3

So, I'm traveling to another star 100 light years away in my spaceship. This ship has a solar sail pushed by a laser beamed from my home star system, so can achieve a velocity close to c. It's also got a robust parachute to slow down with.

I understand that if I measure light coming from my origin star, it will always still seem to be streaming past me at light speed (but will red shift as my speed increases). Light coming from my destination star also travels past me at light speed, and will become increasingly blue shifted as I gain speed.

I also understand that an observer checking on my speed at my origin or destination will always find it to be less than c.

However, will I perceive that in terms of the time it apparently takes me to reach my destination, my speed was greater than c? In other words, will it seem to take less than 100 years to reach the destination? 10 years on my watch, say. Or 1 year. Or a week?

Ie, as far as I'm concerned, while light keeps zipping past me at light speed, do I continue to accelerate unabated to an arbitrary apparent speed?

If not, how do I notice my continued acceleration being prevented?

Benjohn
  • 3,090
  • 2
  • 14
  • 19
  • 1
    Hi Ben. Because we get so many questions like this I wrote the Q/A I've linked to try and produce the definitive article on the subject. Have a look at the linked article and if there are any points still unclear please come back to use with a new question or edit this one. – John Rennie May 07 '14 at 09:34
  • @JohnRennie Thank you! I see that I can simply delete my question. I wonder if the title I used is useful though as that's something I didn't know. I remain confused about the experience I'd have in my ship (instant death from hitting gas molecules or dust, aside)… Does the universe I see apparently flatten in the direction I'm travelling? You say that I feel a constant acceleration of 1g – but I must start to notice that my speed doesn't seem to be increasing, just the universe shrinking? – Benjohn May 07 '14 at 10:03
  • If you're on the rocket then from your perspective you're stationary and it's the rest of the universe that's moving towards you. You would indeed see the rest of the universe Lorentz contracted, and that's the point I make in the last section of my answer where the distance to the star decreases because of the Lorentz contraction. I'm sure there's a question on the site about the effect of interstellar dust at high speed - I'll have a search ... – John Rennie May 07 '14 at 10:28
  • @JohnRennie I've just scanned a link from you to The Relativistic Rocket. It mentions: "As you approach the speed of light you will be heading into an increasingly energetic and intense bombardment of cosmic rays and other particles. After only a few years of 1g acceleration even the cosmic background radiation is Doppler shifted into a lethal heat bath hot enough to melt all known materials." – Benjohn May 07 '14 at 10:32
  • Aha! The question I was thinking of is Would a fast inter-stellar spaceship benefit from an aerodynamic shape?. This doesn't actually calculate heating, but it does show the effect is small up to 0.999c. – John Rennie May 07 '14 at 10:33
  • Re your last comment: maybe this should be a new question ... – John Rennie May 07 '14 at 10:34
  • @JohnRennie Thanks for your answers & suggestions. I think if I want to understand this better I should probably go and have a look at the maths so I can resolve some of the questions myself. – Benjohn May 07 '14 at 20:34

1 Answers1

2

The following assumes that the distance to the star (100 light year) was measured before you got in the spaceship and started moving.

When moving close to $c$ in your frame of reference space around you will be contracted relative to what someone on earth will measure. Thus, your 100 light year journey will actually be shorter in your frame of reference, and will thus take less than 100 years for you to make it to the star.

If you are ever able to report to someone back on earth that the journey took you less than 100 years in your frame of reference they will agree with you, since from the reference frame of earth your spaceship and all its inhabitants underwent time dilation, the slowing down of time relative to another frame of reference. Thus, you would both agree on the time the journey took in your frame of reference, but the person back on earth will say that according to their clocks in the earth's frame your journey took 100 years.

In summation, you will not conclude that in your frame of reference you traveled faster than $c$ because while in transit, due to length contraction, the journey you traveled was actually shorter than 100 light years.

This is an answer to your bolded question, which is a different question than the one you posed at the end about whether or not your spaceship will accelerate forever.

The answer to that question is, as you continue to accelerate away from your origin star the laser propelling your spaceship will be redshifted (not blueshifted as you mentioned in your question) so that you will have less energy per photon than you had at the beginning of your journey (before the photons were redshifted). Additionally, as you get further away from your origin, less and less photons from the laser will reach you; although lasers produce very focused beams, there are quantum limits to how focused these beams can be, so far away from the laser the spread in the beam will cause less and less photons to actually reach you. These two effects combined will cause the energy you can extract from the laser to accelerate your ship to diminish as you get further away until effectively you can imagine that the acceleration the laser provides your ship vanishes.

NeutronStar
  • 5,404
  • 5
  • 36
  • 64
  • "you will not conclude that in your frame of reference you traveled faster than c because while in transit, due to length contraction, the journey you traveled was actually shorter than 100 light years." But length (distance) contraction occurs, just light time dilatation, from the point of view of the Earth-located observer. Time appears longer and distance shorter from Earth. Therefore, if you say that time dilatation makes the journey shorter from the traveler's point of view (as opposed to the view of the Earth-located observer), then also the distance is longer from this point of view. – bright magus May 07 '14 at 05:55
  • @brightmagus Not quite. The length contraction observed from earth will be of the spaceship itself, not of the length of the journey. This is because it is the spaceship moving relative to earth, not the distance between the earth and the destination star. Additionally, I did not say that time dilation makes the journey shorter from the traveler's point of view, I said that it makes the clock on the spaceship show less time passing over the journey than a clock on earth. – NeutronStar May 07 '14 at 17:43
  • $@$Joshua: Well, I'm not talking about time dilatation, but about distance contraction. You didn't say that the journey will take less than 100 years, which would be about time. You said "100 light years" which means distance. If you say that length contraction has something to do here (which I agree with) than the contraction will be observed from Earth, and therefore for the traveler the distance must be longer than for Earth observers. – bright magus May 07 '14 at 17:52
  • @brightmagus: The OP said that the spaceship is able to achieve a velocity close to c, so it's easy to convert distance to time for the spaceship. If, in the frame of the spaceship, due to length contraction, the the distance it has to travel from earth to the destination star is less than 100 light years, it will take less than 100 years to travel that distance since their velocity is close to c. I did not understand what you meant in the last sentence in your previous comment; could you please clarify? – NeutronStar May 07 '14 at 19:03
  • I'm not referring directly to the time in my comments (although distance contraction obviously is affecting the time of the travel). What I mean is that the distance (length) contraction will be perceived by the observer on Earth. The distance from the traveler's point of view will seem longer. That's how it works according to Einstein. – bright magus May 07 '14 at 19:49
  • i.e. if the distance is perceived to be 100 light years from Earth, than the traveler will say it is more. Therefore it is contracted for Earth. – bright magus May 07 '14 at 20:10
  • @brightmagus: Why will the traveler say it is more? – NeutronStar May 07 '14 at 20:13
  • Joshua, He will say that because of the length (distance) contraction as perceived from the stationary frame of reference (Earth). I know it seems strange that it becomes larger after the spaceship takes off, but that's what the theory says. I might ask why did you say that for the traveler the distance seems shorter: "due to length contraction, the journey you traveled was actually shorter than 100 light years"? Distance is not shorter for the moving frame of reference; it is shorter for the stationary one. (I don't think I can add anything else here.) – bright magus May 07 '14 at 20:31
  • @brightmagus: I disagree. Length contraction means that length/distance is shorter for a frame of reference moving relative to you. But this is relative as well, for both the earth and the spaceship will independently claim that they are the stationary frame and the other is the moving frame. Thus, to earth the spaceship is contracted but to the spaceship, the earth, destination star, and the distance between then is contracted. – NeutronStar May 07 '14 at 20:36
  • @brightmagus: http://en.wikipedia.org/wiki/Length_contraction. This says "length contraction is the phenomenon of a decrease in length measured by an observer of objects which are traveling at any non-zero velocity relative to the observer." Distances are shorter in frames of references moving relative to yourself than they would be measured at rest in their own frame; hence, the spaceship measures a shorter distance between origin and destination than an observer at earth (at rest relative to the distance) will. – NeutronStar May 07 '14 at 20:44
  • let us continue this discussion in chat – NeutronStar May 07 '14 at 20:46
  • Nope. "the length (Δx′) of the rod as measured in the frame in which it is moving (S′), is shorter than its length (Δx) in its own rest frame (S).". The primes are used incorrectly here, but the sentence is true. The frame in which your traveler "is moving" is Earth, the frame in which "it is at rest" is the spaceship. – bright magus May 07 '14 at 20:52
  • I sent you a message in chat (I can't see your e-mail address). – bright magus May 08 '14 at 05:45