# Do negative numbers have any physical meaning?

So, mindlessly wandering off into space, thinking about quantum and how cool physics is, I came to a realization that... well.. negative numbers to me make 0 sense.

You have either something, or not something.

It's always a yes or no answer, with everything And everything always has an opposite; it's nonexistence.

I either have a red scarf, or not.

If there are 3 doors, labeled 1 2 3. I have to choose one of them. The choice isn't me choosing which door, the choice is what door i'll pick. I'll either pick door 1, or not pick door 1. The opposite of door 1 is no door 1.

Lets go really small. I have 2 grains of salt. I can't take 3 grains away.

I believe negative numbers were invented by man to create debt. Because it doesn't make any sense in physics. Can someone please explain this to me!!

• Could one of the close voters explain to me how this question is opinion based? Annav's answer provides historical context while BMS and kleingordons answer provide a physical context of negative values; none of these appear to present an opinion. – Kyle Kanos Jun 10 '14 at 13:18
• @KyleKanos while the answers may be good, the question... doesn't even ask a question. The issue of whether or not admitting good answers makes a question good has come up over and over. While I maintain that the possible answers matter for whether an engineering flavored question are on topic, for questions which are so vague that it's not clear what's being asked I think the possibility of someone writing a useful monologue is not relevant. – DanielSank Aug 6 '15 at 22:52
• Heck, Maybe Anna can get that reversal badge from this :) – DanielSank Aug 6 '15 at 22:53
• @DanielSank: There is a question in the title and a second one as a request (hint: see the last sentence). Certainly not the best question on this site, but one that is certainly not opinion-based (which was the point of my remark). – Kyle Kanos Aug 7 '15 at 0:08
• @KyleKanos The title in the question is so vague as to admit more or less whatever answer I want. On those grounds I'd say it's opinion based. The last sentence is a request to explain "this", but "this" is not specified anywhere. There again we get leeway for someone to write whatever opinion they want about whether or not negative numbers have physical meaning. In any case, this question certainly falls under the "unclear what you're asking" category. – DanielSank Aug 7 '15 at 0:49

The first attempts at formulating a model of nature had no numbers in it. Numbers is the province of mathematics. Arithmetic was created really when bartering became necessary as communities became larger and larger and a number system was needed to keep a fair track of who owes what to whom, as you say. It is arithmetic that was the start of mathematics. Not physics.

When land possession started people used arithmetic to keep track of what was what, and finally geometry and then algebra were invented. Negative numbers started coming in solutions of algebraic equations

For a long time, negative solutions to problems were considered "false". In Hellenistic Egypt, the Greek mathematician Diophantus in the third century A.D. referred to an equation that was equivalent to 4x + 20 = 0 (which has a negative solution) in Arithmetica, saying that the equation was absurd.

Negative numbers appear for the first time in history in the Nine Chapters on the Mathematical Art (Jiu zhang suan-shu), which in its present form dates from the period of the Han Dynasty (202 BC – AD 220), but may well contain much older material. The Nine Chapters used red counting rods to denote positive coefficients and black rods for negative.

It is after all a useful way of keeping count of what is owed and what is gained in any human transaction, in two sets of numbers. Instead of using left hand fingers for owed right hand fingers for gain, a symbol instead meaning "left hand".

Lets go really small. I have 2 grains of salt. I can't take 3 grains away.

No, you can count on your right hand "two in hand", and on your left "one in the bush" meaning expecting to get it from somewhere, or someone else's kitchen.

In any case negative numbers existed in mathematics before ever being used in physics.

Now for physics, mathematics is a tool. I have heard it said that "physics theory is a subset of mathematics" I suppose by mathematicians ? But it is not true. Mathematics allows for beautiful self consistent theories where positive, negative, complex and even worse definitions hang together and produce solutions .

Physics takes mathematical self consistent constructs and fits them, imposes them on physical observables by introducing physics postulates and laws on top of the mathematical axioms . These correlate physical situations, space and time changes, and negative numbers come with the package (also complex ones). Solutions of the mathematical equations predict data to be seen in the future. Physics cannot be blamed for negative numbers.

I believe negative numbers were invented by man to create debt.

You are correct, on the first part, but not to create debt, to keep count of debt in a better way than a left hand and a right hand give and take tally.

• Loads of insight @anna. Thanks! So negative numbers came before physics, and are used in physics as a tool to make measurements. But I'm still curious of how it's applied to real world scenarios that don't involve imagination. Debt is more like a reminder of what you owe, or what is to be returned, but there is no real physical significance to this. The symbol is created as a measurement, but can it be used to reference below 0 in the real physical world? Why is the temperature measured below 0? Does the temperature have to pay it back? It simply doesn't make sense. ;( – CoolQuestionsGuy Jun 10 '14 at 4:03
• It is a symbolic way to keep track of measurable quantities in physics, and also on convenience. Physicists really measure temperature from 0 Kelvin and then it is always positive. The 0 of the ice point is a convenient anthropic point ( as we are made mostly of water :) ) to tell us how cold it is. It is the model that is used that says below 0. In the same way that a map is not the terrain, the mathematics is not the physics. It is a description of the physics and negative numbers are convenient in the description. – anna v Jun 10 '14 at 4:09
• But things like geometric symmetry relations really do have negative representations often, rotations for instance (you can rotate one way or the opposite way, or representations of transformations like rotoinversion...and these geometric properties are the basis of a lot of physics... – daaxix Jun 10 '14 at 6:12
• @daaxix No, they are the basis for fitting rotational mathematical formulae to physics obsrvations, imo. There are still postulates that relate the mathematics to observations. – anna v Jun 10 '14 at 8:42
• @annav No picture? – BMS Jun 10 '14 at 15:31

For certain questions you may pose about nature, a negative value makes no sense as an answer. Your question about subtracting grains of sand is an example of one such question. For a vast range of other physical questions, negative numbers have an important role to play. Here's one way to start appreciating this:

We find it helpful to assign numbers to locations in space, called coordinates, in order to measure distances. For these coordinates to make sense, we need to choose a reference point from which distances will be measured in order to assign coordinates. This reference point can be assigned the value of zero in each of the three spatial dimensions.

Now consider one direction, or axis, in relation to the reference point, like the north-south direction. We might decide to give a location a positive coordinate on the north-south axis if it lies north of the reference point. If it lies south of the reference point, we would then give it a negative value. Setting up a coordinate system like this allows to easily calculate distances between two locations using the ordinary laws of arithmetic applied to the coordinates, including the laws relating to negative numbers.

For example, if there is one location that is assigned a coordinate of 3 units north, and another that is assigned a coordinate of 2 units south, then the distance between them is 3 - (-2) = 5 units.

Note that the location of the reference point, and the convention to assign positive coordinates to locations north of the reference point, were arbitrary decisions. That's okay. We still measure accurate distances even if we change these conventions by moving the reference point or making south the positive direction.

I've focused on distance coordinates here, but you'll find that negative numbers often enter into physics in similar ways for other quantities such as velocities, forces, electric currents, and generally speaking anything in physics that is a vector.

There are other ways that negative numbers can be useful aside from vectors, but learning about vectors is a great place to start.

• Wow okay so negative values don't directly apply to nature itself, otherwise you'd be able to get -1 grains of sand, which of course didn't make any sense to me. I'm still new to this, and learning the surface level of all of these mechanics is very VERY interesting to me. Quantum mechanics seem so beautiful, and while I was reading about it, I thought to myself "why do we use negative numbers in physics, when it doesn't make sense in nature?" But thanks to you guys, this forum, i've learned a TON without having to read a book (so far). We use negatives to measure, not to relate directly. – CoolQuestionsGuy Jun 13 '14 at 22:42
• "Wow okay so negative values don't directly apply to nature itself, otherwise you'd be able to get -1 grains of sand". This is the exact opposite of what kleinGordon said. He acknowledged that negative numbers are not much use in counting sand, but have several examples from nature where they do make sense. Do you believe in fractions? By your logic, they don't appear in nature, because you can't have half a hole in something or two thirds of a cloud. Fractions are useless for counting holes and clouds; negative numbers are useless for counting sand, but they are both found "in nature". – Peter Webb Mar 1 '15 at 9:56

Negative numbers might seem weird when you count things, as you've indicated but they do appear in many other contexts. Take a one-dimensional coordinate system, for example. Negative numbers in this context indicate position relative to some arbitrarily defined zero. To cite just one other example, more inline with your own, consider how negative numbers can indicate a decrease in a quantity. You have 3 grains, and 2 were taken away. The change is $-2$.

• the change is 2 less grains. or -2. but there is still 1. So the question would be "how many grains do you have left", i'd say '1'. If the question was "how many grains were taken away", I'd answer '2'. But negative numbers in physics don't exist the same way positive numbers do. They simply don't exist at all in the physical world, to my very very low knowledge haha – CoolQuestionsGuy Jun 10 '14 at 3:27
• @CoolQuestionsGuy If you live in Chicago, there are many days when you can say "it is -10 degrees outside". – LDC3 Jun 10 '14 at 3:43
• Why is it measured as -10 degrees? How is there negative weather? Wouldn't that mean the weather doesn't exist? – CoolQuestionsGuy Jun 10 '14 at 4:04
• @CoolQuestionsGuy Temperature is a measurement of the heat an object has (in the case of weather, it is the air). Saying that the temperature is -10 degrees is similar to saying that the air has (a certain quantity) less heat than air at 0 degrees; a selected temperature which everyone has agreed upon. A negative temperature is not negative weather. Weather is neither positive or negative, it just is. Although some weather does put some people into a negative mood. – LDC3 Jun 10 '14 at 4:35

Ever noticed the difference between negative temperature and positive temperature? You can feel the difference!

• I use absolute scale... – Mitchell Jan 25 '18 at 11:00

A negative number can be antimatter and complex number are a virtual world which is perpendicular to our world and interact with us!

the reason we have matter more than antimatter lies in cross and division if you cross or divide two negative number (antimatter) you have a positive number (matter)

## protected by Emilio PisantyJan 25 '18 at 15:08

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