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Jack Stott asked the Naked Scientists: Dear Dr Chris.I have plucked up the courage to write to you with a question from a colleague of mine which I can't answer.I have no idea why he wants to know this ( I think he reads too many science fiction comics or watches too much 'Star Treck' ) but here goes :-If an object of negligible size & mass is launched from a standing start in a vacuum, and is subjected to an acceleration force of 1 G - how long will it take to reach the speed of light.Hope you are able to provide an answer, or even a formula to calculate an approximate result when and if you have the time.Best RegardsJack Stott BSc(Hon) Elec Eng ScienceWhat do you think?

All that relativity garbage is just that. Garbage. As you aproach the speed of light nothing changes.

There is some weirdness that happens close to the speed of light. I read an article recently about two ships traveling close to the speed of light attached by a rope....does it break or no. Length contraction and other effects.

I didn't quite understand it, it was a bit involved...just thought id add that in.

From the speedy travelers perspective there appears to be no upper bound or speed limit. You keep on going faster and faster. Time dilation effects, you can travel anywhere in the observable universe in a short space of time, by your watch anyway.

It's easy to understand once it's properly explained. Consider two spaceships which start out from rest in the inertial frame S. Connect them with a piece of string which is strung taught. Let each of them accelerate at the exact same rate so that as measured in S they maintain the exact same distance apart. Since the string also undergoes acceleration its speed is constantly increasing. Therefore its length must undergo a Lorentz contraction.

All that relativity garbage is just that. Garbage.

As you aproach the speed of light nothing changes. It doesn't take any longer to accelerate the last half of the way to the speed of light as it does the first half. When you acheive the speed of light nothing happens , nothing changes. If you keep accelerating at 1G twice as long as that then you will be going twice the speed of light.

Since you haven't invented a spacecraft that can accelerate constantly at a 1G acceleration you automatically assume…

Why do you mathematical types persist at this nonsense.

Shut up all ready you have no proof for all that hogwash.

Lorentz contraction in which frame of reference? Not in S, since "as measured in S they maintain the exact same distance apart".

It does, as long as we give a 'inertial' preference to the ship under Pete. But what happens if we define the ship above as being 'inertial' too, at rest in a gravitational field? And if we assume the ship above to be at rest, with the ship under going for it at , ahem, full throttle (one constant uniform G acceleration) it becomes really intriguing Then again, what about the contraction you observe, relative a distance measured in front of you. The ship 'under' should also see the space contracted in front of it, including the space between the ships as I think? What about the ship above, looking back, at the ship 'below', would they agree to it being a same distance between them? As they are defined as being 'at rest' with each other? What would 'at rest' mean there? Different constant distances?

Think so You're defining the ship 'under' as being 'at rest', presenting a uniform gravitational field, aka a 'inertial object' (loosely expressed a planet of some mass). You then go to define the other ship as constantly accelerating in that gravitational field.

Quote from: lightarrowLorentz contraction in which frame of reference? Not in S, since "as measured in S they maintain the exact same distance apart".Lorentz contracted in the frame in which the string is moving. When the string tries to Lorentz contract it breals because in its own istantaneous frame the spaceships are moving apart. I explained all that above.

Where does it say that "as measured in S they maintain the exact same distance apart"?

The distance between the spaceships does not undergo Lorentz contraction with respect to the distance at the start, because in S it is effectively defined to remain the same, due to the same acceleration of both spaceships.

If they maintained the same distance apart, the string wouldn't broke.

Quote from: lightarrowWhere does it say that "as measured in S they maintain the exact same distance apart"? The fact that the ships accelerate at the same rate and thus remain the same distance apart is the entire point of the paradox. In fact that’s what the paradox is all about.Please read it again because it statesQuoteThe distance between the spaceships does not undergo Lorentz contraction with respect to the distance at the start, because in S it is effectively defined to remain the same, due to the same acceleration of both spaceships.I don’t understand what the problem your having is. It’s very simple. As measured in an inertial frame S (in flat spacetime) if two ships accelerate at the exact same rate then they must remain the exact same distance apart at all times as measured in frame S. If you don’t know that they you don’t know the problem at hand because this is what the problem is all about.Quote from: lightarrowIf they maintained the same distance apart, the string wouldn't broke.That's quite wrong. Consider a string whose proper is L_{0}. The proper length of an object is defined to be the length of the object as measured in the frame in which the object is at rest.In the inertial frame S string is moving parallel to its length. In S the string has undergone a Lorentz contraction and as such it will be shortened to the length L = L_{0}*sqrt(1 - v^{2}/c^{2}). Since the ships accelerate at exactly the same rate the remain the same distance apart in the frame S. Therefore after the acceleration has ended and they’re moving at constant speed the distance between them as measured in S will be greater than they were before they started moving. This means that they will be further apart than when they started. Since the properties of the string never changed the string had to break because the ends were moved apart. QED Any questions now?

Any questions now?

I don't understand something. The way this article appears listed it seems as if lightarrow posted last in the thread. When I looked at it when I read the thread it no longer appears that way. What's going on here?

Quote from: Pmb on 07/07/2013 00:54:53I don't understand something. The way this article appears listed it seems as if lightarrow posted last in the thread. When I looked at it when I read the thread it no longer appears that way. What's going on here?It's a relativistic thread. Observers don't necessarily agree on which posting event comes first.

Now for what we actually want to discuss: your acceleration and speed with respect to the world around you. We must take relativistic effects into account. For example, the distance in front of you will CONTRACT the faster you go with respect to those objects. This means that while you traveled, say, 5000 light years according to Earth, from YOUR frame of reference you might have only moved 5 meters (because, again, the distance in front of you contracts-btw to get that to happen, you'd have to have reached about 99.9999999999999999999999999999999999999933 times the speed of light according to Earth's reference frame). What's your speed if you moved 5 meters in however many years? Not even close to c. But again, you're at rest in your frame anyway (and feel an artificial gravitational field). (note: it will look like 5 meters once you hit that speed, but don't lose track of the fact that the faster you go, the more contracted things will get, which means the slower you were, the LESS contracted things were; this post is a vast oversimplification).

It will never reach the speed of light. It would take an infinite amount of energy. This results from Einstein's theory of Special Relativity. However, from the perspective of anyone travelling on this craft, they will experience a contraction in the distances in their direction of travel. So although they can never get to 186,000 miles per second they can (theoretically), nonetheless, achieve a speed such that they can travel a distance that they may initially have measured (before accelerating) as 186,000 miles in less that 1 second as measured on their clocks. If I remember correctly this turns out to be the same time (to get to this speed) as would be calculated by Newtonian mechanics - I would need to check this with some maths to be sure. There are some unfortunate consequences of travelling this fast resulting from time dilation so that should return at some point you would find the earth you left having aged considerably compared to yourself.