Calculating Time Dilation: A Lorentz Transformation

[woodysooner]

Can someone help me with this,

How fast, or should I say near the speed of light would someone have to be to see in their time only 6 days go by, but to someone at rest relative to them see 15 billion years.

You don't have to work it just give me the equation. Is it just the lorentz transformations.

Cheers Woody

to the mentors sorry if you think I'm implying anything with the 6 days please no more warning lol.

 

[VantagePoint72]

Yes it is just the Lorentz transformation:

$$t=\frac{t_0}{\sqrt{1-\frac{v^2}{c^2}}}$$

For the sake of simplicity I'll ignore leap days.
t=15 billion years*365 days/year*24 hours/day*60 minutes/hour*60 seconds/minute=473040000000000000s
t0=6 days*24 hours/day*60 minutes/hours*60 seconds/minute=518400s
v will be expressed in terms of c, so c=1.
A little algebra reveals that:

$$v=\sqrt{c^2(1-\frac{t_0^2}{t^2})}$$

The resulting value for v is: 0.999999999999999999999999399512104c

Someone feel free to check me on that.

 

[Prometheus]

How fast, or should I say near the speed of light would someone have to be to see in their time only 6 days go by,

In order to "see" 6 days go by, the person cannot leave the Earth's orbit, as he he would no longer be able to see the day go by.

I suggest that a person travel in an airplane ever so slightly faster than the Earth's rate of revolution, and in an opposite direction. Thereby, it could take 15 billions years for him to see 6 revolutions of the Earth go by. THis is assuiming that he doesn't run out of gas or life first.

but to someone at rest relative to them see 15 billion years.

For someone to see 15 billion years go by, he would have to have been at rest, and buried, for all of it.

 

[woodysooner]

thanx

thanx a lot last one standing. yeah in 15 billion years person on Earth would die i know that, i think you see where i was going with the six day 15 billion years, not that I'm religious it's just my friends don't think that relativity can explain the discepancy of the days vs years so i wanted to show them that it did.

 

[VantagePoint72]

Hmm...that is an interesting way of looking at it. I'm Christian, so who knows lol

 

[woodysooner]

Last one standing, i have a gift from heaven for you, read Gensis and the Big Bang, not sure who wrote it i just let a friend borrow it but its new like within past two years and you can get it at any book store normally in stock, you will love it. My mom is anti-science extreme christian and that poses big problems for people like you I and all on this forum because that is what drives the world and we know it, but this book takes science and shows how relativity is in the bible and a lot of other good stuff.

Hope this helps and you read it, its a short fast easy read also.

Cheers
Woody

 

[VantagePoint72]

Thanks woody, I'll be sure to check that out. Yes, I definitely know what you're talking about. Basically I call myself an old Earth creationist, not because I care either way but because young Earth creationists tend to be stubborn and practically call us Bible compromising heretics. At any rate, I'm getting completely off the topic of this thread so I'll stop before I get a reprimand from a mod. Thanks again and glad I could help.

 

[chroot]

There will be no more religious talk in this thread. Anything further will be deleted.

- Warren

 

[woodysooner]

sorry

I didn't mean for it to be like that, just wanted to explain the book I won't do that anymore, I tried when i asked the question to know say anything religious.

sorry

 

[VantagePoint72]

yes sorry. didn't mean for it to it go on like that. forget about the rule there, won't happen again warren.

 

[woodysooner]

lastonestanding, everything check out just fine with that, equation and all but what did you use a calculator or what, I have even tried mathmatica and i can't keep it from rounding i want what you have the exact answer. show me how.

 

[VantagePoint72]

Assuming you use windows, the system calculator goes to over 30 digits.

 

[chroot]

woody,

Did you use Mathematica's N operator? N[Pi, 1000], for example, will show you a thousand digits of pi.

- Warren

 

[woodysooner]

I stayed up all night near 8 hours learning mathematica with this prob, but no chroot that only for numbers out past the dec. once something is past 6 0's it rounds to 0 even with the N[]

maybe i don't know how to use it right but i looked at over 50 tutorials.

help me

and systm calc just goes to 30 right??

 

[chroot]

I don't have Mathematica on this computer, but you're saying:

N[Sqrt[299792458.0^2 * (1-(518400.0^2/473040000000000000.0^2))],50]

doesn't work as expected?

 

[woodysooner]

nope

gives 2.99792458*^8 then if you divide by c wow you get 1 lol which i don't want so i have no clue. I have the newest mathematica too.

 

[chroot]

I'll take a look at it when I get home. I don't have Mathematica here.

- Warren

 

[chroot]

Make sure when you divide by c you're also using the N operator there:

N[%/299792458.0, 50]

- Warren