Lorentz Factor Explained for Laymen: Twin Paradox

In summary, the conversation discusses the concept of time in Special Relativity and the use of the Lorentz factor to calculate the time of a journey in the Earth's rest frame. The question also asks for the explanation of the symbols in the Lorentz factor equation. The letter v stands for the speed of the traveling twin or moving frame, and c stands for the speed of light. The inverse of the Lorentz factor, represented by the symbol epsilon, is used to predict the difference in aging between the travelers and those on Earth during the journey. Plugging numbers into the equation yields a value of 0.5, which represents the expected age difference between the travelers and those on Earth upon their return.
  • #1
Santural
19
0
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 :
[tex]\displaystyle\epsilon=\sqrt{1-v^2/c^2}[/tex]?

Which I believe is the inverse of the lorentz factor.

Thanks in advance,
Santural : Below the average layman.
 
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  • #2
Santural said:
So, the only thing is, what does each letter stand for in :
[tex]\displaystyle\epsilon=\sqrt{1-v^2/c^2}[/tex]?
Are asking what v and c stand for? v = speed of the traveling twin (or moving frame); c = speed of light.
 
  • #3
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 [tex]\epsilon = \sqrt{1 - v^2/c^2}[/tex], 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?
 
  • #4
Santural said:
Where is 0.5 derived from?

By plugging numbers into that formula:

[tex]\epsilon = \sqrt {1 - \frac{v^2}{c^2}} = \sqrt {1 - \frac{(0.866c)^2}{c^2}} = \sqrt {1 - 0.866^2} = 0.5[/tex]

Or have I misunderstood your question?
 
  • #5
...:uhh: hehe...um...:tongue: ...really, just um...hehe...my bad...

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

1. What is the Lorentz factor?

The Lorentz factor is a mathematical term used in special relativity to describe the relationship between time, distance, and velocity. It is represented by the symbol γ (gamma) and is calculated by dividing the actual time or distance by the time or distance as measured by an outside observer.

2. How does the Lorentz factor relate to the Twin Paradox?

In the Twin Paradox, one twin travels at high speeds through space while the other remains on Earth. When the traveling twin returns, they have aged less than the twin on Earth. This is due to the effects of time dilation, which is described by the Lorentz factor. As the traveling twin moves closer to the speed of light, time slows down for them, causing them to age slower than the twin on Earth.

3. Can the Lorentz factor be applied to everyday situations?

Yes, the Lorentz factor can be applied to everyday situations. It is often used in GPS technology to account for the time dilation effects of satellites orbiting the Earth at high speeds. It is also used in particle accelerators and other high-speed technologies.

4. How is the Lorentz factor calculated?

The Lorentz factor can be calculated using the formula γ = 1/√(1-(v^2/c^2)), where v is the velocity of the object and c is the speed of light. This formula takes into account the effects of time dilation and length contraction at high speeds.

5. What are the practical implications of the Lorentz factor and the Twin Paradox?

The practical implications of the Lorentz factor and the Twin Paradox are important to consider in space travel and high-speed technology. It shows that as an object approaches the speed of light, time slows down and length contracts, making it difficult for humans to travel at such speeds. It also has implications for the aging process and the concept of time in different reference frames.

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