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Author Topic: Why does an object require infinite energy to travel at a finite speed?  (Read 18311 times)

Offline burning

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Let's not forget that when "you go very fast", you are going very fast relative to something; which means that you are probably going "very slowly" relative to something else.  This must mean that the vast amount of energy you are using, relative to the first thing, you are not using, relative to the second thing.  ???  

Well, if an object is moving at constant velocity through open space, it is using no energy.  If we say that energy is being used, that implies that there is a force accelerating the object.

So an observer in an inertial frame than sees the object as moving slowly at one time, will not still be seeing it as moving slowly at a later time, so they will agree that energy is being expended to accelerate it.  If the observer that sees the object as moving slowly is in a co-accelerating frame, they will feel the effects of the force accelerating them, and will still agree that energy is being expended.
 

Offline yor_on

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yeah it's kind of strange isn't it :)

There are two ways to see motion. Uniform and accelerating, the only motion that we expect to expend 'energy' is the one accelerating, which makes sense as you can think of it as rowing a boat (without resistance). You stop rowing and your boat will glide, you use the oar again, and your boat accelerates. That we don't think so normally, is probably because of the resistance we observe, making us ignore the possibility of something able to just 'move on forever'.

But when in a uniform frame it has some weird implications. One is that they are interchangeable. You define your speed from Earth for example, then looking at the rocket uniformly moving towards you, you say it has 'this speed' relative you. But you are as free to define yourself as being absolutely 'still' and so define that other rocket as the only one moving. That is a direct result of all uniformly moving frames (rockets) being the exact same in Space. That mean that there should be no experiments you can do, inside a room without windows, that will help you differ between those rockets, as far as I understand that is.

It also mean that if you have a light-bulb situated at the front of the room, in the motion of the ship, shining a beam at you (at the back of that same room, near the exhaust) that beam will be exactly the same as on the other ship, no matter how your speeds may differ as compared to Earth.

In a accelerated frame (rocket accelerating) doing the same experiment, you should find that the acceleration actually create a 'gravity', meaning that this light beam now instead will be blue-shifted as it 'falls' into the 'gravity well', situated/created behind your accelerating rocket. and if you are accelerating constantly uniformly at one Gravity (Earth) that light will behave the exact same as light on Earth would do due to Earths gravity, 'accelerating', that is, as far as you're concerned being on that ship observing the light beam 'accelerate/blue-shift'. The blue (and red) shift is the only expression light can use for a acceleration as it only have one 'speed' relative any 'frame of reference' observing it, moving or not.

And the extra energy it gets in that 'blue-shift' is real energy, relative you observing it
that is. No stranger than you can define different 'potential energies'  to your car, relative another car or that pedestrian, and that simultaneously. The question you might need to ask is if this 'blue-shift' then is 'real'? Well, as far as you're concerned it will be.

(Ignoring tidal forces here btw)

You can use those effects to see all kinds of interesting stuff :)

One implication you might draw is that Earth, although being defined as a 'inertial frame' uniformly moving, will not be the same as those rockets 'uniformly moving'. Earth is in fact equivalent to a 'acceleration' of one Gravity as seen when compared to our constantly and 'uniformly' accelerating rocket at one gravity. That's why some say that you are constantly 'accelerating' when on Earth. But this do not hold true when discussing a time dilation. In that case our 'uniformly' accelerating rocket has a infinitely greater time dilation than you will find on Earth.

But, in neither case though, will you notice 'time' acting differently.
« Last Edit: 20/03/2011 16:54:38 by yor_on »
 

Offline yor_on

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What is really interesting here is the way light actually proves that your frame of reference is unique to you. Take three frames of reference and all will see this light a different way, also having different distances defined relative SpaceTime.

We can't see this effect on Earth, at least not normally, but at relativistic speeds it become obvious. So what it points too for me is that all frames truly are unique, and that everything we describe or observe is the result of relations. We're all 'islands' relatively speaking :)
==

One way to see it naively would be to imagine SpaceTime as a 'pool' of usable energy with motion being a way to concentrate it. The problem being here that this 'photon', blueshifting relative you, express itself in a finite interaction, here and 'now'. But the effect is still there. Somehow motion can concentrate the interactions 'energy', even though every interaction take place inside a finite area and time.
« Last Edit: 21/03/2011 13:45:57 by yor_on »
 

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