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In a previous video we talked about the possibility of traveling the galaxy,

traveling to the center of the galaxy.

Our motivation for this was the twin paradox, once we understood it a little

bit more the fact that the person on the rocket traveling, if they travel,

say to the center of the galaxy, and then back again, they could end up

actually making the trip in a reasonable amount of time, and number of years.

And whereas when they got back,

the time that had elapsed on Earth say many thousands of years.

But at least it opened up the possibility of making a trip and

in a sense traveling forward into time when you get back.

But certainly during the trip itself, your clock would just tick away normally and

you would live normally as you could expect, perhaps,

in a situation like that, and make it back in a lifetime.

And then in the previous video clip we talked about equals mc squared and

a few ideas of the concepts of energy.

So now we're in a position to talk a little bit more about

traveling the galaxy, because we mentioned that the practical limit,

unfortunately, is just how you'd actually get the fuel you need,

how you'd propel your vehicle so that you can get it up to the speed of light, say.

Or very close to the speed of light, not actually to the speed of light,

because as you get closer and closer to the speed of light,

it turns out that the energy you need goes up and up and up.

But you can actually do some calculations, we're not going to do these calculations,

I just written some of the key equations up here for

those of you who've had some math, to get a sense of what's involved in this.

Essentially, we're doing a relativistic rocket problem for an acceleration of 1g,

1g being the acceleration due to gravity on or 9.8 meters per second squared.

As we mentioned before, or about ten meters per second squared.

And so you get equations like this relating the time passing on Earth

versus the time passing on the rocket.

Where you talk about these hyperbolic trigonometric functions where sinh of h,

sinh of this value is defined to be e to the x minus e to the minus x over 2 and

so on and so forth.

We have another equation, for the distance travelled, we have equation for

the velocity, because of course the velocity is changing, it's not constant

velocity of motion anymore, but we have acceleration and so on and so forth.

So it get a little complicated there, but let's look at the results.

And so this is a situation where the rocket is traveling a certain distance and

we also want it to slow down, so we can actually stop at the other end and

then maybe come back the other direction.

So we want to figure out okay, how long would it actually take to get a certain

distance throughout the galaxy, and assuming we're gong to actually stop at

the other end, look around, take a few pictures and then head back again perhaps.

So you work out those equations.

Distance of 4.3 light years, essentially to the nearest star.

The time on the rocket, which is an important value for our purposes,

to see if we can live that long, is 3.6 years, so not too bad.

We talked about a 1g acceleration, we showed that

you can actually get up to very high speeds in a very simple,

even simplistic calculation over the course of 300 to 400 days even.

So in 3.6 years you can accelerate up to speeds

where you can actually get to a nearby star system.

What type of fuel might you need to do that?

Well first of all we have to figure out what fuel are we going to use.

We talked about nuclear fission and nuclear fusion and

the fact that essentially what going on there we're turning matter into energy and

in actual fact, you're not turning much matter into energy at all.

Infusion as we mentioned, you're taking two hydrogen nuclei,

fusing them together and essentially getting a helium nucleus out of it.

And because the helium nucleus actually has less matter in it

than the two hydrogen together, if the look at the mass involved,

then the missing mass turns into energy.

And so, actually, you don't have much missing mass in that process, but

because of the e equals mc squared factor, that that c squared value is so

large, a little bit of mass turns into a lot of energy.

And so we could, well maybe we could do something with nuclear fusion, but

that's not very efficient.

Because even though you getting a lot of energy out, you still have

a lot of mass left over, and nuclear fission is even less efficient than that.

So, what we're going to imagine here is we're going to imagine a fuel that's 100%

efficient.

And the only situation we have with that is if you have a matter and anti-matter

collision, essentially and the mass disappears and it turns in a pure energy.

For example, if you have an electron and the anti-matter relation of an electron,

the other particle, the anti-matter partner, as it were, is the positron.

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And for whatever reason, the universe has a lot more matter than anti-matter.

In fact that's a big puzzle that

scientists have various theories about how that could have happened.

Why, why is this great asymmetry,

this great unbalance between the amount of matter as

far as we can tell in the universe and the amount of anti-matter as we call it.

But anyway, we can actually create anti-matter.

You can imagine electrons and

positrons, bring them together, you turn mass completely 100% into energy.

So that's the type of fuel we're imagining here.

So we want to figure out, okay, given that we have enough of this stuff around and

we can actually control it, how much of that would we actually have to take to

fuel our rocket and get to say a near by star system in 3.6 years?

Turns out not to bad actually, about 38 kilograms.

Now the other thing we have to think about here is that,

a lot of this fuel is just going to propel the fuel itself.

Cause the more fuel you add the more mass you have,

the more fuel you need to get going fast enough.

So the more fuel we have here,

the more fuel we have to add on top of that just to get us going any place.

That's one reason why the original Apollo rockets were so massive,

the first stages, because you need to have a lot of fuel just to eventually get that

tiny little capsule on top going toward the moon.

So 38 kilograms, that's not much though, not too bad.

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about 890 or so kilograms.

So a fairly big jump there, but again, sort of we can imagine that.

What if we want to go to the center of the galaxy?

Because that's the example we did before and with the numbers we have here,

1g acceleration, it take about 20 years.

Again, not too bad, we could imagine something like that, but

now look at the amount of fuel that we need to do that.

Again, assuming a pure matter or anti-matter rocket engine that was a 100%

efficient, putting all our fuel into pure energy to propel the rocket.

It comes out to be about 950,000 tons of material there,

roughly speaking.

So, I mean, that's huge, right?

To even get that amount together, but then actually build a ship that can contain it.

And then just for interest, we could even imagine traveling to another galaxy,

the Andromeda galaxy,

nearby galaxy, relatively nearby two million light years away.

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4,000 million tons of the material.

So again, we can see they're real practical,

even in this somewhat fanciful situation where we have this super efficient,

100% efficient, matter, anti-matter engine.

Even there, just trying to get the fuel for

something like that is going to be a relatively impossible task there.

Now, of course, we can think of other more science fiction type of solutions to this.

Things like warp drives or

actually even coming up with some way to manipulate the curvature of space.

The General Theory of Relativity shows, at least in principle,

that if we could do that, we could actually travel far distances in

a relatively short amount of time, with not much energy expenditure.

But again, those are more science fiction at this point then than anything else.

So even though the Theory of Relativity holds out hope that yes,

we could actually travel these long distances in a short amount of time,

in terms of the time elapsed on the rocket, that unfortunately

it's going to be a long time, if ever, that we're able to do such things.