Johannes Kepler – A Mysterious Cosmographist

@ Khurram

How can velocity change from zero to non-zero (or from one value to next) without acceleration?

I already stated that I consider discrete nature of motion to be more appropriate. Suppose I am driving car with speed of 100 km/hrs. It is raining out side. Suppose a downward falling raindrop had vertical velocity of 10 km/hrs whereas it had horizontal velocity of zero.

Now when this drop shall collide with windscreen of my car, it, at once shall acquire the horizontal velocity of 100 km/hrs. In a supposed condition, if that drop was just suspended in air (having zero horizontal as well as vertical velocity), again it at once shall acquire the velocity of 100 km/hrs exactly at the time of collision.

There can be no ``contact period`` in this case...!!!

Now I am driving a super heavy truck with speed of 100 km/hrs. You place a small wooden box before my way. I do not bother to apply brakes or to reduce speed and truck collides with the wooden box with the speed of 100 km/hrs. As a result, that wooden box shall acquire certain mv (i.e. NOT `ma`) and its velocity shall be more than 100 km/hrs becuse of lesser mass of box.

Here we can discuss the issue of ``contact period``. Can you think that velocity of that small box shall increase like 1, 2, 3,...,100 and then more than 100 km/hrs...??? Heavy truck is moving with exact 100 km/hrs. How can the ``contacted`` box have its speed less than 100 km/hrs...??? The transformation of speed of box from zero to 100 (actually more than 100) in a single step is obvious in this case.

In another occassion, I drop a rubber ball on ground. It shall be rebounced back after colliding with ground. In the downside movement, ball was ``accelerating``. Shall its velocity ``at once i.e. in a single step``, not reach to zero, at the time of collision with ground...???

I may not think so but suppose its velocity at once shall reach to zero from let`s say 20 km/hrs. In the same moment, the ball again shall acuire upward speed of exact 20 km/hrs from zero, in a single step; and shall start decelerating.

What is all this...??? I think all motion is only discrete and cannot be continuous. It is useless to try to find any acceleration in any ``contact period``.

Newton`s laws only can ``accelerate`` static objects ... they cannot put them to move with ``constant velocity motion``.

Whenever there is a change in velocity, there is change in momentum. And when there is change in momentum the rate of change of momentum (i.e. force) must be non-zero. It doesn`t matter whether the imparting object is accelerating or has a constant velocity.

What is ``application of momentum``? Do you mean ``transfer of momentum``? That is equivalent to imparting force. Remember, force is RATE OF CHANGE OF MOMENTUM. Force can NOT be non-zero when there is change of momentum. Instantaneous change of momentum would mean INFINITE acceleration and infinite force. That`s why there is no such thing in real life. There is always a non-zero `contact period` .

Issue of ``rate of change of momentum`` shall come if there is really anything like ``contact period``. I do not believe in the idea of ``contact period``. Momentum is imparted in a single ``instance`` which has no ``duration``. So there is only ``change in momentum`` and there is no such thing as ``rate of change of momentum``. If momentum can be imparted to a stationary object without the involvement of ``rate of change of momentum``, its meaning is that continuous velocity motion can be induced into a stationary object without the application of force.

Secondly if you look at the situation more closely, you will find that there is no change in total momentum.

Instantaneous change of momentum would mean INFINITE acceleration and infinite force.

Please try to explain your above words in the light of ``raindrop/ windscreen`` example given above. That was the case of ``instanteneous change of momentum`` but without any ``acceleration`` or ``force``.

Regards!

#39 Urstruly,

I think you mean f=-kx
where `x` is elastic deformation in spring and `f` is the force required to maintain this deformation.

From where are you getting f=ka ....?
Bukhari? or Muslim?

Or did I misunderstand?

Vanderbilt researchers had recently carried out some research on how falling raindrops interact with their targets.

http://www.vanderbilt.edu/exploration/stories/rainsplash.html

There are also tons of high-speed images online that give better idea about what happens at moments close to collision.

(Math provides a model of reality. `In the limit,` the distinction between discrete and continuous becomes merely a matter of the resolution level of measuring instruments, at least in the simple newtonian world)

Re: # 51

That is interesting article but deals with a different issue.

BTW, what is the need of photograph in case of raindrop attached to windscreen? Can it have lesser velocity than windscreen itself...???

A raindrop attached to windscreen will not gain any speed less than the speed of car, right from the very first instance or moment! Its speed shall become equal to the speed of car in one step and not continuously...!!!

Re #49,

Your whole argument is that in a collision, momentum changes instantaneously. Newton`s laws are therefore disproved.
Collisions are not an exotic phenomenon. They have been studied by scientists since the beginning of mechanics. Don`t you think Newton`s laws would have been thrown out long time ago if your claims were true? The source of your confusion is that in elementary physics textbooks collisions are described as instantaneous because they are only interested in the states before and after a collision. They ignore the ``contact period`` . Also, they treat objects as point particles. All this is for simplification. In reality, there is a short contact period. The surface of the two objects interact. There is distortion at the surfaces. It`s the particles that constitute the surface that accelerate from 0 to x and pull along other particles that are bound to them by adhesive forces. The stress can break apart objects (especially, raindrops). These are pretty complex interactions and cannot be described simply. That is why elementary textbooks skip this part and deal only with the states before and after the collision. If you are interested in this subject you should look up more advanced physics texts.

Meanwhile, you can perhaps answer a simple question.
If momentum of an object changes from 0 to x ``instantaneously`` , then what is the RATE of change of momentum? Is it zero? Is it infinite? Is it something else?

Re: # 53


Your whole argument is that in a collision, momentum changes instantaneously. Newton`s laws are therefore disproved.
Collisions are not an exotic phenomenon. They have been studied by scientists since the beginning of mechanics. Don`t you think Newton`s laws would have been thrown out long time ago if your claims were true?

Yes if nature of motion is discrete, Newton`s Laws are then disproved. You say scientists have been studying the phenomenon of collision since long and they have not been uncomfortable with their understandings so far etc. This is NO solid point of yours. I already stated that scientists are perhaps sleeping. Otherwise, they shouldn`t have been so comfortable.

Try to think over the example of ``raindrop`` and ``windscreen`` of a fast moving car. If there is really any ``contact period``, then:

(i) We are having two connected objects.

(ii) One object (car) is pushing the other object (raindrop) in forward direction, from backside.

Over that so-called ``contact period``, velocity of raindrop is supposed to increase continuously from zero to (suppose raindrop was suspended in the air before collision) let`s say 100 km/hrs (i.e. equal to the velocity of car).

In that ``contact period``, car is moving with speed of 100 km/hrs. In the same ``contact period``, car is also pushing the raindrop. Under these conditions, it is impossible for the raindrop to move with any velocity which is lesser than the velocity of car.

Can you think that over that ``contact period``, car was moving with 100 km/hrs whereas raindrop was moving with 10 or 12 km/hrs...???

With these conditions, raindrop should have been ``over-taken`` by the windscreen. In other words, raindrop should have been left behind of the windscreen.

Idea of ``contact period`` is the outcome of the wrong assumption of continuous nature of motion. Reality is that all type of motion is only discrete.

Your words:

``The source of your confusion is that in elementary physics textbooks collisions are described as instantaneous because they are only interested in the states before and after a collision.``

Actually sources of my comprehensions may be deeper than advanced physics books. I read less and think more. Recently I had debate with those Quantum Physics type philosophers who are claiming to have known the ultimate reality. Here I am copying a relevant portion of my post:

``My contention is that space is NOT `composed` of waves but actually space just `holds` waves. Space is the name of nothingness. Space is the name of complete non-resistance for physical entities (waves: matter + energy). Space has no dimensions. Space has no measurements of its own. Space has no vastness. It is not right to say that space is finite or infinite. Because Space is ‘nothingness’. Space has no positive `existence`. Space, being complete non-resistance, neither attracts, nor repels anything. The main page of this site is showing amazement that how comes that matter is ‘suspended’ in space. For me, it is just due to the simple fact that space itself neither attracts, nor repels anything. So there is nothing to wonder for why objects are suspended in space.

We never measure `space`. We only measure `material entities`. For instance, 3 meters of `space` is not 3 meters of `space` in the real sense. 3 meters of space is actually just equal to 3 physical meters. In this way, neither we ever measure space, nor space can be measured. Only material entities can be measured. And since `space` is the name of complete non-resistance, so space offers no resistance even to the measurements of material objects, to their mutual distances or to any other form of their mutual interactions. And if there is `distance` between two material objects, it does not mean that any space of particular measurement `exists` between those two objects. Those two objects are away from one another with distance, which is equivalent to particular number of times a physical object such as a meter. As space is `nothingness`, so it should have no `dimensions` as well. We know of `dimensions` also only in terms of material objects. It is the `geometry` of physical objects, which makes us think as if space is having 3 (Some modern theories of Physics are advocating for even n-dimensions) dimensions.

So I have this type of objections in mind. For me reality is not space because it is a non-existent entity. Reality should be seen in those entities that positively exist. There are two things which are known to have positive existence which are: (i) matter and; (ii) Energy. And since both these things have been found to be made up of single entity i.e. ‘waves’, so instead of considering `space` to be the source of all reality, I think it better to consider `waves` as the source of reality. But we also should properly distinguish between existing entity and non-existing entity.

If waves only have discrete motion, then why to even talk of any kind of continuous physical motion at all? For me, all physical motion, including physical motion of ordinary objects is not continuous at all. All physical motion is discrete. Consider a simple situation. My car is moving at the speed of 100 Km/Hrs and it is raining outside. Suppose vertical velocity of a raindrop was 10 Km/Hrs whereas that drop had zero horizontal velocity. Now when that drop shall collide with my windscreen, it will at once acquire horizontal velocity of 100 Km/hrs. So obviously there has been a sudden change in the velocity of that drop. I can give many other simple such examples. Since the examples are too simple so I assume that readers shall understand at their own. So I confidently proceed that all physical motion is only discrete. Here Zeno`s famous paradox also can be very easily solved. Zeno had argued while assuming continuous physical motion and physical existence of `space`. But since space has no positive existence at all and the motion of physical objects is only discrete, so logically it is possible that material objects can cover distance and so reality is not static but reality is there in variations.

Your Question:

Meanwhile, you can perhaps answer a simple question.
If momentum of an object changes from 0 to x ``instantaneously`` , then what is the RATE of change of momentum? Is it zero? Is it infinite? Is it something else?

There is no question of ``rate of change of momentum`` in the case of instantaneous shift in quantity of momentum.

It is so because ``rate of change`` shall exist if there were any ``duration of time``. Rate of change has to do with T2 minus T1 sort of things.

In the case of ``instantaneous shift``, there is onlt T1 and there is no T2. With no T2, it means that there is no duration. It is not ``span`` of time. It is just a ``point`` of time. Time also should be discrete, after all.

And also remeber that attitude of Newton` laws towards Zeno`s Paradox is like an afraid peagon, who has closed its eyes and thinking that no obstacle exists.

Regards!

Re #54, khuram,
``There is no question of ``rate of change of momentum`` in the case of instantaneous shift in quantity of momentum.``

OK. Then what is the momentum at time T1? Is it 0 or x?

Re: # 55

``OK. Then what is the momentum at time T1? Is it 0 or x?``


Yar it is simple.

Total momentum before the instance of collision = m1v1 + m2v2

Total momentum at the instance of collision = m1v1 + m2v2

Total momentum after the instance of collision = m1v1 + m2v2

Re # 56.
Of course, I know that total momentum is conserved.

I am only asking about the momentum of the raindrop. If you believe in `instantaneous`` change from 0 to x, then you have to explain which of the 2 values applies at the ``instance of change``. 0 or x? it can`t have both , can it?

Re: # 57

[...] -- I am only asking about the momentum of the raindrop. If you believe in `instantaneous`` change from 0 to x, then you have to explain which of the 2 values applies at the ``instance of change``. 0 or x? it can`t have both , can it? -- [...]


Before the instance of change = zero (suppose drop was suspended)

AT the instance of change = x

After the instance of change = x


Because at the instance of change, drop shall acquire the same velocity of car.

How much the momentum of car will be affected...??? this issue requires ``quantitative`` analysis ... so this is the task of science and not the task of Philosophy.

Regards!

Re: #58.
OK. Now we are getting somewhere!

So,
T1 -> Before the instance of change = zero
T2 -> AT the instance of change = x
T3 -> After the instance of change = x

Now, can you explain what is T2 minus T1 ? Is it a non-zero value?

In continuation of my post#:

In my post#5, I had quoted from Steven Weinberg about philosophy. Allow me now to quote of Carl Gauss, one of the greatest mathematicians of all times. According to E.T. Bell (Men of Mathematics, pp. 239-240), ``It will be of interest here to quote what Gauss thought of philosophers who busy themselves with scientific matters they have not understood. This holds in particular for philosophers who peck at the foundations of mathematics without having first sharpened their beaks on some hard mathematics. Conversely, it suggests why Bertrand A. W. Russerll, Alfred North Whitehead and David Hilbert in our own times have made outstanding contributions to the philosophy of mathematics: these men are (were) mathematicians.

Writing to his friend Schumacher on November 1, 1844, Gauss says, `You see the same sort of thing [mathematical inconsistencies] in the contemporary philosophers Schelling, Hegel, Nees von Easenbeck, and their followers: don`t they make your hair stand on end with their definitions? Read in the history of ancient philosophy what the big men of that day - Plato and others (I except Aristotle) - gave in the way of explanations. But even with Kant himself it is often not much better; in my opinion his distinction between analytic and synthetic propositions is one of those things that either run out in a triviality or are false.```

Bell further wrote, ``When he (Gauss) wrote this Gauss had long been in full possession of non-Euclidean geometry, itself a sufficient refutation of some of the things Kant said about `space` and geometry, and he may have been unduly scornful.``

In spite of it, philosophy does contribute lot of useful things to the development of science but its formulations are not always correct and faultless.

Mohammad Gill

Correction:

In my last post, please read in continuation to my post #5:

Mohammad Gill

Re: # 59

khurram,

I am eagerly waiting for this drama to end ...... I have bitten off all my nails ..... when will you ask for that dreadful division ..... when?

Freethinker # 60

So true. Even a minimally acceptable philosopher must recognize that philosophy is logical, human, mental work that could proceed in any number of different ways (which makes philosophy very different from revelationary theology). Also, because of its speculative and mental nature philosophy can soar over and above different domains. Yet within the domain of knowledge identified by prevailing science, philosophy cannot contradict established scientific knowledge and principles, except by the mechanism of a philosopher working strictly as a scientist.

That must be so because otherwise it would be impossible to distinguish between knowledge & logic on one hand and deliberate deceit on the other, and between a scholar and a social charlatan. And we know for a fact that most people are simply trying to deliberate and work as honestly as they can.

Re #62 GT,
LOL!
I am afraid Mr Gill has now distracted us. :)