True/False relativity question.

[bayan]

Homework Statement

The star alpha centauri is 4.25 light years from us, so it takes its light 4.25 years to reach earth. It is impossible, in principle, for any rocket from Earth ever to reach this star in less than 4.25 light years.

Homework Equations

The Attempt at a Solution

My first answer was that the statement was false as length contraction would make the journey distance shorter for rockets F.O.R and the accepted answer is true, which leads me to the conclusion that they must mean 4.25years in Earth's F.O.R

I would like to know how I could identify in which frame they requested the answer in the problem above.

 

[tiny-tim]

hi bayan!

The star alpha centauri is 4.25 light years from us, so it takes its light 4.25 years to reach earth. It is impossible, in principle, for any rocket from Earth ever to reach this star in less than 4.25 light years.
…
I would like to know how I could identify in which frame they requested the answer in the problem above.

the facts given in the question are clearly written in the Earth frame, so you should assume that the question itself is also

 

[bayan]

hi bayan!

the facts given in the question are clearly written in the Earth frame, so you should assume that the question itself is also

Thanks for your reply, so unless there is a specified frame I should just use the one with respect to which data is given? Also is my answer of saying that statement is "false" wrong?

 

[tiny-tim]

yes! … don't make the questions more difficult than they already are!

(and you "false" was wrong)

 

[asteriatic]

I would like to clarify that the statement is true. The distance between Earth and Alpha Centauri is indeed 4.25 light years, and it would take a rocket from Earth at least 4.25 years to reach the star. This is because the concept of length contraction only applies to objects moving at high velocities relative to each other, and the distance between Earth and Alpha Centauri is vast enough that the effects of length contraction would be negligible.

Furthermore, it is important to note that the concept of length contraction is a theoretical concept in the theory of relativity and has not been proven or observed in real-life scenarios. Therefore, it is not a reliable method for calculating the actual travel time to a distant star like Alpha Centauri.

In terms of identifying the frame of reference, it is important to clearly define the reference frame before attempting to solve a problem. In this case, the frame of reference is Earth's frame of reference, as the distance is measured from Earth to Alpha Centauri. In general, it is always important to specify the frame of reference in any problem involving relativity to avoid confusion and ensure accurate solutions.