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There are many questions on Worldbuilding about what item(s) a time traveller should take back in time in order to alter past events or even simply to survive.

There has never as far as I know been any mention of the amount of energy needed for time travel or any explanation of the size or quantity of items that can be taken with the traveller.

According to General Relativity, time-travel is possible in the sense that a traveller through space can age slower than someone who stays at home. (Edit - As pointed out by @Spencer this is called time-dilation)

However

We could travel 10,000 years into the future and age only 1 year during that journey. However, such a trip would consume an extraordinary amount of energy. https://spaceplace.nasa.gov/review/dr-marc-space/time-travel.html

Question

Suppose I want to age 1 year to my stay-at-home friends' 10 years: are there enough resources on Earth to send even one person on such a trip?

What is the energy required for the trip with respect to the mass of the spacecraft for the subjective 1 year trip?

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    $\begingroup$ Given that $\Delta t^\prime = \Delta t / \sqrt{1 - \frac {v^2}{c^2}}$ and $\Delta t^\prime / \Delta t = 10$ we find that $v$ is... and so on. Is this site about arithmetic? $\endgroup$ – AlexP Feb 10 at 23:11
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    $\begingroup$ @JBH: Actually, forward time travel is not only possible, it's inescapable. We are all time travellers moving at the speed of light... $\endgroup$ – AlexP Feb 10 at 23:18
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    $\begingroup$ @AlexP, well... yes... ha ha. In that regard the cost to move me forward in time five minutes is roughly equal to the caloric value of a maple bar donut. $\endgroup$ – JBH Feb 10 at 23:19
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    $\begingroup$ @AlexP Sure, we know that we can calculate the equations to find out the required velocity but this question is about the energy and resources required in order to attain that velocity. Also, as acceleration is necessarily involved, it's not even that simple $\endgroup$ – Mithrandir24601 Feb 10 at 23:24
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    $\begingroup$ I'm quite happy to know the minimum or even quantify the amount of energy at all. I just want to get some order-of-magintude idea. I am not a physicist. That's why I'm asking. Other people ask about subjects they don't know about. Stack Exchange wouldn't exist at all if the askers already knew the answers. You could just say to them, "Go take a degree in X and you can work out the answer for yourself." It would take a lifetime of study just to write one short story. $\endgroup$ – chasly from UK Feb 10 at 23:47
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You can get some details from this site: Relativistic Energy. The gist is that if you assume away (simplify) details so that the mechanism by which you achieve $v\approx .995 c$ is ignored (which gets you $\gamma=10$), then the total relativistic energy is $E=\gamma\: m\: c^2$. Since $E_0=m\: c^2$, the difference required will be: $\Delta E=\left(\gamma-1\right)m\: c^2$. Assuming a magical jump to hyper-speed is allowed to simplify the question.

But you still need to know how much mass you expect to get moving. Suppose the entire habitat, with human, amounted to $m=1000\: \text{kg}$, then this would require approximately $1.3$ times the total annual global energy consumption of all of humanity, at today's rate. (We consume approximately 600 quads from ask sources, or so, each year. That figure, by the way, was about 400 quads back in 2000 or so when I was volunteering to review some of the science going into the IPCC TAR.)

P.S. Keep in mind that this ignores the rocket equation, which would have something else to say about the problem (but then, at first, still discounting relativistic effects.) Further down that page you can find a discussion of the relativistic rocket equation, which would be more appropriately used here, I suppose.

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    $\begingroup$ "1.3 times the total global energy consumption of all of humanity, today." — daily consumption? Yearly? Energy is in J, energy consumption in W, units don't match without a time. $\endgroup$ – Mołot Feb 11 at 7:43
  • $\begingroup$ @Molot I clearly wrote "600 quads... Each year." So I'm talking about the annual energy figure. If you integrate the power over time for one year, this will not yet be about, by a factor of 1.3, to achieve the simplified energy need. Or, put another way, it would take 1.3 years of every bit of human energy use to match the requirement. $\endgroup$ – jonk Feb 11 at 7:48
  • $\begingroup$ @Molot By "today" I merely meant "at the current rate" or instantious rate. $\endgroup$ – jonk Feb 11 at 7:52

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