I have done extensive amount of thought and research on this site and online in general, trying to find original, intuitive, not formal explanations of basic properties such as Inertia and Kinetic Energy. I could not find any satisfactory answers; all of them rely either on definitions (it is so because it is defined so), or on fundamental basic stuff given in nature (Inertia is non-explainable, it just exists).
For example, here Alfred Centauri writes about Inertia:
Similar questions are: "why does electric charge happen?" and "why does gravity happen?" etc. The "art" of physics is in the identification of the fundamental "stuff", stuff for which the question "why" is actually misguided.
I disagree with that; I think that Inertia is not a fundamental property of matter and can be explained based on internal structure of matter.
Further, the ubiquitous misunderstanding of why Kinetic Energy is proportional to velocity square, is mostly explained based on definition of Work, and there is really no original thought of why it should be so, except some thoughts based on symmetry and relativity, which are good, but not too intuitive as well.
I'd like to share my thoughts on the above questions and receive some feedback from this community, whether my thoughts make sense whatsoever.
- Inertia, as ability to resist acceleration, is caused by spring-type connections between fundamental elementary particles. If a particle has no internal structure (it's not composed of any connected-together sub-particles), then it will not have Inertia and will have to move with the speed of light, like photon. A system of two connected particles will always exhibit a property of Inertia, because the connection is like a spring: it holds potential energy. Force applied from, say, left side to the left particle, pushing it to the right, will have to compress the spring and overcome it's stiffness. Then the spring will open up from the right side and push the right particle.
It is well known today that 99% of Inertia (mass) comes from binding energy in particles, similar in mechanism to my description above (let's not discuss the remaining 1%, Higgs field etc... as it is not related to this topic).
Here is a beautiful demonstration video with Photon Box by PBS Space Time that also suggests that mechanism of Inertia.
- 2. Now, if we accept that model and mechanism of Inertia, i.e. we understand how it actually works, then it's very simple to show why kinetic energy increases quadratically with speed. It just trivially follows. Kinetic energy is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Now, what prevents force from accelerating a body? It's Inertia. How does is exactly prevent? By the mechanism described above. You need to overcome Inertia in every point of space, along all the way while the force is acting and pushing the body. So in every small distance ds, you need to invest the energy equal to potential energy of that spring that connects to particles. The higher the distance, the more spring compressions-decompressions will be done, to move the body. Therefore, the energy E that you need to invest to move a body, must be proportional to a distanse s.
E ~ s
Now, obviously, E is also proportional to the amount of such springs in the body, i.e. it's proportional to the amount of matter in the body, in other words, to the mass. We have:
E ~ m * s
Lastly, if the force is stronger, you will compress the springs more and you need more energy to do that. You will cover distance s quicker, having higher acceleration, but you will need to invest more energy. Therefore, the invested energy is also proportional to acceleration you give to a body. We finally come to:
E ~ a * m * s
I can't think of anything else E would depend on. Seems, that's it. So E is the energy you need to invest to move the body, overcoming Inertia, and the body now possesses that same energy through momentum you gave to it's particles.
E ~ v/t * m * v*t
E ~ m * v * v
Does this all make any sense, that is my question!