Is it defying the law of Archimedes?

I shall also recall the view on Ernst Mach, who has clearly shown that the Newton theory does not define what is a force, in his book :
Die Mechanik in ihrer Entwicklung. Historisch-kritisch dargestellt, 1883.

Of course, he is not the only one that has understood, that the action-reaction principle is only a circular reasonning. Linking the expression of a force with the acceleration and mass is a convenient way for us to give a reasonnable explanation of our experience, as human, in this world.

Modern physics has replaced the notion of force by the notion of field. When you study the tunnel effect in quantum mechanics, or the weak or strong interaction in nuclear reaction, it is not possible to keep up with a simple view of a force being nor a acceleration, nor a vector. It does just simply make no sense. It is not that it is complicated. It has absolutely no meaning at all. This is also the case in chemistry, when studying reactions affinity at molecular level, as Will pointed out.

At this scales, we do not rely on action-reaction principle, but we only keep the principle of energy conservation, having in our results not forces with magnitude and direction, but energy states.

I think very interessant the example of Barry, with a jet of water impacting a ball. In his example, we find all the players that Ernst Mach uses to make his own theory of mechanics, trying to avoid any circular reasonning :
"The inertia of objects is induced by the whole set of the other masses in the universe, and rely on a non-specified interaction." See ? No force at all !!!

Why it is so important to go further the Newtonian conception of force ?
Because, if we had to follow only this theory, which is very well understood by Gonzo and Mitchgrunes, we could only see that it is impossible to defy the Archimedean "force", nor the Gravity "force". Only oppositions can be made. And that is not what is observed, by instance in Bose-Einstein condensat experiences.

I keep the feeling that we can do better at macroscopic scale than we are doing now, if we could just have a brand new and practical theory of what is a force. That's why I like very much talking with you, Guys. Great discussion !

 

This is also my opinion, and besides me being quite nothing in this big Universe, I would like also to add to your comment that, being bound to our common -but practical views, I agree, since I use them almost everyday-, we cannot make any dynamical calculations without prescribing initial conditions. The Big Bang itself being the initial conditions of our current and most shared view in Physics.

Without initial parameters, your boat will not sail, the moon would crash on the earth and we would not exist. Playing with initial conditions to match reality in calculations is not fun at all. It' also quit boring because, stuck with Newton's mathematics, we cannot make the boat sail better.

 

This is a condition of force that is often ignored. Force can be defined, as we like (Force = mass x acceleration), but in the end, it is an expression of the relationship of matter.

My physics professor made the point that the human body isn't a velocity measuring device. We can't feel speed, we feel acceleration. However, even acceleration is only felt when there is a gradient of force across or bodies. We feel the seat pushing on us because our bodies are made up of particle that each has its own state of inertia. If a force were applied equally across all of the particles of our body at once, we couldn't even feel acceleration. When we fall, under only the influence of gravity, for example, the only acceleration we would feel is the removal of the forces that oppose our falling. We can't actually feel the forces of acceleration we experience in free fall, because every particle of our bodies are being acted upon equally.

It requires mass to express force and energy. These two things can't exist on their own because they only describe states of matter relative to a frame of reference. The only state of motion that isn't relative, and even that can be expressed in terms of dimensional relativity, is circular motion. If one were to stand at the rim of a spinning space station, the centripetal force would be felt because circular motion is under constant acceleration. It wouldn't matter if your frame of reference changed to a second ring of the spacestation that was moving in opposite circular motion or to the planet the station was orbiting around, or to the Cosmos as a whole. The acceleration felt would remain the same.

Imagine a two tiered space station of opposite spinning rings. The rings spin to provide an artificial gravity for the crew inside. They walk around on the outer hull of those rings. The rings are kept spinning by turning one ring against the other so they have equal speed in opposite directions. Then, consider the rate of rotation relative to the other ring. Astronaut a in ring q watches astronaut b pass by through a window in ring p at a set rate. Then, imagine a force stops ring q from spinning but allows ring p to continue as per the drive between the two rings. Suddenly, astronaut a is floating without an accelerating force while astronaut b suddenly weights twice as much even though both see an unchanged motion between the two rings. That's a universal motion that doesn't matter what the rest of the universe is doing. You could even spin the whole of the Universe so it looked like the ring was not spinning at all and that centripetal force would remain.

 

This is a curious comment. That the "notion of force" has been replaced by the "notion of field". I would go out on a limb by saying that force is not a "notion" ( by definition a belief). In statics or dynamic analysis, forces are the fundamental basis used to design boats, planes etc. You would not design a wing internal spar without knowing the forces which will act on the wing and hence by calculation the spar or the spar's components. I would suggest that not once in the design of a spar, that an engineer tries to apply calculations of fields to come up with a design.

Forces can easily be measured, pounds, kilograms etc and with any element design are not a "belief" but a quantitative value used to determine stresses which is the fundamental basis of design.

"not being an acceleration" I doubt anyone will suggest that an acceleration is a force. An acceleration of a mass, which can be either an increase in speed or a change in direction, will require an input of force. ( or inversely,
a moving mass will act upon another object, and the object will exhibit forces on it

"nor a vector" Engineers and NA's are most certainly required to evaluate forces as a vector in design work. Ie a simple horizontal beam with a force with a downward direction (vector-- force and direction) can impart stresses within the member with vertical shear, horizontal shear flow, tension and compression stresses while the same beam tipped vertically, (and stabilized vertically) with the same force as above acting vertically downward will mainly create compression stresses. In a complex structure/beam/ member/sheet, external forces can be applied from various directions. As a magnitude and a direction define a vector, the analysis of these force vectors are required for the design of the element

" It does just no simply make no sense"
So the question is to whom/who does it not make sense to.

I would be interested in how you would design a beam to meet a certain requirement using a "field notion"

 

Here it is !!!

Sorry to keep on and on this the word "notion", Barry. To me, it is an important wording that I use to accept that any formula that I use are bound to be replaced in the future ( it contains also my hope that they will be ). Today's knowledge will be considered as ignorance by those who will follow us, as it has always been the case in science. It is just the way it goes, we cannot do much about it, it's just a matter of time !

Beam, stringers, spars, arches, sheets,... You talk only about classical mechanics, when I speak about modern physics.... It is a good thing that our civilization has not waited Newton for building such structures, that you can find in very ancient monuments built some thousands of year before Christ !!! Can you show me the force vector on a electron in a PNP junction, in return to this document ????

The mathematics of Hamilton are very interesting. Besides giving you, hopefully, an answer to your question, about what looks like a field applied on classical mechanics, these mathematics applied to the Newtonian gravity were also the start for Einstein to transcend the notion of force. If you are interested, I could show you that, also.

 

I'm way out of my depth here - but didn't Einstein also transcend the idea of a gravitational field, at least with respect to gravity? I.E., space time curvature made the explicit use of gravitational forces AND gravitational fields unnecessary, because they could be subsumed into geometry.

Anyway, imagine trying to model fluid dynamics around a boat using the motions of every particle and field - or rather than wave function that subsumes the complex probability fields of every particle and field. Now bring in quantum field theory, with particles and perhaps entire realities popping in and out of existence, together with the idea that the wave function is a set of complex probabilities associated with an infinite number of different realities, and you wind up with something that cannot be calculated by a finite machine, and cannot even be well estimated by a practical current day computer.

I won't even try to understand the additions to this overwhelming complexity created by the constantly shifting and competing theories of cosmology, some of which change virtually everything that old style relativity and quantum physics assumed. E.g., can an infinitesimal diameter cosmic string be modeled using fields in a higher dimensional space? I have no idea.

So you use crude approximate fluid equations built on continuous differentiable density and velocity fields, without reference to underlying complexities, but there are also forces in those equations. Then you test those models, and use real world data to refine the approximate models, and repeat for as many iterations as you are funded to do. In other words, for practical calculation purposes, forces ARE real.

In the real world, physicists - and I presume engineers - use force calculations a lot. Almost everything you do is an approximation, and trying to develop a field theory for something that is only approximately understood and imperfectly measured is pretty hard, both for practical calculations, and on a theoretical basis. Not only that, but at normal speeds, in many normal conditions, Newton's laws often work at least as well as many of the other approximations being used. While I'm not an engineer, I'm pretty sure you don't need relativity, quantum mechanics, or cosmology, to design a boat.

BTW, the human body can feel the force of winds created by velocity relative to the air. So for all practical purposes, we often know we are moving relative to the air. We ARE velocity sensing devices.

 

Einstein considered gravity an acceleration and not a force.
When we feel a force from the wind, it is because of acceleration. The air molecules are displaced, so there is a change of direction and velocity (acceleration). We are not velocity sensing devices. If we move at the same velocity as the air, we feel nothing.

 

Well, over time we might get a little tired, right?

 

That's pretty right, Mitchgrunes, for what I understand of what you are saying. Terms, definitions and meanings are sometimes so hard to share. I had the pleasure to discover this very simple explanations of the gravity, which may surprise some of us, but is absolutly true, from a mathematical point of view, at least.

There is indeed some very hard difficulties arising when trying to find an "unified theory". The greatest brains of our planets are still burning their neurons at this task, with discutable results. The "decoherence" of the wave functions at big scale makes us prefer, in general, rely on local and practical classical formulas to calculate the wave drag created by a boat when moving on the sea. It is far more efficient than trying to use any field, for now. However, one must note that the difficulty does not lie in the existence of infinite states, especially with probabilities. That is why Planck, Bose, Dirac, have generalized the use of probabilites in what is called the statistical physics, in order to calculate, when possible, macroscopic states of matter with very great success. The energy of every molecule in every mole of a gas (6,022.10^23 molecule per mole - Avogadro number -) in an isolate chamber allows us to calculate the Temperature from the black body radiation. The integration of the energy emitted by every atom allows us to calculate the shape of the beam and the total energy delivered by a LASER. These are examples of what we can do with integration over infinity in probabilies, because, in some cases, the sum of all probabilites is finite. That can be easily seen in the Gaussian integral, for instance :



What can we gain, in making efforts into this field theory ? In the case where its use is the more profitable, in my opinion, you get, as a result, an complete overview of all the results that can be obtained by a system responding to a given cause. This overview is very interessant, because it gives you the choice to find which result is the most releveant to your own case. It also gives you also the faculty to justify that the result you have selected is indeed the most appropriate in your case. Optimisations loops are unnecessary, which is a very great gain of time, because you are are sure that the result you have selected is the best fitted to your own case, instead of results obtained by optimisation in non linear systems, which can skip local minima or maxima, regarding the parameters that you used. A very good example is the Poincarré phase diagram of a billiard, showing you all the possible trajectories of the ball. With this kind of representation, you also gain a verification of your system itself, because if the billiard exhibits some deformations, the phase diagram is affected. It is, intuitively, what you do yourself when trying to estimate if a dice is fake, by looking at the occurence of every number.


(left) Poincarré section of an undeformed billiard ( right) Poincarré section of a deformed billiard


I would rather accept the difficulty of the field theory, if I can gain insights that allow me to better make my job. It certainly lacks, for now, a practical method that we could use to make better boat, and I find it very sad, because, despite our classical or modern theories in naval architecture, I'm not sure that we would come to a very different design of the Kufuh ship, relative to the constraints they had when designing and building such a boat, more that 4000 years from now. I work with some naval architects that do not use but simple formulas to design their boats. Some of them simply do not use formulas at all. Why ? Because the repetition gives the experience and the experience gives the confidence. Drawings of the french frigate the Hermione, re-built in La Rochelle, where I live, where established, at the time, in the XVIII century, by multiplying the rigging diameter by coefficients to obtain the thickness of every planks. As the desired lifetime of these boats was kind of small, the design phase must have been very quick. They were originally designed to last no more than 4 years. (War is War)


Kufuh Ship, in Cairo Museum


Hermione (2014), replica of a french frigate 1779 Hermione


The drawback of applying always the same principle is that you always come with the same results. Sometimes it's good, sometimes not. That is why I keep insist that we must overcome the difficulties, both theorical and practical, because a good answer do not stay a good answer forever. Times and circumstances change, so should we stay humble and always keep our minds open to new ideas. New ideas that would compete to become new theories are required not to invalidate the previous ones. So shouldn't we be afraid of these new ideas. Being suspicious is an excellent thing. Still, knowing that past theories are bound to be replaced in the future, by theories that will incorporate new observations or new conclusions drawn from past observation, the better position is perhaps to be more suspicious with our everyday tools than with new ideas. Just to keep being aware of what we are doing, still seeking solutions to unsolved problems.

I have, very recently, made a small contribution to the work of Patrick Balta -Balta Patrick Architecte naval, architecture navale, Motor yacht, yacht design, catamaran http://www.balta.fr/ by calculating by hand a general formula for the clamped section of a beam under load. We had a very interessant discussion about the hypothetis made for calculations, in general. The fact is, the more simple are the equation, the more hypothetis they contain. I know it's the job of an engineer to master the applicability of each and every formula, but the truth is, ship building is not an exact science. Although you have to be very meticulous and always try to verify these hypothetis, it is sometimes not possible at all to be sure that the boat will not encounter some exceptional conditions that would not fall into these hypothetis. Reality is full of surprises. So, my position is to rely on formulas that contains the lesser hypothetis. Thus I am very interesting in knowing the most general formulas, sometimes very complicated to put into calculations, but with the goal to have a good sleep, knowing that the lifes of sailors are at stake, sailing with boats I have worked on. One may say that the reason I bother you with kind of details, that may seem irrelevant for our everyday work, is that I'm just a sissy. That is very true, in a way. I can't forget the first time I had to design the daggerboard of a racing catamaran. Her first trip was in her Trans Mediterranean record. Each daggerboard weighted 800kg. As a young engineer, I felt uneasy with the loads excerted, and my fears went worse when I met the boat crew, angry tigers, speedthirsty. Of course, no stress tests have been made, prior to this record, like in aeronautics, the domain I lastly studied, after the fundamental physics and the applied physics. The daggerboard paint was almost fresh when they took of for the record, by night. It was the hardest night I have ever had ! So I am very suspicious, from this time, with the simple formulas, and their hypothetis. It may also be that I am French, and that we are known to keep re-inventing the wheel almost everyday....

 

Engineering is based on statistical data. It is irrelevant what the subatomic particles on the lumber or epoxy are doing. A vessel is not affected by each of them, but is the result of a large enough number of particles so statistics become valid.

 

Unless I'm mistaken, Newtonian physics didn't start to break down until it was applied to Solar system dynamics. For everyday stuff closer to home it still works just fine. Also, consider that up until about fifty years ago, almost everything that was made was calculated to four significant digits, and usually only three, because that's the best you could be sure of getting out of a ten-inch slide rule.

 

Three digits are very often sufficient, if correctly chosen, to put you on the right side of the uncertainty of your hypothesis.

The idea is not to say that Newton is wrong, but to call for an improvement in our mathematics skills, if we really want to defy the law of Archimede, which would be very cool.


This principle is widely use to make hydrostatics measurement of ship. So no speed is necessary to maintain a ship afloat. A true competitor to defy the Archimedean principle should then, at least, operate also at zero speed. In consequence Foilers do not defy the Archimedean's principle, because they are "Archimedean" born.

Can we defy Archimede with this formula ? Or (g = 0) Or (rho = 0) Or (V=0).
(g = 0) | not on the earth, my dear | X
(V=0) | design constraint, unless you make boat for no one or no purpose (manned & unmanned vessel) | X
(rho =0) | and makes it float in nothing| X
So can't we, for sure, with this formula, defy the Archimedean's principle.

If we had just start from here the conversation, I doubt that we would have had such a pleasant discussion.

 

Exactly the right way to consider it, to me, and to this guy :



Imagine a two tiered space station of opposite spinning rings. The rings spin to provide an artificial gravity for the crew inside. They walk around on the outer hull of those rings. The rings are kept spinning by turning one ring against the other so they have equal speed in opposite directions. Then, consider the rate of rotation relative to the other ring. Astronaut a in ring q watches astronaut b pass by through a window in ring p at a set rate. Then, imagine a force stops ring q from spinning but allows ring p to continue as per the drive between the two rings. Suddenly, astronaut a is floating without an accelerating force while astronaut b suddenly weights twice as much even though both see an unchanged motion between the two rings. That's a universal motion that doesn't matter what the rest of the universe is doing. You could even spin the whole of the Universe so it looked like the ring was not spinning at all and that centripetal force would remain.



I find this example very relevant, so do the same precedent guy, but I think I may keep the example of Will of as a very tellingly demonstration.



Please excuse my "poor" reference. I find really amazing the way that this youtuber take a really great care in wordings. Wording is everything. It skip the use of formulas, when rigourously applied. Images are sometimes also a good way to explain things.

 

Modern physics doesn't really mean that forces aren't real, but fields are. In fact, many fields are "force fields".

What does all this have to do with boats? Very little, from my point of viw.

I don't care whether you calculate the design of a boat by using forces or fields, or both, as long as it works. If my whitewater kayak wraps around a rock, trapping me underwater til I drown, I will be unhappy, while I remain conscious. If my sea kayak collapses and breaks while doing a cross-bow rescue, I will be unhappy. If someone else's sailboat mast breaks, they too will be unhappy. If a speed boat doesn't have enough power to go fast, its operator will be unhappy. If a submarine collapses under pressure, the people inside, like me in my whitewater kayak, will initially be unhappy, then be neither happy nor unhappy.

It is your job as a boat designer to make us happy. Yes?

So

My understanding is very imperfect, but I think it's a little more complicated than that. Let me try:

In Einstein's formulation, if an object accelerates in an inertial reference frame of reference local to the object, that is due to forces. Those forces are real, in his formulation.

But he found that if he redefined what constituted a "local inertial frame of reference", so that it fell under the influence of gravitational forces at the same rate as a point object, acting only under gravitational forces, would, and blended 3D space and time into a single complicated 4D entity he called "space-time", he could calculate the trajectory such an object acting only under a static gravitational field, as though there were no force. In that new frame of reference, such bodies, in such gravitational fields, can be said to experience no gravitational force, because there is no acceleration.

In non-inertial frames of reference there are "inertial forces" (like gravitational force, centrifugal force, Coriolis force), but that doesn't mean they and their effects aren't real. And other types of forces, like electrodynamic and nuclear forces, are real too.

BTW, he only did that with gravity, not other forces. Other people found ways to expand that methodology, to other forces, but needed to increase the dimensionality of the space. As of my 40+ year old training in undergraduate physics, no one managed to incorporate all of the classical (non-quantum) forces at the same time into such a concept. The idea of a "unified field theory" that would incorporate all forces was something Einstein and others spent a lot of time on, without success.

But in Einstein's formulation there can still be differential gravitational forces within a non-point object, or (perhaps, I'm not sure) in a non-static gravitational field. E.g., various portions of the earth feel tidal forces, because they are somewhat locked together, and therefore cannot all be in an inertial frame of reference (though to some extent, both the earth, and its waters, distort in reaction to those forces).

BTW, in beginning level physics textbooks, "gravity" and "gravitational force" usually mean the same thing. In some more advanced textbooks, such as books on geodesy, gravity incorporates some or all inertial forces. E.g., since a boat is more or less locked onto the surface of the water, "gravity" on board is often defined to include such forces. When you hold a plumb bob while on a boat (which is not an inertial frame of reference), the direction it points to is controlled by the vector sum of the gravitational force (which effectively exists in that non-inertial frame of reference) and centrifugal forces from the spin of the earth, and Coriolis forces from movement over the surface of the earth. (Of course the plumb bob is also subject to non-intertial forces like wind, the rocking of the boat, the effects of electrical charges or magnetic fields, your inability to hold the top end of the plumb bob perfectly still, etc.) I think Earthbound gravity measurements in geodesy measurements always incorporates at least centrifugal force from the spin of the earth.

Lagrangian mechanics, Hamiltonian mechanics, and other differential methods of calculating object trajectories through a "phase space" which directly or indirectly incorporates position and velocity, and perhaps other parameters, do NOT eliminate the idea of forces either. They just give you an alternative way of calculating forces, or of calculating trajectories through phase space without explicitly calculating those forces.

Quantum mechanics is in some senses a lot messier, and is not even consistent with General Relativity. In principle, you don't try to understand exactly what is true, or why it is true, because you are always limited by uncertainties in measurement and observation. Further, such measurements and observations always involve interacting with what you measure and observe, in such a way as to tend to alter what is measured and observed. The best you can do is to estimate the statistics associated with those measurements and observation. E.g., if you observe one atom at a certain time, by a particular method of observation, you can try to estimate the probabilities of finding all possible numbers of atoms (including, with some methods of measurement and observation, non-integral numbers of atoms), using the same method of observation, at another point of time. You can give such limitations a number of different interpretations, but the interpretation is irrelevant to what can be measured and observed.

Eg., in the Many Worlds Interpretation of quantum mechanics, in which there is a multiverse with an infinite number of universes that you can interact with, if you make a "classical measurement" (more or less meaning a measurement that has a very high degree of certainty, also called making a measurement as a "classical observer") that there is one atom at a particular time, what you are really doing is changing the state of the local observer (yourself, and/or your equipment) , so that you are most strongly linked to those universes in which there is one observable atom. (However, in science fiction, you can often move intentionally between those universes, and see another reality, perhaps in the present, past or future, in which different things are true. A lot of science fiction and fantasy shows and movies, like Star Trek, the Marvel universe, etc. have recently fallen in love with the multiverse concept, and they keep shifting between different realities. Yuk! It's so easy to resolve situations and inconsistencies by shifting realities. It means those shows and movies don't need to follow consistent rules about anything. It's not a new idea. Some medieval rabbis resolved what appeared to be biblical inconsistencies by assuming God created more than one universe.)

That gives a very beautiful way of handling entangled distant objects, one of whose states you affect by making an interacting measurement. E.g., if the process that produced two particles would have created them with opposite direction spins, if you make a "classical observation" of one of those objects, and find it has "up" spin, you have not altered the state of both objects so that they only have, respectively, and instantaneously (the effect moving at beyond the speed of light), "up" and "down spins - you have only changed the local observer state to be (mostly) linked to universes in which they always had those states. (The same beautiful logic might apply to Bose Einstein condensates, but let's skip that.)

(And, by the way, there are other multiverse formulations now beyond the Many Worlds one I learned about.)

Anyway, forces in quantum mechanics are basically estimated calculating techniques, which may or may not be "real" - and it doesn't matter. Since all that you can see are the statistics of measurement and observation, and those are inherently imperfect, that which is truly real isn't even theoretically knowable, and may or may not uniquely exist. (In the Many Worlds multiverse, they aren't unique, because there are other universes where other things are real.) The Wave Equation looks like a field equation, because you are applying a differential operator to a spatially distributed probability field, but that doesn't necessarily mean the field is real (or that it isn't). It's just a statistical estimation technique, whose underlying reality, or unreality, is unimportant.

 

We used to have to only worry about whether we used the metric or standard measuring tape. With any luck, we could move to a place in the Multiverse where grinding fiberglass doesn't make you itch.