∆ Tame Warped Space

1.                 Experimenting with tame ‘Warped Space’.

Figure: Just how far can space be curved? The Chandra X-ray telescope has detected fast spinning black holes that may warp space completely around themselves - But does this prove that time exists.


Someone once said that if the air was easily visible, then everyone would instinctively grow up understanding how the birds fly. It is only that we can’t easily see and manipulate the air that stops us from just seeing how it moves and saying ‘well that’s obvious’. Similarly if we could just ‘see’ how throughout the universe space may be twisted stretched bent and warped in many different ways, then is too might give up its mysteries. Perhaps with some simple thought experiments we can get a feel for how this might look, and see how ‘warped space’ makes sense in a timeless view;

Back to >> ∆ Timeless v.Time distinctions (Rhetoric and Semantics).

 NOTE - this section is purely a relaxed and exaggerated thought experiment to loosely explore what the consequences of  'warped space' may mean in highly simplified terms)

It is an observed fact that space itself is ‘warped’ by strong gravitational fields, that this should be true was calculated by Einstein in 1905/15 – and then subsequently directly observed by Arthur Eddington and his team in 1919.

Although Eddington effectively did directly observe the very distinct effects of the suns gravity warping the space around it and therefore deflecting light from distant stars just as Einstein had said it does, to you and I the photographs showing the ‘slightly different’ locations of a handful of stars probably wouldn’t spark a eureka moment.

This is because it takes either a super massive or very rapidly accelerating object to significantly warp space, and even then the effects are very slight and are spread very thinly over millions or billions of kilometres.

We actually live on an object massive enough to warp space, the Earth itself but because the effect is so slight (and because we are actually located within this warped space) we cannot easily see or carry out experiments to directly see the effects of warped space.

Relativity tells us that gravity warps space, and it also tells us that the effects of gravity are completely indistinguishable to the effects of acceleration.

This means that the force you feel seeming to push you back into your seat if you are in a sports car pulling rapidly away from the lights, i.e. acceleration, is completely indistinguishable from the force you feel if you are just laying on your back on the ground, experiencing everyday gravity.

Conveniently this means that we could use either gravity or acceleration to create an area of warped space if we wanted to have some to examine. However both these routes are equally impractical, if we got an object and accelerated it enough to warp some space noticeably enough for us to experiment with it then the object we were accelerating would of course have to be flying out the window at a greater and greater speed and getting further and further away.

So in theory the easiest way to examine warped space in a laboratory would be to place a very ‘massive’ or super dense object on a work bench and do experiments around it. Sadly this too would fail, although it is possible to form chunks of matter millions or billions of times more dense than the Earth (in fact the entire mass of the Earth could be squeezed under gravity into the size of a match box) but such an object would at the very least fall towards the centre of the Earth pulling us and everything around it as it went.

If we had a slightly tamer object there would still be other problems partly because we would ‘be’ in the warped space it created and as such we would be warped with it and everything around us would look normal and also because the area of warped space would become less warped very gradually around the object over 10’s or 1,000’s of km, so we would never really see an area that was warped next to an area that was not so we could compare them.

 

The, Tame Warped space, thought experiment.

 
 

However all is not lost because as a thought experiment we can consider what it would be like if we could bend but not break a few of natures rules and imagine a few exaggerated cases that will make things easier to visualise.

Lets imagine that we could create simple blocks or chunks of ‘tame warped space’[1] to help us to understand just what warping space might mean. So consider entering a laboratory and finding on a large a single ‘1 metre cubed’ block of semi translucent smoky grey matter.

The table has ruler marks along one edge and you can see it is one metre long and the translucent block is marked ‘condensed space’.

 

Condensed space.


Seeing a handy 3 metre long measuring stick nearby and being sensible enough not to go sticking your hands into mysterious looking things in scientific labs you pick up the stick and start pushing it into the ‘block’.

Although the table, and the block of stuff resting on it are both 1 metre long you find that a  full 2 metres of the measuring stick go into the ‘condensed space’ block before the other end of the ruler even starts sticking out of the other side.

 Leaving the stick in place you go round to the side of the block and can see that it seems that there is only a one metre of measuring stick inside the block but it now appears compressed and the usual centimetre markings now seems to be only half a centimetre apart and all the numbers are similarly squashed up along the length of the stick.

Somewhat confused you pull the ruler out and hold it next to the block on the outside, here you find the block measures 1 metre long and the ruler is indeed 2 metres longer than it.

Stretched or Expanded space.

(Note - Reality, dictates that space is only ever 'condensed' just as 'time' is only ever 'slowed' by relativistic effects, but we can imagine the concept of 'expanded space' - which is perhaps how the world might look from inside condensed space).

On another table in the lab you see a second 1 metre cubed block this time marked ‘Stretched space’ pushing the 3 metre stick into this block you find the opposite case, just as you have put in half a metre of the measuring stick you find it is already appearing out from the other side of the block of ‘space’ and you are still holding one and a half metres of ruler outside of the block CHECK LENGHTS

Looking from the side again you see that it looks as if half a metre of ruler has simply been stretched to a full metre, all the centimetres look like 2 centimetres and all the numbers and markings on the ruler seem to be in a stretched out typeface.

 


Having more ruler to play with here you keep pushing it into the block and now you find that it seems like a normal measuring rod again, if you push 10 cm in one side 10 cm comes out the other, all that happens is that when you look at the part of the measuring rod is in the block it always looks like half a metre stretched out to a full metre.

In this way the two blocks of warped space could pretty much be replaced by two large optical lenses or distorting fairground mirrors. If you look at a normal ruler through a 2X magnifying glass you see a similar effect to how the stretched space might look, the markings seem to be twice as far apart and so 10 cm of ruler might seem to take up 20 cm, however the actual ruler won’t in fact change length.

Walking in warped space. 

Now let's consider how it would look to you if the blocks of warped space were still ‘1 metre’ square on the base but two metres high, tall enough for you to walk into.

Walking up to the block of compressed space you push your hand in but it seems to get shorter (or possible looks normal to you from where you stand but compressed like the ruler to someone looking from the side) as it enters the block, unperturbed and seeing how the ruler suffered no ill effects you step boldly completely into the block and as you do everything you see around you outside of the block seems to be twice as big as normal !

However, and this is an essential point, you don’t feel as if anything odd has happened to you, it just seems to you that all of your surroundings have changed and they all seem to have got twice as big.

To someone outside the block however the complete opposite seems true; You will have seemed to have become half your normal size.

All of these effects are greatly exaggerated here, (and we should be aware that you can’t just warp space you must warp ‘rates’ as well)  but this idea shows us that we can consider space being warped without it being impossible to visualize. We can also imagine how a device such as a ‘clock’ could be entered fully or partially into such warped space – or passed through an chunk of it and out again – while still functioning ‘entirely now’, though looking odd and functioning at different ‘rates’ across itself, again but still always ‘now’.

 

Are you shearing that space?

The points to realise here (remembering that this is a hypothetical and exaggerated thought experiment) are that to you inside the block and to an outside observer it always seems that the other person and their surroundings have changed and not yours, and any experiment you try inside or outside of the block will always have sensible results. In effect it is impossible to say which is normal and which is abnormal space they are both equally valid and each just seems different from different points of view. Also that everything adds up, you can walk in and out of the block(s) with no ill effects although your own watch might seem to keep getting misaligned with outside references.

We might seem to have a slight problem here imagining what happens when you are half in and half out of a particular block, how could you left side be 3 feet (CM??) tall and your right side 6 feet, but this is just a result of the forced exaggeration of the thought experiment in practice there would never (??) be such a shear step in space, you would probably only lose 1 mm over 1 million km and even then in a smooth and gradual progression. (MADE UP figures to illustrate point)

Stepping through and out the other side of the block everything seems back to normal again, so you go to the block of stretched space, putting your hand into the block it doesn’t feel any different from normal but it suddenly looks similar to the ruler previously in that every part of it seems twice as big as normal! Boldly stepping all the way into the block you suddenly feel claustrophobic because the entire room around you seems to have shrunk, but again you do not feel that it is you that has changed.

So this shows us some of the nature that warped space might have, distances and dimensions that may seem to become longer or shorter in a sense from ‘normal’ dimensions when looked at from another point of view, but locally, i.e. to you or anything else existing in warped space everything looks normal to you and it is other places that seem distorted. REP

So sadly although it might at first seem we could keep putting unwanted trash into the block of compressed space and gold coins into the block of stretched space therefore halving one problem while doubling our wealth, the trash would seem to double again when we went to chuck it out and our gold coins would shrink as we tried to take them to the shops.

Static rulers in warped space.

In reality, and as explained in relativity, it seems that space really is warped and physical dimensions actually do change particularly when an object is moving very fast (so unlike our blocks space is warped in one direction only). This effect is small but very real it’s called ‘length contraction’ and the faster an object moves (accelerates?) the more its length will be contracted, this effect is completely invisible to us in our everyday lives because a car at normal speeds would be length contracted by less than a billionth of a percent and would have to be travelling at reasonable fraction of the speed of light for it to be contracted any noticeable length.

 This is why it is useful to imagine this fictitious and tame warped space because it is not zipping off at great speed and because the cut off between our warped space and our normal laboratory space is very simple and distinct.

So if we reconsider the effect of just placing the 3 metre long ruler into the ‘compressed space’ and leaving it there we recall we would have half a metre sticking out either end of the block with 2 metres held in the block but compressed into apparently one single metre.

What this scene lets us do is see the effect of warped space on a simple and most importantly static scene.

Finally we consider how things might be if we could create and ‘curve a block of warped space. In this case, the end of a ‘straight ruler’ would be able to hit a place ‘before’ itself.

And if you looked along the ruler, it would appear straight, but you would see the ‘side’ of the ruler at the end of the ruler.

393 'Tame' curved space.


 Back to >> ∆ Timeless v.Time distinctions (Rhetoric and Semantics).


[1] ‘Tame warped space’ is purely a thought experiment. The effects shown here are exaggerated trillions of times, and for simplicity they separate the ‘size’ and ‘rate’ effects you would get in real warped space.

Continue >> ∆ The House of Cards.


M.Marsden

See also ...Chandra Black Hole detector

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