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

I don't believe you have correctly summarized the two-body problem in GR.

http://en.wikipedia.org/wiki/Two-body_problem_in_general_relativity#Post-Newtonian_expansion

 

Log in or Sign up to hide all adverts.

When using the Schwarzschild solution, in the case of radial motion, the mass of the probe does not intervene in the final solution. The calculations are quite involved but I am certain that I have them correct, here is the final result:

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

where :

\(M\) is the mass of the celestial body
\(r_0\) is the initial radial distance of the test probe
\(s\) is the proper time elapsed between \(r_0\) and \(r\)
You are correct for instances when the Schwarzschild solution does not apply, one needs to use the post-Newtonian approximation. I wouldn't call a binary star a "probe". On the other hand, for baseballs and atoms, the Schwarzschild solution is perfectly applicable and the cited Stanford experiment confirms my statement and my calculations with a precision of 3 parts per billion.

 

Log in or Sign up to hide all adverts.

Correct, I predict that two masses of the EXACT same mass (and the same volume, thus the same density) a distance apart from each other will have no acceleration towards each other. However, I don't claim a negative gravity effect, as if the test mass was actually more massive than the earth, the earth would move towards the test mass. The less massive object ALWAYS orbits the greater massive object (due to gravity being a result of a universal density order of which the object is the most dense at the core, and the least dense at the outer boundary of the object, at every scale.) So, what I am saying with my equation using "L" and "S" is that the "L" is the large mass and the "S" is the small mass. You assuming the earth to always be the "L" is your mistake, or possibly my mistake for not telling you this information before hand, depending on your frame of reference....

 

Log in or Sign up to hide all adverts.

Are you saying that they orbit a point in the preferred frame?

 

Eotvos experiment shows your belief to be false.

 

The Schwarzschild solution is a static vacuum solution. It assumes space time is unchanging and there is nothing exterior to the central mass. Thus, it is a 1-body solution to general relativity, and only an approximate solution when there is matter exterior to the central mass. So, of course, nothing in the Schwarzschild solution implies that the path of a falling body depends on its mass, since the Schwarzschild solution contains the assumption that such a mass is zero. But the Schwarzschild solution is not a summary of the whole of general relativity, so it is premature to claim that GR ignores the mass of the falling object based on just a 1-body solution.

An analogous 1-body solution in Newton's Universal gravitation is the typical expression for the gravitational potential: \(U(r) = -G \frac{M}{r}\) and which totally ignores the effect of the gravity of the mass upon the Earth. Thus 1-body solutions to gravitational theories cannot speak to the question of how collision times vary when the mass of the falling body is significant as they contain the assumption that the mass cannot be significant.

 

The Schwarzschild solution works perfectly for predicting the precession of the perihelion of Mercury (and Venus). Last I checked, neither of their masses was zero.
It also works perfectly in predicting the outcome of the experiment being discussed in this thread.

Agreed, it simply works perfectly for the problem in this thread. It also works for the case of the Sun-Mercury-Venus-... system.

Agreed. But this is NOT what is being discussed in this thread. The masses of the falling bodies are NOT significant, atoms and bowling balls' masses are not significant wrt the Earth mass, so the Schwarzschild solution applies. Besides, your claims are refuted even in the case of the Sun-Mercury-Venus case, the Schwarzschild solution works with great precision, the post-newtonian formalism isn't needed. And certainly, it isn't needed for the situation being discussed in this thread.

 

Evidence like this: http://en.wikipedia.org/wiki/90_Antiope

No. It is a point (a place) in their center-of-mass frame, just like you have zero motion in your center-of-mass frame, and like every ponderable body has a center-of-mass frame. It is not in any sense a "preferred" frame respected by the laws of physics, but the laws of physics are symmetrical which allow us to decompose the motion of a binary system into rectilinear center-of-mass motion and elliptical motion of their separation vector.

The Eötvös experiment seems to better support the notion that the force of gravitation is proportional to the test body (i.e. universality of free fall). I don't think there are any named experiments that speak directly to Motor Daddy's specific delusional belief here, because Newton's shell theorem (which Motor Daddy unwittingly relies upon) also depends on the Universal nature of Universal Gravitation. That is, if Motor Daddy was correct, then Newton's own calculations would have shown it 350 years ago since the moon does not orbit the Earth's center, but the Earth and moon orbit the barycenter of the Earth-moon system. Nor would we have two tides each day, because the bulge of the oceans opposite from the moon is caused by the moon pulling on the body of the Earth more strongly than the most distant waters.
http://en.wikipedia.org/wiki/File:Tide_overview.svg

 

You mean that the torsion measured in the wire is not proof enough that the spheres in the Eotvos experiment attract the test probes?

 

So I take it that no classical physics experiment has been done.

It would be interesing though, I think - even if to dispell any doubt, and the cost would be minimal.

1)I can't say much about this, but it seems to me that a suitable vacuum could be achieved.
2)Maybe you wouldn't have to drop the items from a shelf. Maybe you could have a shelf that rushed away downwards at a far greater speed than the items would start to fall, and then it (the shelf) folded out of the way. Entirely possible IMO.
3) But that's what you would be testing for - the modeled discrepancy.

Now note, I'm not saying there is, will, or should be a difference. I'm just quite bemused that a real, physical, classical physics type experiment hasn't been done (or that there's no info on one being done).

 

False.

 

Hi Tach. I did ask the question earlier a couple of times, and got no response, that's why I said I'll assume no such experiment exists.

Thanks for the link. Though a quick reading seems that it doesn't deal with classical objects (lead ball, marble, etc) but with atomic particles. I could be wrong though, and I've downloaded it to read tomorrow.

 

Forget debating about which mathematical model to use; we understand the physics enough to explain the answer in English: closing time between two masses separated by a given length L shortens if either mass is increased. (If this isn't what Motor Daddy was claiming then I retract my endorsement of his post)

The fact that the time differential may be insignificantly small is itself not significant because we aren't discussing practicality here, we're discussing reality. We do not say, for example, that time dilation doesn't exist only because it's impractical to detect. Technically, time dilation exists at all relative velocities, including when you're walking past someone on the street. Likewise, the closing time between the Earth and a baseball IS different than the closing time between the Earth and an atom, bowling ball, neutron star, etc.

 

In Newtonian formalism, yes. In the applicable GR formalism, no. The disagreement between formalisms is very similar to the disagreements on the light deflection by the Sun and the precession of Mercury's perihelion, the two formalisms predict different results (all measurable). Experiment sides with GR.

This is not what MD's claiming.

 

You say "perfectly" -- I say, within experimental limits. Said experimental limits only test GR within about 1% since the GR prediction of 0.4298 arcseconds per year is swamped by the 0.0070 arcseconds per year of uncertainty in contributions of other planets and 0.0065 arcseconds per year in raw observation.
The effect of using a 2-body solution is less than 0.00002% so this astronomical observation is insensitive to the small effect I was talking about.
\(\frac{M_{\tiny \textrm{Mercury}}}{M_{\odot}} \approx 0.000000166\)
The notes for equation 51 in section 3.5 of http://relativity.livingreviews.org/Articles/lrr-2006-3/fulltext.html use the mass of Mercury, even though the effect is below experimental resolution.

You have no basis for this claim.

To within experimental precision, yes. Even in the case of the Moon-mass versus a baseball, it would be inconceivable of how to maneuver a Moon-mass baseball absolute motionlessness exactly one Earth-radius above the surface with enough precision to measure less than 15 seconds of discrepancy.

Actually, you were the one making wild claims about General Relativity disagreeing entirely with Universal Gravitation. To show that they are the qualitatively the same or different in a two-body problem, you need a two-body methodology. Could you identify specifically what claims you think I made that you have refuted?

The topic of a thread is more than one thing. To pluto2 it may have been about a Tower of Pisa drop where two reasonably objects are dropped side-by-side to see if they hit at the same time. To RJBeery and Motor Daddy it may have been about whether the impact time of arbitrary objects dropped in separate times are theoretically different. To AlphaNumeric and myself it seems to have been about the confrontation of experiment and theory which can't be meaningfully done when the necessary precision is greater than the capabilities of the experimental apparatus. Also for me it was about debunking Motor Daddy's claims about gravity which contradict observation.

For Tach, who introduced a comparison between my Universal Gravitation-based two-body calculations and a particular one-body solution of General Relativity, what was the topic? It can't be about answering a question pluto2 asked since Tach compares his understanding of GR with my calculations from Newtonian theory. It can't be about ignoring irrelevant effects, since GR only differs significantly from the predictions of Newtonian theory when velocities get close to the speed of light, and nowhere do we get velocities higher than escape velocity from Earth. (It takes 8400 years (34800 orbits) for GR to cause Mercury's orbit to shift 1 degree.)

So pluto2's topic is not what Motor Daddy concerned himself with, which I addressed and then moved on to other things, which prompted you to introduce claims about general relativity, which I criticized, causing you to claim I was off-topic. This is special pleading. Please defend your positions like an adult or abandon them in the future.

 

Are you asking if two such objects have been dropped at the same time, as if in a race? Or just whether two such onpbjects have been dropped and the rate they each fall at compared to the limits of our ability to measure?

When I first provided the link to the Stanford article, I thought I was giving an extreme example, of what I thought you were asking.., a comparrison of an atom and a classical object like a baseball.

If all you are asking is if the rate that two objects of different masses and even different sizes have both been measured to fall at the same rate, relative to the earth.., the answer is yes... Again the extreme case of the marble or smaller object is demonstrated by the experiment that underlies the Standford Press Release. For larger objects there have been many many tests. As rpenner mentioned none with a drop of 200 meters, but he did reference a lab with a 142 meter drop in vacuum. It is likely that at some point a simutaneous test of two objects has been conducted, at the lab rpenner referenced, but I have no specific reference for that.

Taken together the results of experiments with everyday masses like baseballs, bowling balls, cannon balls etc. and the experiment referenced in the Stanford Press Release that measured the affect of gravity on a single atom, provide result equivalent to what I thought you were asking, at a far greater accuracy than would be possible dropping an atom and a bowling ball together. In the case of atoms and bowling balls, different methods of measurement are required for the different masses. I believe the Stanford article claimed an accuracy of within 7 billionths of a second, the margin of error for their results.

I don't have a copy of the research paper the Stamdford article references, but I would expect that if it does mention the same agreement that the Press Release does, it would not only describe the methods used for the case of an atom, it would also at least reference experimental tests of larger classical objects.

 

The two masses in the link are not equal. If they were equal and orbited a mutual center of mass then the closing speed between the two objects would be 0 m/s. However, that does not speak as to the motion of that center point in the preferred frame, as two objects of equal mass could have a 0 m/s closing speed, all the while orbiting a more massive object.

 

The two masses in the link are not equal. If they were equal and orbited a mutual center of mass then the closing speed between the two objects would be 0 m/s. However, that does not speak as to the motion of that center point in the preferred frame, as two objects of equal mass could have a 0 m/s closing speed, all the while orbiting a more massive object.

 

What MD doesn't understand is that the above approximation works only for \(M_{\oplus}>>M_A, M_B\) and he inadvertently concludes that there is no attraction for \(M_A=M_B\). It is amazing that he even knows about the formula (though he presented a caricature version of it).

The above approximation is a consequence of \(\sqrt{1+x}=1+x/2\) that is valid ONLY for \(x<<1\)