Doesn't Zenos dichotomy paradox basically proves that the universe is quantized?
>That which is in locomotion must arrive at the half-way stage before it arrives at the goal.– as recounted by Aristotle, Physics VI:9, 239b10
Because there has to be a point where distance can't be halved any more, to make sense of motion.
it could be that space is continuous but particles move in quantized leaps therefor bypassing the need to reach the half-way point
Or, you can cover an "infinite" number of intervals in a finite amount of time.
A good example of how something that is obviously false can be sold as truth by using the right language.
>implying simple word play proves that distances are quantized in our Universe
You're an idiot.
A good example of how acting superior on the internet and using greentext doesn't prove anything
so aside from you just being a dickbag, all your saying is that the contradiction is due to "language".... enlightening.. hope I can be that smart one day.
Really, this contradiction shows that there is a limit to the degree our numerical system can describe reality. Whether this limitation is due to the real world being quantized, and our numerical system not being quantized is a different issue. Its a good explanation of the discrepency, but is not yet proven or scientifically established to my knowledge
You actually end up moving -1/12 meters back
Literally the worst interpretation.
Infinite is a mathematical concept, it doesn't exsists
Whoa
>Infinite is a mathematical concept, it doesn't exsists
And yet, physics relies on the Universe being a differentiable manifold
>Really, this contradiction shows that there is a limit to the degree our numerical system can describe reality.
It shows no such thing. Again, you're assuming that it is a law of physics that one cannot cover an infinite number of intervals in a finite time. I'm saying that maybe this is not a rule of physics. The math works just fine.
>Infinite is a mathematical concept, it doesn't exsists
Whatever.
Seems to work fine in practice. I don't see a problem with it.
>Because there has to be a point where distance can't be halved any more, to make sense of motion.
It seems, and correct me if I've got you wrong, like you're suggesting that there is a "bottom" to how many times distance can be halved, and further suggesting that objects in motion must therefore be advancing in units of this length, at some rate, and that this is what makes motion possible.
But I'm not sure that your second suggestion follows from your first, and I'm not sure your first suggestion is correct in the way you're suggesting it.
Planck length is the scale at which quantum effects dominate, and at scales lower than Planck length it stops being meaningful to talk about things existing in discrete places, because at such scales things exist as clouds of possible locations. BUT that is not to say scales lower than Plank length cannot exist. Planck is not the smallest distance that exists; it is the smallest distance that is meaningful. I do not believe I have encountered any theory suggesting that there is a smallest distance that exists.
I am not certain there is a single book or article that addresses exactly what you're contemplating, but I strongly believe that you would find further study of Planck units to be very helpful.
>Zeno's """"paradox""""
more like
>Zeno can't into infinite sums
Shit moves that's all that matters
as distance to travel decreases so does proportionally time to travel it.
Ergo your infinite distances are covered by infinitesimal time slices, literally a convergent infinite sum.
all fucking idiots. kil yourselfs
No it proves that [math]\sum_{n=1}^{\infty}\frac{1}{2^{n}} = 2[/math]
If you want to prove that the universe is discrete and not continuous then what you have to do is to prove that at some point you couldn't do the next step.
If you want to move a 1kg object a meter you know what force you need.
What about 1/(2^10000) meters? That would be one of the steps. If you cannot find a force that will produce this motion then clearly the universe is discrete.
What about 1/(2^99999999999999999999999999999999999999999999) meters?
You would have to do it. Can you?
I'd say probably not, the universe is not continuous in my perspective.
People don't move by division. They move in finite steps. You don't walk 2 feet by going half the distance forever, you take a 1 foot step, then another
>If you cannot find a force that will produce this motion then clearly the universe is discrete.
lol
what if I find a force that moves 1 meter and another that moves 1 + 1/(2^10000) meters?
checkmate discretists
pretty shit argument desu
There is no fallacy.
Everything Zeno says is true if you stand at the point where the arrow lands. By moving the end before the end, you create the fallacy.
You can see the fallacy for what it is by slicing a loaf of bread whose size is unknown. How can you cut it in half if you don't know how big the loaf is to start?
How can the arrow travel half way if you don't know how far the arrow is going to go?
In math we call that convergence and divergence.
The world is neither discrete nor continuous. Those are both stories of the world. Your story of the world can be either depending upon the intent of the story.
>force corresponds to distance of travel
fyi, F=ma
>mathematical concepts can't describe the real world
That's what you sound like.
Forces aren't required to move objects. Only to accelerate them.
You can move any object any distance by applying a force to accelerate it forward, then apply the same force to decelerate it to a stop.
Your argument employs a fundamental lack of understanding
>what if I find a force that moves 1 meter and another that moves 1 + 1/(2^10000) meters?
Uhh... then that would evidence of continuity. You would need to keep subdividing though.
I think you did not understand my post.
Things are either discrete or continuous. What you are saying is like saying there exists a number that is not even nor odd.
Yeah but how are you going to move an object without applying the force?
The point is still stands, can you actually keep subdividing distances infinitely and move objects those exact distances?
>how are you going to move an object without applying the force?
The net force is 0
I did equilibirum and mechanics in high school too, autist.
Why are you focusing on that shit and not on the fucking point?
>Uh, your post is not reflecting exactly how these things happen so uhh I cannot get it
Fucking hell.
I'm even the guy you were arguing with but please just stop posting. you're only embarressing yourself
>Yeah but how are you going to move an object without applying the force?
without a force applied an object can either stand still or have constant velocity, which is actually is matter of frame of reference.
force does not directly correspond to distance, but to acceleration, namely you can apply 1N of force to an object and it will in fact travel an infinitesimal distance in, respectively, infinitesimal timespan
not even*
Okay.
You apply a force to the object that moves it n meters per second.
Then you want to STOP IT after the second to you apply the same force to the opposite direction.
Then you want to apply ANOTHER smaller force that will make it move n/2 meters per second.
Then repeat.
Are you even picture the scenario here? Are you literally autistic?
You need to find differences forces because if you just make the object move and have it continue moving, presumably in a vacuum, then you are not really proving anything about distance.
>You need to find differences forces
what the fuck?
>You can't move a crate with a forklift one meter
>you have to move it half a meter
>then brake
>then get into a smaller forklift
Philosophers, not even once.
>he doesn't know that force equals mass times acceleration
>calls me autistic
ok m8
>Are you even picture the scenario here?
in spite of your extreme incompetence, interestingly, I can
and as we are speaking in abstract concepts, I see no lower bound for force value, just as I don't see the upper
>You need to find differences forces because if you just make the object move and have it continue moving
>make the object move and have it continue moving
>in vaccum
let F be force applied to the object of mass m for time t, resulting in movement of velocity v
F=ma
a=F/m
v=a*t=Ft/m
in vacuum you only need to apply F for time t to make the object move, and the velocity from the moment you stop applying the force moves at constant velocity
correction
>and the OBJECT from the moment you stop applying the force moves at constant velocity
I've always thought so. And doesn't the fact that we have a Planck length back that up?
planck length is defined in classical physics only as a smallest measurement of length possible
measurement, not the actual value
anyhoo, this guy right here tells it much better than I do
physics.stackexchange.com
Not even that, it's just a unit of length defined using fundamental constants. It's maybe within a factor of 10 of the smallest measurable length.
There's no known significance of the length just yet but it's a useful to bring up if you want to talk about things in terms of a VERY small length.
Btw people, quick question. Is nuclear energy quantized? Its not a result of electrons movement
it's being released in distinct amounts, so yes it is quantized
let there be abstract nuclear reaction
A = B + γ, where γ is the photon
E(γ)=m(A)c^2 - m(B)c^2
there we have defined the amount of energy released in a singular nuclear reaction
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sorry... hit the wrong post to reply to.. was aiming for one above... guy just trying to reduce the problem to "language", being insulting, and not explaining any argument. Your response solves the dilemma conceptually, but I think it sidesteps the issue, Of course the laws of physics do not exclude infinite intervals in finite time... they don't exclude quantized distance either. where does that leave us? who has the burden of proof? I dunno