Is Inertia responsible for kinetic energy increasing quadratically with speed?

Question

Here are two modern definitions of inertia:

Wikipedia https://en.wikipedia.org/wiki/Inertia: "Inertia is the resistance of any physical object to any change in its state of motion."

Merriam-Webster dictionary https://www.merriam-webster.com/dictionary/inertia: "A property of matter by which it remains at rest or in uniform motion in the same straight line unless acted upon by some external force"

Notice that in both definitions inertia is a property of an object or matter! This is very misleading, because it doesn't reflect the physics (even at a high level) of how inertia is applied to matter. Inertia is an inherent property of space, it's not a property of matter, although it applies to matter! It is proportional to the amount of matter in an object (mass), no doubt about that, but it is really a force of resistance that a space applies to an accelerating/decelerating object. A definition of inertia along these lines would provide much better picture of a real situation, real physical process.

Because of our current definition of inertia, a lot of people have a lack of understanding of basic things:

Why does kinetic energy increase quadratically, not linearly, with speed? Why does kinetic energy increase quadratically, not linearly, with speed?

or

Why is the amount of work required to accelerate a body from 10m/s to 20m/s three times the work needed to accelerate a body from 0m/s to 10m/s?https://www.reddit.com/r/askscience/comments/40bi9z/why_is_the_amount_of_work_required_to_accelerate/

Notice that these are very popular questions, but no one gave a satisfactory answer to these questions, as authors of these questions complain. People want to know the real physical reason; they want to understand WHY kinetic energy is speed square, WHY it makes sense to define work as force by distance. Answers like "the work was just DEFINED like that and the rest follows" - these answers do not answer the actual questions people ask.

So INERTIA is the real answer to these questions! If you just make it clear to people that every bit, every meter of space resists acceleration, then it's quite obvious why energy increases quadratically with speed. Inertia is much like friction with the space, the only difference is - this friction only applies when you are changing your velocity; it does not apply at constant velocity. So the more space you travel with acceleation, the more friction you need to overcome, the more work you have to do (evergy to spend) to overcome that friction (force of resistance to your acceleration). So that's why the energy you spend to maintain acceleation is proportional to distance you travel with that acceleation. And, when you go with constant acceleration, the distance traveled is proportional to speed square.

Inertia is essentially a force applied on an object that moves with acceleation. So when the object accelerates in space, there are two forces acting on it - the force that pushes it and the force of inertia that resists the acceleration. By second law of Newton, the resulting acceleration is proportional to the resulting force, which is pushing force minus force of inertia. Let's illustrate it using the question from reddit.com: When you accelerate a body from 0m/s to 10m/s, you travel 5 meters in first second. Same acceleration continues, and during the next second a body changes speed from 10m/s to 20m/s, traveling 15 meters. So - same acceleration for the same amount of time (same resulting force), but a body traveled 3 times more distance. 3 times more resistance to overcome -> 3 times more energy to spend. So during the next second you have to apply more pushing force on your object, to maintain the same aceleration, than during the first second. Simply because the resistance is higher.

Should we really consider inertia as a real natural force that applies on matter during space-matter interaction under acceleration? I am not sure, but it is certain that if we look at it that way, the above questions become simple to answer. As to WHY and HOW inertia acts like this, what is the real mechanism - nobody knows so far (2017). There are theories but all of them have issues.

The idea that inertia is a property of space, is not new. Albert Einstein tried to modify it, as in GR objects modify space, so inertia becomes a property of object-space interaction. More recently, there were several research efforts trying to explain inertia as a force acting in space against accelerating matter:

http://www.calphysics.org/haisch/science.html ; https://physics.fullerton.edu/~jimw/general/inertia/

Inertia seems to be one of the most fundamental properties of space and our world. It is as fundamental as energy, if not more. Stable world is not possible without inertia. If there is no inertia, a simple push would accelerate an object to infinite speeds (let's forget relativity here), and that same object could be completely and immediately stopped after collision with a small piece of space dust. That object wouldn't carry any energy. Even the famous E = mc2 shows that no inertia results in no energia. Space must have inertia in order for energy to exist in forms we know (concentrated as physical matter in fixed locations in space). To put it philosophically, Vishnu (inertia) keeps the world stable while Shiva (energia) tries to tear it apart.

Comments

The usual definition of kinetic energy from the Newton equations is sufficient. Note, any friction leads to irreversible energy loss which is not the case here: the work of an external force becomes entirely the probe body kinetic energy and nothing is lost in space. That is why the mass is a property of bodies, not the space. I vote to close this question as irrelevant to this forum.

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This is not graduate-level, voting to close. 500+ rep users please upvote the closevote in the link if you agree.

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Vladimir, 1. What is the usual definition of Kinetic Energy from Newton equations? Yes, you can just DEFINE something, but as my question says, explain how this definition meets real physics. 2. That's a good point about "friction", there is no friction in terms of energy loss to space, you just have to overcome constant resistance, like when moving with friction; that was my only basis for analogy with friction. So you need to pass additional energy to the object to overcome that resistance. I hope I explained my analogy with friction. 3. Try to think yourself - why kinetic energy increasing quadratically with speed.

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with all respect due, you must frame your question ( if any ). For example, "It is possible to reword entirely the classical motion analysis without changing anything to the equations" or "the rewording of classical mechanics, while it doesn't conflict with mainstream physics, opens the mind to new ideas" or else "Optimizing the dictionnary of mechanics saves more than 30% of pupils efforts and may increase the number of young physicists by a factor 2". Possible grants for the latter ... Anyway, it's more a kind-forum discussion introduction than a question for PO ! :)

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The Newton equation may be written like this: $m\cdot dv=F\cdot dt$. Multiply both sides with $v$ and rewrite it like this: $m\cdot d(v^2 /2)=F\cdot dx$ since $v\cdot dt=dx$. You have the energy equation in a differential form here. It says that the work $Fdx$ of the external force $F$ do displace the body along the distance $dx$ is equal to the kinetic energy increment: $dK=d(mv^2 /2)$.

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Vladimir, really? With my B.SC. in physics I know that the work is DEFINED as the integral of Fdx over x. And the rest follows, right? So if you look in these questions that people ask, there are a lot of answers like yours - because it's defined like that. The whole question is - WHY it is defined like that? Note that Newton himself didn't define Energy or Work, he did not even believe in conservation of energy; he only recognized quantity of motion (momentum).

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Maxim13, if the force is conservative, i.e., if it is a gradient of some potential: $F=-\nabla U$, then the quantity $E=K+U$ does not depend on time, i.e., it is conserved. It is an integral of motion, which is equal to the same value at $t\gt 0$ as at $t=0$. It is of practical use.

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Vladimir, sure, of course we all believe in energy conservation. I really appreciate your attention to my humble attempt to think about inertia. I really need some concrete points where am I wrong? Where am I mistaken in my post? Why inertia could not be seen as real conservative force, a field force, exactly like you defined in your previous comment, a force that arises against accelerating bodies? Is personal chat available on this site? We could take it there.

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Vladimir, I have sent you an email to your wanadoo email that I found on your website. Thanks in advance.

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This is all nonsense. The whole point of defining energy is to get a scalar quantity that's conserved -- part of this turns out to be the kinetic energy. That's all there is. 

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@igael - this is not about re-wording. I am asking a question here - should inertia be viewed as conservative force that space applies on accelerating matter? I am providing some rationale and examples supporting my view. I am not getting any concrete points - what's wrong in my theory, where I am mistaken. Nobody really wants to think. My question requires thinking. You are correct in one thing - if I am right, it does not change any current equations of mechanics. I don't have an understanding of physical nature of that force, so I cannot create any real mathematically formulated paper. But this is not just re-wording, this is a conceptually different view, agreed? And it's not a new view - refer to the link to Einstein's book. I guess I am asking for peer review here, but nobody is interested.

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@Maxim13 : I understand what you mean. Physicists are not trying to explain the thoughts posted by Newton and Einstein in peculiar contexts at peculiar times. Now, they explore the motion concept on a finest level, further from the human experience than ever. Here, you will find anybody interested by the topic.