Space, Space-time and a thought experiment

When reading about space and time on this board it got me thinking. What is space-time? Does it have any properties of it’s self or is it simply something where things can happen?So I thought of a box. Imagine this box (1 cubic mile) that is impenetrable to all particles, fields and forces including gravity. Next you need some kind of theoretical machine that can suck out any remaining particles, fields and forces including gravity from inside the box.So what are you left with? What properties does this box contain? Is their some way that you can define what is in the box?The only property that is left that springs to mind is distance. You can still say that you have got half way across the void by comparing yourself to the box. But then is that a property of the box or the void?As nothing will ever change in the box can you say that time is passing? If you can how could you measure the passing of time?I guess this would go in Big Bang and Cosmology

Thread moved here from the Proposed New Topics forum.

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What is space-time?

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Space-time is a mathematical construct that allows us to make calculations that can precisely predict what we should observe in certain circumstances.Now, assuming that there is a correspondance between real life things and our mathematical constructs, one may ask (and I believe that this is what you are asking), to what real-life thing does space-time correspond? That is a good question, and it would be interesting if this has a good answer. (I know that Kant answered: "Nothing,", but that was two and a half centuries ago, and I don't know whether anyone has refuted his claim since then.)

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"The fact that a believer is happier than a skeptic is no more to the point than the fact that a drunken man is happier than a sober one." -- George Bernard Shaw

In the modern understanding (Including QM) even the empty space still has some quantum field fluctuations which are quite complex.
Complex enough that there are no known exact solutions for the equations (Depending on the model there are some good approximate solutions though). So, nothing doesn't sound like a good answer for that question.

Ok, if you want to ask a question this deep, it is important to get some of the terminology sorted out: particles are merely excitations of fields, and forces are merely exchanges of particles. So you are just left with fields!Imagine the universe as the ocean. Things in the universe are not objects floating in the ocean but actually properties of the ocean itself, such as a particlar wave, or collection of waves. Here the ocean represents all of the fields that make up our universe.Time is defined by the metric field, which is also responsible for gravitation; if you remove the metric field you have lost time and distance. So your box contains just space, not space-time, and it doesn't even have a concept of distance. It is just an infinite collection of idelaised points. However, it does still have a concept of topology: which points are neighbours of other points? This means that although there is no distance in your box, there is still some idea of the shape of the space. It could have the topology of a sphere, a torus, something really weird, or perhaps something really boring such as the normal space of our everyday experience.The metric field is almost certainly not fundemental, so this sort of concept is very important to our understanding of reality. In other words, good question

Thanks for the reponces all!. I am reading Fabric of the Cosmos and getting a bit lost! I did a biology (with honours in genetics) but that was four years ago. I have since moved in construction project management so my mathes may be a bit fuzzy. I only really ever got stats as part of highier maths because I had to use it for most of the experiments - still use it a little.So space can have a shape without distance? I understand that space and time are the same thing (or almost the same thing) but how can you have a series of points that relate to each other without distance? The concept of seperate points with out distance does not seem possible. If distance did not exist then everything would surely be in the same place or everything would be in different places with no relationship between each object.Could you expand on what you mean by idealised points?Edited by Fragallrocks, : Learn to spell first.

Certainly At first sight it look this way. But this is where topology comes in. Take a flat piece of paper, preferably infinite in size. pick a point and move around a bit. Take away any concept of distance, and you may as well be not moving, so your infinite piece of paper might as well be a single point. We say that the "deformation retract" of the plane is a point. In other words, there is nothing to stop you collapsing the plane down to a single point.But now think of the same piece of paper with a hole cut into it. As you move around you can ask yourself how many times you've encircled the hole - score +1 for each clockwise circle and -1 for each anti-clockwise circle. You cannot collapse this space into a single dot because you would lose that piece of information. The hole presents an "obstruction" to the deformation retract of the space, and the best you can do is collapse the space down to a cirlce - essentially the loop that encircles the hole. The deformation retract of a plane with a single hole is a circle - in math speak.In other words, a plane with a hole in it is like an integer variable becasue you can count the number of clockwise or anti-clockwise encirclings of the hole. A plane with two holes is a (ordered) pair of integers. So even though there is no distance, there is still some structural information, and this is what topolgy is all about.Consider a finite plane with no edges and no loops. We call this a sphere (or surface of a sphere in non-math speak). That same plane with two integers is a torus (think of the two different ways you can encircle a donut!) With one integer and one variable that can be +1 or -1 is a Klein Bottle. And with two +1/-1 variables we have RP2 - the real projective plane in 2d. This exhausts the possibilities for finite 2d planes without edges (boundary as we say).There are actually several steps in-between having just topology and having distance. Distance is regarded as quite a high-level concept, completely contrary to everyday thinking.Edited by cavediver, : No reason given.

When I said "nothing" I meant it literally; Kant claimed that space and time are abstract concepts made up in our minds to organize our sensory perceptions with no reality behind them.If you don't like that, then you'll have to argue the point with him. Except that he's dead. So it should be an easy debate.

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"The fact that a believer is happier than a skeptic is no more to the point than the fact that a drunken man is happier than a sober one." -- George Bernard Shaw

Quite. Whenever we get the old "ahh, but there are still the quantum fields, so it's not quite nothing", I wonder what they thought there was extra to the quantum fields to begin with!!!

So as the box is finite it can have a shape based on how you can move around within the space. But if there is infinite space with no other makers there is no distance because however you move you are still in the centre?Do we know the topology of the universe that we live in?Just to go back to the time thing. Does the box have a means of measuring/perceving time if there is nothing in the box that will ever change? i.e. if there is no distance there is no time(that not quite put correctly but I cannot think how else to phrase it.Edited by Fragallrocks, : No reason given.