# Modifying Newton's First Law of Motion

This has no meaning.
There is nothing like "all other forces" in GR. GR is a theory of gravity, curvature of spacetime. There is no treatment of EM "in GR".
Have you ever heard of the electromagnetic tensor?

Electromagnetism cannot also be defined as curvature of something...
I agree, and I made no such claim.

exchemist:

Four-vectors in GR are objects that transform in a particular way (using the Lorentz transformations) when you change reference frames. They are constructed so as to maintain the form of familiar definitions of quantities like $\vec{p}=m\vec{v}$. To run with the example of momentum, the problem is that the Newtonian 3-momentum is not conserved in collisions when you change reference frames. Therefore, we need to find some kind of similar quantity that is properly conserved when we change frames. What we end up with is 4-momentum, which happens to be $(c, v_x, v_y, v_z)$.

4-force is defined as $\bf{F}=\frac{d\bf{P}}{d\tau}$, that is the rate of change of the 4-momentum with respect to the proper time. In GR, the derivative is actually a covariant derivative.
Exactly. So the concept of force still exists in GR, but the Newtonian concept of it has to be changed, to allow for the fact that velocities (and therefore momenta and kinetic energies) are frame-dependent. Is that right?

Exactly. So the concept of force still exists in GR, but the Newtonian concept of it has to be changed, to allow for the fact that velocities (and therefore momenta and kinetic energies) are frame-dependent. Is that right?
Well, velocities are obviously frame dependent even in Newtonian/Galilean relativity.

But, yes, in relativity (special or general), it is most useful to work with quantities that are not frame dependent, wherever possible. That's why we use rest mass rather than relativistic mass, and why most time-dependent quantities are expressed in terms of proper time rather than in terms of some other random time variable.

One more thing about force (and I warn that I'm by no means an expert on this): it turns out that the spatial direction of the acceleration of an object is not always the same as the spatial direction of the net force, even in special relativity. To describe that, we need something more general than the three-dimensional $\vec{F}=m\vec{a}$. Hence 4-force.

Have you ever heard of the electromagnetic tensor?

I agree, and I made no such claim.

So if your understanding is that just because some qty in electromagnetism can be expressed in tensor form, it is in GR. Pl note that tensor like scalar and vector is a math tool, GR does not have copyrights over it. And by the way fluid mechanics also has tensors, so that is also 'in GR'. Yeah?

So if your understanding is that just because some qty in electromagnetism can be expressed in tensor form, it is in GR.
Correct.

Pl note that tensor like scalar and vector is a math tool, GR does not have copyrights over it.
Thanks for letting me know.

And by the way fluid mechanics also has tensors, so that is also 'in GR'. Yeah?
That's right. GR can cope with fluid mechanics.

Can it be said that GR "sub contracts" areas of physics to EM and shows up to arrange the overall configuration subsequently?

Well, velocities are obviously frame dependent even in Newtonian/Galilean relativity.

But, yes, in relativity (special or general), it is most useful to work with quantities that are not frame dependent, wherever possible. That's why we use rest mass rather than relativistic mass, and why most time-dependent quantities are expressed in terms of proper time rather than in terms of some other random time variable.

One more thing about force (and I warn that I'm by no means an expert on this): it turns out that the spatial direction of the acceleration of an object is not always the same as the spatial direction of the net force, even in special relativity. To describe that, we need something more general than the three-dimensional $\vec{F}=m\vec{a}$. Hence 4-force.
Yes indeed, of course. Is this something to do with the apparent rotation of an object moving fast relative to an observer?

Exactly. So the concept of force still exists in GR, but the Newtonian concept of it has to be changed, to allow for the fact that velocities (and therefore momenta and kinetic energies) are frame-dependent. Is that right?
It seems you have a choice of how to work GR, force or curved spacetime...Remember these:

Force is a term of art.
In a geometrical theory about the manifold of space time, there can be no gravitational forces. Particles travel along the straightest possible lines for such a manifold, the geodesics.

In an algebraic description of the same physical theory in terms of a specific set of generally applicable coordinates will have particles undergoing non-zero coordinate accelerations and by Newton's definition, $$\vec{F} = m \vec{a}$$, this is a force.

Two descriptions of the motion of the same particle in the same theory, so which one is correct? Whichever best conveys what you are choosing to teach.

In the geometrical picture, there are no gravitational forces.
For the algebra in a cartesian coordinate system, there are ("fictitious") gravitational forces because the partial derivatives in cartesian coordinates are not geometrically informed. Same physics, different pictures, different derivatives, different definitions of time and acceleration and force.

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Correct.

Thanks for letting me know.

That's right. GR can cope with fluid mechanics.

So James R says anything which can be mathematically expressed in Tensor form is "in GR".

And he also feels that GR can cope with fluid mechanics?

James R, it is apparent that few impressionable members follow you blindly, so you have a higher responsibility, please do not misteach. Seek help from those who know that there need not be any correlation between areas of physics (which require tensors for mathematical formulation) with GR.

Can it be said that GR "sub contracts" areas of physics to EM and shows up to arrange the overall configuration subsequently?

you can make kind of that statement for Kaluza Klein theory, but not for GR.

you can make kind of that statement for Kaluza Klein theory, but not for GR

Not wishing (or being able) to be argumentative but just to dig a little deeper perhaps into my layers of ignorance, some EM effects do seem (on the surface and to my level of understanding ) to be subsumed into the spacetime curvature model (ie GR?) .

eg A ray of light is subject to a gravitational field . Are there other (macro) EM or other manifestations that are not subject to GR in the same way?

Again ,referring to my "second hand" understanding of this topic I was under the impression that GR only broke down in situations described as "singularities".

Maybe that was what you were getting at with the point you made about the KK model (which I am not familiar with) ?

The God:

So James R says anything which can be mathematically expressed in Tensor form is "in GR".
GR is a model of space and time. Almost everything else we know about physics can sit happily in that model. There are some residual issues with the merger of quantum physics and GR, of course, but that's another topic.

Put it this way: the rest of physics works OK in the Newtonian world of absolute time and space, most of the time. It works even better in the Einsteinian world of GR, because GR is a more accurate model of time and space. This is not to say that GR is the perfect or final model.

And he also feels that GR can cope with fluid mechanics?
Of course. What's special about fluid mechanics that means it no longer works in curved spacetime? Do you think it doesn't work or can't be formulated against a GR background? On what possible basis?

James R, it is apparent that few impressionable members follow you blindly, so you have a higher responsibility, please do not misteach.
Get off your high horse and make an argument, if you have one. Empty criticism is pointless. It's like you're just trying to pick a fight with me for no reason other than your own amusement. Grow up.

Seek help from those who know that there need not be any correlation between areas of physics (which require tensors for mathematical formulation) with GR.
From you, you mean? What help have you to give? All you provide is empty criticism. I await your "help".

The realm of relativistic hydrodynamics
Hydrodynamics or fluid dynamics is the study of the behaviour of fluids such as water and air - water flowing down a canal, but also, for instance, air flowing around an airplane fuselage. The term relativistic hydrodynamics (or relativistic fluid dynamics) refers to the study of flows in the arena of special or of general relativity. Special relativity will come into play when the velocities attained by certain portions of the fluid or by the fluid as a whole approach the speed of light. General relativity comes into play when there are sufficiently strong gravitational fields - either because the fluid's environment features such fields, or because the mass and energy of the fluid are sufficient to generate their own strong gravity.

http://www.einstein-online.info/spotlights/hydrodynamics_realm

It seems that The God has abandoned this thread. Or, more accurately, run away.

hansda:

Yes. In GR there is no force of gravity, so you just add the effects of the other three forces together and determine the resulting motion against the background of the local spacetime.

When three other forces are added vectorially for the resultant force, time is considered as it is considered in Newtonian Model. If this resultant force is considered against the background of local spacetime, time is simultaneously considered as in Newtonian Model and as in spacetime. Do you think, physics can be done this way, with two different models of time?

No. The reaction force to the electromagnetic force of the chair pushing up on your body is not a gravitational force - it is the electromagnetic force of your body pushing down on the chair. Action and reaction forces always act on two different objects. The force on your body due to the chair cannot be a reaction to the gravitational force on your body, because both forces are acting on your body. That is true even in Newtonian physics.

My point is that we never feel "weight", as such, even in Newtonian physics. We only feel those "reaction" forces you're talking about.

What we feel as weight is basically the "reaction force" as per Newton's Third Law of Motion.

I have no idea what you mean.

The forces of nature, which are yet to be discovered; can be considered as hidden forces of nature.

No, it can't. Take the advance of the perihelion of Mercury, for example. That's quite a famous example of where Newton fails and Einstein succeeds.

Newtonian Model is still considered when satellites are launched.

Newtonian physics cannot explain length contraction. It's an effect of the invariance of the speed of light - a postulate of Einstein's relativity.

Length contraction is real/physical or just an optical effect?

Yes, in principle. And if it was tested, it would be found that no such compressive force exists.

This is only your prediction but not a confirmation.

Do you feel a compressive force on your body right now? You're whirling around the centre of the galaxy at a speed of about 200 kilometers per second as we speak.

Do you imply that length contraction is an optical effect.

Do you feel a compressive force on your body right now? You're whirling around the centre of the galaxy at a speed of about 200 kilometers per second as we speak.

This is only your prediction but not a confirmation.

No! The math does not imply, nor permit, any 'compressive' force. You cannot argue against GR just because you want to, you have to produce a compelling case for reexamination of what has been demonstrated time & again. You cannot say "Well, overall it's a good 'theory' but in this particular case it's wrong..."

hansda:

When three other forces are added vectorially for the resultant force, time is considered as it is considered in Newtonian Model. If this resultant force is considered against the background of local spacetime, time is simultaneously considered as in Newtonian Model and as in spacetime. Do you think, physics can be done this way, with two different models of time?
When you're talking about adding two force vectors at a particular point in space at a particular time, there's no problem with relativistic time effects. They don't come into it.

What we feel as weight is basically the "reaction force" as per Newton's Third Law of Motion.
Yes.

The forces of nature, which are yet to be discovered; can be considered as hidden forces of nature.
We don't seem to need any hidden forces, as things stand. (Having said that, we do have some problems with dark energy etc. that remain open.)

Newtonian Model is still considered when satellites are launched.
Yes. It works well enough for many purposes. That doesn't mean it's 100% correct. It doesn't explain the precession of the equinoxes completely, and it gets the bending of light by gravity wrong, too.

Length contraction is real/physical or just an optical effect?
It's an effect of viewing something from a different frame of reference than the rest frame of the something. I wouldn't exactly describe it as an optical effect, since it's separate from anything to do with the propagation of light from one place to another.

This is only your prediction but not a confirmation.
Correct. But if things turned out differently we'd have to throw out lots of other results from relativity that have been confirmed experimentally.

No! The math does not imply, nor permit, any 'compressive' force. You cannot argue against GR just because you want to, you have to produce a compelling case for reexamination of what has been demonstrated time & again. You cannot say "Well, overall it's a good 'theory' but in this particular case it's wrong..."

Did I say that, GR is wrong?