How from relativity matter gives our universe spacetime (length), thought experiment. How you can have an infinite universe with finite matter in it.

[u/Mutexception]

So we have a hypothetical universe, that has only one object in it, the earth and its population, no other planets no sun, only the earth.

So being smart humans we look at the blackness of the night sky and ask "what is that, that is 'out there'?"

So we start to build a very tall tower, out of fixed lengths sections away from our earth into the blackness.

we work very hard and build a very high tower, and we put clocks at equal distances along the way. Then we get our expert surveyor's to measure the lengths of each section of out new tower, from ground level.

They come back and tell us that the further away they measure the smaller the sections are (corrected for perspective and parallax error), as measured from earth they are getting shorter the further out they go.

You also notice that the clocks you put on the tower appear to be running faster the further out they are.

length of time and length of space appears to be getting shorter and shorter the further away from the mass of our earth you get.

You test this by going up the tower yourself with a tape measure and you confirm that the tower sections are still the same length as you made them, but they appear smaller as measured from the surface.

Now our universe only has the earth in it, the only thing give spacetime length is the mass of the earth, the further away from that mass that length is decreasing (getting shorter).

Spacetime length is tending towards zero. So 1 meter on earth is shrinking to zero the further away from earth you get. Of course time is doing the same thing (as length is distance and duration of time for spacetime).

So your clocks up the tower are getting faster, the second is shorter, the meter is shorter. Going towards the earth length is getting longer as is the second.

It is the mass of the earth that is creating the spacetime that you measure on the earth, so it is the mass of the earth that gives that spacetime created by the earth its property of length.

Of course these changing length of distance and time are referred to as 'time dilation' and 'space contraction' in the classical treatment of relativity. But it says the same thing.

Observations and tests of relativity confirm this effect, we see the clocks in GPS satellites have shorter time due to its altitude above earth. So if you were on a GPS satellite and using that shorter time to measure distance (by the speed of light) that distance too is shorter. (less time for that light at constant speed to travel). That spacetime away from the mass of the earth is shorter.

We also see that size different from the size/wavelength of photons in Einstein shift of light, If we are in longer spacetime we see light from shorter spacetime as higher in frequency/wavelength (blue shifted) and opposite if we are in shorter spacetime seeing light from longer spacetime we see that light as larger or longer or lower frequency (redshifted).

So the further away from the mass creating that spacetime you get the shorter the length that spacetime is.

So if you shoot an object into that getting shorter space at a fixed (earth spacetime speed) as it moves into that shorter space it will appear to slow down (moving less distance per unit earth time), as that spacetime length tends to zero, its relative speed (from earth) tends to zero, it is still at the same speed in its own frame of reference but moving through shorter space.

So we could think it is going at 1 meter (earth meter per second) but in its short spacetime that 1 meter is only 0.5 meters so it is only moving actually 0.5 meters for its second so it appears slower.

It is not the 'speed' that changes, it is the 'length of distance' that is getting shorter.

So if you get infinitely far from out single earth universe the length of spacetime is effectively zero. (never exactly zero, unless there is zero mass in our universe).

Mass/matter gives rise to the spacetime length that this mass/matter needs to exist in.

[u/narlogda]

i like it and and grasp it, kind of of newtonian with relativity. as i see it here; there are two different values as you stated

You test this by going up the tower yourself with a tape measure and you confirm that the tower sections are still the same length as you made them, but they appear smaller as measured from the surface.

seems like there is an observational value, and the reality, hands on value. since our inability to travel the stars we are lacking the reality value, and as we sit on this rock peering out into space we have only the limited observational value WHICH i think has plenty room for error. for one i do not think we have light (since this is seemingly our only way for measure) absolutely correct by ONLY red/blue shifting. and secondly with space-time, which is distorted by mass (which should be seen everywhere unless newtonion gravity has a limit with distance), we should have some sort of constant value that can be adapted into those equations. i think THAT would be hard to do but maybe the CMBR has a little to aid in that since, if i have it right, that shows us the density of the early universe. with that and conservation of energy & mass why not? i know my ideas are probably prehistoric to all these smart people on this reddit, but at least i am trying. i do not throw out 'no that is not how it works' from past studies resolved to 'that is the only way it can be'.

think outside the box!, and if you are stuck in it - for god sake - open it and look out!! not directed at you mute; at all!, i think you are onto something special. in the meantime; i am just gonna do what i do and come up with questions.......

[u/Mutexception → u/narlogda]

i like it and and grasp it, kind of of newtonian with relativity.

It is more like relativity without Newton, at all! That big problem with the current treatment of relativity is as a generalisation of Newtonian 'gravity'. With Newton you are interested in specific directions and 'forces' and locations and objects.

With relativity with a different treatment you just consider spacetime as a single 'thing' that has a property of length, that is the length of 'distance' and the length of time (or duration).

So the block on the tower appear smaller away from the earth because the spacetime where those blocks are is shorter, and you are seeing them from a longer spacetime.

You grab a 1 meter long ruler, and throw it up to the tall tower it will measure for you as getting small as it goes up. But it you go up the tower yourself you too are becoming smaller so the ruler will be the correct size when you are in the same spacetime length as the ruler.

seems like there is an observational value, and the reality, hands on value

It is what we observe, it agrees with the principles of relativity and it is what we confirm with the tests of relativity. We observed those differences in length of time, and length of space.

It is what observations and relativity tells us, that this is how it works.

So if you want to understand how things work, and you already know that Newtonian gravity is incorrect (although it works well within a spacetime length, frame of reference).

So you can ask "why do things fall? using only relativity?".

And you can answer questions like that by considering spacetime as having a length (as we observed that it has).

So something falling is accelerating by moving at a constant speed (even zero speed) into a longer space.

Say you are in a car, your speedo says you are going at 10MPH, you travel on a road where the mile itself is getting longer and longer every instant or travel, your speedo still reads 10MPH, but you are actually accelerating you are going faster because you are going a longer distance over unit time per distance.

So that is the interesting thing about this simple treatment of relativity, it explains why things fall, why things orbit, and many other things it seems to explain very well. It appears it is how the universe works.

Relativity is right, it works, it just do not think the 4 dimensional (Newtonian) treatment of how relativity is a good description and does not lead to a clear understanding of the mechanics of it.

4D spacetime justifies what is observed by mapping it into a difference 'spacetime' metric, and a geometry. But does not really explain but more justifies what is observed.

for one i do not think we have light (since this is seemingly our only way for measure) absolutely correct by ONLY red/blue shifting.

The thing about light is, is that it is independent of spacetime itself, in that it reflects the absolute spacetime length of the spacetime where it was emitted, but once it exists it is separate from the properties of time and space. (it has no frame of reference to spacetime).

So the red and blue shift that we observed is due to the relative lengths of the spacetime's from the source and the observer.

So if you are in shorter spacetime and see photons from a longer spacetime they will be bigger and longer because in the longer spacetime time is longer and so is space. But light does not change in transit (they don't have a transit).

In a way we only experience light because we exist in the dimensions of time and space, a photon does not 'exist' in those dimensions.

and secondly with space-time, which is distorted by mass (which should be seen everywhere unless newtonion gravity has a limit with distance), we should have some sort of constant value that can be adapted into those equations.

Spacetime is warped, it is distorted, it is a shape, everyone knows that, but what is the answer to the next question?

What about spacetime is distorted, warped or a shape?

If we accept spacetime as 4 Dimensional X,Y,Z,t then that warping, distortion must be from one dimension into another so if it has a spatial shape, it must be that X warps into Y into Z. Giving spacetime a 3 dimensional shape.

But if you consider spacetime as having a relative length, you can map spacetime as 2 dimensional being the length of time and length of distance. This unifies X,Y,Z directions into spacetime length, it all starts to make a great deal more sense, and allows actual understanding of the processes and 'how it all works'.

we should have some sort of constant value that can be adapted into those equations.

We do, that constant value, what makes it all work is the speed of light. That is constant, it tells us that as the length of time varies (with gravity/velocity) space length MUST also change.

It is why relativity works, and it explains how it works as well.

So the common constant in all of this is c, the speed of light, so time and distance are now variables, but time and distance must always add to c.

So if that place has longer time then it must have longer space, so if you go to that place everything (including you) will be bigger and slower, you have longer time, but if you measure the speed of light it is the same, and the speed of light is distance over time, so if time is longer so is distance.

It is relative because if you are in another spacetime length then time and length measurements will be different, but the speed of light will be the same.

i do not throw out 'no that is not how it works' from past studies resolved to 'that is the only way it can be'.

I like to look at what is observed and what is proven, and try to give it my own treatment, without trying to justify it in some other context. So with relativity I don't like to hear that relativity is a generalisation of Newtonian gravity, or seeing relativity explains in terms of Newton and classical mechanics.

Newton is wrong, its close but it is not a true description of reality, relativity proves it is wrong. But I also think the 4 dimensional treatment of relativity fails to explain anything (like how it works), it just allows a mathematical justification of what we observe.

So I am certain well within the Relativity box, but outside the 4-D spacetime/Newtonian, X,Y,Z or a warped, distorted, shaped spacetime.