Undergrad Time travel to the Andromeda Galaxy

[Dnj23]

TL;DR

Time travel traversal to the Andromeda Galaxy

Hi,

I recently learned that if you can travel at the speed of light, or nearly, you can reach the Andromeda Galaxy within 30 years, due to time dilation and bypassing 2.5 million years on Earth. Is this true?

 

[Ibix]

You can't travel at the speed of light (it turns out to be self-contradictory to try to describe it), but your "nearly" is answerable. You can get to Andromeda in an arbitrarily short time by your clocks, yes, due to time dilation. Brutal acceleration may be required for particularly short times. However, in any case, Earth clocks will measure you taking at least 2.5 million years and all your family will be 5 million years dead by the time you get back.

Edit: the above is all "in principle". Calculating the fuel requirements (even assuming the most efficient possible fuel and rocket) is depressing.

 

[PeroK]

Summary: Time travel traversal to the Andromeda Galaxy

Hi,

I recently learned that if you can travel at the speed of light, or nearly, you can reach the Andromeda Galaxy within 30 years, due to time dilation and bypassing 2.5 million years on Earth. Is this true?

In theory, a spaceship could travel to Andromeda in any finite time according to the ship's clocks. The problem is being able to accelerate while in the vacuum of space.

30 years sounds like it might be right for a ship accelerating at $10m/s^2$ (which would create artificial Earth-like gravity on board).

Such a ship could, given sufficient fuel, get up to any speed less than the speed of light (relative to Andromeda).

 

[Ibix]

But does it take light to travel from Andromeda in +-30 years in that relative time?

I'm not quite sure what you are asking. You won't beat a light signal to Andromeda, if that's what you are asking. From the Earth's point of view this is straightforward to understand - the ship is going almost as fast as light but not faster.

Explaining it for an accelerating ship is quite complex. But if you imagine the ship accelerating more or less instantaneously then coasting, the ship sees the distance to Andromeda length contracted and Andromeda rushing towards them. So light taking less than 2.5 million years is simple - it's a much shorter distance.

 

[Dnj23]

And

I'm not quite sure what you are asking. You won't beat a light signal to Andromeda, if that's what you are asking. From the Earth's point of view this is straightforward to understand - the ship is going almost as fast as light but not faster.

Explaining it for an accelerating ship is quite complex. But if you imagine the ship accelerating more or less instantaneously then coasting, the ship sees the distance to Andromeda length contracted and Andromeda rushing towards them. So light taking less than 2.5 million years is simple - it's a much shorter distance.

How long does light take to reach us from Andromeda, from Andromeda light perspective?

 

[Ibix]

How long does light take to reach us from Andromeda, from Andromeda light perspective?

There is no "perspective of light". Trying to define one is part of the self-contradiction I mentioned in my first response, so this question is unanswerable.

 

[PeterDonis]

bypassing 2.5 million years on Earth

I'm not sure what you mean by "bypassing", so let me suggest extending your scenario as follows: you get in your rocket ship and travel to Andromeda, in such a way that only 30 years elapses for you on board the ship. When you reach Andromeda, you turn around and travel back to Earth, again in such a way that only 30 years elapses for you on board the ship. When you arrive back at Earth, you find that 5 million years have elapsed on Earth. Is that what you mean by "bypassing"?

 

[Dnj23]

I'm not sure what you mean by "bypassing", so let me suggest extending your scenario as follows: you get in your rocket ship and travel to Andromeda, in such a way that only 30 years elapses for you on board the ship. When you reach Andromeda, you turn around and travel back to Earth, again in such a way that only 30 years elapses for you on board the ship. When you arrive back at Earth, you find that 5 million years have elapsed on Earth. Is that what you mean by "bypassing"?

Well, yes

 

[PeroK]

And

How long does light take to reach us from Andromeda, from Andromeda light perspective?

Light has no perspective. The laws of special relativity apply in "inertial reference frames", all of which move at less than the speed of light relative to each other. Light has, therefore, no "rest" frame, hence time and distance have no meaning.

Many popular science sources says things like: light travels zero distance in zero time. But, mathematically, there is a difference between "zero" and "undefined".

It's more precise to say that time and distance are undefined for light itself.

 

[Dnj23]

I'm not quite sure what you are asking. You won't beat a light signal to Andromeda, if that's what you are asking. From the Earth's point of view this is straightforward to understand - the ship is going almost as fast as light but not faster.

Explaining it for an accelerating ship is quite complex. But if you imagine the ship accelerating more or less instantaneously then coasting, the ship sees the distance to Andromeda length contracted and Andromeda rushing towards them. So light taking less than 2.5 million years is simple - it's a much shorter distance.

Ok. I said light, not a ship.

 

[PeterDonis]

Well, yes

Ok, good. Then yes, what you describe is true.

 

[PeterDonis]

I said light, not a ship.

And the answer to your question "how long does it take" for light is that the question is not well-defined, so it is unanswerable.

 

[Dnj23]

You can't travel at the speed of light (it turns out to be self-contradictory to try to describe it), but your "nearly" is answerable. You can get to Andromeda in an arbitrarily short time by your clocks, yes, due to time dilation. Brutal acceleration may be required for particularly short times. However, in any case, Earth clocks will measure you taking at least 2.5 million years and all your family will be 5 million years dead by the time you get back.

Edit: the above is all "in principle". Calculating the fuel requirements (even assuming the most efficient possible fuel and rocket) is depressing.

I'm not asking traveling at the the speed of light with any craft. Does light itself from Andromeda get here to Earth due to time dilation?

 

[Dnj23]

And the answer to your question "how long does it take" for light is that the question is not well-defined, so it is unanswerable.

Ok

 

[phyzguy]

I'm not asking traveling at the the speed of light with any craft. Does light itself from Andromeda get here to Earth due to time dilation?

Yes, light gets here from the Andromeda galaxy. That's why we can see it.

 

[PeterDonis]

light gets here from the Andromeda galaxy

Yes, but not "due to time dilation".

Does light itself from Andromeda get here to Earth due to time dilation?

No. It just gets here. The concept of "time dilation" has no meaning for light.

 

[phinds]

Does light itself from Andromeda get here to Earth due to time dilation?

No, time dilation has nothing to do with light getting here from anywhere in the universe. It gets here for exactly the same reason that the light bulb in a room gets to your eyes if you look at it.

EDIT: I see Peter beat me to it.

 

[Janus]

30 years sounds like it might be right for a ship accelerating at $10m/s^2$ (which would create artificial Earth-like gravity on board).

Such a ship could, given sufficient fuel, get up to any speed less than the speed of light (relative to Andromeda).

This is in line with the amount of time it would take in Ship time to get to Andromeda assuming you accelerate for half the way and then slow back down to come to a relative stop with respect to Andromeda for the other half.
As far as fuel is concerned: Even with a photonic rocket at 100% efficiency, it would take 4.2 billion metric tons of fuel for every kilogram of payload to make such a trip.