Infinity.

[Holy Roller]

Cabal, the important thing to understand is that the U235 was split, and the mass of the two remaining elements ends up being less (<--- keyword) than the original U235 element. The missing mass was converted into energy. In order for the mass to turn into energy, though, the mass had to reach a state of "infinity" first, as expressed in the Lorentz transformations.

 

[ArnautDaniel]

Trinity was a 10K yield precisely because one element (uranium 235) was split into two elements (forgot which ones); their combined mass being less than that of the U235.
The missing mass is what turned into the energy that created that 10K yield. Thus, by looking at Trin's 10K yield and all its energy release, you are effectively looking at an infinite yield of that 0.1% uranium mass that was converted directly into energy. The remaining 99% remaining, finite mass ended up being those two new elements.

There's no "infinite yield" of anything.

A finite amount of mass went "missing" and a finite amount of energy went un-missing.

There are no infinities involved.

You are confusing the idea that an object with non-zero mass would have its apparent "mass" appear to approach infinity as its velocity approached that of light (and note, it never gets to go the speed of light so there is no infinity), with the fact that mass can be converted to energy.

These are entirely different things.

 

[ArnautDaniel]

Cabal, the important thing to understand is that the U235 was split, and the mass of the two remaining elements ends up being less (<--- keyword)than the original U235 element. The missing mass was converted into energy. In order for the mass to turn into energy, though, the mass had to reach a state of "infinity" first, as expressed in the Lorentz transformations.

It never reaches a state of "infinity" (whatever that means).

 

[Holy Roller]

Well given that we've had larger nuclear explosions since Trinity, I'd have to say that the explosion at Trinity was "finite" so that it is sensible to say we've had larger ones.

Here's what it looks like after Cheny stepped off the plane:

 

[ArnautDaniel]

Here's what it looks like after Cheny stepped off the plane:

So you try to hunt out atheists through public displays of a lack of understanding of science?

 

[Holy Roller]

You are confusing the idea that an object would have its mass appear to approach infinity as its velocity approached that of light (and note, it never gets to go the speed of light so there is no infinity), with the fact that mass can be converted to energy.

E=MC^2 and its role in fission.

 

[Radagast]

It's understood that mass turns infinite before it turns into energy.

 

[ArnautDaniel]

E=MC^2 and its role in fission.

Trust me, I know the relevant mathematics and physics.

There is no infinity involved.

You had an initial mass m1 a final mass m2 and some different dm > 0 so that:

dm = m1 - m2

That dm turned into an amount of energy e by:

e = (c^2)dm = (c^2)(m1 - m2).

The mass just disappeared, it never accelerated, it never reached an infinite state, it simply became an amount of energy. In fact it simply became the energy contained in the motion of the fissile products.

That is if the original atom had been stationary and then split into two moving fissile products then a certain amount of mass would have had to be lost to account for the kinetic energy of the products (seeing as the original atom had no kinetic energy).

Otherwise it would have split into two stationary products...which really wouldn't be a split since nothing would have moved at all really.

The speed of light enters in not as a velocity but as a constant of a particular relation.

In this case it simply reflects the fact that we chose our energy units and our mass units oddly. We should have chosen them differently so that we wouldn't need the speed of light at all. (In fact most theorists define the energy so that they can drop the constant c term in things like this).

 

[Radagast]

Well we are talking physics here and not mathematics.

Your notion for the naturals rests on some notion of a limit.

The equivalent in my analogy would be that given a particular well-defined event (sometime around "now" say) you could give a series of other events and consider the time interval between them and demonstrate that the time interval increases every time and so will never stop growing.

So since you've demonstrated a sequence of time intervals that never stop growing (and presumably aren't bounded either) you've demonstrated that time is "infinite".

Even then you have exhibited that time is "infinite" you've only exhibited a certain property of a certain sequences of time intervals between certain events for which every interval is finite.

Of course we are in the realm of physics and not of mathematics.

So you'd have to:

1. Tell me how on earth you are empirically ever going to define such a sequence of events

and

2. Assuming you could actually define the time interval clearly, how you are ever going to demonstrate that the sequence grows without bounds

It is just nonsense from a physical point of view.

You just don't get those nice sequences and limits in physics.

I'm having difficulty following your argument. Assuming for the moment that the expansion of the universe continues forever, are you saying that there is in practice no clock that can tick off infinitely many one-second intervals, and therefore an expanding universe would not really be infinite in time?

 

[Holy Roller]

This should help. It's actually an easy read, and entertaining for the novice. Enjoy!

 

[ArnautDaniel]

I'm having difficulty following your argument. Assuming for the moment that the expansion of the universe continues forever, are you saying that there is in practice no clock that can tick off infinitely many one-second intervals, and therefore an expanding universe would not really be infinite in time?

You can't start with a statement like "assuming the universe continues forever". That is meaningless.

You can only talk about physical measurements.

There is never going to be a physical measurement that "the universe continues forever".

The best you might do is to exhibit a sequence of physical measurements that might lead to the conclusion you want - rather like the notion of infinity with the naturals, which basically says that since every successive natural is larger than the last, and the growth isn't bounded then the sequence of naturals goes to infinity (with more rigor).

We should never never talk about anything as being "physical" that isn't related to well-defined physical measurements.

 

[Holy Roller]

The mass just disappeared, it never accelerated, it never reached an infinite state, it simply became an amount of energy. In fact it simply became the energy contained in the motion of the fissile products.

That is if the original atom had been stationary and then split into two moving fissile products then a certain amount of mass would have had to be lost to account for the kinetic energy of the products (seeing as the original atom had no kinetic energy).

Otherwise it would have split into two stationary products...which really wouldn't be a split since nothing would have moved at all really.

It looks like you're making life difficult on yourself by trying to re-invent the wheel, A/D.
The energy released by fission is bona-fide radiation, not a kinetic energy transferred to the new elements.
I was kinda hoping you were going to read the article I sent downrange.

 

[Holy Roller]

A/D this should help:

Any time energy is generated, the process can be evaluated from an E = mc2 perspective. For instance, the "Gadget"-style bomb used in the Trinity test and the bombing of Nagasaki had an explosive yield equivalent to 21 kt of TNT. About 1 kg of the approximately 6.15 kg of plutonium in each of these bombs fissioned into lighter elements totaling almost exactly one gram less, after cooling [The heat, light, and electromagnetic radiation released in this explosion carried the missing one gram of mass.][4] This occurs because nuclear binding energy is released whenever elements with more than 62 nucleons fission.

Also:

Mass–energy equivalence says that a "body" (i.e. a mass) has a certain energy, even when it isn't moving.

See what I placed in bold. Also, here's the link.

 

[ArnautDaniel]

It looks like you're making life difficult on yourself by trying to re-invent the wheel, A/D.
The energy released by fission is bona-fide radiation, not a kinetic energy transferred to the new elements.
I was kinda hoping you were going to read the article I sent downrange.

In physics there is a simple notion called "conservation of energy"

Now let us assume our original item was stationary, then anything contained within the item that moves as a result of the fission had to gain its energy from somewhere...the only place here is from the conversion of mass into energy.

So yes all kinetic motion of the fissile products has energy which comes from the conversion of mass to energy.

Now fissile products includes not only the two or three atomic nuclei produced in the fission but also the free neutrons that are created and move to the next nuclei to catalyze more fission. Also any alpha particles created in the process gain their kinetic energy that way and so forth.

Also any excitations in the electromagnetic field (which I presume is what you mean by "bona fide" radiation) get their energy from the fission.

Since we assumed the original item was motionless the only place these things can get their energy is from that mass that was lost.

...

There is still no place for your "infinity" to exist.

And moreover we now need quantum physics to explain things, and I'm afraid to find out how much you misunderstand that subject.

 

[ArnautDaniel]

Any time energy is generated, the process can be evaluated from an E = mc2 perspective. For instance, the "Gadget"-style bomb used in the Trinity test and the bombing of Nagasaki had an explosive yield equivalent to 21 kt of TNT. About 1 kg of the approximately 6.15 kg of plutonium in each of these bombs fissioned into lighter elements totaling almost exactly one gram less, after cooling[The heat, light, and electromagnetic radiation released in this explosion carried the missing one gram of mass.][4] This occurs because nuclear binding energy is released whenever elements with more than 62 nucleons fission..

1. Heat is the kinetic motion of matter and includes the kinetic energy of fissile products of the explosion, as I stated earlier.

2. Light and electromagnetic radiation are the same thing (or rather light is a particular range of electromagnetic radiation).

So what I stated above agrees with this.

...

I'm still not seeing where this endless posting of links to things you don't understand is supposed to take things.

 

[Cabal]

Trinity was a 10K yield precisely because one element (uranium 235) was split into two elements (forgot which ones); their combined mass being less than that of the U235.
The missing mass is what turned into the energy that created that 10K yield. Thus, by looking at Trin's 10K yield and all its energy release, you are effectively looking at an infinite yield of that 0.1% uranium mass that was converted directly into energy. The remaining 99% remaining, finite mass ended up being those two new elements.

Again, having problems with the bolded phrasing: I don't understand what you mean by "an infinite yield of that .1% uranium mass." A maximal yield, perhaps, in that you're converting that fraction into pure energy output (splitting the atom is ridiculously energetic after all, at least in terms of the scales involved, due to mass-energy equivalence).

But not infinite. 200 MeV/fission is hardly infinite. Surely if this were true and we obtained infinite pure energy output, Trinity would have effectively wiped out the entire universe.

Cabal, the important thing to understand is that the U235 was split, and the mass of the two remaining elements ends up being less (<--- keyword) than the original U235 element. The missing mass was converted into energy. In order for the mass to turn into energy, though, the mass had to reach a state of "infinity" first, as expressed in the Lorentz transformations.

The Lorentz transforms are used to illustrate the alteration of mass and spacetime from the p.o.v of (or observation of) a particle whose velocities are close to c. However, the only way you're going to get "infinity" mass/energy out from them would be for the neutrons/U235 nuclei to be travelling at exactly c. However, this by definition requires that infinity energy be supplied / infinite work be done on the reactant particles, which is physically impossible. This is why c is the upper speed limit, if you like, of matter with non-zero rest mass.

The Lorentz transforms don't really apply in nuclear fission as you need slow neutrons so the U235 can capture them, hence cadmium/D20 moderator in nuclear reactors. (Ok, to be fair, you don't have moderators in nuclear weaponry as statistically you'll have a few slow ones but it's thus a hugely inefficient process). The only thing that does apply is mass energy equivalence, and that at most (per fission reaction) takes the rest mass of the U235+n combo (which will always be finite) and then releases the .1% as energy via E=mc^2, which is only ever finite also, about 200 MeV/reaction.

Not trying to be a pain here, I just really don't see how "infinity" applies to this scenario as the only time it ever applies are for scenarios that are physically impossible.

On reflection, there would be very few times in physics where actual infinities are involved? As an example, one can have a half decent gravitational model describing the orbit of a small body around a large body. You can keep the larger body fixed (infinite mass) and your model works fairly well, but if you want to be ultra-precise you've got to accept that it's not infinity and instead restore the finite mass of the larger body and work a barycentre into your model. Terrible example, I know - I was just pondering this discussion earlier, and I really am finding it quite hard to think of an actual physical infinity. Sure, you can approximate to infinity a lot of the time, but that's not quite the same thing.

 

[Radagast]

You can't start with a statement like "assuming the universe continues forever". That is meaningless.

You misquote me, but never mind.

You can only talk about physical measurements.

OK. I see. From such a radical empiricist p.o.v. certainly no actual infinities can exist -- at best potential ones.

But that leads me to ask -- do you believe that electrons exist, or only the measurements made on them?

 

[Radagast]

This should help. It's actually an easy read, and entertaining for the novice. Enjoy!

Thanks for the help, but like the other people responding to your posts, I'm not actually a novice.

 

[[serious]]

It's understood that mass turns infinite before it turns into energy. The equation I showed was meant to illustrate this fact.

I've seen a couple pages of this on the read through and I've got to say that you have absolutely no idea what you are talking about. Nothing in the mass/energy transformation has anything to do with infinity. During a nuclear fission reaction, U235 is struck by a neutron which is absorbed to form U236. U236 spontaneously splits into to daughter cells and some free neutrons released. These daughter cells can be a variety of elements, but their mass (plus the mass of the released neutrons) is less than U235. This mass is released in the form of photons (gamma rays specifically). The total energy of the system is unchanged. Nothing, at any point of this process, goes to infinity. To have infinite anything here (mass, energy, anything) would result in infinite gravitation. Please note that nuclear reactions aren't the only mass conversions we see, just one of the more spectacular. any chemical reaction that produces heat is converting some mass to energy, as is any reaction that produces visible light. Even the freezing of water would result in a small mass conversion.

Ultimately, mass is just another form of energy. There is nothing magic about it. There is nothing infinite about it.

 

[Psudopod]

Originally Posted by Holy Roller

It's understood that mass turns infinite before it turns into energy. The equation I showed was meant to illustrate this fact.​

This is just wrong and it's easy to demonstrate if you think about it. If at any point any amount of mass "turned infinite" the resultant gravity would destroy the earth. The fact that we're here means that Holy Roller's misunderstood the concept.

On an related note, I'm still not sure of the point of this thread.

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