Q: if you travel closer to c, will you see length(distance) contraction

[ppppppp]

Q: if you travel closer to c, will you see length(distance) contraction between andromeda and earth?

 

[JesseM]

Length contraction refers to coordinate distances in a given frame, not what is seen visually (visual appearances are different because of the Penrose Terrell effect, see the animations here)...but in the coordinate sense, yes, in your rest frame the coordinate distance between Earth and Andromeda at any given moment of coordinate time would be less than the coordinate distance in the Earth/Andromeda rest frame.

 

[ppppppp]

hi, if i travels at 0.99999c, i will measure time between andromeda and I (events happens in andromeda) shrink to only 0.00447 x 2 millions yrs compared with a person in rest on earth?
Is this right, from t' = t x (1-v^2/c^2)^0.5

So if i travels to 0.99999999999999999999...c, then i can see things happen in andromeda just a few hours ago, because time dilation, i measure time between andromeda to me only a few hours different? (according to t' = t x (1-v^2/c^2)^0.5)

so if this is right, then we just need to make a nano telescope travel at 0.999999999...c (circling around Earth or whatever), we can see everything happens on andromeda almost in real time?

 

[JesseM]

hi, if i travels at 0.99999c, i will measure time between andromeda and I (events happens in andromeda) shrink to only 0.00447 x 2 millions yrs compared with a person in rest on earth?
Is this right, from t' = t x (1-v^2/c^2)^0.5

I don't know what you mean by "time between andromeda and I"...time between what specific events? That formula for time dilation, it tells you the relation between the time t' in the Andromeda/Earth frame between two events which happen at the same position in that frame (like two events at the center of Andromeda, or two events on Earth) and the time t between the same pair of events in your frame if you are traveling at v relative to Earth/Andromeda. And actually it would normally be more common to use the symbol t for the frame where the events happen at the same position (Earth/Andromeda) and t' for the other frame, in which case the formula is written t' = t / (1 - v^2/c^2)^0.5. Either way, if you look at the formula you can see the time is greater in the frame moving relative to Earth/Andromeda, reflecting the idea that clocks which are at rest relative to Earth/Andromeda (the ones that measure the time in that frame) are measured to be running slowly in the frame of the moving observer, so in the observer's frame these clocks take longer to tick forward by a given amount (a larger time in the observer's frame).

So if i travels to 0.99999999999999999999...c, then i can see things happen in andromeda just a few hours ago,

When you say "just a few hours ago", it sounds like you may not be aware of the relativity of simultaneity, which means different frames can completely disagree on whether an event on Earth and an event on Andromeda happened "simultaneously" or whether they may have been a gap of many years between them. Likewise, an event in Andromeda which occurred just a few hours ago in the Earth/Andromeda frame might have occurred thousands of years in the past (or thousands of years in the future) in the frame of someone moving at high speed relative to Earth/Andromeda.

But to rephrase your question, if we have an event in Andromeda that occurred just a few hours before the present time on Earth, according to the definition of simultaneity in the Earth/Andromeda frame, it is true that someone who at this moment is traveling past the Earth at an enormously high speed might see the light from that event in Andromeda just a few hours later. But from the Earth's perspective, his time is enourmously dilated, so what seems like a few hours to him will actually be thousands or millions of years in the Earth frame, and he will have moved thousands or millions of light-years away from Earth by the time the light hits him, thus this is no use for people on Earth who want to know what was happening in Andromeda a few hours ago.

so if this is right, then we just need to make a nano telescope travel at 0.999999999...c (circling around Earth or whatever), we can see everything happens on andromeda almost in real time?

No, because again although it might see the event a few hours later according to its own clock, from our perspective this would be because its clock is running very slow, so in our frame it takes millions of years for its clock to tick forward by just a few hours.