Physics vs. Math

[Monster]

Is it all a big time conspiracy?

When I was in school, I never understood why mathematicians hated the physicists.

Until I re-read some of the "laws" in physics.

If you know math, you know that equations have a certain implied truth value.

For example, f(x) = x² unambiguously states that f is function parameterized by x that computes x².

A statement like y = x + 3 implies that y = x + 3 and x = y - 3, among other things.

So, WHY on Earth do physicists write things like E = mc² and call it an "equation" without defining the circumstances at which this applies? They call E "energy", but energy is a very ambiguous term. What is energy?

If you look at this ridiculous formula, E = mc², written down by a man who slept 22 hours a day (certainly not the most healthy thing to do), you could state a number of things:

• If m equals zero, E is also zero.
• If m (=mass) is like 1 metric ton (1000 kg), E is 89,875,517,873,700,000,000 J (=Joule), or roughly 90 EJ (Exajoule), because the speed of light c (in vacuum) is 299,792,458 km/sec.

There is already the implication that speed of light (previously assumed to be constant), has been found to be not-so-constant and dependent on the medium light travels through. In vacuum it is still assumed to be constant.

To equate energy with mass is sort of phony. Because it is not stated what kind of energy E is (physicists have all kinds of specialized formulas for specific kinds of energy), and under which circumstances mass applies.

This is just ONE minor example of that great conspiracy.

I think what they told us in school about physics was bullshit ... when real-life engineers have to deal with formulas with multiples integrals in them to deal with only the tiniest bits of actual reality.

This is a big-time conspiracy to keep the masses uninformed about the real properties of physics.

Grab a beer and ponder this for a while.

 

[Monster]

Another phony "law" in physics is one of Newton's: F = ma (i.e. force equals mass multiplied by acceleration).

If we use our cube again of 1 metric ton (1000 kg), say, traveling at a velocity of 5 m/s (meters per second), and no acceleration (a=0), the force would be 0 N (0 Newton). Does this make any sense?

 

[McSick]

E = mc^2 is a relativistic equation. You have your applied energies like chemical, thermal, potential, kinetic...ect. However Eistein's equations were about relativity. Things are much much different. As for no mass, this does happen with photons (massless particles of light!). Their equation for energy in relativity are E = hf where h is planks constant and f is frequency. Now these are all "equations" in a mathematical sense. They are all functions just written differently. We could say f(m) = mc^2 where f(m) is equal to E. All that is required for a function is that it takes in variables and produces and output. The variable doesnt even have to be part of the equation! f(x) = 1. This is a function that takes in x and produces and output. You can get more formal but his equations are for sure functions. And the biggest thing I think you are missing...These equations are VERY simplified. In reality in a college level course, you soon learn there is much much more to the equations. So you can take into account the medium in which light is in. So you can take into the account of blah blah blah. This leads to a lot of differential equations which would be kinda hard for people to grasp when starting out in physics.

As for F = ma. Think about this, If a force is applied to an object, it will either change direction or velocity. So if your cube is in space constantly traveling NEVER changing its velocity...Then nothing is being applied to it. It makes total sense if you really think about it. Acceleration is your change in velocity over time......If your velocity is not changing ever....then neither is your acceleration..which means no force is applied. F=ma = m(dv/dt) = (E/c^2)(dv/dt) ....it can be written in so many different ways.

 

[Monster]

(thinking)

 

[Monster]

How come photons have no mass when they can be used to clean surfaces, for instance?

 

[Monster]

As for F = ma. Think about this, If a force is applied to an object, it will either change direction or velocity. So if your cube is in space constantly traveling NEVER changing its velocity...Then nothing is being applied to it. It makes total sense if you really think about it. Acceleration is your change in velocity over time......If your velocity is not changing ever....then neither is your acceleration..which means no force is applied.

What is the force of the cube, traveling at constant speed, when it crashes into something? I mean, it's exerting kinetic force on the target object then, doesn't it? Because then, there's a deceleration, and suddenly there would be a force vector, right?

 

[Monster]

In electronics, for instance (which originated from physics) : Normally, you would assume that, say, a plate capacitor (with two metal plates facing each other, separated by an isolator), would accumulate charge in a predictable manner. How come there's no equation to compute that as a function of time?

 

[Jason2022]

A statement like y = x + 3 implies that y = x + 3 and x = y - 3, among other things.

So, WHY on Earth do physicists write things like E = mc² and call it an "equation" without defining the circumstances at which this applies? They call E "energy", but energy is a very ambiguous term. What is energy?

(math major here) Physics equations can indeed be understood to mean more than one thing - cause they're equations.

If you look at this ridiculous formula, E = mc², written down by a man who slept 22 hours a day (certainly not the most healthy thing to do), you could state a number of things:

• If m equals zero, E is also zero.
• If m (=mass) is like 1 metric ton (1000 kg), E is 89,875,517,873,700,000,000 J (=Joule), or roughly 90 EJ (Exajoule), because the speed of light c (in vacuum) is 299,792,458 km/sec.

Well, of course, no mass would be no energy.

I think what they told us in school about physics was bullshit ... when real-life engineers have to deal with formulas with multiples integrals in them to deal with only the tiniest bits of actual reality.

This is a big-time conspiracy to keep the masses uninformed about the real properties of physics.

No, not really. There is nothing illogical about the basics. However, though, some advancements lately have gotten into stuff like parallel universes, really weird stuff bordering on the spiritual (Science proving the supernatural?).

 

[Eljo12]

Let's focus now on the relationship between physics and mathematics (and mathematicians). How do we learn the rudiments of physics? We start from the physics of the pioneers, and especially from the physics of Isaac Newton, that of the apple that falls to the ground.
The most popular example is precisely that of relativity: the laws of Newton's mechanics are valid as a first approximation, provided that all the speeds involved are "infinitesimal" with respect to the speed of light (about 300,000 km / s). And already here it would be unnerving: the sign of equality = can not be abused lightly! Physicists, obviously, equate different things, with the convention that the error committed is negligible. But how negligible? It depends.
On the contrary, the mathematician detests ambiguities, and tends to use binary logic: a proposition can be true or false, but tertium non datur. Is it true or is it false that a bullet travels along a parabolic orbit? At school they teach you that it is true, but in the real world it is not: because that of the parabolic orbit is an approximate theory that disregards friction, any external chaotic interference, and more. I'm not saying that physicists are charlatans, on the contrary: for a physicist, the projectile draws a parabolic trajectory as long as certain hypotheses are satisfied. In this sense, the physicist has produced a theorem with all the trappings; unfortunately, he did not describe reality exactly. Mathematically, the physicist has found an approximate solution to the problem, but can not guarantee that it is a real solution.
For physicists, it is this fun: to build ever better theories, that is, better approximations of reality. On the contrary, the mathematician sometimes remembers the ancient idealist who imposed on reality to adapt to (his) theories. Understand that, if you do not give an adjustment, the mathematician risks falling into nihilism. In fact, the man in the street might even suggest that it is not even worthwhile to find exact theories for the real world, since the approximate theories work very well and can even help humanity. The approximations already allow us to send satellites in orbit, although with some risk of failure. If we waited for the exact resolution of the fluid dynamics equations, we would still be busy with the traveling pigeons and the smoke signals.
In summary, can a mathematician love physics? Of course it can, there are even mathematical physicists.