[Geezer (OP)]

It seems to me that there is no "force of gravity", although gravity clearly accelerates mass. What's wrong with this reasoning?

We know that;

1) F = m.a

2) We can measure the acceleration (a) of a free falling object in a gravitational field, and the acceleration is independent of the mass (m) of the object.

3) We can consistently measure the mass (m) of an object independently of any gravitational field.

We can conclude that a free falling object in a gravitational field is experiencing an accelerative force which is the product of its mass (m) and the acceleration (a) that we observe.

Except that;

We also know by observation that the acceleration of the object is constant, regardless of its mass, so the accelerative force (F) must be proportional to the mass of the object.

We might express this as;

F[prop]m

Therefore, F = K.m (K is some constant)

However, we also know that F = m.a

So we have just proved that a is a constant! (Which was obvious in the first place.)

What it does not seem to prove is that there is any "force of gravity". All it seems to tell us is that gravity accelerates matter. Either that, or F does not equal m.a

Where am I going wrong?

 

[Soul Surfer]

You are forgetting that the acceleration due to gravity is not constant and varies as you approach the body and the equations are only true for one instant the moment the body falls a little towards the gravitating mass the acceleration and therefore the force increases.

[Geezer (OP)]

You are forgetting that the acceleration due to gravity is not constant and varies as you approach the body and the equations are only true for one instant the moment the body falls a little towards the gravitating mass the acceleration and therefore the force increases.

But I'm talking about a particular distance and a specific instant in time. Why does your argument prove that there is a force of gravity? My reasoning and math is not very complicated. If it's wrong, it should not be too difficult to shoot it down in flames (which, BTW, is fine with me - I'd just like to be able to understand this because it has been bugging me for a long time.)

[Robro]

I do not think that there is a "Force" of gravity. I tend to think of gravity as a consequential artifact of electromagnetism. There is plenty of mathematics to describe what happens in a gravitational field, but it leaves the definition up to "curved space-time", which in itself is not really a definition but just another description of what happens. I do not think that mainstream offers a "definition" of gravity or space-time. Same goes with "magnetic force" and "electric charge". I do not think anybody really knows "what" these things are, but their effect have many good descriptions.

[JP]

Geezer, I think you're basically reasoning along the same lines as one of the postulates of general relativity: the equivalence principle.  In GR, gravity isn't a force, either.  Your proof above is similar to Einstein's famous elevator experiment.  If you're in an elevator, the "force" you experience as it accelerates upward at 9.8 m/s² is indistinguishable from gravitational acceleration at the earth's surface (if you look only at a point, clearly, since you can tell that the earth's gravity is decreasing as you move away from it).  If you follow through to the logical conclusion, our "force" of gravity is just an acceleration, so there's some reference frame (a freely falling one) in which this acceleration vanishes.  Then if you add in lots of fancy math, you end up at general relativity.

[Geezer (OP)]

Geezer, I think you're basically reasoning along the same lines as general relativity, and in GR, gravity isn't a force, either.  Your proof above is similar to Einstein's famous elevator experiment.  If you're in an elevator, the "force" you experience as it accelerates upward at 9.8 m/s² is indistinguishable from gravitational acceleration at the earth's surface (if you look only at a point, clearly, since you can tell that the earth's gravity is decreasing as you move away from it).  If you follow through to the logical conclusion, our "force" of gravity is just an acceleration, so there's some reference frame (a freely falling one) in which this acceleration vanishes.  Then if you add in lots of fancy math, you end up at general relativity.

Kewel! Would it be a bit late to expect a jaunt to Norway to pick up the prize?

[JP]

Probably.  By the way, I was editing something into my post as you quoted it, so you probably missed it.  You might want to check this out:
http://en.wikipedia.org/wiki/Equivalence_principle

You're assuming the equivalence of inertial mass and gravitational mass in your equation.  There's no fundamental reason we know of yet why they should be the same, but they appear to be. 

[Geezer (OP)]

Probably.  By the way, I was editing something into my post as you quoted it, so you probably missed it.  You might want to check this out:
http://en.wikipedia.org/wiki/Equivalence_principle

You're assuming the equivalence of inertial mass and gravitational mass in your equation.  There's no fundamental reason we know of yet why they should be the same, but they appear to be. 

Thanks!

(I wonder if he thinks I'm really going to read that. There's an awful lot of words and math and stuff  [])

[Soul Surfer]

What I was pointing out was that this force is not a fixed value but bears a relationship with distance from the gravitating object.  This is an inverse square law which corresponds with the normal dimensionality of things because the surface area of a sphere increases as the square of its radius.

All you are pointing out with your mathematical arguments is that there is a common constant of proportionality in this relationship this is the quantity which we call mass.  That is, mass is not something fundamental but just comes out of the way things behave.
If you are familiar with dimensional analysis where we express all measurements and observations in terms of mass, length and time,  if one includes gravity into all the relationships it is possible to eliminate mass entirely and express everything in terms of length and time.  Nowadays even these measurements are being looked on as not the fundamental properties of the universe and it is suggested that everything should be really expressed in terms of momentum and energy.  note this does reintroduce the concept of mass but this can be easily removed by replacing it with its energy equivalent via the famous e=mc^2.  that is mass is really just a form of localised energy.

[Phractality]

F = ma only works at non-relativistic speeds. As you near the speed of light, m increases, so for a constant acceleration, the force must also increase. The more general definition of force is f = δp/δt; i.e., force is the time rate of change of momentum.

At non-relativistic speeds, δm = 0, so vδm/δt = 0. The change of momentum at non-relativistic speed is simply δp = mδv; at relativistic speed, it is δp = mδv + vδm. So δp/δt = mδv/δt + vδm/δt. Acceleration is a = δv/δt, so mδv/δt + vδm/δt = ma + vδm/δt.

F = δp/δt works not only for objects with rest mass, but also for photons. Although a photon is not considered to have mass and force in general relativity, it certainly could by this definition.

[Geezer (OP)]

F = ma only works at non-relativistic speeds. As you near the speed of light, m increases, so for a constant acceleration, the force must also increase. The more general definition of force is f = δp/δt; i.e., force is the time rate of change of momentum.

At non-relativistic speeds, δm = 0, so vδm/δt = 0. The change of momentum at non-relativistic speed is simply δp = mδv; at relativistic speed, it is δp = mδv + vδm. So δp/δt = mδv/δt + vδm/δt. Acceleration is a = δv/δt, so mδv/δt + vδm/δt = ma + vδm/δt.

F = δp/δt works not only for objects with rest mass, but also for photons. Although a photon is not considered to have mass and force in general relativity, it certainly could by this definition.

Thanks! So does this mean you believe there is a "force of gravity"?

[Phractality]

So does this mean you believe there is a "force of gravity"?

I believe masses accelerate toward one another, resulting in a rate of change of momentum which can be calculated from Newton's law of gravitation or from general relativity. You may explain that acceleration in terms of a gravitational field, but what is a field but a mathematical description of an effect?

I prefer to explain the cause in terms of interacting æthereal waves, but I'm not permitted to describe that model except in the New Theories section.

[MikeS]

So does this mean you believe there is a "force of gravity"?

I believe masses accelerate toward one another, resulting in a rate of change of momentum which can be calculated from Newton's law of gravitation or from general relativity. You may explain that acceleration in terms of a gravitational field, but what is a field but a mathematical description of an effect?

I prefer to explain the cause in terms of interacting æthereal waves, but I'm not permitted to describe that model except in the New Theories section.

What acceleration?
"An object in free-fall is in actuality inertial, but as it approaches the planetary object the time scale stretches at an accelerated rate, giving the appearance that it is accelerating towards the planetary object when, in fact, the falling body really isn't accelerating at all. This is why an accelerometer in free-fall doesn't register any acceleration; there isn't any."
http://en.wikipedia.org/wiki/Equivalence_principle
 []

[imatfaal]

Mike - go to the top of the newly reopened Blackpool Tower Eye (crazy place crazy name) - step off.    So why are you gonna be unable to post the results of your experiment?  We are conflating GR and Newtonian mechanics - to describe an object falling off a desk as not accelerating is futile, whilst quite clearly also correct.  GR is a model that works very well - especially in cosmological distances and masses, Newtonian mechanics is another model (or in fact a limit of GR) that works very well in human distances and masses; but let's be clear - neither of them are correct in absolute terms.  you use the model that is most appropriate for your situation

[Geezer (OP)]

"This is why an accelerometer in free-fall doesn't register any acceleration; there isn't any."

Which only goes to prove you should not believe everything in Wikipedia. That statement is complete bollocks nonsense.

The reason an accelerometer does not measure acceleration in free fall is because there is no difference between the "sensor" and the "mass" of the accelerometer. They are both experiencing the same acceleration. That could be any value, including zero, but it sure as heck does not prove there is no acceleration.

[MikeS]

"This is why an accelerometer in free-fall doesn't register any acceleration; there isn't any."

Which only goes to prove you should not believe everything in Wikipedia. That statement is complete bollocks nonsense.

The reason an accelerometer does not measure acceleration in free fall is because there is no difference between the "sensor" and the "mass" of the accelerometer. They are both experiencing the same acceleration. That could be any value, including zero, but it sure as heck does not prove there is no acceleration.

If you correct for time dilation within the fall, there will be no acceleration, only a constant speed.

This should be easily testable.  We now have the capability to measure time dilation over distances as small as a meter.  It should therefore be possible to drop an optical atomic clock through a few meters and measure whether it has accelerated or not.

We, as a species do not have the ability to differentiate small differences in the gravitational field.  Neither, we do not have the ability to differentiate small differences in the passage of time.  Instead we 'smear' the passage of time to an average.  This was obviously beneficial to our species.

[imatfaal]

Drop an atomic clock?  They have to custom-build hovercarts to move them around to avoid the bumps of going over door lintels.  The most recent and accurate atomic clocks rely on fountains of matter falling under gravity and constrained influenced by lasers and microwaves - not sure that would take well to being dropped, my casio f91-w would be more accurate and might not need millions to rebuild afterwards.

The best accuracy over a long period of an atomic clock (USNO rubidium fountain) is around 1*10^-16 of a second.  Even if the experiment introduced no error what so ever this would not allow the time differential to be measured. 

More importantly you do not just need to calculate the gravitational time dilation you need to calculate the correct four vector in a solution of the einstein equations/tensors - which to all intents is impossible, the assumptions you would have to make would drown any actual figures.  do the sums for just the time dilation and you get nonsense.  Drop something from 20m high, in the first second you will travel 5m, the second second you will travel 15m yet the variation in time dilation is unmeasurable.

[MikeS]

Drop an atomic clock?  They have to custom-build hovercarts to move them around to avoid the bumps of going over door lintels.  The most recent and accurate atomic clocks rely on fountains of matter falling under gravity and constrained influenced by lasers and microwaves - not sure that would take well to being dropped, my casio f91-w would be more accurate and might not need millions to rebuild afterwards.

The best accuracy over a long period of an atomic clock (USNO rubidium fountain) is around 1*10^-16 of a second.  Even if the experiment introduced no error what so ever this would not allow the time differential to be measured. 

More importantly you do not just need to calculate the gravitational time dilation you need to calculate the correct four vector in a solution of the einstein equations/tensors - which to all intents is impossible, the assumptions you would have to make would drown any actual figures.  do the sums for just the time dilation and you get nonsense.  Drop something from 20m high, in the first second you will travel 5m, the second second you will travel 15m yet the variation in time dilation is unmeasurable.

I don't see why there would be a problem as time differential has already been measured over distances as small as one meter as previously mentioned.

posted on August 29th, 2011
“(…) if one clock is placed one centimeter higher than another clock, the higher clock is affected by less gravity, so it goes faster. That difference could be read out in the 18th decimal place of the clocks in one second averaging time. Until now, clocks have been thought of as tools for sharing a common time. But with clocks like this, conversely, we can understand that time passes at different speeds, depending on the time and place a clock is at.”
http://techcrunch.com/2011/08/29/video-new-atomic-clock-reaches-a-100-quadrillionth-of-a-second-accuracy/

[JP]

Here's another interesting point, Geezer.  Say we decide to use Newton's laws in an accelerating reference frame.  For the sake of making your grumpy, let's assume it's a rotating reference frame.  Suddenly we find that everything is experiencing a centrifugal force that is proportional to mass. 

Now let's say we spent our entire lives in this rotating reference frame.  We might not even realize it's rotating and we might assume that centrifugal force is some fundamental force in the universe.  Eventually someone bright would come along and figure out that the magic centrifugal force can be explained by the fact that all our experiments and observations have been done in a rotating reference frame, and that centrifugal force is just an artifact of us having formulated all our theories in rotating coordinates.

Now imagine instead we grew up in a reference frame that was accelerating with respect to the natural, inertial, free-falling frame.  We didn't realize  we were in an accelerating reference frame, so when we formulated all our physical laws, we got this fictitious force that was always proportional to mass, and called it gravity.  Then one day, Einstein came along and figured out that the "force" of gravity appears because we're working in reference frames that can be thought of as accelerating with respect to the inertial one in which gravity disappears as a force.

The analogy is quite good, actually.  Fictitious forces are proportional to mass, and pop up whenever you try to formulate Newton's laws in an accelerating reference frame.  Einstein's genius was to realize that gravity is also a fictitious force if you regard free-fall as the appropriate "non-accelerating" reference frame. 

[imatfaal]

I don't see why there would be a problem as time differential has already been measured over distances as small as one meter as previously mentioned.

That's the problem Mike - you don't see any problems that contradict your preconceptions.  Do the maths!