Is space/time truly continuous?

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Is space/time truly continuous?

So IANAQ(uantum)P(hysicist), but I know enough to be a danger to myself and others. I was perusing wikipedia when I stumbled onto the Planck Length. You can derive the Planck Length from the constants G (gravitational constant), h (Planck's constant), and c (speed of light). It is, in theory, the smallest distance at which physics makes sense. It's about 1.6e-35 meters.

Wiki posts an interesting thought experiment. Let's say you're measuring how big something is by throwing photons at it and picking up the ones that reflect. You can resolve smaller features as you decrease the wavelength of the incident photons. If you shrink the wavelength to less than the Planck Length, allegedly a mini-black-hole would appear to swallow the photon, preventing you from measuring with any greater accuracy. I can kindof see how this ties in to Heisenberg's uncertainty principle...

You can derive the time that it takes for a photon to traverse the Planck Length in a vacuum, or you can make the Planck Length the wavelength of a wave and calculate its period. This results in Planck Time, around 5.4e-44 seconds.

To me (remember, IANAQP) it seems natural to assume, then, that Planck Time is the smallest measurable unit of time, and that time is therefore discrete multiples of Planck Time, as distances are all discrete multiples of Planck Length. Does anyone have any indication of how right or wrong this view may be?

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Re: Is space/time truly continuous?

That was also my thought - that spacetime is quanticised and discrete, and that many functions of quantum physics are probably manifestations of the universes' procedures for precisely getting an object's position when it needs that position.
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Re: Is space/time truly continuous?

Remember, Quantum Physics is a mathematical model that describes reality, not vice versa. Just because the system breaks down at certain values and edge conditions, does not dictate reality does the same. (see also Godel's Theorum)

Edit: Thought this was interesting, relevant (Hawking on Uncertainty+Physics): http://www.physics.sfasu.edu/astro/news ... 030308.htm

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Re: Is space/time truly continuous?

Indon wrote:That was also my thought - that spacetime is quanticised and discrete, and that many functions of quantum physics are probably manifestations of the universes' procedures for precisely getting an object's position when it needs that position.

int Universe::GetPosition(Object foo)
{
// HACK: we should use floating point here instead, but our target architecture only supports integers...
}

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Re: Is space/time truly continuous?

thats a pretty crappy architecture for coding The Universe on.
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Re: Is space/time truly continuous?

DeadCatX2 wrote:int Universe::GetPosition(Object foo)
{
// HACK: we should use floating point here instead, but our target architecture only supports integers...
}

This definitely made me LOL ^_^. It explains so much.

IANAQP either, nor anywhere near resembling one. Nonetheless, why should we infer that spacetime is discrete/quantized simply from our inability to measure smaller intervals? Is it not perfectly possible there are physical limits to measurement rather than the phenomena being measured?

On the other hand, it would provide a very handy resolution to certain ancient Greek paradoxes: sorry Zeno, you can't really divide distances and objects an infinity of times after all!
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Re: Is space/time truly continuous?

diotimajsh wrote:IANAQP either, nor anywhere near resembling one. Nonetheless, why should we infer that spacetime is discrete/quantized simply from our inability to measure smaller intervals? Is it not perfectly possible there are physical limits to measurement rather than the phenomena being measured?

Possible, but I believe that below the Planck Length, physics stops making sense. This implies to me that it is the limit of physics, and not necessarily the limit of observation.

diotimajsh wrote:On the other hand, it would provide a very handy resolution to certain ancient Greek paradoxes: sorry Zeno, you can't really divide distances and objects an infinity of times after all!

I remember reading a book about infinity, once, and it said something along the lines of Zeno was simply manipulating the way in which we represent numbers, and not actually making an observation about the physical world.

Of course, one could also consider the point at which the divided distance starts permitting the effects of the Strong Force (I've also heard this called the "Color Force" and/or "Quantum Chromodynamics"=QCD, as per daydalus' linked article) to be felt would be "close enough", but I digress.

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Re: Is space/time truly continuous?

The question is truly unanswerable.

We know that our understanding breaks down at that scale. But we don't know what the laws of physics are. They might be continuous. They might be discrete. We simply don't know.

And even if they look discrete at that scale, they might be continuous at a lower one. Or look continuous there and be discrete at a lower one. Or else reality could be stranger than we think and that apparent scale could be an emergent property of something that doesn't at all look like our naive notions of space-time.

We simply don't know. Not only don't we know, we don't really have enough information to speculate in a useful way.
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Re: Is space/time truly continuous?

IANAQPY, but here's my take on it: maybe we can't tell what part of the interval [0,x] our particle is in due to Planck length, but we can instead check whether it's in the interval [x/2,3x/2] to figure out which side of the interval it's in (given that we already know that it's in the interval [0,x]). And we can still measure whether it's in [pi*x, x+pi*x], even though pi is irrational. I'm pretty sure you can't do that with discrete space time.
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Re: Is space/time truly continuous?

DeadCatX2 wrote:Possible, but I believe that below the Planck Length, physics stops making sense. This implies to me that it is the limit of physics, and not necessarily the limit of observation.
But then, why why should we assume that our current understanding of physics is adequate to deal with such minute lengths, or that our (possibly very impoverished) understanding is completely accurate? As btilly and daydalus said, respectively: "We know that our understanding breaks down at that scale," and "Just because the system breaks down at certain values and edge conditions, does not dictate reality does the same."

DeadCatX2 wrote:I remember reading a book about infinity, once, and it said something along the lines of Zeno was simply manipulating the way in which we represent numbers, and not actually making an observation about the physical world.
Well, he was certainly intending to make observations about the world, since his paradoxes were designed specifically to defend Parmenides' view that all change is illusory.
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Re: Is space/time truly continuous?

DeadCatX2 wrote:I believe that below the Planck Length, physics stops making sense.
If it did, how could phenomena such as T-duality exist?

What do you mean when you suggest that time and space are quantized? Do you mean that distances and lengths of time can only take on certain values (this is not the case)?
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Re: Is space/time truly continuous?

Robin S wrote:
DeadCatX2 wrote:I believe that below the Planck Length, physics stops making sense.
If it did, how could phenomena such as T-duality exist?

I'm no quantum theorist, but is that actually a phenomena, or is it just a theoretical construct designed to help string theory make sense?
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Re: Is space/time truly continuous?

How are you defining the difference? Is it directly observable, do you mean? Well, no, but then (pretty much by definition) neither is anything else which would demonstrate the meaningfulness of scales below the Planck length.
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Re: Is space/time truly continuous?

Robin S wrote:How are you defining the difference? Is it directly observable, do you mean? Well, no, but then (pretty much by definition) neither is anything else which would demonstrate the meaningfulness of scales below the Planck length.

Well, I mean, does it exist outside of the string theory framework?
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Re: Is space/time truly continuous?

diotimajsh wrote:
DeadCatX2 wrote:Possible, but I believe that below the Planck Length, physics stops making sense. This implies to me that it is the limit of physics, and not necessarily the limit of observation.
But then, why why should we assume that our current understanding of physics is adequate to deal with such minute lengths, or that our (possibly very impoverished) understanding is completely accurate? As btilly and daydalus said, respectively: "We know that our understanding breaks down at that scale," and "Just because the system breaks down at certain values and edge conditions, does not dictate reality does the same."

Well, at this point it's really just musing, as I don't think I'll ever fully understand quantum physics. However, it seems to me to make sense. Energy levels are in discrete quanta, which are defined using Planck's Constant (h). It, therefore, makes intuitive sense that you could derive discrete "distance quanta" or "time quanta" using h.

It just feels right. We can simulate particles interacting in reality using the appropriate physics, high-powered computers, and femtosecond time steps. From there, it seems natural that this might be how the world operates; "God" evaluates the state of the universe, calculates the next state using God Physics (which we model inaccurately with Human Physics), and then increments time by one "unit". Once everything has settled into place, God re-evaluates the state of the universe, calculates the next state, and increments time by one unit, again.

Robin S wrote:
DeadCatX2 wrote:I believe that below the Planck Length, physics stops making sense.
If it did, how could phenomena such as T-duality exist?

...that link appears to be far beyond my capacity for understanding...

Robin S wrote:What do you mean when you suggest that time and space are quantized? Do you mean that distances and lengths of time can only take on certain values (this is not the case)?

I think you understand my suggestion. As above, I imagine that Reality is actually a Simulation on a really, really powerful computer, and that there is some "time step" parameter passed in from the command-line. So any measurable period of time would be composed of an integer number of "time quanta". You indicate that this is not the case, though...why? (try to keep it in terms that someone who took intro-to-quantum could possibly digest)

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Re: Is space/time truly continuous?

Indon wrote:
Robin S wrote:How are you defining the difference? Is it directly observable, do you mean? Well, no, but then (pretty much by definition) neither is anything else which would demonstrate the meaningfulness of scales below the Planck length.

Well, I mean, does it exist outside of the string theory framework?

More relevantly, does it exist within any scientific theory that has generally accepted experimental confirmation?
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Re: Is space/time truly continuous?

I think there's an important point to be made here.

By "shortest length possible", do you mean that the universe is a lattice, and everything moves in discrete lengths, like in a gigantic 3-d game of Life, for example? Do you suspect that our 3-d lattice is a cubic lattice? Is it a hexagonal-close packed lattice? An s-orbital is perfectly spherical - how is that possible in a discrete world? I think there are a lot of inherent contradictions if you try to assume any sort of discreteness in distance. I've only done a bit of high-school level physics/a bit of advanced chemistry, but my understanding of it is that all measurements have an inherent error bar attached to it, and the error bar never goes lower than the planck length.

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Re: Is space/time truly continuous?

I don't really know myself, and I'm not sure that anyone knows. Philosophically, there's something very pleasing about that idea to me: everything in the universe is finite, and there are finitely many possible universes. There's a lot of movement in the discrete direction historically: first we thought matter was infinitely divisible, then we found out it wasn't. We later found out that a lot of other things (energy states for example) are discrete, with the advent of quantum physics. I wouldn't be too surprised to learn that time and space itself is discrete. Perhaps this is why relativity (a very geometric, continuous theory) doesn't work well with small scales?

I'm not a physicist, I don't know. I don't think it's out of the realm of possibility though.

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Re: Is space/time truly continuous?

tantalum has already given reasons why time and space are not discrete. These reasons are generally accepted by theoretical physicists, I believe.
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Re: Is space/time truly continuous?

tantalum wrote:By "shortest length possible", do you mean that the universe is a lattice, and everything moves in discrete lengths, like in a gigantic 3-d game of Life, for example? Do you suspect that our 3-d lattice is a cubic lattice? Is it a hexagonal-close packed lattice? An s-orbital is perfectly spherical - how is that possible in a discrete world?

Suspect hexagonal - all the best boadgames had hexes not squares.... but seriously: An s orbital (of a H atom) is large compared to the plank length. Plank length is to an s orbital as an atom is to Jupiter. So, of course IANAQP, but it seems that saying an s orbital cannot be spherical if space is quantised is a bit like saying Jupiter cannnot be spherical if matter is made of atoms.

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Re: Is space/time truly continuous?

DeadCatX2 wrote:int Universe::GetPosition(Object foo)
{
// HACK: we should use floating point here instead, but our target architecture only supports integers...
}

Except that since floats are placed on a binary architecture, they're still discrete - just at a smaller level.

Edit: Kind of comparable to the level we're talking about, in fact. Ridiculously, tinytiny small.
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Re: Is space/time truly continuous?

tantalum wrote:By "shortest length possible", do you mean that the universe is a lattice, and everything moves in discrete lengths, like in a gigantic 3-d game of Life, for example?

Yup, that is my suspicion. There may be other dimensions involved, but in general I hypothesize the existence of a discrete "distance quanta" of which all distances are integer multiples of.

tantalum wrote:Do you suspect that our 3-d lattice is a cubic lattice? Is it a hexagonal-close packed lattice? An s-orbital is perfectly spherical - how is that possible in a discrete world? I think there are a lot of inherent contradictions if you try to assume any sort of discreteness in distance.

As mentioned by BeerBottle, I don't see the contradiction with an s-orbital being spherical while existing in a discrete, quantized "lattice". Consider that we only need 39 decimal places of Pi to compute the circumference of any circle that fits in the known universe with precision on the order of a hydrogen atom's diameter, so you can make something that looks a lot like a circle out of discrete lines. The Planck Length is about twenty-four orders of magnitude smaller than the atomic radius of hydrogen; I'm pretty sure you could make a convincing sphere on such a lattice.

Robin S wrote:tantalum has already given reasons why time and space are not discrete. These reasons are generally accepted by theoretical physicists, I believe.

If you're referring to "you can't make a sphere on a discrete lattice", I'm afraid I'm not convinced. (plus, that's only one reason, and you never expanded on "T Duality") If you make your lines small enough, you can't tell what you have isn't a circle; the same should apply to 3d spheres as opposed to 2d circles.

Daydalus mentioned that just because the math breaks down like that, doesn't mean reality breaks down like that; our math is just a model for reality. Perhaps the converse (inverse? contrapositive?) is also true; just because mathematics can describe a perfect sphere doesn't mean that one can necessarily exist.

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Re: Is space/time truly continuous?

Cycle wrote:We later found out that a lot of other things (energy states for example) are discrete, with the advent of quantum physics. I wouldn't be too surprised to learn that time and space itself is discrete.

Only under the right conditions. Most of the time, energy states are not discrete at all - look up something about spectra of unitary operators sometime. Some operators give you discrete spectra, some give you continuous spectra.
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Re: Is space/time truly continuous?

DeadCatX2 wrote:If you're referring to "you can't make a sphere on a discrete lattice", I'm afraid I'm not convinced.
Ok. How about: if relativity is accurate, there can be no absolute reference frame. A lattice based on Planck lengths, however small-scale, is still an absolute reference frame. Also: if an object at the speed of light travels one Planck length in one Planck time, how far does an object at half the speed of light travel in the same time?
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Re: Is space/time truly continuous?

Robin S wrote:Ok. How about: if relativity is accurate, there can be no absolute reference frame. A lattice based on Planck lengths, however small-scale, is still an absolute reference frame.

Are you sure that's how relativity works? It seems to me to be perfectly consistent, because you can't physically move the lattice - if it exists, it's no more an 'absolute reference frame' than background radiation from the big bang - natural, ubiquitous, and just a part of how spacetime works.

Robin S wrote:Also: if an object at the speed of light travels one Planck length in one Planck time, how far does an object at half the speed of light travel in the same time?

It has a 50% chance of moving one planck length per planck time.
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Re: Is space/time truly continuous?

Indon wrote:That was also my thought - that spacetime is quanticised and discrete, and that many functions of quantum physics are probably manifestations of the universes' procedures for precisely getting an object's position when it needs that position.

int Universe::GetPosition(Object foo)
{
// HACK: we should use floating point here instead, but our target architecture only supports integers...
}

I thought the consensus was that the Universe is written in Lisp or Perl.
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Re: Is space/time truly continuous?

tantalum wrote:By "shortest length possible", do you mean that the universe is a lattice, and everything moves in discrete lengths, like in a gigantic 3-d game of Life, for example? Do you suspect that our 3-d lattice is a cubic lattice? Is it a hexagonal-close packed lattice? An s-orbital is perfectly spherical - how is that possible in a discrete world?

The radius of an s orbital approximately equals 10^-8 cm. The Planck length approximately equals 10^-33 cm. If space did come in discrete quanta, it would almost certainly become smoothed out in the 25 orders of magnitude that separate the two.

The Planck length has no true theoretical meaning. It has never arisen naturally in the course of calculation, though people often use it for convenient metrics (i.e. measuring the size of the universe in number of Planck lengths during the inflationary period).

People derived the Planck length by taking three naturally occurring constants: G, c, and h, and arranged them in the only matter you can arrange them to get a unit of length: (hGc-3)1/2. While you can boldly speculate that this has some significance in the grand scheme of things, it does not necessarily have that significance. Indeed, physics could very well operate on discrete or continuous values.

tantalum wrote:I think there are a lot of inherent contradictions if you try to assume any sort of discreteness in distance. I've only done a bit of high-school level physics/a bit of advanced chemistry, but my understanding of it is that all measurements have an inherent error bar attached to it, and the error bar never goes lower than the planck length.

Not really any inherent contradictions. Let me put it for you another way around: we know that there exist objects which, near perfectly, resemble lattices. Yet we know that in reality, we only have atoms. All of the orbitals have an azimuthal dependence, so none of the orbitals come in box shapes, yet out of those interactions, we get something that resembles a lattice. It surprises me that you feel comfortable with a lattice arising from spheres but not spheres arising from a lattice, when the principle behind these phenomena do not differ. Essentially, you have orders of magnitude difference that wipe away the discretization.

Also, the fundamental error limit does not exist within a single observable, but rather sets of observables. A more precise measurement in one yields a less precise measurement of the others.
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Re: Is space/time truly continuous?

Robin S wrote:
DeadCatX2 wrote:If you're referring to "you can't make a sphere on a discrete lattice", I'm afraid I'm not convinced.
Ok. How about: if relativity is accurate, there can be no absolute reference frame. A lattice based on Planck lengths, however small-scale, is still an absolute reference frame.

Imagine an infinite 2d grid. Imagine there is no (0,0) point; you could use any point you wanted as (0,0), but it doesn't matter because no point is (0,0). All the math still works. You could even distort local points on the grid relative to other points, if you wanted.

I believe there's something about space expanding and such. There's also a theory that constants aren't really constant. If the Planck Length is derived from those constants, but those constants are changing, that also explains the distance between two points changing.

Indon wrote:
Robin S wrote:Also: if an object at the speed of light travels one Planck length in one Planck time, how far does an object at half the speed of light travel in the same time?

It has a 50% chance of moving one planck length per planck time.

And the probability of light moving through one Planck length of glass in one Planck time would be about 67%. (typical glass has a refractive index of about 1.5)

It doesn't necessarily have to be a Planck unit, that number is just conveniently tiny.

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Re: Is space/time truly continuous?

Trying to understand the universe is like floating inside a cup and observing the particles float around next to you. While the cup is on a washing machine that's on, during an earthquake.
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Re: Is space/time truly continuous?

So... the greeks ran into this problem a few millenia ago, I believe. Somebody discovered the existence of irrational numbers, and Pythagoras reputedly murdered the chap to prevent this fact from getting out.

So if you say everything is in planck lengths, we can assign them integer multiples of this length, no? So what is the distance between opposite vertices on a square made of planck lengths? 1.414~ planck lengths? What if you were to travel in the direction of the diagonal, for presumably 1 planck length, which is the smallest you can move at a time. Would the distance between your current location and the opposite point be .414 lengths? Isn't that smaller than the planck length, which is by definition the smallest length possible?

You are rationalizing on the macroscopic level. I can argue with you about the perfection of a sphere for pages, but I think this simple argument illustrates the same concept as the sphere, and doesn't get caught up in complications.

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Re: Is space/time truly continuous?

So, I just thought of a counter, and before you post it, i'm going to reply to your counter.

I was thinking that you might argue that you can't move diagonally, and you can only move in the x, y, z directions, and therefore, it's not possible to move diagonally to end up .414 planck lengths away.

So the counter to this is velocity. If you want to move at a 45deg angle to what's presumably the "correct" orientation of the lattice, then you have to travel the "Manhattan" distance, which, as the name implies, is simply the sum of the X and Y components. Standard velocity logic implies that if you want to travel 10 meters at 1 m/s, you will take 10 seconds. If you want to travel 10 meters at a 45 deg angle, you have to take 14.14 seconds, since in order to move to that point, you have to "zigzag" there at a very, very small scale. As n->0, the zigzag function jumps to 10 seconds, smoothing out the discontinuities, but since you claim n doesn't go all the way to 0, but stays at a very small number, there is no way to smooth out the discontinuities.

Basically, if your theory were true, it would take 14~ seconds to travel 10 meters at 1 m/s

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Re: Is space/time truly continuous?

tantalum wrote:So... the greeks ran into this problem a few millenia ago, I believe. Somebody discovered the existence of irrational numbers, and Pythagoras reputedly murdered the chap to prevent this fact from getting out.

So if you say everything is in planck lengths, we can assign them integer multiples of this length, no? So what is the distance between opposite vertices on a square made of planck lengths? 1.414~ planck lengths? What if you were to travel in the direction of the diagonal, for presumably 1 planck length, which is the smallest you can move at a time. Would the distance between your current location and the opposite point be .414 lengths? Isn't that smaller than the planck length, which is by definition the smallest length possible?

You are rationalizing on the macroscopic level. I can argue with you about the perfection of a sphere for pages, but I think this simple argument illustrates the same concept as the sphere, and doesn't get caught up in complications.

Aren't you implicitly assuming that the world on the quantum scale works the same as Euclidean geometry, which is essentially assuming what you're trying to prove?

notzeb wrote:Only under the right conditions. Most of the time, energy states are not discrete at all - look up something about spectra of unitary operators sometime. Some operators give you discrete spectra, some give you continuous spectra.

I'm aware of what you said about the spectrum of unitary operators (having taking functional analysis), but I don't know how the math applies to quantum mechanics. I'm guessing that a unitary operator is calculated based on the physical situation, and the spectrum of that operator is the possible energy states? Or something like that?

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Re: Is space/time truly continuous?

Cycle wrote:Aren't you implicitly assuming that the world on the quantum scale works the same as Euclidean geometry, which is essentially assuming what you're trying to prove?

This is generally called "Begging the Question", fyi.
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Re: Is space/time truly continuous?

It has a 50% chance of moving one planck length per planck time.

Would that mean an infinitesimal chance of any object in motion suddenly moving at the speed of light by "rolling a series of ones" when it "rolls for movement points", to stretch a metaphor?
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Re: Is space/time truly continuous?

Quite possibly, yes. However, the planck length is so small that the chances of any particle in the universe ever deviating from its' course in a scale significant to newtonian physics is about comparable to... what's that thing called when entropy spontaneously reverses itself to create things like perfect replicas of the human brain?

Probably rarer than that, methinks.
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tantalum
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Re: Is space/time truly continuous?

You are absolutely right in that I'm assuming everything works the same way on the quantum scale - and I'm trying to reach a contradiction from that assumption to show that this original assumption can't be possibly true.

ian
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Re: Is space/time truly continuous?

if the planck time is the amount of time it takes a photon to cross the planck length, how long it does it take something travelling slower?

Indon
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Re: Is space/time truly continuous?

It has a chance per planck time to cross a planck length in proportion to its' speed relative to the speed of light - so an object moving at 20% of the speed of light has a 20% chance to move a planck length each planck time.

Now, where this might break down is how the system interacts with objects moving at relativistic speeds - what effect does relative time have on it, I have no clue. I'm no quantum theorist.
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daydalus
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Re: Is space/time truly continuous?

Indon wrote:Quite possibly, yes. However, the planck length is so small that the chances of any particle in the universe ever deviating from its' course in a scale significant to newtonian physics is about comparable to... what's that thing called when entropy spontaneously reverses itself to create things like perfect replicas of the human brain?

Probably rarer than that, methinks.

Boltzmann’s Brains

PhantomReality
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Re: Is space/time truly continuous?

What a cool friggin thought expiriment. I had a similar though while meditating on the nature of the universe when i was younger.

I was thinking about it in terms of if you had to model the universe in a computer you'd have to keep track of every specific point. You know how fast light travels, and how many of said points that light could travel in a given amount of time then the amount of time it took light to move from one point to a directly adjacent point would be the smallest unit of time.

I thought it was pretty cool and smart back then but i was never able to get anybody to take me seriously when i explained it because my friends weren't geeky enough.

cool friggin stuff tho
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