Yes, but besides what Ken G says (which I agree with), at that level, we can't say what causes anything.

I mean, if the question were what causes this particular substance to smell like molasses, we could give a answer that included a chemical breakdown of the components--that would probably be satisfactory to the questioner, but it wouldn't really answer for the ultimate cause.

If wish to apologise to all who may have been offended by my previous post, and thank all those who replied to it. I may have been too confrontational.

I do not actually believe that there is any sort of rift between mathematicians and physicists. And I accept that each of us, when answering a specific question, will stress different aspects of the mainstream science, depending on the question that was asked. I have absolutely no problem with this. What I wanted to draw some attention to was that, in stressing some side of the issue, sometimes we may lose sight of the other sides.

Ken G's reply to my post was quite satisfactory, but I would nevertheless like to go a little deeper in understanding where he (and others) are coming from. A while ago in another discussion, Ken wrote to me:

I'm wondering how he and the others here reconcile what he told me then -- that "force" is first and foremost something we measure (which I would rephrase as "a force is a physical/empirical thing") -- with what you've been saying in the present thread -- that the distinction between a force and a curvature of spacetime is merely a mathematical property of physical models (in other words, that "a force is a mathematical construct").

__________________
"A witty saying proves nothing" Voltaire.
"All your bias are belong to us" Ara Pacis.

No. Force is real. We perceive forces through our senses (sound, touch, etc.). We measure them and compare them with other measurable phenomena via the structure and language of math.

Math doesn't contruct the force. Forces simply are. Math is how we relate quanities of force with other things.

You also wrote:

Can you have a force without an acceleration? According to F=ma, no!

But that's not the whole picture, as other things equal F besides just m*a. For example, gas in a pressurized container exerts a force measured in psi (or hectopascels per cubic centimeter... I think). No acceleration, but there's definately a force.

F=ma in all situations where m is not bound by another artifact (such as the cylinder containing the pressurized gas). It only holds for where m is free to move in any direction as determined by the force that's applied to the mass.

"Abstract?" That's about as concrete as you get when it comes to dynamics!

__________________
"Toward no crimes have men shown themselves so cold-bloodedly cruel as in punishing differences of belief." - James Russell Lowell

Well, I guess that settles it.

__________________
"A witty saying proves nothing" Voltaire.
"All your bias are belong to us" Ara Pacis.

First of all, I see no need for you to apologize, as nothing you said was offensive or attacking, it was merely designed to stir up a buzz-- and succeeded. Discussions here would be pretty dull if no one was willing to go out on a limb and get called for it! But what I would say about the way to reconcile the idea that forces are defined by how they are measured with the question of whether or not gravity is a force is that your drawing this distinction is actually quite central to the equivalence principle, which is in turn central to the theoretical lines we are trying to draw and are finding that we cannot reach a definitive answer.

Put differently, using a completely empirical definition of a force is still not guaranteed to be able to say if gravity really is a force. The equivalence principle stymies that effort by saying that if gravity is a real force, it must act to be mimicked by an acceleration of the reference frame. The OP could have just as easily been stated "is the inertial mass really the same thing as the gravitational mass, or does it just work out that we can treat them as equal for all the systems we've observed?" How does one answer a question like that empirically? If A mimics B in all empirical ways, then we cannot empirically distinguish them, but we also cannot state categorically that they are the same. That is the reason the OP really cannot be answered, each theory that one might choose to apply will find a different answer, and the observations that can distinguish them have not been done and may not even exist.

__________________
Logic is the grammar of truth.

Meaning and absolute certainty are incompatible, and profound meaning and absolute certainty are profoundly incompatible.

The only thing intelligence is capable of is recognizing itself.

If it waddles like a Force and quacks like a Force, it's close enough. See also the Centrifugal debate. Whether it fits one person or another's definition of "force" is basically irrelevant, it has an effect on how the world works and has to be taken into account regardless.

__________________
"If this were play'd upon a stage now, I could condemn it as an improbable fiction."
Shakespeare, Twelfth Night
"The Mayan symbol for "book" looks a lot like a triple hamburger, but I've never seen them claiming it as proof the Mayans had Big Macs." - KaiYeves
"Distance doesn’t matter much in space, where if you just start a thing off with the right kind of shove, sooner or later it will get where you want it to go." -Frederik Pohl, Mining the Oort

True! As I've experienced many times by being called on various things, quite a few by yourself! (coriolis...)

__________________
"Toward no crimes have men shown themselves so cold-bloodedly cruel as in punishing differences of belief." - James Russell Lowell

I disagree. Nitrogen looks, smells, sounds, and feels (waddles and quacks) just like air. But breathing pure nitrogen will kill you deader than deer caught in the headlights.

As KenG said, even if something is 99% the same, you still can't say x=y, so long as there is even the possibility of a defining difference.

When it comes to gravity, the various equations surrounding force abound. To say that gravity is a force requires one to verify that gravity can be substituted for a force in all the equations. The problem is, you can't. It simply doesn't hold, despite Wikipedia's article on force which contends otherwise.

It boils down to this (ie, the following statements, as stated, are true):

1. All bodies in non-gravitational free-fall which experience a force experience a correlating acceleration which is equal to the ratio between the force and the mass.

That acceleration can be measured by an on-board accelerometer.

2. All bodies in free-fall experiencing a change in their velocity relative to a neighboring massive object (such as the Earth) appear to be accelerating in a direction parallel to the line between the body's center of mass and the object's center of mass.

That acceleration can NOT be measured by an on-board accelerometer.

The point is that regardless of the similarities between gravity and traditional forces, there is a difference.

It's that difference which sets gravity apart from a force.

Gravity is not a force. It's a warping of the space-time in which all affected matter and energy exist, as both matter and energy are affected by gravity.

Consider Newton's First Law: "A particle will stay at rest or continue at a constant velocity unless acted upon by an external unbalanced force." Thus, a planet will continue in a straight line unless acted upon by a force.

But is gravity really a force? No. Gravity simply warps space-time in the solar system such that a planet's orbit really is a straight line. All on-board accelerometers can measure any force enacted upon a free-falling body. No on-board accelerometer can measure the effect of gravity upon a free-falling body. Thus, gravity is not a force.

Can't recall who thought that up ealier, but way to go! That's a very appropriate point of view with respect to helping us increase our understanding of gravity.

__________________
"Toward no crimes have men shown themselves so cold-bloodedly cruel as in punishing differences of belief." - James Russell Lowell

The reason that Einstein claimed that gravity is not a force is more simple. Forces come in pairs and gravity does not as far as Einstein was concerned. The reason that all of the fundamental forces list gravity with it is because Einstein thought that possibly all forces were the result of geometry as Riemann suggested.

Anyway, this is the way I heard and read it and the nomenclature has stuck since.

Wow!!! My head hurts