The Heart of Alice

We covered the topic in “the Wonderland” why Gryphon sees a time dilation on Alice’s clock. We saw that time dilation was just a perception and it was caused by the deformation of the electromagnetic signals coming from a moving clock. We will cover the same incident in this section by using Alice as a base this time because, similarly, Alice also sees a time a dilation on Gryphon’s clock. 

I’m presenting here again the result animation about Gryphon in the Animated Figure 1- the Wonderland section. This animation showed how the time dilation according to Gryphon’s reference system occurs in detail. We will understand how time dilation occurs for Alice by using the information in the animation. 

Alice observes a time dilation on Gryphon’s clock.

Gryphon and Alice are two reference systems that are mobile to each other. It is not important for these two reference systems which one is moving or which one is immobile because both these reference systems may regard themselves immobile and the other mobile. As Gryphon observes a time dilation, Alice must also observe a time dilation on Gryphon’s clock. If we showed Alice as immobile and Gryphon mobile, we would reach the same results.

We can mention such a General Rule depending on this situation:
The effect occurring for Gryphon at any moment must also occur similarly for Alice. Alice must get the same results when she measures the tick-tack intervals of Gryphon’s clock. If Gryphon sees the image of Alice (Ghost of Alice) at a certain distance, Alice must also see Gryphon’s image (Ghost of Gryphon) at the same distance. We should consider these principles in our new animation. If we provide these principles, we can see how time dilation occurs for Alice. Of course, we could regard Alice as immobile and create the animation; however, we will not do that here. We would like to see as observers how time dilation occurs for Alice when she is mobile. 

We may consider like this to reach a conclusion by taking the general rule into account: 
We already know how incidents occur for Gryphon. If we create a SYMMETRY AXIS between Alice and Gryphon, we can obtain the necessary information for Alice without difficulty. All the incidents occurring for Gryphon on the left side of the symmetry axis must be simultaneous with the incidents occurring for Alice on the right side. We will also maintain The Principle of Relativity by Albert Einstein by using the symmetry axis.

Principle of Relativity: The same law  of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good.

As we know what to do, we can create the animation that will show what kind of an incident occurs. The incidents occurring on the right side of the symmetry axis will be exactly the same with the incidents occurring on the left side. To sum up, in any t moment;

• Alice will be at the same distance to the symmetry axis as Gryphon will be.

• Alice will see the Ghost of Gryphon at the same distance from the symmetry axis as Gryphon sees the Ghost of Alice. 

• If a signal reaches Gryphon, Alice will also receive a signal.

• Which value Gryphon measures on the Alice's Clock, at the same time Alice will measure the same value on the Gryphon's clock.

Animated Figure 2 - In order to show each and every detail, the animation was made in 1024 pixels.