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How fast would you have to travel for a week of space ship time to arrive back at Earth in 100years in the future?

This is a classic time dilation problem related to special relativity. Here's how we can solve it:

**Understanding the Concepts**

* **Time Dilation:** According to special relativity, time slows down for an object moving at high speeds relative to a stationary observer. The faster the object moves, the more significant the time dilation effect.
* **Lorentz Factor (γ):** This factor quantifies the amount of time dilation. It's defined as:

γ = 1 / √(1 - (v²/c²))

where:
* v is the relative velocity between the observer and the moving object.
* c is the speed of light (approximately 299,792,458 meters per second).

* **Time Dilation Equation:**

t' = γ * t

where:
* t' is the time measured by the stationary observer (Earth time in this case).
* t is the time measured by the moving observer (spaceship time).

**Setting Up the Problem**

* t' (Earth time) = 100 years = 100 * 365.25 * 24 * 3600 seconds (approximately 3.156 x 10^9 seconds)
* t (Spaceship time) = 1 week = 7 * 24 * 3600 seconds = 604,800 seconds

**Solving for the Lorentz Factor (γ)**

We can rearrange the time dilation equation to solve for γ:

γ = t' / t = (3.156 x 10^9 seconds) / (604,800 seconds) ≈ 5217

**Solving for the Velocity (v)**

Now that we have γ, we can plug it into the Lorentz factor equation and solve for v:

5217 = 1 / √(1 - (v²/c²))

Square both sides:

5217^2 = 1 / (1 - (v²/c²))

Rearrange to isolate (v²/c²):

1 - (v²/c²) = 1 / (5217^2)

v²/c² = 1 - (1 / (5217^2))

v²/c² ≈ 0.99999996327

v² ≈ 0.99999996327 * c²

v ≈ √(0.99999996327) * c

v ≈ 0.99999998163 * c

**Answer**

You would need to travel at approximately **99.999998163% the speed of light** for a week of spaceship time to correspond to 100 years of Earth time.

**Important Considerations**

* **Technological Impossibility:** Reaching such speeds is currently beyond our technological capabilities. It would require enormous amounts of energy and face immense engineering challenges.
* **Relativistic Effects:** At these speeds, other relativistic effects would become significant, such as increases in mass.
* **Acceleration and Deceleration:** This calculation only considers constant velocity. The time spent accelerating to and decelerating from these speeds would also affect the total time dilation.
* **Energy Requirements:** The energy required to accelerate a spaceship to such speeds is astronomical, far beyond our current capabilities to produce or contain.






How does Erich von Daniken propose that ancient aliens took advantage of time dilation to travel to earth over eons of earth time?




Erich von Däniken, in his various books like "Chariots of the Gods?" doesn't explicitly delve into the technicalities of time dilation in the way a physicist would. However, the *implication* is central to his ancient alien hypothesis. Here's how his ideas connect with the concept:



* **Vast Distances:** Däniken's core idea is that advanced extraterrestrial beings visited Earth in the distant past. These aliens would have come from star systems potentially light-years away.



* **Time as a Barrier:** Traveling such immense distances at sub-light speeds (far slower than the speed of light) would take lifetimes, even for beings with lifespans far exceeding human years. This poses a problem for any civilization trying to explore other planets.



* **Exploiting Relativity (Implied):** While he doesn't write out equations, the argument implies that highly advanced aliens understood and could utilize the principles of Einstein's theory of relativity, including time dilation.



* **Near Light Speed Travel:** According to relativity, the faster an object moves, the slower time passes for it relative to a stationary observer. If aliens could travel at speeds approaching the speed of light, time dilation would become significant. For the aliens on the spacecraft, the journey to Earth might take only a few years (or even months, depending on the speed), while thousands or millions of years pass on Earth.



* **Asymmetric Timeframe:** So, from the alien's perspective, the journey to Earth might be manageable. They could travel here, interact with early humans (according to Däniken's theories), and return relatively quickly. But, because of time dilation, a huge amount of time would have passed on Earth since their departure. This fits into the idea that the alien visits happened thousands of years ago.



**In short, the premise is:**



* Aliens are advanced enough to achieve near-light-speed travel.
* Near-light-speed travel causes significant time dilation.
* Time dilation allows them to traverse vast interstellar distances in a relatively short subjective time.
* While a short time passes for the aliens, vast eons can pass on Earth during their travels, fitting into the historical timeline he proposes.



**Important Considerations:**



* **Däniken's theories are largely speculative:** They are based on interpreting ancient artifacts and myths in a way that supports his extraterrestrial hypothesis, rather than on rigorous scientific evidence.
* **He simplifies complex physics:** Däniken's discussions often gloss over the immense technological challenges involved in achieving and surviving near-light-speed travel. The energy requirements, shielding from radiation, and navigation challenges are enormous.
* **Alternative Explanations:** Most scientists find that there are more mundane and logical explanations for the artifacts and mysteries that Däniken uses to support his claims.



While his ideas are intriguing and have captured the public imagination, they are not generally accepted within the scientific community. The application of time dilation is just one part of the puzzle, and the overall hypothesis lacks strong evidence.