Talk:Equation of motion
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[edit] Equation 2
I wonder if it's very correct to say that 
, or (u+v)/2, even if the time difference is assumed to be very small... that's probably why I never have encountered those equations, at school or at the university... Might be useful though for physics programming, for example. —The preceding unsigned comment was added by 82.181.203.54 (talk) 12:01, August 21, 2007 (UTC)
[edit] From theunnies.
A theory of time.
We propose a theory of 'time' starting with the newtonian, s = ut + 1/2 at^2, as follows. I would welcome learned and comments on it, please, by email, < theunnies@yahoo.com >
we postulate that all phenomena is the effect of fluctuations of dynamically vibrating ‘time’.. All phenomena, including space, is nothing but the dance of time .Time doesn’t need any medium to vibrate in,.except the ubiquitous fundamental cosmic infinite-dimensional, for want of a better word , “ consciousness”. In itself ,Time is multidimensional but not infinite dimensional. Its time that’s ever vibrating in myriad dimensions of consciousness. Our 3-D space is the field effect of one type of particular vibration of time. Time is incessantly and continuously shrinking and stretching or distorting the configuration of our space which we ‘see’ as motion, electromagnetic fields or matter or energy. , which are all but manifestations of different modes of vibration of time. Time cannot be created nor destroyed. To roughly express this concept, we start with the familiar Newtonian,
s = ut +1/2 a(t ^2) yielding an expression for ‘t’, t = -1 + or – (1/a) [square root of (u^2 + 2as)], we postulate that time ‘t’ vibrates with respect to uni-directional space ‘s’ . Hence derive the expression for change of ‘t’ with respect to ‘s’ dt/ds = + or – (1/(u squared +2 ‘as’ ), setting u = 0, we obtain, dt /ds = + or – 1/(root of 2 ‘as’) for us on earth, since ‘a’ =32 ( approx) we obtain, dt/ds =+or- (1/4.root of 2) .1/(s^1/2) hence, { + or – (dt/ds) } = k/ (s^1/2)……(A)
we interpret this as the expression for “vibration of time” with respect to space ‘s’, since there are both + and - signs.on the LHS as space is set rigid at 3 –dimensional and positive on the RHS.
Note : In eqn (A) above, keeping the domain as ‘s’ and (dt/ds) as the co-domain. , from the plot of 1/(root of ‘s’), I derive that when ‘s’>1; the larger the‘s’ is , ( as in cosmic distances)the less is the change in the vibration of time ‘t’ [ that is to say that dt/ds rises slower (or,drops faster) than the rise in ‘s’)] and, in the region ‘s’ <1 , the smaller ‘s’ becomes ( like in subatomic scales), the larger is the vibration of time, which tends to become infinite as ‘s’ approaches zero.
If ‘s’ becomes negative,then vibration of ‘t’ becomes imaginary; .means that as long as space is a non-zero quantity , time ‘t’ keeps vibrating dynamically. Thats in space,there are no stationary energy or matter ever possible. Everything will for ever be in motion including space ,as everything is times vibrations.only.
This explains why at quantum levels ( lets say at Bohr levels)and in nanocosms, ( where ‘s’is <1) time’t’ behaves differently than at macroscopic ( Einsteinian ) levels, where we can say ‘s’ is >1. I postulate that ‘s’ is =1 at the level of a molecule. Or,something that we can directly ‘see’ or directly ‘measure’.
we postulate here that energy ‘e’ is proportional to {s.(dt/ds)}. (ie, ‘space’ times ‘vibrations of time with respect to space’).The constant of proportionality is to be experimentally determined .
Since both ‘s’ and vibrations of time w.r.t ‘s’ can never attain non-zero values , energy’e’ is always >0 and hence can be represented by a square number. The constant of proportionality will have the dimensionality kg/sec.so that you get dt/ds as seconds per meter as the vibration of time’t’, in the metric of space, ‘s’. I deduce that the constant of proportionality ‘k’ must be numerically much smaller than 1.(To be verified experimentally).
This eqn is to be used to calculate the vibration ( dt/ds) of time’t’ with respect to distance ‘s’ in space from experimentally measured or, theoretically calculated energy ‘e’ from e= mc^2.. To obtain different vibrations of time ‘t’, values of space ‘s’ and energy ‘e’ could be manipulated ( either expanded or contracted, radiated in or removed) to get any desired vibration of time.
Its not in space that we move Its in time that we move.. Its change in our time ‘t’ brought about by changing our speeds of motion ie reducing space between the moving object and its destination, (by deliberate shrinking of space that surrounds the moving object in its immediate vicinity), that gives us the illusion that we are moving in space.. Time is the ‘shrink factor ‘ and is inversely proportional to the time measured by our external clocks. The less the time applied the more is the shrink factor and faster we reach our destination.
I further postulate that energy,‘e’ which is the product of space’s’ and the vibrations of time’t’w.r.t space ‘s’.is a constant conserved quantity within any closed system of space-time. For a constant energy universe ( like that of ours) ( t) = e.ln(s) + c Where, ’t’ is time, ‘e’ is energy ‘s’ is the extent in mtrs of the closed space in which the system being considered is operating and, ‘c’ is the constant of integration .
Now, From (A) we get, {( d)^2) (t}/ (ds^2) = -- or + (1 /2k){1/{(s).(root s)}…….(B)
means that ‘t’ could vibrate with accelerating or decelerating paces w.r.t space ‘s’. Since we can continuously differentiate this expression any number of times , this means that there is no limit to the ratechanges in accelerations of ‘t’ w.r.t ‘s’.
I interpret this as different rates of vibrations yield multi dimensional space.
Again, (dt/ds = a constant ‘c’, where ‘c’ is the speed of light in vacuum) is a particular vibrational state of time ‘t’ suitable for our 3-D space configuration.. In that case ‘s’= ‘e’/k .‘c’ ie, s = mc/k means ‘s’ is proportional to mass.
Our DNA bio-senses is designed for a specific form of time vibration where the speed of light ‘c’ is considered as a constant. . It cant realize or grasp endless vibrations of ‘t’ w.r.t ‘s’ and hence comprehend multidimensional space. We are sensually designed only for a three dimensional space corresponding to just one single half vibration of time in the positive direction ( apparently justifying the concept of the thermodynamical unidirectional arrow of time ).
In equations (A) and (B) above we have ‘s’ as unidirectional space in 3-D .as refernce variable. Even our electromagnetic waves can have an orthogonal three dimensional configuration as specified in the’left hand thumb rule’ or some such picturesque representation.
All phenomena takes place in vibrating time’t’.The lesser the space is, the more vigorous these vibrations of time . when time vibrates at more than normal levels due to paucity of space ‘s’ as inside an atom or quantum object, it gives the impression that causality is violated and matter or energy ‘moves’ speedier than light .
And, pray, where does time ripple in ?
we postulate thirdly, that it does in the most fundamental entity, “consciousness” ( for want of a better nomenclature).
Life is a specifc ripple of ‘time’ weaving matter and energies in specific proportions at a specific temp and pressure ( which are again special manifestations of ‘time’ itself. Life is a special configuration of vibrating ‘time’ in our 3-D slice or cut out from a multidimensional multiverse. Matter is nothing but energy storing devices to store maximum energy taking up minimum space. Vibrations of time at atomic space level would be superluminal and hence electrons seems to jump from energy state to state, its path hidden from any experimental view.
Potential Applns of this theory arein the fields of 1. deep-space travel, when superluminal speeds have to be the norm.Manipulating vibrating time may offer a solution. 2. in investigating "life" , fluctuations of time may explain mutations and what we now call evolution.
A side question answered. Q : why is our space 3-D? A: because, electromagnetic field is defined in an orthogonal 3-D space .Light is an EM energy and we ‘see’ everything with the aid of light, which can operate only in its 3-D configuration.. Hence our space in which we presume that light is moving, is defined by the 3-D s. of EM ‘waves’. Viz, the direction of propagation, direction of electrical field and direction of magnetic field. We can visualize everything within this limited cut out only.
Correct me where I am wrong. theunnies.
Can anyone remember how those 4 equations are derived (presumably, from Newton's Laws)? -- Tarquin
Hey, maybe It's different in Australia (though I cannot understand why), but I have always been taught that displacement is represented by x, and s represents speed (as distinct from velocity, speed is distance traveled over time, velocity is displacement over time and is a vector) Just a thought.
[edit] Notation
Is anyone else bothered by the fact that at least 3 different notations are used in this article, e.g. d = distance = s; initialocity = u = v0 = vi; etc. etc.
- Also, why 'current'? These equations work perfectly well if the 'final velocity' is not current. Ian Cairns 16:48, 13 Oct 2004 (UTC)
- To go from (equation 2) average v = s/t to (motion equation 2) s = 1/2 * (u + v) * t, you need to remember that under a constant acceleration, the average velocity is half the final velocity. -- Anonymous Coward
- If we're being picky, d represents distance (a scalar) while s represents displacement (a vector). It does bother me, but they're all easily derived using mental logic. ThomasWinwood 19:07, May 11, 2005 (UTC)
[edit] Missing equation
What happened to s = vt - ½at²? ThomasWinwood 19:08, May 11, 2005 (UTC)
[edit] Torricelli's Equation
Torricelli's Equation Should this be merged and redirected?Atomiktoaster 00:32, 10 Jun 2005 (UTC)
[edit] Theunnies ON E > mc ^ 2 and DARK MATTER AND DARK ENERGIES and the nature of Time.
These are my blog on dark energy / dark matter.
Thought that you may be an interested party .
About the concept of Dark matter ;quotng from Wikepedia .(U May skip this 2 paras of quotation, if--59.93.83.111 13:15, 23 June 2006 (UTC)theunnies--59.93.83.111 13:15, 23 June 2006 (UTC) you know all that)..
after that, its all my 'original" thinking.
The two paras from wikepedia :
"In cosmology, dark matter refers to matter particles, of unknown composition, that do not emit or reflect enough electromagnetic radiation to be detected directly, but whose presence may be inferred from gravitational effects on visible matter such as stars and galaxies. Dark matter explains several anomalous astronomical observations, such as anomalies in the rotational speed of galaxies (the galaxy rotation problem). Estimates of the amount of matter present in galaxies, based on gravitational effects, consistently suggest that there is far more matter than is directly observable".
again from WP: "The dark matter component has vastly more mass than the "visible" component of the universe . At present, the density of ordinary baryons and radiation in the universe is estimated to be equivalent to about one hydrogen atom per cubic meter of space. Only about 4% of the total energy density in the universe (as inferred from gravitational effects) can be seen directly. About 22% is thought to be composed of dark matter. The remaining 74% is thought to consist of dark energy, an even stranger component, distributed diffusely in space. Some hard-to-detect baryonic matter (see baryonic dark matter) makes a contribution to dark matter, but constitutes only a small portion. Determining the nature of this missing mass is one of the most important problems in modern cosmology and particle physics. Its urgency is underlined by David B. Cline in a 2003 article in Scientific American, in which he writes: "The terms . . . 'dark matter' and 'dark energy,' serve mainly as expressions of our ignorance"
Now on, its all me :
We can enlighten our ignorance to some extend by the following lines of thought.
From elementary considerations,
There are the following three regions in the linear graph associated with the relationship, e=mc ^ 2 ; 'c' being constant vel of light in vacuum.and, is taken as =186,000 miles per sec,in 4-D space-time.
(1). e > mc ^ 2 (2). e < mc ^ 2 and, (3). e = mc ^ 2, which demarcates the boundary between regions (1) & (2).
Area (1) exists,even in the first quadrant ,because c ^ 2 (ie, 186000 ^ 2),is NOT infinity. Its [ atan(infinity)] ie, (inverse - tan infinity) which is 90 degrees.Hence, [atan( 186000 ^ 2)], is < 90 degrees.If space is continious, then, the space between e-axis and the line e=mc ^ 2 exists, even if it be less than planck length ,when mas is subatomic.. ( Planck length is applicable only where we can consider space existing as lumps of discontinous quanta).
[As the slope of the line e=mc ^ 2 is,[taninverse (3.4566 x 10 ^ 10)]= tan inverse (1,86,000^2) = 89.99999.....9s recurring ad infinitum....... degrees,or, say,(90-$) degrees, where,$>0.(angle $ could be called Planck angle for microcosmic mass, but the point made is still valid)] .
This implies that, for events in this region where e > mc ^ 2,'C' cannot be taken as a constant but has to be greater than 186,000. An element of this 'slice' of an area in the graph,is associated with every mass 'm'.For negative masses and for negative energies,(ie,for non-electromagnetic masses and non-electromagnetic energies) represented in the third quadrant ,this area in the graph above the line e=mc ^ 2 dominates and is much more significant too .
This accounts for the possibility of dark matter at the extreme levels of both MACHOs and WIMPS ( ie, Brayonc and non-baryonic ; or Electromagnetic and non-electromagnetic ranges of mass / energy).The region of the MACHOs could be the first qudrant area above e=mc ^ 2 ,in the region e>mc ^ 2 and, of WIMPS is in the third quadrant space in the area e>mc ^ 2 above the line e=mc ^ 2.
The fact that the equation e=mc ^ 2 has no existence in the fourth and second quadrant of the cartesan graph may be interpreted as equivalent to the physical fact that there is no positive energies associated with negative EM mass and no negative energies associated with positive EM mass. This is the limitation of energies whose source is EM mass and not the limitation of universes not based on EM mass and EM energies.
Therefore, this forms the basis of our postulation that there exists velocities C*, much higher than that of light . This is the basis of postulating negative mass and negative energy too. We further postulate that C* will not be a constant.C* will be a variable quantity.
Not only that, we postulate that C* varies as the dimensions of the universe in which certain events occur.
C* is a function of the dimension of a universe.
One value of C* is 'c' which remains constant in a 3-D universe like that of ours.
Any velocity 'v' less than 'c' or, any velocity C*, more than 'c', cannot remain a constant , unless forced by 'external' forces to do so. 'c' is the only possible velocity that is independent of "time' in a 3 dimensional universe..'c' is the limiting velocity of 3-D Electromagnetic space..
For the propogation of EM waves we need all of the three orthogonal dimensions. no more , no less. That forms the basis and rationale of our electromagnetic space being of 3 dimensions.'Time'is just an artificial man-made mathematical artifact to take measurements of changes .Its just an artificial virtual backdrop.
The evolution of space in a 'sequential' order with a constant velocity is taken as ' time' in 3 dimensional universe..'Time' is just like one of the qualities of our universe.This sequence is applicable only to the electromagnetic beings and entities which are the constitutuents of our universe.
In an open system, which the cosmos is, there is nothing absolute about this quality ,we call 'time'. The term 'Cosmos", we use here, to embrace all types of universes , multiverses mathematically real, physically existing in 3 dimensions, and mathematically imaginary too. That is why energy in our 3dimensional universe, is a linear function of lumpen mass( or,rest mass) alone. On either side of our universe,be it at the level of microcosm or of the macrocosm, only multiverses and multidimensionalities can exist, in which velocities ( ie, changes in space measured with time) vary chaotically and, non-linearity reigns.
When 'm' is small, this area e > mc ^ 2 tends to be zero,until 'm' becomes negative. When 'm' becomes negative ( energies will also become negative), most of the occurances will have to acquire velocities greater than C. because the area e > mc ^ 2 opens up and expands vastly. Events will vanish out of our 3 dimensional universe into universes of varying superluminal velocities. The nearest to a mass-less medium that we can imagine is our own mind and, may be, the heightened awareness of a cosmic consciousness.
But when 'm' becomes large and assumes the 'mass'of a family of galaxies or of the entire "Electromagnetic matter" in the universe,the energies associated with 'm' in the regions (1),(2) and (3),in the first quadrant itself, will also tend to be substantial. In region (1) it is C* that is applicable and not'c'.In region(2) it is 'v' that is applicable and not 'c'. Nearer to region (2) ie,nearer to the boundary-line separaing regions 1 and 3 , is when 'c' is applicable. The maximum EM-energy extractable from lumpen mass'm'in a three dimensional universe is equal to mc ^ 2.
Now, it has become obvious that dark energgy or dark matter exists in the region (1) ,where C* is applicable. What should then be the power to which C* ought to be raised to get the rate of exchange between mass and energy , in this region ?
Now, C*, is a variable quantity of the order of say,10 ^ 100 to 10 ^ 1000 , which is the speed of that entity which has superluminal varying velocities. But in this time-less , space-less and mass-less, so to say, " Cosmic Consciousness Region" of energies and heightened "awareness" only , we have to redefine the term meaning of 'speed' itself .We may have to invent new mathematics language and processes that have no analogies in our 3dimensional universe..Thats a different excercise altogether and not covered in this discussion.
The max limit of 'v', in the region e < mc ^ 2 is 'c', whereas 'c'is the minimum limit of C* .No max limit for C* is postulated .We can assign C* those values that suits the experimental measurements or calcuated values of the 'Dark energy'. This is the basis of the fact that the effects of dark energy being discernible to us only when we consider events at the level of the formation and motion of clusters of galaxies and, not at the level of even single galaxies .
The analogy of the straightline graph reveals also that at the level of the microcosm, ie when 'm' is negligibly small, the events can occur only very close to the speed of 'c' ; as at the subatomic ranges theres no sufficient space possible ( see the graph below) in the region, e < mc ^ 2.
In the regions where e > mc ^ 2, energies are NOT conserved, much like in the quantum worlds where energies can be spontaneously created and destroyed too.
Of course 'matter' or 'energies ' at this range and scale are obviously beyond the pale of 4-D space-time and hence Dark Matter to us in the dimensions in which we operate.
e=mc ^ 2 is the maximum electromagnetic energy available in 3-D space from electromagnetic mass. Energies which are beyond electromagnetic range will manifest in 4-D as effects without revealing its source and hence remain for ever "dark' to us.
To recaptulate, ( AT THE COST OF SOME REPITITIONs ) In the linear graph in the cartesan plane of the eqn e = mc ^ 2, or, of ,y= x . 1860000^2 , sketched .as a green broken line, below;
('x' axis showing mass and ,'y' axis showing energy. slope of the broken line in green, in degrees , is = [tan-inverse(186000^2)]. Note " there is plenty f area for higher forms of non-EM energies to exist in the region e > mc ^ 2 and, hardly any area when mass is subatomic nearer zero in the region e < mc ^ 2.
Note: In the plotted graph below , the point ( 2.9 , 1x10 ^11 ) , shown by the intersection of the two dotted black vertical and horizontal lines is, almost exact to the calcuated value (using e=mc ^ 2), for a mass of 2.9 gms, the maximum extractable energy is 1.02x10^11 energy-units. The unextractable non-electromagnetic energy equivalent, lying above it ,for the same mass is much more. And, it is this energy thats a likely candidate for "Dark Energy".
The quantity of DARK ENERGY associated with a mass of 2.9 units, in universes of various dimensions can also be calculated ( read out from this graph )..
the same graph of y = x.(3.4566x10 ^ 10), in log scale is as below.
in regions 2,where e < mc ^ 2
the energies extractable from mass 'm' at velocities 'v' less than 'c' is rather given by the relationship e = 1/2 mv^2.where 'v' is a variable velocity. To extract the maximum energy from mass 'm' it has to be speeded near to the velocity 'c'. In a gravitational field you may like to add 'mgh' too for the potential energy component. where, 'v' < 'c'. But at velocities ='c' gravitational potential plays no role as matter ( in its rest mass format) gets converted to massless ( inertia-less), radiating energy waves.
In region 3, where = mc ^ 2
since 'c' is constant,the equality e = mc^2 holds. This energy is the maximum energy that could be eked out of a mass 'm'and is always greater than any [mgh + 1/2 mv^2], where v < 'c'.
In region 1 above, where e > mc ^ 2
In this region, the velocity C* of mass 'm' is always greater than 'c', and, C* is variable too , In this super region,the energy mass conversion formulae can still be of the form e = m C* ^ 2 , where C * = [c ^ ( K D-1) / 2] where 'k' is the scaling factor charcteristic to the dimensions of the universe under consideration. The value of 'K' is to be determined from experimental observations. . 'D' is the dimensions of the universe under consideration . For 3 dimensional universe k=unity. the value of the scaling factor k coud be a complex number too . Dimensions of ' higher ' universes could be fractional or imaginary Also, K could approx be given the value, ( C / C* ).,
For example, from the graph above, we find that for a mass of 2.9 mass units , one of the corresponding energy reading is, 2 x (10 ^ 11) energy units . Note that the maximum energy derivable from a mass of 2.9 units is only 1 X (10 ^ 11) enrgy units.in a 3 dimensional Electromagnetic universe, when we calcuate using the mass-energy exchange rate .mc ^ 2
Therefore , the dark energy component associated with a mass of 2,9 mass units = [.2 x (10 ^ 11) energy units ,minus 1 X (10 ^ 11.energy units ] = (1 X 10 ^ 11 ) energy units.
The speed element C* here in this higher universe, works out to be 2,62,612.87 mps ( from the approximate relationship, 2 x 10 ^11 = 2.9 (C*) ^ 2.).. We have now a way of calculating the dimensions f the universe, in which this much dark energy is generated by this much of mass. . For lack of observational data at this range of C*, we assume that the charcteristic constant of proportioanlity ' k' =1 ( or nearly unity, as the region under cnsideration is not far away from the line e =mc ^ 2 applicable for 3dimensions.where we take k=unity). Then we can calculate the dimension where this energy 2x(10 ^11) could be extracted from 2.9 mass units. We get that such a dimension, D, is near to 3.057 ( a fractal higher dimension higher than 3).,from the relationship e = m X ( C* ^ 2) where C* =C ^ [ (D-1) /2 ] ^2.
Alternately, we can say that for a mass of 2.9 mass units, the energy associated with it up to ( 1 X 10 ^ 11) energy unts could be extracted in 3 dimensional space .But almost an equal amt of energy is associated with the same amount of mass in 3.057 dimensions .In hogher dimensions than that the energy available from the same mass of 2.9 units increases exponentially the effects of which would leave their tell-tale marks in our 3 dimensional universe also..It could even be possible that , "measured " Dark Energy may pertain to energies associated with non-fractal higher dimensions, only..Energies associated with fractal dimensions may not have effects on universes with integral dimensions at all.
All of the possible enrgy-states beyond (1 x 10 ^ 11) energy units just in the one case of a mass of 2.9 units is actually missed out by us. But, If we THINK that we are missing out only 96 % of the total energy density ( see wikepaedia quote above) then we can easily see that we can only be aware of universes of .D.. dimensions and not beyond that or, that perhaps gravitational energy range is only from universes of that many dimensions; Beyond of those dimensions we can get no clue whatsoever regarding energy ;atleast that of the gravitational denomination.
D imension "D" at that range for a mass of 2.9 units can be calculated .as follows :
If , 4 % of the max ' visible ' energy extractable from a mass of 2.9 units is = (1 X 10 ^ 11 ) energy units, then 100 % energy ( incl dark energy ) available from the same mass of 2.9 mass units is , ( 25 X 10 ^ 11 ) energy units.
First calculate C* from the relationship e = m C* ^ 2 { therfore, 25 X (10 ^ 11) = 2.9 X (C* ) ^ 2 }. . hence,we work out C* = 2.936 X 10 ^ 5.5 mps Now use the relationship C* = c ^ {(Dk-1) / 2} where , K = C / C* ie, (1.86 X 10 ^ 5 ) / (2.936 X 10 ^ 5.5) = 1/ 4. 999 approx = 1/ 5 say. hence we work out , D = 16.310
Now, the physical interpretation of this is, that gravity from a dimension not higher than about 16 dimensions only can have any effect on the
" measured " density of dark matter associated with a 2.9 units of mass units , in our universe..
yet Another interpretation is ,The larger the mass is, the higher the dimensions from which it can get influenced.
Note :The value of C* is postulated as a constant for a particular dimension of the universe .For example, for dimension 10, the value of C* = c ^ (10k-1)/2 , where 'c' is the applicable velocity to our 3-D universe. Note again that C* here is a constant for the 'D' dimensional universe, ie, C* = constant value [c ^ {(kD-1) / 2 }]. If, D=10.then the energy exchange rate for the 10 dimensional universe is,a constant [{c ^ { (10k-1) / 2} ] ^ 2 ie, for ten dimensional universe , e ( the maximum extractable energy from a mass 'm') = m(C*) ^ 2 where,. C* being the characteristic constant for any ten-dimensional unverse.
For D=3 for example, C* = c and d=3;yeilding the eqn e=mc ^ 2 for the universe with dimension 3.Here we take 'c' as a constant velocity of EM waves ,as observed from experimental results such as the total heat, light,sound, and radiation and residual mass energy outputs as measured when an atomic particle is split,in our 3-D universe. .Whenever we calculate 'c' backwards from any of these experiments we get a constant value for 'c',if the dimensions of the universe in which we take the measurements is 3.
for dimension 10 universe , for example, the "dark"energy asociated with each bit of the rest mass'm' ( as observed in our 3-D universe) would be e= m C* ^ 9, the variable value of C* in the superluminal velocity region is assigned to tally with the observational results gathered. Alternately, here we have a method of determinating the dimension of the universe in which we have to account for the darkmatter which we find experimentally, or by calcuation.
With this postulate, for region 1, we can account for the mass-energy of dark matter . Dark energy is not a conserved quantity, if we take atonce all types of universe in all dimensions into account.But dark energy ( just like normal electromagnetic energy) is conserved for a universe of any specific dimension, within the bounds of those dimensions.
Depending on experimental observational facts , we can now account for any amount of dark energy discerened ('measured'indirectly , of course) in any part of the universe,because, we can assign any arbitrary value for the scaling factor, 'k', for the superluminal velocity regions , where e > mc ^ 2 .
From the values used to obtain the results of calculation to agree with that of 'observation',we can determine the dimensionality of the space or the scale at which the event, whose tell-tale signs we 'measured' in our universe , actually occurred.
It is the 'interpretation of " Facts" and, "Figures" that shapes, gives ' a form and a habitation' to Matter, dark or otherwise.
I hope I have given you some food for thought .
Dark matter expresses in 3 dimensional Electromagnetic universe thru its effect on gravitational phenomena. Now, what exactly is 'gravitational energy' , which is certainly not derivable from Electromagnetic energies ( as is evident from the types of radiating energies emenating from an atom smashing process indicating that no gravitational energy can emenate from atom smashing ),is the subject of my next blog, which I will send you later.
PS : Gravitational energies or potentials and probabilites.
Just as an indicator of that, i postulate here itself that the dimension in which 'gravitational energies' operate 'instantaneously', are wide and varied. Gravitational energies are independent of space-time or even a medium for it to'traverse'.It doesnt traverse .it is already there pre-existing in the structure of all dimensions.This means that Gravitational energies are transcedental to space-time.Their source and origin are not in the 3-D universe at all.
Gravitational energy shapes both space-time and matter simultaneously in a tri- symmetric manner, which appears as Space-time curvature ( ie, mass shaping space and, space giving mass its inertia), to the electromagnetc energies like that of light .This is just the characteristic effect of gravitational energy applicable to a 3-D universe as ours, only.The effects of Gravitational energy ( to be nomenclatured differently for other dimensions) in other dimensions would certainly be different.
there has to be a single entity which manifests itself as ,'dimensions'; 'gravitational energies or, some other "probabilities and 'potentialities" which manifests as "electromagnetic waves and matter"and, even as 'life forms' at suitable conditions.
OR, should there be ? Why cant there be infinite repititions of one and the same fractal pattern made up of a multiplicity of origins and forms and strands of varying energies coursing, vibrating and lashing thru quantum vaccuum that spontaneously ( ie, without the need for any cause for it to occur; events that transcends causality) manifest differently in different dimensions yet stringing all of them together offering networks of instantaneous communications ( instantaneous= that which requires no time or, time-independent transcedental ) , as if there is a common origin or source when looked at from macro-dimensions? Single source and multilitude of sources are the same and not diffreent except when viewed at diffrent scales.. Isnt zero and infinity the same , only seemingly different depending on the scale at which you 'observe'.?
Gravitational potentials could well be one such quantum-strand weaving itself thru a multiplicity of universes / multiverses existing in different dimensions .
Now, thats enough food for thought for the day .
Hi, I would like to suggest some corrections in this article. There are many examples of equation of motions, but in fact there is only one equation of motion for mechanical systems,
where, m is the system mass and a is the acceleration. Thank you.
Paulo
[edit] Displacement question
My science teacher told me that they changed the pronumeral for displacement from "s" to "R". Is this OK? The Updater would like to talk to you! 07:48, 22 March 2007 (UTC)
I was taught it was x, and s was for speed (distance over time NOT velicty which is displacement over time). R is resistance isn't it...? don't motion formulea only use lower case? —Preceding unsigned comment added by 202.45.119.135 (talk) 23:02, 19 November 2007 (UTC)
Notation is abused all the time, however, "r" is the radial distance in polar co-ordinates, "x" is one of the components (the others usually "y" and "z") in cartesian co-ordinates and "s" is something high school teachers come up with for displacement as they've already used "d" for distance. "R" is almost always resistance. At any rate it really doesn't matter as long as it's clearly labeled. Durinix (talk) 13:32, 2 April 2008 (UTC)
[edit] Only one equation?
Why is this article called "Equation of motion" when it is clearly about more than a single equation? Even the opening sentence says "equations of motion". --Dr Greg (talk) 13:15, 4 March 2008 (UTC)
