I have a space ship that can accelerate and hold .99 of light speed indefinitely. If I leave the earth and attain that speed more or less immediately how long to I have to stay in space on a round-trip voyage at that speed for 1000 years to pass on the Earth?
You have a .99 of C speed spaceship. How long do you have to travel for 1000 years to pass on Earth?
t’= tsqrt(1-v[sup]2[/sup]/c[sup]2[/sup])
t’=1000sqrt(1-.99^2)
So 1000 years on Earth would be roughly 141 years on your ship.
From the Point of View of someone on Earth.
IIRC (It’s been years since I looked at this) you can only reconcile clocks if you stop and compare, there by introducing acceleration and hence “special” relativity into the equation?
Otherwise, the reciprocal applies, from the PoV of Earth, time is slower than on your ship…
There is no fixed “this is the baseline real time” hence, “relative”-ity.
What’s ill posed about the question is that it implies the people on the space ship could check their calendars at the exact moment that people on Earth see the 1000 year marker tick by. However, events that happen in different locations can’t be said to be at the same time in any fundamental way, nor can we generally even say which event happened first. Perhaps it was the realization that a moment in time is only meaningful locally that, more than anything else, let Einstein work out his special relativity and then his general one.
Ah, yes, that was what I was trying to remember- simultaneous is only applicable in a single point, or if two observers are at-rest in the same time and space frame.
Thanks.
No the OP’s question was correctly posed. It’s a round trip and the speed of 0.99 c is attained very quickly. Grey’s answer is correct ignoring the short time of acceleration. 141 years will have passed on the ship at the end of the round trip.
I don’t know if it was clumsy wording or a real misapprehension, but the easy answer to the OP as written is: 1000 years, duh (from the perspective of us on Earth).
:dubious: Misapprehension on your part? The OP wasn’t clumsily written.
Sorry! My mistake. The OP says “round trip” and there is nothing ill posed about the question. I missed that, and apologize.
I think you’ve got the ‘‘special’’ part backwards. Special relativity is only applicable for inertial (nonaccelerating) reference frames. General relativity is required to deal with non-inertial reference frames.
So, 70.5 years out, 70.5 years back, barring acceleration and deceleration time–which outta be a real ass kick when you change directions–and it’s not so bad, if you look out the windows on the other side on your way home.
Other side of the universe, but the same side of the rocket ship if you want a different view. Unless this rocket ship has a reverse gear. 
:smack: Correct.
And if that window is smudged he’s screwed, and will have to read yet again that one magazine somebody left in the head.
I like “reverse” in a rocket.
I disagree with that as it’s a very artificial limit to place on special relativity and you don’t require Einstein’s field equations nor even the full power of general covariance to deal with accelerated frames of reference.
Where accelerated frames tend to fall down is when you try you try to make them spatially extended, though that’s not to say sensibly spatially-extended frames don’t exist e.g. a Rindler coordinate chart.
You could travel in a circle at constant speed (from the pov of the Earthbound observer) without altering the results to get rid of the turnaround.
This is hardly my area of expertise so I happily defer to your correction and thank you for fighting my ignorance. Actually, your response is a quite a bit over my head so I can’t claim to even really understand it. But I’m gonna try!
However, let me just say I hope I didn’t lead anyone astray with my post as I was merely regurgitating what’s in my old college physics book. Anyhow, the only reason I had responded is because I’ve been reading back through that book for funsies and coincidentally just happened to get to the chapter on special relativity a couple of days ago.
Here’s the relevant (but apparently misleading) passage from that book, keeping in mind that I’m not disputing you in any way - just trying to explain where I’m coming from:
So is my misunderstanding here due to the book I’m reading being out of date physics-wise? Or was that part of the course material just simplified for that level of physics? (Same book & class that physics majors took at that university which is as far as I studied in that field while obvioulsy physics majors continued on.)
I’m guessing the latter, since this 900 page book doesn’t actually cover general relativity. In fact, besides the portion that I quoted, the only other mention of it is in a footnote for the section explaining the (non)paradox of the traveling twin. It says merely that
The body of that text meanwhile claims:
Either way, I hope it wasn’t too far off the mark to suggest that the post I quoted seemed to have confused ‘‘special’’ and ‘‘general’’ relativity, at least at the layman’s level. To recall, that post claimed that the introduction of accelertion is what would bring on the ‘‘special’’ in the relativity - rather than excluding it as I thought it would.
(And on preview, does your response to Leo Bloom mean that speed changes rather than direction changes are the important factor as far as acceleration and special vs. general relativity go? Also, could you shed a bit of light on what you mean about a spatially extended frame? Would this come into play for the constant speed circle about the earth you mention to him - is there a maximum radius beyond which general relativity would be required?)
The only complication in dealing with accelerating reference frames in special relativity is that you have to use calculus, instead of just algebra, to do the calculations.
The confusion arises because the postulates of special relativity refer to inertial frames of reference, but there is nothing to stop you extending this to accelerated observers. We don’t need to use Einstein’s field equations which describe how mass-energy warps spacetime and we don’t need to use the full power of general covariance which frames the laws of physics in a manner that is true for any arbitrary spacetime coordinate system which are the two hallmarks of general relativity. For me anything you do in Minkowski spacetime (i.e. trivial flat spacetime) is special relativity as that is the ‘mathematical space’ of special relativity.
For example if you wanted to work out the time experienced by an observer travelling in a circle (in some frame) at a constant speed you could approximate that in inertial frames by an observer travelling at constant speed whose path is a regular polygon in the same frame. Each side of the polygon can be described by a different inertial frame and the more sides the polygon has the better the approximation. The limit of infinite sides perfectly describes the circular motion and the result is unsurprising as time dilation depends on relative speed rather than relative velocity. Similarly we can describe any other accelerated observer by approximating them as a series of inertial observers and then taking the appropriate limit of those approximations. As Chronos points out, in fact, we already have something called calculus which lets us do this without ever even having to actually going to the trouble to construct any of these approximations.
The slight problem is that, whilst inertial reference frames are spatially extended in that they assign coordinates (i.e. a place in space and a place in time) to all points in spacetime, accelerated reference frames only really assign coordinates to events at which the accelerated observer is coincidental to or are at least nearly coincidental to. The reason for this that there just isn’t a general ‘good’ way to spatially extend the frames of accelerated observers. In other words accelerated frames tend to tell you what happens ‘over here’ from the point of view of an accelerated observer, but not what happened ‘over there’ (of course we can still work out what an accelerated observer would observe in terms of the light hitting their eyes), using general relativity doesn’t add anything to this.
Since the OP was answered, I hope that continuing my tangent won’t be too frowned upon.
In a nutshell, I’m now disappointed in my old textbook’s coverage of SR, based on what I’ve learned from this thread and additional reading I’ve been doing as a result. The author seems not to have understood SR as well as you all do and made a few apparent errors on the subject.
The very first sentence in the book, from the preface: ‘‘This introductory calculus-based physics textbook is aimed at students majoring in physics, other sciences, and engineering.’’ And since the author didn’t shy away from any calc throughout the book, you’d think he’d at least mention what you just simply explained if he knew that. But instead he explicitly claims a few times that GR is required for accelerated reference frames because SR can’t handle them.
I guess he must have plenty of company since one of the articles I’ve now read says that is probably the most common misconception about SR. From googling his name, I believe he’s still publishing so hopefully his subsequent/current books cover the subject in a better manner.
I’m also less than impressed with his coverage of the traveling twin ‘‘paradox’’ since he waves it off simply as predictions of SR not being valid during acceleration. I’ve now read a couple of other in-depth, and presumably correct, explanations that would have been appropriate for a text at level in my opinion.
Asympotically fat - as I mentioned above, your first response went cleanly over my head. However, I think I got the gist of your follow-up, particularly in light of the additional reading I’ve been doing in the meantime. I actually recognized and understood what you meant (at a basic level of course) about the Minkowski/flat spacetime being the ‘‘mathematical space’’ of SR as compared to the mass-energy warped spacetime of GR!
And your second paragraph was particularly helpful in understanding the concept of how calculus would be used to treat a constant speed circular path as a polygon of inertial frames with an infinte number of sides. It may have been a long time since I ended up a course or two this side of a math minor, but your plain text explanation was very understandable and enlightening. Even though a cursory knowledge of relativity is the best I’ll ever have, I’d like to think my grasp of the subject is ever so slightly less tenuous now.
On a final note, the textbook I’ve been referring to does cover relativistic momentum in addition to relativistic mass. But then the author describes the speed of light being an ultimate limit purely in terms of infinite mass as opposed to energy/momentum. One of the things I’ve since read is that this is another common misconception of SR and that mass does not actually increase with speed - it’s really just the momentum/energy. I believe there is or has been some disagreement of opinion on this matter. If you all have any comments in that regard I’d be interested to hear them.
How small can this circle be?
Or the distance between multiple back-and-forth trips at some other location?
Or how close the location does the rocket’s reference frame of reference get to be (Pauli?)
Doesn’t the rocket’s (massive system) drag/effect the observer’s?
I think the first three questions amount to the same question. Assume quote marks are scattered liberally in these queries.