Or witches.
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.
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.
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?
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 when velocity reaches c.
I will do my best. I’m trying to learn, and there’ve been interesting posts. Is it necessary to agree or disagree?
The PhysicsForums thread that I posted sums up my understanding of the definition of zero.
I thought SD’s mission is to fight ignorance (which I have plenty of). I’ve been asking questions and following links.
I thought this post was interesting and helpful. Thanks
It’s been my (admittedly limited) experience on SD not to engage a poster when there are unicorns.
I enjoyed this post. Thank you.
Thank you for this post.
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.
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”.
Because they are massless, as in having zero 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.
Let me know if you have any questions.
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.
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 
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.
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.
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.
Quoting the entire post using the speech bubble icon retains the coding but using the selection method of quoting does seem to break it.
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.
That makes sense. Is there some kind of limit below which nothing in the natural universe can exist?
Neutrino oscillations let us put a lower bound on neutrino mass. It’s complicated though, because of the mixing.
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.
Absolute zero I’d think.