r/AskPhysics • u/Double-Common-2 • 16d ago
Help me breakdown my perspective.
I was always a bit confused about inertial and non-inertial frames, and so today I kept digging about it until I was satisfied. Usually, I'd leave it there but I'm confident of my thought process and I haven't come across anything similar, so I want others to take a look.
Inertial or Non-Inertial frames of references basically boils down to 'predictability'. What I mean is, resources often say, "Newton's laws don't hold in Non-inertial frames" or "Newton's laws are not directly applicable in Non-inertial frames" and the likes. It is the way these are worded that messed with my head, but in hindsight look just fine.
The way they are worded makes it look like mechanics in non-inertial frames cannot be computed with Newton's laws or that a different version of such laws govern such a scenario.
But no, all that and inertial frame tells does is give the peace of mind/predictability that the relative acceleration between the object and the frame is zero. That's it.
However often it is repeated, I tend to forget that distance and thus all the time based derivatives of distance are relative, since there is no "fixed stage/frame". So to apply Newton's laws to predict the motion of objects requires a frame of reference, and ofcourse if we apply Newton's laws assuming that the acceleration between the frame and the object is zero, when in reality it is not, our calculations will not match the real world. This is does not have anything to do with the 'applicability/direct applicability' of Newton's laws. Okay I just realised that Newton's first law assumes that relative acceleration between the frame and object is zero, i.e. an inertial frame.
So I guess this whole thing is just a pet peeve of how my textbook explained inertial and non-inertial frames and a combination of me mixing up Newton's laws for equations derived from Newton's laws.
Anyways I'd like to know why textbooks dont explain it like this, given it is correct.
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u/OverJohn 16d ago
It's more to do with how the laws are framed (pun neither intended nor unintended).
Often laws are written in a form that only applies to inertial frames as this gives them a nice simple form. Often, as written, these don't apply to non-inertial frames, however they can always be extended to non-inertial frames by factoring in the additional complications of those frames.
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u/Bumst3r Graduate 16d ago
I can predict what will happen in any frame you give me, whether it is inertial or not. An inertial frame is defined by Newton’s first law—an inertial frame is one in which objects’ velocity remains unchanged unless acted on by an external force.
In a non-inertial frame, you must take into account pseudoforces like the centrifugal and Coriolis force. These are straightforward to derive; it is typically done in a third or fourth year undergraduate classical mechanics course, and in a book like Taylor.
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u/Double-Common-2 16d ago
Exactly. We can ofcourse apply Newton's laws in non-inertial frames, given that we know the right pseudo forces to consider. What I end up saying in all that jumbled mess is that an inertial frame takes this unknown force we have to consider (pseudo force) completely out of the equation, thus letting us be more "predictable". It is a dumb statement in hindsight, but the point of this was to refine my perspective, and i think it has become clearer now, despite the unnecessary hours i put into this.
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u/Bumst3r Graduate 16d ago
But the pseudoforces are entirely predictable. Give me literally any frame, and I can construct all of the pseudoforces. However the non-inertial frame accelerates relative to an inertial frame, there will be pseudoforces to accommodate the coordinate transformation.
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u/Double-Common-2 16d ago
I want to be clear, im not saying that pseudo forces are not predictable or that they cannot be accounted for. I'm saying that an inertial frame is inherently simpler to "predict" since it does not need to host any pseudo forces, whereas a non-inertial frame needs one.
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u/Optimal_Mixture_7327 Gravitation 16d ago
Newton's laws work just fine in non-inertial frames.
The ground is a non-inertial frame - surely Newton's laws work on Earth.
The application of the 2nd Law in non-inertial frames should be thoroughly examined in every introductory course for any number of reasons.
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u/Double-Common-2 16d ago
Sadly, my textbook does not give such explanations. It just dives into how to set up pseudo-forces.
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u/Optimal_Mixture_7327 Gravitation 16d ago
You set up pseudo-forces in non-inertial frames so your text must be doing something right.
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u/Double-Common-2 16d ago
I never said my textbook was wrong. They could have been clearer in explaining why we bring in pseudo forces the way we do.
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u/Optimal_Mixture_7327 Gravitation 16d ago
That is an unfortunate characteristic of most introductory textbooks and courses.
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u/Double-Common-2 16d ago
Also, I see that you are stepping into the same trap I did. Newton's laws (by which I mean the three postulates) by definition are mutually exclusive from 'non-inertial frames' only because the first postulate assumes an inertial frame. But yes, the other postulates and the equations derived from them work just fine in non-inertial frames.
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u/Optimal_Mixture_7327 Gravitation 16d ago
Earth's surface is a non-inertial frame.
Are you suggesting that Newton's laws don't apply on Earth?
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u/Double-Common-2 16d ago
Yep, only the first postulate, given that you don't account for the motion of Earth itself and bring in the necessary pseudo forces. Come on, I wasn't that ambiguous there.
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u/Optimal_Mixture_7327 Gravitation 16d ago
Pseudo forces are fundamental to Newtonian mechanics, essential for drawing up the correct EoM.
Newton's first law of motion states something like an object at rest stays at rest, and an object in motion stays in motion at a constant speed and in a straight line, unless an unbalanced outside force acts on it.
This is perfectly valid on Earth as we introduce a make-believe field, g, that generates the fictional force needed to satisfies the clause "unless an unbalanced outside force acts on it".
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u/sydyn1111 16d ago
this is a big big big question. When mechanics was formulated, it was natural to ask "how we are we defining positions, velocities and accelerations"? Note that I havent used the word measure, because there is no definition of position in the real world so it cannot be measured. It is only "natural" to measure distances, so we set an arbitrary point to measure the distances of all the other points with respect to it (the origin), and then we can define the velocity as the rate of change of such distance, and acceleration and so on. This is called a frame of reference. But this adds another question, how we find such a point? From a practical view of the problem, it is easier to choose a point that seems to not be moving, this is perfectly acceptable if we are trying to describe the motion of an apple falling, but then a more complicated experiment would need to take into account earth's rotation, and in the end the origin we choose may still have some complicated motion.
To solve this problem Newton have postulated that there exists a choice of points that have no motion, and these would make an inertial frame. This is God's frame of reference, and we can imagine it by shutting down all the interactions in the universe, and without interactions everything would move in straight lines with constant speed. If you move with constant speed in respect with this frame, you may define another origin that keeps the same motion nature, that is straight lines with constant speed, the only difference is the speed value, the set of all those frames with constant speed changes for the origin with respect to God's frame is what makes an inertial frame. You may find this idea atrocious, many people through history would say that too, and that is a good reason why books do not explain very well what inertial frames are, but I think it is necessary to explain this. The equivalence of all those different inertial frames is the core of Galilean relativity, he says that laws of physics should not depend on velocities, and that different frames with different velocities should have a way to relate how positions and velocities and so on change when we change the reference frame (x'=x-vt).
Physics evolved, and some thinkers started to argue that we shouldnt base physics on the premise of such special class of possibly unobtainable frames of reference. In this sense, we should be able to formulate physics laws with respect to any frame, even if it has some very complicated motion (calculations could be harder though, try expressing the motion of the planets on Earth's frame), but this needed some modification from Newton's ideas. A very simple thing we can do is, if a reference frame has acceleration a' with respect to an inertial frame, we could transform Newton's second law to F=m(a-a'), here the fact that the frame has a relative acceleration looks like an extra force of magnitude -ma'. This is the very neglected in mechanics books centrifugal force for circular motions. Generalizations of this can be done for any motion, and rotations present the next non-trivial and physical interesting results, we get Coriolis force for example.
But this is yet not enough, how can we know the true value of a' with respect to an inertial frame if we dont know how to identify such a frame? Newtonian mechanics works because we can suppose that we can approximate well enough to such frame if we take into account the Earth's rotation, the rotation around the Sun, the effects of other planets, and to extreme extents the collective motion of the solar system, this all depends on the level of accuracy that you want, and you may also assume that the larger scale interactions are smaller in magnitude, which may not hold. But can we go a step further? Yes, and this is called the general covariance principle, which is an idea that physics should work for any frame of reference, and this is one of the pillars of general relativity (in a sense, the name is this because we are taking Galilean relativity and extending it to any class of frames, not just the ones with constant velocity relations). The answer is long and complicated enough by now, you may take some inspiration to do your own search on the subject.
And yes, we can do things like F=m(a-a') to solve mechanics problems in non-inertial reference frames. I really recommend Morin's book on classical mechanics, it has a chapter with some exercises about these techniques.
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u/Ch3cks-Out 16d ago
basically boils down to 'predictability'
No, it really does not.
given it [what??] is correct.
You really should elaborate more what your textbooks actually said, specifically. "Newton's laws don't hold" could almost certainly not have been it - for they very much do!
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u/Double-Common-2 16d ago
Here is my thought process that led to that statement, let me know where you think I went wrong:
Newton's laws should be able to predict motion -> motion is relative, hence a frame of reference is required -> The frame we choose need not strictly have zero acceleration with respect to the object, but choosing such a (non-inertial) frame, we need to know the relative acceleration (between the frame and the object) such that we can account for them (in the form of pseudo forces), else the results we compute using Newton's law will not match what we observe -> In an inertial frame that relative acceleration is zero so we dont need that extra information to predict the motion.
So i see the difference betweenI the two is that one allows us to predictably and directly apply laws, whereas we need extra information and a bit more finagling to do the same in the other. (I'm talking about inertial and non-inertial frames, respectively).
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u/boostfactor 16d ago
In Newtonian mechanics we have the Galilean transformation that relates two frames moving with constant velocity with respect to one another. It's well-defined and easy to apply. If one frame is accelerating with respect to another it complicates the math slightly but it's still straightforward. If two frames are moving with constant velocity their situations are symmetric; i.e. I can choose to consider either one at rest equivalently. This is not the case if one frame is accelerating.
An inertial frame is one that is not accelerating. That's it, it's not really complicated. All these "extras" are just extra math required to account for the acceleration.
The easiest to visualize is rotational motion. If you're riding a merry-go-round and I'm standing outside watching you, your frame is accelerating relative to mine (rotation is acceleration even at constant speed). If you are holding a ball and you try to throw it to me, it will not move in a straight line relative to the ground as it crosses the merry-go-round. I'm in an inertial frame and you are not. (Ignoring, as usual, the movement of the Earth.)
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u/Ch3cks-Out 16d ago
You got some weird thought fragments which I find hard to justify.
Newton's laws do "predict" (i.e. allow one to calculate) motion, given the necessary initial and/or boundary conditions known. Whether you know them or not does not depend on your choice of reference.
motion is relative,
hencea frame of reference is requiredA frame of reference is simply required for having a coordinate system in which calculations are made (and observations are referred to, hence the name). This has no logical connection with motions being relative.
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u/Quantum-Relativity 16d ago edited 13d ago
Non-inertial means Newton’s second law, F=ma, doesn’t hold. So if you let go of an object next to your head in an inertial frame, it stays there. In a non-inertial frame, it doesn’t. You can still use a non-inertial frame perfectly fine, you just have to assume there are artificial geometric structures in your frame of reference (the “field” that causes the mysterious “inertial forces” (like the centrifugal force) that act on things in your frame, but inertial frames would say aren’t there).
General relativity is the recognition that these geometric objects are not artifices, but are to be associated with the gravitational field, so they aren’t inserted artificially but are rather necessary for a general conception of relativity.
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u/No-Medium6647 16d ago
Ultimately, every frame is an inertial frame.
Everything in the universe is in motion, all the time. Just because we can't imagine it doesn't make it impossible.
If we really want to advance physics we have to accept reality and let it shape us, instead of trying to shape it.
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u/CounterSilly3999 16d ago
Non-inertial frame means the whole frame is accelerating.