Clock postulate calculations?

[StrangeDays]

Let me start by saying I most likly have no idea what I am doing. Also, that I realize the factor by which the moveing clock differs from the stationary one will be very very small. Sorry if this belongs in the math fourm, i thought it might require physics knowledge.

What I'm having problems with is the systems of measurement and how they work together.

gamma = sqrt(1-v^2)
v relitive to the speed of light.
60 Miles per hour = 26.8224 Meters per second
26.8224/299792458 = 8.946989587×10^-8(m/s)/c
(8.946989587×10^-8)^2 = 8.00486227x10^-15
1-8.00486227x10^-15 = 2.00486227x10^-15
sqrt(2.00486227x10^-15) = 4.477568838x10^-8
gamma = 4.477568838x10^-8


And now I'm totaly lost.
How is time measured? What do I multiply gamma with to get an actual # of how much of a second the clock is off?

and/or do I have no idea what I am doing?

 

[dlgoff]

1-8.00486227x10^-15 = 2.00486227x10^-15

This step is incorrect. It should be 1000000000000000x10^-15 - 8.00486227x10^-15 = 999999999999992x10^-15 which is almost 1.

 

[R0man]

It's great that you are exploring the clock postulate and trying to understand how time is affected by motion. Let me try to break down the calculations for you.

First, the clock postulate states that time is relative and can be affected by motion. This means that an observer's perception of time can be different depending on their relative motion to an event or object.

The equation you are using, gamma = sqrt(1-v^2), is known as the Lorentz factor and it helps us calculate the difference in time between a stationary clock and a moving clock. This factor takes into account the speed of the moving clock (v) relative to the speed of light (c).

In your example, you have converted the speed of 60 miles per hour to meters per second (26.8224 m/s) and then divided it by the speed of light (299792458 m/s). This gives you the value of v (8.946989587×10^-8 m/s)/c.

Next, you squared this value (8.946989587×10^-8)^2 to get 8.00486227x10^-15. This value represents the difference in time between the stationary and moving clock. However, this is a very small value and may be difficult to understand.

To get a more tangible result, you can subtract this value from 1 (1-8.00486227x10^-15) to get 2.00486227x10^-15. This represents the fraction of a second that the moving clock is ahead of the stationary clock.

To get an actual number, you can take the square root of this value (sqrt(2.00486227x10^-15)) which gives you 4.477568838x10^-8. This means that for every second that passes for a stationary clock, the moving clock will be 4.477568838x10^-8 seconds ahead.

In summary, your calculations are correct and you are on the right track. Time is measured in seconds and the Lorentz factor (gamma) helps us understand the difference in time between a stationary and moving clock. Keep exploring and asking questions, that's the best way to learn!