Where is the edge of the universe

[Adrian07]

Where is the edge/boundary of the universe may sound like a simple question but I can see 3 possibilities.

1 Observed, this puts us inside a sphere looking out towards an edge which is beyond visible range, some estimates appear to give up to around 50 bly away.

2 Expanding universe theory, a timeline of expansion clearly puts us on the edge of an expanding sphere looking inwards.

3 The no edge scenario

1 and 2 are opposites, 3 could fit in with 1 if the universe was infinitely old and large.
So which one is correct or is it possible to merge them all together

 

[mfb]

There are no hints of any edge in space - the universe looks the same in all directions, and theories without an edge can describe this perfectly. The big bang could be an "edge in time".

 

[PeterJ]

An edge would make no sense at all. This suggest that our usual notion of space and time makes no sense, which of course it doesn't, since it gives rise to the question you've asked.

 

[phinds]

Where is the edge/boundary of the universe may sound like a simple question but I can see 3 possibilities.

1 Observed, this puts us inside a sphere looking out towards an edge which is beyond visible range, some estimates appear to give up to around 50 bly away.

No, it puts us exactly where we are, which is a place of no particular significance (other than to us) in an expanding universe that has no center and no edge. If you mean the observable universe (the 50BLY radius), then we are at the center of it and it has an "edge" of a sort but only in the same sense that there is an "edge" to a sphere that I define as having a 10ft radius centered on my left eyeball.

2 Expanding universe theory, a timeline of expansion clearly puts us on the edge of an expanding sphere looking inwards.

No, it does not put us "looking inward", it has exactly the same as the answer above

3 The no edge scenario

Yes, that is correct

1 and 2 are opposites

No, they are not. They both describe the existing universe.

3 could fit in with 1 if the universe was infinitely old and large.

No, 3 fits in with 1 quite nicely and certainly does not require an infinitely old universe.

 

[Adrian07]

Please describe a shape that has no edge or boundary or are you saying the universe is shapeless.
How do you measure expansion without an edge or boundary to relate that expansion to. You can use any point you like and the boundary is the point the expansion has reached, no boundary gives rise to infinite space.

 

[Mordred]

one shape that has no edge is the surface of a ball much like an ant on a beachball. The surface of the beachball looks flat. However this would hold for a finite curved universe.
Were reasonably confident that the universe is flat so one
of the few shapes is a torus.

Keep in mind that no one knows if the universe is finite or infinite.
How do we measure expansion? We judge the rate of expansion by the movement of galaxies by measuring its redshift. In every direction non gravitationally bound galaxies are moving apart.
Take a 3 dimensional grid. With each vertical, horizontal and Z directional line intersection as a coordinate.
Each coordinate is moving apart regardless of direction or cross direction.
This essentially means the space between coordinates is increasing. Or space between galaxies.

 

[phinds]

Please describe a shape that has no edge or boundary or are you saying the universe is shapeless.
How do you measure expansion without an edge or boundary to relate that expansion to. You can use any point you like and the boundary is the point the expansion has reached, no boundary gives rise to infinite space.

I think your problem here is that you think of the universe as expanding INTO something, which is not the case. The universe is all there is. It is not expanding into something outside of itself. If it were, THEN there would be an edge, but it isn't so there isn't.

 

[Mordred]

The FAQ subforum has some decent articles on this. Also the balloon analogy in the sticky threads also has related material. I believe Phinds signature links to a balloon analogy.
Please read those mentioned articles they will clear up a lot of misconceptions.

 

[phinds]

MY balloon analogy discussion is here:

www.phinds.com/balloonanalogy

 

[Mordred]

Thanks Phinds it would be nice to get our signatures back lol.

 

[phinds]

Thanks Phinds it would be nice to get our signatures back lol.

The price we pay for "progress" ?

 

[Chronos]

You could argue that all three are true, but, meaningless. 1] The universe is about 13.8 billion years old and the 'beginning' is currently at a proper distance from us of a little under 50 billion light years. Obviously you can't see the universe before it was born so the observable universe is effectively a sphere a little under 100 billion light years in diameter. 2] We reside at the oldest place in the observable universe. Everything else is younger than us, therefore, we reside at the temporal edge of the universe. 3] The is no edge of the universe. An edge implies the existence of something 'beyond' or 'outside' the universe, which [as already discussed] is forbidden by definition. It is also true the question is meaningless is the universe is infinite. That's the easy way out and the odds are very good you will never be proven wrong.

 

[petm1]

2] We reside at the oldest place in the observable universe.

I like this, does it help when I add 'as measured using the youngest photons'.

 

[Mordred]

assuming you can get those baby(youngest photons) to cooperate

 

[Chronos]

The point is when you talk about the 'edge' of the universe, you can only frame it in temporal terms - from the birth of the universe to the present. That is like talking about the 'edge' of Monday. The universe does not recognize our definition of 'edges'.

 

[Adrian07]

It occurs to me that if we have no edge or nowhere then a 4th option of Everywhere should be included if only for consideration.

While I agree any 3d shape can have a surface without edge it still has boundaries. With the Earth gravity stops you walking to the moon and its surface stops you falling towards the center, so we have a 2d edgeless surface with boudaries. I can see edgeless in these circumstances but not edgeless with no boundaries.
The balloon analogy is well known as is its brother the fruit bun to explain the expansion of space,

Post 7 I do not think the universe is expanding into anything unless you regard time as something, it is pretty obvious that space cannot expand into space.
Chronos post 12 point 2 are you absolutely sure I thought that today would be the youngest place as yesterday would be older than today etc

 

[julcab12]

It occurs to me that if we have no edge or nowhere then a 4th option of Everywhere should be included if only for consideration.

Edge, center and boundary are defined states and restricted to space. For instance, I have a ruler. I can say it has an edge and center bec. i can subjectively define a limit to the ruler when in fact it isn't the case especially when you zoom it in. So what we knew as edge is limited to our observation and remain temporal since nothing is certain. Same is true with our universe with a temporal edge(SLS).

 

[Chronos]

... Chronos post 12 point 2 are you absolutely sure I thought that today would be the youngest place as yesterday would be older than today etc

Are you younger today than you were yesterday? Due to the finite speed of light, everything we observe is a consequence of events that occurred in our past - i.e., when the universe was younger than it is at present.

 

[petm1]

Edge, center and boundary are defined states and restricted to space. For instance, I have a ruler. I can say it has an edge and center bec.

Restricted to space/time, each edge, center, and boundary with a defined state are temporal in nature. Using the photon as our ruler, with all photons traveling outward from emission, I would think the younger photons show us a outer edge of the universe we see as smaller. Yet what about the surface of last scattering if we were to call an inside edge of the universe it must be the view we see from the oldest photons that we see from all directions in space.

 

[SecretOfnumber]

Big Bang came from nothing ,to understand the"edge" science have to explain how that is possible...

 

[skydivephil]

The "big bang" is a rather ambigous term here. Seom people describe it as you say but a more responsible approach it to say the standard model of cosmology (known as LCDM) describes the universe as expanding froma hot dense state for the last 13.8 bio year . What happened before that is an open question.

 

[Adrian07]

Chronos is today older than yesterday.

So consensus is that the universe has no edge, I find this most unsatisfactory and is not the first time I have found I can't explain it so it does not exist.

 

[martinbn]

So consensus is that the universe has no edge, I find this most unsatisfactory and is not the first time I have found I can't explain it so it does not exist.

It is not like that. There is no evidence of an edge nor there is theoretical need for one, so why introduce one.

 

[Boy@n]

Ok, there in no edge to space-time, yet there seems to be an edge to matter within infinite space-time when looking at various images of Universe... Are those images wrong?

 

[Mordred]

those are representations of the Observable universe. the Observable universe is finite we can only see and measure so far after all

 

[petm1]

Are you younger today than you were yesterday? Due to the finite speed of light, everything we observe is a consequence of events that occurred in our past - i.e., when the universe was younger than it is at present.

Everything we observe is the same amount of time. The age of the atom at emission of a photon plus the duration of the photon always add up to the same present. Say I look out in the night sky with my hand out in front of me. The age of the atom within my hand plus the duration of the young photon I receive from it should be the same amount of time as the young atom in a galaxy far far away plus the duration of the old photon I receive right next to it. So even it we are the oldest part of matter we observe we are still seeing back the same amount of time from our view of our shared present. How else do you think of phased space always being relative.

 

[Chronos]

You are missing the point. The atoms in your hand are older [relative to the age of the universe] than the atoms that emitted photons you observe from the distant universe. All photons you observe from the distant universe were emitted when the universe was younger than it is now.

 

[Adrian07]

Exactly the photons are traveling from the past to the present or future, the present is younger than the past.

 

[mfb]

I think you are using two different concepts of "younger". It is impossible to resolve this.

1) Less time has passed since the big bang (age of the universe at that point)
2) Less time has passed until now (similar to the age of humans: measured from "birth"=event to now)

 

[petm1]

The duration of a photon from emission til reception added to the age of the emitting atom at emission will always equal the age of the atom that is receiving the photon in the present. Could you please show me the error in my thinking.

 

[phinds]

The duration of a photon from emission til reception added to the age of the emitting atom at emission will always equal the age of the atom that is receiving the photon in the present. Could you please show me the error in my thinking.

Sure. A photon is emitted from a billion year old atom a billion light years from here and thus by your reckoning is 2 billion years old when it gets here. It hits a newly formed H2O atom that is 1 second old.

 

[HallsofIvy]

The duration of a photon from emission til reception added to the age of the emitting atom at emission will always equal the age of the atom that is receiving the photon in the present. Could you please show me the error in my thinking.

"The time it takes a letter to go from me to my nephew, added to my age, at the time I mail the letter, will always equal the age of my nephew." What is the error in my thinking?

Age of an emitting atom at emission, added to any duration, will be the age of that atom at the end of the duration, just the time it takes a letter to go from me to my nephew add to my age when I send it will be my age when he receives it.

In other words "The duration of a photon from emission til reception added to the age of the emitting atom at emission" will be the age of the emitting atom at reception.

In asserting that it is also the age of the receiving atom, you appear to be thinking that all atoms are the same age. And that is not true.

 

[Adrian07]

mfb post 29
I think you may be right or perhaps, if this makes sense, time today is younger than yesterday, however I am older today than I was yesterday.

 

[phinds]

mfb post 29
I think you may be right or perhaps, if this makes sense, time today is younger than yesterday, however I am older today than I was yesterday.

How do you define time in a way that makes it younger today than yesterday? Are you running time backwards?

 

[petm1]

In asserting that it is also the age of the receiving atom, you appear to be thinking that all atoms are the same age. And that is not true.

I was under the impression that all matter, in the form of atoms, formed just after the decoupling of photons we see as the cmbr. I did not know new atoms were formed all the time I thought that new atoms were just a recombination of existing atoms into heaver ones not new ones. Thanks.

 

[Thomas1989]

I didn't want to start yet another thread, so I'll post this here, it's quite closely related.

I've only recently started to comprehend that our universe could be flat and infinite, and has no boundary, this is really crazy. I still don't understand how the universe could have a finite age, a beginning in time and yet be infinite in spatial extent.

There are some truly brilliant minds here, I was hoping somebody might be good enough to explain exactly how this is mathematically possible.

 

[Adrian07]

I am not classed as brilliant but basically what you see in this thread is what you get regarding boundaries of the universe, got no idea about the maths though. As far as being edgeless goes imagine there is nothing outside the universe then you cannot have an edge as there is no outside you require an inside and outside to define the edge.
Thats space and you should be able to see the arguments caused when you include time.

 

[mfb]

explain exactly how this is mathematically possible.

It would have been infinite in its spatial size all the time.

 

[Boy@n]

Tu

I didn't want to start yet another thread, so I'll post this here, it's quite closely related.

I've only recently started to comprehend that our universe could be flat and infinite, and has no boundary, this is really crazy. I still don't understand how the universe could have a finite age, a beginning in time and yet be infinite in spatial extent.

There are some truly brilliant minds here, I was hoping somebody might be good enough to explain exactly how this is mathematically possible.

Observable Universe is flat and has finite size... Google Universe and change results to images...

So, based on what I read in this thread it seems Universe is considered to be infinite while Observable Universe is not.

I too would appreciate to see proper explanations.

It makes me also think that then we don't really know what's beyond that which we can observe (if anything), so, why do we need dark matter and dark energy theory to explain where the missing mass is? It could well be beyond that which we can observe, no?

 

[phinds]

Observable Universe is flat and has finite size... Google Universe and change results to images...

Based on what I read in this thread it seems Universe is considered to be infinite while Observable Universe is not.

I'd appreciate too to see proper explanations.

The universe is undefined in shape and size. Might be infinite, might be finite and unbounded. Believed to NOT be finite and bounded as that causes a myriad of problems in physics and seems unreasonable.

The observable universe is a well-defined sphere based on you and extending out for about 50billion light years in all directions.

 

[Mordred]

Tu

It makes me also think that then we don't really know what's beyond that which we can observe (if anything), so, why do we need dark matter and dark energy theory to explain where the missing mass is? It could well be beyond that which we can observe, no?

Dark matter and dark energy is not an explanation in regards to shape or edge of the universe.

dark matter explains the missing mass that attributes to the rate of galaxy spins, by Newtonian physics the outer edge of a galaxy would spin slower than the outer edge. This does not occur, it was found that having dark matter the spin works out correctly. this explanation does not cover all the evidence of dark matter which is numerous. However it covers what led scientists to infer its existence.

dark energy is an energy term used to explain the rate of expansion. It was thought at one time that the universe was static. However Einsteins GR predicted either a contracting or expanding universe. Hubble later showed that it was expanding. Dark energy is said to be the cause of that expansion. There is still debate on the cause of expansion mechanism. Could be false vacuum as stated by A. Guths false vacuum model. Could be a bounce as LQG states (hopefully I have that part right LQC is not my familiarity).

In an infinite Universe the only things we can confirm is the observable portions only, no matter how far back in time we look we will never see an edge or border to the universe not that one exists,. The flat geometry was once considered indicative of an open universe (infinite) however later research showed that other flat shapes such as a torus can be flat and finite.
other classical geometries of a closed universe are circle or sphere, and saddle both these geometries are finite geometries.

here is a straightforward link on Universe geometry

http://abyss.uoregon.edu/~js/cosmo/lectures/lec15.html

 

[mfb]

Dark energy is said to be the cause of that expansion.

Dark energy is the cause for the acceleration of the expansion. The universe could expand without dark energy as well.

 

[Mordred]

Yeah I should have worded that better lol

 

[Boy@n]

The universe is undefined in shape and size.

That seems to me to be the most certain thing we can say on this topic.

All else are just various possible scenarios/theories with higher or lower degree of probability to describe truth of nature.

Though, I find all of them fascinating, because we infer so much from so little (all from light and particles hitting our planet). Amazing.

 

[Adrian07]

Another question.
Draw a simple time-line for the universe from BB to present day.
1 Where on that time-line has the universe expanded to.
2 Where on that line do we sit.

The answer to both appears to be the same place. This appears to make no sense at least as far as the observable universe goes. Any explanations. Am assuming time and space expand at the same rate.

 

[Mordred]

Time does not have a spatial component. It neither expands or contracts. Rather its observed rate changes as described by GR and SR.

If your referring to the relation of light speed of travel and the observable universe.
Yes the universe is 13.78 billion years old.
The observable universe today has a radius from our locale of 47 billion light years.
As light travels towards us space is expanding.
Thats how we see further than the age of the universe.
See the FAQ sub forum for more detail.
During the first second of the universe. The universe exponentially expanded. Then expansion slowed down during the matter dominated era. This matter dominated era lasted till roughly 7.3 billion years after the BB. during the matter dominated era gravity was dominant and caused a contraction. However enough vacuum or dark energy was created referred to as the cosmological constant or Lambda \Lambda in the lambdaCDM. The cosmological constant became dominant leading to a lambda dominant era where expansion is increasing.

 

[Boy@n]

Am assuming time and space expand at the same rate.

Well, I guess current science says that space and time are not separate, but one 'thing' as spacetime.

Barbour has different opinion though, that time doesn't really exist, that time is merely our perception of motion of all things.

 

[Mordred]

{\scriptsize \begin{array}{|r|r|r|r|r|r|r|} \hline S=z+1&a=1/S&T (Gy)&R (Gly)&D (Gly)&D_{then}(Gly)&D_{hor}(Gly)&D_{par}(Gly)&a'R_{0}\\ \hline 1090.000&0.000917&0.000378&0.000637&45.731&0.042&0.056&0.000&20.164\\ \hline 849.077&0.001178&0.000574&0.000953&45.543&0.054&0.072&0.001&17.299\\ \hline 661.405&0.001512&0.000866&0.001419&45.325&0.069&0.092&0.002&14.917\\ \hline 515.214&0.001941&0.001301&0.002103&45.073&0.087&0.118&0.003&12.919\\ \hline 401.336&0.002492&0.001943&0.003106&44.782&0.112&0.151&0.005&11.230\\ \hline 312.629&0.003199&0.002891&0.004574&44.448&0.142&0.193&0.007&9.791\\ \hline 243.528&0.004106&0.004284&0.006717&44.066&0.181&0.246&0.011&8.558\\ \hline 189.701&0.005271&0.006328&0.009846&43.629&0.230&0.313&0.016&7.496\\ \hline 147.771&0.006767&0.009322&0.014408&43.131&0.292&0.399&0.024&6.576\\ \hline 115.109&0.008687&0.013699&0.021057&42.563&0.370&0.507&0.036&5.776\\ \hline 89.667&0.011152&0.020093&0.030744&41.917&0.467&0.644&0.053&5.079\\ \hline 69.848&0.014317&0.029424&0.044849&41.182&0.590&0.816&0.079&4.469\\ \hline 54.409&0.018379&0.043031&0.065385&40.348&0.742&1.032&0.116&3.935\\ \hline 42.383&0.023594&0.062863&0.095274&39.400&0.930&1.303&0.172&3.467\\ \hline 33.015&0.030289&0.091754&0.138771&38.325&1.161&1.640&0.253&3.056\\ \hline 25.718&0.038884&0.133830&0.202060&37.105&1.443&2.057&0.372&2.694\\ \hline 20.033&0.049917&0.195082&0.294128&35.722&1.783&2.572&0.547&2.376\\ \hline 15.605&0.064080&0.284235&0.428027&34.154&2.189&3.202&0.802&2.096\\ \hline 12.156&0.082263&0.413945&0.622664&32.377&2.663&3.964&1.176&1.850\\ \hline 9.469&0.105605&0.602597&0.905329&30.363&3.207&4.876&1.722&1.633\\ \hline 7.376&0.135570&0.876751&1.315024&28.084&3.807&5.950&2.520&1.443\\ \hline 5.746&0.174038&1.274606&1.906448&25.507&4.439&7.190&3.683&1.278\\ \hline 4.476&0.223420&1.850354&2.753067&22.602&5.050&8.581&5.378&1.136\\ \hline 3.487&0.286815&2.678630&3.944165&19.346&5.549&10.082&7.837&1.018\\ \hline 2.716&0.368198&3.856519&5.562897&15.738&5.795&11.615&11.390&0.927\\ \hline 2.116&0.472674&5.494908&7.622994&11.826&5.590&13.062&16.471&0.868\\ \hline 1.648&0.606794&7.688893&9.965115&7.742&4.698&14.289&23.622&0.852\\ \hline 1.284&0.778970&10.465993&12.220152&3.709&2.889&15.203&33.467&0.892\\ \hline 1.000&1.000000&13.753303&13.999929&0.000&0.000&15.793&46.686&1.000\\ \hline 0.848&1.178769&16.127949&14.832270&-2.203&-2.596&16.037&57.611&1.113\\ \hline 0.720&1.389495&18.618735&15.419791&-4.150&-5.766&16.198&70.616&1.262\\ \hline 0.611&1.637894&21.189539&15.814752&-5.855&-9.590&16.300&86.034&1.450\\ \hline 0.518&1.930698&23.813226&16.071344&-7.332&-14.156&16.363&104.265&1.682\\ \hline 0.439&2.275846&26.470879&16.234284&-8.601&-19.575&16.400&125.793&1.963\\ \hline 0.373&2.682696&29.149943&16.336240&-9.687&-25.986&16.420&151.192&2.299\\ \hline 0.316&3.162278&31.842341&16.399447&-10.612&-33.558&16.429&181.147&2.700\\ \hline 0.268&3.727594&34.543144&16.438244&-11.399&-42.492&16.438&216.465&3.175\\ \hline 0.228&4.393971&37.248853&16.462174&-12.069&-53.030&16.462&258.104&3.737\\ \hline 0.193&5.179475&39.957670&16.476843&-12.637&-65.454&16.477&307.189&4.401\\ \hline 0.164&6.105402&42.668392&16.485825&-13.120&-80.101&16.486&365.051&5.185\\ \hline 0.139&7.196857&45.380278&16.491324&-13.529&-97.369&16.491&433.258&6.110\\ \hline 0.118&8.483429&48.092876&16.494692&-13.877&-117.723&16.495&513.659&7.200\\ \hline 0.100&10.000000&50.805908&16.496757&-14.172&-141.718&16.497&608.434&8.487\\ \hline 0.085&11.787686&53.519206&16.498025&-14.422&-170.001&16.498&720.152&10.003\\ \hline 0.072&13.894955&56.232831&16.498643&-14.634&-203.342&16.499&851.842&11.791\\ \hline 0.061&16.378937&58.946390&16.499128&-14.814&-242.642&16.499&1007.074&13.898\\ \hline 0.052&19.306977&61.660009&16.499432&-14.967&-288.969&16.499&1190.057&16.382\\ \hline 0.044&22.758459&64.373666&16.499625&-15.097&-343.577&16.500&1405.752&19.311\\ \hline 0.037&26.826958&67.087345&16.499751&-15.207&-407.947&16.500&1660.006&22.763\\ \hline 0.032&31.622777&69.801037&16.499835&-15.300&-483.825&16.500&1959.712&26.832\\ \hline 0.027&37.275937&72.514739&16.499894&-15.379&-573.267&16.500&2312.997&31.628\\ \hline 0.023&43.939706&75.228445&16.499938&-15.446&-678.699&16.500&2729.438&37.282\\ \hline 0.019&51.794747&77.942154&16.499972&-15.503&-802.978&16.500&3220.325&43.947\\ \hline 0.016&61.054023&80.656031&16.499836&-15.551&-949.475&16.500&3798.968&51.804\\ \hline 0.014&71.968567&83.369743&16.499861&-15.592&-1122.161&16.500&4481.054&61.065\\ \hline 0.012&84.834290&86.083456&16.499884&-15.627&-1325.718&16.500&5285.075&71.981\\ \hline 0.010&100.000000&88.797170&16.499905&-15.657&-1565.665&16.500&6232.831&84.849\\ \hline \end{array}}

Time now (at S=1) or present age in billion years: 13.753301 'T' in billion years (Gy) and 'D' in billion light years (Gly)

Look at the 7.6 billion year timeline you can see where the change over occcurs in the last columm.

this graph is for a theoretical galaxy at the edge of the observable universe today. or stretch 1090 which is the first row. the S row 1.000 is when the BB occurred at 10^-43 seconds.

the a'R^o column shows the distance increase to the hypothetical galaxy. you can see the change in contraction and expansion related to its recessive velocity in S=1.648 or first column

the calculator is developed by forum members and is in the sticky or pinned thread above "look 88 years into the .." thread above.

http://www.einsteins-theory-of-relativity-4engineers.com/TabCosmo9.html

here is a quote from wiki that's appropriate

The metric expansion of space is the increase of the distance between two distant parts of the universe with time. It is an intrinsic expansion whereby the scale of space itself is changed. That is, a metric expansion is defined by an increase in distance between parts of the universe even without those parts "moving" anywhere. This is not the same as any usual concept of motion, or any kind of expansion of objects "outward" into other "preexisting" space, or any kind of explosion of matter which is commonly experienced on earth.

the keyword is scale of space itself is expanding

 

[Mordred]

This wiki page has some decent coverage which I don't often say for wiki pages lol.

http://en.wikipedia.org/wiki/Metric_expansion_of_space

the images unfortunately do not show great detail in the slight contraction mentioned above.

 

[RByrne6722]

Try to imagine 3 orthogonal (mutually perpendicular) planes.

That’s pretty easy; the corner of any cube shows how 3 orthogonal planes meet. It defines the 3-dimensional (3-D) space we live in. Look at the corner of your room, 2 walls and the ceiling are 3 mutually perpendicular planes (in most normal rooms).

Only, we don’t live in a 3-D space. Time is a dimension. We appear to live in a 4-dimensional (4-D) space.

We can’t actually visualize 4 orthogonal planes. The 4 planes of ordinary space and time are mutually perpendicular, but we have 3-D eyes and can’t see or draw 4-D space. We can draw 2-D spaces and build 3-D spaces, but images beyond that are not possible (yet).

However, we can describe it mathematically. It’s not too difficult to do, just add a 4th dimension to the X, Y & Z Cartesian coordinates, call it T if you will.

Our 3-D (X,Y, Z) space is within this 4-D (X, Y, Z, T) space.

Wouldn’t our 3-D space be expanding within 4-D space? What are the boundaries of this 4-D space? What would constitute an edge in 4-D space?

What if the universe is actually 9, or 11 or 12 dimensional?

The expansion of 3-D (and 4-D etc.) space would be subsumed by these higher dimensions, wouldn’t it?

There's an edge to a sheet of paper, but I'm not so sure there's an edge to the Universe.

You might enjoy reading Flatland by Edwin Abbott