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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, 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/s^{2} 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.

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:...sorry, you cannot view external links. To see them, please REGISTER or LOGINYou'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.

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.

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

Quote from: Geezer on 30/08/2011 07:21:06So 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 ćthereal waves, but I'm not permitted to describe that model except in the New Theories section.

"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.

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.

I'm not grumpy!I was only pointing out that the twit who wrote that in Wiki obviously has not the faintest idea how an accelerometer actually works.

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.

It's quite all right to think of gravity as a force, so long as that force is not a 4-force. I explained all this at...sorry, you cannot view external links. To see them, please REGISTER or LOGINPlease forgive me for the misssing images. They are missing drawings and missing equations. I'll get it up to date sometime in the future.The concept of force in GR is used in "Basics Relativity," by Richard M. Mould. Springer-Verlag Press

Quote from: Pmb on 03/09/2011 22:45:12It's quite all right to think of gravity as a force, so long as that force is not a 4-force. I explained all this at...sorry, you cannot view external links. To see them, please REGISTER or LOGIN

It's quite all right to think of gravity as a force, so long as that force is not a 4-force. I explained all this at...sorry, you cannot view external links. To see them, please REGISTER or LOGIN

Do you have a copy of this text? If so then turn to page 83 where Einstein answers your question. Einstein writesThe gravitational field transfers energy and momentum to the "matter" in that it exerts forces upon it and gives it energy:...

Quote from: Pmb on 05/09/2011 19:15:53Do you have a copy of this text? If so then turn to page 83 where Einstein answers your question. Einstein writesThe gravitational field transfers energy and momentum to the "matter" in that it exerts forces upon it and gives it energy:...Found it, thanks! But now my brain hurts.

Gravity produces the effect of acceleration by altering the passage of time (by warping or bending space-time).

The question is why?

Gravity remains a great mystery. The bendy space/time model seems to work really well in terms of describing and predicting the effects. I wonder it we will ever get much further than that.

Quote from: Geezer on 12/09/2011 21:13:41Gravity remains a great mystery. The bendy space/time model seems to work really well in terms of describing and predicting the effects. I wonder it we will ever get much further than that.Is there a scientific theory that's can do more than being able to describe and predict effects?

Quote Geezer"It seems to me that there is no "force of gravity", although gravity clearly accelerates mass. What's wrong with this reasoning?F = m.a"Acceleration is a change in velocity over time. So just by varying the passage of time you can have an acceleration. Any gravitating body dilates the passage of time near its surface.Gravity produces the effect of acceleration by altering the passage of time (by warping or bending space-time).Normally one would expect a force to be required to produce an acceleration but in this instance it is brought about by the geometry of space-time.

Quote from: MikeS on 11/09/2011 12:23:18Gravity produces the effect of acceleration by altering the passage of time (by warping or bending space-time).So, if I'm in free fall and observe my velocity using my wrist watch, I will find that my velocity is constant? I don't think so []

Your watch in free fall measures more distance being covered per unit time precisely because each unit of time is getting longer.

Quote from: MikeS on 19/09/2011 10:32:16Your watch in free fall measures more distance being covered per unit time precisely because each unit of time is getting longer.Erm, are you sure about that? If that were the case, you wouldn't observe any acceleration at all because the time to travel any distance would be proportional to the distance traveled, which would mean you had constant velocity.

Normally one would expect a force to be required to produce an acceleration but in this instance it is brought about by the geometry of space-time.

Mike - do the maths! If I drop a ball out of my office window (well my old office) after a second the ball is doing 10 metres per second - after two seconds it is doing twice that speed; please don't tell me that this effect is due to time dilation.And if you read the thread on falling into black holes you will find that time doesn't actually come to a stop a the Event horizon of a black hole - that is an artefact of using the wrong form of coordinates for the job; whilst schwarzchild coordinates are great for outside the black hole near the eh they create a mathematical singularity (ie you get undefined/infinite answers) - better choices of coordinates remove this anomaly.

I forgot to mention that Newton defined force as F = dp/dt, not F = ma. The former is in the beginnning of the Principia and the later is Euler's expression for the force/mass/acceleration relastionship. The expression F = dp/dt is relativistically correct, where generally F = ma is not.

Quote from: Pmb on 22/09/2011 02:52:52I forgot to mention that Newton defined force as F = dp/dt, not F = ma. The former is in the beginnning of the Principia and the later is Euler's expression for the force/mass/acceleration relastionship. The expression F = dp/dt is relativistically correct, where generally F = ma is not.What's the difference?

Quote from: Geezer on 22/09/2011 08:22:18Quote from: Pmb on 22/09/2011 02:52:52I forgot to mention that Newton defined force as F = dp/dt, not F = ma. The former is in the beginnning of the Principia and the later is Euler's expression for the force/mass/acceleration relastionship. The expression F = dp/dt is relativistically correct, where generally F = ma is not.What's the difference?They don't always have the same value, e.g. for v << c the mass of a rocket which is accclerating from its engines being turned on, and when the velocity is relativistic. Its best to define F = dp/dt and when v << c and m = constant.

Can rockets achieve relativistic velocities?

Quote from: GeezerCan rockets achieve relativistic velocities?Theoreticaly, yes. But that would be to impractical to build.