Jump to content
Objectivism Online Forum
AllMenAreIslands

Of what does Space consist?

Rate this topic

Recommended Posts

Regarding the position of quantum mechanics stating that every particle has a non-zero probability of being anywhere; one ought not to confuse a potential with an actual, so saying each particle is spread out over all of space doesn't follow.

No potential is involved, only actuals. Every particle is spread out over all space. That is what fills the "full plenum".

Fully consistent application of the metaphysical principle that there are no actual infinities leads to the following reasoning.

An electron can be considered a point particle on the basis that it has no detectable internal structure and at large enough distances the away from it both the mass and charge are equivalent to a point source. But this is an approximation of convenience. It can't possibly actually be a point particle because it would have an infinite mass density and charge density. Therefore an electron must have an extent in space.

This principle also applies to the boundary of an electron. A sharp rigid boundary would also be an infinitesimally thin space with a fixed amount of mass or charge within it. This is another infinity that cannot exist. In mathematical terms there can be no discontinuity in the first derivative of the mass or charge distribution. So not only must an electron have a non-zero extension, its mass and charge must shade off toward zero only gradually.

At great distances the mass and charge can only approach zero asymptotically and never quite reach it, or there would again be a discontinuity.

This reasoning produces a picture in agreement with experiment and the quantum theory.

Share this post


Link to post
Share on other sites
Well, this is not primarily a physics thread, but the electromagnetic rope theory has no facts to back it up. That is, there is no evidence that there are these electromagnetic ropes. The guy presenting that theory brings up interesting points about current theory, but saying all atoms are interconnect by ropes doesn't solve the problems, and there is no evidence to support his theory. Besides, how are the particles supposed to be pumping energy into the system of threads as he indicates?

Added on edit: Besides, there is a glaring contradiction to the tension theory. For anything like a rope or rubber bands under tension, the further apart the two such tied together entities are moved the higher the tension gets -- i.e. the harder they pull together. This is quite the opposite of what is observed -- that gravity gets weaker when two things are pulled apart; likewise with magnetism, the further apart one pulls the magnets, the less attracted they are to each other. So, the tension idea is out, as it contradicts observation.

But getting back to the theme of this thread, I'm glad your realize there is no nothing ;)

I hope you are not always so quick to say "X is out" before you understand it.

In response to your first question about "no evidence". There is no evidence of photons, wave packets, waves, electrons, protons, etc. I see the computer in front of me and a table. If I look very closely I may see little balls and call them atoms. Nobody has ever seen a single electron, photon, graviton, or a magnetic "field". Everything else, the particle models of electrons, protons, and light, and the wave models, are purely hypotheses. They are assumed to exist in order to explain some image on a plate, some reaction, etc. This is what we do in science, we pose structures to explain natural phenomena.

You are not yet understanding the theory. In response to your question "how particles pump energy into the system of threads" there are 2 more videos that begin to address this question:

The "glaring contradiction" is a misunderstanding of the theory. The rubber band analogy is not used to illustrate the theory but to help convey the concept of tension. It's a bad analogy in my opinion. Gaede doesn't always do the best job and there are some things I disagree with, so let me clarify as I do not want you to be misled. This is the "physics and mathematics" forum and, I believe, the question of this thread is either trivial or is about what unseeable/invisible entity intervenes between two visible entities to cause the effects of gravitation, magnetism, etc.

Consider any thread or rope of your everyday life. It is self evident that, when you coil this into a loop, it will straighten itself back out if nothing acts to stop it. This is best seen with a particularly stiff thread. Less stiff ones work too, but it is not as evident because their own weight/inertia keeps them coiled against the stiffness/tension that would normally re-straighten it.

Now, the way to visualize an atom under the rope hypothesis is as a loop in a thread. This thread does not have any "weight" because weight and inertia are properties of the atom by virtue of how they interact via the thread. The looped/coiled thread of the atom has a tension on it, as any entity which is not straight would. Therefore it is trying to straighten itself. However, since the ends of the thread are not "free" but rather attached to other atoms, all it can do is pull on every other atom. The thread does *not* stretch like a rubber band. It is purely the tension of the loop that is pulling. The increase of this pull with decreasing distance is a simple matter of geometry. As two objects approach each other the angles the interconnected rope makes with all the atoms increases. You can imagine that two loops in a stiff wire, connected by a rope in between, will not affect each other because there is 0 angle. As objects become very far apart the ropes become nearly parallel to a line through the centers of the two objects, and the angle approaches 0. There is always some constant amount of pull between any two objects because of the tension in the loops, however, so no matter how far you are away from an object such as a star there is some finite pull on you.

With magnetism, the model presented in the video fits perfectly.

Share this post


Link to post
Share on other sites

In response to "there is something there everywhere".

The reason for this is that shape precedes location. We can imagine all kinds of shapes that do not have location. Any image I conjure up in my head is a shape without location. But it is impossible to imagine or conceive of location by itself. The concept of location demands an object. Saying there is something everywhere is analogous to saying all objects that exist have location.

In response to quantum and the indeterminacy principle:

This is a simpler problem than most realize. The issue here is that location is a static concept and velocity (and by extension momentum) is a dynamic concept. Therefore, at an instant (a specific precise location) velocity is undefined. I don't mean it's 0, I mean it is entirely undefined. There is no concept of velocity without *at least* two locations. On the other hand the location of a movING object is entirely undefined. Of course, a moving object does not have *a* location. Where's a moving ball? The quantum uncertainty principle is simply saying that, when an object moves it doesn't sit still and when it sits still it doesn't move. The quantification of both location and velocity is a matter of assigning each of these "average" values based on a mathematical framework that fits observations (and thus correctly correlates the motions of objects). An object that moves from A to B is assigned some "average location" parameter, the simplest way would be to just give it location (A+;)/2. It is quite obvious that as the distance-traveled (A-B) becomes large this "average location parameter" describes the physical situation much worse. Imagine glimpsing a race car once, then again a mile down the road. You have two locations (0,1). At each of these locations you have no idea what the velocity is, you only know that it traversed a distance 1 in a single "unit time". So you say its velocity was 1 at location 0.5. Or you could report exactly what happened, that it went from 0 to 1, but then again you don't have a single location parameter (which is what quantum drives at). Then one objects "but it's velocity is precisely defined", but it isn't. All you have are two locations. You don't know if the object accelerated or decelerated. You are *assuming* it moved uniformly between the two measurements and thus assigning it a velocity, which is really just an "average velocity" unless the object really did move *perfectly uniformly* from A to B.

Supernatural interpretations like Copenhagen and "infinite extent" of objects are the result of too much math, too little logic, and a poor (or nonexistent) philosophical foundation.

The reason that, in a classical sense, there is no theoretical upper limit to accuracy has to do with the mathematical models of light of the time. Light was a continuous entity in the 19th century. Therefore, at any 2 instants I can take a measurement (via light) and record 2 locations. If I think my accuracy is not good enough I can measure between shorter and shorter instants, as long as I want until I'm satisfied. This is because, again, my method of observation is *continuous*. There is no fundamental limit to the interval between observation/detection of light emitted by the object under study.

On the other hand, in quantum, light is a discrete entity. It comes in discrete units quantified by h. Therefore when we take a measurement the best we can do is detect 2 "photons" and record the two locations they indicate. That's as good as it gets. We have to wait for the next "unit" of light to come along and tell us where the object ended up. This places a theoretical upper limit on the degree of accuracy we can attain, at least by measurements with light. Indeed you'll hear a lot of quantum mathematicians state that the indeterminacy principle "has to do with bouncing a photon off the object you're observing".

So it comes as no surprise that the fundamental upper limit on measurement accuracy is defined in terms of the fundamental unit of light, quantified by h, since light is how we do most of our measuring/observing.

Share this post


Link to post
Share on other sites
In response to "there is something there everywhere".

The reason for this is that shape precedes location. We can imagine all kinds of shapes that do not have location. Any image I conjure up in my head is a shape without location. But it is impossible to imagine or conceive of location by itself. The concept of location demands an object. Saying there is something everywhere is analogous to saying all objects that exist have location.

It cannot be that shape precedes location because shape is simply a description of the locations of the parts an entity.

You are *assuming* it moved uniformly between the two measurements and thus assigning it a velocity, which is really just an "average velocity" unless the object really did move *perfectly uniformly* from A to B.

Are you seriously proposing that the first law of motion is wrong?

Instantaneous velocity is undefined? What is wrong with defining it as the ratio of distance traveled per time interval in the limit as the time interval approaches zero? Are we all deceived by our calculus texts?

As for "infinite extent" of objects, if in one's philosophy the Universe is finite then the extent is not infinite.

Share this post


Link to post
Share on other sites
It cannot be that shape precedes location because shape is simply a description of the locations of the parts an entity.

A description of locations of parts? So we needed the parts first in order to describe their location. Without the parts (with shape) we could not describe these locations. Shape comes first. We can imagine shape without location but not vice versa.

Are you seriously proposing that the first law of motion is wrong?

Are you proposing that the situation described in the 1st law (an object in motion is not acted upon) is ever reflected in reality?

Instantaneous velocity is undefined? What is wrong with defining it as the ratio of distance traveled per time interval in the limit as the time interval approaches zero? Are we all deceived by our calculus texts?

Perhaps you are deceived by your calculus text into thinking something can move without moving because you have not thought on the matter carefully. You said velocity is "ratio of distance traveled per time *interval*". A distance-traveled necessarily invokes TWO locations and a time interval necessarily invokes TWO times. Instantaneous is a SINGLE time and a SINGLE location. Instantaneous velocity is an explicit contradiction, the two words are mutually exclusive.

The derivative is the change in location with time as the change *approaches* 0, never when it is 0! Infinitesimal is NOT zero. To equivocate the two is reification of 0.

As for "infinite extent" of objects, if in one's philosophy the Universe is finite then the extent is not infinite.

Grames, we're talking about ONE object here, not every object that exists (universe). Every object is finite because it has shape. This is self evident and ubiquitous, besides being the only definition of "thing" that can be used consistently.

Edited by altonhare

Share this post


Link to post
Share on other sites
Instantaneous velocity is an explicit contradiction, the two words are mutually exclusive.

That statement is false, and contradicts what is taught in every calculus and physics class. Let X(t) be the position of an object at time t. Then the velocity of that object at time t, V(t), is defined as follows, where the limit is calculated as dt goes to 0:

V(t) = (lim X(t+dt) - X(t))/dt

As an example, suppose that X(t) = ct for all t. Then V(t) = c for all t. In that case the object has constant velocity equal to c at each moment in time.

As another example, suppose that X(t) = ct**2 (where "**" indicates exponentiation). In that case V(t) = 2ct. At time 0 velocity is equal to 0. At time 1 velocity is equal to 2c. At time 2 velocity is equal to 4c. Obviously the object is accelerating as time progresses.

The concept of instantaneous velocity is made possible by the calculus which was developed by both Newton and Leibniz several hundred years ago. The concept of velocity ("instantaneous" is redundant) is well-defined, fundamental to physics, and not at all controversial. It contains no contradiction.

For further information, look here:

http://en.wikipedia.org/wiki/Velocity

http://en.wikipedia.org/wiki/Differential_calculus

http://en.wikipedia.org/wiki/Calculus

John Link

Edited by John Link

Share this post


Link to post
Share on other sites

Also, quantities derived from veloccity such as energy and momentum are real and conserved, why would we need a conservation law for nonsense?

How could general relativity work if at any given instant velocity was undefinable?

Share this post


Link to post
Share on other sites

John,

"contradicts what is taught in every calculus and physics class"

Am I in the right forum? I thought this was objectivism, where we think for ourselves. Most calc/physics classes aren't taught by objectivists, nor are they even often taught by people with a strong capacity for reason.

Motion: TWO or more locations of an object

In calculus we examine when these locations because arbitrarily close, the difference becomes infinitesimal. Never zero!

In science, motion demands a minimum of 2 locations. "Instantaneous" implies a single "time", i.e. a single location. Instantaneous motion (or velocity) is contradictory. What is meant by this term is "infinitesimal motion".

"is calculated as dt goes to zero"

Right, never at 0. Just try evaluating it at 0... you always get 0, obviously.

"The concept of velocity... is well defined"

Of course it is. Instantaneous velocity is the contradictory term, velocity is fine.

For future reference you can spare me the freshman calc/physics lectures.

Grames:

I'm not sure what you mean by GR "working", but the differential equaitons involved are dealing with, as I said, infinitesimal motion. Not instantaneous motion. Instantaneous motion is a contradiction in terms.

Motion (2 instants):

---------

00

---------

---------

0 0

---------

Motionless (1 instant, "instantaneous"):

---------

0

---------

Edited by altonhare

Share this post


Link to post
Share on other sites
Motion: TWO or more locations of an object

In calculus we examine when these locations because arbitrarily close, the difference becomes infinitesimal. Never zero!

In science, motion demands a minimum of 2 locations. "Instantaneous" implies a single "time", i.e. a single location. Instantaneous motion (or velocity) is contradictory. What is meant by this term is "infinitesimal motion".

"is calculated as dt goes to zero"

Right, never at 0. Just try evaluating it at 0... you always get 0, obviously.

While X(t+dt) - X(t) is equal to 0 when dt is 0, the velocity is defined as the limit of the ratio of X(t+dt) - X(t) divided by dt as dt goes to 0. If we let dt=0 then we have (X(t)-X(t))/0 = 0/0, which is not defined. However the limit of (X(t+dt) - X(t))/dt as dt goes to 0 is defined for many functions X. I gave two such examples in my previous post, one with constant velocity and one with constant acceleration. To repeat the definition I gave in my previous post, the velocity at time t (i.e., the instantaneous velocity) of an object whose position is given by the function X(t) is defined as follows:

V(t) = lim [(X(t+dt) - X(t))/dt] as dt goes to 0

There is no need to use the concept infinitesimal in order to define the concept of instantaneous velocity, but we do need the concept of limit. You can find the definition of limit here: http://en.wikipedia.org/wiki/Limit_of_a_function

Edited by John Link

Share this post


Link to post
Share on other sites
If we let dt=0 then we have (X(t)-X(t))/0 = 0/0, which is not defined.

Exactly. Velocity "at an instant" is undefined, precisely as I said.

"Instantaneous" velocity/motion of an object:

-----

0

-----

Motionless object:

-----

0

-----

So "instantaneous" velocity is the same as "motionless"?

Moving object:

-----

0

_0

-----

Any questions?

How is the concept "motionless" anything like the concept "motion"? How is the concept "location" anything like the concept "velocity"? Motion and motionless are conceptual opposites. "Instantaneous velocity" makes no more sense than "downward up" or "square circle".

Differentiation "works" because you start with an equation that expresses at *least* two values of the dependent and independent variables. x=k*t+b expresses as many values as you care to plug in. Just try to take 4=k*3+1 and get a velocity. You cannot, because this expression gives you only ONE location at ONE instant. On the other hand the expressions: 4=k*3+1 ; 5=k*4+1 gives you TWO instants. Now you can calc a velocity = 1. The object WAS at 4, then it WAS at 5.

What if you make dt (or dx) equal 0? Let's see: 4=k*3+1 ; 4=k*3+1. Velocity = 0/0, i.e. undef

This is elementary level stuff. Something does not move when it sits still and it doesn't sit still when it moves.

Share this post


Link to post
Share on other sites
Exactly. Velocity "at an instant" is undefined, precisely as I said.

Yes, (X(t)-X(t))/0 = 0/0 which is undefined, but that is NOT the definition of velocity.

Altonhare, it appears to me that you are not interested in having a rational discussion but rather only in arguing your point regardless of how thoughtful a response you might receive. I am therefore no longer interested in continuing this discussion with you. If you are really so convinced that instantaneous velocity is an invalid concept then I suggest you publish an article to that effect in journals of physics and mathematics so that no more students will be subjected to the irrationality introduced by Newton, Leibniz, and the generations of mathematics and physics professors since their time.

John Link

Edited by John Link

Share this post


Link to post
Share on other sites
Yes, (X(t)-X(t))/0 = 0/0 which is undefined, but that is NOT the definition of velocity.

Altonhare, it appears to me that you are not interested in having a rational discussion but rather only in arguing your point regardless of how thoughtful a response you might receive. I am therefore no longer interested in continuing this discussion with you. If you are really so convinced that instantaneous velocity is an invalid concept then I suggest you publish an article to that effect in journals of physics and mathematics so that no more students will be subjected to the irrationality introduced by Newton, Leibniz, and the generations of mathematics and physics professors since their time.

John Link

How about this. Define "instantaneous" and "velocity" such that "instantaneous velocity" is not an oxymoron.

Share this post


Link to post
Share on other sites
Am I in the right forum? I thought this was objectivism, where we think for ourselves. Most calc/physics classes aren't taught by objectivists, nor are they even often taught by people with a strong capacity for reason.

If you think Objectivism or objectivists have a monopoly on being able to perceive, conceptualize, and reason you are mistaken.

Your idea of instantaneous velocity is also wrong. The method of dividing zero distance by zero time is naive, and unphysical. For a moving object, the principles of conservation of energy and momentum constrain the possible values for instantaneous velocity to a real and non-zero value. How to compute that value and avoid dividing zero by zero is what Newton and Leibniz figured out. Your lack of understanding of their mathematical innovation is not their failure, it is yours.

Share this post


Link to post
Share on other sites
If you think Objectivism or objectivists have a monopoly on being able to perceive, conceptualize, and reason you are mistaken.

Your idea of instantaneous velocity is also wrong. The method of dividing zero distance by zero time is naive, and unphysical. For a moving object, the principles of conservation of energy and momentum constrain the possible values for instantaneous velocity to a real and non-zero value. How to compute that value and avoid dividing zero by zero is what Newton and Leibniz figured out. Your lack of understanding of their mathematical innovation is not their failure, it is yours.

You are failing to think in the most essential language. I have not claimed to "debunk" the equations nor disagree with their practical value.

Just because some celebrities and/or "learned men" uttered these sounds "instantaneous velocity" or inscribed these symbols on paper, are they now sacrosanct? Of course not. In order to learn something we have to think in the most essential language.

Newton and Leibniz may have been rigorous in their mathematics, but they were loose with their language. They did not care to define their terms because they were not interested in the *qualitative* aspects of their work, but only with the quantitative aspects. They worked out the quantitative aspects perfectly, but missed the translation into the qualitative language of physics. They have perfect rationalism but without reason, i.e. they did not connect their logical framework to physical essentials.

Object: shape

Motion: Two or more locations of an object

Instantaneous: Static, a single location, 0 "time", motionless

Velocity is the measurement/quantification of motion. Therefore velocity requires at least two locations of an object. Instantaneous motion/velocity is an oxymoron.

On the other hand:

Infinitesimal: Arbitrarily small, the act of incessantly reducing some measurement, etc.

Infinitesimal velocities are fine. We are saying, here, that we can measure the object's two locations as close as we want.

Is the logical statement x=0 the same as the statement x->0? In the latter case x is always finite, no matter how small we imagine it. These statements are explicitly, qualitatively different.

Newton and Leibniz (and others that came before them, less formally) calculate the velocity as the change in location GOES TO 0, never when it is 0! Never ever! Newton himself would scoff at calculating velocity without at least 2 locations, i.e. calculating the velocity of something motionless. They simply confused "infinitesimal" with "0". But it's exactly this distinction which makes their calculus possible in the first place. They didn't truly understand the physical, qualitative connection.

Share this post


Link to post
Share on other sites
Instantaneous: Static, a single location, 0 "time", motionless

This is your mistake. Here you assert that a ratio of zero distance divided by zero time is equal to zero velocity. The proper answer is "does not compute", "undefined", ∞. "Static" and "motionless" have no meaning referenced to zero time.

Share this post


Link to post
Share on other sites
This is your mistake. Here you assert that a ratio of zero distance divided by zero time is equal to zero velocity. The proper answer is "does not compute", "undefined", ∞. "Static" and "motionless" have no meaning referenced to zero time.

Show me where I ever said such a stupid thing as "0 dist divided by 0 time equals 0 velocity". I, and others in this forum, maintain that it is as you said, "undefined, does not compute, etc."

Static and motionless mean a single location of an object, as opposed to dynamic/motion which is 2 or more locations of an object. I put time in quotes in this definition intentionally because, in fact, as you pointed out "time" is actually undefined without motion. I'm glad you understand so well! Instantaneous velocity is a self contradiction and an oxymoron.

Share this post


Link to post
Share on other sites
Show me where I ever said such a stupid thing as "0 dist divided by 0 time equals 0 velocity". I, and others in this forum, maintain that it is as you said, "undefined, does not compute, etc."

Static and motionless mean a single location of an object, as opposed to dynamic/motion which is 2 or more locations of an object. I put time in quotes in this definition intentionally because, in fact, as you pointed out "time" is actually undefined without motion. I'm glad you understand so well! Instantaneous velocity is a self contradiction and an oxymoron.

No, over a zero time interval the even words "static" and "motionless" are meaningless, as well as velocity. Over a zero time interval there is no measureable difference between any objects moving at any speed, or at no speed at all.

Share this post


Link to post
Share on other sites
You are failing to think in the most essential language. I have not claimed to "debunk" the equations nor disagree with their practical value.

The words "instantaneous velocity" are the best, most precise words, and they fully, accurately and correctly capture the intended qualitative meaning. A meaning built up inductively, not brought down to earth rationalistically.

The words "instantaneous velocity" are fully intended to convey the opposite meaning of "average velocity."

The instantaneous velocity of an object is, for some particular moment in time, the exact velocity of that object at that exact instant in time.

Isaac Newton figured out how to define it and calculate it with impeccable precision.

Share this post


Link to post
Share on other sites

For those still struggling with the idea of space not being a physical 'thing', but rather a mathematical 'thing' (in the same manner that a set, group, etc. is):

Quarks have a property called 'color charge'. A quark can be either red, green, or blue. (And an anti-quark is anti-red, anti-green, or anti-blue.) There are several mathematically ontologies one can assume when dealing with the three different colors of quarks. The first is that the 'color charge' labels entirely different particles. There are red up quarks, blue up quarks, and green up quarks, and each is an entirely different kind of particle. Another ontology has that there is one particle called an 'up quark', and the up quark can have a color of either red, green, or blue. And, of course, since this is quantum mechanics, any superposition of the three works, too. The quark is described as being in a "color space", with positions along a 'red' axis, 'blue' axis, and 'green' axis. All that's required of the position is that its distance from the origin is 1 (normalization), a mathematical way of saying the quark has exactly one color, even if that color is a mix of colors. And, of course, the space can be rotated about so that red becomes blue, or green. You get the same physics, just what you call what color changes. This "color space" is not a physical entity, though. It's just a geometric, intuitive way of picturing this stuff in our heads. There is no fluid or aether or whatever permeating it, whatever that means. Because you have, say, a red quark, a blue quark, and a green quark (together forming a proton), doesn't mean you have to have something at every point in the color space between each of the quarks. And the fact that it doesn't mean this doesn't imply that there's some weird, spooky non-entity called a "nothing" between them either. If you're arguing about entities/non-entities called "nothings", you're just playing with words rather than discussing anything meaningful.

Four-dimensional spacetime is more complicated because of its direct link to what we consciously perceive. There isn't a set origin, positions in it don't have to be normalized, etc. (And, in quantum field theory, space is a parameter rather than an observable anyway.) But similarly to the quarks, you can use multiple ontologies. Say you have the electromagnetic field (of which photons are excitations). You can say that there isn't one electromagnetic field defined everywhere, but instead infinitely many different kinds of particles, each one defined only at one point in spacetime. And a given observed photon could then be a superposition of different kinds of particles. But that's not the way we do things. Instead, we say that a photon is a photon regardless of where it is, so the photons we observe (which are wave packets, and have extension over space) are in a superposition of different positions. We consider position a property of the particle, just like color a property of the quark, and can build a 'space' from it. Just because one 'photon' (say a hypothetical photon with a definite location, rather than a real photon with extension over space) and another 'photon' are at positions with a finite distance ('distance' being a mathematical notion, not a physical object) between them doesn't mean there's some sort of object, fluid, aether, "nothing", whatever between them. There's no logical way to derive that there is. There are no laws of physics saying there is.

Share this post


Link to post
Share on other sites
No, over a zero time interval the even words "static" and "motionless" are meaningless, as well as velocity.

Motionless is defined as one location of an object. Static is just a synonym. It is the conceptual opposite of motion.

Over a zero time interval there is no measureable difference between any objects moving at any speed, or at no speed at all.

You're not getting it. This is not an issue of measuring, this is an issue of definitions. zero "time interval" is another way of saying a single location. There is not motion at a single location by definition. There is no "time" without motion either, by definition.

0

vs.

0

_0

How hard is this?

y_feld, do you have any justification for anything you said? Can you define "instantaneous" such that it is not contradictory with "motion" or "velocity"?

You said:

"The instantaneous velocity of an object is, for some particular moment in time, the exact velocity of that object at that exact instant in time."

Can you possibly illustrate for us velocity at an instant? Is this velocity:

0

???

Or is this:

0

_0

???

If you can visualize an object moving without moving, two instants in a single instant, you must have special eyes.

Share this post


Link to post
Share on other sites

Velocity -- the rate at which the position of an object changes as time progresses.

To say that an object has a velocity is to say that the position of that object is changing at a certain rate. Instantaneous velocity means that, at the instant in question, the position will change at a certain rate were time to progress from that instant. (And time progresses. I'd cite a source, but I think you can find one on your own.) It makes sense because the particle is at a different position (unless the velocity is 0) at any time before or after the instant in question, regardless of how little before or after.

Don't like derivatives? Don't like calculus? Feel free to go back to the 16th century.

Share this post


Link to post
Share on other sites
Motionless is defined as one location of an object. Static is just a synonym. It is the conceptual opposite of motion.

No it is not. If motionless is to have any meaning at all, it is the case of zero distance travelled over any time interval. If there is no time interval, then motion is by definition impossible and there is no way to apply the differentia of the definition of motion to distinguish between objects.

It occurs to me that you are making exactly the same mistake as old Zeno in Zeno's Paradox, which "proved" that motion was impossible. Only in your version, you slice time up into ever smaller intervals and then say for a time interval of zero nothing can move. You are not so brave as Zeno to follow your logic to its forced conclusion that motion is impossible, but it has been done already in Zeno's fletcher's paradox:

The arrow paradox

“ If everything when it occupies an equal space is at rest, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless. ”

—Aristotle, Physics VI:9, 239b5

In the arrow paradox, Zeno states that for motion to be occurring, an object must change the position which it occupies. He gives an example of an arrow in flight. He states that in any one instant of time, for the arrow to be moving it must either move to where it is, or it must move to where it is not. It cannot move to where it is not, because this is a single instant, and it cannot move to where it is because it is already there. In other words, in any instant of time there is no motion occurring, because an instant is a snapshot. Therefore, if it cannot move in a single instant it cannot move in any instant, making any motion impossible. This paradox is also known as the fletcher's paradox—a fletcher being a maker of arrows.

Whereas the first two paradoxes presented divide space, this paradox starts by dividing time - and not into segments, but into points.

Refutation of Zeno is left as an exercise for the student. But if you count yourself as satisified to take Zeno's side in this dispute, I will refuse to correspond with you any further as you would have demonstrated yourself beyond the reach of reason.

Share this post


Link to post
Share on other sites

Grames,

You said motionless is "0 distance-traveled over any time interval". The problem is, the term "time interval" invokes motion. How did you measure this time interval? You watched a clock hand, or a photon went from an atom to your eye, or whatever. Therefore, the object in question moved relative to *something* (the clock hand, the photon, etc.) even though it may not have moved relative to your ruler.

In order for an object to have 0 velocity relative to anything (like a ruler) it must have a finite velocity relative to something (like a clock hand). The object it physically at TWO locations and may have 0 velocity relative to the ruler but not relative to everything! Ironically in order to have 0 velocity relative to anything an object must have a finite velocity relative to something. Which of course means it's not motionless, by definition.

No I am not falling into the Fletcher's paradox. That's moronic and I don't even care to go into the fallacies in it.

I reiterate. Motionless is defined as ONE location of an object. That's it. As soon as you say anything about a "time interval" you are invoking motion (2 locations) and the object is no longer motionless by definition. Saying anything about "time interval" or "0 velocity" in the definition of "motionless" is a nonsensical contradiction. Both of them imply that the object in question is moving relative to something.

Share this post


Link to post
Share on other sites
Velocity -- the rate at which the position of an object changes as time progresses.

What is this "thing" you call time that is engaged in the action of "progressing"? Do you mean the clock hand is moving around? Or the atom is shooting a photon at your eye? Or the pendulum is swinging back and forth?

To say that an object has a velocity is to say that the position of that object is changing at a certain rate.

Absolutely! Change=rate=motion, the quantification of which we call "velocity".

Instantaneous velocity means that, at the instant in question, the position will change at a certain rate were time to progress from that instant. (And time progresses. I'd cite a source, but I think you can find one on your own.)

So the "instantaneous velocity" is the velocity an object *would have* if it is later at an infinitesimal distance from its current location? So we're talking about two locations, not one, i.e. location x and x+dx. We can make dx arbitrarily/infinitesimally small, but never 0! When dx=0 we are not dealing with motion or velocity anymore, but with the static concept location i.e. the object is at x. When dx>0 we have TWO locations x and x+dx and we are dealing with the dynamic concept motion and its quantitative counterpart velocity. Instantaneous, by definition, involves only one location. Therefore the so-called "instantaneous velocity" is a contradiction and is more aptly termed "infinitesimal velocity".

Instantaneous velocity: A single location of two locations of an object.

It makes sense because the particle is at a different position (unless the velocity is 0) at any time before or after the instant in question, regardless of how little before or after.

Of course! A different position/location is a second one. But this is not "instantaneous".

Don't like derivatives? Don't like calculus? Feel free to go back to the 16th century.

I'm sorry you must have had a terrible calc experience sometime. Your teacher probably didn't make clear the difference between dx=0 and dx>0.

Edited by altonhare

Share this post


Link to post
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now

  • Recently Browsing   0 members

    No registered users viewing this page.

×