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Speed is defined as 'change of distance' over 'change of time'. As an equation it is 'v=(s2-s1)/(t2-t1).

In this equation speed is a derived notion from the 'extensions' (in Spinozas language) of distance and time.

That is one doesn't measure speed directly; but one must measure it indirectly. The basic measurements are of space and time.

Is it actually possible to show that speed can be, in fact, measured directly?

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    I don't understand what you mean by "directly". All sorts of equations have a dependence on velocity, from air resistance to magnetic field strength around a moving charged particle. But you need some time somewhere or nothing will change. – Rex Kerr Dec 30 '14 at 14:26
  • Special relativity says no, and that seems to be working out OK. In that framework, you cannot even necessarily measure it with distance and time, since different observers will not agree upon those measures. Every observer is at rest unless accelerated. Since this is a direct paradigmatic axiom for a pretty accepted paradigm, I think this is really pushing the edge between science and philosophy you were asking about... – jobermark Dec 30 '14 at 15:04
  • What does an accelerometer measure? --Maybe you could explore the terms of your question a bit further and try to spell out really explicitly what you're expecting sometime to explain to you in an answer? – Joseph Weissman Dec 30 '14 at 15:18
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    Yes. Highway patrolmen do it all the time. – David H Dec 30 '14 at 16:24
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    @weissman: Its to do with Spinozas description of phenomenal reality as extension (he does briefly go into physics in his Ethics); but is also to do with what are the fundamental qualities in Physics, those that are directly measureable. – Mozibur Ullah Dec 31 '14 at 14:56
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No, this is not possible, because velocity is defined as distance divided by speed. In the SI system there are some non-derived base units, like time, distance, etc., but velocity is not one of these:

The seven SI base units and the interdependency of their definitions. Clockwise from top: kelvin (temperature), second (time), metre (length), kilogram(mass), candela (luminous intensity), mole(amount of substance) and ampere (electric current). The second of time, kelvin and kilogram are defined independently of any other base units. The metre is defined in terms of the speed of light, so depends upon the definition of the second. The definitions of the other base units are more complicated.

(http://en.m.wikipedia.org/wiki/International_System_of_Units)

There is an answer talking about the speedometer in a car. However, the speedometer always slips a little bit and is therefore not accurate. Also, the speedometer essentially measures voltage, and they have a formula for velocity depending on voltage. This formula is not derived from the definition of velocity but from an earlier measurement of... distance and time.

The doppler effect which is used by GPS tracking systems mentioned in the other answer is based on a phase difference in the received GPS signals which is caused by a different distance to the satellites on different moments. So essentially this method uses distance and speed as well.

The highway patrolmen mentioned in the comments measure time over a predetermined (short) distance.

  • All physical measurement is approximate and subject to physical error due to friction and slippage. So your objection is to all physical measurement whatsoever; not just to speedometers. You are saying that a speedometer doesn't measure speed because no exact physical measurements are possible at all. Likewise a scale doesn't measure gravitational attraction directly; it measures the compression or stretching of a spring. So you are objecting to all physical measurement. Isn't that right? – user4894 Dec 31 '14 at 18:13
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    @user4894 that is true, but the second argument against the speedometer approach (the "Also,...") is an essential one. – Keelan Dec 31 '14 at 18:15
  • So scales don't measure weight for the same reason. Can you name any physical apparatus that measures anything by your logic? – user4894 Dec 31 '14 at 18:16
  • @user4894 stopwatch and ruler are just examples. I'm not objecting against physical measurement. I'm objecting against you saying that one can measure speed without measuring distance or time, for the exact reason mentioned in my answer. A speedometer is gauged, so your approach is not correct. – Keelan Dec 31 '14 at 18:23
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    @user4894 a speedometer measures voltage and then uses a relationship between voltage and velocity. The exact characteristics of this relationship are found by measuring distance and time. The naming is confusing, yes. Then, I didn't talk about a mechanical stopwatch. Indeed, a ruler. If you look up the definition of the meter, you will find that it is in fact defined by a (special kind of) ruler. – Keelan Dec 31 '14 at 18:33
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The speedometer in your car measures speed directly.

It works by measuring the current generated by a magnet turning in direct proportion to the turning of some component of your automobile.

The details are here. http://en.wikipedia.org/wiki/Speedometer#Eddy_current

When the car or motorcycle is in motion, a speedometer gear assembly turns a speedometer cable, which then turns the speedometer mechanism itself. A small permanent magnet affixed to the speedometer cable interacts with a small aluminum cup (called a speedcup) attached to the shaft of the pointer on the analogue speedometer instrument. As the magnet rotates near the cup, the changing magnetic field produces eddy currents in the cup, which themselves produce another magnetic field. The effect is that the magnet exerts a torque on the cup, "dragging" it, and thus the speedometer pointer, in the direction of its rotation with no mechanical connection between them.

This shows that speed can be computed directly by an analog mechanical device; and that this is a common everyday occurrence all over the world. There's no tiny little guy frantically computing derivatives inside your car's dashboard.

By the way, your question contains a logic error. You say: "That is one doesn't measure speed directly; but one must measure it indirectly." But that doesn't follow. Just because a given quantity is defined a certain way in physics, that has nothing to do with how we measure that quantity in everyday life.

After all, gravitational attraction is defined in a very complicated way by the modern theory of gravitation; yet to measure the gravitational attraction between my body and the earth, I simply step on a scale. I don't need to take a graduate level class in general relativity.

  • The same can be said for radar guns, which rather than relying on eddy currents use doppler shifts. The photons are not calculating derivatives, they are simply following the rules of physics. – Cort Ammon Dec 30 '14 at 22:08
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    I've forgotten most of my electrodynamics, so I'llk have to think about this; thanks too for catching the logic error - however I just mean in terms of the equation determining speed; if I really felt that 'must' meant 'must' I wouldn't be asking this question. – Mozibur Ullah Dec 31 '14 at 15:09
  • @MoziburUllah You need to review electrodynamics to understand the Wiki link I gave? You know that a magnet spinning in a coil of wire induces an electrical current in the wire, right? That's how a car speedometer directly measures speed. I don't understand your remark about "must" meaning "must." Is this some kind of Clintonian thing, like the meaning of "is?" If "must" doesn't mean "must," you are denying the law of identity. Only politicians are allowed to claim that a thing isn't what it obviously is. – user4894 Dec 31 '14 at 18:06
  • @virmaior Two people have now objected to my response (and evidently negged it as well) using an argument that essentially says that all physical measurement is impossible. When you measure a physical quantity using a physical apparatus, you always measure something else as a proxy for the thing you're looking for. Particle physicists don't measure particles. They measure the artifacts that hypothetical particles create in their cloud chambers. Saying a speedometer does not measure speed because it only induces a current that drives the speedometer, I regard as the worst kind of sophistry. – user4894 Dec 31 '14 at 21:57
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    @Keelan I'll post an official question here when I get a chance so that others can chime in about this interesting topic. All the good articles about the philosophy of measurement are behind academic paywalls so it's hard to find good source material. – user4894 Jan 5 '15 at 18:35
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This article http://nujournal.net/HighAccuracySpeed.pdf describes how a GPS receiver could measure the speed at which it is moving directly.

I have no idea whether the cheap GPS in your car will do this; it is obviously easy to make two consecutive location measurements and calculate the speed from those, but the article describes a much more precise direct measurement (within 0.01 knots, which would be 18 meters / hour or 5 mm / second).

Nice quote from the article: "Proof of speed is possible even though we may not be able to prove an exact location where that speed was achieved. Incidentally, this is not the first time such a problem occurred. It is well known in physics that it is impossible to determine both velocity and position of an electron. We can accurately determine one or the other, but not both..."

And the last quote gets us into the realm of Quantum Mechanics, where speed cannot be defined the way you suggest anymore. Speed doesn't describe movement, at best it can describe the probability of various changes in location, without even knowing the location.

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