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    Beam Me The Farthest, Scotty!
    By Johannes Koelman | December 26th 2012 08:54 AM | 23 comments | Print | E-mail | Track Comments
    About Johannes

    I am a Dutchman, currently living in India. Following a PhD in theoretical physics (spin-polarized quantum systems*) I entered a Global Fortune

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    What is the farthest we can theoretically go? Would we ever be able to visit the galaxies shown in Hubble's Extreme Deep Field? Could we even travel beyond these and reach the edge of the observable universe?

    Suppose you are a googolionaire and money is of no issue. Suppose also that technology has evolved dramatically and that money will buy you the latest rocket technology capable of cruising close to the speed of light. Thanks to relativistic time dilation, for every year you age you would travel much farther than a light year. If you accelerate your rocket to higher and higher energies and speeds closer and closer to the speed of light, this dilation effect increases and the distance traversed between your birthdays would increase without limit.


    Nope, can't go there...


    But why so clumsy? Why not take maximum advantage of time dilation and travel at exactly the speed of light? You would travel over many light years while your time would be standing still. So you better invest your capital in a transporter. A transporter that converts you into an energy pattern and beams this pattern to a target where you are reconverted into matter. If all of this would be available and reliable technology, would you be able to visit the most distant galaxies?

    The answer is a clear "no". There is a limit to how far you can see into the past universe, which defines the observable universe, but there is also a limit to how far light can travel into the future universe. We could call this the reachable universe. And the disappointing news is that the reachable universe is much smaller than the observable universe. Virtually all the galaxies shown in the Hubble Extreme Deep Field, although observable to us, are not reachable by us.

    The fact that the reachable universe is much smaller than the observable universe is a direct consequence of the accelerated expansion of the universe.

    We know since Edwin Hubble's 1929 galaxy redshift observations that our universe is expanding. And since the end of the last century, we know that
    this expansion is accelerating. It is the acceleration that makes all the difference. It puts fundamental limits to where you can travel, no matter how far you travel.

    Sounds enigmatic? Time for an analogy that clarifies the fundamental impact of acceleration on the performance of transporters.


    On ants, worms, and chess boards


    Imagine an ant walking along an incredibly long worm. While the ant is walking, the worm grows. Let's assume the worm grows linearly. This means that the speed at which the distance between its head and its tail grows is in constant proportion to the speed at which the ant walks. Now suppose the worm is so long that its growth outruns the walking ant by a factor hundred. So for every centimeter the ant walks, the worm grows by a meter. Under these circumstances, will the ant be capable of walking from the tail of the worm to its head?

    The
    surprising answer is "yes". This can be understood using a simple animation. The linear growth of the worm can be realized by cell division happening at a fixed number of discrete positions along the length of the worm. You need a gigantic number of such 'division sites' for the worm to grow a hundred times faster than the ant can walk, but the key point to note is that the number of growth sites is finite and constant. The animation shows ants (orange dots) passing one such division site. And if ants can pass one such site, they can pass arbitrarily many.



    Now this would be a nice analogy for photons traveling in an expanding universe, were it not that the universe is not expanding linearly. Rather, the universe is undergoing an accelerated expansion. And that makes all the difference.

    Back to the ant and the worm. Suppose the growth of the worm undergoes an acceleration. Such an accelerated growth can be realized by allowing not for a fixed number of division sites, but to have division sites at given length intervals. This means that if the worm doubles in length, so does the number of division sites. Below animation shows an ant walking along a worm undergoing accelerated growth. The ant walks large distances but never reaches the position on the worm represented by the stationary green segment.



    The key point to make here is that although the ant is perfectly capable of passing any division site, each time it does so additional division sites pop up in between the ant and the distant position it tries to reach.

    Now this accelerating worm growth provides a suitable analogy to our expanding universe. Replace the ants by photons and the growing worm by expanding space, and you immediately recognize photons send out into space can not reach every position in the universe.

    If you do the math, you will find that although we can see galaxies that are currently up to 46 billion light years away from us, the furthest we can ever travel is to galaxies that are currently less than 16 billion light years away from us. Even a powerful light pulse that we would send out right now would not be able to reach galaxies currently further than 16 billion light years away. Our reachable universe is much smaller than our observable universe.

    Although a universe undergoing accelerated expansion will never come to an end, in a certain way we are already 'more than halfway thru'. Again, an analogy is in order.

    Imagine a a game of chess played on a board composed of infini-stretch rubber, a magical material that stretches without limit. The board is pulled at its edges so that the whole board undergoes an accelerated expansion. The pieces move over the board at constant speed, and each next move will therefore take more time then the one before. Time will never come to a halt, and the game will continue forever. Yet, depending on the nature of the acceleration, the number of moves remaining may be finite.

    In the universe we live in, we have entered the end game. The number of moves remaining is limited. All because of the accelerated expansion. An acceleration we were unaware of less than twenty years ago.

    Comments

    Johannes Koelman
    Ok, I predict at least one question about wormholes and/or tachyonic warp drives...
    blue-green

    The linear example of the ant exploring a uniformly elongating worm is very counter-intuitive to me. The animation doesn't help much. Later, I'll try to make it through the analytic descriptions in Wiki, that is, if other chores don't keep piling up at an accelerated rate. Perhaps there is a hopeful analogy concerning deficit spending, as in my country (or client) will eventually pay off what it owes so long as s/he doesn't exasperate the challenge by creating more debt at an accelerated rate. Of course the payback period may be astronomically long … but hey, with the new cosmology, the lifespan of the universe is theoretically unlimited as is its potential size.

    Instead of saying, “its growth outruns the walking ant” it would perhaps be more honest to say “its INITIAL growth RATE outruns the walking ant.”

    If I can clean one window in one minute and the total number of windows to clean increases by another two windows every minute, how can I ever be expected to clean all of the windows?

    Johannes Koelman
    The linear growth model is indeed counter-intuitive. You make the remark:
    Instead of saying, “its growth outruns the walking ant” it would perhaps be more honest to say“its INITIAL growth RATE outruns the walking ant.”

    That seems incorrect. At any moment in time the worm's length increases 100 times faster than the ant can walk.

    If I can clean one window in one minute and the total number of windows to clean increases by another two windows every minute, how can I ever be expected to clean all of the windows?
    It is not "the total number of windows to clean" that increases by two a minute, rather it is the "the total number of windows". The growth is both in windows to clean as well as in windows already cleaned. That helps enormously...

    1. If the worm and the ant are part of the same local environment (and not in parallel universes..), it stands to reason that they both grow in size at the same (accelerated) rate. It is unreasonable to assume that growth only occurs to the worm and not to the ant. The rate of growth may however be variable at different locations. in which case both worm and ant still grow at the local rate assuming that the size of the worm does not span more than one growth location.
    2. Using your analogy of the total number of windows to clean in relation to the number of windows already cleaned growing at the same rate, it also stands to reason that the distance travelled by the ant increases at the same rate as the rate of growth of the worm at the location of the worm.
    3. Assuming that growth occurs not only forward, but in all directions, the ant (if not moving at all in relation to its location on the worm) will find itself at proportionate distances from head and tail(?) at all times, and therefore moves at the same speed as its host. Any forward speed travelled by the ant towards the head under accelerating conditions is proportionate to the speed under not accelerating conditions. So the total progress of the ant is also relative to the speed of the growth plus actual forward speed of the ant.
    4. Therefore, the ant will make progress towards the head of the worm, given enough time.
    4. No need to take this further from the perspective of the observer.

    My take as a lawyer....

    How about warp technology using the Alcubierre Drive. NASA is actually working on it. See http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20110015936_2011016... - it at least has some promise. If, and that's certainly a big if, it could be achieved then the ability to contract and expand space around an object would allow "speeds" far in excess of C

    Hank
    What promise? They can't even figure out the math - and the math is the easy part. Talking about a bunch of theoretical math is not really 'working on it'.
    The Alcubierre Metric is only the consequence of a hypothetical set of conditions. In other words, given those conditions, then you're off to Tau Ceti for lunch. What most people don't appreciate is that the givens, the hypothetical conditions, aren't known to be physically real, and it's not very clear that they can be arranged to be real by some clever contrivance.

    Arnab R
    Must Admit that Even if NASA or for that matter other Foundations like ESA resolves WARP Drives in a Mathematical sense..it's not Possible to contrivance that in Practice..
    I am not being a skeptic here with a more than a harsh comment as You may mark it to be..but the fact is that it's an issue in which we don't have much room for improvement..it's written in the fundamental laws..

    I Guess a bit of Analogy will do here..

    Can You ever store a bit of Anti-Matter in a tray composed of our regular matter ??..At this moment..it's a clear NO..and can we improve someday in this context, so that we are able to store some Anti-matter in reality ??..I Guess, very few us will answer in the affirmative..
    Johannes Koelman
    Nonsense knows no limits. And NASA isn't immune to that.

    Long story short: Alcubierre drives represent a cute science fiction concept, and nothing more than that. But even if we would assume it is possible to build contraptions capable of contracting and expanding the space around it, such devices would be subject to the same limitation of not being able to travel to galaxies further than 16 billion light years away. Simple reason being that perturbations in metric propagate at the speed of light.

    In terms of the ant-worm analogy: if the ant starts eating the worm (rather than walking over it) it would not make this ant any more capable of reaching the head of an exponentially growing worm.
    Arnab R
    He he..

    True that..Nonsense knows no Limit !!! However stuffs like Alcubierre Drives and all are always appreciated as a mean of a bit of intellectual exercise..Just like the notion of Gravity Trains..
    The article is based on the idea: worms stretch or not ?
    I think it is not an interesting point, because if a "worm" is a "superconductor" it will not change the final effect for the information it is running on it ....

    This article is , somehow, a "part two " of the other one : Splitting black holes- Take 2 .
    Superconducting black holes is a new concept full of promises , for example it can explain the " entanglement" mechanism.....

    A superconducting neuron is short-circuiting your brain.

    Yes, Mr. Anonyrat , maybe.... But I had this idea, after this : http://arxiv.org/pdf/1203.0533v2.pdf .
    My entire brain melted and...Thank you , for opposites my point !! It is a goood sign !!
    PS : How many neurons in a single worms ?

    Michael Martinez
    13 billion years ago a galaxy emitted a beam of light that has just struck the Earth.  In that 13 billion years both the Milky Way and that other galaxy have moved in opposite directions.
    How long will light from the older galaxy be able to reach Earth in such a scenario?  At what point does the acceleration of movement away from each other make two objects essentially invisible to each other?

    Would it not be when the combined speed of both moving objects exceeds the speed of light?  That is, galaxy X moves at .5 light speed and galaxy Y moves at .5+alpha light speed.

    Do we really expect the galaxies to achieve such speeds, or am I being too simplistic?
    Johannes Koelman
    Michael -- most (if not all) of your questions are answered in this article.
    Quentin Rowe
    Why not go further than the observable universe - this is much easier!In fact, we do this constantly by the mere fact of existing. 
    Of course, this notion rests heavily on a Level 1 multiverse being physically real.
    The concept is simple, that eventually if you go far enough, you will eventually
    reach an exact copy of you and your immediate environment.
    There being an infinite number of exact copies is of no use however.
    It is the near exact copies that matter more. These you experience everytime
    ypu make a decision or experience change, which is of course at every single moment
    The challenge therefore would be how to tap into this very real property of a Level 1 multiverse..
    Johannes Koelman
    It took me a while to understand what you mean (I think I do now). your 'exact copy' can only be an exact copy if he has the same experiences and the same memories as you. that means he must live in an observable universe exactly equal to yours. 'Swapping identity' (whatever that means) with that exact copy of yours, would therefore not get you anywhere really. (I am sure there will be lots of people who would disagree with me on this.)

    And the 'near exact' copies? Even these would still not get you to the XDF galaxies (nor to their 'near-exact copies')...
    Quentin Rowe
    There is no identity swapping - you are already there, by definition.This is a property of a level 1 multiverse.

    To clarify your understanding of what relevance near exact copies have, you just need to understand that change is required for an event to occur, so exact duplicates are essentially all one thing.

    Let me re-emphasise: this 'transporting' beyond the visible horizon is a natural&fundamental property of a Level 1 multiverse. This is very relevant to your post, and could do with more discussion before being brushed aside.
    Johannes Koelman
    What I mean is that the "no-go" statement discussed in the above blog post trumps the "level 1 multiverse possibilities" that you highlight.

    Each of your (exact or near-exact) copies in the level 1 multiverse can peek at billions of galaxies up to tens of billions of light years away. All these galaxies are copies of galaxies that you can see. Most of these galaxies are out of your reach, and this holds even if you could teleport yourself. But each copy of you lives in a universe with laws of physics that are a copy of your laws of physics. That means that none of your copies can reach the (copies of the) distant galaxies that are out of your reach.
    I've read the article you suggested but I can't understand a thing or two, so to speak: the article state that the Hubble distance (is not constant ok) is about 14 billion light-years right now, beyond that distance galaxies recede from us with superluminal speed.
    The age of the universe is 13.7 billion years so I'm guessing this is exactly the same estimate (given a photon travelling at a constant speed of light leaving the big bang in our direction would take roughly 14 billion years). Is this just a coincidence?? It seems too strange to me.
    Furthermore, the article says that we can currently see objects 46 billion light-years farther because, in the mean time, the universe has expanded during the voyage of that photon. What?!? Given that when we see an object far away (light years) we are seeing it as it was in the past (years), how is this possible?? We now see objects older than the universe itself? I don't understand this, really. The current estimate of the age of the universe doesn't take into account the expansion rate? Or is it the space that has stretched so much that is like the photon has travel faster than the speed of light in our direction?
    Could you enlighten me please?

    Johannes Koelman
    The fact that the age of the universe and the Hubble constant are almost equal is indeed considered a coincidence. Also, we do not see objects older than the universe, it is just that the expansion of space has in the meantime brought them further away from us.

    The model to keep in mind is that of the above exponentially expanding worm. Light rays are represented by the ants walking along the worm. However, the exponential growth rate for the worm varies with time, and that makes things messy. But even for the uniformly exponentially growing worm, light rays (ants) that reach you after a certain travel time come from parts of the worm much further than the distance travelled by the ant.
    MikeCrow
    beyond that distance galaxies recede from us with superluminal speed.

    I don't believe there's any evidence of superluminal expansion of the Universe after  re-ionization, and any evidence before then is Theoretical. The CMB defines the "Photon" edge of what we'll ever be able to see.
    Never is a long time.
    What is the difference between the future horizon and the horizon in a Rindler space?

    (Btw, I can only post using TorBrowser. Using Firefox or Safari on a Mac results in "Service not available". Anyone knows a solution)