Blog of Veikko M.O.T. Nyfors, Hybrid Quantum ICT consultant

Quantum Mechanics demystified, a try

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Special Relativity

Mass and energy are equivalent.

Partly formed by momentum (e.g. photon in mind):

$\hspace{1em}E=\sqrt {p^{2}c^{2}+m^{2}c^{4}}, \hspace{1em} p=mv$

Energy for a moving object (?):

$\hspace{1em}E=\frac{1}{\sqrt {1-\frac{v^{2}}{c^{2}}}} mc^{2}$

Time and mass are dependent of velocity

For time, time dilation: \(\\t^{'}=\frac{t_0}{\sqrt {1-\frac{v^{2}}{c^{2}}}}, \hspace{1em} \text{where}\\ t_0=\text{proper time of the object in move}\\ v=\text{relative speed between objects}\\ t'=\text{time observed in observing object's frame}\\\)

Why would that be: This is how I am reasoning cause for time dilation. Time is fourth dimension on top of our 3D world. As it is hard for a human to comprehend 4D, let’s imagine we were in space with only one spatial dimension. We only could move on X axis direction. Additionally we had time dimension which is running in perpendicular T-axis.
Me and my pal are stationary at the same spot on X and T axis. Now my pal starts moving fast to the right on X axis. As time is running, my pal also goes upwards on T axis. Me myself staying still on X axis, but time is running for me as well i.e. T is increasing.
We both have a clock device, based on light running between two opposite mirrors. Whenever certain amount of rounds between mirrors have taken place, one second is ticked. From my standpoint light in my pal’s light clock light is traveling not straight but along a zig-zag kind of curve, which is somewhat longer than the curve my clock’s light was traveling, being stationary along X axis and only moving on T axis upwards.
Now that speed of light is constant and my pal’s clock light has traveled a longer journey, it must be my pal’s clock must have been ticking more slowly.

I have two synchronized precision clocks A and B 18x10^8 m apart from each other.
A satellite is traveling above on the sky with speed 1.8x10^8 m/s, in line with my clocks. There’s a clock C in the satellite, which is synchronized with my clocks.
I measure with my clocks it takes 10 seconds for the satellite to take from over clock A to over clock B.
What will the clock C show when over clock B?

\[10=\frac{t_0}{\sqrt {1-\frac{v^{2}}{c^{2}}}} \Rightarrow t_0=\sqrt {1-\frac{v^{2}}{c^{2}}}*10= \sqrt {1-\frac{(1.8*10^8)^2}{(3*10^8)^{2}}}*10=8\]

Thus, satellite’s clock ticked 8 times whereas mine did 10.

Relative mass: \(\\m=\frac{m_{0}}{\sqrt {1-\frac{v^{2}}{c^{2}}}} \text{where}\\ m_0=\text{rest mass of the object in move}\\ v=\text{relative speed between objects}\\ m'=\text{mass observed in observing object's frame}\\\)

Lorenz’s transformation

Frame of reference with ‘ is moving along x axis in stable speed u.
Point S=(x,y,z) in view of moving reference frame with ‘ becomes S=(x’,y’,z’). Also time gets changed.
Traditional Galilean transformation needed to be enhanced to comply with Maxwell equations:





Relativity factor

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