A **major advantage of Physics** *in terms of speed-of-light unit*

**is**we do

**NOT**have to

*deal with huge numbers*if we are to make a

**down to the pen and paper calculation**.

*This is possible because speed of light is a constant even though a large number*. So you can compute everything

*as if*

**speed-of-light = 1**and the numbers and the related parameters such as what are known as

**Lorentz factors can be dealt like small numbers**, especially the

**rapidity factor beta.**

*There is other definitions for rapidity factor?*

**I think**its just in terms of

**hyper-trigonometric functions,**.

*thats all*For gamma you can *expand the gamma in terms of beta*,** beta always ***runs from ***0 to 1**. Then **gamma** will be a **binomial expansion**. The binomial expansion is **credited to Newton**, what a **man** for *Physics and Mathematics at the same time*.

**To get gamma** *there are 2 cases*; ( — one ) you can either **expand to a small number of power of beta; ***if the beta is small* or ( — two ) *if it ( — beta ) is close to 1*, which is when people say ”

*we are dealing with an*

**ultra-relativistic particle here**” you can do a trick. Chose a

**good power of beta**,

*large enough*so that

**you do not incur**( — more than necessary )

**round off errors in your binomial expansion**, which is not a mathematical problem as much as it may sound like, nonetheless it is, but take help

**from your Physics intuition**if you are to enjoy certain privilege, you do not have to carry everything like a computer does.

*This is of-course dependent on the physics problem*.

The

equationsyou have to solve, NOT themathematical rigorwhichcan take your valuable time. FORthe same problemto be solved easily,Physicists often work in a, theyreverse directionsolveall theirproblemsthrough some kind of invisible unionandcreate methods and resourcesthat are unified to a great deal, sothey can kick your ass if need be and you won’t have any one to complaint to.

That *above* ” … ” means you have to browse through some of the literature and only useful textbooks and have in mind what it is that you are looking for and not **waste too much time in getting inspired about mathematics all over again**. The first time around you did ( — enough maths ) in high-school ( — and it ) is enough to have made you a **physicist or a related expert** so you must have by now made yourself comfortable; *what it is that you have to keep in mind*, again there are hidden but unified ways physicists do this ( — solve problems ), hence there is often so much hue and cry about physics and you go home with the ideas that these people are basically **very arrogant**. **Call 911 if you think so**. ( Call 9-11 if you think Physicists are arrogant, thats all I can tell you)

Now **the thing in my mind** would be while trying **to find out gamma is to truncate gamma at a power of beta**. If I chose **at say 11**, then depending on what are the **actual binomial numbers** I am expanding **I may end up at say 22**, thats **the power of beta ( — is 22 )**. But **Binomially** you may have to use formulas only for **beta-power=11**. *Certain things have been so formulated they take care of themselves once you make suitable changes*.

There are **well defined expressions in mathematics that give you the gamma therefore at a chosen power truncation**. Suppose for my case **beta=0.99 ( — ultra-relativistic as noted above)**, then I have to put in my values **before** *or* **after** calculations and get a **desired value** for my **gamma or their functions**. *If* **beta=1**, life is easier because all you have to do is “**sum**” *all your *binomial coefficients. This is where you can **match** your expansion **carefully**.

You have to be very very careful eg about

what powers you have on your actual expression before expansion, a short function say withpower -3/2and you have to chose theright summation theorems. But forPhysicsthecases might be easier,nature does not invent mathematics for the sake of claiming pleasure ( — we do), what works; works,, and every good physicist can tell you a bit about such complexity.howsoever simple it may be, not less at-least, more comes from the actual situations being complex in nature

Let me not procrastinate therefore and tell you, *once you have your* **betas expanded** you can make as many differentiation you want and as per your requisition *put your* **beta values** and **sum the coefficients to get your desired results**.

The article I am writing is titled “**speed-of-light-unit**” I just gave you a bonus.

**Here is what you need to remember when doing speed-of-light-calculations**. *You have to be* **consistent in the units**, *when* you are **doing the calculations** you can put in every equation ( — “classically” as defined below ) a **c=1**. *The equations become simpler*. The difference between **c=1** *and* **beta=1 **is the latter is an **unit-less fraction;** *where always:* the denominator is **c = 2.99 x 10 (to the power 8) meters/s **( — in SI unit )** ( — **or another value as per any unit you chose **). ****The numerator is always in the same unit as the denominator**, so when you take the ratio it ( — **must** ) always resides inside [0, 1].

So** its ( — beta’s ) units are hidden ***although canceled out if you were consistent*. But for **c=1** it is not a physical variable, its a physical trick, **its** ( —** c’s** ) **units are indeterminate** as all you have to do is keep in your mind that it has been removed for a while, but once the **calculations are on** which is what *comes up without warning you*, you have to be **not only consistent with the equation** but you **have to be consistent with every single variable you have in your calculation**. *Its fun*. Basically you can do so because it ( — **c** ) is a constant and you can apply ALL mathematical operations that you can, that works on constants, *whose units need not bother you*.

But when you have to calculate/compute to find the result of your equations you **have to be sure about two things**

1. **how many c’s are needed by that particular variable.**

2. **What is the “classical” unit of the variable**. eg mass has a ” classical ” unit of (GeV/c)/c, momentum has a ” classical ” unit GeV/c and so on. (– classical defined below )

Nobody told you this, they told you

SIandcgsunits etc, speed-of-light units, but notclassical units, a classical unit is a unit where you can use anything,cgs, SI etc, as per your need in the situation, so you do not have to worry about theGeVorwhateverunits but be consistent about it in achosen segment, the number of c’s must beclassicallysatisfied.

**SO** one additional point;

3. **Energy has no c in it**, it’s a GeV, momentum has **1 c**, GeV/c, mass is **2 c**, (GeV/c)/c.

Compared to energy; momentum is 1-c down, compared to momentum; mass is 1-c down but compared to energy; mass is 2-c ( — = c{to the power 2} = cc ) down.

You can **make a list of all other variables**, probably I have never had a need to go beyond. So all you have to look for is **if you are expressing E = energy in eV**, you better look for and **multiply** or **leave as it is**; to momentum 1 c.

So if you express **momentum in eV** you know that somewhere either you **have multiplied** a c, or you **have yet to**, if you do not; **excesses will show up** as **10 {to the power – 9 }**, **10 { to the power – 8 }**, **10 { to the power 12 }** and so on.

**That is a good way of finding out if there is an error or not**. It is called **order of magnitude in Physics**. **Your orders must be very close to each other; ***unless you know something is supposed to be off by, say:* **10 { to the power – 5 }** so you ( — can ) call it a first order smallness and reject the higher orders such as its square ( — because that will be orders of magnitude smaller, fractions of orders of 0.00001 are included but fractions of order 0.0000000001 are neglected ) and cubes.

Once you have done this all, in this way you will see some beauty and you can take them all and put all the ugly factors inside parentheses and declare on twitter you have discovered something that other **suckers** were missing.

**Thats all I had to say.**

( — Tonight on CBS you can expect two important things coming, stay tuned )

Here are two sites you might find useful

Summing binomial coefficients.

Categories: approach to understand Universe, basic physics, experimental high energy physics, Ideas, Methods, particles and their properties, Physics, quantum mechanics, Relativity, Research Article, Under Review

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