Time and distance at constant C: A sieries of questions for Umbran or other physicists.

[MarkB]

OMG... Bell's Theorem means we have no free will!

I already told you that tomorrow.

 

[Scott DeWar]

MarkB, I saw you had ninja'd me the day after tomorrow.

 

[Scott DeWar]

Ok, I am going to attempt some math in this post. Please, no comments until I post -END-<end>.

http://www.disclose.tv/news/nasa_as...l&utm_source=facebook.com&utm_campaign=buffer

Meteor 2015 TB 145 Velocity =

78,830 MPH = [78,830 * 1.6] = 126,128 KPH; 126,128/3600 = 35,035 M/S
</end>
Time dilation formula

<end>1/sqrt(1-v^2/c^2)

[1 / (1 - 35035^2 / 300,000^2)^ -2] =
1 / (1,227,451,225 / 90,000,000,000) ^-2 =
1/ (.01363834694)^2 =
1 / 0.1167833333 =
8.56286570597

So, as an exorcise of thought, I am going to say that a ship has taken a mining crew to dig for . . . we will say platinum . . . . yup, that sounds good, to the meteor 2015 TB 145 and it was sent to be timed with the rock's passing by earth at 1.3 lunar distances on 31 Halloween.

All this in theory at a minor level of depth for approximations.

</end>So, given the above formula on time dilation is the final number I have 8.56286570597, what is the final answer's unit of measure? Seconds per day of decrease?

IE: 100 days on the rock and you will be 856.2865 seconds younger then those people on earth?


<end></end>-END-

 

[Umbran]

I am wondering what you're trying to calculate, especially considering relevance to the thread topic.

 

[Scott DeWar]

Time dilation. It was mentioned somewhere up on the thread. I am having trouble doing math for some reason. I know how, its just . . . . sometimes I look at it and it stares back at me tauntingly saying ,"your brain is now scrambled"

 

[Staffan]

</end>So, given the above formula on time dilation is the final number I have 8.56286570597, what is the final answer's unit of measure? Seconds per day of decrease?

IE: 100 days on the rock and you will be 856.2865 seconds younger then those people on earth?

The result is a ratio: for every unit of time that passes in the accelerated frame of reference ("on the ship"), X units pass in the frame at rest ("on Earth"). So for every day on the ship, 8.6 days pass at home.

Except you made a rather big mistake by putting the speed of light at 300,000 - the right value is 300,000,000 m/s (rounded a bit). You also forgot the 1-(v^2/c^2) on your first line. The two combined lead to a dilation factor that's pretty much too low to be noticed in your example (1.0000000432, or about one day extra in 70,000 years).

It's probably easier to use c itself as the unit of speed (that is, instead of expressing a speed as 100,000,000 m/s, it's 0.33c), because that gets rid of the huge "divide by 90 quadrillions" step (c^2 = 90 quadrillion m^2/s^2). That way, the time dilation equation simplifies to:

1 / (1-v^2)^-2

That is: take the speed you're traveling at as a fraction of the speed of light. Square it, and subtract it from 1. Divide 1 by the root of the result.

So let's take the example earlier of 1/3 the speed of light and plug it in:

1 / (1-(1/3)^2)^-2 =
1 / (1-1/9)^-2 =
1 / (8/9)^-2 = 1 / 0.943 = 1.06

In other words, when traveling at 1/3 the speed of light, you experience a time dilation of about 6%. Travel for 100 subjective years, and 106 years will have passed at home.

 

[Scott DeWar]

A BIG mistake from the gittgo. See, I should have knowen that. That is why I tried to do it.

 

[Umbran]

8.56286570597

That's not what I get. I get Gamma = 1.0000678...

Think of it this way, the thing is moving at 0.011% the speed of light. You don't start seeing human-noticeable effects until you get up around 10% the speed of light.

 

[Scott DeWar]

I will double check my math and make corrections tomorrow.

 

[Umbran]

I will double check my math and make corrections tomorrow.

Note that with those calculations, there's a problem. Not that you didn't get the math right, but one of experimental error.

The article quotes speeds of 35 km/sec (78,000 mph). That's reported to what we in the business would call "two significant digits".

It isn't *exactly* 35 km/sec. Maybe it is 35.4 km/sec. Or 35.43 km/sec. We don't know. The answer is rounded off to 35, the measurement reported with limited precision. We don't know what comes to the right of the decimal point.

Numbers I calculate from that must also be of limited precision. I reported a gamma above of 1.0000678. Most of that is garbage - I don't know it is really 1.0000678. I can't trust those far out decimal places. I can only count on the first two places in my answer being right. Gamma = 1.0 At the level of precision these measurements are taken, the time dilation effect will not be measurable.

In order to see an effect down around the fifth or sixth decimal place, I'd need a *very* precise speed measurement - like 35.01243 km/sec. I have to know the speed of the thing down to the single centimeter or millimeter per second in order to start to trust my calculation of the effect.