Time Dilation – The gist of this phenomenon is that if two observers travel in different speeds their clocks also run at different speeds. The clock setup taken up to prove this phenomenon is shown below (simplified diagram):
In the diagram, the lower rectangle represents a light source and light detector setup, and the top rectangle represents a mirror. When this setup is stationary, let the time taken for the light to travel from the source to the mirror and back to the detector be t1. And when the setup is moving, let the time taken be t2. According to this phenomenon t1 < t2. If t1 or t2 is taken as the basic unit for the clock, then its clear that the clock will run slower when its in motion. Refer this link for detailed explanation on how this is working.
Lets take a look at the following setup:
Well as you can see the clock setup has been tilted by 90 degrees, otherwise this setup is perpendicular to the previous setup. And if you calculate the numbers you’ll find that the Lorentz factor is different for these 2 setups. We clearly know that there have been a lot of technological improvements since Einstein had given this theory to the world. This light emit, reflect and detect setup for a clock is pretty much primitive.
Let me ask a question: Why are we not using the sand glass for keeping our time? Well you can give hundreds of reason. Why are we not using pendulum clocks? There are some environments in which it won’t give the accurate time. Why are we not using crystal oscillators in GPS satellites? Same answer. I am asking these questions to reason why we can not accept the theory of relativity anymore. I’ll explain this philosophy with an example.
Lets take a circle. We can very easily mark the center of the circle. Lets take a triangle. We can apply some geometric calculations and still mark the center of the triangle. Now lets say for a long time we only know about circles and not triangles. And we know that there is only one geometric shape that is a circle and we know how to mark the center of the circle. It has been established that for a geometric shape the center is from equal distance from any point in the periphery of the geometric shape. Remember we know only about circles; no rectangles; no squares; no triangles. Now after lot of experimentation and exploration (????) a mathematician discovers about a new geometric shape triangle. Now he knows from his past experience that the center of a geometric shape is from equal distance from any point in its periphery. The mathematician traces a new shape as shown below.
Now as per his discovery the center point of this new geometric shape is another shape. Some may immediately disagree with this and some may have confusion if there is a possibility that a center point of a shape could be another shape. This can not be true due to two reasons.
1. The proposed shape for the shape of the center point of a triangle depends on where we started first. If we have started outside the triangle we would have gotten a completely different shape. So the shape of a center point may not change based on where we start tracing the center point from.
2. A point is a one dimensional entity (though it may be given different dimension co-ordinates to identify its place). But here the point becomes 2 dimensional function. The fundamental assumption itself becomes wrong in this case.
Now try to compare this example with time dilation phenomenon. 1. Lorentz factor is the main output of this phenomenon. But that itself changes when we change the clock setup. So this can not be true. 2. Time is a single dimension. You can not confuse it with other dimensions because you can not measure time correctly. You can not bend distance and other dimensions because your clock runs slow when you speed up. You must build a clock which runs the same in all the speeds.