Do all objects really fall at the same velocity to the ground in vacuum?

Wait a minute, Tach. Ignoring the fact that you just responded with mathematical models after I said to forget them, are you suggesting that this statement:

"The closing time T between two masses, A and B, separated by length L shortens if either mass is increased"

is false in GR formalism and/or REALITY?!

Mathematical adeptness is not horribly useful if you don't also apply common sense.

 

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Could you stop moving the goalposts and read the OP?

I didn't claim you are off topic. I showed that your claim about the applicability of the 1-body solution to the OP and that you need to post-newtonian formalism in order to address it is WRONG. You are trying to use a jack-hammer to kill an ant.
On a different topic, please lay off the personal attacks, try sticking to the science.

 

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Because you claim so? Experiment says that you are wrong.

I can understand that you can't follow the math but can't you read the simple words describing the experiment?

 

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I was addressing pluto2's post #4, which he stated

and I replied with

I fed him some pseudo.

 

No squirming around Tach. Is the following statement true or false in reality and under GR? Don't confuse yourself with the math, and don't just point to an experimental paper. Use common sense!

"The closing time T between two masses, A and B, separated by length L shortens if either mass is increased"

 

...as in a Natural Philosopher. So you can't follow the math and you can't follow the experimental evidence.

The above shows that you definitely were not able to follow the simple formula:

\(s \sqrt{\frac{2M}{r_0}}=r_0 arctg \sqrt{\frac{r}{r_0-r}}-\sqrt{r(r_0-r)}\)

See that \(M\)? What does it stand for? What is its influence?

 

If you begin with a fixed mass, for the earth and two separate but different masses, the gravitational force is dependent on the total mass, so the acceleration in the closing speed between the earth and the larger mass would be greater. In most classical conditions insignificantly.

If on the other hand you begin with the earth or any other planet and both a marble and a bowling ball resting on the planet.., you then raise each one at a time an equal distance above the earth, the accelerations or closing speeds will be equivalent. In this case the total mass contributing to gravitational field is the same.

In a strong gravitational field the problem becomes more complicated because the objects can no longer be treated as point masses and the gravitational attraction or force is not uniform throughout, each object. An extreme case involving a neutron star or black hole, exagerates the issue. In this case it is not difficult to understand that the force of gravity, on that portion of the onject closest to the center of gravitational mass is greater than it is on that portion away from the gravitational mass.

There is another unspoken aspect of GR which is important to the question in the weak field. The principle of equivalence between inertial and gravitational mass. If one accepts the principle of equivalence.., and it has been demonstrated to be accurate repeatedly, then the inertial resitance to the acceleration of an object by a gravitational field is the same as its inertial resitance to that acceleration and is the same for all objects. The result is the object experiences free fall, and all objects, in vacuum, experience free fall and fall at the same rate.

Again in a strong field, where gravitational forces begin to overcome the electromagnetic and strong forces, the situation changes because the affect of gravitational attraction is not uniform throughout the "falling" object.

 

You didn't answer my question. You're going to get a lesson in the dangers of tossing common sense out the window while memorizing your maths.

"The closing time T between two masses, A and B, separated by length L shortens if either mass is increased"

True or false?

 

This does not sound anything like the original question. I assume that what you are taking about is where the total mass involved is different, when the masses of A and/or B is increased. In that case given a fix distance, yes, the time is shortened.

The original question did not involve a variation in the total mass.., or a strong gravitational field. It involved objects of unequal mass, raised up from and above the surface of the earth and then dropped. The total mass never varies. In vacuum, both objects accelerate equally toward the ground. The difference in mass has no affect on the results.

 

The OP doesn't state whether or not the objects are dropped at the same time. Of course this is a crucial point because Galileo's logic was enough to prove this case:

 

Basically what happens in reality is that the masses are lifted a distance away from the "surface of the earth" (say sea level), which we know all resides inside the total earth when the mass of the atmosphere is accounted for. I said it many times before, we live IN the earth. We live IN the solar system.

...anyway, when you lift those masses a distance away from the surface of the earth the "earth" gets less massive. You have effectively disrupted the density order of the object the earth, because you moved more dense material into a less dense area of the earth when you moved it away from the center of the earth. That disruption in the order creates the "return force" of that mass in order for the density order to once again be restored, where the equilibrium shape of objects in the universe is a sphere, with it's core being the most dense and the outer boundary being the least dense. Disrupt the equilibrium density order and you've created the force of "gravity".

 

When did Galileo ever, conduct his experiment in vacuum?

With everyday objects and the earth, in vacuum, any difference would be beyond any margin of error. Even so, if dropped together their combined affect on the earth, pulls the earth toward them equally. While again their individual inertial restances and the action of the Earth's gravitational influence on each individually, are equal and they both fall at the same rate....

The two falling objects would have some affect on one another but trying to include that in the discussion is just getting too far off into the theoretical... It would be far too small to measure.

 

What does the formula tell you, RJ? Can't you stop trolling for a minute and try reading simple math?

 

OnlyMe aren't you the guy that asked for that bridge problem solution? I have no interest in dealing with you, thanks.

I can read it just fine, but what the formula says is inconsequential; we're discussing reality.

"The closing time T between two masses, A and B, separated by length L shortens if either mass is increased"

True or false? Stop pointing to the work of others and take responsibility by actually stating YOUR opinion.

 

Whose "reality"? Yours, a "Natural Philosopher" who understands neither math nor experiment and replaces them with "common sense"?

The formula I cited IS my work, so it is MY opinion. I could also show the derivation, not that it would matter in your case.
As an aside, it is common practice in mainstream physics to cite the experiments of OTHERS.

 

I think you are confusing the Eötvös experiment which measured the difference of attraction of samples of different compositions to the Earth (or, in repeats, to the Sun) with the Cavendish experiment which measured the attraction of laboratory masses to each other.

See the Figure 1 of Section 2.2.1 of http://relativity.livingreviews.org/Articles/lrr-2006-3/fulltext.html for an illustration of how Eötvös' experiment tested the equivalence principle and how precision has improved over the years.
Of interest to pluto2 and Lakon would be the sentence

See T.M. Niebauer, M.P. McHugh, J.E. Faller "Galilean Test for the Fifth Force" Physical Review Letters 59: 6, pp. 609-612 (1987) http://prl.aps.org/abstract/PRL/v59/i6/p609_1
And H. Dittus1, W. Vodel, R. Greger, St. Lochmann, C. Mehls, H. Koch, S. Nietzsche, J.v. Zameck-Glyscinski "Drop tower tests of the Weak Principle of Equivalence — One step to space missions for gravitational physics" Advances in Space Research 32:7, pp 1301-1305 (2003) http://www.sciencedirect.com/science/article/pii/S027311770390336X
But it's unclear from the abstracts alone if these tested different masses or merely different compositions with the same mass.

Actually, here \(M_A\) and \(M_B\) are, following the disucssion of Motor Daddy and RJ Beery but using Newtonian models instead of Motor Daddy's baseless formula, two separate masses dropped in different runs from the same height with corresponding fall times of \(t_A\) and \(t_B\) respectively. Thus \( t(M) \propto \left( 1 + \frac{M}{M_{\oplus}} \right)^{\tiny -\frac{1}{2}} \approx 1 - \frac{M}{2 M_{\oplus}\) where, as you say, the approximation is only valid when \(M << M_{\oplus}\).

 

Fine, so you believe the statement to be false.

"The closing time T between two masses, A and B, separated by length L shortens if either mass is increased"

Mass A is a baseball, Mass B is the Moon, L is 1 meter. Closing time at 1.62 m/s^2 = 1.111 Seconds
Mass A remains a baseball, Mass B is increased to be the Earth, L is 1 meter. Closing time at 9.8 m/s^2 = .452 Seconds

The statement is true.

Simple garden variety common sense. You can see why I don't really care what formalism you use, we can all picture this in our mind's eye. If you want to keep the physical dimensions (i.e. the radius) of Mass B equal then your time differential will only become exacerbated.

So, Tach, have we just proven GR to be false or is it possible that you modeled the problem poorly?

 

I wonder what happens with two masses, one corresponding to the positive numbers and the other corresponding to the negative numbers, they attract or repel each other? :scratchin:

 

The third option is that you are incapable of comprehending what was said:

Yet, you continue to troll using your "common sense" approach to science, sorry to "natural philosophy".

So, in the formula that I showed you what does M represent, the mass A or the mass B?

 

I have no idea, or perhaps just no recollection of what you are referring to!