[Geezer (OP)]

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.

[imatfaal]

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.

well no more than usual anyway

[Geezer (OP)]

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. 

Yes. That makes sense JP (except that I'm not sure there is such a thing as a rotating frame when you are looking at it from within a non-rotating frame  [])

I'm not sure that Newton's laws are necessarily incompatible with an accelerating frame. I think that's more a misapplication than anything else.

The only thing we know about gravity is that it produces acceleration. It's meaningless to apply F=ma to derive a "force" when the acceleration is obviously independent of mass. There is nothing wrong with using fictitious forces if they help in solving problems, but we should be aware that they are fictitious.

[Pmb]

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

http://home.comcast.net/~peter.m.brown/gr/grav_force.htm

Please 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

[Geezer (OP)]

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

http://home.comcast.net/~peter.m.brown/gr/grav_force.htm

Please 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

Well jolly good, but what exactly do you mean by 4-force? Einstein was pretty clear about gravity not being a force. Is this an alternative theory? 

[Pmb]

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

http://home.comcast.net/~peter.m.brown/gr/grav_force.htm

Please 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

Well jolly good, but what exactly do you mean by 4-force? Einstein was pretty clear about gravity not being a force. Is this an alternative theory? 

A 4-force is dwfined in the link above. I'll try to get it up today. In the mean time I'll just say that a 4-force is defined as F = DP/dt where D/dt is the absolute derivative defined here
http://home.comcast.net/~peter.m.brown/math_phy/absolute_derivative.htm

Also, Einstein never opposed the notion of gravity not being a force. In fact he used that notion in his text The Meaning of Relativity. Do you have a copy of this text? If so then turn to page 83 where Einstein answers your question. Einstein writes

The gravitational field transfers energy and momentum to the "matter" in that it exerts forces upon it and gives it energy:...

I wrote an article about how Einstein viewed gravity. It's online here
http://xxx.lanl.gov/abs/physics/0204044

[Geezer (OP)]

Do you have a copy of this text? If so then turn to page 83 where Einstein answers your question. Einstein writes
The 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.

[JP]

Do you have a copy of this text? If so then turn to page 83 where Einstein answers your question. Einstein writes
The 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.

Like everything else, so much misunderstanding comes from not realizing that fundamental concepts in Newtonian mechanics don't generalize simply to modern physics, be it relativity or quantum mechanics.  The word "force" groups together a lot of things in Newtonian mechanics that not only can change the energy/momentum of an object, but which also all satisfy F=ma.

In GR, gravity and all other forces can still change the energy/momentum of an object.  But gravity is modeled by Einstein's equations, which can be interpreted geometrically.  Non-gravitational forces all still satisfy something similar to F=ma. 

So gravity is special for reasons that have been discussed at length in this thread already.  What you choose to label it as isn't nearly as important as understanding that it's different.

[MikeS]

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.

[Geezer (OP)]

Gravity 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  []

[MikeS]

Geezer you are obviously quite right.  The question is why?  Each of the above statements (in my last post) I believe to be true but the time dilation factor is no where near enough to account for the acceleration.

Added 19-09-11
Using a gravity calculator to check gravitational acceleration over 2000km, equating acceleration to the strength of gravity at any altitude and equating that to the time dilation feature, it can be estimated, time dilation is enough to account for the acceleration.

[Geezer (OP)]

The question is why? 

How the heck would I know  []

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.

[JP]

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.

Is there a scientific theory that's can do more than being able to describe and predict effects?

[Geezer (OP)]

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.

Is there a scientific theory that's can do more than being able to describe and predict effects?

Picky, picky! Some theories provide a bit more insight into the underlying mechanisms than others. The underlying mechanism of gravity remains mysterious (unless somebody figured it out while I wasn't paying attention.)

As I can see no harm in teaching you how to suck eggs, I should point out that "science" literally means "knowledge" (which you would know if you had ever taken the trouble to study a bit of Latin.) The fact that we promulgate a bunch of theories to explain "what" stuff does does not necessarily contribute to the "knowledge" of how the heck it does it. Ergo (another Latin word), a "theory" does not necessarily contribute to science.

[MikeS]

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.

Gravity 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  []

Geezer

An object free falling to Earth is seen to be accelerating.
An object free falling to Earth is experiencing time dilating more and more the closer it gets to the Earth.
Time dilating allows more distance to be covered per unit time.
This is acceleration due to time dilation.
This is an affect of gravity.

Your watch in free fall measures more distance being covered per unit time precisely because each unit of time is getting longer.  This effect is probably being diluted by other gravitating bodies like the solar system, our galaxy etc.

Time dilation due to the gravity of the Earth is a very small effect in the much larger picture.  To put this into context we must remember that gravity can make time stand still at the event horizon of a black hole or the passage of time could be infinite.  This gives a huge rage to the potential passage of time.

[Geezer (OP)]

Your 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.

[MikeS]

Your 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.

Geezer
Yes, when observed from a great distance this is true.  The geometry of space-time produces a constant velocity.  I 'believe' it is in accordance with relativity.

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.

[imatfaal]

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.

[MikeS]

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.

imatfaal
Yes, I think it is due to time dilation and I agree it sounds impossible but, I suspect, that may just be a matter of scale and our arbitrary way of measuring the passage of time.
"gravity can make time stand still at the event horizon of a black hole" "from the perspective of a distant observer" I should have added. 

[Pmb]

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.