How is a Vaccum mathmatically described?

[Gregory Wood]

Anyone know what books and astrophysicist has this knowledge?

Thank you,
Greg

 

[jambaugh]

This is a very very broad question and you'll need to give a bit more context if you want a useful answer. Start with where you stand in terms of academic studies, why why you want to know this and the context of its application.

Here is the "smart ass" short answer to show you what I mean. "We describe the vacuum with a vector in a Hilbert space." ( "or with a subspace of a Hilbert space if the vacuum is degenerate.") This sort of answer is not likely to be useful to someone asking the question. We need context and that is a group effort. So let's begin with "why do you ask?"

 

[Gregory Wood]

I was a commercial pilot with four courses short of a Geology degree. I also have a B.S. in Business Education.

who can help me to mathematically describe the following?

The measurement of standard atmospheric pressure in psi or millibars reduced to the vacuum of space. Then convert this to a mathematical equation explaining such density variations.
Thank you,
Gregory Wood

 

[PeterDonis]

The measurement of standard atmospheric pressure in psi or millibars reduced to the vacuum of space.

"Vacuum" means zero psi/millibars absolute. This is, of course, an approximation--there are always going to be a few stray atoms and such around, and in fact satellites in low Earth orbit still experience measurable atmospheric drag, so there clearly isn't a vacuum at the altitudes at which they are orbiting, even though AFAIK we can't directly measure the pressure at those altitudes with, say, a pressure gauge.

Then convert this to a mathematical equation explaining such density variations.

I'm not sure "convert" is the right word. We explain such density variations basically using the Earth's gravity and thermodynamics. But we don't derive those equations from measurements of pressure at particular points. We derive them from Newton's laws of gravity (in this context general relativity is not necessary) and the laws of thermodynamics. Much of the actual modeling has to be done numerically, since we can't solve the relevant equations analytically except for very simple cases.

 

[Gregory Wood]

I would be curious to know how Newton's laws of gravity or other laws can depict a density-gravity scalar that ranges from Earth's atmospheric density-gravity to the vacuum of space density-gravity? In simplified equations. Anyone?

 

[Gregory Wood]

Are there equations that explain vacuums lower that that of normal space?

 

[PeterDonis]

I would be curious to know how Newton's laws of gravity or other laws can depict a density-gravity scalar that ranges from Earth's atmospheric density-gravity to the vacuum of space density-gravity?

Google on "hydrostatic equilibrium". That relates the pressure gradient to the density of any fluid in a gravitational field.

Are there equations that explain vacuums lower that that of normal space?

If you mean, are there equations that have solutions describing such vacuums, of course there are. The laws of physics allow for pretty much any density you like, until you get to such high densities that possible quantum gravity effects come into play. But that's something like 120 orders of magnitude more dense than ordinary matter.

I'm curious why you appear to expect that the laws of physics set some kind of limit on what densities are allowed. Observed densities of things in the universe range over many, many orders of magnitude.

 

[Dadface]

https://www.math24.net/barometric-formula/

Is this of any help?

 

[Nidum]

The measurement of standard atmospheric pressure in psi or millibars reduced to the vacuum of space. Then convert this to a mathematical equation explaining such density variations.

(1) That should be referenced to the vacuum of space . Actually you can leave the terms 'the .. of space' out . For measuring atmospheric pressures a vacuum is just somewhere where the pressure is so low that it can be considered to be effectively zero .

Vacuum's sufficiently good for this purpose can easily be produced using standard methods and equipment . This is very convenient because it means that a reference vacuum can be provided anywhere that one is needed .

The pressure at any location in the atmosphere is mainly controlled by the altitude and by the temperature . To a lesser extent it is controlled by local variations in the composition of the air .

If there is any wind at the location the value of the pressure needs careful definition since the perceived value can be different depending on the means of measurement .

(2) More complete vacuums where the pressure is reduced to extremely low values are needed for things like cathode ray tubes , electron beam welding equipment and scientific research . Achieving these levels of vacuum is much more difficult .

(3) Pressure , temperature and density in any sample of air are related by the gas laws . These laws can have a simple or more complex formulation as required for a particular problem .

 

[sophiecentaur]

Are there equations that explain vacuums lower that that of normal space?

What would call "normal space"? It's been estimated that the average density of the universe is around one proton per m³. That would imply that there are regions with much less than that.
I really don't know why we should expect "equations", associated with vacua except the statistics of finding a particle (proton) in a given volume. As I remember, such low probability events are often best described in terms of a Poisson distribution.

PS Would the OP be something to do with the plot of a SF book?

 

[Gregory Wood]

Google on "hydrostatic equilibrium". That relates the pressure gradient to the density of any fluid in a gravitational field.
If you mean, are there equations that have solutions describing such vacuums, of course there are. The laws of physics allow for pretty much any density you like, until you get to such high densities that possible quantum gravity effects come into play. But that's something like 120 orders of magnitude more dense than ordinary matter.

I'm curious why you appear to expect that the laws of physics set some kind of limit on what densities are allowed. Observed densities of things in the universe range over many, many orders of magnitude.

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Because I can't find any physics that show a mathematical model which measures vacuums beyond the normal vacuum of space.
Is there anyone working on it?
Can't there exist an absolute bottom level of matter, space and time which contains reciprocal negative vacuum pressures ascending well below the normal vacuum of space?
Super Quantum vacuums that are occasionally breached into by a new Big Bangs influx of energy?
Breached because their tolerance vacuum levels reached a set magnitude?
You mentioned observed densities in the Universe over many orders of magnitude.
What about an equation showing negative orders of magnitude so low that it dilutes space and time close to "True Nothingness" nearly void of any particles time space or events?
An opposite of gravity negative equation showing negative density vacuum pressures.
Maybe it might be added to Einstein's gravitational equation and measured in exact form as his cosmological constant.

 

[Drakkith]

Can't there exist an absolute bottom level of matter, space and time which contains reciprocal negative vacuum pressures ascending well below the normal vacuum of space?

Not according to the laws of nature as currently understood by science.

Super Quantum vacuums that are occasionally breached into by a new Big Bangs influx of energy?
Breached because their tolerance vacuum levels reached a set magnitude?
You mentioned observed densities in the Universe over many orders of magnitude.
What about an equation showing negative orders of magnitude so low that it dilutes space and time close to "True Nothingness" nearly void of any particles time space or events?
An opposite of gravity negative equation showing negative density vacuum pressures.
Maybe it might be added to Einstein's gravitational equation and measured in exact form as his cosmological constant.

No offense intended, but this is just a bunch of technical jargon strung together in ways that make little to no sense. It's a bit like asking if there's a color red so intense that you can measure the polarization of the taste. A few points:

1. The big bang does not work like you (and most people) think it does. Not according to the standard model of cosmology at least (the model currently accepted as accurately describing the evolution of the universe from its known beginnings to the current day).
2. "True nothingness" as you described it does not exist. Spacetime cannot be diluted and cannot be gotten rid of.
3. Spacetime (aka "the universe") cannot be breached as far as we know. General Relativity doesn't even describe spacetime in such a way as to allow for a "breach". The commonly purported idea of a singularity breaching the universe into another is nothing but sci-fi material or extreme speculation by physicists who are working somewhat outside the realm of known physics.

 

[Gregory Wood]

What would call "normal space"? It's been estimated that the average density of the universe is around one proton per m³. That would imply that there are regions with much less than that.
I really don't know why we should expect "equations", associated with vacua except the statistics of finding a particle (proton) in a given volume. As I remember, such low probability events are often best described in terms of a Poisson distribution.

PS Would the OP be something to do with the plot of a SF book?

I'll read your link to "gas laws." I would at least like to write down an imaginary graph showing a negative vacuum within a vacuum. How may you graphically represent that one? You have Black hole material leading to somewhere like another Big Bang in another dimension. Since the density pressures of a black hole are so high might they then potentially be able to crack open or breach another possible even lower vacuum like a "Super Quantum Vacuum" that is located everywhere in time and space? I have long believed in the "possibility" of these vacuums.The website "Great Courses" really helped me to understand gravity, astrophysics and particle physics from top professors. Besides that, you are correct in speculating that my hypothesis will be in new episodes of movies I've written.. II have much more to add to this subject.. Greg

 

[Drakkith]

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