Lorentz Factor Explained for Laymen: Twin Paradox

[Santural]

I looked up Twin Paradox, and I understand the concept of time in SR, and also understand the Einstein synchronization convention concept, but now there is just something I don't get here:
I looked at twin paradoxes and apparently you must use the Lorentz factor (or it's inverse, anyway) to figure out the time a specific journey would take on the Earth rest frame (or along the lines. Can't put it in words.)
So, the only thing is, what does each letter stand for in :
$$\displaystyle\epsilon=\sqrt{1-v^2/c^2}$$?

Which I believe is the inverse of the lorentz factor.

Thanks in advance,
Santural : Below the average layman.

 

[Doc Al]

So, the only thing is, what does each letter stand for in :
$$\displaystyle\epsilon=\sqrt{1-v^2/c^2}$$?

Are asking what v and c stand for? v = speed of the traveling twin (or moving frame); c = speed of light.

 

[Santural]

Right! Thats part of what I need. However:
Wikipedia says:

Consider a spaceship traveling from Earth to the nearest star system: a distance d = 4.45 light years away, at a speed v = 0.866c (i.e., 86.6% of the speed of light). The round trip will take t = 2d / v = 10.28 years in Earth time (i.e. everybody on Earth will be 10.28 years older when the ship returns. Those on Earth predict the aging of the travellers during their trip will be reduced by the factor $$\epsilon = \sqrt{1 - v^2/c^2}$$, the inverse of the Lorentz factor. In this case ε = 0.5 and they expect the travellers to be 0.5×10.28 = 5.14 years older when they return...(goes on and on)

(I added the bold).
What is that epsilon? Where is 0.5 derived from?

 

[jtbell]

Where is 0.5 derived from?

By plugging numbers into that formula:

$$\epsilon = \sqrt {1 - \frac{v^2}{c^2}} = \sqrt {1 - \frac{(0.866c)^2}{c^2}} = \sqrt {1 - 0.866^2} = 0.5$$

Or have I misunderstood your question?

 

[Santural]

... hehe...um... ...really, just um...hehe...my bad...

I guess I was being a LITTLE dumb there, sorry.