Non-Contiguous Space-time

[maeklos]

I was wondering if anyone could shed light on the non-contiguous properties of space-time? Named, how either space or time must have holes in it.<br /><br />As in, if space were contiguous, as in, being made up on a smooth fabric, then movement would be impossible. Why? Well, as we all learn in basic math, between any two points chosen arbitrarily on a line lie an infinite number of pre-existing points. Since, if space (reality, space-time, whatever) were contiguous, an infinite number of points between a beginning and a destination would contain an infinite number of other points. And each point would take an amount of time, no matter how small, to pass. Since there's an infinite number of points, no matter how quickly you skipped across them, it would still take an infinimate amount of time to get from Point A to Point B.<br /><br />This means that either a) space is non-contiguous and has "holes" or "ripples" in it; or b) that time moves in stilted jerks.<br /><br />Any thoughts on this? <div class="Discussion_UserSignature"> </div>

 

[Mee_n_Mac]

I have but 2 things to say. First in going from A to B I don't bother stepping on every point. Those I do step on are finite in number and have a finite distance between them. Thus I get from A to B in less than infinite time. Second I predict that someone else will point out how the concept of infinity can be misused in the physical world and so Zeno's dichotomy paradox ... isn't.<br /> <br />Hint: Each of your infinite points has a 1/infinity distance between them. How long does it take to traverse 1/infinity ? <div class="Discussion_UserSignature"> <p>-----------------------------------------------------</p><p><font color="#ff0000">Ask not what your Forum Software can do do on you,</font></p><p><font color="#ff0000">Ask it to, please for the love of all that's Holy, <strong>STOP</strong> !</font></p> </div>

 

[maeklos]

True, you don't bother to physically travel over every point, but you at least pass over/through every point along a straight line. Since even passing by a point requires some finite amount of time, you still get an infinite amount of time taken to traverse between two points.<br /><br />This goes back to there being a finite number of points between Point A and Point B. <br /><br />This may point to reality, space-time, whatever, evidencing a wave-form structure, with our perception of reality skipping across the peaks of the waves. <div class="Discussion_UserSignature"> </div>

 

[vandivx]

"Second I predict that someone else will point out how the concept of infinity can be misused in the physical world"<br /><br />I won't, let Zeno have his day too <img src="/images/icons/wink.gif" /><br /><br />this is what you get when someone with mind bent on philosophy (read rationalistic mind) medles with physics<br /><br />vanDivX <div class="Discussion_UserSignature"> </div>

 

[tdamskov]

Not sure if this is what you mean. But it has been shown that there is a smallest possible "unit" of time, a Planck unit. Between two Planck units, any particle will appear to jump from one position to another.

 

[alokmohan]

Question unanswered.

 

[maeklos]

I remember the "Planck instant"...so, that spawns to other questions. What happens between one Planck unit and the next? Does reality just freefall from one to the next? <br />Likewise, how does the interaction between something traveling at the speed of light and these Planck units work? Again, it seems to suggest a waveform, with Planck units have differing amplitudes...the faster an object moves, the fewer units it hits, missing the "shallower" peaks, until it reaches a point where it's hitting one unit in a billion, one in a hundred trillion, so on. Since an object still needs some ties to the temporal reality, it can't physically leave behind the time wave completely.<br /><br />But then that's just an uneducated shot in the dark that I made up on the fly at 10am without my usual cup of tea. =) <div class="Discussion_UserSignature"> </div>

 

[maeklos]

Seems to lend credence to superstring theory, then? If space-time can be quantized, then this means that it may also be manipulated...but then it goes back to the whole "what happens in between?" argument. What exists between two quantized units of space-time? Is there actually nothing in between, that is, as matter moves in realspace, its constituent components are actually undergoing a form of quantum tunneling on a micro level, moving from Point A to Point B to Point C at the smallest level possible? <div class="Discussion_UserSignature"> </div>

 

[vogon13]

Points seperated by <10^-43 meters have no points between them. <div class="Discussion_UserSignature"> <p><font color="#ff0000"><strong>TPTB went to Dallas and all I got was Plucked !!</strong></font></p><p><font color="#339966"><strong>So many people, so few recipes !!</strong></font></p><p><font color="#0000ff"><strong>Let's clean up this stinkhole !!</strong></font> </p> </div>

 

[maeklos]

How so? <div class="Discussion_UserSignature"> </div>

 

[vogon13]

It just is.<br /><br /> <div class="Discussion_UserSignature"> <p><font color="#ff0000"><strong>TPTB went to Dallas and all I got was Plucked !!</strong></font></p><p><font color="#339966"><strong>So many people, so few recipes !!</strong></font></p><p><font color="#0000ff"><strong>Let's clean up this stinkhole !!</strong></font> </p> </div>

 

[vogon13]

Smart ass answer:<br /><br />God didn't ink them in.<br /><br /> <div class="Discussion_UserSignature"> <p><font color="#ff0000"><strong>TPTB went to Dallas and all I got was Plucked !!</strong></font></p><p><font color="#339966"><strong>So many people, so few recipes !!</strong></font></p><p><font color="#0000ff"><strong>Let's clean up this stinkhole !!</strong></font> </p> </div>

 

[maeklos]

Wouldn't this mean that reality follows a non-linear geometry and that all the basic geometry we learn in school is, technically, a theoretical math and not a real-world application? <img src="/images/icons/smile.gif" /> <br /><br />Further thought: Could these non-existing points in realspace be involved with the spontaneous propogation of matter? I seem to recall at one point that matter has been observed to spontaneously "appear" in lab studies. Are these propogagations the result of matter squeezing through the "cracks" made by the non-existing points in realspace, or the end-result of a quantum tunneling event? <div class="Discussion_UserSignature"> </div>

 

[kyle_baron]

<i><br />Points seperated by <10^-43 meters have no points between them. </i><br /><br />Ahhhh, that would be<10^-33 centimeters, which is the planck length. 10^-43 seconds would be planck time, which is the time it takes light to travel the planck length. Let's not confuse our plancks. <img src="/images/icons/wink.gif" /> <div class="Discussion_UserSignature"> <p><font size="4"><strong></strong></font></p> </div>

 

[kyle_baron]

<font color="yellow"><br />How so? </font><br /><br />Because, below this length, the scale of the quantum fluctuations become enormous. This is the length of a typical vibrating string. <br /> <br /><br /> <div class="Discussion_UserSignature"> <p><font size="4"><strong></strong></font></p> </div>

 

[kyle_baron]

<font color="yellow"><br />Smart ass answer: <br /><br />God didn't ink them in.</font><br /><br /><img src="/images/icons/smile.gif" /> <div class="Discussion_UserSignature"> <p><font size="4"><strong></strong></font></p> </div>

 

[kyle_baron]

<font color="yellow"><br />matter has been observed to spontaneously "appear" in lab studies. Are these propogagations the result of matter squeezing through the "cracks" made by the non-existing points in realspace, or the end-result of a quantum tunneling event? </font><br /><br />I don't think anyone has the answer to this question. But if I were to speculate, I would say they're one in the same. Non existing points in real space, would be equivalent to a non- spacetime dimension.<br /><br />By the way, I do like the way that you worded your question, very interesting. <div class="Discussion_UserSignature"> <p><font size="4"><strong></strong></font></p> </div>

 

[vandivx]

<blockquote><font class="small">In reply to:</font><hr /><p>I was wondering if anyone could shed light on the non-contiguous properties of space-time? Named, how either space or time must have holes in it.<br /><br />As in, if space were contiguous, as in, being made up on a smooth fabric, then movement would be impossible.<p><hr /></p></p></blockquote><br /><br />do you believe that there is something physical out there in space, like ether of some kind? - because if not (which btw is typical in post Einstein times) such querry would be dishonest to say the least because you would be smuggling in something called 'stolen premise' into your inquiry (i.e., you would base your querry on some kind of ether being there while explicitly denying it)<br /><br />otherwise that is an interesting question about the contiguity of space (which really translates into the contiguity of ether querry) even if the rest of your post about those inifinte points on line is pure Platonic giberish (you have to learn to separate physical reality and abstract concept of mathematics and not equate the two which is something that many ancient philosophers failed to do, however we have made some progress since those times or did we?)<br /><br />my own idea is that the space (movement in it) is discontinuous although I don't know if Planck length plays any role in it (it may be just arbitrary or artificial 'Platonic' construct that has no particular physical significance in the description of reality)<br /><br />vanDivX <div class="Discussion_UserSignature"> </div>

 

[kyle_baron]

<font color="yellow"><br />my own idea is that the space (movement in it) is discontinuous although I don't know if Planck length plays any role in it (it may be just arbitrary or artificial 'Platonic' construct </font>font color=yellow><br /> that has no particular physical significance in the description of reality) <br /><br /><br />Yeah, your right, it's not based on a physical construction. However, it is based on the NATURAL constants of the speed of light, and the law of gravity(Gravitational Constant), as stated in this Wiki Link:<br /><br />http://en.wikipedia.org/wiki/Planck_length<br /><font color="yellow"><br /> that has no particular physical significance in the description of reality) </font><br /><br />I would disagree about the description of reality. Because the speed of light, and law of gravity are universal in nature, and unchanging in time.<br /><br /><br /><br /><br /><br /><br /><br /> <div class="Discussion_UserSignature"> <p><font size="4"><strong></strong></font></p> </div>

 

[kyle_baron]

<font color="yellow"><br />"You have to learn to separate physical reality and abstract concepts of mathematics...." <br /><br />Yep, you're very right. The informational 'virus' of philosophical idealism still has not been expunged. Some say that many religious ideals also have this kind of 'computer virus' effect, as it infects the brains and one cannot get it off the hard drive! and meanwhile it causes all kinds of damage and problems! </font><br /><br />Nope, he's wrong, and so are you. Although you do have excellent debating skills, and are quite poetic. <img src="/images/icons/wink.gif" /> When the mathematics are based on the natural constants of the speed of light and the law of gravity, for the planck length, do you actually think that the two natural constants = an artificial answer? I doubt it.<br /> <div class="Discussion_UserSignature"> <p><font size="4"><strong></strong></font></p> </div>

 

[vandivx]

"I would disagree about the description of reality. Because the speed of light, and law of gravity are universal in nature, and unchanging in time."<br /><br />I have no problem with those but with mixing them up and hoping something new about reality was discovered, it is like that idea that there is some deep significance to the time it takes for light to cross the diameter of the proton (or something like that was proposed) <br /><br />that's like I have no problem with triangles but I have problem with them being proposed to be fire for example (or something like that was being proposed in Plato times, I believe by Plato himself or perhaps he had other similar ideas like that, never paid much attention to that giberish and so have only foggy memory of that)<br /><br />vanDivX <div class="Discussion_UserSignature"> </div>

 

[kyle_baron]

<font color="yellow"><br />I have no problem with those but with mixing them up and hoping something new about reality was discovered, it is like that idea that there is some deep significance to the time it takes for light to cross the diameter of the proton (or something like that was proposed) </font><br /><br />I don't see it as something discovered, or as a deep significance. The Planck Length simply sets the parameters or limits on spacial size, with our current knowledge of our space/time dimension. I guess each person will interpret it somewhat differently.<br /> <div class="Discussion_UserSignature"> <p><font size="4"><strong></strong></font></p> </div>

 

[kyle_baron]

<font color="yellow"><br />Therefore, ON the quantum level, and that IS the Planck time, distance, or whatever, light speed is not necessarily constant, nor relevant. At such levels ALL deterministic theories break down, simply because at that level, events are not deterministic, but probabilities. </font><br /><br />That would be, BELOW the Planck Length, or Planck Time, that the theories break down. There are no clear mathematics, beneath these parameters or limits. <br /><font color="yellow"><br />Therefore, light speed is not necessarily relevant. It might be in some cases, but it's NOT necessarily so. Light speed is very likely exceeded... the confirmed non-locality effects which showed that Einstein was WRONG about quantum effects</font><br /><br />We had this arguement before. Nothing is moving faster than the speed of light (other than your imagination). A change in a particles spin at a distance farther than light can travel DOES NOT VIOLATE SPECIAL RELATIVITY because no particles are exchanged, or any forces are involved. <br /><font color="yellow"><br />Philosophical idealisms, which your posts appear to be promoting, have no place in the sciences. Ideas are NOT primary in the sciences. They are secondary to events in existence</font><br /><br />No, I'm just defending the status quo, using the facts from more than one physicist. And I see no reason to change my mind. When you say things like "Not necessarily", "It's likely the case", and "very likely exceeded" you're not stating facts, but using wishful thinking in trying to prove Einstein wrong. Well, your not alone, every other physicist on the planet would like to prove Einstein wrong! Then, you take one obscure website, and run wild with the ideas presented there. I would need at least 3 or more physicists opinion's, before I would agree that Einstein's theories are wrong at the quantum level.<br /><br /><br /><br /><br /><br /><br /> <div class="Discussion_UserSignature"> <p><font size="4"><strong></strong></font></p> </div>

 

[vandivx]

"I was wondering if anyone could shed light on the non-contiguous properties of space-time? Named, how either space or time must have holes in it.<br /><br />As in, if space were contiguous, as in, being made up on a smooth fabric, then movement would be impossible."<br />----------------------------<br />as I pointed out such argument for non-contiguity as you made is not a valid argument at all (reasoning about contiguous infinity of points that would prevent movement) but the query about (non-)contiguity of space-time can be argued for in other ways<br /><br />there is another kind of reasoning for non-contiguity and that is that contiguity is when you think of it incomprehensible, for example when we find one day that we cannot find any more constituents of particles, then that one particle at which we would stop would be 'contiguous' something, i.e., something further undivisible, something that has no parts, something that is a fundamental 'whole' the contiguity of which preventing us to understand it in terms of its constituents - because that's how we understand anything, by seeing how it is made up, how it works based on how its parts work and once we can't see any underlying structure we are at the end and can't understand unless we find other means of inquiry and go deeper still<br /><br />when it comes to space-time, unless you believe that it is something physical, something like ether - not ether of the old times necessarily - you can't really discuss its contiguity or non-contiguity because that would beg the question - (non-)contiguity of what... failing that will embroil you in mysticism and or in dishonesty (of stolen concepts) because you would talk about physical properties - contiguity - of something which you in turn deny existential, that is physical status (you can't rationally argue for properties of a void)<br /><br />once you have established that there is something physical out there that we call space-time you can start making theoretical models o <div class="Discussion_UserSignature"> </div>

 

[kyle_baron]

<font color="yellow"><br />If you accelerate an object which is one planck length long, surely it contracts to be less than one planck length. </font><br /><br />Surely? How much ya wanna bet <img src="/images/icons/wink.gif" /> that there is no contraction to less than 1 Planck Length? According to Brian Greene (string theorist) contracting to just the planck length results in a cosmic BOUNCE. He states that the geometry of the contraction is reversed. Believe it or not.<br /><br />Also, thanks for the link. I found it interesting. But it may be a little out dated (2002).<br /> <div class="Discussion_UserSignature"> <p><font size="4"><strong></strong></font></p> </div>