified even if the measurement of such is always of limited precision.
Maybe, but just to make sure we're clear and agreeing: you can measure instantaneous velocity.

#### Paul Colby

Gold Member
One can certainly infer an approximate "instantaneous" velocity from measurement. Most quantities I can think of are actually inferred from measurements. How direct these are depends on the methods and models employed. Take velocity. What comes to mind? Radar gun? Two consecutive position measurements? None of these are instantaneous but arguments can be made about the rate of change of the velocity over the measurement period being small or negligible.

#### russ_watters

Mentor
One can certainly infer an approximate "instantaneous" velocity from measurement. Most quantities I can think of are actually inferred from measurements. How direct these are depends on the methods and models employed. Take velocity. What comes to mind? Radar gun? Two consecutive position measurements? None of these are instantaneous but arguments can be made about the rate of change of the velocity over the measurement period being small or negligible.
No, radar guns measure speed from doppler shift of reflected radio waves. They are single-point/instantaneous measurements.

There are also speedometers (and clutches) that measure speed from centrifugal force.

There may be other methods I'm not thinking of.

Speed and speed measurement do not in theory or practice require a multi-point position over time comparison.

#### Paul Colby

Gold Member
No, radar guns measure speed from doppler shift of reflected radio waves. They are single-point/instantaneous measurements.
Well, you might want to review how these things actually work. Measuring a doppler shift in under a period of the radiation shifted ain't happening.

#### russ_watters

Mentor
Well, you might want to review how these things actually work. Measuring a doppler shift in under a period of the radiation shifted ain't happening.
...now you are talking about the nature of light: Photons are not little (or long), continuous waving strings that you can break apart into pieces of a wave, or it isn't like watching a peak and waiting for the next peak and measuring how long it took to arrive. Photon emission, absorption and reflection are instantaneous processes/events.

 Sorry, turns out I was wrong about how it is done in practice; they do indeed measure beat frequency between outgoing and incoming waves using a counter.

That said, it should be possible in principle to measure the frequency directly.

#### Paul Colby

Gold Member
And radar guns measure photon energy.
Good heavens, not at RF frequencies. My point is instantaneous measurement implies unlimited bandwidth. Nothing has infinite bandwidth. IMO you are paving over the measurement time which is always finite and non-zero.

#### russ_watters

Mentor
Good heavens, not at RF frequencies. My point is instantaneous measurement implies unlimited bandwidth. Nothing has infinite bandwidth. IMO you are paving over the measurement time which is always finite and non-zero.
Late edit to the previous post; the principle for radar guns uses beat frequency/wave interference, and not a direct energy measurement. Apologies.

Nevertheless, an energy measurement should be theoretically possible. There doesn't need to be a sampling frequency. You could theoretically bounce a single photon off an object and measure its energy on return.

BvU

#### Paul Colby

Gold Member
You could theoretically bounce a single photon off an object and measure its energy on return.
I argue even this has finite measurement time and uncertainties. Idealization is fine. Any method can be refined until the model requires fixing. The thing about measurement is it's not all theoretical. Bit of a mix.

 It occurs to me one would have to solve the QM interaction of the photon with a real material surface and include the time delay experienced in interacting over a skin depth. Sound complicated.

#### sepcurio

I'm pretty sure that radar guns use frequency counters to measure the returning signal, which of course is not instantaneous.

) ...that measure speed from centrifugal force.
That might be a case of instantaneous measurement or perhaps continuous measurement.

There is also the special case of measuring the velocity of a zero-mass particle in a vacuum. If you can determine what the particle is from a single data point, e.g., that it is a photon, then you can infer its speed is c.

But there is always the issue of simultaneity which cannot be avoided and seems to exclude instantaneousness.

#### Paul Colby

Gold Member
Centrifugal force is not an instantaneous measurement. Just looking at the thing takes some time.

#### russ_watters

Mentor
I argue even this has finite measurement time and uncertainties.
Can you list them? Are you confusing error and signal propagation delay with measurement time?

Consider also the centrifugal governor/speedometer; rotating weights move apart when spun faster, to move a needle on a dial. There is no time component to what is being measured; it is measuring instantaneous position.

#### russ_watters

Mentor
Centrifugal force is not an instantaneous measurement. Just looking at the thing takes some time.
Yeah, you are confusing the time to take or process the measurement with the nature of the measurement. By this logic, weight has a time parameter as well.

"Speed measurement -- Limitations to "instantaneous" measurements?"

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