IN WONDERLAND

We can move on to our main topic “Why Gryphon observes a time dilation at the clock on the right side” by summarizing chapters Airport and On Air.

Animated figure 1- As both clocks get closer to Alice with equal speed from equal distance, it can be observed that the slope of the bar will not change for Alice. This shows that both the clocks work simultaneously from Alice’s perspective.

Animated Figure 2- Now it is necessary to understand whether both clocks work simultaneously from Gryphon’s perspective or not. If we answer this question too, our job will become easier. Therefore, it is enough to understand whether the slope of the bar changes from Gryphon’s perspective or not. For that purpose, let’s mount a pen to either edge of the bar and imagine that Main Frame moves on the direction of the axis X. Let the pen mark the position it stands. What type of curve will it draw?

We already know that the slope of the bar won’t change for Alice. Accordingly, the pen must draw a line according to Alice’s reference system. The line drawn for Alice will be uniform sinus curve. If we assume the slope of the bar changes for Gryphon, the pen cannot draw a uniform sinus curve.

Now that the pen cannot draw two different lines both for Alice and Gryphon at the same time, the line drawn for Alice will be valid for Gryphon, too. The line that the pen will draw is the only one and it is always a uniform sinus curve. This issue shows that the slope of the bar is same for Gryphon and, therefore, both the clocks work simultaneously for Gryphon, too.

Therefore, a very important result comes to surface. Time dilation is not a real effect; it’s just a perception.

Animated figure 3- Firstly, let’s understand how Gryphon will see the bar. Everything we see comes to us from past. The electromagnetic waves that carry images cover a distance from the source they are sent until they reach our eyes. If the light comes far from distance then the information it carries belongs to that far in the past. 

As both edges of the bar are at different distances from Gryphon’s perspective, a deformation caused by time differences is formed on the visual image of the bar. As a result of this deformation, even if the clocks do not move on the direction of the axis X, Gryphon will inevitably observe that the bar doesn’t stand straight and level. 

In my own studies, I name the images of the objects "GHOST" and the objects themselves "SPRING". These notions ease the explanation of the visual events. What we always see is GHOST. We can never see an object’s SPRING. 

Animated figure 4 – The animation below informs us about how the bar will look like from Gryphon’s position. A bar parallel to the ground is moving up and down. As can be seen, as the bar is moving constantly, Gryphon never sees it straight and level. The image of the bar changes depending on the oscillation frequency and the length of the bar. You can test how the bar might look like from different angles by changing the Gryphon’s position.

Animated figure 5- By the way let’s see how length contraction takes place. We can easily explain how length contraction takes place by using the notions “GHOST” and “SPRING”. The same vision principle we covered at figure 3 and 4 lies behind the length contraction. The moving frames relative to each other are included again; however, we should also take the dimensions of the object and reckon the signals coming from in front of and behind the object. The objects that move away are observed as if they were squeezed in length.

Animated figure 6- It is more accurate naming Length contraction as Length Deformation. It is because the length deformation might occur both as contraction or extension. Length extending is seen on the objects getting closer to each other and length contraction is seen on the objects getting far away from each other. In other words the changes in length occur always on the Ghost not on Spring.

Animated figure 7- Now we can move to why Gryphon sees time dilation. A signal sent by the clock actually brings two information to Gryphon. The coordinate of the clock according to Gryphon at the time the signal was sent and the time when the signal was sent. When the signal arrives Gryphon will see the image of the clock at that point and at that clock value.

Animated figure 8- It is enough to pay attention to the signals sent consecutively by the principle above to understand how the times dilation is. We see this situation in the animation below.

The clock on which Alice sits sends the signals with fixed intervals. We see a ruler bound to Gryphon’s reference system in the animation. The ruler is a helper showing the coordinate of the signals sent. Each signal sent is going to Gryphon with “c” light speed. Thus the speed of the signals according to this ruler is “c”. When a signal arrives to Gryphon, with the information carried by signal, Gryphon sees image of the clock (GHOST) at the coordinate the signal sent and at the times the signal sent.

You can clearly see the details of the events taking place during the Time Dilation in the animation if you set the Radio Buttons to “Show the principle”.

Let’s set the Radio buttons to “Show Intervals” and pay attention the arrival intervals of the signals to Gryphon. Alice’s slowing and accelerating change the time between the two neighbor signals arriving Gryphon. Because of this change Gryphon sees a time dilation at Alice’s clock.

Let’s set the Radio Buttons to “Show the FULL EVENT”. The signals are coming to Gryphon from Spring. However, Gryphon certainly doesn’t see the clock at Spring and the signals arriving it determine where and how it will see the clock. What it sees is the clock at GHOST and it sees that this clock works at different speed.

As can be seen, time dilation is just a perception. We have already mentioned above that the clock at Spring and the clock of Gryphon should work simultaneously. In the animation, the bar standing on the minute hands shows that the clocks work simultaneously.

Let’s set the Radio Buttons to “Show the Math”. In the upcoming window we see what type of a math Gryphon will meet when comparing the signals reaching it and the signals of its own clock. This math is the real math representing Time Dilation. This equation has another very important meaning, because this math represents the Doppler Effect's math. In other words, the reason of the Doppler Effect and Time Dilation is dependent to same principles and reasons we see here. It is not mentioned above but the math of length deformation is also dependant to this math.

Let’s set the Radio Button to “Compare the Clocks”. You can compare the Gryphon’s clock and the clock at Ghost easier. Time dilation can be in both directions just like length deformation. Namely, while we can see a clock ticking slower, we can see a clock ticking faster than normal. Thus naming it as time deformation is more accurate. 

Let’s set the Radio Buttons as “Speed of Ghost”. In this animation 5 pixel/frame value has been used for velocity of light. Speed of Alice may change between 0 – 5 pixel/frame, namely any value between zero and velocity of light. As the important thing here is the proportion, this animation gives us the exactly same situation in the nature. That the movement speed of Ghost is different than the movement speed of Spring might catch your attention. This is an effect that relativity does on our perception speed. Perception speed is inversely proportional to time dilation. We see that the events in our movement direction take place faster while the events behind our direction occur slower. Length contraction is not included in this animation because our focus is on time dilation.

We handle the situation just for Gryphon here; Alice will also see a time dilation on Gryphon’s clock. I will mention that in the next chapter.

Universal Velocity of Light Postulate 

The speed of a signal is independent from the source that sends it. I would like state that this is what Albert Einstein said.

Universal Velocity of Light: The light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body. 

In the animation we see that his postulate is preserved. The speed of signals sent from Alice’s clock is not “c” according to Alice, but it is "c" according to Gryphon. Alice Law uses Einstein’s this postulate really well and as it should be.

The reason and math of the time dilation is never included in “Lorentz Transformations”. The shortcoming in relativity theory is a result of a deficiency in Electromagnetic Theory.

Please focus your thoughts and studies on Alice Law swiftly. The future is inside the Alice Law. 

IN WONDERLAND

"Welcome to the Wonderland. If the White Rabbit gives you something to eat, don’t eat it. You may shrink and get lost in the grass."

Linkedin Alice Law Discussion Group:
http://www.linkedin.com/groups/Alice-Law-3901881?trk=myg_ugrp_ovr

Alice Law is the future of physics.
Please help it become widespread and well-understood.

Han Erim

  aliceinphysics.com

Establish: December 2001

Copyright © 2000-2011. Han Erim. All Rights Reserved.