| HN Mirror

> Either you don't realize what you're saying or you are playing a game of deception.

I'm sorry you feel that way. I'm just trying to help you understand source of those equations.

> 1. This equation is indeed a core law of the universe.

Let me show you step by step where the equation v² = 2ad comes form.

Let's consider an object moving in any way. It may have some mass, it may be massless, it doesn't matter.

Let's call the distance it moved so far d. Because object moves, d is a smooth function of time so we might be interested with its first and second derivative. Let's call the first derivative v and second derivative a. Those might be constant or might be also some functions of time.

Then let's say we are interested in a very specific type of motion. A motion where at t=0 first derivative was equal zero, and second derivative is constant through the whole motion.

So we have second derivative equal some constant value a. Because integration is the opposite of derivation to calculate v we need to integrate a over time t. This is a purely mathematical operation. And gives us v = at Then we want to calculate the function d itself for this specific motion. To do that we need to integrate over time again and we get d = at²/2 This again is purely mathematical operation that doesn't rely on any connection to the world we live in.

So we have:

d = at²/2

v = at

when we calculate t from the second equation and put it in the first one we get:

d = av²/2a²

by rearranging we get:

v² = 2ad

All of the above is true and pure math. Even if universe didn't exist or worked completely differently (for example if real objects didn't really move in smooth motions but teleported instead) this equation and its derivation would still exist, it just would not reflect reality.

So this equation comes from pure math and a concept of how movement might work, defined by purely mathematical means. It doesn't have to describe our universe and existence of this equation doesn't depend on the existence of our universe or how movement actually works in our universe. So it's not a core law of universe, just a mathematical consequence of considering one specific type of motion that we think might happen in our universe.

> It is extremely interesting because it has a specific meaning. It expresses the kinetic energy of a massive body in motion.

Yes, but that's all. There are many other forms of energy. And what's way more interesting, that we get from considering kinetic energy, is the concept of energy itself, that it can come in many forms and can get transferred from one form to another and that transfer is mediated by work done by forces acting on moving bodies over some distances.

> 3. More specifically, it means that E = mc² does not represent what Einstein claimed it did. It represents the maximum kinetic energy that a massive body can have. This is why it is extremely interesting.

Absolutely not. Kinetic energy defined as mV² (with 1/2 or without) is only the approximation what the kinetic energy of a massive body is when it travels at slow speeds. When the speeds get near c best approximation of kinetic energy that we know is

Ek = (1/sqrt(1-v²/c²) - 1)mc²

It's not immediately obvious but this equation can be approximated by mv²/2 for small v (by using Maclaurin series expansion of part of it and taking only first terms).

This better equation again is purely mathematical result derived by considering of how adding movements must work if there is such a thing as the maximum speed of movement (that we called c).

You can see that this equation tends to infinity as v approaches c. So there's no maximum kinetic energy. You can pump energy into the moving body by applying the force to it to do the work regardless of what speed the body has already. Buy pumping in more energy you just bring the speed closer to c but you never reach it no matter how much you pump in.

Maximum kinetic energy doesn't make sense conceptually. If there was such thing then by putting in the work to accelerate the body, at some point, all the work you put in so far would reach this maximum kinetic energy. This would need to happen at speed below c because there's no amount of force you can apply (over whatever time) to make massive object travel at exactly c.

What then? When you already reached maximum kinetic energy, what if you would still try to put in more work? Where would the work go then if not into kinetic energy?

> Thank you for the exchange.

I have some fringe opinions about some aspects of physics as well and I would very much like if someone with more intimate knowledge of math involved would point out exactly what's wrong with them.