Why objects with different mass fall with same velocity?

[jainabhs]

Why objects with different mass fall with same velocity??

It is long said and proven that objects with different mass free-fall with same velocity.
Suppose the mass of Earth is M and mass of an object in free fall is m1. As we know Earth's gravitational acceleration constant is g = 9.8m/sec2 so m1 will experience uniform accleration and so uniformly increasing velocity. But here why don't we take acceleration caused by mass m1 (though negligible with respect to earth) into calculation. According to GR, large mass of Earth has caused spacetime to curve in such a way that any free falling object would experience g = 9.8m/sec2. But what about the tiny turbulance in spacetime fabric, caused by free falling mass m1?? I think if we take this negligible acceleration by m1 into calculation then we would get different free falling velocities (Though the difference would again be negligible)for different masses. There is one more reason for this, suppose free falling mass m1 is not tiny but considerably massive with respect to earth, then I think both Earth and mass m1 would follow resultant spacetime curvature caused by both masses and in that case m1 , I think ,will not experience g = 9.8 m/sec2 but something more than this value.

In my description above I have neglected air resistance, gravity is the only acting force.
I may be wrong somewhere in my understanding, please correct me.

Please help.
Thanks in anticipation.
Abhishek Jain

 

[pmb_phy]

But here why don't we take acceleration caused by mass m1 (though negligible with respect to earth) into calculation.

There is no reason why you couldn't. However we don't do that very often becase in practice we take one body as the gravitational source and the other body as a test body whose mass is insignificant to the source. This tells us something about the field generated by the source. For instance a falling person in the Earth's gravitational field is akin to a very very very heavy sphere (600 lbs) sitting on a trampoline. If you rolled a BB onto the trampoline the indentation due to the BB would be negligible for all practicle purposes and thus the shape of trampolines surface would be independant on the fact that there is a BB rolling around somewhere on the trampolines surface. However if there were two heavy and identical spheres sitting on the tramp then each would make a significant change in the shape of the trampolines surface.

If you want to take both masses into account then, in Newtonian gravity, the procedure is outline in my web page at

http://www.geocities.com/physics_world/mech/two_accel.htm

I hope that helps.

Best regards

Pete

 

[MeJennifer]

If you take into account both masses then it is obviously not true that all masses fall at the same speed.

Unfortunately when people talk about general relativity they almost exclusively talk about test masses and ghost observers. It is warranted for calculative purposes. For instance, we can assume that the mass of a rock falling towards the Earth is zero in comparison with the mass of the earth.

But the shadow side is that root principles of general relativity are ignored. Sometimes we don't want to calculate but instead understand, and then it is completely wrong to ignore anything. In fact, everything, particles and observers alike will contribute to the combined field. One can justifiably argue that for instance the Schwartzschild solution is not a solution to the theory of general relavitiy, since the field does not interact with anything so how can we claim something like that in nature could even in principle exist? Saying that something exists but what cannot be measured would obviously be completely non falsifiable, a very bad thing for any scientific theory.

Even if we consider a simple solution with two equal valued non rotating and electrically neutral masses, a solution which cannot even be written down algebraically, we have to admit that we could only demonstrate the equations of motion not the existence of the surrounding field. Since each object that would measure the field would actually contribute to it in a non-linear fashion. The field is holistic and not separable into constituents.

Applying Ockham's razor we could even claim, with some validity, that the field of one single object does not exist. There is only a field between at least two objects.

 

[pmb_phy]

But the shadow side is that root principles of general relativity are ignored.

How so?

Sometimes we don't want to calculate but instead understand, and then it is completely wrong to ignore anything.

That is a personal choice. I like Wheeler's First Moral Principle which is stated in Spacetime Physics - Second Edition, Taylow and Wheeler, page 20 which states

Never make a calculation before you know the answer. Make an estimate before every calculation, try a simple physical argument (symmetry! invariance! conservation!) before every derivation, guess the answer to every paradox or puzzle. Courage: No one else needs to know what the guess is. Therefore make it quickly, by instinct. A right guess reinforces instinct. A wrong guess brings the refreshment of suprise. In either case life as a spacetime expert, however long, is more fun!

I love that quote. One of my favorites in physics!

In fact, everything, particles and observers alike will create Weyl curvature.

Please clarify: What is Weyl Curvature and how is it different from Riemann curvature? Why do you use it rather than Riemann curvature?

One can justifiably argue that for instance the Schwartzschild solution is not a solution to the theory of general relavitiy, since the field does not interact with anything so how can we claim something like that in nature could even in principle exist? It would be completely non falsifiable.

Please elaborate: Since when does the field not interact with anything? Place a large satelite into orbit and it will be neccesary to make corrections on orientation since tidal forces will exert a torque on most objects and thus cause them to rotate out of place.

Applying Ockham's razor we could even claim, with some validity, that the field of one object does not exist. There is only a field between at least two objects.

What evidence do you have that the Earth's gravitational field does not exist? Seems quite certain that its there to me.

Best regards

Pete

 

[yogi]

Applying Ockham's razor we could even claim, with some validity, that the field of one single object does not exist. There is only a field between at least two objects.

That is a very profound notion - I can't think of a way to falsify it

 

[jainabhs]

So according to Pete if I take acceleration caused by free falling small mass into account, the velocity of free falling object would depend on mass m1 too. Hence every free falling object would fall with different velocity(I agree that the difference is very very negligible...)

 

[pmb_phy]

So according to Pete if I take acceleration caused by free falling small mass into account, the velocity of free falling object would depend on mass m1 too. Hence every free falling object would fall with different velocity(I agree that the difference is very very negligible...)

Even in the case where the falling object is a test particle and the source is something like the Earth then all objects will not fall at the same rate. There is another effect wherein the acceleration is a function, not only of position, but also of the velocity of the test body. I.e. the gravitational force is velocity dependant.

Best regards

Pete

 

[russ_watters]

I think if we take this negligible acceleration by m1 into calculation then we would get different free falling velocities (Though the difference would again be negligible)for different masses.

You just answered your own question. If you can't fit the numbers on the screen of a calculator, the effect is probably too small to be worth taking into account.

Certainly, for the interaction of larger bodies, it is not negligible and it is taken into account.

 

[Voltage]

So according to Pete if I take acceleration caused by free falling small mass into account, the velocity of free falling object would depend on mass m1 too. Hence every free falling object would fall with different velocity(I agree that the difference is very very negligible...)

Only if you dropped them separately at different times. If you dropped them together they'd fall at the same rate because collectively they act like a single mass m1 + m2 + m3 etc that exerts a "pull" on the Earth mass M.

 

[pervect]

If you actually want to work this sort of problem out and want to get the right answer, you have to avoid treating the Earth as a point mass. The Earth will not move as a rigid body due to the falling mass - calculations that treat the Earth as a point mass won't get the right answer if one is actually interested in calculating what physically happens.

One will find that the change in the shape of the Earth is in fact the dominant effect for when it hits the ground.

Going back to GR-related points for a bit, the principle of geodesic motion is an approximation. It's a very good approximation, though. The line of thinking above can lead to the Paperpatrou equations, which are still an approximation, but a slightly better approximation than geodesic motion. The Paperpatrou equations, for instance, show that a spinning test body will deviate from geodesic motion due to gravitomagnetic forces.

 

[bernhard.rothenstein]

attraction between two bodies

http://www.geocities.com/physics_wo...tic solution as well? all the best bernhard

 

[pmb_phy]

http://www.geocities.com/physics_world/mech/two_accel.htmDid you present a relativistic solution as well?
all the best
bernhard

No. That seemed to be a very complex problem well outside my current level of expertise. I'd bet that robphy would have some input on solving such a problem. As far as a weak field approximation? I might be able to swing that. I dunno.

Best Regards

Pete