Undergrad Could I travel to andromeda in my lifetime?

[tomasbede]

Hi, this is my first post on here. Let's say I departure from Earth in a spaceship and reach a speed very close to c, as I go faster time would run slower and I would feel as if I was going faster and faster with no speed limit, even though I'm not going faster than c. Because my time is distorted, space would shrink making it possible for me to reach another galaxy in my lifetime. By the time I got to andromeda, life in Earth would have disappeared 2.537 million years ago. But for me it would have only been a couple of years, days or seconds, depending on how close I got to c.

I've been intrigued by relativity lately and I'm trying to understand it before I get to the math. Am I right thinking what a wrote? If not, what's wrong and what would be the correct way to put it.

I would also like to know how hard is the math behind relativity, I'm a 3rd year engineering student.

PS: English is my second language, sorry if I wrote something wrong.

Thanks!

 

[Dale]

Hi @tomasbede, welcome to PF

Am I right thinking what a wrote?

Yes. Here is my favorite page on the topic http://math.ucr.edu/home/baez/physics/Relativity/SR/Rocket/rocket.html

I would also like to know how hard is the math behind relativity, I'm a 3rd year engineering student.

You should easily be able to handle the math. It is just some algebra for the basics and some integrals for the more advanced stuff.

 

[tomasbede]

From my perspective, in respect to earth, would I feel like I'm going faster than c as my time is distorted? Wouldn't that contradict the fact that nothing can go faster than c?

 

[Ibix]

From my perspective, in respect to earth, would I feel like I'm going faster than c as my time is distorted? Wouldn't that contradict the fact that nothing can go faster than c?

Yes. That's a hint that you aren't thinking about this correctly. In fact, you will never feel anything odd. If you aren't accelerating then you can always consider yourself stationary.

Described from the Earth's rest frame, your clocks run slow and you get to Andromeda because you age slowly. Described from your rest frame your clocks are normal. However, the distance between Earth and Andromeda is length contracted because it is they who are moving. Since they aren't very far apart and are moving fast, Andromeda reaches you in a short enough time that you can live through it.

It's worth noting that the relativistic rocket equations are truly depressing. Actually doing this journey would take millions of tonnes of fuel per kilogram of payload, even with a 100% efficient total conversion drive.

 

[MeJennifer]

It's worth noting that the relativistic rocket equations are truly depressing. Actually doing this journey would take millions of tonnes of fuel per kilogram of payload, even with a 100% efficient total conversion drive.

Even if you find a way the radiation would kill you unless you make an even more massive spacecraft .

 

[pixel]

Even if you find a way the radiation would kill you unless you make an even more massive spacecraft .

Not to mention collisions with tiny particles that would have devastating effects at speeds near c.

 

[Dale]

From my perspective, in respect to earth, would I feel like I'm going faster than c as my time is distorted? Wouldn't that contradict the fact that nothing can go faster than c?

There is no inertial frame in which you are going faster than c. You could make a coordinate system which used the Earth frame for distance and your ship time for time. Such a frame would be non inertial, so there would be no restriction to less than c and light would also not travel at c in that non inertial frame.

 

[Herman Trivilino]

Hi, this is my first post on here. Let's say I departure from Earth in a spaceship and reach a speed very close to c, as I go faster time would run slower and I would feel as if I was going faster and faster with no speed limit, even though I'm not going faster than c.

As your speed increases you would observe the distance to your destination shrink. That distance approaches zero as your speed approaches c. This is called length contraction.

As your speed increases people on Earth would observe your clocks running slower and slower. People on Earth would observe the rate at which your clocks run approaching zero as your speed approaches c. This is called time dilation.

So note that it is you who observes the contraction of lengths measured by Earth observers. And it's people on Earth who observe dilation of the time mesured by you.

You currently have all the math background that's needed to work through a book like Spacetime Physics by Taylor and Wheeler. That's an excellent introduction to the topic.

 

[tomasbede]

You currently have all the math background that's needed to work through a book like Spacetime Physics by Taylor and Wheeler

Thanks, I will definitely check it out!

 

[pervect]

Thanks, I will definitely check it out!

A very old but very easy-to-grasp book is Bondi's "Relativity and Common Sense". I hear Mermin has a more modern text out with a similar approach, but I've never read it. A more advanced college level textbook would be "Space-Time physics", by EF Taylor. The first few chapters of the previous edition are available online at the author's website, http://www.eftaylor.com/.

PF Insights has a graphically oriented tutorial using a diagramatic approach with little math. https://www.physicsforums.com/insights/spacetime-diagrams-light-clocks/ . It's based on using space-time diagrams and light clocks, and contains a reference to the published paper. The published version isn't available online, but the preprint can be found if you look at the discussion thread of the article.

 

[PeroK]

Thanks, I will definitely check it out!

There's a free online text here:

http://www.lightandmatter.com/sr/