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## A doubt from Dimensional Analysis

st=u+0.5a(2t-1), both dimensionally or any other

The equation refers to the displacement in the tth second and hence it should have the dimensions of speed; since it is the displacement in one second.

Under this consideration, the equation is dimensionally and otherwise correct.

## Limitations of Homogenity

“What are the limitations of homogenity?”

The question is acutually”What are the limitations of dimensional analysis?”

The dimensional analysis is based on the principle of homogenity of dimensions. The question is already discussed earlier  HERE

## Ron writes on Light and Relativity

Let me start by saying I am NOT a physicist.  That much should be painfully clear soon enough.  Please bear with me as I am not certain I have the language and in depth knowledge to explain myself adequately.

A few years ago I began experiencing parallels between the world of human behavior and physics.  At the time it seemed simple enough.  That is until I started teaching myself physics.  But at its core it seemed to make sense, the rules of life recycle themselves in different forms.  Out of simple ideas comes complexity.  Newton’s laws, thermodynamics… pascals principle, snells law, red and blue shift, wave particle duality and on and on… all seem to have their parallels in human behavior and on the surface seem to follow the same mathematical equations. Then I ran into the most famous of physics equations E=MC^2.  It makes sense in human behavior.  The energy (work) we can get out of an individual is relative to that individuals’ mass.  The more matter we attach to the individual, knowledge, life experience etc (therefore increasing their mass) the more we can get out of them in the form of energy… but then the problem of the speed of light squared.  The only known constant (light speed) is a problem in human behavior.  At least to this point I know of no known behavioral constant.

I juggled the idea of it being a relative constant.  Constant for the individual but relative as it would differ for everyone.  The speed of cognition, or thought speed, would remain the same in potential throughout life of a given individual.  Or that it was just a theoretical potential that humanity had yet to obtain.  I even juggled the idea of it being a collective ability, but all of these options cause problems with the original equation.  This has forced me to contemplate the nature of light and left me with questions I simply lack the understanding of physics to answer.

Is the speed of light truly constant or is it only constant as it relates to the big picture?  As in: our perception of time as it relates to all time that has ever existed would appear as a single point in time.  The older we get the more time seems to “fly by”  if we as humans could continue to live for 13 billion years would the perception of an hour become so perceptively small that we wouldn’t even know it has passed?   Is it therefore possible we can only understand and therefore measure the speed of light at a specific point in time, even if we try to come back and remeasure and compare the speed of light now with the speed of light fifty years from now the difference between the two would be imperceptivity small as a result of the displacement in time as it relates to the whole of time?

If the four dimensionality of time/space is linked shouldn’t time expand as space expands? And vice versa… if the speed of light is to remain constant as measured under such conditions isn’t light actually slowing down/speeding up over time as it relates to the whole of existing time/space?  It’s a distance displacement problem…. If points A and B are actually farther apart but light travels the same distance in the same time the “speed” may seem constant but time has actually expanded to give the light more “time” to cover that distance.  The speed of light would therefore be constant as a relation to perception and not as it relates to physical principles. Like the fact that the perception of time changes as we get older even though the actual measure of time remains the same.

How can light exist forever?  At the speed of light we theoretically freeze time for that photon but that would also require an infinite amount of energy to obtain and maintain. So even a subatomic particle with a lifespan of a nanosecond would appear to exist for all eternity but in actuality would still only exist for a nanosecond.  Because quite simply…it can’t have infinite energy and if it can I don’t understand how.  Thermodynamics: no system is a perfect system and will experience energy loss, Newton: equal and opposite reaction, if something begins it has to end to balance the equation.

Is it therefore possible that light is born of the fourth dimension… we experience it in the dimensionality of space as long as it loses its energy to the three dimensions.  A photon folds and pushes its way through space/time  The initial energy of the photon is high and generates bigger leading waves which resist the photon holding it from passing the “speed of light” as the energy dissipates/photon begins to die those folds restricts the photon less allowing it to maintain the speed of light.  We experience light because of its “ripples” in three-dimensions light dissipates as the waves of space become less folded in front of the photon.  But this would mean the photon eventually loses enough energy that it can no longer be perceived in the third dimension….  So what happens to it??  Imagine : A man running through a corn field has to exert the energy to push the stalks aside but  over time if the corn stalks are slowly spaced out even as he loses energy he can maintain his pace, because there is less impeding his path.  Our perception of light would be like being in a helicopter looking down on the field.  In the begging the field is densely packed with cornstalks and they slowly spread out until there is none.  We only know the man is there while he is running through the corn because he pushes the stalks aside and we see that movement but once there are no stalks or he lacks the energy to continue running we no longer have a way of measuring his presence.

That brings me for some reason to a theory of Dark matter.  Why?  Well what happens to photons that no longer move with enough force to be visible.  Like that guy running from a cornfield into an empty field.  How would we know he is still there?  If it was an infinite number of guys all stopping in that empty field we would know they are there by the depression their weight leaves in the field.  Or more accurately by the stones in the field rolling towards a depression we cant actually see.  The thought: An infinite number of “massless” (or perceived mass less) subatomic particles would still have infinite mass.  Infinite mass would supply more then enough gravitational pull even spread out over infinite distance to cause the continued and speeding expansion of space as more and more visible photons “die” contributing its “dark masslessness”.  Any dark matter existing within the universe would act as force… a moving invisible mass existing only on the 4th dimension pushing upon any objects in its way.  But because energy propagated internally expanding outward in all dimensions would compound on the outside as those energy’s converge.

I hope you followed those questions.  I don’t know what these ideas would do to theoretical physics but it would allow for the relativity of cognitive speed between individuals and reopen the door to “what the hell is dark matter in relation to human behavior” but that’s something different all together.

## M – Theory, String Theory and more

Nijisha’s Question: There are various forces we see in nature, and among them, gravitational force is the weakest. If we think about it ,the entire earth is pulling on us and yet we can manage to pick thinks up. I’ve heard somewhere that we can explain this weakness of gravitational force with the help of extra dimensions ( Something related to M theory? ). Can you explain this theory ?

Ans:

It’s a little bit difficult to discuss in detail the M theory in detail as such at School level. However, I’ll try to give a brief idea about it.

M-theory is an extension of string theory in which 11 dimensions are identified. This is a theory currently in development

To quote from Wikipedia:

“In the 1980s, a new mathematical model of theoretical physics called string theory emerged. It showed how all the particles, and all of the forms of energy in the universe, could be constructed by hypothetical one-dimensional “strings,” infinitely small building-blocks that have only the dimension of length, but not height or width. Further, string theory suggested that the universe is made up of multiple dimensions. We are familiar with height, width, and length as three dimensional space, and time gives a total of four observable dimensions. However, string theories initially supported the possibility of ten dimensions—the remaining 6 of which we can’t detect directly. This was later increased to 11 dimensions based on various interpretations of the ten dimensional theory”

In M-theory may stand for membrane. (Some claim M for mother, matrix,mystery etc)

M-Theory brought all of the string theories together. It did this by asserting that strings are really 1-dimensional slices of a 2-dimensional membrane vibrating in 11-dimensional space.

Though M – Theory is developed mathematically, it is not proved physically. Scientists and Mathematicians take M-Theory as the only theory developed so far which can explain all the aspects of Universe (or multiverse) as a whole. But, I am sure, new theories will come and take over as we develop our understanding further.

Stephen Hawking’s New work The Grand Design talks about the Multiverse and the God’s intervention in the creation of Universe (which he says not necessary)

Ref:

(I fear that I’ve brought more unknowns in explaining the one unknown. However, it will be good if the discussion goes on.)

## A problem from Dimensional Analysis

if force F us given in terms of timeT and distance X f=AsinCT +BcosDX then the dimensions of A/B is equal to

## Limitations of Dimensional Analysis

“What are limitations of principle of homogeneity of dimensional analysis?”

The dimensional analysis has the following limitations

1. It fails while using it to derive a relation among physical quantities, if there are more than 3 unknown variables on which a given physical quantity depends
2. It does not tell whether a given Physical quantity is a scalar or a vector.
3. It does not tell us the value of constants involved
4. It does not always tell us the exact FORM of a relation
5. It cannot be used for deriving logarithmic, trigonometric or exponential relations
6. A dimensionally correct equation may not always be the correct relation. (Because there are more than one physical quantity having the same dimensions)

Know some more? Write them as comments to this post

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