RoR: Forum

I'll start with # 7 (law of free fall). It seems to state the following:

Under equivalent resistance (e.g., wind resistance or "drag"), all bodies fall to earth at the same rate.

Now, if you simultaneously drop things of similar shape, then they should hit the ground at the same time. Of course, there are apparent exceptions. If you drop a ping pong ball and a marble from a high-enough point, then the marble will hit first -- even though they are the same shape. This is because the ping pong ball is so light that air resistance becomes a differentiating factor. In a vacuum (all the air removed), the ping pong ball would fall just as fast as the marble. Indeed, even a feather would fall as fast as a marble. A crucial question is: what did it take for us to discover this law?

One answer is that we needed to empirically witness things dropped inside of a vacuum (to fully neutralize the effects of resistance). Another is that we didn't necessarily need a vacuum -- we could find a way to fully account for resistance, and then subtract it from our raw data. But what about arriving at this law after a full, conceptual understanding of gravity?

Would that work?

If it would work, then would we ever even need to empirically see 2 things dropped simultaneously -- in order to arrive at this law?

Hmmm.

Ed

Post 1

Monday, February 20, 2012 - 8:16pm

Ed:

The thing is that one needn't construct a vacuum to observe the effect. One can drop the two bodies within a very heavy elevator so that each body can experience the same wind resistance, i.e. none, and observe if they hit the bottom of the cage simultaneously.

I propose that for final verification by experiment that the two bodies be one of heavy mass and one of light ... Barney Frank and Nancy Pelosi fluffed up to a similar size as Barney.

Post 2

Monday, February 20, 2012 - 8:35pm

Sam,

You crack me up! :-) It seems that your elevator experiment was invented for no other reason than to effect the calculated demise of Barney Frank and Nancy Pelosi -- two notorious value-vampires.

:-)

Ed

Post 3

Monday, February 20, 2012 - 11:16pm

Ed, you might want to begin with an actual science book before analyzing the validity of Harriman's many claims antecedent to your using Harriman as a study guide. (See the discussions here and on other Objectivist boards.) For instance, the "law of electrolysis" is actually a plural: there are two related laws.

As a question of philosophy, what is the difference between a "law" and a "statement of fact"? The "law" of gaseous diffusion might be an example of an observed fact.

Also, it may be that we still do not have a "full, conceptual understanding of gravity." Einstein might have said that Newton surely did not and Newton might have said the same about Galileo. Yet, Galileo discovered the law of falling bodies. But Galileo arrived at that by beginning with pendulums and from there rolling marbles down inclines. He might never have done the Pisa Experiment. The event is still debated. Moreover, the Greeks had the experiential knowledge to come to the same facts (laws) and it is pointless to argue why they did not.

I know that you chose to focus on "shape" to control for resistance, but dropping a 1-lb. cube of lead and a 10-lb. ball of lead you will see them hit the ground at the "same" time (within accepted limits). The differences in drag would be negligible.

I am not sure how you could gain "a full, conceptual understanding of gravity" without experiencing it. To me, that seems impossible, a rationalist fallacy. And experience it as we do every living moment, that alone does not bring "a full conceptual understanding" of it.

Also, I am not sure of the quantitative relationship (if any) between knowing scientific laws and doing well in life. (In Rational Optimist, which you read, Ridley makes the point that we do not get products by applying science. Science comes from discovering the principles behind the inventions. The inventions come first.) The Romans built aqueducts that functioned for nearly 2000 years specifically because they did not (fully) understand gravity. Simply put, they overbuilt. But this means that much of what we have constructed will not last.

Finally, these are, of course, all from physics (and physical chemistry). Science is broader than this. With your experience and education in health and medicine, are there some other "22 laws"?

Post 4

Tuesday, February 21, 2012 - 6:24pm

Mike,

Ed, you might want to begin with an actual science book ...

I accept that as a piece of advice. No single text, Harriman's or others, stands alone as some kind of a special gateway to truth. In looking at these laws, I will definitely find other sources -- either corroborative or not.

For instance, the "law of electrolysis" is actually a plural: there are two related laws.

Okay, this is a start. Now, I can take this knowledge as a springboard for when I get to that law.

As a question of philosophy, what is the difference between a "law" and a "statement of fact"? The "law" of gaseous diffusion might be an example of an observed fact.

Well, I'd say that a law is some kind of invariance or regularity. That's why I said that discovering a law is like discovering a seam in the fabric of reality. The seam may run on for a while. It may run on forever. It certainly runs farther than the concrete situation witnessed by a single researcher. Statements of fact, alternatively, can be very simple and even subjective. The sentence: "I am hungry." is a statement of fact, but you can't get a law from it.

Also, it may be that we still do not have a "full, conceptual understanding of gravity." Einstein might have ...

I acknowledge your point about conceptual understanding growing, but I should have been more clear. What I meant to ask is: If you knew the formula for gravity:

F = G [m1 x m2] / r^2

... then would you ever need to witness 2 things dropped at the same time in order to arrive at the law of free fall?

I am not sure how you could gain "a full, conceptual understanding of gravity" without experiencing it. To me, that seems impossible, a rationalist fallacy.

Yes, of course. I think you are reading into it a little too much. It's an acceptable fact that before arriving at the law, you would have witnessed free fall. Every human does. But what I was asking is whether you can arrive at the law of free fall without ever witnessing a comparative free fall (2 objects dropped simultaneously).

The inventions come first.

I acknowledge that, too. If someone says science doesn't work, then point to the market -- point to smart phones, ultrathin laptops, and that new taser accessory that cops will soon be getting, which takes an HD movie of each taser victim, or the new "Tesla death-ray" type of gun that cops will soon be getting -- which administers shock right through the air (no wires needed).

With your experience and education in health and medicine, are there some other "22 laws"?

Great question. I will soon start a new thread on that.

:-)

Ed

(Edited by Ed Thompson on 2/21, 6:28pm)

Post 5

Tuesday, February 21, 2012 - 11:17pm

Ed, you will have to get someone who really knows this to explain it, Merlin Jetton or Marty Lewinter, perhaps, or maybe one of the engineers, Fred Bartlett or Luke Setzer... I goto the symphony but I cannot play an instrument; I goto the art museum but I cannot paint. I enjoy physics, but I cannot explain it any better.

I recommend The Feynman Lectures for the full treatment. From that massive three-volme set of lectures - physics is two years at Cal Tech - are now two smaller out-takes, Six Easy Pieces and Six Not-So-Easy Pieces.

(Also, this would go a lot easier with TeX ("tech") a mathematical typesetting system invented by Donald Knuth aboiut 1978 (Wikipedia here) and given free first to the American Mathematical Society and thence to the whole world. It is a language upon which eventually were built HMTL, XML, etc. \bold{If you knew...} Knuth still works on it. At one point, he created a "Punk" typeface for the library...)

If you knew the law of gravity completely, then yes, you could know to expect two bodies of unequal mass to fall at the same rate.

We can show with algebra that Newton's Laws make Kepler's Laws required for a conservative force field.

It is not just F = GMm/r^2, but setting that equal to F = ma and then expressing it in vector notation.
ma = GmM/r^2.
Then express acceleration as the second change over time of distance (or radius or then angle to show it completely). Divide both sides by little m and then multiply both side by r^2 and then by dt^2 so that you have a differential equation r^2 dr = GM dt^2... Solve that... Then do it again for angles just to be complete... And you can be as complicated as you want with unit vectors for rigor...

Anyway, just algebraically, the little m drops out (divide both sides by m) so it does not matter what the different falling masses are. A planet of any size our distance from the Sun would take the same 365.25 days to make an annual orbit, i.e., "equal areas in equal times" or T^2 = k (R^3): the square of the period is proportional to the cube of the radius (semi-major axis). i.e. bodies of different weight fall in the same time.

Similarly, at any distance from the Sun, it does not matter what the mass of a planet is: it will have the same period at that distance. Thus, any falling body will hit the ground at the same time. Celestial mechanics and terrestrial mechanics are One.

It is all integrated and expressed equivalently from different starting points because reality is real and A is A.

The other beautiful demonstration is deriving E=mc^2 from Maxwell's Equations.... (Way beyond my skills. I am just in the audience, clapping....)

And I see by Google that today is Heinrich Hertz's birthday.

(Edited by Michael E. Marotta on 2/22, 6:25am)

Post 6

Wednesday, February 22, 2012 - 9:49am

yes - he and George have something in common... ;-)

Post 7

Friday, August 31, 2012 - 10:59pm

Hello everyone,

Permit me three points to this scientific discussion:

1) Gravity is a universal law not because it's the only factor involved in the calculation of a falling object. Rather, it's a co-efficient in each and every example.

Drag can obviously act as a co-efficient, too. In other words, pennies and quarters are assumed to have the same density and form--hence relatively equal drag--but clearly not so a leaf.

2) Maxwell is a central figure in special relativity as the one who first calculated the speed of light as a constant. This, of course was done in the context of the electromagnetic spectrum.

The Lorenz (Fitzgerald) generalization of electromag spec works its way into the Newtonian modification as F=MA(G), gamma being universal to all mechanics--cv Einstein on Special Relativity.

Coupled with the Planck h as measurable quantities of Energy, algebraic padoodling will yield E=MC^2.

From what we now know, expanding the Planck h into Maxwellian form isn't hard: if E is a discreet quantity of h,and h is convertible into Max's, it follows from Aristotelian identity that Max's = either MA(G) or C^2.

Likewise,the process can be reversed via a five-dimensional representation of General Relativity.

The hard part to understand is why Lorenz should be a coefficient to newtonian mechanics in the first place. Now it's measurably confirmed; in 1905, not.

Lastly, A=A is formal logic. It tells us nothing as to what may really exist. For example, Max's equations do not work on the quantum level.

BH

Post 8

Sunday, September 2, 2012 - 7:51am