4 ms·

So the question becomes where does the 11k come in? It was just wrong?

by jtbayly 15d ago

petersumskas 14d ago
Current me if I’m wrong but I think that was a calculation based on a specific velocity at some fraction of C. Whereas a constant 1g acceleration would far exceed that fraction and thus shorten the time significantly.
- jtbayly 14d ago
  > Of course that as you get closer to C, the traveling object will experience time dilation (relative to observer), so the time passed will be less. At 99.999% C, the traveler would take ~11,000 years to arrive to Andromeda. When you say constant 1g acceleration, do you mean acceleration well past the speed of light? I thought we were talking about all speeds less than the speed of light.
  - enfield-argent 12d ago
    You can accelerate constantly at 1g without ever reaching the speed of light. A constant acceleration takes you from non-relativistic speeds to 0.1c, then to 0.9c, then to 0.999c, then to 0.9999c, , and so on, without ever reaching 1c (impossible if you have mass) -- but it takes increasingly more energy to accelerate. The Lorentz factor, which governs time dilation and length contraction, is calculated as (1 / sqrt(1 - v^2 / c^2)), where v is the relative velocity of the object and c is the speed of light. You can replace (v^2 / c^2) with the factor beta^2, where beta is the ratio of v to c, e.g. 0.99999 in this case. Since (1 / sqrt (1 - 0.999...)) grows without bound in the limit as beta approaches (but doesn't reach) 1, if you keep accelerating, the time dilation keeps getting larger, without limits. It just takes a LOT of energy to do so.
    - jtbayly 12d ago
      Thank you for sticking with me. I was still at a loss for the answer to how it could take 11k vs 28 years or so. I asked AI. lol The thing I didn’t realize is the massive difference between 99.999% vs 99.9999% of the speed of light. I took 99.999% to mean "effectively the speed of light.” Relativity is weird.

So the question becomes where does the 11k come in? It was just wrong?

by jtbayly 15d ago

So the question becomes where does the 11k come in? It was just wrong?

Current me if I’m wrong but I think that was a calculation based on a specific velocity at some fraction of C. Whereas a constant 1g acceleration would far exceed that fraction and thus shorten the time significantly.

jtbayly 14d ago
> Of course that as you get closer to C, the traveling object will experience time dilation (relative to observer), so the time passed will be less. At 99.999% C, the traveler would take ~11,000 years to arrive to Andromeda. When you say constant 1g acceleration, do you mean acceleration well past the speed of light? I thought we were talking about all speeds less than the speed of light.
- enfield-argent 12d ago
  You can accelerate constantly at 1g without ever reaching the speed of light. A constant acceleration takes you from non-relativistic speeds to 0.1c, then to 0.9c, then to 0.999c, then to 0.9999c, , and so on, without ever reaching 1c (impossible if you have mass) -- but it takes increasingly more energy to accelerate. The Lorentz factor, which governs time dilation and length contraction, is calculated as (1 / sqrt(1 - v^2 / c^2)), where v is the relative velocity of the object and c is the speed of light. You can replace (v^2 / c^2) with the factor beta^2, where beta is the ratio of v to c, e.g. 0.99999 in this case. Since (1 / sqrt (1 - 0.999...)) grows without bound in the limit as beta approaches (but doesn't reach) 1, if you keep accelerating, the time dilation keeps getting larger, without limits. It just takes a LOT of energy to do so.
  - jtbayly 12d ago
    Thank you for sticking with me. I was still at a loss for the answer to how it could take 11k vs 28 years or so. I asked AI. lol The thing I didn’t realize is the massive difference between 99.999% vs 99.9999% of the speed of light. I took 99.999% to mean "effectively the speed of light.” Relativity is weird.