# A question concerning density, mathematical proof.

• Mathematica
• Dragongod
In summary: Seems like you're contradicting yourself. In summary, current science describes a solid, liquid, and gas, as having different densities. Solids have the highest density, then comes liquids, and finally gases. They say in between the particles lies "empty space." Can someone please describe to me the properties of "empty space" because as far as I can logically reason, its impossible for "nothingness" (the absense of matter and energy) to exist.

#### Dragongod

Current science describes a solid, liquid, and gas, as having different densities. Solids have the highest density, then comes liquids, and finally gases. They say in between the particles lies "empty space." Can someone please describe to me the properties of "empty space" because as fas as I can logically reason, its impossible for "nothingness" (the absense of matter and energy)" to exist.

Also, mathematics currently states that one can divide infinitely into any value. Doesn't this show that matter is already infinitely dense, meaning that "empty space" (the absense of matter and energy) doesn't actually exist. Doesn't this basically state that matter is filled infinitely with more matter? If this is true then Stephen Hawking's definition of a black hole having a singularity would not hold up because all matter would already be a singularity(infinite matter, no room for empty space) in of itself.

Firstly, there are many liquids that are more dense that many solids (e.g. Mercury is more dense that Ice, for example).

Between the atoms lie 'empty space', often put in inverted commas because even empty space may not have precisely zero energy, this energy appears as short lived virtual particles, constantly blinking in an out of existence.

The effect of the energy is still being debated, however any effect is likely to be cosmic in scale. On the scales you are referring to (spaces between atoms), empty space is, for all intents and purposes, empty space.

you in no way addressed what i was saying. I am debated whether or not MATHEMATICS proves that empty space can't exist. To answer this question you have to discuss whether being able to divide into any value translates that matter is already infinitely dense. If it doesn't then that would mean mathematics is wrong. If it does then that would mean physics is wrong.

Dragongod said:
you in no way addressed what i was saying. I am debated whether or not MATHEMATICS proves that empty space can't exist. To answer this question you have to discuss whether being able to divide into any value translates that matter is already infinitely dense. If it doesn't then that would mean mathematics is wrong. If it does then that would mean physics is wrong.

This is VERY strange. Mathematics proves NOTHING in physics. You can't take mathematical axioms and derive ANY physical principle. You are confusing mathematical descriptions of a theory with it being mathematical principle! Theoretical physics USES mathematics as a language to convey an idea. But it isn't mathematics! You might as well say that English was the source of Dan Brown's The Da Vinci Code, instead of the MEDIUM of communication.

Secondly, if space is filled with singularities, the universe will be OPAQUE! Since we like mathematics so much, you can DERIVE this consequence. Put lots of singularities in a straight line and figure out the probability of photons getting through let's say from the sun to the earth.

Thirdly, if you think that there are "mathematics" that claim so-and-so, please indicate what these are in detail, rather than just give you interpretation of what it is. Please show specific citation.

Zz.

well ok if division has nothing to do with physics then i guess i am wrong but as far as i know physics uses division such as F=energy/distance and many more formulas that incorporate division and overall mathematics. The label VALUE would translate in physics as MATTER and therefore the CONCEPT (you can divide infinitely into any value) in mathematics would translate in physics as: you can divide (go into) any matter or mass forever.

you are confusing tool for reality (are you?) If you use abacus to count mosquitos, you can not say that the world population of mosquito is limited
by the abacus's beads. You raise the question which has nothing to do with physics or mathematics- is world what we are thinking about it or not? That does not mean it is stupid, it is just outside the natural sciences.

then,already in relativistic physics the "empty" spaces are filled with fields, which behave like matter in many cases. And if we go quantum, we will come to Dirac vacuum with virtual particles, mentioned in above post

wait so what you are saying is that i can't use mathematics to represent reality. That seems to be the prevailing argument here and if that's true why do we as a society study math. i am not trying to sound mocking. :) i just don't understand why not. I mean according to your example if there were enough Abacus's beands i would be able to count all the mosquitos in the world, given i had enough time as well. Therefore mathematics in that example could work to represent reality accurately.

but also as far as i know in relativistic physics "empty space" is the absense of matter and energy. Which by the way makes no sense to me. I don't see how its possible for "nothing" to exist. By definition "nothing" can't exist.

Dragongod said:
well ok if division has nothing to do with physics then i guess i am wrong but as far as i know physics uses division such as F=energy/distance and many more formulas that incorporate division and overall mathematics. The label VALUE would translate in physics as MATTER and therefore the CONCEPT (you can divide infinitely into any value) in mathematics would translate in physics as: you can divide (go into) any matter or mass forever.

Er... division? DIVISION?

What exactly is "as far as you know" about physics and what makes you think you have an accurate knowledge of what you are talking about? All you are doing in this one is semantics, NOT physics.

And you obviously decided to drop the notion of empty space being a bunch of singularities since you didn't even address it. Or maybe you didn't see it since light couldn't make it from your screen to your eyes since space should be completely opaque.

Zz.

Dragongod said:
but also as far as i know in relativistic physics "empty space" is the absense of matter and energy. Which by the way makes no sense to me. I don't see how its possible for "nothing" to exist. By definition "nothing" can't exist.

And what is the reason why the world should conform to YOUR sense? Is your sense complete as in NEVER ever changing? I can tell you many things that makes "no sense" to you, simply because you haven't acquired the knowledge on how they work!

Just simply using what makes sense to you as a justification for something to be valid or not is a very poor and weak methodology.

Zz.

Dragongod said:
To answer this question you have to discuss whether being able to divide into any value translates that matter is already infinitely dense.

How is that ? Are you still whinning about the Casimir-effect ?

If it doesn't then that would mean mathematics is wrong. If it does then that would mean physics is wrong.

How is that ?

marlon

Dragongod said:
wait so what you are saying is that i can't use mathematics to represent reality.
Breathtaking. No, you can use math to represent reality, but you can also use math to make up a world that doesn't exist.

Math is both a tool and a language (as ZZ already said), just like a hammer and the English language. You can use the English language correctly to say "The sky is green." but that doesn't make it true. Similarly, you can use a hammer correctly to drive a nail, but that doesn't mean you can build a house. You must become proficient in the specific use of the tool/language and the application of that tool to reality.
but also as far as i know in relativistic physics "empty space" is the absense of matter and energy. Which by the way makes no sense to me. I don't see how its possible for "nothing" to exist. By definition "nothing" can't exist.
Why not? There is a word for it, presumably that word (by definition) was made to describe something that exists.

Lets get slightly technical here: there is real, physical evidence for the fact that matter is made up of atoms and atoms are, by and large, empty space. The evidence is incontrovertible. For example, if you take a thin film of gold and fire a stream of electrons at it, some will bounce back and some will go throught (Rutherford experiment). By monitoring and quantifying this, you can figure out exactly how much empty space there is inside an atom. But the evidence is much, much bigger than just that one experiment.

So:
I am debated whether or not MATHEMATICS proves that empty space can't exist. To answer this question you have to discuss whether being able to divide into any value translates that matter is already infinitely dense. If it doesn't then that would mean mathematics is wrong. If it does then that would mean physics is wrong.
You can use math to prove that empty space can't exist, just like you can use the English language to say that the sky is green. But then you're not applying either one to reality correctly.

Also, "density" - you're using the word incorrectly. Density has little to do with empty space or the lack thereof. On a macro scale, you can assume a solid is truly a solid - it has no empty space (and that, indeed, is how the density equation works). But that still doesn't mean its infinitely dense. On the macro scale, density works just fine as its own independent property of matter.

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If this is true then Stephen Hawking's definition of a black hole having a singularity would not hold up because all matter would already be a singularity(infinite matter, no room for empty space) in of itself.

Singularity in the context of GR does not necessarily mean infinite mass. Although, if you had any matter with an infinite mass you would have a singularity, everywhere. So your hypothesis can not be correct.
I think that you're confusing singularity with the event horizon which a black hole has. Even you (who can be roughly approximated to a spherically simmetrical perfect fluid) have a singularity inside you.

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## What is density and how is it calculated?

Density is a measure of an object's mass per unit of volume. It is typically calculated by dividing the object's mass by its volume.

## What are some common units of density?

The most commonly used units of density are grams per cubic centimeter (g/cm3) and kilograms per cubic meter (kg/m3). Other units include pounds per cubic inch (lb/in3) and ounces per cubic inch (oz/in3).

## How is density related to the mass and volume of an object?

The density of an object is directly proportional to its mass, meaning that as the mass increases, so does the density. However, the density is inversely proportional to the volume, meaning that as the volume increases, the density decreases.

## What is the mathematical proof for the relationship between density, mass, and volume?

The mathematical proof for the relationship between density, mass, and volume is the formula D=m/V, where D is density, m is mass, and V is volume. This formula shows that density is equal to the mass divided by the volume.

## Why is density an important concept in science?

Density is an important concept in science because it allows us to compare the amount of matter in different objects and substances. It is also a key factor in understanding the physical properties and behavior of materials, such as their buoyancy or ability to float in a liquid.