Q: How far away is the edge of the universe?

Physicist: If you ever hear a physicist talking about “the edge of the universe”, what they probably mean is “the edge of the visible universe”.  The oldest light (from the most distant sources) is around 15 billion years old.  Through a detailed and very careful study of cosmic inflation we can estimate that those sources should now be about 45 billion light years away.  So if you define the size of the visible universe as the present physical distance (in terms of the “co-moving coordinates” which are stationary with respect to the cosmic microwave background) to the farthest things we can see, then the edge of the visible universe is 45 billion light years away (give or take).  However, that “edge” doesn’t mean a lot.  It’s essentially a horizon, in that it only determines how far you can see.

Of course, if you wanted to know “how far can we see?” you would have asked that.  The picture of the universe that most people have is of a universe enclosed in some kind of bubble.  That is, the picture that most people have is of a universe that has an edge.  However, there are some big problems with assuming that there’s a boundary out there.

If you decide that space suddenly ends at an edge, then you have to figure out how particles would interact with it.  Obviously they can’t keep going, but bouncing off or stopping both violate conservation of momentum, and disappearing violates conservation of mass/energy.  Moreover, if you say that spacetime has a definite edge at a definite place then you’re messing with relativistic equivalence (all of physics works the same in all positions and velocities).  It may seem easy to just put an asterisk on relativity and say that there’s an exception where the edge of the universe is concerned, but the math isn’t nearly as forgiving.

The nicest theories today suggest that there is no boundary to the universe at all.  This leads to several options:

Three possibilities for a homogeneous (same everywhere), edgeless universe.

1) A negatively curved, infinite universe. This option has been ruled out by a study of the distribution of the Cosmic Microwave Background.

2) A flat (non-curved), infinite universe. The measurements so far (devotees may already know how to do these measurements) show that space is flat, or very very nearly flat.  However, infinite universes make everyone nervous.  An infinite universe will repeat everything in the visible universe an infinite number of times, as well as every possible tiny variation, as well as every vastly different variation.  All philosophy aside, what really bothers physicists is that an infinite (roughly homogeneous) universe will contain an infinite amount of matter and energy.  Also, the big bang (assuming that the Big Bang happened) would have had to happen everywhere at once.  As bad as the mathematical descriptions of the Big Bang traditionally are, an infinitely large Big Bang is much worse.

3) A curved, finite universe. This is the best option.  You can think of the universe as being a 3-dimensional space that is the surface of a 4-dimensional ball, in the same way that the surface of a balloon is a 2-dimensional space wrapped around a 3-dimensional ball.  Of course, this immediately begs the question “what’s inside the ball?”.  Well, keep in mind that what defines a space is how the things inside it relate to each other (the only thing that defines space is rulers).  So even if you turned the “balloon” inside-out you’d still have the same space.  Or, if you’re not a topologist, then remember that there’s nothing outside of space, and the surface of the 4-d sphere is space.  Now, be warned, the “3-d surface of a 4-d ball” description isn’t entirely accurate.  Right of the bat, we don’t live in 3 dimensions, we live in 3+1 dimensions (not “space” but “spacetime”), and the metric for that is a little weird.  Also, when you talk about “the shape of the universe”, you probably mean “the shape of the universe right now”, and sadly there’s no way to universally agree on what “now” means in a universe with any rotating stuff in it.  That being said, the “surface of a sphere” thing is still a good way to talk about the universe.

Since our best measurements show that space is very flat, if the universe has taken the 3rd “curved, finite” path (it probably has), then it must be really really big.  This is for the same reason that you can easily show that a ball is curved, but may have some difficulty showing that the Earth is curved.

Also, to answer the original question: the universe doesn’t have an edge.

This entry was posted in -- By the Physicist, Astronomy, Physics, Relativity. Bookmark the permalink.

47 Responses to Q: How far away is the edge of the universe?

  1. christopher says:

    couldnt be a bubble with stuff in it, with the surface of the bubble (or edge of the universe) expanding at the speed of light? if that were the case wouldnt it remove the problem of ‘how would particles interact with the edge’ since particles could never reach the edge?

  2. The Physicist The Physicist says:

    It might.
    However, it wouldn’t clear up the mathematical difficulties (as much as they count), and that doesn’t seem to be the way the universe is.

  3. Constantine says:

    I really enjoy your blog; but does your account of a “A curved, finite universe” still allow the universe to be infinite in extent? Most cosmologist I have read, James Bullock (of Irvine) as well as my research on WMAP shows that it is flat, infinite in extent and finite in volume.

    Nasa WMAP reads this: “Thus the universe was known to be flat to within about 15% accuracy prior to the WMAP results. WMAP has confirmed this result with very high accuracy and precision. We now know that the universe is flat with only a 0.5% margin of error. This suggests that the Universe is infinite in extent; however, since the Universe has a finite age, we can only observe a finite volume of the Universe. All we can truly conclude is that the Universe is much larger than the volume we can directly observe.”


  4. The Physicist The Physicist says:

    Any positive curvature necessarily implies a finite universe. What that quote is referring to is the fact that, whether or not the universe is infinite, we can only see a finite part of it.
    When you hear about things like the “size of the universe” what you’re almost always hearing about is the size of the visible universe.

  5. Constantine says:

    Thank you Physicist. So, when it comes to the actual size of the universe (and not just the observable universe), are the most convincing theories positing that the universe is infinite or finite? Is it right for me to assume that, from everything I hear, it is unknown because it is unobservable, but it is “possibly” infinite in actuality?

    Also, does the curvature you suggest agree with the WMAP quote? I’m not a physicist, but a poet, so please bear with me. 🙂

  6. The Physicist The Physicist says:

    Not sure what “.. flat to within about 15% accuracy..” means, but it looks like we more or less agree.
    The measurements so far show that the universe is extremely flat, so either it is infinite (definite possibility) or it’s so big that its curvature is undetectable (so far). To do that, the universe would need to be so big we’d need a poet to describe it.

  7. David says:

    So it has no edge but we know it is flat? If that is the case than it would be bigger in the x and y plane than the z plane. So in that respect w
    ouldn’t there be an dge in the z plane?
    Furthermore, in order to know or even to implied or guess that the universe is flat than you have to have some reason why you think one plane is smaller than the other 2. That could only be found by taking some reading of both edges of one plane and not the others.

    Example: if you are in a fish tank and a 1ft cube of water is all you can detect you could say that the water is infinite in every direction. However if on one side you detect the glass of the tank than you know it is not infinite in all directions. Now to think it is flat you would have to detect a barrier on 2 opposite sides of the tank.
    Just seems that saying it is flat but there is no edge is a paradox.

  8. nina says:

    If we were traveling out frim the centre of our solar system when would we know we have reached the edge of it?

  9. The Physicist The Physicist says:

    There are a lot of different ways of defining the boundary, so it depends who you ask. That’s also why this is funny.

  10. David Medlyn says:

    If from the vantage point of our Earth in the Milky Way galaxy, we look back and say that the beginning of the Universe started about 13.73 billion years ago. And if Hubble’s 42 Law is correct, looking the other way, the universe is expanding at an accelerated rate of 42 miles per second per 3 million light years.

    So, as you say above: if the furthest point of the expanded universe is 45 billion light years away and light travels at a constant speed, time must be expanding or accelerating to make up for the 31.27 billion-year discrepancy. Am I mad?

  11. The Physicist The Physicist says:

    @David Medlyn
    You sound happy enough.
    The extra distance comes from the fact that the object that emits a given photon continues to get farther away. If you were on a long road trip across an expanding planet, you’d find that (by the time you get where you’re going) the distance you traveled is less than the present distance to your starting point.

  12. David Medlyn says:

    So, that’s pretty amazing in itself. The universe in around 14 billion years has travelled about 45 billion light years. It opens two questions that have bothered me:

    1. At approximately what point (light years from the Big Bang) did the universe reach light speed? and
    2. Could we see any of that matter after it has attained light speed or are the photons coming towards us drawn back at a negative rate?

  13. The Physicist The Physicist says:

    @David Medlyn
    There’s a post here that tries to cover that. But in short:
    The expansion of the universe isn’t described by a speed, it’s described by a speed per distance. Right now it’s around 70 kilometers per second per megaparsec. The speed of light is never really involved one way or the other, in large part because this isn’t real speed so much as “the generation of more distance”.

  14. David Medlyn says:

    Thanks, that Wikipedia link was really interesting. Nine pages plus four pages of references. I am still wondering if anyone has worked out at what distance from the initiation of the universe did the outer rim reach light speed. And at that point, would we be able to see light emitted from that matter or would it be travelling faster in the opposite direction than the light travelling in our direction?

  15. tyler says:

    This article is wrong.The furthest thing we’ve ever taken a picture of is 13.1 billion light years away not 45.

  16. David Medlyn says:

    I don’t think this Wikipedia article is necessarily comparing what’s visible to us here on Earth. What is important is the application of Hubble’s law which has the expansion of the universe at 42 miles per second per 3 million years. Therefore at some time the outer sections of the universe reached light speed and if the mathematical calculations are correct the place has travelled a distance of around 46 billion light years. And since light travels (normally) at a constant speed, space itself must be expanding. I know I’m applying basic Australian bush logic to what are obviously complex and advanced cosmic mathematics, but it is really fascinating territory.
    Lawrence Krauss said recently that Einstein had said that if you’re moving faster than the speed of light, you’re actually going backwards in time. This opens up the notion that if light in the outer edges of the universe is being “dragged” along by the surrounding expanding space, then is that outer rim going backwards in time? And if Hubble’s acceleration law has no upper limit, does that mean that eventually the outer edge of the universe will go so far back in time that it will arrive back at the Big Bang? …. just a thought.

  17. TomA says:

    Wouldn’t the correct answer be, No one knows, everyone just guesses.

  18. David Medlyn says:

    I think new frontiers in all science often begin with a guess, an embryo of a new direction, then some mathematician ponders on the hypothesis and works some formulae around the notion. Usually they are good communicators so once one starts, others join in. Eventually, a mathematical solution is completed and may remain the new benchmark until proven wrong – which often happens. That’s the joy of it – constant advancement of knowledge and improvement. I think the Japanese have a name for it – Kaizen.
    Surely my initial questions are within current mathematical knowledge:
    1. When did the outer edge of the Universe reach light speed?
    2. Can we see objects beyond that point? (by visible light or other methods)
    3. Does Hubble’s 42 Law have an upper accelerated speed limit?
    4. Does Einstein’s theory that “if you are going faster than the speed of light, you’re actually going backwards in time” continue to apply exponentially?
    4. If so, will the outer edge of the Universe eventually go so far back in time that it will end up at the Big Bang?
    I know the last question is a bit out there, but the whole concept is fascinating and I’m hoping someone can fill in the gaps.

  19. angel1969 says:

    Howdy y’all. Something tells me if there is something flat out there than there has to be a North and South, pardon that please, up and down. I’ve noticed many things in our own Galaxy spin counter clockwise. This has to be a clue about where it all came from and
    where it’s all goin’. Tie in String Theory and we’ve got a multi layered time-space cake. I don’t know which layer is older, but with a focused beam of gamma, x,micro,radio,etc into a powerful magnetic field spinning c-clo-wise coupled with recording equipment like at the L.H.C. we can see if there is an up and down to our Universe. Let’s talk, and think about it. Peace Out. : l

  20. Robert H Gale says:

    Well,so many questions,and so many answers. I believe at the end of the visable
    universe( appro. 45 billion light years) the known vacuum of “space” continues without end.when we say universe we are saying the material segment here.
    imagine that beyond that realm is the emptiness of “space”.
    Infinity rules, And as Woody Allen stated” Eternity is an awlful long time, Especially
    toward the end!……..

  21. David Medlyn says:

    Hi Robert, Recent science tells us that the empty space that we all thought was just a vacuum of nothingness, may well be filled with dark matter with a mass exceeding the rest of the hard stuff. And with the Giant Hadron Collider we seem to be getting closer to understanding the weird particles that may utilise the dark matter to come in and out of existence. Your mention of the “space” beyond the edge of the expanding Universe is interesting. Maybe it is also full of dark matter, or another matter for that matter.
    In closing, I just thought I would mention that the “edge of the visible Universe” is no longer visible because that edge has long since reached beyond light speed (Hubble’s 42 Law) so the light emitted from the outer edge cannot get back to us because space itself has stretched and its travelling therefore faster than the speed of light from our observation point in the Milky Way Galaxy. Remarkably, in the 13.7 billion years since the Big Bang, the Universe has expanded to around 46 billion light years.
    But I still cannot get anyone to tell me at what point did the outer edge reach light speed?

  22. Michael Knepfle says:

    If traveling faster than the speed of light means traveling backward in time then how would one travel forward in time to the future? With this theory is it possible? Would you have to go so slow in time that it’s already happened?

  23. Wee leg says:

    There is no bounds to space

  24. David Medlyn says:

    Hello Wee leg,
    That is a short but interesting comment. I have often wondered how infinity played a part. I once thought that the formula for the secret of the Universe could be 1 to the power infinity. If, as Lawrence Kraus suggested, a Universe from nothing, then Infinity might play an important role in that.
    Can you please expand on what you think?

  25. Sean Martin says:

    I believe that a edge is at the end of the universe,i dont no what this edge is, or made from.Some kind of barrier, which nothing can pass through.Everything that is rushing towards it,is about to retract and bounce back the way it came.All back to the big bang,all stars,planets,galaxies me and you.And the process starts all over again,everything just gets compressed again and Bang.So i think the universe is somewhat flat.

    P.s I will be looking forward to see what the (JWST)James Webb space telescope can see.

  26. David Medlyn says:

    Interesting that you start with the word “believe”. It is like what religions use. I reckon it matters little what we believe – it’s what is true that is important. However, you raise an interesting possibility of exponential expansion of the Universe resulting in a time warp. Have you got any theories that might support your belief?

  27. Shabeer Haroun says:

    I take it that modern mathematicians, physicists are using Earth as a point of determining the actual time and distance to the furthest part of the universe. Can one determine the current position of planet Earth in relation to the big bang in terms of time and distance travelled. I think the best yardstick to use in calculating the actual size of the universe would be the epicentre of the Big Bang, otherwise there will be no basis of proof using calculative methods. Can anyone identify the epicentre of the Big Bang, should it had been the source of the expanding universe. Just a logical question from a logical thinking person.

  28. Logan C. says:

    After reading all of what is said, the question I have is would it be possible that if there is an edge, did the Big Bang come from it, and would it repeat if that barrier is hit? Also, is that barrier breakable in any way and what would happen if it was to break or get punctured? Is that barrier the mark of the end, or is it where the vacuum of space starts, just beyond the barrier that is the end of the universe? Just something I’ve thought about.

  29. David Medlyn says:

    Maybe there is an edge to the Universe. Maybe there is a barrier. But one thing is true: the only thing we know for sure, is we don’t know everything.
    The more we know about Quantum physics, the more we may learn about the macro physics of the Universe. That’s what is so fantastic about science – we just keep seeking and recording and sharing, and all the time endeavouring to avoid myth and dogma.

  30. shane evans says:

    hi, i’m a 15 year old math enthusiast, i wanted to findout the diameter, vlum,… of the universe, insted i found some serious mind F***! WE NEED TO FIND OUT MORE!

  31. shane evans says:

    can you guys recomend me a book to read?

  32. David Medlyn says:

    So you found a place where the mathematics got a little more difficult – the logic got different, but the search is still the same. Hang in there son. By the time you get to my age, the logic will have got even more unfathomable.

  33. Alan Christ says:

    if you have to clocks set to the same time floating around in space the speed in whitch the distance is traveled is redundent
    becouse the time indecated on both clocks will always match no matter how far or close the clocks are to eachother and no matter how fast or slow you travel between them ,, this can not be disputed , it is correct,,,

    Alan Christ

  34. Jerry says:

    Alan, you are incorrect.
    If one of those clocks is stationary (well, nothing is truly stationary.lol, but you get the idea) and the other accelerates towards the speed of light huge discrepancies will occur.
    Einstein covered that decade’s ago.

  35. Empathy says:

    Why are there rules of physics and not just everything random?

  36. Jim Earnest says:

    Travel to the exact edge of the universe then, one step further.

  37. David Medlyn says:

    Interesting notion Jim. Get to the edge of the Universe and take another step. I guess it demonstrates part of the Infinity theory. It’s all fascinating out there, where quantum physics too plays a part and particles can be in two places at the same time, or at the same place at two different times. I guess it goes to show that the only thing we know for sure, is that we don’t know everything.

  38. Zach says:

    Michael Knepfle,
    we’re always traveling forward in time. Time is also connected to space, however, so if something was to travel through space at an extremely high rate of speed, time for that object would actually slow down. In another sense, you could accurately say that time would speed up the world around him. Therefore, he would be traveling faster through time than the rest of us (and into the future, as you are describing) for the duration of his near light speed travel. He couldn’t go back, though. It’s a one-way trip!

    Also, a question to David and the physicist: I still can’t wrap my head around why/how the universe is 14 billion years old but it is 45 billion lightyears big. That would mean it had to have been expanding at greater than light speed for quite some time, which makes no sense.

  39. EarnieP says:

    Expanding Universe

    I am obviously not a scientist, was not even a very good student. Poor math skills had me avoid math, physics, and chemistry classes like a balloon would (if it could) avoid a cactus patch.
    So please forgive my poor uneducated attempt at explaining my late might musings.

    My thoughts;

    1.) For reference, consider the light from the very first instant of the Big Bang as ‘A’.
    And the current light from the center(?) origin point of the Big Bang as ‘Z’.
    With the rest of the alphabet spread out equal distance between those two ‘end’ points (A-Z).

    2.) So in an expanding Universe the distance between each letter-point is growing larger over time, but each letter-point’s observable light ‘time-moment’ remains the same.

    3.) Say that point ‘M’ is midway from the first moment of Big Bang ‘A’ till the current ‘now’ ‘Z’.
    In such an example it seems it would be impossible for the observable time-point of ‘M’ (or any other point other than ‘A’) to remain the same. As it would not be the same mid time-point for say the six billion year old Universe as in the fourteen billion year old Universe.

    4.) The observable light (time-moment) of the leading edge ‘A’ of the expanding Universe in every direction (everywhere), regardless of how far in distance and time it has traveled, will always be that first instant of the Big Bang.
    ‘A’ was the ‘now’ then, and remains the same ‘now’ forever. In other words, the leading edge of the expanding Universe will always be the first moment of the Big Bang.

    5.)So the Big Bang is not something that happened, it is something that is still happening.

    Is any of this true?

    [Seems like I read somewhere there actually was no light at the instant of the Big Bang, but came along some time later. So maybe ‘A’ would not represent the first instant of the Universe but some time-point later?]

    Please keep your explanations simple enough for a ‘balloon’ to understand (as if they could.) 😉

  40. It is not necessary that the particles are moving at the speed OF LIGHT after THE big bang.The universe may be expanding and moving in speed which is far less than that of light.

  41. David Medlyn says:

    Lawrence Kraus (University of Arizona) mentioned in a recent presentation that Hubble’s Law tells us that some parts of the Universe have already reached light speed. I guess that is the combination of their acceleration away from the “Big Bang” and the so-called expansion of space itself. There is some literature that says in the 14.7 billion years since the BB, the Universe has expanded to over 46 billion light years wide. In which case maybe your leading -edge “A” would now be invisible to us.

    Way down here is Australia, this is the sort of stuff that keeps us awake some nights.

  42. Prateek Ruia says:

    David, I guess, 46 billion light years in not as far as the universe has gone. Its much beyond. 46 billion light years is the particle horizon. Its how far one can see from any point in space.
    The universe is 13.77 billion yrs old. So, light travelled for 13.77 billion years to reach us. But the objects from which light started are at present 46 billion light years away from us, due to the expanding space. So, if we draw a sphere of radius 46 billion light yrs around us, that’s how far we can see.
    But space has expanded at an even faster rate. So, there is matter much beyond 46 billion light years and that is not the extant of space.
    But we will be constantly moving away from the objects beyond 46 billion light years faster than the speed of light.
    In other words, light from objects beyond 46bly will never reach us.
    So our observation limit is 46 billion light years. But we actually really look only 13.77 billion light years back. In this time this matter has moved to 46 billion light yrs from us.
    This is the particle horizon, or the limit of observable universe.
    Now, the most interesting question is, if nothing can exceed the speed of light, then has this expansion of space warped time?
    Also, what happens to the unobservable universe? Does it move back in negative time, relative to the Big Bang?
    Even the observable universe must be moving back in time?
    M not very clear about this. Will certainly want to explore.

  43. Prateek Ruia says:

    We should first understand that we are not viewing the universe, but the ghost of our immediate neighbourhood in the universe.
    I worked out this example, but correct me if I am wrong.
    Suppose all human beings were created all at once, cramped in separate houses in a football field.
    You and all your siblings were created in one particular house. All of you were outside your house, when the field began to inflate. A postcard of your house was sent out to you when you were born. In 13 years, you moved 1300 miles from the exact spot that you were born. This postcard reached you today.
    Meanwhile, because of the inflation, in these 13 years, the location of your house actually moved 4600 miles from you.
    So, you see your house as it was 13 yrs ago, but it has moved 4600 miles by now.
    Similarly, your siblings sent you postcards at different times in these 13 years, but actually, they moved from the places they sent postcards from.
    Your farthest sibling is 4600 miles from you now.
    But, that is only about your house. There were thousands and billions of houses in that football field.
    They are now too far apart from you for their postcard to reach you.
    In essence, you see only the ghost of your small neighbourhood in the universe.
    I hope this makes some sense

  44. David Medlyn says:

    Hello Prateek,
    I think the 46 billion light years is the diameter not the radius. Which is kinda weird if many are telling us that the universe is most probably flat.

    Also, you mention: “In this time this matter has moved to 46 billion light yrs from us”. This may be incorrect unless like many politicians, you believe we are the centre of the Universe.

    The other consideration is that if a proportion of the outer rim has already reached light speed (and beyond if you add the expansion of space) it will already be invisible to us.
    Some other questions:
    1. I wonder at what distance from the Big Bang did the leading edge reach light speed? 2. When will our Solar System in the Milky Way Galaxy reach light speed?
    3. And what will happen when we do?

  45. Prateek Ruia says:

    David, there needs to be a deeper understanding here.
    Please read the following article to understand observable versus entire universe.

    Just imagine you are in the middle of the ocean. Your complete field of vision is your observable universe. That would be a sphere. The horizon where the curvature of the earth doesn’t let you see beyond is the limit of your observable universe. Although the ocean exists far beyond your observable universe.
    Our observable universe is not limited by curvature, but how far light can beat expansion.
    2. The centre only means the point of the observer. The observer’s field of observation is always a sphere in which the observer is at the centre
    3. The diameter of our observable universe is 93 bill light yrs, not 46
    4. Our observable universe is like a drop in a lake. The drop is spherical, but the lake is flat.
    5.There’s no leading edge that’s reached light speed.Actually the interstellar space itself stretches at a rate much greater than speed of light. Just imagine a patterned balloon inflating or rather a rubber sheet stretching. The points on the sheet get separated and move apart, not because they are moving, but the space between them is stretching.
    6. Actually , this stretch only applies to vast empty spaces between galaxy clusters . governed by Einstein’s general relativity.
    Wherever, there is mass and energy, like local groups, galaxy clusters, wherever gravitational forces are at play, this interstellar expansion force is too tiny to overcome gravity.
    But wherever there is void / vast empty space, this expansive force is there like a cosmological constant, stretching empty space like a rubber band.
    7. Our solar system will never reach light speed, coz it is gravitationally bound to the galaxy and many galaxies in our local group are also bound together by gravity. So, milky way and local group won’t fall apart.
    Please verify all information provided for accuracy.


  47. Prateek Ruia says:

    Dr. Ghatak,

    You are imagining a static universe.
    Fortunately, or unfortunately, our universe gets much more interesting than that.

    The universe is expanding.
    It means, the empty space between galaxies is expanding.
    Like a rubber sheet being stretched.

    Think of expansion of space as multiplying factors for distances, instead of fixed velocities.
    On the other hand, light has been moving at a fixed velocity of 300,000 Km/sec or 1 Light-year/year.

    So lets say, your star was initially at S
    and the earth, as it should have been, was at E

    Now, because of expanding space, S came to S’ and E came to E’

    Light, L started from S at time 0, ie. t = 0
    At t = 13.7 bly, L reached E’

    Space is expanding between L and S’
    and space is expanding between L and E’
    But since L is moving towards E’, this distance gradually narrows.

    I have back calculated and found that if we consider,

    S and E to be 6.427 billion light years away initially
    Expansion of Space at a constant rate of 1.1545 times in 1 billion light year,

    then, after 13.7 billion years (by)

    S’ and E’ shall be 46 bly away.
    while L would have reached E’

    So, now, from the viewpoint of the observer at E initially, (at t=0)
    all points within 6.427 bly initially will be at a maximum distance of 46 bly today (at t=13.7 by)
    However, E itself would have moved to a position, E’ relative to its initial position, E.

    So, you can draw an imaginary sphere around E’ with a Radius of 46 bly.
    That will be your observable universe for the particular observer at E’

    Now, what happens to the universe and the points outside this boundary of 6.427 bly from E ?
    Suppose, at t=0, there was a star 8 bly away from E,
    At t = 13.7 by, the light from that star will not reach E’
    simply because light from that star, S is not able to catch up with the rate of expansion between S and E

    So, a major part of the universe remains out of bounds for the observer at E’

    In fact, Hubble calculates that the entire universe must be 10^23 times the observable universe.

    If you need the calculations for the above example, please send me your email id, i will send you the excel sheet.

    However, please note that the actual equations governing the expansion rate of space is much more complex and involves a differential equation.
    My calculations are just a simplified model, more intended to prove to myself how space can expand at a very nominal rate and still light cannot catch up.

Leave a Reply

Your email address will not be published. Required fields are marked *