Does Nuclear Reaction Energy Contribute to the Existence of Infinity?

[Dale]

Does infinity exist in the universe? Of course it does. ... It's the number of posts required to convince a troll on the Internet he's wrong.

 

[DrGreg]

To be pedantic, the official mainstream* mathematical view is that infinity doesn't exist as a number (although, of course, it does exist as an abstract concept). Any statement that includes the word (or symbol for) "infinity" is, strictly speaking, a shorthand convention for a rather more precise statement.

For example, when we say "there are an infinite number of points in a line", that is a shorthand for the more precise statement "there is no upper bound for the number of distinct points we can select from a line".

Given $\gamma = 1 / \sqrt{1 - v^2/c^2}$, we never ought never to say $\gamma = \infty$ when $v = c$, but we can say $\gamma \rightarrow \infty$ as $v \rightarrow c$. This is itself a mathematical shorthand for the more precise statement that, for any (large) number $\gamma_0 > 0$ it is possible to find a velocity v₀ such that, whenever v₀ < v < c, then $\gamma > \gamma_0$.

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*I say "mainstream" because there may be some esoteric branches of "modern" maths that take a different view.

 

[Tac-Tics]

*I say "mainstream" because there may be some esoteric branches of "modern" maths that take a different view.

You could simply leave it as this:

Infinity is not a real number. The real numbers are a logical extension of the rational numbers, of course, but they do not include any value greater than any other or less than any other. The real number system are the ones that best correspond to our intuition. They have an extremely mature theory behind them. Science has implicitly made the assumption that all measurements are approximations of real numbers since the advent of physics. They are what people mean by "number" in an informal sense an overwhelming part of the time. Your test scores are real numbers. Your IQ is plotted against a real bell curve. Currency is handled electronically as floating point numbers (computer approximations of reals).

But reals do not have infinitely large quantities! Infinity is something that must be added in later, but it is not so straightforward until you understand the idea of a limit!

 

[JesseM]

*I say "mainstream" because there may be some esoteric branches of "modern" maths that take a different view.

Infinity can be treated as a number (as opposed to just a limit) in complex analysis, which is not really so esoteric as mathematics goes (it's basically just calculus applied to functions on the complex numbers)

 

[Max™]

Does everyone else agree? Is energy and mass indistinguishable in this regard?

More or less.

Relativity actually suggests that everything, even space-time, may only be distinguishable as energy gradients.

The proven aspect though, is that yes, Mass is just a lot of Energy tangled up in one location. Thus REST mass.

I have always wondered why such equations don't have limits set such as "valid only when v is less than c.

They do, they're just hidden inside of Quantum Mechanics.

 

[Naty1]

Originally Posted by Naty1

No fission or fusion is fundamentally different from simple "combustion"...It would be better to compare fission/fusion with chemical reactions: the former involved nuclear energies and nuclear mass changes, the latter does not

The mass of combustion products is slightly less than the mass of combustion reactants.

I agree, but I thought the basic difference is that chemical reaction energies come from changes in the electron orbit energies rather than changes in the nucleus, which is true for fission/fusion...is that accurate?

But do typical combustion changes involve nuclear changes which chemical reactions usually do not?? never thought about that...wood to carbon via a campfire..yea, I guess carbon could have a different nuclear makeup than "wood" ...?

 

[Dale]

I agree, but I thought the basic difference is that chemical reaction energies come from changes in the electron orbit energies rather than changes in the nucleus, which is true for fission/fusion...is that accurate?

Correct, the binding force involved in chemical reactions is EM, the binding forces involved in nuclear reactions are the strong and weak nuclear forces. Any bound system shows a mass deficit which is proportional to the binding energy. The principle is the same, but the magnitude is obviously much different.