Be very careful of using the word "zero".

[Catastrophe]

I have started this thread here, because zero is inextricably linked with infinity and an "infinite" "Universe".

Yes, we have to watch our semantics very carefully, in questions of cosmology.

Consider this:

The law of gravity, specifically Newton's Law of Universal Gravitation, describes the force of attraction between objects with mass. It states that every object in the universe attracts every other object with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

If anyone wants to be pedantic about gravitation, then substitute zero spacetime gradient; it does not affect the discussion.

According to this, there can be no such thing as zero-gravity.

The law of gravity, specifically Newton's Law of Universal Gravitation, describes the force of attraction between objects with mass. It states that every object in the universe attracts every other object with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between their centres.

OK, for practical purposes, with the square of increasing distance as denominator, force (gravity) falls off very rapidly until, for practicable purposes, it becomes immeasurably small, and/or is swamped by the attractions from other objects. But it never becomes zero (nothing).

So one use of nothing, or zero, means nothing large enough to measure, or immeasurably small.

Another use of 0 (zero) is as a placeholder in defining numbers. 134 means one hundred, three tens, and four units. 104 means one hundred, no tens, and four units. Elsewhere, 140 means one hundred, four tens and no units. So 0 can mean no units, no tens, or other similar connotations.

Or 0 can mean not just too small to be measured, but too small to be considered to exist at all.

Consider division by 0. Here, again, we find different possible interpretations.

One possibility is to suggest that "nothing" does not exist, so you cannot divide by it.
Another alternative is to say that 0 can be interpreted as very, very small (immeasurably small); in which case the numerator becomes immeasurably large. Yet again, one might argue that division by zero might be interpreted as division by infinitely small, in which case the numerator becomes infinitely large (viz infinite).

Language being what it is (not always entirely scientific), I cannot see "division by zero" (meaning infinity) as being any less acceptable than "zero gravity" (meaning not measurably affected by gravity).

Cat

 

[Helio]

Thanks Cat.

Zero has had a twisted history and it seems many like to keep twisting.

An easy way to think of zero is from a physical representation of say, apples. If I have an apple in my right hand I have 1 apple in that hand. If the other hand had no apple then it has 0 apples. Zero represents the number of something I could have but don't.

It can also fall between positive and negative numbers as, say, a lake whose water level varies day to day and often, during the summer, it has a negative value compared to the "normal" level.

There was a lot of debate in the 16th and 17 centuries, from what I can tell, on how zero was to be seen, especially as something is tossed straight up into the air. They had a hard time accepting it could have no motion when at the top.

 

[Catastrophe]

Helio, thank you for your wise comments.

The way I see it is that "what if you have an immeasurably small residue of apple remaining in one hand" (to further your example). Very likely a few atoms remain when you let go of it. OK, I am pressing semantics, but that is what my post was about. Vide "zero gravity".

Cat

 

[Curiosity killed the cat]

Its all just a matter of scale, and scale is relative. Planck admitted that it was feasible for things to exist at a scale smaller than one planck length. It was simply beyond human comprehension that anything could be smaller than a planck length. However, reality doesn't have to adhere to the constraints placed upon it by mathematicians.

Relativity is based upon the comparison of objects existing in space-time, but space and time are enigmatic phenomena, which combine to form a single phenomenon, which we call space-time, and although the ratio of distance to time remains constant, not all observers clocks or measurements of distance remain comparable. Time and distance as we think of them, do not actually exist !

From zero, nothing can emerge "ever," Our universe didn't come from nothingness, because nothingness is an impossibility, there are two intangibles with properties that can evolve into tangibles, and those intangibles are space and time aka space-time.

Do you not accept Einsteins theory of gravitation Cat ?

 

[Catastrophe]

Do you not accept Einsteins theory of gravitation Cat ?

Why do you ask that? My choice of model was simply based on what I thought most would find easier to understand.

What was the intention of your curiosity?

Cat (very much alive)

 

[Astraeus]

I can certainly appreciate the definitional distinctions being explored here. I think semantic or otherwise, it is valuable to understand what is meant, precisely, by the use of "zero".

In physics, especially cosmology, the role of zero often slips between three interpretations:

1. The mathematical zero — a defined number, used for placeholding or representing no quantity.
2. The physical zero — a limit or boundary condition, such as absolute zero temperature or zero-point energy, where "zero" doesn’t imply nothing, but rather the lowest state measurable or permitted.
3. The conceptual zero — a philosophical or metaphysical placeholder for "nothingness", which is rarely well-defined in physics and often leads to confusion when mixed with the above.

Regarding gravity, you're absolutely right: Newtonian gravity never fully reaches zero; the force asymptotically approaches it as distance increases. The field persists—however faint—throughout space. So “zero gravity” is always shorthand for net gravitational force below measurable threshold, or more precisely, “microgravity” in orbital conditions.

As for division by zero, it’s often misunderstood even in mathematical circles. While the limit of a function as a denominator approaches zero may tend toward infinity, division by zero itself remains undefined—not because it tends to infinity, but because it breaks the rules of consistent operation within the number system. Infinity isn’t a number; it’s a directional behavior in a limit context.

From a foundational standpoint, I think it's helpful to ask: when we say “zero” in physical law, are we referencing an actual absence? Or simply a limit state where contribution becomes negligible or undefined?

This isn’t just semantics—it shapes how we build models. For example, treating spacetime curvature as truly zero implies a complete absence of mass-energy influence, which is different from a region where curvature exists but is flat to within tolerance.

 

[Catastrophe]

Anyone interested in the ancient beginnings of zero might appreciate this link.

https://www.science.org/content/article/concept-zero-has-been-around-lot-longer-we-thought

Cat

 

[Greenlight]

but "zero gravity" doesn't mean no gravity.

It means freefall.

 

[Catastrophe]

but "zero gravity" doesn't mean no gravity.

It means freefall.

What is the meaning of zero gravity?


Definition: Zero Gravity or Zero-G can simply be defined as the state or condition of weightlessness. It also refers to the state in which the net or an apparent effect of gravity (i.e. the gravitational force) is zero.

Whether this is correct use (I point out that it is not) does not affect the semantic argument. My point is in the different meanings of "zero".


Cat

See also:

Definition of ZERO

the arithmetical symbol 0 or [SYMBOL] denoting the absence of all magnitude or quantity; additive identity; specifically : the number between the set of all negative numbers and the set of all positive numbers… See the full definition

www.merriam-webster.com

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