An Infinite Numer of Objects?

To have a meaningful discussion... about either physics or "metaphysics" you need to define your terms. You haven't defined what "object" means.

There is a finite amount of "mass" in the Universe as a mathematical exercise, I guess you could keep dividing it infinitely...

But anything that could realistically be called an "object" by any definition of "object" I can imagine is made up of one or more atoms.

Atoms have a minimum amount of mass... so finite mass means finite atoms.

But without definitions of the words we are discussing, we will get nowhere.

Can we assume that an object must have at least one atom and finish with it?

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Mathematics would allow it, at least the mathematic interpretation that allows infinitesimals. Physics will not. When you get to the quarks and the leptons you are done. Also physics has no formalism that would allow you to call something with zero mass an object. So a finite number of objects in infinite parts are not allowed.

You can't have an infinite number of objects either. If you did you would have the problem that it would have taken MORE than an infinite amount of energy to create them. If that is the case then you have some daunting questions to answer. If there are an infinite number of particles what is the cardinality of that infinity? Is it the lowest order of cardinality, that of aleph naught, also termed aleph zero? Then what is the cardinality of the infinite energy, it would need to be greater than the cardinality of the infinit objects wouldn't it? So is it: continuum, the first inaccessible cardinal, the first hyper_Mahlo cardinal? Or a higher level? Which one? Why?

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Just noticed that the topic is "Infinite *Numer* of Objects". Ha! Maybe that's what's been causing all the confusion. Very Happy

In any case, I don't see why an infinitely divisible object would have "zero mass" (TheCorrectResponse). On the same post, why should we need more energy than is contained in a certain amount of matter to produce that matter? Finally, again it seems to me unreasonable to rule out parts of material objects physicists have yet to identity. But then IMHO physicists have been known to do unreasonable things. Very Happy

As for a definition of "object," I have none. But it is good luck for all of us that we can in fact have meaningful discussions without (explicit!!) definitions of our terms.

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You cannot keep dividing real objects, when you get to a quark or lepton you are done. If you aren't assuming current science I just took the position that since an object's mass isn't infinite eventually you would run out of mass, so zero mass. Since it can't be done in real life you are free to hypothesize that you would always have some mass even after infinite divisions.

If you are talking about real life you are stuck with a smallest size.

The reason it would require more energy than is contained in the total mass is because no process is 100% efficient you lose energy to the system, entropy increases.

One further problem in real life is even if you had an infinite amount of objects you could never know that. The universe has a mass/energy attribute called gauge invariance, meaning you can tell relative energy/mass amounts but never the absolute total in the universe.

If I had an infinite number of objects I know that I would have at least an infinite amount of energy equal to continuum or greater and that I can never know.

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"Infinity" sounds like a good explanation.

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"Great fleas have little fleas upon their backs to bite 'em, And little fleas have lesser fleas, and so ad infinitum. And the great fleas themselves, in turn, have greater fleas to go on; While these again have greater still, and greater still, and so on."
A. De Morgan Budget of Paradoxes

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The building blocks we're made of are of a certain size,
If we were made of smaller stuff the more we could . . . umm . . . dichotomize? . . . analyze? . . . (aw, nuts!!!)

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TheCorrectResponse wrote:

The reason it would require more energy than is contained in the total mass is because no process is 100% efficient you lose energy to the system, entropy increases.

So the total amount of energy in the universe - aka mass - is and must be decreasing...?

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No the total amount of mass/energy remains a constant, if you assume the universe as a closed system. You are talking about two different things.

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How can total mass/energy be the same if humans are able to estimate the life of our sun?

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There is a basic law of Physics.... Energy can Neither be created nor destroyed (let's ignore Relativity right now since the concepts without it are basically the same...).

This means the amount of energy in the Universe never changes. This is a basic law of Physics that we assume can never be broken (under Relativity we change the definition of energy to mass-energy but the law applies).

This is called the law of "Conservation" of energy.

Let's take the Energy "lost" by the inefficiency of an Engine first (since it is the easiest). The "lost" energy isn't destroyed... it is just "lost"... and in this case the energy that is lost is changed to unusable heat and sound.

So if you burn gasoline that has 100J (J is joules which is a unit of energy) and the engine is 20% efficient... this means that 20J of the energy will be used to do the desired work (i.e. moving the car).

But it is a law of Physics which has never been broken that the amount of Energy used to move the car, plus the amount of energy lost as heat, plus the amount of energy last as sound plus whatever little bit of energy I forgot about will equal exactly 100J

The Amount of energy before is exactly the amount of energy after... no matter what you are doing.

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Cicerone... to answer about the Sun...

The Sun has a lot of nuclear potential energy in to form of Mass (to talk about the Sun we need to use the ideas of Relativity, namely mass is energy, since this is a nuclear reaction).

However this energy isn't destroyed... it is merely converted to light.

Every Joule that the Sun's energy is decreased... means exactly one Joule is increased somewhere else.

The amount of energy stays the same.

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ebrown, Sorry, but I'm missing your point. If we use oil to use in our cars, and we burn it as "energy." It's gone. What is produced is carbon monoxide; not exactly equivalent to replacement "energy."

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No Cicerone... the energy is not "gone" it can't just be "gone" unless it goes somewhere. Energy can not be destroyed... it can only be converted into other forms of Energy... but the total amount of Energy is the same.

If you use "gas" (I am going to change your word "oil")... the energy doesn't disappear. It is converted in to three main areas.

1) The kinetic energy of the car.
2) Heat... which is sent into the air (you will notice your engine get hot).
3) Sound.
4) (there may a small amount to something I am not thinking about.

Kinetic energy of the car also doesn't disappear... as the kinetic energy of the car lowers (i.e. the car slows) the energy has be be converted into of forms of energy.

This is why when you use the brakes... the brakes get hot... the kinetic energy of the car is transformed into heat. The heat is then sent to the air.

Likewise the friction of the car as it goes through the air, or the friction of the wheels on the road converts the kinetic energy to heat or sound.

Ultimately the energy from the gas you burn gets converted mostly into kinetic energy and heat... then most of the kinetic energy gets converted into heat by friction.

But the amount of energy is always the same... every time you burn 100J of gas... it doen't disappear... it is just converted into 100J of other types of energy.

The amount of energy is always conserved.

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cicerone imposter wrote:

ebrown, Sorry, but I'm missing your point. If we use oil to use in our cars, and we burn it as "energy." It's gone. What is produced is carbon monoxide; not exactly equivalent to replacement "energy."

You are thinking of energy in terms of "fuel" but in Physics every piece of matter (and anti-matter too, I suppose...) is "energy" in one form or another. From that viewpoint, carbon monoxide is just as much a form of energy as gasoline.

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fishin wrote:

cicerone imposter wrote:
ebrown, Sorry, but I'm missing your point. If we use oil to use in our cars, and we burn it as "energy." It's gone. What is produced is carbon monoxide; not exactly equivalent to replacement "energy."

You are thinking of energy in terms of "fuel" but in Physics every piece of matter (and anti-matter too, I suppose...) is "energy" in one form or another. From that viewpoint, carbon monoxide is just as much a form of energy as gasoline.

fishin, Thanks for that clarification; my brain refuses to "see" things that are beyond the observable with simple explanations.

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All the objections here that I can think of concern an infinite number of objects existing at one time. As it turns out, the scenario I had in mind involves an infinite number of things existing over time: say from T1 to T10. And that is the curious thing about it: on the scenario you would have an infinite number of objects existing during a finite interval such as that between T1 and T10, although only a finite number of things existing at each time during the interval.

The idea is as follows. Time is said to be densely ordered if between any two times there is another. If time is dense then between any two times, there is an infinite number of times. Say time is dense. If one adds that every instant between T1 and T10 is occupied by some object, and that no object during the interval exists at more than one instant, you get an infinite number of objects during the finite interval.

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esmagalhaes wrote:

All the objections here that I can think of concern an infinite number of objects existing at one time. As it turns out, the scenario I had in mind involves an infinite number of things existing over time: say from T1 to T10. And that is the curious thing about it: on the scenario you would have an infinite number of objects existing during a finite interval such as that between T1 and T10, although only a finite number of things existing at each time during the interval.

The idea is as follows. Time is said to be densely ordered if between any two times there is another. If time is dense then between any two times, there is an infinite number of times. Say time is dense. If one adds that every instant between T1 and T10 is occupied by some object, and that no object during the interval exists at more than one instant, you get an infinite number of objects during the finite interval.

I thought I had addressed this earlier but apparently I had it in a draft response and cut it before posting but...

Yeah, there are two (at least!) ways of looking at your issue. If the objects are created and remain there through time then eventually you run out of mass to make more objects.

But if you reuse the mass then the possibility exists that an infinite number of objects could be created over time. This is the way our univerise operates with regard to the creation of stars, planets, etc...

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It still doesn't help you in a real world application. Again, processes aren't 100% efficient. You would eventually reach the point where entropy keeps increasing until you reach an equilibrium temperature where not enough energy exists in a usable form to keep creating your objects of infinity. What you are actually describing is one possible end scenario to the universe. It is called the heat death scenario.

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TheCorrectResponse wrote:

Again, processes aren't 100% efficient.

But the biggest process of all - the one that takes us from one complete state of the universe to the next - is, they say, 100% efficient, in the sense that both states have the same quantity of energy.

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An Infinite Numer of Objects?

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