# Is the distance between any object infinite?

Hi, I just finished grade 11 in high school and I have a question that is there in infinite amount of space in between objects?
Here is my logic:

***First off what is the minimum distance matter can move within the midst of space? I'm thinking there is no minimum.

On a 2-dimentional graph there is an object at (0,0) and (0,10) (any point would work) objects A (0,0) & B (10,0). Lets say every unit in between them is 1m so ultimately the distance between them is 10m.Let us say object A shoots a bullet at object B, it has to travel through about 10m of space to get there, right? Well the bullet could theoretically .1m , .08m, .002m, .0000000432m through space; so we could keep and keep on putting those zeroes in meaning that the bullet would have in infinite distance to cover to get to object B. Get it? First it needs to move 10m which means it has to cover 5m two times, or 2 meters, 5 times, or 0.00000000000078 x amount of times or 0,0000000000000000000000000000000098969584 m y amount of times and so on?

So is there an infinite amount of space/distance-to-cover between object A & B?

Now I've asked many people in school about this and no one knew the answer and would mumble something about asymptotes and one said something about Zola's or Zopha's dilemma (I know I'm getting the Z guys name wrong, sorry), I hope some thing there gets the gears turning.

jedishrfu
Mentor
• Alex Stoishkov and Amrator
phinds
Gold Member
If two objects are X distance apart, X cannot be infinite because there is always X + 1.

The confusion comes from trying to apply numerical rules to something that is not numerical. It doesn't matter how many zeros you add, you STILL have a number and it is not infinity

• Alex Stoishkov and Amrator
@phinds so say a pixel is traveling across the screen of a computer, it moves from 0,0 to 0,1 to 0,2 and so on. Are you saying that an object moves like that through space? So it does not move smoothly but sorta teleports from 0,0 to 0,1 and so on? i'm sorry i'm not sure how to phrase what I have just asked, I hope it makes sense.

phinds
Gold Member
I understand exactly what you are asking but I have no idea how you inferred that from what I said. I made no comment on the granularity of space-time. I don't think there's any proof one way or the other, but my belief is that it is continuous.

• Alex Stoishkov
What is "granularity" of space?

Guys, I'm thinking that space cannot be gridded, cause there would be minimum movement distances for objects. For example say that an object received 0.0000001N it would not be able to move to the next point on the "grid" of space but if it got 0.0000002N of energy if would move to the next point. I am thinking that this is not what happens on the space fabric, I'm thinking that the bullet mentioned above, moves smoothly from one point on the grid to the next, not suddenly appearing at the second point. Hope that makes sense.

• Jack Loranger
phinds
Gold Member
What is "granularity" of space?
Granular means "grainy" as in "made up of grains" instead of smooth. My original post made no comment on whether space-time is smooth or not but as I said in my next post, I personally think (without any proof) that it is.

• Alex Stoishkov
Hmm, I searched up granularity of space and I've figured out that this topic belongs in the quantum section

phinds
Gold Member
Hmm, I searched up granularity of space and I've figured out that this topic belongs in the quantum section

• Alex Stoishkov
It hasn't been answered but that's because nobody knows the answer but thanks for your input, that's the furthers this conversation will probably go.

russ_watters
Mentor
It hasn't been answered but that's because nobody knows the answer but thanks for your input, that's the furthers this conversation will probably go.

• Alex Stoishkov, Amrator and Jack Spell
Hi Ujellytek

I think you're putting two different concepts together and maybe getting a bit mixed. Here goes...

First the infinities. Infinity is a math concept pure and - I was going to say simple, but let's be real - pure and wonderfully complex. However, we don't see infinities in real word space/time - infinities pop up all over the place when trying to model the real world and we've got some fabulous tricks to deal with them (google why 1+2+3+4.. = minus 1/12). But that's just maths and models; there are no specific evidence of any infinite (or infinitesimal) distances, temperatures, densities or the real world - just areas where our models break down. For example, we can't accurately say that black holes have an infinite density, only that the density is tending towards infinity and then who knows... that's when the model breaks down!

Next Grainy space. You are absolutely spot on that this belongs in the quantum section! Quantum mechanics is possibly the most thoroughly tested and accurate theory we have; as we've been able to measure distances, time, magnetic moments and zillion other things to greater and greater accuracy, QM predictions have been shown to be accurate to within a few parts per many trillions of whatever is being measured. It's all good stuff! And if you extrapolate from the maths to real life (*warning*) then it certainly looks like life isn't continuous at the tiny (plank) scale, but quite digital!

Why the warning? For similar reasons that you can't take EVERY maths concept and map it to real world (infinity as a case in point), you can't be sure that our interpretation of QM is correct - in fact QM interpretations are akin to religious wars to some! Is life grainy? I've no idea... but spend some time in the QM threads and you'll quickly have a far better understanding than I do :-)

Regards
Matt

• Alex Stoishkov
This discussion just provoked a thought. General Relativity allows that space and time can be interchanged by motion. This is a continuous function of velocity (itself a continuous variable) as described by the Lorenz transforms. It is this continuity that precludes the 'granularity' of space or time. Both must be continuous variables.

Drakkith
Staff Emeritus
So is there an infinite amount of space/distance-to-cover between object A & B?

No, the distance between A and B can be divided into an infinite amount of 'pieces', but there is NOT an infinite amount of distance between them because each piece also gets smaller as you divide the distance into more pieces.

• Alex Stoishkov
Hey - I got no beef with Einstein! If he say's it's a continuous function then my mortgage is on it being a continuous function!!

That said (:-) continuous functions are maths concept and no matter how well the maths describes the world, maths and the world are not the same. And even the Duke himself didn't get his relativity and quantum mechanics to stack up at the tiny level.

There's a fabulous paper written by Eugene Wigner called The Unreasonable Effectiveness of Mathematics in the Natural Sciences and it can make your brain ache and pancake in equal measures; but the underlying message (to me anyway - Wigner was a bit before my time to ask) is as maths as a descriptor of reality, not as an equivalence.

• Alex Stoishkov
Drakkith
Staff Emeritus
There's no need to get into the details of the granularity of space. The concept is so far over the head of the OP (and most members for that matter) that it serves no purpose. Let's try to keep the discussion at a level appropriate for the OP.

@Drakkith I see what you mean. But wouldn't it mean that if an object could move less than 0.002 m or less than 0.0000000000000001m or less
than 0.(lots of zeroes)0001m that an object could theoretically move an infinite amount of times before moving 1m.
#13
@mgkii About the 1+2+3... = -1/12: My math teacher told me it is inpossible to add numbers infinitly because infinity is only a concept, not a variable

@ujellytek you're getting infinity confused here; you can't move an infinite number of times - infinity isn't a number. Have a browse around wiki etc on infinity; the penny will drop.

mqkii>"you're getting infinity confused here; you can't move an infinite number of times - infinity isn't a number. Have a browse around wiki etc on infinity; the penny will drop. "

Imean that you could do if forever, always moving lesser and lesser amount and never reaching your destination

@ujellytek Your maths teach was correct - you can't actually add all the numbers, but you can define a mathematical function that is the sum of the set of all integer numbers. For the same reason, you can't actually move (in real space) an infinite number of times, but you can make models that deal with infininte /infinitesimal distances.

russ_watters
Mentor
@Drakkith I see what you mean. But wouldn't it mean that if an object could move less than 0.002 m or less than 0.0000000000000001m or less
than 0.(lots of zeroes)0001m that an object could theoretically move an infinite amount of times before moving 1m.
#13
@mgkii About the 1+2+3... = -1/12: My math teacher told me it is inpossible to add numbers infinitly because infinity is only a concept, not a variable
It should be easy to see that if you move in 1 step of 1 meter, 2 steps of 1/2 meter, 3 steps of 1/3 meter, the total is always the same.

You shouldn't need to take the logic any further to get the above, but introduction of infinities and infinitesimal is easily solved with calculus.
Imean that you could do if forever, always moving lesser and lesser amount and never reaching your destination
Nowhere in this analysis has time been included, so you have no basis for saying that. However, it should be obvious enough that if your speed is constant, the total time follows the same math i gave above and the total time is therefore always the same regardless of the number of steps you choose to split the trip into.

Wow thanks for everybody's input, this is all so mind blowing for me I'm getting tears in my eyes (anyone else get that when so many things all of a sudden make sense?)

• mgkii
Drakkith
Staff Emeritus
@Drakkith I see what you mean. But wouldn't it mean that if an object could move less than 0.002 m or less than 0.0000000000000001m or less
than 0.(lots of zeroes)0001m that an object could theoretically move an infinite amount of times before moving 1m.

That implies that motion is discrete and an object moves X distance Y number of times between 0 and 1 meter, where X is an ever decreasing number as Y increases. As far as we know, this isn't how nature works.

Imean that you could do if forever, always moving lesser and lesser amount and never reaching your destination

Only if you also decrease the time step between each jump. The entire point is that time and distance are continuous, not discrete. An object traveling at 1 m/s moves 1 meter every 1 second. If you decrease the time, the distance also decreases. Nothing about this implies that distance is discrete.

I'm getting tears in my eyes (anyone else get that when so many things all of a sudden make sense?)

Lol - 40 years old and it's still happening to me.

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