# If it walks like a duck?

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I have always considered gravity to be a force. Then the end all of all conversation came along.

Okay,I kind of gave it that name because it seems to me that when I see it used it is generally ment to stump, or end a disputed opinion.

“The statement” :    “Gravity is not a force. It is a space/time  curvature.”

The first time I met “the statement” I was like; “What?” ... So, it served it’s purpose.

I tried to imbrace it. Think in new ways. I never seemed to quite get it. For this reason, or that reason. Depending on the opinion, and how  rhetorically gifted  the person whom I was in conversation with was... But then, the other day while reading another thread I saw the statement venture into the  conversation. It pricked my annoyance, and I started thinking about it to consider why, besides the fact my being the lesser rhetorically then most, does “The Statement” bother me so much?

I think I figured it out, and now I’m afraid I can’t do the thought justice. The thought is, “What’s the difference?

Consider Newtons First Law. What is the exception?... Force!  What is the effect?.... Acceleration....

Now, consider “the statement”. And....

What happens to an object following  Newton’s First Law when it incounters space/time curvature?.... Acceleration?.... Hmm....

I have tried my best to take the stunting sting out of the end all of all conversation,  but of course if someone would like to tell me what the difference is. Please do.

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A freefalling person accelerates yet feels no force, therefore, it follows gravity is not a force; it''s curved spacetime. Don''t get hung up about not understanding it, scientists have been trying to nail it down for a long time without complete success; it still wont tie in nicely with the other forces.

Edited by StringJunky

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1 hour ago, StringJunky said:

A freefalling person accelerates yet feels no force, therefore, it follows gravity is not a force; it''s curved spacetime. Don''t get hung up about not understanding it, scientists have been trying to nail it down for a long time without complete success; it still wont tie in nicely with the other forces.

you have to feel the force....

So, I have to feel the force, or it is not a real force? Hmm. That concept seems  awfully familiar...I’m not hung up on it but have become curious. Is there a discrptive that defines what is taking place in Newton’s first law before the exception occurs and acceleration begins. I have been looking for an existing formula that might define what I’m thinking. I’m sure one exist. Wanting to examine energy values. Why? I don’t know, but I will admit I might be hung up on that.

Let me think a minute. I’m a standing passenger on a bus the bus suddenly swerves. I have to brace myself. Which way do I brace. I didn’t feel the fictitious force until the swerve,but there will be an uncomfortable energy encounter if I don’t brace. If I don’t  brace work is being done, okay even if I do brace work is being done. If I remember correctly that requires force, and might even be the formula I’m thinking of.

Hmm? It sure seems sometimes like people are saying that until and unless you feel a force nothing is happening?

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4 minutes ago, jajrussel said:

Is there a discrptive that defines what is taking place in Newton’s first law before the exception occurs and acceleration begins.

I'm not forcing the chair down its forcing me up.

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24 minutes ago, dimreepr said:

I'm not forcing the chair down its forcing me up.

Lol... I have to admit that as far as numbers go my mass might be unimpressive to the unknowing, but it is being accelerated toward center mass at a rate resulting in a weight of 212 pounds on the scale I use. Still, I would like to point out that I don’t usually have to force my chairs down. They do, usually hold me up except for once not too long ago, and believe me I knew I was falling. I will admit I didn’t feel anything other than the release until my butt made contact with the ground. My first thought was  I hope the neighbors didn’t see... there was no time to be graceful. It was go, plop. Just about as fast as you can say it. Go, plop.

Hmm,  it doesn’t seem very economical to by chairs you have to force down...

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6 minutes ago, jajrussel said:

Lol... I have to admit that as far as numbers go my mass might be unimpressive to the unknowing, but it is being accelerated toward center mass at a rate resulting in a weight of 212 pounds on the scale I use.

1 hour ago, jajrussel said:

before the exception occurs and acceleration begins.

the potential difference is weighing me down.

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5 hours ago, jajrussel said:

I have always considered gravity to be a force. Then the end all of all conversation came along.

Okay,I kind of gave it that name because it seems to me that when I see it used it is generally ment to stump, or end a disputed opinion.

“The statement” :    “Gravity is not a force. It is a space/time  curvature.”

The first time I met “the statement” I was like; “What?” ... So, it served it’s purpose.

I tried to imbrace it. Think in new ways. I never seemed to quite get it. For this reason, or that reason. Depending on the opinion, and how  rhetorically gifted  the person whom I was in conversation with was... But then, the other day while reading another thread I saw the statement venture into the  conversation. It pricked my annoyance, and I started thinking about it to consider why, besides the fact my being the lesser rhetorically then most, does “The Statement” bother me so much?

I think I figured it out, and now I’m afraid I can’t do the thought justice. The thought is, “What’s the difference?

Consider Newtons First Law. What is the exception?... Force!  What is the effect?.... Acceleration....

Now, consider “the statement”. And....

What happens to an object following  Newton’s First Law when it incounters space/time curvature?.... Acceleration?.... Hmm....

I have tried my best to take the stunting sting out of the end all of all conversation,  but of course if someone would like to tell me what the difference is. Please do.

We have discovered that Newtonian physics is not the ultimate description of the universe. So if you view it through a Newtonian lens, then there will be some difficulties.

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5 minutes ago, swansont said:

We have discovered that Newtonian physics is not the ultimate description of the universe. So if you view it through a Newtonian lens, then there will be some difficulties.

if it walks like a duck it might be a swan.

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Posted (edited)

It may help to consider that force is any interaction that unopposed causes an inertia change. (acceleration). Then consider that the metric of relativity is one of freefall (unaccelerated state). This may seem arbitrary but all physics definitions must apply accurately to its underlying mathematics. So under relativity the freefall state has no acceleration and under mathematics this entails that there is no force involved. f=0 under f=ma applications of the metrics of GR. When you have acceleration become involved you then involve "Rapidity". of the field equations of GR. Which involves other tensors.

The trick to understand is that GR applies the term spacetime as opposed to a separation of space and time as per Newtonian physics. When you seriously apply the definitions of force and the laws of inertia under a spacetime metric the way of thinking of how force is involved becomes tricky unless you take a close look at how the equations are being applied under both Newtonian and GR. The distinction lies in the mathematics of the geometry metrics. Newtonian being 3d while GR is 4D.

Hint the baseline geometry state under GR has all objects in freefall, so no acceleration. Thus no force is involved. This is literally the reasoning behind the statement gravity isn't a force but a result of variations in spacetime curvature. The baseline metric (metric tensor) of GR has no gravity itself as it is modelling the geometry of spacetime. Changes to the geometry is seen as gravity by this argument gravity is merely an observed effect of the spacetime variations. How one observes that effect involves the spacetime conditions of each different observer. Hence you have different mass values depending on which observer is measuring the mass of the event (object being measured). This in turn means each observer could measure different quantities for the mass term under f=ma. So treating all events in freefall state becomes a simplification where the geometry spacetime changes accounting for the different observers measuring the same said events

Edited by Mordred

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Posted (edited)
33 minutes ago, Mordred said:

It may help to consider that force is any interaction that unopposed causes an inertia change. (acceleration). Then consider that the metric of relativity is one of freefall (unaccelerated state). This may seem arbitrary but all physics definitions must apply accurately to its underlying mathematics. So under relativity the freefall state has no acceleration and under mathematics this entails that there is no force involved. f=0 under f=ma applications of the metrics of GR. When you have acceleration become involved you then involve "Rapidity". of the field equations of GR. Which involves other tensors.

The trick to understand is that GR applies the term spacetime as opposed to a separation of space and time as per Newtonian physics. When you seriously apply the definitions of force and the laws of inertia under a spacetime metric the way of thinking of how force is involved becomes tricky unless you take a close look at how the equations are being applied under both Newtonian and GR. The distinction lies in the mathematics of the geometry metrics. Newtonian being 3d while GR is 4D.

Hint the baseline geometry state under GR has all objects in freefall, so no acceleration. Thus no force is involved. This is literally the reasoning behind the statement gravity isn't a force but a result of variations in spacetime curvature. The baseline metric (metric tensor) of GR has no gravity itself as it is modelling the geometry of spacetime. Changes to the geometry is seen as gravity by this argument gravity is merely an observed effect of the spacetime variations. How one observes that effect involves the spacetime conditions of each different observer. Hence you have different mass values depending on which observer is measuring the mass of the event (object being measured). This in turn means each observer could measure different quantities for the mass term under f=ma. So treating all events in freefall state becomes a simplification where the geometry spacetime changes accounting for the different observers measuring the same said events

If the rate you are freefalling continuously increases with time, how is that not acceleration? Is it not called "acceleration" because an external force has not been applied, and it is a specific word requiring specific conditions to be called acceleration?

Edited by StringJunky

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Posted (edited)
25 minutes ago, StringJunky said:

If the rate you are freefalling continuously increases with time, how is that not acceleration? Is it not called "acceleration" because an external force has not been applied, and it is a specific word requiring specific conditions to be called acceleration?

Careful here. time is part of the spacetime geometry itself, it is more accurate to state that gravitational acceleration  is due to changes of the spacetime geometry. If there is no change in the spacetime geometry then you have no acceleration. A freefall object approaching a planet is being affected by different spacetime conditions at each location as it approaches higher and higher gravitational potentials.

A good visual aid take two parallel lines, in a homogenous and isotropic (uniform spacetime) these parallel lightpaths will remain parallel. However if you then take those lines and have them approach a common centre of mass, this no longer remains the case. The lightpaths no longer remain parallel to each other as the approach the CoM. The spacetime metric is no longer in a homogeneous and isotropic state. (you now require further tensors to show the variations from this state.) (rapidity). Time itself will be seen as varying for each observer as well as mass and the calculated force under the Newtonian treatment for every observer.  In freefall towards the planet the spacetime itself becomes curved. =gravity. Hence gravity is a result of the of curvature.

Edited by Mordred

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1 hour ago, Mordred said:

It may help to consider that force is any interaction that unopposed causes an inertia change. (acceleration). Then consider that the metric of relativity is one of freefall (unaccelerated state). This may seem arbitrary but all physics definitions must apply accurately to its underlying mathematics. So under relativity the freefall state has no acceleration and under mathematics this entails that there is no force involved. f=0 under f=ma applications of the metrics of GR. When you have acceleration become involved you then involve "Rapidity". of the field equations of GR. Which involves other tensors.

The trick to understand is that GR applies the term spacetime as opposed to a separation of space and time as per Newtonian physics. When you seriously apply the definitions of force and the laws of inertia under a spacetime metric the way of thinking of how force is involved becomes tricky unless you take a close look at how the equations are being applied under both Newtonian and GR. The distinction lies in the mathematics of the geometry metrics. Newtonian being 3d while GR is 4D.

Hint the baseline geometry state under GR has all objects in freefall, so no acceleration. Thus no force is involved. This is literally the reasoning behind the statement gravity isn't a force but a result of variations in spacetime curvature. The baseline metric (metric tensor) of GR has no gravity itself as it is modelling the geometry of spacetime. Changes to the geometry is seen as gravity by this argument gravity is merely an observed effect of the spacetime variations. How one observes that effect involves the spacetime conditions of each different observer. Hence you have different mass values depending on which observer is measuring the mass of the event (object being measured). This in turn means each observer could measure different quantities for the mass term under f=ma. So treating all events in freefall state becomes a simplification where the geometry spacetime changes accounting for the different observers measuring the same said events

Lots of insight there to ponder +1

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Posted (edited)

My thanks, this will help those that have some understanding of the field equations. Though it may be too advanced for the OP. If you have no stress tensor where $T_{\mu\nu}$=0, then you have no curvature term. All light paths will remain parallel and there will be no acceleration (changes in magnitude or direction). Curvature due to mass or acceleration are defined by changes to the stress tensor. This in turn results in changes to the lightpaths that follow the spacetime paths.

Edited by Mordred

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On 1/5/2019 at 2:27 PM, Mordred said:

It may help to consider that force is any interaction that unopposed causes an inertia change. (acceleration). Then consider that the metric of relativity is one of freefall (unaccelerated state). This may seem arbitrary but all physics definitions must apply accurately to its underlying mathematics. So under relativity the freefall state has no acceleration and under mathematics this entails that there is no force involved. f=0 under f=ma applications of the metrics of GR. When you have acceleration become involved you then involve "Rapidity". of the field equations of GR. Which involves other tensors.

The trick to understand is that GR applies the term spacetime as opposed to a separation of space and time as per Newtonian physics. When you seriously apply the definitions of force and the laws of inertia under a spacetime metric the way of thinking of how force is involved becomes tricky unless you take a close look at how the equations are being applied under both Newtonian and GR. The distinction lies in the mathematics of the geometry metrics. Newtonian being 3d while GR is 4D.

Hint the baseline geometry state under GR has all objects in freefall, so no acceleration. Thus no force is involved. This is literally the reasoning behind the statement gravity isn't a force but a result of variations in spacetime curvature. The baseline metric (metric tensor) of GR has no gravity itself as it is modelling the geometry of spacetime. Changes to the geometry is seen as gravity by this argument gravity is merely an observed effect of the spacetime variations. How one observes that effect involves the spacetime conditions of each different observer. Hence you have different mass values depending on which observer is measuring the mass of the event (object being measured). This in turn means each observer could measure different quantities for the mass term under f=ma. So treating all events in freefall state becomes a simplification where the geometry spacetime changes accounting for the different observers measuring the same said events

I have a couple of questions about this.  I'm understanding that forces come in pairs, or in other words that there isn't a positive charge without a negative charge, and so forth.  I have seen some information on zero-point energy and I'm wondering if this has anything to do with what you're talking about when you mention an interaction that is unopposed.  I've always thought about this in a different context, such as comparing the charge of the substrate to the charge of the electrons and holes in a semiconductior.  I don' t think that this is what you mean, and I wonder if you can provide some more information on how the calculus is done.

Also, what is the difference between what you're saying about "Rapidity" and what another member might say about a "Pet Theory" where direction is a quantity?  It sure does sound similar, if it isn't the same thing exactly.   What is this "Rapidity" made from?  I would assume that since it is expressed as a hyperbolic, that it's related somehow to the concept of "orthogonality" that we have always used to distinguish Newtonian 3D from GR 4D.  I think that if I could understand exactly what you mean in this post that it would go a long way towards showing why a certain "Pet Theory" is somehow incorrect.

Also, how is "freefall" defined mathematically?  What physical quantities (or if we're using dimensional analysis, what dimensions) is it made from?  These are the questions that I have a lot of difficulty understanding.  I think that the "Pet Theory" resolves or answers these questions in a very solid way, mathematically speaking.  I think that the "Pet Theory" shows that the geometry of spacetime is not treated correctly when we use the traditional methods for modeling the Newtonian 3D component.  It seems to be the right approach, it just seems to me to be incorrect due to the inability to specify "what" is being modeled differently when we add "Rapidity" to the model.  It changes something, but do you know what it is that is being changed?  Can you describe what this thing is that is different after we add "Rapidity," and can you say why it is something other than a difference in direction?

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Proper acceleration (the acceleration 'felt' by the object being accelerated) is the rate of change of rapidity with respect to proper time (time as measured by the object undergoing acceleration itself). Therefore, the rapidity of an object in a given frame can be viewed simply as the velocity of that object as would be calculated non-relativistically by an inertial guidance system on board the object itself if it accelerated from rest in that frame to its given speed.

see this link for the above on Rapidity

When you define freefall it is a state of constant inertia as per Newton's laws of inertia. ie f=ma lol. In GR all frames of reference are inertial frames even the rest frame in SR. This is one of the distinctions between SR and GR. Every coordinate location in GR is an event and all events are a frame of reference which is an inertial frame. In a state of constant inertia no force is applied so if every reference frame is in constant inertia there is no force

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From the wiki:

" Mathematically, rapidity can be defined as the hyperbolic angle that differentiates two frames of reference in relative motion, each frame being associated with distance and time coordinates."

It looks to me as if we have time and distance twice (in two frames) and that they relate to one another by a direction (hyperbolic angle.)  I'm wondering what evidence there is that this direction is the correct direction.  I don't think that it's possible to express the correct direction using a tensor at all.  By axiomatic definition these things have to be perpendicular to one another, and we know that they aren't or else everything would be just like it is in Newtonian space.  Right?  How do you think this gets worked out in the model?  It really seems to me as if the rapidity is something real, except that it can only be used to express relationships in a single direction.  In other words, it's useless for modeling relativistic Doppler effect.  The geometry is wrong (not really wrong, it is correct, it's just that it isn't what people think it is) for this purpose.  Another type of geometry will be necessary to make a more accurate mathematical representation.

Understand that the math and geometry that I'm referring to is based in the same Euclidean 3-space that is familiar to everyone, except that it uses a different metric.

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Posted (edited)

There is a simplified example showing the Minkowskii spacetime diagrams with a brief example of the Hyperbola involved. See the hyperbola in invariance and on

a little side not the twin paradox with the turnaround twin would generate a similar hyperbola the plot would look much like c^2/C^4 if you run through the twin paradox calcs

see 2d plot. The point of the acceleration change in direction lead to the rotation on that plot

edit :{later correction to last post }

-oops I made a mistake to that plot had the powers inverted...the space and time coordinates would fall on the hyperbola

$x^2-c^2\tau^2=\frac{c^4}{g^2}$

Lewis Ryder has how this is derived from the 4 momentum, If requested I can latex in his solution from the Minkowskii line element

$ds^2=\eta_{\mu\nu}dx^{\mu}dx^{\nu}$

Edited by Mordred

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The twin paradox is different in a subtle way that you might not see.  In Minkowski space we're traveling along a geodesic, while in the twin thought experiment one or both of the twins must make at least one complete turn.

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Posted (edited)

yes however rapidity includes acceleration change. The acceleration change from constant velocity for the travelling twin will generate a hyperbolic rotation on the spacetime diagram.

side note once you accelerate you are following a different geodesics. I won't go into great detail on how this rotation is shown on the Minkowskii tensor but simply state that the tensor undergoes a rotation.

Edited by Mordred

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16 hours ago, steveupson said:

I have a couple of questions about this.  I'm understanding that forces come in pairs, or in other words that there isn't a positive charge without a negative charge, and so forth.

Those are actually separate concepts. Mass only attracts (there is no positive and negative mass) and yet you still have Newtonian force pairs.

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9 hours ago, steveupson said:

From the wiki:

" Mathematically, rapidity can be defined as the hyperbolic angle that differentiates two frames of reference in relative motion, each frame being associated with distance and time coordinates."

It looks to me as if we have time and distance twice (in two frames) and that they relate to one another by a direction (hyperbolic angle.)  I'm wondering what evidence there is that this direction is the correct direction.  I don't think that it's possible to express the correct direction using a tensor at all.  By axiomatic definition these things have to be perpendicular to one another, and we know that they aren't or else everything would be just like it is in Newtonian space.  Right?  How do you think this gets worked out in the model?  It really seems to me as if the rapidity is something real, except that it can only be used to express relationships in a single direction.  In other words, it's useless for modeling relativistic Doppler effect.  The geometry is wrong (not really wrong, it is correct, it's just that it isn't what people think it is) for this purpose.  Another type of geometry will be necessary to make a more accurate mathematical representation.

Understand that the math and geometry that I'm referring to is based in the same Euclidean 3-space that is familiar to everyone, except that it uses a different metric.

OK as so often happens Wiki gets bogged down in detail.

Here is an untangled version.

Formally the rapidity alpha is a quantity associated with and derived from a velocity V.

$\alpha = {\tanh ^{ - 1}}\left( {\frac{V}{c}} \right)$

Note this is an observed or apparent velocity, not a relative velocity.

As you observed this is the so called hyperbolic tangent.

The justification of this term is that it give an easy way (formula) to compose (add) velocities to find their resultant.

For two velocities V and U the vector addition yields

$W = \frac{{U + V}}{{1 + \frac{{UV}}{{{c^2}}}}}$

However we may simply add the rapidities thus

${\alpha _W} = {\alpha _U} + {\alpha _V}$

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2 hours ago, swansont said:

Those are actually separate concepts. Mass only attracts (there is no positive and negative mass) and yet you still have Newtonian force pairs.

You lost me.  The OP begins "I have always considered gravity to be a force..."  You seem to be saying the same thing, that mass is an attractive force.  I don't think that is correct, although I do agree that electromagnetic force and mechanical force are not the same.  A better argument might be that, because of the way the calculus is done (the way that our derived units are calculated), gravity is more akin to acceleration, as expressed by the Equivalence_principle.

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Just now, steveupson said:

You lost me.  The OP begins "I have always considered gravity to be a force..."  You seem to be saying the same thing, that mass is an attractive force.  I don't think that is correct, although I do agree that electromagnetic force and mechanical force are not the same.  A better argument might be that, because of the way the calculus is done (the way that our derived units are calculated), gravity is more akin to acceleration, as expressed by the Equivalence_principle.

Having a + and - charge has nothing to with forces coming in pairs, and vice-versa.

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9 minutes ago, studiot said:

OK as so often happens Wiki gets bogged down in detail.

Here is an untangled version....

Nice, that makes a lot of sense.  It deals with the difference in velocity as if both frames are either moving at different speeds in the same direction, or different speeds in the opposite direction.  It doesn't really accommodate for situations where the frames are moving at different speeds in different directions, which is the same issue that you run into with the relativistic Doppler model.

8 minutes ago, swansont said:

Having a + and - charge has nothing to with forces coming in pairs, and vice-versa.

haha, this IS fun.

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On 12/29/2018 at 3:57 PM, StringJunky said:

A freefalling person accelerates yet feels no force, therefore, it follows gravity is not a force; it''s curved spacetime. Don''t get hung up about not understanding it, scientists have been trying to nail it down for a long time without complete success; it still wont tie in nicely with the other forces.

Freefalling person feels force of stretching because lower part of body tryes to fall faster, also length of body tryes to stretch it at acceleration like in Bell's spaceship experiment.