5
   

Newtonian mechanics had to be wrong

 
 
uvosky
 
Reply Mon 27 Aug, 2012 06:30 am
Yup , it had to be so , I think it could be seen even if Michelson , Morley didn't do their classic experiment which implied constancy of velocity of light or even Lorentz, Poincare, Einstein , Minkowski didn't develop those path breaking , ingenious ideas ... Consider this :-
By Newton's laws a particle of mass m in uniform circular motion experiences a centripetal force equal to m v^2 / r ( v is the uniform speed and r is the radius of the circle ) . Now start inflating the circle by
increasing it's radius more than any fixed value (namely make the radius tend to infinite value) and now , for the particle , choose it such that the quantity mv^2 = momentum x velocity such that mv^2 ~ br (b being a nonzero finite quantity) ; now the circle becomes a straight line ( since a straight line can be considered to be a circle of infinite radius) the particle still moving with a uniform speed ; but due to the properties of the particle chosen the force mv^2 / r acting on the particle is a finite nonzero quantity since mv^2/r is asymptotic to
a finite nonzero quntity. So what we have is a particle with huge(sufficiently large) mass moving with uniform speed in a straight
line experiences a net finite non-zero force ! which is directly contradictory to Newton's first law of motion! , so we see that Newtonian mechanics is self contradictory.
 
DrewDad
 
  1  
Reply Mon 27 Aug, 2012 06:36 am
@uvosky,
Can you calculate the limit of mv^2/r as r approaches infinity?

Calculating with infinities is tricky....
uvosky
 
  1  
Reply Mon 27 Aug, 2012 06:48 am
@DrewDad,
Off-course calculations with infinities are tricky , but if you take the mass of the particle to be sufficiently large (>n , for any real n ) then
m/r does give a nonzero value and so does mv^2/r , so the force never vanishes... but off-course I can be wrong , I have expressed the whole idea to some of my friends and teachers in school , none are absolutely sure about the correctness of the idea , but they all do think that it has something to it ; so don't hesitate to criticize the idea.
DrewDad
 
  1  
Reply Mon 27 Aug, 2012 07:07 am
@uvosky,
I'm pretty sure the whole thing breaks down at "radius of length infinity."
DrewDad
 
  2  
Reply Mon 27 Aug, 2012 07:10 am
@DrewDad,
http://www.wyzant.com/Help/Math/Calculus/Limits/

m/r does not give a value at all when the r is infinity. It is non-zero, but only because it is undefined. You cannot simply say "non-zero" and then assume it is a positive real number.
uvosky
 
  1  
Reply Mon 27 Aug, 2012 10:13 pm
@DrewDad,
Actually I think from non-zero I can conclude positive because both m and r are positive! and I don't understand why are you not considering
that m is sufficiently large ! have you never heard of (+infinity/+infinity) producing a positive ( non-zero) finite value !
Still if you can give a rigorous counter argument I will accept it.
DrewDad
 
  1  
Reply Tue 28 Aug, 2012 07:04 am
@uvosky,
I'm sorry, but you can't just perform arithmetical functions using infinity.

Infinity isn't a number, it's a concept.

Try again.
uvosky
 
  1  
Reply Thu 6 Sep, 2012 04:53 am
@DrewDad,
That infinities are ''concepts only'' is a very backdated view , infinities are
real entities in hyper-real number fields and in some models of smooth-
infinitesimal calculus , even in projective geometry we introduce lines at infinities , otherwise the concept of treating straight lines as circles of
infinite radius would n't arise.
DrewDad
 
  1  
Reply Thu 6 Sep, 2012 06:54 am
@uvosky,
If you're so convinced that you're right, then submit it for publication. Personally, I doubt that you will prosper in that endeavor.

When you're calculating with everyday arithmetic (as you're doing here), you don't use infinity.

If you're doing set theory or something, you might get away with it.

You remind me of those clowns who square -1, then take the square root, in order to "prove" that -1 = 1.
uvosky
 
  1  
Reply Fri 7 Sep, 2012 04:10 am
@DrewDad,
I would of course get it published in a journal , but I am
trying to come up with a rigorous presentation ( and now a days none
actually do the trick you mentioned to prove -1 = 1 ) .
Zarathustra
 
  2  
Reply Fri 7 Sep, 2012 05:44 am
@uvosky,
I just picked a few things so you don’t think I am making fun of you, but here are some of the more glaring errors.

First, you only get your straight line *AT* infinity. Before you reach an infinite radius you can only *approach* a straight line. So when you can demonstrate a circle of infinite radius in our universe let someone know and we will see what happens there. Also you are limited to a velocity of the speed of light. If the mass gets large enough it would take a greater velocity than c to keep it in orbit.

Second, you are not free to increase mass indefinitely and certainly NOT to infinity which is what you are saying with the mass being greater than any real number. You are constrained by the Chandrasekhar limit. Eventually your mass would contract to a black hole.

Third, you cannot do basic math operations on infinity, in other word you cannot divide by infinity.

If you feel this *is* possible I have two simple questions that should be very easy for you to answer.

What is one billion divided by Aleph nought

What is one billion divided by the first hyper-Mahlo

*Please show your work*

Lastly there are not different sizes (as in "bigness") of infinity there are infinities with different cardinality. Cardinality does not relate to size or "bigness". You can choose the same “big number” in both Aleph nought and continuum. Cardinality is more akin to density. So while you can have the same big number in the set of integers and the set of real numbers, for any arbitrary unit (or portion of the set) there will be more real numbers than integers. So in that sense one is “denser” than the other, not "bigger".

With the addition that Newtonian Physics has not been shown to be internally inconsistent (that is why we still use it) I would say it will be a long while before you get your article published.
oralloy
 
  1  
Reply Fri 7 Sep, 2012 11:18 am
@Zarathustra,
Zarathustra wrote:
Third, you cannot do basic math operations on infinity, in other word you cannot divide by infinity.


I think I once heard something about a branch of mathematics that found a way to deal with multiples of infinity in a manageable way. And that physicists had found a way to make use of the resulting equations.

I couldn't tell you any details though.
Zarathustra
 
  1  
Reply Sat 8 Sep, 2012 01:45 pm
@oralloy,
I don’t know what you are referencing, unless you are talking about perturbation theory or the re-normalization rules; these are used extensively in QM, in fact you cannot do QM calulations without them. These however are NOT dealing with “real” infinite quantities. The “infinities” come up in the equations because we do not know how to write the equations correctly yet.

So a strange “dance” is done (one that has been shown to be mathematically consistent) which goes: start by writing down these incorrect equations, then do this and that and this, bundle and sweep the infinites to one side, fix this up, fix that up, and these are the answers and they are correct. It is messy but it does work.

Eventually we will know better how to write our starting equations and this “dance” will be allowed to go away. I assure you that you cannot answer the two questions I posed using perturbation techniques. But if you can, great, provide the answers.

How do we know this works? It it didn’t work you wouldn’t be using a computer because they never could have been invented.
oralloy
 
  1  
Reply Sat 8 Sep, 2012 04:29 pm
@Zarathustra,
Zarathustra wrote:
So a strange “dance” is done (one that has been shown to be mathematically consistent) which goes: start by writing down these incorrect equations, then do this and that and this, bundle and sweep the infinites to one side, fix this up, fix that up, and these are the answers and they are correct. It is messy but it does work.


That might be what it was. It was awhile ago that I heard it, but that sounds like it might fit what I heard about.
Zarathustra
 
  2  
Reply Sat 8 Sep, 2012 05:34 pm
@oralloy,
What it amounts to is analogues to a word problem like:

Johnny had an apple-stand and he started his day with 6 apples in his inventory. During the day he sold 12 apples to his customers and bought 8 apples from his suppliers. How many apples did Johnny have in inventory at the end of the day; show your work? Answer: 6 apples - 12 apples + 8 apples = 2 apples.

We know that there is no such thing as negative 12 physical apples but we have to use that because of the way we did the problem. This is pretty much what the techniques above are doing when they deal with “infinities”. Except that they are dealing with (usually) mass and not apples. The infinities only exist in the calculation, not physically.

However, the difference is we can restate our calculation to make it logical in time and so demonstrate reality without negative apples. The physicists aren’t able to do that with their calculation so they are stuck with this work around. But you can see that, just as there are really no negative apples, these infinities don’t represent real things or measures. They are certainly not “infinity” in the way the poster is using that term i.e. the set of real numbers.
0 Replies
 
uvosky
 
  1  
Reply Thu 13 Sep, 2012 11:36 pm
@Zarathustra,
First of all theoretically it is possible to demonstrate circle with infinite radius , theoreticians have known this for years ; and that kind
*approaching* ... *at* things you were using are very old school classical
Bolzano - Weierstrass calculus , and for the other errors you picked , they
were largely erroneous ! , first of all I was working within Newtonian mechanics with the aim of showing it's inconsistency without going into
light-speed postulates , so by stating to stop at light speed you made the first fundamental error , similarly by invoking Chandrasekhar limit you made a same error because that criterion cannot be derived within
the model I was working , secondly one-billion is not infinity ,
hyper-Mahlo can be shown to exist within ZFC only by " assuming that
ZFC is consistent " , and in most of theoretical models we build , we do not use Newtonian-mechanics ( unlike you said " ... we still use Newtonian
mechanics '' ) .
Zarathustra
 
  2  
Reply Fri 14 Sep, 2012 02:02 am
@uvosky,
Putting this as kindly as I can…I really can’t figure out what it is you are trying to do as your posts are difficult to follow and since I think it likely that you aren’t here for a critique but rather for praise I will just note a few things in general and then leave you to whatever it is you are doing.

First, if you are trying to create a new gravity theory it must still reflect reality. In the real world you cannot exceed the speed of light and you cannot increase mass infinitely. If you are, rather, just attempting to show that Newtonian physics is not internally consistent you must still deal with the theory as it is, including its boundary conditions. General Relativity does not refute Newtonian mechanics it expands it so that if Newtonian Mechanics is invalid then so is General Relativity. Therefor you have to include the two limits I noted in the other post. If not then you aren’t working with recognized physics. You aren’t permitted to make up yourself how physics works.

Also, while circles with radius of infinite size are possible in math, along with many other things, they do not exist in the real world and even if they did it is moot as this could never be observed. How does one measure such a circle?

I would also point out that in your description you have a mass in a curved, actually circular, orbit which is not orbiting anything. Actually including a mass to orbit makes all the things I pointed out previously even more problematic. Unless you feel an object can act this way.

Another point is that I did not say 1 billion was an infinite quantity. You posted a couple of times how you could do math on finite and infinite quantities. So I gave you two examples of a finite number divided by an infinite quantity. To make it easy on you I used 1 billion in both examples for the finite quantity and I provided you two different “infinities” to use. You just posted something that I did not really say and ignored the calculations that, according to you, are possible. Why didn’t you do the calculations? They are not possible to do, that is why.

Lastly, I don’t know what physics you think people use today when dealing with gravity but I have found it to be Newtonian physics. When determining everything from the load on a truss to the necessary “stickiness” of a tire tread, to determining the dynamics of the vehicles in a fatal accident Newtonian physics is used.
Thomas
 
  3  
Reply Fri 14 Sep, 2012 03:35 am
@uvosky,
First of all, neither of Newton's three laws of motion talks about circular motion at all. So if someone made a mistake, it would be the person who worked out their application to circular motion. It wouldn't be Newton himself.

More importantly, though, your argument implies the unstated assumption that you can "choose" m*v^2 to be of a certain value. But in the real world, mass points will not yield to your choices; they only yield to forces. Your m*v^2 will not approach infinity proportionately to r unless you apply an infinite force to the mass (*). In the physical world, though, you don't have infinite forces at your disposal, so your scenario is unphysical.

Newton's laws exist to describe physical reality. You made up an unphysical scenario and observed that Newton's laws don't describe it. How does that refute Newton's laws?
_______
(*) Alternatively, you could wait an infinite time for the acceleration to complete. You don't have that at your disposal, either.
uvosky
 
  1  
Reply Fri 14 Sep, 2012 03:59 am
@Thomas,
As far as I know of historical matters Newton himself derived mv^2/r .
What I am trying to show is that Newtonian mechanics is inconsistent
when dealing with large masses ( massive bodies ) , which inconsistency is
also shown by many other theories of physics.
uvosky
 
  1  
Reply Fri 14 Sep, 2012 04:08 am
@Zarathustra,
Calculation of load of track ... etc. are not the main headaches of physics.
Some of the many theories of mechanics or in broader sense of gravity
are:- relativistic mond theory , gauge theory etc.
 

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