Modifying Newton's First Law of Motion

[someguy1]

Good question.

Yes thank you for recognizing that.

Here I am following the concepts of calculus, where two consecutive instants of time are at an infinitesimal duration of time apart. You can also see II.9 of my paper.

Nothing of the sort is even remotely true in calculus. We typically model time as the real number system. Surely (I hope) you will agree that there are no two consecutive real numbers, for exactly the mathematical reason I gave earlier. You can ALWAYS split the difference between two real numbers.

I did not read your paper, being myself mostly ignorant of physics. But I do know math, and I can tell you that if your understanding as expressed above is important to your reasoning, you have a flaw in your paper.

If $$t_2 - t_1 = dt$$, where $$dt$$ is infinitesimal duration of time; $$ \frac{dt}{2}$$ is not used in calculus.

You have made a subtle semantic shift. You initially talked about consecutive instants. If time is modeled by the real numbers then there is a third instant, or real number, between any two different instants or real numbers.

But now you are talking about "infinitesimal durations," whatever that means. It certainly has no meaning in calculus, since there are no infinitesimals in the real numbers. There was a recent thread about that on this board in which I clarified that point.

$$dx$$ and $$dy$$ are not "infinitesimal durations." This is simply a casual, informal, and generally confusing locution used by calculus students and most physicists. Rather, $$\frac{dy}{dx}$$ is a particular limit as defined in math.

Typically nobody complains about this mis-terminology unless it's in a context that matters, such as when someone seeks to refine or reformulate Newton yet doesn't realize that there are no infinitesimals in the real numbers and that derivatives are limits, and NOT ratios of infinitesimals.

I very much challenge you to find two instants or two real numbers $$t_1$$ and $$t_2$$ that have no third instant or real number between them.

When you say you have two real numbers whose unsigned difference is $$dt$$, what you really mean to write is that their difference is $$\Delta t$$, a strictly nonzero real number. Please go find your old freshman calculus book and clarify your understanding on this point before going on to refute or refine old Sir Isaac.

 

[danshawen]

If the force is having a duration, say the duration is time T. Here force can be considered as a function of time. So within the interval of time T, at every instant of time the force will be having some value.

Now you are contradicting yourself, so I will leave the thread for long enough for someone else to convince you, you are killing what was briefly a brilliant idea. It is yours, after all. I was not nearly bold enough to think of such a powerful idea, and this was not for want of trying.

But I do love serendipity, another path to success. All of my efforts in science since I was born are not as significant as the discovery you just made, evidently, by mistake. This in no way detracts from the achievement.

To be clear, hansda has discovered a way to make a minor modification of Newton's laws on the quantum scale, and by means of this, has also explained why photon and electron energy levels and interactions within quantum atomic structures are quantized, something else that is very difficult to show from first principles.

 

[hansda]

This statement is based on Instantaneous Force

What is Instantaneous Force ?

Consider force as a function of time. So at every instant of time the force will be having some value. This can be considered as Instantaneous Force.

and from this statement Newton's first law can be concluded

How is Newton's first law concluded (finished)?

If no force is applied to a particle at any instant of time; its state of motion at the previous instant of time will continue along with the time. This will result into Newton's First Law of Motion.

So, this statement can be considered as Modified Newton's First Law of Motion

How modified?

or Instantaneous Law of Inertia

Law of inertia

(Objects at rest stay at rest

objects in motion stay in motion

unless either are acted on by a external force)

What's Instantaneous about that law?

Newton's First Law of Motion is also called Law of Inertia. Mine is Instantaneous Law of Inertia. So there is little modification.

 

[danshawen]

Yes thank you for recognizing that.



Nothing of the sort is even remotely true in calculus. We typically model time as the real number system. Surely (I hope) you will agree that there are no two consecutive real numbers, for exactly the mathematical reason I gave earlier. You can ALWAYS split the difference between two real numbers.

I did not read your paper, being myself mostly ignorant of physics. But I do know math, and I can tell you that if your understanding as expressed above is important to your reasoning, you have a flaw in your paper.




You have made a subtle semantic shift. You initially talked about consecutive instants. If time is modeled by the real numbers then there is a third instant, or real number, between any two different instants or real numbers.

But now you are talking about "infinitesimal durations," whatever that means. It certainly has no meaning in calculus, since there are no infinitesimals in the real numbers. There was a recent thread about that on this board in which I clarified that point.

$$dx$$ and $$dy$$ are not "infinitesimal durations." This is simply a casual, informal, and generally confusing locution used by calculus students and most physicists. Rather, $$\frac{dy}{dx}$$ is a particular limit as defined in math.

Typically nobody complains about this mis-terminology unless it's in a context that matters, such as when someone seeks to refine or reformulate Newton yet doesn't realize that there are no infinitesimals in the real numbers and that derivatives are limits, and NOT ratios of infinitesimals.

I very much challenge you to find two instants or two real numbers $$t_1$$ and $$t_2$$ that have no third instant or real number between them.

When you say you have two real numbers whose unsigned difference is $$dt$$, what you really mean to write is that their difference is $$\Delta t$$. Please go find your old freshman calculus book and clarify your understanding on this point before going on to refute or refine old Sir Isaac.

Nor can any time interval ever really be measured more than once. You can set up similar conditions with similar velocities of similar movements, but this is not the same thing as measuring the exact same time interval twice.

 

[hansda]

I did not read your paper, being myself mostly ignorant of physics.

Please read II.9 of my paper alongwith the References.

 

[danshawen]

Please read II.9 of my paper alongwith the References.

Already did that, hansda. Apologies for not taking some of it as seriously as I probably should have.

 

[someguy1]

Please read II.9 of my paper alongwith the References.

With apologies, I will not be reading your paper. I wouldn't know enough physics to judge it or understand it.

My point is this:

a) If by "consecutive instants of time" you mean to use the colloquial, inaccurate, but mostly harmless language of physicists and naive calculus students; and this point is not germane to your argument; then my objection is of no consequence.

b) But if your concept that there are consecutive instants of time is germane to your argument, then that is a flaw in your argument and any subsequent conclusions are potentially compromised.

I make no claims as to which case is true. You have to be the judge of that. But I do hope at least that you understand that there's a real number strictly between any two distinct real numbers; and that there are no infinitesimals in the real numbers.

ps -- To show that I am an open-minded fellow of good will, I did click on your link with the intention of reading your paper. I saw that I needed to log in to Google. That's against my religion. Isn't there some general rule on discussion forums that if you are going to link a paper, it needs to be freely available without a login or paywall or other administrative impediment?

 

[The God]

See second paragraph of II.6 of my paper.

There is a difference between definition and plain use of some term.

You should follow these steps...

1. Define 'force' first. Rather you can refer to force definition in physics and see if it can exist without time duration.

2. Then see if force can be exerted on anything with dt = 0. If yes, give one example, that will be your instantaneous force.


PS : but somehow I like you, first 'anti wave' and now 'instantaneous force'.

 

[someguy1]

Well ... ya know, this was buggin' me. So I did log in to your site, using my fake Facebook profile (yes I know, FB claims these don't exist. I have several and they're easy to create).

I have to tell you honestly you were far better off letting me have the impression that you know what you're talking about but are speaking colloquially about infinitesimals. Once I actually read your section II.6 I was dismayed and you lost every shred of credibility.

Here is your passage, direct from your paper:

Here dt can be considered as the infinitesimal [2] unit of time, as it is used in the operation of differentiation or integration. This dt is non-zero but very close to zero, between two consecutive instants of time.

My God. First, as I've already explained and as any freshman calculus book will confirm, there are no infinitesimals in the real numbers and $$dt$$ is NOT repeat NOT an infinitesimal. I know that calculus students are generally confused about this but since I have now unconfused you in my recent posts, you have no more reason to labor under this totally incorrect understanding.

Secondly, there are no infinitesimals involved in differentiation and integration. None whatsoever. We use the formalism of limits. You can look up limits online or in any text on calculus or real analysis.

If you are making some sort of argument based on nonstandard analysis (NSA), you should make that clear. However, although NSA is frequently invoked in discussions of infinitesimals, NSA is actually very technical and logically far more complicated than the real numbers. It is not going to help you in this discussion.

Finally you claim that there are consecutive instants of time (pure nonsense in and of itself) yet there's some mysterious $$dt$$ BETWEEN these nonsensical "consecutive" instants. If they're consecutive, what's in between them? What the heck are you talking about.

And the claim that $$dt$$ is "nonzero but close to zero" -- what the heck does that mean? I challenge you -- right here, publicly -- to name a real number that's "nonzero but close to zero" that can't be divided by 2. On the contrary, every real number can be divided by 2, since the real numbers are a field. And interestingly even in nonstandard analysis, every infinitesimal can be divided by 2 because the hyperreals are a field. You are imply deluded. That's a strong word and I did not use it before you INSISTED that I read your paper.

I emphasize that I did not come here to attack your ideas or call you an ignorant crank. I only wanted to make the simple point that your colloquial speech regarding infinitesimals is incorrect but generally harmless, and to set you straight on the actual math.

But now, after you have INSISTED that I log on to a site and read your paper, I see that you have totally embarrassed yourself. After reading the quoted paragraph, I can not take a word you say seriously. You simply have no idea what you're talking about. The fact that you insisted that I read the mathematica nonsense in section II.6 shows that you are not speaking colloquially, but actually believe these logically inconsistent and mathematically false ideas.

The other thing that's weird is that you inserted this awful paragraph in a context where it wasn't even needed. You started defining your erroneous notion of $$dt$$ without even using it in your argument.

To sum up, before I read II.6 I was willing to give you the benefit of the doubt. But now that you've insisted and I have complied in reading II.6, I am compelled to label your paper as, well, misguided. I'm being charitable.

Off-topic but of interest, you reference Eric Weinstein's site. I found out recently that Eric is the brother of Brett Weinstein, the professor at the center of the recent campus craziness at Evergreen college that's been in the news lately.

ps -- I see that besides II.6 you asked me to read II.9. But that's even worse. From II.9:

This infinitesimal dx can be considered as the smallest non-zero value.

Sir you have lost every possible shred of credibility. After reading this I'll just come out and say it. You're a crank. First, dx is not an infinitesimal, it's a differential. Secondly, there is no smallest non-zero real number. You can always divide a real number by 2. And even in systems containing infinitesimals, such as the hyperreals of NSA, you can STILL divide any infinitesimal by 2, since the hyperreals, just like the reals, are a (mathematical) field. [In math a field is a system where you can always divide except by 0. As contrasted with a field in physics, which is a different usage of the word].

You should never have insisted that I read your paper. Before I read it I was willing to give you the benefit of the doubt. You have now removed all doubt. It reads like the work of an ignorant crank, at least regarding calculus, infinitesimals, and real numbers.

I apologize for piling on. The mathematics in your paper is just awful. "Not even wrong."

ps -- The rest of II.9 continues your physics argument but depends on your erroneous claims about $$dx$$. So your errors are material and invalidate the rest of your argument.

 

[Confused2]

I fairness to hansda he could easily have learned calculus like what I did - the teacher might have been a bit more rigorous but if so I was asleep at the time. My education later moved on to the unit impulse which is the differential of the unit step. The unit step is 0 for (say) t < 0 and 1 for t >= 0 . The unit step is the integral of the unit impulse and the unit impulse is the differential of the unit step. Nobody cared how wide or high the unit impulse was because it worked. For relligious reasons I also choose not to sup with the Devil (or Google/Facebook/etc) so I can't see what hansda has written but it does kind'a sound like he's addressing his impulses rather badly. Mathematically a step change is entirely acceptable - at least with my maths. Physically a step change probably needs a bit of an examination of the impulse causing it on account of my (and hansda's?) maths being a bit dodgy.

 

[someguy1]

I fairness to hansda he could easily have learned calculus like what I did ..

Yes I'm perfectly well aware of how confused people are after taking the usual course in calculus. And as I said, the confusion about infinitesimals is generally harmless.

However after reading the paper -- which I wish I hadn't, since I didn't want to pile on the way I did and I feel bad about it yet can't actually retract anything I said -- Hansda claims that $$dx$$ is the smallest real number and then he bases the rest of his argument on that. So it's just wrong. He's not saying, "Let $$dx$$ be an infinitesimal change in $$x$$ ..." which is mathematically wrong yet perfectly acceptable since we know how to formalize the idea. Rather, he's basing an argument on thinking that there's a smallest real number and then he's using that to derive a set of real numbers that prove something or other. So I can't accept it.

For the record I wish I hadn't read the paper since then I wouldn't need to pile on with pejoratives like crank and such, and I do understand your point about the casual use of infinitesimals in physics arguments. But even the most casual physicist isn't going to claim there's a smallest real number and then base their argument on that. All in all I wish hansda would engage with what I'm saying rather than insisting that I read the paper, which makes things much worse.

 

[exchemist]

Yes I'm perfectly well aware of how confused people are after taking the usual course in calculus. And as I said, the confusion about infinitesimals is generally harmless.

However after reading the paper -- which I wish I hadn't, since I didn't want to pile on the way I did and I feel bad about it yet can't actually retract anything I said -- Hansda claims that $$dx$$ is the smallest real number and then he bases the rest of his argument on that. So it's just wrong. He's not saying, "Let $$dx$$ be an infinitesimal change in $$x$$ ..." which is mathematically wrong yet perfectly acceptable since we know how to formalize the idea. Rather, he's basing an argument on thinking that there's a smallest real number and then he's using that to derive a set of real numbers that prove something or other. So I can't accept it.

For the record I wish I hadn't read the paper since then I wouldn't need to pile on with pejoratives like crank and such, and I do understand your point about the casual use of infinitesimals in physics arguments. But even the most casual physicist isn't going to claim there's a smallest real number and then base their argument on that. All in all I wish hansda would engage with what I'm saying rather than insisting that I read the paper, which makes things much worse.

You have my sympathy. But yes he is a crank, I'm afraid.

Still, you have been flying the flag for proper mathematical understanding, so your posts have not been wasted. We scientists do sometimes get lazy and forget about the concept of limits, so it's a good corrective.

 

[Confused2]

Having established that number theory and blood sports are separate things - I think someguy1 is doing just fine.

 

[danshawen]

I have a suggestion.

Start with a rotating (accelerating) vector that has instantaneous velocity, direction and magnitude. For the moment, the model needs no physical description or bindings other than the math.

Begin reducing the magnitude until it is below the threshold for determining position provided by the uncertainty principle. This much geometry is allowable.

Something is still rotating, but because it is below some lower physical limit (as yet undefined) to physical acceleration, it retains the characteristics of a change of direction without actually moving, other than to rotate or flip spin state. Can't really be called a "vector" any more, because it has no magnitude. F=ma no longer makes sense, because 'a' is really undefined. And because of this, 'F' still exists as well, but like 'a', it is no longer really a vector quantity. It becomes an atomic structure equivalent of acceleration, and also "instantaneous force". It is entanglement that underpins atomic structure, not a hodgepodge of EM, electroweak, and strong forces. And none of those three forces is responsible for the quantization of EM interactions we clearly see with spectroscopy.

Why is this of any benefit to understanding quantum physics conceptually?

1) because electrons don't need to spiral in, losing energy due to work being done on them as they oscillate in a cloud about an atom. In practice, QM simply ignores this possibility. This explains why it can't happen. There are mechanisms for gaining or losing energy. They are quantized according to a few simple rules, and electrons can never lose that last quantum of energy because of the differential between that "instantaneous force", and the energy level below the ground state is incompatible with the emission of the quantized energy amount of that last photon.

2) because the lower limit defined for acceleration is the fundamental basis of time, and the quantization of the entire atomic structure then consists of light travel time (its physical dimensions and energy levels) DIVIDED BY the fundamental basis of time defined and required for a complete cycle of entanglement spin flips for paired electrons. Spectroscopic observation and analysis already confirms how it works from there.

In other words, quantum mechanics has been rebuilt from scratch and in this theory, time can be reintroduced without the division by zero that would be necessary if an instant of time (time itself) were set proportional to a velocity, including the speed of light in a vacuum.

Combined with the statistical and probability density quantum theories which are already in place, conceptually this idea could really go places we never went before.

We need a shorter, more descriptive name for hansda's 'instantaneous force'. 'atomic entanglement force'? 'EEM force'? It's not actually a force like the other Lagrangian or Hamiltonian terms, but it underpins all of those other fundamental forces in there. You won't find a description with Noether's theorem, either. This is much better than gauge theory alone. For one thing, the Law of Conservation of Mass / Energy operates perfectly fine on the quantum level, because you have another mechanism for squirreling away or getting back energy that is unaccounted for. Large amounts for shorter times, smaller amounts for longer times.

I think there might even be a prediction of how to build neutrinos from photons, and without "breaking any symmetries" or violating any of those other conservation laws which are there basically because the variable for time was tossed out and replaced with unitarity. The seesaw mechanism would be another example of one of those "instantaneous force" spin flips, possibly mediated by a hidden entanglement variable with an antineutrino.

Looks like Hansda's "instantaneous force" is going to be a force to be reckoned with.

 

[danshawen]

Does this make your model work, hansda? I have removed the conceptual roadblock of an instant of time from your model by replacing that instant with the real lower limit on the nature of time itself, which is pure 'entanglement', or 'instantaneous force', or 'instantaneous acceleration', whichever one of these you wish to call it.

It doesn't really matter now whether it is really something that takes place in an instant or time or not, so long as nothing else in the universe is faster than that process actually is. Even if something else happens faster, I doubt it is even essential to the model. Besides which, that would violate the uncertainty principle, so it is impossible.

It is taking Galileo's and Newton's laws down a level to realize the fundamental nature of time itself. It makes both fundamental particles and atomic structure itself possible.

And you have realized the most fundamental nature of a universe filled with only time and energy transfer events involving bound and unbound forms of energy, both of which are conserved. You can build every part of it from scratch, working only with the fundamentals of time and energy.

 

[The God]

Danshawen,

Your pumping in entanglement in this thread is unwarranted. Your claim, as I understood, that change in state of entangled particle, could be construed as application of instantaneous force, appears to be incorrect. Not only on the score that you are mixing QM and classical, but on the very definition of entanglement itself..

Pl see below as extracted from wiki..

...........An entangled system is defined to be one whose quantum state cannot be factored as a product of states of its local constituents; that is to say, they are not individual particles but are an inseparable whole.......

Bold is mine, no elaboration required, you can figure out that there is nothing called instantaneous force here.

 

[exchemist]

Danshawen,

Your pumping in entanglement in this thread is unwarranted. Your claim, as I understood, that change in state of entangled particle, could be construed as application of instantaneous force, appears to be incorrect. Not only on the score that you are mixing QM and classical, but on the very definition of entanglement itself..

Pl see below as extracted from wiki..

...........An entangled system is defined to be one whose quantum state cannot be factored as a product of states of its local constituents; that is to say, they are not individual particles but are an inseparable whole.......

Bold is mine, no elaboration required, you can figure out that there is nothing called instantaneous force here.

Dan tries to work entanglement into everything, even his grocery shopping list.

 

[Write4U]

Newton said; "......., unless acted upon by a force"

I also agree with your logic, but is this not already implied by the term "acted upon"?

 

[danshawen]

Dan tries to work entanglement into everything, even his grocery shopping list.

I do that because without a basis of time that is faster than light propagates, light cannot propagate in ANY inertial reference frame. The conclusion that time dilation was "all the way to infinity" for the frame of reference of a photon was always based on the mathematical mistake of a divide by zero in relativity's proportional math, and the conceptual error of equivocating the speed of light as the basis of time itself.

Time dilation still works for intervals of time at our scale for different frames of reference, as advertised. Length contraction works as well.

Minkowski rotation has to go because space is an artifact of time. Ancient Greek solid geometry applied to relating time to space is the "classical" mistake that must be corrected. Spatial geometry in terms of distances 'light travel time' has no meaning at all for quantum entanglement. Space is not derived fron the basis of time by means of a division by zero either. An instant of time is not proportional to a velocity, even an invariant one.

The basis of time itself is an instant, not a velocity, and this is why the proportional math of relativity only works for v < c. It never worked for entanglement, and that's a problem.

Something is faster. That something that is faster than the propagation of light in a vacuum is entanglement, which until now has been excluded from relativity because of that conceptual division by zero.

Instantaneous force, instantaneous inertia, and instantaneous acceleration all have meaning. Newton's laws have been extended to the quantum domain by means of hansda's analysis.

Sooner or later, Einstein's analysis had to show cracks. E=mc^2 still shines, but parts of the Lorentz transformation will need modification to avoid that divide by zero. Every time (pun intended) you see a time interval equivocated with an instant of time, that will need revision so that a divide by zero never appears in any of the math, because it was always an error in the use of proportional math, as much a conceptual problem as the one Galileo had with the epicycles of Ptolemy.

 

[danshawen]

Extra for our experts:

Does the Higgs mechanism work at the speed of light, or is there a possibility it could be faster? Relative to what, exactly?

You might think that a particle physicist who discovered what we know to be the Higgs would be able to speak to this question without the uncertainty we already know will be forthcoming.

Think again. Think better and also more consistently and completely, not harder.

Science knowledge may either be inconsistent OR it may be incomplete, but pseudoscience, of which the Ptolemaic system is the best example, will be both, rather like assuming a tail wags a dog, and making predictions based on an overly complicated or convoluted model with an obvious flaw. This is a scientific means of demarcation, not a philosophical one.