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# Tag Archives: dimensions

## A doubt from Dimensional Analysis

What about the correctness about the relation,

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

Prakash Adhikari asked

**Answer**

The equation refers to the displacement in the **t ^{th} 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

Paraser asked

“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

**Ashmeeta Bhattarai** asked:

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

**The dimensional analysis has the following limitations**

- 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
- It does not tell whether a given Physical quantity is a scalar or a vector.
- It does not tell us the value of constants involved
- It does not always tell us the exact FORM of a relation
- It cannot be used for deriving logarithmic, trigonometric or exponential relations
- 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