# Is zero in mathematics the same as zero in physics? **URL:** \ **Category:** Factual Questions\ **Created:** [March 16, 2022, 7:54pm UTC](https://boards.straightdope.com/t/is-zero-in-mathematics-the-same-as-zero-in-physics/961206 "2022-03-16T19:54:08Z")\ **Posts on this page:** 20\ **Page:** 5
**Author:** ![DSeid](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dseid/32/20194_2.png) [@DSeid](https://boards.straightdope.com/u/DSeid)\ **Post date:** [March 25, 2022, 12:32pm UTC](https://boards.straightdope.com/t/is-zero-in-mathematics-the-same-as-zero-in-physics/961206/85 "2022-03-25T12:32:32Z")
> [@HMS\_Irruncible](#): > > Unless of course we’re trying to explain things that float, such as very small rocks. Or witches. ---
**Author:** ![Cheesesteak](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cheesesteak/32/3694_2.png) [@Cheesesteak](https://boards.straightdope.com/u/Cheesesteak)\ **Post date:** [March 25, 2022, 12:45pm UTC](https://boards.straightdope.com/t/is-zero-in-mathematics-the-same-as-zero-in-physics/961206/86 "2022-03-25T12:45:37Z")
> [@Richard\_Pearse](#): > > Zero isn’t unique in this aspect though, the same issue applies to other numbers. I think this is an interesting point. A problem you have with zero not quite actually equaling zero may also be a problem with one not quite actually equaling one. If you have 1 kilo of apples, remove 1 kilo of apples, and are left with a non-zero amount of apples… the issue isn’t with the concept of zero, it’s with 1 not equaling 1 or apples not equaling apples. ---
**Author:** ![k9bfriender](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/k9bfriender/32/3283_2.png) [@k9bfriender](https://boards.straightdope.com/u/k9bfriender)\ **Post date:** [March 25, 2022, 12:46pm UTC](https://boards.straightdope.com/t/is-zero-in-mathematics-the-same-as-zero-in-physics/961206/87 "2022-03-25T12:46:41Z")
> [@DPRK](#): > > If the mass of, let’s say a neutrino is non-zero, then it is not zero. The problem is not with the definition of zero. > [@HMS\_Irruncible](#): > > The best tool for this purpose is very tiny numbers, and the supply of those is more than adequate to this purpose. We can’t, needn’t, and mustn’t redefine zero to include very tiny numbers. Especially as there are things with _zero_ mass or charge. A photon doesn’t have a tiny mass, it has _zero_ mass. A neutrino doesn’t have a tiny charge, it has zero (electrical) charge. Redefining zero to mean close to, but not quite zero would mean that we would need to come up with a different word for what we now call zero, putting us back where we started, except now with a needlessly complicated extraneous and redundant system. ---
**Author:** ![Pasta](https://avatars.discourse-cdn.com/v4/letter/p/ecccb3/32.png) [@Pasta](https://boards.straightdope.com/u/Pasta)\ **Post date:** [March 25, 2022, 5:08pm UTC](https://boards.straightdope.com/t/is-zero-in-mathematics-the-same-as-zero-in-physics/961206/88 "2022-03-25T17:08:30Z")
> [@EastUmpqua](#): > > Do you think the definition of zero could be refined with respect to modern physics? GR refined Newtonian physics. A refined definition of zero might be necessary as our technology allows for more precise observations (e.g. CERN, JWST…) No. Zero mean zero. For instance, if you say “Intergalactic space is not actually empty”, that’s interesting to talk about, but we aren’t trying to redefine “empty” in the discussion. In that sentence, the word “empty” means truly empty, and the sentence points out that space isn’t that. In no way does that imply that “empty” is a problematic concept. If just means that space is not empty, and true empty is the exact concept we need to express how space is something else. Another way of saying it: “Zero” means zero, and if something is not zero, we have other words or numbers for those cases already, such as “0.001” or “not zero”. Why try to remove the perfectly useful concept of “zero”? It is that very concept that is needed to talk about the interesting cases that aren’t zero. At the risk of making this post too long, consider a practical example. 1000 pennies are dropped from a plane flying at 36,000 ft. On the ground below, I place a cardboard box out to maybe catch a lucky penny. The odds are low, say 1 in a million. After a few hours, I close the box without looking inside to see if I caught a penny. How many pennies are in the box? Is it zero? One? Ten? Given the odds, it’s probably zero. But it could also be one. Two would be crazy. In this scenario we are asking a very simple question that “should” have a single number answer, and that answer might be zero or it might not. Do we decide that the definition of “zero” is wrong because of our uncertainty or because of the particular probabilistic nature of the experiment? Of course not! We don’t quite know how many pennies are in the box, but we can talk about different outcomes using probability and whatnot. And the concept of “zero” is invaluable in those discussions, without any modification to it. @EastUmpqua, there is some desire in the thread to hear you directly respond to posts to better understand if there is still a disconnect. Could you do that? That is, could you say whether you don’t agree with or don’t follow part of the above so that I (or others) may expand on it? ---
**Author:** ![EastUmpqua](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/eastumpqua/32/6025_2.png) [@EastUmpqua](https://boards.straightdope.com/u/EastUmpqua)\ **Post date:** [March 25, 2022, 8:14pm UTC](https://boards.straightdope.com/t/is-zero-in-mathematics-the-same-as-zero-in-physics/961206/89 "2022-03-25T20:14:03Z")
> [@k9bfriender](#): > > A photon doesn’t have a tiny mass, it has _zero_ mass. Mass and energy are equivalent, so photons have relativistic mass, but are defined as massless. Does light have mass?. It seems like there are areas of physic that could benefit from an expanded definition of zero . For example the [Lorentz transformation](https://en.wikipedia.org/wiki/Lorentz_transformation) when velocity reaches c. ---
**Author:** ![EastUmpqua](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/eastumpqua/32/6025_2.png) [@EastUmpqua](https://boards.straightdope.com/u/EastUmpqua)\ **Post date:** [March 25, 2022, 8:20pm UTC](https://boards.straightdope.com/t/is-zero-in-mathematics-the-same-as-zero-in-physics/961206/90 "2022-03-25T20:20:39Z")
> [@Pasta](#): > > there is some desire in the thread to hear you directly respond to posts to better understand if there is still a disconnect. Could you do that? That is, could you say whether you don’t agree with or don’t follow part of the above so that I (or others) may expand on it? I will do my best. I’m trying to learn, and there’ve been interesting posts. Is it necessary to agree or disagree? ---
**Author:** ![EastUmpqua](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/eastumpqua/32/6025_2.png) [@EastUmpqua](https://boards.straightdope.com/u/EastUmpqua)\ **Post date:** [March 25, 2022, 8:47pm UTC](https://boards.straightdope.com/t/is-zero-in-mathematics-the-same-as-zero-in-physics/961206/91 "2022-03-25T20:47:18Z")
> [@Exapno\_Mapcase](#): > > It would help if you told us what you think the mathematical definition of zero is. The PhysicsForums thread that I posted sums up my understanding of the definition of zero. > [@Exapno\_Mapcase](#): > > BTW, I’m asking other posters please not to supply a mathematical definition of zero. We can’t get to the source of the OP’s confusion unless they specify their own thinking. I thought SD’s mission is to fight ignorance (which I have plenty of). I’ve been asking questions and following links. > [@Senegoid](#): > > _Is_ there a mathematical definition of zero (short of going into definitions of subatomic granularity)? > > In geometry, a “point” is undefined. It is understood that you can only define things in terms of other things that are already defined, thus you have to start somewhere with a few undefined terms. Likewise, facts are proved via arguments that use prior known facts as premises, thus you have to start somewhere with a few unproven facts (axioms). > > Isn’t there something similar in algebra? We have some axioms. Aren’t there also some undefined terms also? I thought this post was interesting and helpful. Thanks > [@Richard\_Pearse](#): > > How many flying pink unicorns do you have? > > It sounds more like you have a problem with the concept of “nothing”. It’s been my (admittedly limited) experience on SD not to engage a poster when there are unicorns. > [@Buck\_Godot](#): > > Maybe also getting a bit towards the OP, I would say that at its fundemental level math is really just set of rules for symbol manipulation. Using these rules you can write sequences of symbols that follow those rules and if by following those rules you are able to write a particular elegant set of symbols than other mathematicians become very happy and invite you to their ivory towers to talk about the special ways you manipulated your symbols and may even give you modest amounts of money. Why on earth do they do this? > > Now what physics has discovered, is that there is a correspondence between the sets of symbols you can write down following the rules and observations you make in the real world. You can make an observation about the real world, translate it into symbols, manipulate those symbols according to the rules, and then when you look at what you end up with, by some miracle it matches what you later observe. This miracle always seems to hold and in cases where it doesn’t hold physicists get very excited and work out new different ways to translate the observations into symbols are invented so that it works again. > > That this symbol manipulation and translation allows one to predict and manipulate reality. This is why people are willing to pay people some people money to manipulate symbols all day, and other people money to make observations and see how well they translate into symbols. > > One of the symbols mathematicians manipulate is zero. Depending on the application it gets translated by physicists into a variety of different observations, and works really really well. I enjoyed this post. Thank you. > [@DSeid](#): > > Probably also need them to offer their physics definition as well. If the issue is definitions. > > My WAG though is that the issue is what they consider abstractions vs reality: like a perfect circle or an infinitely small point being possible and useful as mathematical abstractions but when applied to reality are useful metaphors without exact physical analogs. We treat real world items as if they are these abstractions but they are not quite. > > Of course though in physics sometimes those abstractions have a basis in reality - as mentioned already one fundamental particle of a certain type is exactly the same as another of that type differing only by where/when it is and where it is going. > > I don’t think that’s a problem with definitions per se. It is an issue with how we use abstract concepts as tools to describe reality that is messier than ideal forms. Thank you for this post. > [@DPRK](#): > > If you say that your space-time is a real manifold, say to set up a quantum field theory, it does not necessarily mean that you believe the mathematical real numbers physically exist in some philosophical sense. But when physicists talk about zero as a real number or as an integer, they do mean the same thing as mathematicians. [As far as I can tell!?] That is the nature of theoretical physics, and, while there is a lot to work on, the issues are not really with simple mathematics like if a particle has spin zero, is that really zero. If there is any kind of problem there, it is with your quantum theory, not with representation theory. This is interesting, but I’m not sure I understand. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [March 25, 2022, 8:54pm UTC](https://boards.straightdope.com/t/is-zero-in-mathematics-the-same-as-zero-in-physics/961206/92 "2022-03-25T20:54:02Z")
Mass is one specific form of energy, but it’s not the form of energy photons have. They have another form of energy. “Relativistic mass” is a waste of a concept, because it’s just another word for “energy”, and isn’t actually mass. ---
**Author:** ![k9bfriender](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/k9bfriender/32/3283_2.png) [@k9bfriender](https://boards.straightdope.com/u/k9bfriender)\ **Post date:** [March 25, 2022, 9:04pm UTC](https://boards.straightdope.com/t/is-zero-in-mathematics-the-same-as-zero-in-physics/961206/93 "2022-03-25T21:04:05Z")
> [@EastUmpqua](#): > > Mass and energy are equivalent, so photons have relativistic mass, No they don’t. And there really is no such thing as “relativistic mass” either, it’s entirely a function of momentum, not mass. If someone throws a baseball at you and it imparts momentum to you, that didn’t come about because the baseball became more massive. The entire idea of “relativistic mass” is that an object traveling relative to you at relativistic speeds will seem to have more momentum than newtonian mechanics would call for, it does _not_ have more mass. The equation for energy is E^2 = (pc)^2 + (mc^2)^2, momentum and mass are two different terms there. A photon has momentum, the “p”, but does _not_ have mass, the “m”. > [@EastUmpqua](#): > > but are defined as massless. Because they _are_ massless, as in having zero mass. > [@EastUmpqua](#): > > Does light have mass?. I’m not sure what you did there. It _almost_ looks like a link, but it’s not. Did you mean to cite something that supports your claim? I could cite dozens or more articles, both scholarly and journalistic, that say that no, light doesn’t have mass, but, given that I have no idea what level you are at, or how you have come to the conclusions that you have come to, it’s easier to just go ahead and cite the question into google, so you can see for yourself. [https://www.google.com/search?q=Does+light+have+mass%3F&rlz=1C1ONGR\_enUS957US957&sourceid=chrome&ie=UTF-8](https://www.google.com/search?q=Does+light+have+mass%3F&rlz=1C1ONGR_enUS957US957&sourceid=chrome&ie=UTF-8) Let me know if you have any questions. > [@EastUmpqua](#): > > It seems like there are areas of physic that could benefit from an expanded definition of zero . For example the [Lorentz transformation](https://en.wikipedia.org/wiki/Lorentz_transformation) when velocity reaches c. How could a redefinition of zero possibly help there? For one, nothing can reach c. It either is massless, in which case it never goes at any other velocity, or it has mass, in which case it can never reach c. Approaching c also doesn’t really mean anything, as you are only approaching c in relation to something else. You experience nothing yourself as you accelerate. Your time doesn’t slow down, it still passes at one second per second. Your mass doesn’t increase, it is still one kilogram per kilogram. ---
**Author:** ![Richard\_Pearse](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/richard_pearse/32/13144_2.png) [@Richard\_Pearse](https://boards.straightdope.com/u/Richard_Pearse)\ **Post date:** [March 25, 2022, 9:12pm UTC](https://boards.straightdope.com/t/is-zero-in-mathematics-the-same-as-zero-in-physics/961206/94 "2022-03-25T21:12:38Z")
> [@EastUmpqua](#): > > Mass and energy are equivalent, so photons have relativistic mass, but are defined as massless. Does light have mass?. Your link is broken. However, the mass (m) of photons is indeed zero. The general equation is E2 = p2c2 + m2c4. Here p is the momentum of the photon and m is the mass. The energy of the photon comes from the momentum, not the mass. Mass is zero, proper zero, just like zero in maths (and it _is_ maths). Edit: @k9bfriender beat me to the equation while I was trying to work out how to do superscript 😉 ---
**Author:** ![Richard\_Pearse](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/richard_pearse/32/13144_2.png) [@Richard\_Pearse](https://boards.straightdope.com/u/Richard_Pearse)\ **Post date:** [March 25, 2022, 9:34pm UTC](https://boards.straightdope.com/t/is-zero-in-mathematics-the-same-as-zero-in-physics/961206/95 "2022-03-25T21:34:24Z")
If you redefine zero then equations like E=mc2 wouldn’t work anymore. So what you need to show is a concrete example of what would be achieved by redefining zero _and_ explain what you would replace the current zero with, because we need zero as it is currently defined. And then you need to show why we couldn’t just _keep_ the current definition of zero and use small numbers for small quantities / measurements. ---
**Author:** ![EastUmpqua](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/eastumpqua/32/6025_2.png) [@EastUmpqua](https://boards.straightdope.com/u/EastUmpqua)\ **Post date:** [March 25, 2022, 9:40pm UTC](https://boards.straightdope.com/t/is-zero-in-mathematics-the-same-as-zero-in-physics/961206/97 "2022-03-25T21:40:43Z")
> [@Richard\_Pearse](#): > > If you redefine zero then equations like E=mc2 wouldn’t work anymore. So what you need to show is a concrete example of what would be achieved by redefining zero _and_ explain what you would replace the current zero with, because we need zero as it is currently defined. And then you need to show why we couldn’t just _keep_ the current definition of zero and use small numbers for small quantities / measurements. Ok. I learned a lot from this thread. But I don’t have time for the assignment. Thanks for the posts. ---
**Author:** ![k9bfriender](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/k9bfriender/32/3283_2.png) [@k9bfriender](https://boards.straightdope.com/u/k9bfriender)\ **Post date:** [March 25, 2022, 9:43pm UTC](https://boards.straightdope.com/t/is-zero-in-mathematics-the-same-as-zero-in-physics/961206/98 "2022-03-25T21:43:21Z")
> [@Richard\_Pearse](#): > > Edit: @k9bfriender beat me to the equation while I was trying to work out how to do superscript Heh, I just didn’t bother. I tried to do it the old board way, it didn’t work, so I just went with carrots. ETA: it also seems to break superscript when it is quoted. ---
**Author:** ![Richard\_Pearse](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/richard_pearse/32/13144_2.png) [@Richard\_Pearse](https://boards.straightdope.com/u/Richard_Pearse)\ **Post date:** [March 25, 2022, 9:45pm UTC](https://boards.straightdope.com/t/is-zero-in-mathematics-the-same-as-zero-in-physics/961206/99 "2022-03-25T21:45:37Z")
I guess the short answer to your title question is that, yes, zero in mathematics and physics is the same. When a measurement or quantity is a very small number rather than being zero, we just use a very small number instead of zero. If a quantity or measurement was thought to be zero but improved detection techniques show that it is not zero, instead of saying zero is wrong, we say that the quantity is not zero. ---
**Author:** ![Richard\_Pearse](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/richard_pearse/32/13144_2.png) [@Richard\_Pearse](https://boards.straightdope.com/u/Richard_Pearse)\ **Post date:** [March 25, 2022, 9:47pm UTC](https://boards.straightdope.com/t/is-zero-in-mathematics-the-same-as-zero-in-physics/961206/100 "2022-03-25T21:47:48Z")
Quoting the entire post using the speech bubble icon retains the coding but using the selection method of quoting does seem to break it. ---
**Author:** ![k9bfriender](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/k9bfriender/32/3283_2.png) [@k9bfriender](https://boards.straightdope.com/u/k9bfriender)\ **Post date:** [March 25, 2022, 9:49pm UTC](https://boards.straightdope.com/t/is-zero-in-mathematics-the-same-as-zero-in-physics/961206/101 "2022-03-25T21:49:57Z")
> [@Richard\_Pearse](#): > > When a measurement or quantity is a very small number rather than being zero, we just use a very small number instead of zero. If a quantity or measurement was thought to be zero but improved detection techniques show that it is not zero, instead of saying zero is wrong, we say that the quantity is not zero. For instance, neutrinos’ mass is _very_ small. How small? We don’t know, it is too small for us to measure, we can only put upper bounds on it. But we know that it is not zero, because if it were, it would behave differently, with the oscillation between flavors being the key piece of evidence that it must not be zero, even if it’s so close that we can’t tell the difference with actual measurements. ---
**Author:** ![EastUmpqua](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/eastumpqua/32/6025_2.png) [@EastUmpqua](https://boards.straightdope.com/u/EastUmpqua)\ **Post date:** [March 25, 2022, 9:56pm UTC](https://boards.straightdope.com/t/is-zero-in-mathematics-the-same-as-zero-in-physics/961206/102 "2022-03-25T21:56:08Z")
> [@Richard\_Pearse](#): > > If a quantity or measurement was thought to be zero but improved detection techniques show that it is not zero, instead of saying zero is wrong, we say that the quantity is not zero. That makes sense. Is there some kind of limit below which nothing in the natural universe can exist? ---
**Author:** ![Pleonast](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pleonast/32/1183_2.png) [@Pleonast](https://boards.straightdope.com/u/Pleonast)\ **Post date:** [March 25, 2022, 10:02pm UTC](https://boards.straightdope.com/t/is-zero-in-mathematics-the-same-as-zero-in-physics/961206/103 "2022-03-25T22:02:22Z")
> [@k9bfriender](#): > > > [@Richard\_Pearse](#): > > > > When a measurement or quantity is a very small number rather than being zero, we just use a very small number instead of zero. If a quantity or measurement was thought to be zero but improved detection techniques show that it is not zero, instead of saying zero is wrong, we say that the quantity is not zero. > > For instance, neutrinos’ mass is _very_ small. How small? We don’t know, it is too small for us to measure, we can only put upper bounds on it. > > But we know that it is not zero, because if it were, it would behave differently, with the oscillation between flavors being the key piece of evidence that it must not be zero, even if it’s so close that we can’t tell the difference with actual measurements.   Neutrino oscillations let us put a lower bound on neutrino mass. It’s complicated though, because of the mixing. ---
**Author:** ![Richard\_Pearse](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/richard_pearse/32/13144_2.png) [@Richard\_Pearse](https://boards.straightdope.com/u/Richard_Pearse)\ **Post date:** [March 25, 2022, 10:16pm UTC](https://boards.straightdope.com/t/is-zero-in-mathematics-the-same-as-zero-in-physics/961206/104 "2022-03-25T22:16:18Z")
I believe there is always some small amount of activity in the quantum field but that’s well outside my layman’s understanding of physics. ---
**Author:** ![DSeid](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dseid/32/20194_2.png) [@DSeid](https://boards.straightdope.com/u/DSeid)\ **Post date:** [March 25, 2022, 10:21pm UTC](https://boards.straightdope.com/t/is-zero-in-mathematics-the-same-as-zero-in-physics/961206/105 "2022-03-25T22:21:57Z")
Absolute zero I’d think. [Previous page](https://boards.straightdope.com/t/is-zero-in-mathematics-the-same-as-zero-in-physics/961206.md?page=4) [Next page](https://boards.straightdope.com/t/is-zero-in-mathematics-the-same-as-zero-in-physics/961206.md?page=6)