Clock behavior at High Velocities — Temporal Flux?

The behavior of clocks at high speeds is a tantalizing phenomenon explained by Einstein’s theory of relativity. According to this theory, time is not absolute but relative to the observer’s frame of reference. As an object approaches the speed of light, time appears to slow down for that object relative to a stationary observer. This phenomenon is known as time dilation.

Time dilation affects clocks at high speeds as follows:

• Clocks run slower at high speeds: If you were to travel in a spaceship at a significant fraction of the speed of light, your clock would run slower compared to a clock on Earth. This means that less time would pass for you than for someone on Earth.
• The faster you go, the slower time runs: Time dilation becomes increasingly pronounced as you approach the speed of light. At everyday speeds, the effect is negligible, but at high speeds, it becomes significant.
• Time dilation has been experimentally verified: Experiments with atomic clocks flown on airplanes and satellites have confirmed the predictions of time dilation.

The implications of time dilation are profound:

• Astronauts age slower: Astronauts on the International Space Station experience time dilation, albeit a small amount, due to their high orbital speed.
• Time travel is theoretically possible: If one could travel at or near the speed of light, they could travel into the future relative to those who remain on Earth.

Before thinking about the beautiful fruit of Time-Travel, wait a minute;

Special relativity indicates that, for an observer in an inertial frame of reference, a clock that is moving relative to them will be measured to tick slower than a clock that is at rest in their frame of reference. This case is sometimes called special relativistic time dilation. The faster the relative velocity, the greater the time dilation between one another, with time slowing to a stop as one approaches the speed of light (299,792,458 m/s).

Did you notice clock at rest in their frame of reference will be faster, but, here’s the catch; if you launch a rocket ship and go to the space to explore the vast land, you will not notice a single ounce. That’s because, with relative to you who is that rocket ship, no change in time or time-dilation would be perceived, and you’ll just waste your time. Basically what would happen is that people on Earth, would not perceive any difference. In reality, the time-dilation would be fractional.

If you travel at 1% of Light Speed, which assuming you are 80kg, would take around 3.5950207 * 10¹⁴ kJ of Energy. And, Earth in itself has an upper limit of 4.4 * 10¹³ kJ of Energy. (Note this the upper limit, and energy on Earth varies from 2.6 * 10¹¹ kJ to 4.4 * 10¹³ kJ which is still 9 times less than the energy required to move you at light speed, not accounting for Gravity and all).
Assuming you would get that much energy from Sun; still if you travel like 60 years in the Space at 1% light speed, which is 2,997,924.58 m/s. And, the time dilation would be a whopping 160 minutes, I’m not kidding; it would be 160 minutes, and anyone would hardly notice. With current technology severely limiting the velocity of space travel, however, the differences experienced in practice are minuscule: after 6 months on the International Space Station (ISS), orbiting Earth at a speed of about 7,700 m/s, an astronaut would have aged about 0.0005 seconds less than those on Earth.

Mathematics of Theory of relativity

Time dilation can be inferred from the observed constancy of the speed of light in all reference frames dictated by the second postulate of special relativity. This constancy of the speed of light means that, counter to intuition, the speeds of material objects and light are not additive. It is not possible to make the speed of light appear greater by moving towards or away from the light source.

Consider then, a simple vertical clock consisting of two mirrors A and B, between which a light pulse is bouncing. The separation of the mirrors is L and the clock ticks once each time the light pulse hits mirror A.

In the frame in which the clock is at rest (see left part of the diagram), the light pulse traces out a path of length 2L and the time period between the ticks of the clock Δt is equal to 2L divided by the speed of light c:

From the frame of reference of a moving observer traveling at the speed v relative to the resting frame of the clock (right part of diagram), the light pulse is seen as tracing out a longer, angled path 2D. Keeping the speed of light constant for all inertial observers requires a lengthening (that is dilation) of the time period between the ticks of this clock Δt`from the moving observer’s perspective. That is to say, as measured in a frame moving relative to the local clock, this clock will be running (that is ticking) more slowly, since tick rate equals one over the time period between ticks 1/Δt`

Straightforward application of the Pythagorean theorem leads to the well-known prediction of special relativity:

The total time for the light pulse to trace its path is given by:

The length of the half path can be calculated as a function of known quantities as:

Elimination of the variables D and L from these three equations results in:

Time dilation equation

which expresses the fact that the moving observer’s period of the clock Δt` is longer than the period Δt in the frame of the clock itself. The Lorentz factor gamma (γ) is defined as:

Because all clocks that have a common period in the resting frame should have a common period when observed from the moving frame, all other clocks — mechanical, electronic, optical (such as an identical horizontal version of the clock in the example) — should exhibit the same velocity-dependent time dilation.

So, Time-travel via space-travel is a bad idea, not bad, a terrible idea.