What is Space made of?

[Mordred]

2 hours ago, studiot said:

I'm banging on about 'empty space' for a reason.

Back along Mordred mentioned symmetry breaking and I mentioned Higgs and the Principle of Least Energy.

 

This is because using our best standard model equations Higgs' great insight was to show that 'empty space' is in an energetically higher state than space permeated by what we now call the Higgs Field ie non empty.

It would seem that Nature does indeed abhor a true vacuum.

This came up in one of the earlier pages. You hear a lot of current YouTube videos stating fields are fundamental. Yet at the same time under QFT fields are simply a geometric distribution of values.

Some quantities being physical (measurable) in this case and strictly mathematical.

The problem with occupancy with fields is under QFT is the probability density functions.

Using Higgs as an example with the above the field encompasses all spacetime however at each location there is a probability of occupancy of a Higgs boson. However the Higgs boson is extremely short lived.  Also to get  a Higgs boson that probability also requires sufficient energy that in essence requires another particle interaction. 

In essence the Higgs field is not a sea of Higgs particles flying around to get a Higgs boson requires another particle interaction to mediate.

This is the problem with all gauge boson fields (specifically gauge boson fields) force fields for short)

While the field may be described as existing everywhere the occupancy will be in a state of constant shifting occupancy where every location has a probability of having a particle.

So the best we can state is everywhere there is in spacetime a field  however that also does not mean that all of spacetime is filled due to fields

In essence space still serves as the arena the volume , whose occupancy is determined by the field probability density functions. This is true for all particle fields under QFT. Including matter fields

Now there's a mouthful lol.

To borrow a line from the Sean Carroll video in one of our pinned threads.

"To get a Higgs boson one must poke the field "

Edited August 4 by Mordred

[MigL]

1 hour ago, geordief said:

Just because I was wondering ,do excitations of the fields attract gravitationally ?(think the answer should be  "yes") 

A local energy density, in excess of the baseline, which would manifest as a particle, would modify local space-time curvature just like any other energy/stress/momentum  does under GR.

 

1 hour ago, Mordred said:

"To get a Higgs boson one must poke the field "

Essentially what experimental Physicist do.
To test at really small scales, we need to poke really hard, with equipment as large as the LHC.

[Mordred]

15 minutes ago, MigL said:

 

Essentially what experimental Physicist do.
To test at really small scales, we need to poke really hard, with equipment as large as the LHC.

 

precisely

[studiot]

Other uses of the word 'space' give thought.

The absence of something that could be or should be there.

So interstitial space can form a container space for atoms or ions in a lattice.

In fact if there is a lattice atom missed out then we have a lattice space and perhaps a screw dislocation.

Or if we have a crack in the lattice we have a griffiths weakness which may or may not propagate to a large space/weakness. Depending upon the shape of the space further lattice damage may be promoted or resisted.

A cation is an atom or molecule that has lost one or more electrons. The cation takes up less space than the parent atom.

Sometimes things are not always there. For instance a passing ray (photon) may hit (interact with) a bound electron.
Or it may miss it since the electron is not always 'there'. So what is in the space where the electron is sometimes ?

 

A forest fire needs two things. Air and a forest.

A gap (firebreak) in the forest is, well space, and prevents a fire spreading.

The Karman line conventionally marks the division between the atmousphere and 'Space'.

 

[Mordred]

1 hour ago, studiot said:

Other uses of the word 'space' give thought.

The absence of something that could be or should be there.

So interstitial space can form a container space for atoms or ions in a lattice.

In fact if there is a lattice atom missed out then we have a lattice space and perhaps a screw dislocation.

 

Sometimes things are not always there. For instance a passing ray (photon) may hit (interact with) a bound electron.
Or it may miss it since the electron is not always 'there'. So what is in the space where the electron is sometimes ?

 

Interesting thought, I should add not all spaces are physical spaces in physics such as momentum, phase, lattice, etc space. Numerous mathematical spaces to show relations are more often than not confused with physical spaces.

1 hour ago, studiot said:

So what is in the space where the electron is sometimes ?

good question one might state the quantum fields  exists in regions where there is no particle such as the electron but then you get into the question are fields fundamental. From a mathematical angle fields are simply a geometric treatment and are not descriptions of fundamental reality but a means of describing nature without defining nature. Its one of the reasons I always feel that the best way to treat space is simply the volume aka the arena.

Particularly since particles such as the electron has no internal structure but are on close examination best described as a field excitation.

I suppose one could argue that space is filled with field interactions involving field coupling constants in essence the potential energy terms. However the danger of that is that neither mass nor energy exist on its own but are simply properties.

I seem to recall a very old paper that argued all of nature can be described in terms of source and sink. Somehow seems appropriate. Seriously doubt I can find that paper now I read it roughly 30 years ago.

 

Edited August 4 by Mordred

[geordief]

7 minutes ago, Mordred said:

Interesting thought, I should add not all spaces are physical spaces in physics such as momentum, phase, lattice, etc space. Numerous mathematical spaces to show relations are more often than not confused with physical spaces.

good question one might state the quantum fields  exists in regions where there is no particle such as the electron but then you get into the question are fields fundamental. From a mathematical angle fields are simply a geometric treatment and are not descriptions of fundamental reality but a means of describing nature without defining nature. Its one of the reasons I always feel that the best way to treat space is simply the volume aka the arena 

There is a well known remark about time stopping everything happening at once.

 

https://quoteinvestigator.com/2019/07/06/time/#:~:text=Dear Quote Investigator%3A Albert Einstein,doesn't happen at once.

 

Can we say the same about space ?(did someone famous  actually say it ? I  thought they did.) ie that space "prevents things all being at the same place"

[Mordred]

52 minutes ago, geordief said:

There is a well known remark about time stopping everything happening at once.

 

https://quoteinvestigator.com/2019/07/06/time/#:~:text=Dear Quote Investigator%3A Albert Einstein,doesn't happen at once.

 

Can we say the same about space ?(did someone famous  actually say it ? I  thought they did.) ie that space "prevents things all being at the same place"

I do recall that statement but cannot recall who said it.

I was studying something else when I came across an intriguing definition of spacetime.

"Spacetime is a manifold \(\mathcal{M}\) on which there is a Lorentz metric \(g_{\mu\nu}\)  the curvature of \(g_{\mu\nu}\) is related by the matter distribution in spacetime by the Einstein Equation

\[G_{\mu\nu}+\Lambda g_{\mu\nu}=\frac{8\pi G_N}{c^4}T_{\mu\nu}\]

https://amslaurea.unibo.it/18755/1/Raychaudhuri.pdf

The above statement clearly defines how GR treats spacetime 

I actually like that definition far far better than the one I provided in the OP.

 

On 5/30/2015 at 8:11 PM, Mordred said:

D) spacetime is any metric that includes the time component as a vector. This is the 4th dimension, in GR the time component is treated in coordinate form.

 

Edited August 4 by Mordred

[studiot]

5 hours ago, geordief said:

What is the connection between space-time and space?

Is space timeless? A 3d surface in 4d space-time?

No the t or ct axis has the same extent as the other axes.

 

However raising the subject of surfaces is important and I don't think I properly brought it out in my last post.

 

1 hour ago, Mordred said:

Interesting thought, I should add not all spaces are physical spaces in physics such as momentum, phase, lattice, etc space. Numerous mathematical spaces to show relations are more often than not confused with physical spaces.

 

1 hour ago, Mordred said:

Its one of the reasons I always feel that the best way to treat space is simply the volume aka the arena.

 

If you have a volume it is either finite or infinite.

If finite it has surface(s)

A finite volume such as the crystal lattice in my earlier example has a particular surface.

If you introduce a crack then the volume doesn't change but the surface increases.

This increase requires energy.

So a space not only possesses volume but also surface area.

[Mordred]

42 minutes ago, studiot said:

No the t or ct axis has the same extent as the other axes.

 

However raising the subject of surfaces is important and I don't think I properly brought it out in my last post.

 

 

 

If you have a volume it is either finite or infinite.

If finite it has surface(s)

A finite volume such as the crystal lattice in my earlier example has a particular surface.

If you introduce a crack then the volume doesn't change but the surface increases.

This increase requires energy.

So a space not only possesses volume but also surface area.

 

agreed the tricky part here is coming up with a physics way to describe the boundary conditions of a finite space.

Mathematically this is done through the use of constraints. For a simple example the constraints on the Observable universe event horizon is determined by causality to the observer. Finite groups are also constrained in one fashion or another including renormalization as well as Feymann integrals example one loop integrals.

I suppose an accurate description could be that the volume of space is determined by the boundary conditions with the applicable constraints of the theory for finite space as opposed to infinite unbounded space.

A good example of this is Stokes theorem directional/vectorial surface element as applied to hypersurfaces under GR

 

Edited August 4 by Mordred

[MigL]

I think we run the risk of confusing the mathematical models of dimensional spaces with physically realizable spaces.
Space-time is not physically realizable, as the time axis, for orthogonality reasons, has to be imaginary.
Similarly, for the usual notion of spaces, which are simply volumes, boundaries are simply mathematical constructs, as are horizons, or curvature produced topological boundaries.

2 hours ago, studiot said:

7 hours ago, geordief said:

What is the connection between space-time and space?

Is space timeless? A 3d surface in 4d space-time?

No the t or ct axis has the same extent as the other axes.

You're going to have to explain what you mean by that, Studiot.

Space-time can be foliated into causal, 'present' surfaces, unique to each observer, so, while space is not timeless, I, as a unique observer can define a foliation, or 3D surface, that is causally connected to my present instant in time,
And so can every other observer define their own unique foliation.

Edited August 4 by MigL

[Sensei]

I have not bothered to participate in this (idiotic IMHO) thread, but..

Quote

 

What is Space made of

 

This question creates the idiotic philosophical question, "does everything must have to consist of something".

(which will be endless loop of dependencies)

Edited August 4 by Sensei

[dimreepr]

19 hours ago, geordief said:

There is a well known remark about time stopping everything happening at once.

 

https://quoteinvestigator.com/2019/07/06/time/#:~:text=Dear Quote Investigator%3A Albert Einstein,doesn't happen at once.

 

Can we say the same about space ?(did someone famous  actually say it ? I  thought they did.) ie that space "prevents things all being at the same place"

This reminds me of Will self, trying to describe Einstein's block universe; trying to compress 3D into 2D is easy, we do it every day with a map, we can do it in 4D but only individually, i.e. x and y is the map and z is the time spent in each portion of the map.

 

[studiot]

On 8/4/2024 at 9:53 PM, MigL said:

You're going to have to explain what you mean by that, Studiot.

Space-time can be foliated into causal, 'present' surfaces, unique to each observer, so, while space is not timeless, I, as a unique observer can define a foliation, or 3D surface, that is causally connected to my present instant in time,
And so can every other observer define their own unique foliation.

I've been away again but here is a quick answer.

Sorry I should have corrected the use of the word surface to hypersurface since we are talking about ll manner of dimensionality, including beyond 3.

I amt talking about causality, which is a physical property, not a mathematical one.

 

I am warning about loss/restriction of information when you choose a subspace or manifold to work in.

 

For instance

 

The is no such thing as a tangent (at any one point) to a curve or derivative of a function in one dimension.

There is only one tangent to a curve (at any one point) or derivative in two dimensions.

When we get to three dimensions we have to ask the question "Which Tangent ?" and "Which Direction ?" since there is an infinity of tangents and the derivative becomes a directionsal derivative.

So we can happily take a plane as a subspace of a solid, so long as we work only in that plane.

[awful]

Can empty and flat space be described as a lattice of clocks that all tick at the same rate? It wouldn't be actual clocks because they would affect each other.

[iNow]

1 hour ago, awful said:

a lattice of clocks that all tick at the same rate?

At the same rate according to which observer?

[Mordred]

2 hours ago, awful said:

Can empty and flat space be described as a lattice of clocks that all tick at the same rate? It wouldn't be actual clocks because they would affect each other.

Not sure what you mean but under GR one can have a series of clocks along the null geodesic (proper time). The FLRW metric does something similar except the clocks are viewed by a commoving observer. As INow mentioned one must also specify the observer.

[awful]

If there are different observers then it wouldn't be flat?

[Mordred]

1 hour ago, awful said:

If there are different observers then it wouldn't be flat?

That's not correct by any means.