Possibly dumb question, but I know my niece is going to ask me about this, and I'd like to be able to give her a solid response: does this mean that most distances within our universe are illusory? If not, why not?
To expand on that thought a little bit, with a hologram, the projected object is an illusion, and can be made to appear to move at arbitrary speed by e.g. rotating the projection apparatus. On a larger scale, it's possible to create the illusion of FTL movement by e.g. rapidly rotating a laser projector in space and then traveling a long distance from it, so that at a certain distance from the source, it appears that there is a projection from the source which is rotating faster than light.
If this theory models the universe as a 3D (or more) projection from a 2D surface, why is it not possible to cause objects within our perceived 3D+ universe to appear to move faster than light by causing some sort of change to the 2D surface itself? I assume there is a reason this is not possible within the bounds of this theory, but I have no idea what that reason might be.
Yes, but it's not the case that everything is equidistant. Allow me to illustrate with a simplified example from lower dimensions.
(Warning: pseudoscientific bullshit ahead)
Picture a transparent sphere, covered in tiny dots. Imagine that you live on one of these dots and the others are stars. Now, mark 'your' dot and look around on the sphere to find the dot that is farthest away, on the opposite side. If the internal radius of this sphere is 1 unit, then the distance to that dot (traveling on the surface of the sphere) is pi units. Imagine yourself in Edwin abbott's Flatland, but thanks to relativity you know this flat universe to be finite and bounded, such that if you set out in any direction in a straight line you will eventually arrive back at your starting point.
Now, let's designate that point opposite you on the sphere as the Maximally Distant Star. There's no doubt, no matter what route you take along the surface of the sphere, this is as far as you can go before you begin coming back, if that makes sense. But suppose you were able to transit across the interior of the sphere instead of across the surface. It's still the farther point from you, but by transiting by volume instead of on the surface the distance is only 2 units, or 63% as far as it appears to the surface-dwellers.
Of course, this realization is of little help in figuring out how you as a Flatlander can access that theoretical 'volume' so as to shorten your transition time. If you could, you'd seem to disappear at your existing location (most likely by shrinking down to a point, or possibly seeming to turn inside out, or both) and then reappear at your destination, assuming you hadn't been eaten by the great old ones said to inhabit that forbidden space by famous horror author J. Q. Likecraft.
This makes sense, but seems to be an answer to a different question about the curvature of spacetime. How does it relate to the universe being a hologram?
It doesnt. The hologram is a metaphore. Once upon a time our 3/4 dimension world was encoded upon a world with fewer dimensions LIKE a 2d hologram contains the info of a 3d image.
This world didnt last very long. Under our concept of time it happened long ago, but we can see evidence of it smeared across the sky in the cosmic microwave background. (A 2d image that should look the same no matter where you stand in our 3d space.)
Only indirectly (I did warn you I was gonna bullshit a bit). One obvious way would be in a spherical projection onto a flat surface, but that makes it harder to explain the basis of the curvature first.
I apologize for being so vague; I'm trying to develop something more solid related to this idea, but I'm at that in-between stage of not being ready to properly articulate it yet.
Distances are "illusory" to some extent anyway. On a large scale, relativity makes both time and space dependent somewhat on other factors. On a small scale, quantum mechanics similarly de-absolutizes position (space) and momentum.
Space and time as absolutes appear to be a construct, a consequence of us being highly complex neural networks trained at a specific scale of the Universe - the "human scale" - as beings about 1 ... 2 meters in size. Absolute time and absolute space appear to be very real on this scale. But as soon as you leave this order of magnitude, and climb either up or down on the scale of things, this turns out to be mere provinciality.
Up or down several dozen orders of magnitude. Time and space exist for the cells in our bodies, and for mountains, moons and most stars. Time and space only break down substantially for things smaller than molicules or large enough to twist spacetime back in itself (black holes). A mouse is no further away from the moon than a dog or elephant.
Time exists for the mountain. The mountain moves through time and is effected by time. The mountain is incapable of perceiving time. Neither can bacteria perceive dimensions, but they are still controlled by them.
A mountain is a part of spacetime. But it does not "exist" for the mountain.
Certainly the mountain is affected by the environment and can be modelled with the spacetime concepts. But the mountain does not perceive anything, and therefore cannot compute isExist (spacetime)
I'm willing to call bullshit on this. Space and time may be constructs but they are "helpful" constructs in that they model specific forces which apply to both us and the mountain. I perceive the waste of this body over time: the mountain is subject to these same wastes and transformations as this body.
I don't think so. The holographic universe a "projection" in the sense that the information can be thought of as living on the boundary of a given space, with the maximum entropy / information contained therein proportional to the boundary's surface area (on a quantum level, a bit is a measurement of area). But this isn't super shocking if you're aware of the idea of "light bubbles" (the generalisation to three dimensions of a light cone) which already describe the limits of how information in a region of space can propagate.
Distance was already an illusion, insofar as it represents a non-unique projection of a spacetime using purely relativistic techniques. :) But the speed of light isn't going to be got around by any of these models. If anything, the models will explain this limit better.
POSTSCRIPT:
I recommend the Hammock Physicist as a random physicist who can explain concepts like this at just the right level of detail for the HN audience. http://www.science20.com/hammock_physicist
I wouldn't think being "right wing" would be sufficient to explain using the phrase "jewish elite".
Like, can we not treat "the people who say things like 'jewish elite' " and "people who are right wing" as being the same group?
I mean, I'm not saying they don't have an overlap
( It is probably true that P(a person is right wing | they say stuff about "the jewish elite") > P(the person is right wing) ),
but I'm concerned about the social incentives that might be created/contributed-to if they are treated as if they are the same.
... It's clearly a collaborative site with hundreds of authors, at least two of whom are right-wing authors, who have presumably got to the top being controversial and attracting attention from outside the normally quiescent community of readers talking about entropic gravity, thus convincing the algorithms their content is worth showcasing.
HERETICS, THE LOT OF THEM! BURN THE DATA CENTER WITH FIRE!!!
Perhaps a bit of a tangent, but another way I have always perceived relative distances measurements is with the following analogy:
You are awake, walking around a basketball gymnasium, it's 100x100x100ft. A nice, large room. All other details preserved as well. Surely, our little brains can't contain a 100x100x100ft gymnasium; our little heads would explode trying to fit something so large into it. Yet, when we dream, we are perfectly capable of revisiting this large room in our mind, full spatial properties preserved.
While there are many encoding strategies, looking at how the brain encodes information (or a more simplistic neural network), this gives, in my opinion, a good intuition as to how distance and spatial properties can both differ and relate between two "universes".
You can also observe that our final "view" of the gymnasium is just the surface of the complex underlying thought-structure of the brain. We very much, on a daily basis, only see the surface of what is a very very complex process going on inside the brain.
There is just so much more to discuss on this subject, including the intricacies of how all events are stored in the brain with cross-connections/relations to other events. Basically, every memory-dimension (time, temperature, happiness, anger, feelings) are all stored in nice gradients with connections to other memories. i.e. The only thing making you think that some past event, yields to some "next" event, is a series of synaptic connections, saying it does. I think the deeper you dig, the more you see how things breakdown from this simple linear view of events happening in your day-to-day life. I'll end here for now at risk of being vague unless asked for further clarity. :)
This reminds me of Kurzweil's explanation of dreaming, as offered in "How to create a mind" book. He claims that during dreaming we experience random, uncoordinated activation of synaptic links and some small portion is recorded in memories. It is only when we recall our dreams that we infuse meaning into them, building a structured and sequential narrative around random stimulus so that our mind can make sense of these memories.
This is falsified by people who have had interactions with waking people while asleep, conducting conversations and interactions, even if nonsensical. So there is online processing during dreams, not just a "ghost" memory left behind afterwards.
My opinion is "no", because causality still exists on a 2D surface. The speed of causality will limit information from entangling with other information faster than a given rate in an offset of X or Y - if there was no limit, there'd be an infinite amount of calculations occurring on the surface in an infinitely short amount of time. You can sorta imagine it as the cells in an area of Life must be "recalculated" to fill in when you left or arrived. That certainly might translates into a different type of causality here, as it does seem that this reality is pretty intent on limiting the ability to change things here instantly.
Which reminds me of Feynman's theory that there was only one Electron and it was everywhere in the universe all at once over an infinitely long period of time, and could even travel in time if it had to.
> If this theory models the universe as a 3D (or more) projection from a 2D surface
Further, would such a projection suggest a possible mechanism for entangled particles to interact at distance (e.g. the particles are separated in 3D-space, but are co-located in 2D-space)?
> [...] why is it not possible to cause objects within our perceived
The universe is currently not in the holographic phase. That is thought-provoking, though. Let's assume that this is plausible. During the holographic phase, the speed limit wouldn't apply. There are a few interesting theories that require FTL during the big bang.
What I find interesting is that the universe went through two very distinct phases and we have two distinct physical theories.
Calling it "holographic" was probably a bad idea because it generally makes people think about Star Trek. You're not quite as far off when you think about lasers shining through a photograph of an interference pattern in order to reproduce a light field that a human observer will perceive as a 3D object.
If you look a that photograph in normal light it just looks like a lot of black and white lines and blotches smeared out over the surface instead of the original object that was photographed. In a holographic model of the laws of physics, the entire content of the universe is encoded somehow onto a 2D surface. If you could somehow see that surface, it would not be obvious that it encoded anything in particular. Where the analogy falls down is that there is no laser that projects a 3D image from this surface. There's just a set of 2D laws operating on the 2D information. To anyone on the "inside", as it were, the universe still appears to be fully 3D with 3D laws of physics.
IANAPhysicist, but I think T-duality in String Theory [1] also makes distances "illusory".
"If string theory is a correct theory of Nature, then this implies that on some deep level, the separation between large vs. small distance scales in physics is not a fixed separation but a fluid one, dependent upon the type of probe we use to measure distance, and how we count the states of the probe." [2]
Brian Greene also explains why in an accessible way in the Chapter 10 of The Elegant Universe [3], which I recommend.
Can anyone illuminate what relationship, if any, this has to anti-deSitter space? Both seem to deal with lower-to-higher 'projections' of spacetime but I've struggled to find a good intro to AdS.
To expand on that thought a little bit, with a hologram, the projected object is an illusion, and can be made to appear to move at arbitrary speed by e.g. rotating the projection apparatus. On a larger scale, it's possible to create the illusion of FTL movement by e.g. rapidly rotating a laser projector in space and then traveling a long distance from it, so that at a certain distance from the source, it appears that there is a projection from the source which is rotating faster than light.
If this theory models the universe as a 3D (or more) projection from a 2D surface, why is it not possible to cause objects within our perceived 3D+ universe to appear to move faster than light by causing some sort of change to the 2D surface itself? I assume there is a reason this is not possible within the bounds of this theory, but I have no idea what that reason might be.