3.1415926
1 apple minus 1 apple does equal zero, but it’s virtually impossible to accurately “minus 1 apple” in real life because of the observer effect. As you say, ‘maths don’t accurately describe the universe.’
~Max
Maths describes physics accurately, physics describes the world accurately, therefore maths describes the world accurately, if you use them right and your measurements are up to the task at hand.
But what the OP means with “zero in physics” is not clear to me, it sounds like the worst possible marks you can get in physics in an exam when you do not answer a single question correctly, if you use the Spanish school score (where ten is the best score, in Germany it would be a 6, 1 is the best, go figure. Don’t you use letters for that in the USA?). So a zero in maths is the worst possible result in a subject, zero in physics is the worst possible result in another, and both will make your parents disappointed with your performace, in Spain. And in Germany a zero in either subject is not even possible.
In my first test in Freshman physics I got an 85. Out of 160. But that was a B+ because the test was scored on a curve.
So tell me what definition of a mark you’re using.
That’s the problem with the OP. Physics applies mathematics in the forms of measurements, experiments, and theory to reality. One apple minus one apple may be mathematics but only in an elementary arithmetic word problem sort of way. It might be considered a measurement, though that’s not the usual way the word is used. It is not theory.
At best it can be considered an experiment, although it’s one that would get you flunked in any classroom. No experiment can be valid without defining terms and explaining output. A true physics experiment would define what removing an apple would mean. Does it mean moving an apple from one location to another? Eating the apple and changing its physical form in the digestive system? Blasting it with radiation until it turns to photons? Throwing it into a black hole?
Those operations are physics. Saying “1 apple minus 1 apple equals zero” is mere wordplay. Nothing physical is taking place. It has no definitive answer, and none can be demanded.
Seems like the OPs problem is one of semantics rather than mathematics or physics. That’s down the hall.
Even staying within the realm of mathematics, zero isn’t always zero.
So when is zero not zero?
When it’s used to define an arbitrary point on a number scale as the “origin point” (commonly and conveniently often labeled O, not to be confused with 0), which may not necessarily be at the bottom-most end of that number scale.
This appears in physics when, for example, we label a certain temperature as “zero degrees” when that temperature is far from the least possible temperature. We define “zero altitude” as a certain arbitrary altitude (often, sea level) which is hardly the least altitude there is. We define “time T=0” to be a certain arbitrary point of interest in a time-line, such as the moment a rocket engine is fired, even though times prior to that exist and are meaningful (thus the backwards count-down “T minus 10”, “T minus 9” etc.)
Within the realm of pure mathematics, we model any of these physical situations by drawing a line and putting the 0 point somewhere on the line that isn’t at any end of the part of the line we’ve drawn: Thus, the commonly seen “number line” with 0 (or O) somewhere in the middle.
I think zero in maths is exactly the same as zero in physics. There may be times when zero is not achievable practically, but that doesn’t mean that the zeroes are different, just that one of them is not achievable in the real world.
The apple example is weird seeing as you’re not taking a different apple away from an existing apple, you’re removing the same apple, which is identical. I guess you could look very closely and observe that some of the apple remains, but that just means you haven’t removed all of the apple, it doesn’t mean zero apples means something different from zero in maths.
Agreed - I mean, 1 kilo of sand minus 1 gram of sand is not zero, even though both quantities are 1 - because the units are different. Apples are not uniform enough to be a formal and completely precise unit.
Numbers are abstract - they can be manipulated using mathematics without any specific working units, or, they can be used to express quantities or magnitudes of units, but they are still numbers and mathematics still works on them.
I would say rather than the zero of maths being ‘the same as’ the zero of physics (which could imply there are two different concepts of zero that happen to be alike), there is a concept of zero that spans all disciplines where mathematics applies (including physics)
I mean, I wasn’t really joking about the semantics thing.
The OP is basically asking a question about semantics rather than physics or mathematics. It is trying to get to a single platonic ideal of something called “zero” about which the OP has some kind of vague hand-wavy idea but no actual definition while everybody else is responding based on their own, more concrete but not universally accepted (especially by the OP) definitions.
There’s little of real math or physics otherwise, though the OP invokes both. In math, one is taught to be careful about definitions and postulates, and this thread violates that from the get-go.
Is that really common? I don’t remember ever encountering it.
If you are working with and naming points, yes. A vector from the origin to point A is generally named \overrightarrow {OA}.
Well, okay, I don’t know how common it is, but I think it is. I’ve certainly seen it. You can generally tell the letter O from the number 0 because it is wider, more circular rather than oval, and commonly set in italic.
Poking around with image searches, I found this example that shows the origin labeled with both O and 0 so you can see the difference, from this page:
Another page with this example:
It looks to me like all of your examples (and @naita’s) are using O for the origin point in two or three dimensions, rather than zero on the number line.
Although I guess you could argue that the origin point is the origin point, no matter how many dimensions (1 or more).
Granted. The coordinate system in two-or-more dimensions is just a bunch of orthogonal number lines. The concept behind “origin” is that it is really just an arbitrarily selected point from which the numbers proceed in all directions, rather than it being truly “zero” in the sense of, y’know, zero of anything.
It is really common; see here:
https://math.ucr.edu/home/baez/torsors.html
But not common, I think, to use imprecise language. Physicists are well aware of “mathematical” concepts like zero, groups, torsors, and vector spaces.
[quote=“DPRK, post:35, topic:961206”]
? The part I “don’t remember ever encountering” was using the letter O instead of 0 for the zero point on the number line. I didn’t see anything like that in your link.
Fer chrissake, I can’t get it to quote the text I’m trying to quote!
Why, open yer eyes, dude! It occurs twice right there in the word “torsors”!
Okay, I’ll try again:
OK, I misunderstood your question. I have no idea if using “O” instead or “0” is common or not, for the reason that they look pretty similar. No idea if some of those “O”'s are really Omicrons, either.
When one is working in one dimension, one often doesn’t even have a labeled diagram at all.
This PhysicsForums thread is interesting. I still don’t understand how the mathematical definition of zero can apply to any descriptions of the natural universe.