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For most physical measurements, zero is the same regardless of the units used for the measure:

$0 \mathrm{mi} = 0 \mathrm{km}$

$0 \mathrm{s} = 0 \mathrm{hr}$

but for absolute temperatures, different systems have different zeros:

$0 ^\circ\mathrm{C} \neq 0\,\mathrm{K}$

Are there any other physical, measurable quantities (other than temperature) that have different zero points?

I'm looking for measurable quantities that are applicable anywhere -- things like voltage or temperature, not local quantities like "distance from the Empire State Building".

Joe
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    This question (v1) seems like a list question. – Qmechanic Apr 09 '15 at 20:24
  • @Qmechanic, I think it is a list question, but with very few reasonable possible answers. – Joe Apr 09 '15 at 21:04
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    Celsius is not an absolute temperature scale. But Rankine is, and $0~\text{R} = 0~\text{K}$. – tpg2114 Apr 09 '15 at 21:12
  • @tpg2114, that's not what I mean. Both Celsius and Rankine can be used to measure absolute temperature (what temperature is this object?) and relative temperature (how much hotter is this than that?). Used to measure absolutes, Celsius and Rankine have different zero points. Used to measure relatives, 0C = 0R. – Joe Apr 09 '15 at 21:15
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    @tpg2114, that answer would just be restating the question. – Joe Apr 09 '15 at 21:18
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    I think my comments just go to show that the intent of the question isn't very clear... It took several read-throughs and your comments to understand what you are trying to get it. – tpg2114 Apr 09 '15 at 21:20
  • Isn't the answer to that, any non-absolute scale? You can invent infinitely many scales choosing different origin points. Or do you mean like, widely used, or used at all? – luk32 Apr 10 '15 at 00:47
  • @tpg2114 - I got the intent right away. – Hot Licks Apr 10 '15 at 00:54
  • I'm thinking that there must be some measurements in quantum mechanics that are like this, but I don't know the topic well enough to hazard a guess where. – Hot Licks Apr 10 '15 at 00:56
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    It seems like what makes temperature unique is not that it has a zero point but that the zero point (absolute zero) is meaningful. Pretty much any quantity could have absolute and relative versions (date-time versus time interval, position versus displacement) but the zero is usually arbitrary, without universal physical meaning. A lot of the answers are like this right now, so it's not terribly interesting. – Cascabel Apr 10 '15 at 01:08
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    @Jefromi, of the seven basic SI units, I think the zero points for most of them are quite meaningful. – Joe Apr 10 '15 at 01:11
  • @Joe Well, if all you want is units trivia, I guess that works too - just having everyone mention the absolute version of every relative measurement doesn't seem that useful? – Cascabel Apr 10 '15 at 01:17
  • @Jefromi Time has a meaningful absolute zero, as the beginning of the universe. – OrangeDog Apr 10 '15 at 09:04
  • Length - http://notch.tumblr.com/post/13170951247/kelvin-is-awesome-celsius-and-fahrenheit-are – MPeti Apr 10 '15 at 20:36
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    Since only differences in voltage are meaningful (as with all potentials), voltage is just as local as "difference between one position and the position of the ESB". – ACuriousMind Apr 10 '15 at 22:25
  • Key words here: SI and absolute (definition 5). – Mazura Apr 11 '15 at 19:58

10 Answers10

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Time, in which case each system's zero point is often called its epoch:

http://en.wikipedia.org/wiki/Epoch_%28reference_date%29

Gnubie
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    I don't think this answers the question. Temperature is scale in which changing the scale forces you to change the zero point. The zero point and the unit of time are independent; if I was measuring time in seconds and I want to change it to minutes, I don't shift $t=0$, I just divide everything by $60$. – Javier Apr 09 '15 at 21:33
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    @JavierBadia Not time intervals, dates. Like if you are converting 2015.26 A.D. to seconds since the big bang. – Christopher King Apr 09 '15 at 22:53
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    @JavierBadia: you don't really have to change the scale and zero point at the same time. For example, degrees Celsius and Kelvin use the same scale, but different zero points. – sumelic Apr 10 '15 at 15:01
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    @JavierBadia Rankine and Kelvin use different scales and same zero point. Temperature's zero point is independent from the size of a degree. – cpast Apr 12 '15 at 07:48
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    @JavierBadia The Islamic calendar has a 354 day year with a zero point somewhere around 622 AD. To convert between Islamic years and Christian years you need to scale as well as change the zero point. – CJ Dennis Apr 13 '15 at 09:17
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    Excellent answer, and I think a very close analogy to temperature scales. The Gregorian (AD/BC) attempts to put year 0 at the birth of Christ (sort of), the Hebrew calendar puts year 0 at the creation of the world, the Roman calendar put year 0 at the founding of Rome, the Julian period puts day 0 at the confluence of several astronomical cycles, etc. – Jay Apr 13 '15 at 13:21
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    @Jay Just nitpicking, but most of your examples wouldn't have a year 0 at all as far as I know: everything started with year 1 (which is still the natural way to count anyway: the 1st year of your life, your 1st year at university... those are year 1s, not year 0s). That said, unlike t=0, year 1 (or year 0) is not an instant, it's a period (the first period following the reference). – Bruno Apr 13 '15 at 16:12
  • @Bruno Yeah, that's part of what I meant by "sort of". The other part being that when many of these "base events" actually happened is debatable. I was trying to cram an answer into a comment. :-) And yes, a year isn't an infinitesimal point, like 0 on a ruler or a thermometer, but the beginning of a year is, and that's the point. – Jay Apr 13 '15 at 22:28
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Sound can be measured in deciBels ($\mathrm{dB}$) but also as an intensity measured in $\mathrm{W/m^2}$.

$0\,\mathrm{dB}$ on this scale is equal to $1\times10^{-12}\,\mathrm{W/m^2}$.

Reid
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Matthew Steeples
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  • I didn't know that. I knew the deciBel was logarithm but I never stopped to consider that it would be difficult to represent absolute silence. – Michael Lorton Apr 09 '15 at 18:33
  • I don't think it's just a case of representing absolute silence, but more of a case of if something is purely logarithmic it can't start at 0 – Matthew Steeples Apr 09 '15 at 18:35
  • Is the Richter scale be similar? – HDE 226868 Apr 09 '15 at 18:40
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    Yes, any logarithmic scale (see @rghome's answer) will have an arbitrary 0 point. Richter Scale translates to energy (of which there can't be a negative number) so 0 lines up with a very small amount. – Matthew Steeples Apr 09 '15 at 18:44
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    @MatthewSteeples right, the consequence is that absolute silence is at -∞dB. – hobbs Apr 09 '15 at 21:34
  • Another example is $\mathrm{dBm} = \mathrm{dBW} - 30$ – Alfred Centauri Apr 09 '15 at 21:57
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    Sound cannot be measured in dB, or at least that is not very precise. dB is used to express a ratio. So you can measure difference in intensity on a logarithmic scale. So more like a "difference" between sounds. I also don't think 0dB is 10^-12 Wm^-2; 0dB is no difference so shouldn't it be 0 any unit? – luk32 Apr 10 '15 at 00:57
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    I wouldn't call "dB" a unit of measurement at all. It's a notation for numbers. The real number which is the reciprocal of 10 can be written as "1/10", or "0.1", or "-10 dB". – Lee Daniel Crocker Apr 10 '15 at 18:29
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    "dB" is a common (although slightly sloppy) abbreviation for the unit strictly known as dB(SPL). – David Apr 10 '15 at 23:58
  • @David Maybe for you. As someone who deals with music, 0 dB to me means 0 dBFS (clipping). – Cole Tobin Apr 11 '15 at 06:04
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Luminosity.

The Magnitude of a star is a logarithmic scale with an arbitrary zero point.

The SI unit of brightness is the Candela or or there is luminosity if direction is not accounted for.

From Wikipedia:

In SI units luminosity is measured in joules per second or watts. Values for luminosity are often given in the terms of the luminosity of the Sun, which has a total power output of 3.846×1026 W.[2] The symbol for solar luminosity is L⊙. Luminosity can also be given in terms of magnitude. The absolute bolometric magnitude (Mbol) of an object is a logarithmic measure of its total energy emission.

rghome
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  • If you used a different unit to express brightness (such as candlepower), the zero point would still be the same. – Joe Apr 09 '15 at 18:42
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    @Joe: some units of luminosity (including candlepower) have the same zero point. Others (the example given here is magnitude of a star) do not. A zero magnitude star is rather brighter than 0 candela ;-) In fact, in this example the scales don't even run in the same direction, a larger magnitude number is dimmer. – Steve Jessop Apr 10 '15 at 09:15
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Another example of an arbitrarily selected zero point is longitude. This was not always measured from the Greenwich meridian - Paris has been used, and the ancient Greeks (Ptolemy, specifically) used an island believed to exist off the west coast of Africa* in order to avoid dealing with negative numbers.

Really, though, none of the examples anyone have mentioned do what temperature does in terms of having a natural zero point which is not universally used. All of these examples (as of this posting) are either logarithmic scales (and all have a true zero point at negative infinity), are measuring position rather than quantity.

And you can't do this for time because of relativity - there's no reasonable point of reference for the International Terrestrial Reference Frame (i.e. the time kept by an ideal clock on Earth's surface at sea level) at the beginning of the universe, so we can't measure from the big bang even if we could otherwise determine the "age of the universe" down to the nanosecond.

Temperature has an arbitrary zero point because people have been measuring temperature since before the fact that there is an absolute zero was discovered.

*Of course there are such islands, but it's not known which he used and none correlate precisely to his maps.

Random832
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  • While I agree with your statement, the non-Kelvin temperature scales mentioned in the question are all measuring position rather than quantity too – Matthew Steeples Apr 09 '15 at 20:32
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    @MatthewSteeples Not really. Thermodynamic temperature means that the temperature of an object is a quantity, which is related to the amount of thermal energy in the object vs its heat capacity. – Random832 Apr 09 '15 at 20:34
  • I'm not saying that temperature itself is a position, just the non-Kelvin temperatures. Kelvin is the "true" measure and the rest of them are just points on that scale (in the same way that the logarithms are points on their respective scales) – Matthew Steeples Apr 09 '15 at 21:23
  • Ptolemy used Atlantis as the 0 point? – Michael Apr 10 '15 at 01:45
  • @Michael No, he used the "Fortunate Isles" which most people identify with either the Canaries or Cape Verde. His location for them wasn't accurate enough to tell. – Random832 Apr 10 '15 at 01:47
  • Interestingly, the Big Bang is in theory THE point in time where time is absolute. That is, time everywhere agrees what it is - 0. Since then, time has diverged depending on the speed at which you travel in the universe. So in a sense, the Big Bang is analogous to 0 Kelvin. – slebetman Apr 11 '15 at 22:03
  • @slebetman But there's no coherent definition of what speed the Earth has been traveling for the first ~10 billion years. – Random832 Apr 12 '15 at 03:41
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Height / altitude. From Wikipedia:

  • Indicated altitude – the altimeter reading
  • Absolute altitude – altitude in terms of the distance above the ground directly below
  • True altitude – altitude in terms of elevation above sea level
  • Height – altitude in terms of the distance above a certain point
  • Pressure altitude – the air pressure in terms of altitude in the International Standard Atmosphere
  • Density altitude – the density of the air in terms of altitude in the International Standard Atmosphere

I suppose you could define an "absolute altitude" as distance from the center of the Earth.

Hugh Allen
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  • Especially if you consider indicated and pressure altitude as pressure and density altitude as density, the quantities they actually measure. – Jan Hudec Apr 10 '15 at 14:14
  • Distance from the center of the earth is geocentric altitude. The one you are calling true altitude is also known as geopotential altitude, assuming you mean above the mean sea level or some other reference surface and not above the actual local level of the sea.

    Fun fact, Mt. Everest isn't the place on earth's surface with the highest geocentric altitude.

     – Doug McClean Apr 13 '15 at 02:29
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Motion.

Velocity is obviously relative, and no "absolute rest" frame is known to exist.

Even acceleration, which is in a sense absolute, is sometimes specified relative to a local inertial frame (ie. freefall), sometimes relative to the distant stars (so you can talk about the acceleration of astronomical bodies due to gravity), and most commonly in everyday life, relative to the Earth. You think you are sitting still at your desk, but relative to a local inertial frame you are actually being accelerated upwards at about $9.8 m/s^2$ due to the pressure of the chair on your ass!

Community
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Hugh Allen
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Gauge pressure.

From Wikipedia:

Gauge pressure is zero-referenced against ambient air pressure, so it is equal to absolute pressure minus atmospheric pressure.

Hugh Allen
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  • This perfectly addresses the question. Just as pressure is typically referred to as "gauge" or "absolute", the Kelvin scale for temperature is referenced as absolute temperature, while Fahrenheit and Celsius are examples of gauge measurements. These come up together in the Ideal Gas Law -- students are constantly reminded to use absolute measurements for temperature and pressure. – jdj081 Apr 13 '15 at 02:15
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Gravitational potential energy (in a constant gravitational field such as near the Earth). This is the usual scenario in elementary questions for high-school students. One may use the starting point of a body as zero or the end point or the ground.

Drone Scientist
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The scale used to define positions on a highway depends on the point chosen for the Zero Marker. There is a difference between defining a position on a highway, like Mile #25 or Exit 125, and a distance on that highway: it's 30 km from Km 15 to Km 45.

The same thing is true in temperature scales, where we need to distinguish between labelling a position ("the freezing point of water") and measuring a temperature difference ("the freezer was 38 Celsius degrees cooler than the room")

I once read a news report saying, "February's average high of -6 degrees Celsius was twice as cold as the historical average of -3 degrees Celsius..."

DJohnM
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  • "twice as cold" Excellent. So if the average temperature is 1 C, but today was -2 C, it's ... negative twice as cold? – Jay Apr 13 '15 at 13:16
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One that has many zero points is the standard Gibbs free energy of formation:
each element has their own zero point.

LDC3
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