Will a continually shrinking sphere ever arrive at a situation where the length of the radius is equal to zero?
Yes
No
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Will a continually shrinking sphere ever arrive at a situation where the length of the radius is equal to zero?
That depends -- does it shrink linearly ("it shrinks by 1 cm per hour") or does it shrink exponentially ("it halves its radius each hour")?
Logically? No, because if it did have a radius of zero it would stop shrinking and also stop being a sphere. Thus it would not be a "continually shrinking sphere."
Mathematically? No, because "continually shrinking" implies it would reach zero only after an infinite span of time and "ever arrive" implies a finite endpoint.
Physically? No, because a length of zero does not exist in the universe. This has not been experimentally verified yet, but nevertheless the theory that space is quantized (divided at the smallest scale into units) is highly likely. A universe with quantized space would have a "minimum size" which is greater than zero.
Right!
What you're saying seems to me to be the case. But...
At the foundations of modern quantum theory are implicit mathematical assumptions like that the radius will arrive at zero. These assumptions produce infinities in the equations and those infinities are then 'treated' by mathematical techniques called 'renormalization.'
They never measure an infinite mass. They never measure an infinite charge. There are no infinite lengths or infinite velocities being measured. As I see it the infinities only enter the equations because of logical errors in the mathematical interpretations.
A surprising number of physicists, including multiple Nobel Prize winners, seem to accept what appear to me to be faulty and illogical assumptions.
http://i.imgur.com/hqu3iiB.png
Last edited by Haba Aba Daba Aba; 03-20-2017 at 05:51 AM.
by this logic a boy would never become a man because he would no longer be a boy! lol
if you are going to interpret the question as something other than a semantic trick, then you have to accept the continuity of the sphere as it becomes a point, just as we believe the man is the same person as the boy
the answer, then, to the question is, yes, if you shrink the sphere so it no longer has a radius then it becomes a pointa sphere is a mathematical object and is, therefore, not bound by the laws of physics--ie, a sphere can have an arbitrarily small radiusWhat you're saying seems to me to be the case. But...
At the foundations of modern quantum theory are implicit mathematical assumptions like that the radius will arrive at zero. These assumptions produce infinities in the equations and those infinities are then 'treated' by mathematical techniques called 'renormalization.'
They never measure an infinite mass. They never measure an infinite charge. There are no infinite lengths or infinite velocities being measured. As I see it the infinities only enter the equations because of logical errors in the mathematical interpretations.
A surprising number of physicists, including multiple Nobel Prize winners, seem to accept what appear to me to be faulty and illogical assumptions.
http://i.imgur.com/hqu3iiB.png
Something that is ever shrinking would shrink for infinity.
For the object to shrink to infinity, it must exist to infinity.
If a radius of zero implies that the object no longer exists, or is no longer respective to its defining characteristics, then it has stopped ever shrinking, for it cannot do so without existing.
Therefore, I would answer: No.
Analogously speaking,
Would an immortal being ever die?
Reality: no, Planck length sets a minimum size of objects, which it could never be smaller than. A black hole does have width, for example.
Theory: no, it may reach an infinitesimally small radius without reaching zero. (If it would reach zero it would become a point instead: a 0-dimensional object.)
What exactly did you think would happen if it did hit zero? Suddenly convert from a 3-dimensional object into a 0-dimensional one?
"continually" doesn't usually mean "forever" or "without end"...for example, the sentence, "the road was continually in disrepair the last two years" means the road was "in disrepair, intermittently, over the last two years"...likewise, "continually shrinking" means shrinking at regular intervals of time...for "continually" to mean "forever", the sphere has to shrink in such a way that the radius never reaches zero even after innumerable shrinking intervals...an example of such a sequence is zeno's paradox where each interval reduces the radius by one half; here, the radius can never be zero since each step only gets you halfway therecontinually
adverb
1. very often; at regular or frequent intervals; habitually.
2. without cessation or intermission; unceasingly; always.
failing such a pattern, a finite number of shrinking intervals--"continually shrinking the sphere"--will reduce the radius to zero
Last edited by ae1905; 03-20-2017 at 01:30 PM.
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