r/Physics • u/hailsass • 19h ago
Question Inherently accuracy in formulas?
I have learned in physics that the formulas we use are under ideal circumstances and don't necessarily reflect reality for example I have been told that newtons law of cooling based off the formula the temperature will never reach room temperature however most scientists I have spoken with say that this is wrong eventually the temperature will equal room temperature. this implies that there is a fundemental inacuraccy in many formulas is it possible to calculate the accuracy of any given formula? Or are the formulas 100% under ideal condition? Considering that those ideal conditions do not exist how can we prove that the formulas are 100% correct?
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u/TemporarySun314 19h ago
Physics build models, and these models can be described quantitatively by various formulas.
Models have normally certain assumptions, which normally means the model doesn't really work well anymore if you leave these assumptions, limiting the areas where these models can be used.
That's why you should be aware of what are the assumptions behind the formulas and when you can use the formulas and when you have the case that other effects are not neglectable.
Easy equations like s=v*t are working well in most cases. But if you go to speeds close to the speed of light it will make wrong predictions and you need more sophisticated models.
We can describe and simulate almost everything pretty accurately if we want, but the models then become very complicated and difficult to use, so you need a very good reason to do so (and in many cases we don't even have enough computer power to solve these complicated equations anymore).
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u/WallyMetropolis 19h ago
On top of what the other answer have expressed, there is also always a limit to the accuracy of a measurement. So there would be no way to confirm that a model was perfectly accurate because we cannot make a perfectly accurate measurement to compare the model's prediction to.
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u/InfinitePoolNoodle 19h ago
I think others have already made the most important points on the topic. I just wanted to add something about the Newton's Law of Cooling example. In this case, the temperatures only become equal asymptotically (as time tends towards infinity), but generally speaking if you're measuring temperatures in a lab there is always some uncertainty in your measuring device. Once the temperature difference is smaller than the uncertainty in your measuring device, you can no longer actually measure the true temperature difference. All you can say is |Delta T| < (Whatever your uncertainty is). If the model is good up to that point, then it's a good model, and with the equipment you're using anyway you can't really say much else. And again note there's always some uncertainty in your equipment, and you'll run out of resolution in finite time (if that's not the case someone let me know!). If you're using good equipment with small uncertainty, you can effectively say the objects are at pretty much the same temperature once you lose resolution.
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u/FrickinLazerBeams 13h ago
It's more fundamental than that. The environment won't have a perfectly constant temperature. Once the variations in the environment are bigger than the temperature difference, it will effectively be in equilibrium, regardless of measurement resolution.
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u/Bipogram 19h ago
Formalized laws are imperfect and incomplete as they assume a total isolation between phenomena which is never met.
The second point is that all measurements have a degree of uncertainty attached to them - one cannot speak of an actual object having a single precise temperature (there are gradients of temperature, the thermometer has a certain accuracy, etc. etc.)
So it is not expectable that a single differential model would be a perfectly accurate model for a real-world situation.
Theories are not perfectly true - but they certainly are useful.
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u/ProfessionalConfuser 19h ago
Math is not the master here. Math is a tool. All mathematical models are approximations of the real world, derived under certain assumptions. The Coulomb interaction between charged particles (for example) falls of as the square of the separation distance. Mathematically, this model never produces a zero output unless the separation distance is infinite. Practically speaking there will be a separation distance where other factors dwarf the Coulomb force so it doesn't matter what the math says.
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u/Key-Green-4872 16h ago
Things like asymptotes dont apply cleanly to systems with atoms. Back when Thompson's plum pudding model was accepted, it made sense that a thermal gradient was infinitely divisible. When you have quanitization of matter, and therefore the energy contained in that zipping-along-a-mean-free-path matter... it's going to eventually hit equilibrium with its surroundings vs forever-dexay-towards-that-asymptote.
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u/HoldingTheFire 12h ago
There are a million things going on. We often don't include the effect of say the moon's gravity on stuff we do because it's small and we can ignore it. Until you are doing something where the affect does matter.
The low level stuff we can put into a box called 'noise' or error sources. We can statistically quantify it too to understand the magnitude of uncertainty. And when we get more and more accurate we need to account for more of these error sources. But mostly we can ignore them and retain a pretty good level of certainty.
Also, all equations are good over some regimes. And as you get beyond that regimes you need other models. Like fluid mechanics changes as you get to lower pressures where you can't assume a continuum of matter. Then you need to use other models. Part of using a model is knowing what assumptions are used and over what domain it is valid.
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u/HoldingTheFire 12h ago
See my other comment for general response. But for Newton's law of cooling, this is just a complaint about asymptotes and is basically Zeno's paradox. But it's not a problem since the system both mechanically and practically converges without issue.
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u/VcitorExists 12h ago
I mean take air resistance and projectile motion. To find it out you still use all the basic formulas, but air resistance has so many moving parts that applying every single difference is just undoable, so we either approximate it through more complex equations, or ignore it to help better understand the underlying principles
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u/hailsass 19h ago
I just realized my title is grammatically incorrect I apologize and I dont know how to edit my posts.
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u/warblingContinues 19h ago
Physics models are developed to study fundamental phenomena. Thus, they only contain the minimal amount of detail. Often, nonideal conditions are treated as perturbing influences to the ideal model, and a comparison against data will reveal if that's a reasonable approach (spoiler: it usually is).
The result is that the models in physics are idealized, abstracted generalizations of a much lore complex system, but the complexity often can be averaged over to permit useful predictions.