I'm not sure what the concern is with this one,

A philosophical concern rather than a physical one. Why this particular relationship between Force, mass and acceleration? Why not

**F = **m

**a**^2,

**F = **ln (m

**a**) or

**F**^2 = 1 / (m cosh (

**a**) ) or any of the infinite number of different mathematical relationships I could posit?

(Other than the reason that, 'Well, that's the way we observe it"! Which is an

*answer*, true, but seems a bit of a cop out

)

Yes, the universe would look

*very* different to ours if such a fundamental law about force acting on an inertial mass, but who is to say that in the multiverse there are infinite numbers of such different universes with sentient creatures puzzling the very same thing about their own different laws.

Is there a deeper reason why our laws of physics are the way they are? For example, the reason why we (seem?) to have inverse-square laws - Newtonian gravity and Coulomb's laws is that we have three space dimensions. If there are more or less dimensions then this square law changes. And it

*might* be the case that on certain scales - the very big and very small - space isn't quite three dimensional and these laws would change. (Experiments are being carried out on some of these issues to test this idea.)

One. If one accepts the proposition that a body in motion tends to stay in motion, then it can be restated as a body at a constant velocity does not require applied force. Applied force is needed to cause a body to change its velocity. Acceleration is simply change in velocity.

Sure this is Newton' s first law. Nice. And F = ma is Newton's 2nd law, and we have Newton's third: for every action there is an opposite and equal reaction. Yet some of the concepts used in all three are fundamentally axioms that I can still ask: why do we observe the universe seemingly applying these axioms? Are there deeper reasons?

Of course, solar sails seem to create a problem with this thought process. Massless photons exert force on sails generating propulsion.

Photons have a momentum through their energy. When they are absorb by the matter - say that on a solar sail - the photon has been stopped and its momentum is now zero, and by conversation of momentum the matter gains this momentum.

Probably worth noting that force is defined (its unit, the newton, is defined) in terms of mass, time and distance (which are units that would have pre-existed it). Therefore, the only observation necessary for a 17th century scientist was that acceleration is proportional to force. Hence F=ma (with F being a newly-defined unit). As for why F=ma....I'm not sure we fully understand that.

The Newton was defined, as far as I can tell, by the equation F = ma, so it's kinda a circular argument! If Newton had found a different equation. say Force was proportional to mass

*squared *and acceleration to the power of 1 and a half, then the Newton would be defined by those relationships.

It is weird to think that, before Newton, humankind didn't really have a good grasp of the mathematics of how forces actually worked. They did have a good intuition of how it did work, of course - otherwise ancient cultures wouldn't have been able to put up big buildings, ships., catapults etc...!