The engineers have developed the EM drive into something useful and have built a vessel that will be suitable for exploration (nuclear power source, in front of a big comm dish/crud shield, with an egg-shaped pod protected by a huge water jacket, all a-spin for non-weightlessness). You are one of the dozen selected for the trip.
The math suggests that you will reach .9c after about 4 years, right at the midpoint of the journey, which would be something like 2.5ly. At that point, you are expected to flip the drives around and start braking for your arrival. But, of course, you and the crew will be experiencing time dilation, so “light year” will not be exactly meaningful in your reference frame.
The question is, how do you figure out when you are halfway there and need to start slowing down? Which is not as good as “Where are the good bistros around α-Cen-B?” but you have to be able to get there before that question comes up.
The same way that you do all your navigation - the position of the stars.
The math is not difficult to work out the expected time it will take, but you aren’t going to make precision navigation decisions based solely on that.
You’ll have to allow for the distortion of view. When you’re travelling at an appreciable portion of the speed of light, some things behind or to the side of you, look like they are in front.
Sure, but I’m kind of assuming if we know how to build a ship that will get us there, we have a nav computer that will make the relativistic calculations. Or Chronos can use his slide rule, I guess.
Unless of course there’s ‘another layer’ underneath relativity (which is underneath apparent Newtonianism), that only manifests clearly and measurably toward the extremes, then we could be in trouble.
But, Chronos’ slide rule will experience the effects of special relativity – it could become too short to use. And mine would fare no better, neither the bamboo one or the metal one.
This is not correct. The occupant in the space vessel that is traveling at 0.9c will see the outside world as compressed along the direction of vessel motion, but objects inside the craft will appear normal. Only an outside observer in an unaccelerated reference frame will see objects within the spacecraft as being compressed along the axis of motion. Special relativity is well understood, and in fact the basic calculations of time and distance transformations can be made by anyone with basic algebra and some very simple trigonometry. Calculating the total effects in a non-inertial reference frame (e.g. when the vessel is under acceleration) is a little more complex but can be understood by anyone who has passed a couple semesters of basic calculus and knowledge of hyperbolic trig functions.
The bigger problem, assuming that you have some kind of propellantless or inertial propulsion which eliminates the need to carry [POST=16494836]massive amounts of propellant[/POST] is the waste heat produced by the nuclear reactor or whatever other heat engine used to accelerate the vessel and provide environmental control and other support services to keep the occupants alive. While it is popularly thought that space is ‘cold’, it is actually a nearly perfect vacuum, and like a high quality thermos or vacuum flask, that means it keeps the interior well insulated and retains the heat that is generated within, only expelling excess heat through the mechanism of radiation. Even keeping low power spacecraft or small shuttlecraft from overheating is a challenge–hence why the STS Orbiter Vehicle e.g. ‘Space Shuttle’) always orbited with the cargo bay doors with attached radiator panels fully open–much less a large vessel occupied for years or decades. Any spacecraft carrying people on an interstellar journey would require radiating panels with enormous surface area.
Do observers see rates of nuclear decay remaining constant within their reference frame? I can’t see how it could be otherwise, but I also can’t work out how that works across differing reference frames.
Interesting. You could mount the engines at the end of a long boom structure, couldn’t you? The heat would be well away from the insulation of the interior. The ship in 2010 had this design.
That prompted me to check out how the ISS handles the problem. Turns out it has large radiator panels that do just that. Overview of the whole system here.
ISTM that the rate of nuclear decay for any given mass of material is essentially a clock, and would therefore be observed to behave like any other clock with respect to relativistic time dilation.
I guess it works the same way as relativistically delayed muon decay, which is a well confirmed phenomenon: from the external observer’s point of view, it’s all about time dilation, while from the particle’s point of view it’s length contraction of the traveled distance.
The really funny part is that it doesn’t even require that. Suppose that you knew absolutely nothing about relativity, and thought that the speed of light was infinite, and you wanted to plan out a trip using a constant-acceleration drive. You’d use ordinary Newtonian kinematics to calculate what amount of time you’d want to accelerate forwards before turning the ship around-- OK, so the derivation of those formulas (if you’re going to do it right, not in the handwaving way used by algebra-based textbooks) requires calculus, but the formulas are widely taught to and used by students who don’t have any calculus. So anyway, you calculate the time needed, and set your clock on the ship for the event.
Well here’s the really nifty part: As long as you’re traveling in a straight line, that timer on board your ship will actually go off at the correct time for the relativistic turnaround point, even though you didn’t use relativity to calculate it.
I’m not following this. The time that passes on a ship traveling near the speed of light will be far less than Newtonian kinematics would predict, right? So how can this be true?
The effect of this is that if the traveler measures his speed according to the assumption that the distances to various objects remain the same, his computed speed will appear to be linearly increasing way beyond the speed of light. Moreover, time dilation would cause an accelerometer in the space ship to show that he’s continuously accelerating in a perfectly Newtonian fashion. Funny how that all works out!
Ok, but Newtonian kinematics doesn’t “know” either of those things, right? So I don’t se how anything is netting off to make the alarm clock go off at the correct time. Newtonian kinematics would predict that the trip would take (say) 5 years, so you’d set your alarm for 2.5 years and take it on board the ship. But in the reference frame of the ship the journey actually takes (say) 1 year and you want to start decelerating in 6 months. It seems to me that your alarm clock will go off 2 years too late.
Or, to put it a slightly different way… Newtonian kinematics doesn’t predict the time dilation, but it predicts that the ship can exceed the speed of light and not increase in mass as it approaches that limit. Those factors cancel out, in terms of trip time as experienced on the ship. I think I have that right.
EDITED TO ADD: Riemann, when you say that Newtonian kinematics predict that the trip would take 5 years, how long would relativistic math say it would take?