Is space "real"? Anssi asked a very good question about "space" which you all need to think about. Now that is a question with one and only one answer! I am curious as to what responses it might produce on this forum. Personally, I loved it. -- Dick
That wasn't the question Russ. There was no mention of "a universal reference frame"; there was only one reference frame of any interest at all, the ship's. The question is a bit more subtle than that. Have fun -- Dick
Einstein thought that space is not a neutral backdrop, but has properties that can be conditioned by the matter embedded in it, and that these properties can have measurable gravitational effects on matter and upon the EM radiation propagating though it. This is probably approximated best in contemporary thought by the LQG folks, who modeling space as if it has a fine-scale structure that might be probed by its interaction with the EM propagating through it. (Google on "Fotini Markopoulou" and GLAST for details.
Using an on-board inertial nav system, the spaceship could return to the approximate location. Since all measurements are approximations, no matter how accurate the inertial nav system, the EXACT location could never be relocated or verified. This is probably not the 'one and only answer' that you have in mind, but you did invite responses, right?
No: Nothing at all about a ship in the main question and the example with the ship is only trying to use the ship to find a location in space. That is what a universal reference frame is. The reference frame of a ship is always the same and always stationary and doesn't say anything at all about the nature of the universe. We've had people ask the question before; could I leave a buoy of some sort as a marker, stationary in space, and come back to it later? Sure - but you can't call it stationary wrt space, just wrt itself.
But wouldn't the accelerometers of the inertial nav system need some refference for the sensing of acceleration ? Can an acceleration be performed relative to nothing ?
Accelerometers can bring you back to a location that is stationary wrt the ship's origional stationary-wrt-itself position and that's it. Just like my buoy.
And accelerometers work pretty well without two masses that are accelerated rellative to each other ?
I suggest that space is just a relationship between entities. It is meaningless without at least two entities (or two points) that can then be distinguished from each other by the fact that a distance exists between them. If you remove one of these points then space has no meaning. Since the concept requires more than a single point then it must represent a relationship.
Hehe, "interesting thread" :) Yup. Keyword "concept". "Space" is one of the concepts we use to comprehend reality around us. I think the "subtle issue" Doctordick is referring to is about do we go about assuming the ontological reality of things (of space in this case). And like you say, the concept of space is meaningless without distances between some things we have defined as things that exist (however we understand "distance"). And like Russ is saying, the idea of "locations" is meaningless unless we relate them to the locations of some "things" (that we have also defined. I'm sure this question has been asked many times before by people wanting to know how space is defined in relativity, but this time it was actually mentioned in slightly different context. It came up during a discussion in an AI forum, about the relationship between our mental models of reality, and the ontological nature of that reality itself. I think I said all I needed to say there, so; http://tech.groups.yahoo.com/group/ai-philosophy/message/12228 Now I would curious as to what responses the whole post might produce on this forum. :) -Anssi
There is no space, it's turtles all the way down. Seriously though, even in general relativity space is an entity. If you want to remove space from the equation you need a completely relational theory (GR is not a completely relational theory). So far no one has been able to publish a realistic theory of gravitation and EM forces in a purely relational fashion. So perhaps space does exist. On the other hand, today it's bon ton to be a LQG researcher, and that's not relational either. Perhaps purely relational theories are meant for looners in shacks, who will tell?
When we talk about the ontological nature of something, can this not be regarded as forming a mental model? The notion/idea/concept of what reality "really is" must still be a mental construct/model. The contemplation of reality via any mental process must surely lead to a limited comprehension of that reality (a reality which must surely include all mental processes and much more besides). Space is a word. The word signifies a shared comprehension concerning reality (another word which seems to signify something about one's ability to comprehend). Because a comprehension is shared doesn't make it valid (or invalid). If everyone agrees that 'space is real' then it is real. This does not necessarily reflect any actuality.
May I suggest the following : http://www.ilovephilosophy.com/phpbb/viewtopic.php?t=153992 I also suggest meditating about this aspect of the question: Size has always been viewed physically but with the advent of computers and digital information the real size of things should be seen as combinational. Why complicate something very simple ? There is no time or space or anything, just COMBINATIONS. A very simple example: say that the universe is made of only one number (0 to 9) and there are only three time intervals in the whole lifetime of this universe. How large is it really ? Well 10*10*10 are all the possible combinations, that is the possible sequences of this one number times the 3 time intervals. Now just extrapolate this to any large number of particles, having any large number of states times any large number of time intervals for any universe. It would be something like Z to the X times Y, where X is the number of possible states and Y is the number of time intervals. Z is the number of particle states and/or number of particles. Z^X*Y. This is a universe, with all time and space included. Obviously an insanely huge number, but mathematically and conceptually very simple. Even more interesting is the space to time converter or viceversa. Conside that all the combinations Z^X*Y can be equivalent to 2^N so instead of having many particles and states you can have a universe with only one bit of information that can follow a sequence of combinations that contain all the possible combinations of a universe, like a DVD is a stream of bits that design a 2 hour movie. In this case it is a universe with ONE bit having many (huge number!) of time intervals (N). Or you can convert it to a universe having a given huge number of BITS but that is still because it contains all the possible combinations. So in this case it is a universe with a huge number of bits (or particles if you like) but with only one time interval, hence no time. 2^N=M so a one bit universe with a number of time intervals (N) is equivalent to a universe with a number of bits (M) but only one time interval, hence no time (a frozen universe of combinations). Time can be converted into space and vice versa because they are both arbitrary concepts, only information and combinations exist. So lets take this up to another level. Just how big is our universe then ? Lets consider something like 10^1000 particles and call that N. Each particle can be in maybe 10^100 different states and call that S. So S^N are all the possible combinations of all these particles through all their states and call that C. Now lets throw in time, and say that there are maybe 10^1000 time intervals and call that T. So that would be C^T all possible combinations of all particles for all of time. Of course our real universe is only a very small subset of this, but it maybe really isn't as big as we think. S=10^100 no. of different states for each particle; N=10^1000 no. of particles; C=S^N no. of all possible combinations of states and particles; T is the number of time intervals, 10^1000; SIZE of UNIVERSE=C^T SIZE=((10^100)^(10^1000))^(10^1000) This number can be converted to 2^X where X is probably really big. So the universe is just a simple number, 2^X. The universe is not infinite in size but limited by the time intervals, 10^1000, and particles which are really simply numbers or bits 10^1000, and states of these items maybe 10^100. These numbers are large excess approximations, real elementary particles are probably only a few hundred or thousand, time probably can't go down to less than 10 to the minus 200 seconds, etc. This is just an extrapolation of a universe as a series of bits just as a DVD contains 40 billion bits and can produce a 2 hour movie. This is the informational content, or measurements of the entire universe, or state space it can occupy. We are a small subset of bits of this number. The laws of physics are just a series of strong filters allowing mostly only the major combinations, but quantum physics kind of tells us that all the combinations are possible and do indeed exist. The problem is what external space are these bits or particles or numbers occupying ? They must be floating in some other material, or item. It is this item that can create experiences, consciousness, reality and matter as parts of these combinations of bits are grouped as people and life and experiences. Very odd, but makes some sense....
Combinations of what? Combination of numbers, or bits, or any item - entity that can be distinguished from another. A pure number - item in an abstract mental space. A pure measurement.... everything we perceive is a sequence of measurements, numbers and comparisons between said measurements. At least according to the scientific - physics decoding of the world (and also a language with symbols mapping onto the comparisons ?)
2^N=M so a one bit universe with a number of time intervals (N) is equivalent to a universe with a number of bits (M) but only one time interval, hence no time (a frozen universe of combinations). Time can be converted into space and vice versa because they are both arbitrary concepts, only information and combinations exist. I am not getting into the language - semantics complications of it all, but just trying to show that it seems that if we just view the universe as information - mathematics the entire deal is just a combination of numbers that can eventually be mapped onto any kind of decoding and encoding of this information into any kinds of categories desired; the combinations, group of bits, can be broken up or merged in any way possible.
The laws of physics seem to be simply the combinations that have the highest probability of being repeated. I think this view could be a better view of the many worlds theory of quantum physics since in a pure combinational view all the combinations exist, only that we find ourselves within a given combination. Odd but somehow related to the many worlds - infinite parallel universe theories ..... But then again if all the combinations exist, we simply find ourselves in a quirk combination that seems to follow very strict laws, but these laws don't really exist they are just a design or pattern or painting superimposed on a subset of the combination of bits.
Interesting approach. However if you want to approach it from that perspective you have to take quantum mechanics into account. In QM you cannot simply add up the individual states of particles, they combine in QM! So the number is actually very much higher than you reason here. You might be interested in reading "The End of Time" by Julian Barbour.