Field Question

[geordief]

44 minutes ago, studiot said:

Expansion (and contraction) are actually peculiar processes.

Here is a simple block that expands (equally) in all directions, as shown by the arrows.

But it has a hole in the middle.

Can you tell which way the sides of the hole move?

That is does the hole get larger or smaller?

Is the block physically realistic?

Can I imagine it being heated or cooled   uniformly  so as to expand or contract?

Edited May 4, 2018 by geordief

[swansont]

2 hours ago, MikeAL said:

OK, let's play with gravity for a second. According to the proposition of weakening field strength because of universal inflation we would expect that the ability of mass to curve space around it lessens as space itself expands. Perhaps imperceptibly so on the scale by which we can measure. If we backtrack through time, however, we get the ability of mass to bend space (and slow time but lets keep it simple) increasing backward through time, until a very small mass can bend a huge amount of space. This seems to fit, at least in broad strokes, with suggestions around the big bang, does it not? Infinitely tiny yet somehow containing the entire universe, time not existing in any appreciable way.

In Newtonian terms, if the force is changing, G is changing. That should show up in looking at distant galaxies, where we are getting signals from long ago. What is the evidence that this is true?

 

https://en.wikipedia.org/wiki/Time-variation_of_fundamental_constants#Gravitational_constant

The gravitational constant G is difficult to measure with precision, and conflicting measurements in the 2000s have inspired the controversial suggestions of a periodic variation of its value in a 2015 paper.^[12] However, while its value isn't known to great precision, the possibility of observing type Ia supernovae which happened in the universe's remote past, paired with the assumption that the physics involved in these events is universal, allows for an upper bound of less than 10⁻¹⁰ per year for the gravitational constant over the last nine billion years.^[13]

[studiot]

32 minutes ago, geordief said:

Is the block physically realistic?

Can I imagine it being heated or cooled   uniformly  so as to expand or contract?

 

Realistic of what?

Your choice of scenario, so long as it is clearly stated.

[MikeAL]

7 hours ago, studiot said:

Can you tell which way the sides of the hole move?

That is does the hole get larger or smaller?

You haven't told me the direction of expansion of the hole, only the outer walls. 

7 hours ago, Strange said:

Please show the mathematics that supports this claim.

And now you have gone from asking questions to proposing an alternative to GR and standard cosmology, perhaps this should be moved to the Speculations forum.

A bit jumpy there, Strange. I just explained the logic to you. It is not an alternative to GR at all. GR tell us that at the time of the Big Bang there must have been infinite density in a tiny space, and that it is the point that time started. You can check out the maths on it for yourself if you like. A field density change would fit right in there I would think.

 

[geordief]

6 hours ago, studiot said:

 

Realistic of what?

Your choice of scenario, so long as it is clearly stated.

All right,if I take a 2d plane at rt angles to the walls I want to populate the block with  equally spaced /sized  spherical  objects. 

With expansion the distance between the spherical objects increases and  the object (discounting the hole) gets larger uniformly.

As for the hole it also increases if we say that the distances between opposite walls increase.

I can build the 3d block up from these 2d planes.

Am I close?

Edited May 4, 2018 by geordief

[MikeAL]

6 hours ago, swansont said:

In Newtonian terms, if the force is changing, G is changing. That should show up in looking at distant galaxies, where we are getting signals from long ago. What is the evidence that this is true?

We could look at the an answer to this by visiting the NASA site.

Then came 1998 and the Hubble Space Telescope (HST) observations of very distant supernovae that showed that, a long time ago, the universe was actually expanding more slowly than it is today.  https://science.nasa.gov/astrophysics/focus-areas/what-is-dark-energy

Does this not suggest a stronger gravitational attraction?

[swansont]

20 minutes ago, MikeAL said:

We could look at the an answer to this by visiting the NASA site.

Then came 1998 and the Hubble Space Telescope (HST) observations of very distant supernovae that showed that, a long time ago, the universe was actually expanding more slowly than it is today.  https://science.nasa.gov/astrophysics/focus-areas/what-is-dark-energy

Does this not suggest a stronger gravitational attraction?

What analysis shows this?

The thing about all this is that everything has to be consistent with a model. You can't just look at one piece of data. So no, it does not suggest stronger gravity. It suggests some other factor that accelerated the expansion.

[Mordred]

No it means that one requires DE or a preferable term Lambda for the cosmological constant. It does not imply a stronger gravity.

[MikeAL]

36 minutes ago, swansont said:

The thing about all this is that everything has to be consistent with a model. You can't just look at one piece of data. So no, it does not suggest stronger gravity. It suggests some other factor that accelerated the expansion.

Some other factor, but not gravity? How can you be so sure? 

I'm not looking at just one piece of data. The gravity is a field (no pun intended) that you chose to explore when discussing a potential diminuition of fields in general, which seems reasonable based on simple extrapolations of the physics. The fact is our current understanding of gravity is not complete and seems to be showing a lot of problems. We keep adding bits to the existing theory to try and make it better (dark energy, dark matter),  but at some point, the theory simply needs to be gutted and reworked. The same site, NASA, also suggests: 

A last possibility is that Einstein's theory of gravity is not correct. That would not only affect the expansion of the universe, but it would also affect the way that normal matter in galaxies and clusters of galaxies behaved. This fact would provide a way to decide if the solution to the dark energy problem is a new gravity theory or not: we could observe how galaxies come together in clusters. But if it does turn out that a new theory of gravity is needed, what kind of theory would it be? How could it correctly describe the motion of the bodies in the Solar System, as Einstein's theory is known to do, and still give us the different prediction for the universe that we need? There are candidate theories, but none are compelling. So the mystery continues.

1 hour ago, Mordred said:

No it means that one requires DE or a preferable term Lambda for the cosmological constant. It does not imply a stronger gravity.

Hi Mordred, I can see that you are very well informed in your field, so you probably have a better handle on this than me, but I have just run across an article on discrepancies between different ways of measuring Hubbles Constant, and I thought of particular note was this quote: 

“Do we really know what makes up all of the radiation in the Big Bang?” wonders Freedman. “Is there a new kind of particle we aren’t accounting for? Or are dark energy’s or dark matter’s properties changing over time?

Over the next few years, researchers like Freedman will be trying to poke holes in how each method conducts its analysis -- before possibly invoking a revised model of cosmology. https://science.nasa.gov/science-news/news-articles/hubbles-contentious-constant-news

[Mordred]

Well Freedman has a valid point in the quote above. One of the potential possibilities for DM not DE is sterile right handed neutrinos which the mathematics of the particle models predict should exist. However we have yet to discover any. Either in nature or in the lab. Then there is the possibility of the supersymmetric particles in terms of the quote itself. 

For DE the Higgs field metastability may garnish some insights. Here is the related articles

 

DARK MATTER AS STERILE NEUTRINOS

http://arxiv.org/abs/1402.4119
http://arxiv.org/abs/1402.2301
http://arxiv.org/abs/1306.4954

Higg's inflation possible dark energy

http://arxiv.org/abs/1402.3738
http://arxiv.org/abs/0710.3755
http://arxiv.org/abs/1006.2801

 This is where I myself feel the best potential is in addressing DM, DE and inflation. 

Now here is the trick. Most of the mass of the universe involves DM and DE along with radiation. Baryonic matter only makes up roughly 4.6 percent. Ordinary baryonic matter is insignificant as a player to how our universe expands or contracts. Radiation comprises a portion of the 4.6 percent but its equation of state due to kinetic energy is a large factor. Matter has an EoS of zero. Where radiation w=1/3.

https://en.m.wikipedia.org/wiki/Equation_of_state_(cosmology)

Edited May 5, 2018 by Mordred

[Velocity_Boy]

20 hours ago, MikeAL said:

I have a small question that has been teasing me of late.

If the universe is expanding, and total energy can neither be created nor destroyed, and every inch of the universe is a field (eg magnetic field), then why doesn't field strength weaken as the universe expands?

Mmm..but do Cosmologists really know for sure that the universe is expanding? And not just all the galaxies we can observe and detect?

What I mean by this....could not the universe be either infinite...thus, no need for expansion....or could it, conversely, by static with fixed and finite boundaries? And just be comprised of galaxies that are expanding and accelerating away from each other? Maybe such as expanding clumps of particulate matter swirling from the center of a vortex in a cup of liquid that had been stirred? This last scenario could explain why no discernible loss in field strength.

And remember that the law of entropy increase from Thermodynamics doesn't apply either, since the universe is likely not a closed system.

Third...yeah I know I'm asking more questions and not doing a great job of answering yours...but are we sure every inch of our universe is a magnetic field? What about vacuum? And black holes? 

I think until we figure out what the hell Dark Energy is we cannot answer your question. Indeed, DE could be an energy infusing entity itself that is stopping the electric field from lessening.

Whew...I think I feel a headache coming on.

[Mordred]

Yes we know for sure it is expanding. There is plenty of evidence not only the recession of galaxies and redshift. The thermodynamic history,  BB nucleosynthesis and the CMB are also pieces of evidence.

 Expansion can occur in both a finite and infinite universe. It is a decrease in overall density.

 Forget your vortex, the universe follows the cosmological principle and is homogeneous and isotropic. A vortex has a centre and preferred direction. The universe mass distribution does not. On large scales it is well approximated as a uniform distribution. (sampling above 100 Mpc).

 The universe is electromagnetically neutral it has no inherent global charge and is certainly not BH's.

 This should show the last statement you made as incorrect.

Edited May 5, 2018 by Mordred

[MikeAL]

2 hours ago, Mordred said:

One of the potential possibilities for DM not DE is sterile right handed neutrinos which the mathematics of the particle models predict should exist. However we have yet to discover any. Either in nature or in the lab. Then there is the possibility of the supersymmetric particles in terms of the quote itself.

Very insightful, and a bit over my head as well. Let me ask though, why the fixation of attributing mass only to particles? Particles arise as fluctuations of their fields right? If we condense energy, particles pop out.  http://www.askamathematician.com/2010/01/q-is-it-true-that-all-matter-is-simply-condensed-energy/ 

Why not ascribe mass to energy before it even becomes a particle? A particle to me seems a bit like a Schwarzchild radius in the fact that it represents a type of event horizon beyond which energy transforms itself into a differently recognizable object (or more measurable form of energy). But the sudden emergence of the particle with mass should not preclude mass existing in the energy from which it was created.

[Mordred]

Mass involves energy, but energy is a property. Energy isn't something that exists on its own. In field treatments however its Ok to equate a field energy. Particles being field excitations. These definitions are extremely important to always remember

Energy the ability to perform work

mass resistance to inertia change. 

 Einstein showed the mass energy relation via e=mc^2.

Also keep in mind all fields are an abstract device, where one assigns a collection of functions or values to a geometric basis. One can mathematically equate any collection of functions or values to any geometric space and even stack any arbitrary number of overlapping fields. This is done far more often than most ppl realize.

Dimension in physics is any independant variable just as it is in mathematics. These dimensions relate to the number of degrees of freedom a system has.

 In the equation of state link I posted above there is a particularly useful formula relating to DE.

 That being the scalar modelling equation. The time derivitave in fact relates to the kinetic energy terms with the scalar field potential energy. So lets include those definitions to the above.

Potential energy. The ability to perform work due to its position relative to another position 

Kinetic energy the ability to perform work due to its motion.

 As this thread is about fields I will post some previous topics I posted awhile ago.

This may help with understanding QFT treatments with the above

I am developing a list of fundamental formulas in QFT with a brief description of each to provide some stepping stones to a generalized understanding of QFT treatments and terminology. I invite others to assist in this project. This is an assist not a course. (please describe any new symbols and terms)

 

QFT can be described as a coupling of SR and QM in the non relativistic regime.

 

1) Field :A field is a collection of values assigned to geometric coordinates. Those values can be of any nature and does not count as a substance or medium.

2) As we are dealing with QM we need the simple quantum harmonic oscillator

3) Particle: A field excitation

 

Simple Harmonic Oscillator

[math]\hat{H}=\hbar w(\hat{a}^\dagger\hat{a}+\frac{1}{2})[/math]

the [math]\hat{a}^\dagger[/math] is the creation operator with [math]\hat{a}[/math] being the destruction operator. [math]\hat{H}[/math] is the Hamiltonian operator. The hat accent over each symbol identifies an operator. This formula is of key note as it is applicable to particle creation and annihilation. [math]\hbar[/math] is the Planck constant (also referred to as a quanta of action) more detail later.

 

Heisenberg Uncertainty principle

[math]\Delta\hat{x}\Delta\hat{p}\ge\frac{\hbar}{2}[/math]

 

[math]\hat{x}[/math] is the position operator, [math]\hat{p}[/math] is the momentum operator. Their is also uncertainty between energy and time given by

 

[math]\Delta E\Delta t\ge\frac{\hbar}{2}[/math] please note in the non relativistic regime time is a parameter not an operator.

 

Physical observable's are operators. in order to be a physical observable you require a minima of a quanta of action defined by

 

[math] E=\hbar w[/math]

 

Another key detail from QM is the commutation relations

 

[math][\hat{x}\hat{p}]=\hat{x}\hat{p}-\hat{p}\hat{x}=i\hbar[/math]

 

Now in QM we are taught that the symbols [math]\varphi,\psi[/math] are wave-functions however in QFT we use these symbols to denote fields. Fields can create and destroy particles. As such we effectively upgrade these fields to the status of operators. Which must satisfy the commutation relations

 

[math][\hat{x}\hat{p}]\rightarrow[\hat{\psi}(x,t),\hat{\pi}(y,t)]=i\hbar\delta(x-y)[/math]

[math]\hat{\pi}(y,t)[/math] is another type of field that plays the role of momentum

 

where x and y are two points in space. The above introduces the notion of causality. If two fields are spatially separated they cannot affect one another.

 

Now with fields promoted to operators one wiill wonder what happen to the normal operators of QM. In QM position [math]\hat{x}[/math] is an operator with time as a parameter. However in QFT we demote position to a parameter. Momentum remains an operator.

 

In QFT we often use lessons from classical mechanics to deal with fields in particular the Langrangian

 

[math]L=T-V[/math]

 

The Langrangian is important as it leaves the symmetries such as rotation invariant (same for all observers). The classical path taken by a particle is one that minimizes the action

 

[math]S=\int Ldt[/math]

 

the range of a force is dictated by the mass of the guage boson (force mediator)

[math]\Delta E=mc^2[/math] along with the uncertainty principle to determine how long the particle can exist

[math]\Delta t=\frac{\hbar}{\Delta E}=\frac{\hbar}{m_oc^2}[/math] please note we are using the rest mass (invariant mass) with c being the speed limit

 

[math] velocity=\frac{distance}{time}\Rightarrow\Delta{x}=c\Delta t=\frac{c\hbar}{mc^2}=\frac{\hbar}{mc^2}[/math]

 

from this relation one can see that if the invariant mass (rest mass) m=0 the range of the particle is infinite. Prime example gauge photons for the electromagnetic force.

 

Lets return to [math]L=T-V[/math] where T is the kinetic energy of the particle moving though a potential V using just one dimension x. In the Euler-Langrange we get the following

 

[math]\frac{d}{dt}\frac{\partial L}{\partial\dot{x}}-\frac{\partial L}{\partial x}=0[/math] the dot is differentiating time.

 

Consider a particle of mass m with kinetic energy [math]T=\frac{1}{2}m\dot{x}^2[/math] traveling in one dimension x through potential [math]V(x)[/math]

 

Step 1) Begin by writing down the Langrangian

 

[math]L=\frac{1}{2}m\dot{x}^2-V{x}[/math]

 

next is a derivative of L with respect to [math]\dot{x}[/math] we treat this as an independent variable for example [math]\frac{\partial}{\partial\dot{x}}(\dot{x})^2=2\dot{x}[/math] and [math]\frac{\partial}{\partial\dot{x}}V{x}=0[/math] applying this we get

 

step 2)

[math]\frac{\partial L}{\partial\dot{x}}=\frac{\partial}{\partial\dot{x}}[\frac{1}{2}m\dot{x}^2]=m\dot{x}[/math]

 

which is just mass times velocity. (momentum term)

 

step 3) derive the time derivative of this momentum term.

 

[math]\frac{d}{dt}\frac{\partial L}{\partial\dot{x}}=\frac{d}{dt}m\dot{x}=\dot{m}\dot{x}+m\ddot{x}=m\ddot{x}[/math] we have mass times acceleration

 

Step 4) Now differentiate L with respect to x

 

[math]\frac{\partial L}{\partial x}[\frac{1}{2}m\dot{x}^2]-V(x)=-\frac{\partial V}{\partial x}[/math]

 

Step 5) write the equation to describe the dynamical behavior of our system.

 

[math]\frac{d}{dt}(\frac{\partial L}{\partial\dot{x}}-\frac{\partial L}{\partial x}=0[/math][math]\Rightarrow\frac{d}{dt}[/math][math](\frac{\partial L}{\partial\dot{x}})[/math][math]=\frac{\partial L}{\partial x}\Rightarrow m\ddot{x}=-\frac{\partial V}{\partial x}[/math]

 

recall from classical physics [math]F=-\nabla V[/math] in 1 dimension this becomes [math]F=-\frac{\partial V}{\partial x}[/math] therefore [math]\frac{\partial L}{\partial x}=-\frac{\partial V}{\partial x}=F[/math] we have [math]m\ddot{x}-\frac{\partial V}{\partial x}=F[/math]

 

I am still working on this one but you should find it useful nonetheless

 One of the topics of interest is the study of field treatments in physics. This study encompasses a vast array of different treatments under a plethora of different metrics. A layperson trying to learn how to model fields is faced with a daunting challenge if doing so as a self taught study. Even under formal educational systems, the topic itself presents challenges in terms of its diverse nature of applicable mathematics and potential treatments.  My goal as per a request by another forum member is to help clarify what fields are, why they are so important in physics and detail some of the fundamentals to basic field modelling. In essence detailing the essentials of fields that is inherent in any field treatments.

 So to begin with lets start with the primary question of interest. What is a field?, and the related oft asked question "what makes up a field"?

A field is an abstract tool under a coordinate basis, where each coordinate are assigned one or more values. Essentially it is a collection of objects, events, values of any kind applied to a geometry or metric for short. So the second question of "What is it made up" ? is already addressed by the simple fact, it is an abstract device, that we can assign any function under a given arbitrary metric treatment. So in Cartesian coordinates [latex]\mathcal{F}(x,y,z)[/latex]. I will denote field with [latex]\mathcal{F}[/latex].  Under polar coordinates [latex]\mathcal{F}(r\theta\phi)[/latex]

Coordinate systems : As mentioned above, we map our quantities under a coordinate basis, however we place no priority on any particular coordinate system. Why should Euclidean flat coordinates have a higher priority than Cartesian or cylindrical ? or The Schwartzchild vs Newton or any other coordinate system under QFT or String theory ?. They all have their range of validity and accuracy dependent upon the objects/system under examination. The Newton approximation is equally valid in our everyday lives. It is only when relativistic effects become measurable under examinations, that we require GR. The aforementioned theories each has its strengths and weaknesses when compared to one another.  As the expression goes, "The universe cares not how we measure it". Every theory evolves as new research is presented, so one should be aware that new developments may or may not address previous problems within a given theory.  However there is some basic geometries common to all physics theories. Though they may be represented under lower and higher dimensions. (see degrees of freedom). 

The most commonly known is the Euclidean geometry that we are all familiar with.

-Euclidean: Everyone is familiar with the 3 dimensions, (x,y,z). These are orthonormal axis, they are 90 degrees from one another. "In linear algebra, two vectors in an inner product space are orthonormal, if they are orthogonal and unit vectors. A set of vectors form an orthonormal set, if all vectors in the set are mutually orthogonal and all of unit length. An orthonormal set which forms a basis is called an orthonormal basis." https://en.wikipedia.org/wiki/Orthonormality.

also see list of trigonometric identities, as these are preserved in the Euclidean frame.

https://en.wikipedia.org/wiki/List_of_trigonometric_identities

it is only under relativistic affects do we require transformations to preserve the trigonometric identities in particular Pythagorous theorem.

[latex] c^2=a^2+b^2[/latex]

in 3d a common one can apply to the last

[latex]s^2=x^2+y^2+z^2[/latex] for the purpose of this article I will denote this with the lower case for S, to avoid confusion with upper case S for separation. In the former s is the longest line of a 3 dimensional triangle.

In the Euclidean frame there exists a theory of relativity called Galilean relativity and subsequently Galilean invariance. Although this article is not specifically about GR and SR, All modern treatments employ the tenets of GR. So we will detail the transformation rules between absolute time and variable time in accordance to observers and some common different classes of observers. In order to model time we add time as a fourth dimension. A dimension under physics and mathematics is any independent variable. So four dimensions 3 spatial one of time. (t,x,y,z) to give time dimensionality of length, we apply the constant c, not to be confused with the speed of light. (ct,x,y,z) so a field can now be represented by [latex]\mathcal{F}(ct,x,y,z)[/latex]. In polar coordinates. [latex](ct,r\theta\phi)[/latex]. (surface of a sphere such as the Earth.)

Degrees of freedom and dimensions:  A common confusion arises, by a vast majority of laymen first learning any field treatment. That being the use of higher dimensions beyond the 3 spatial and 1 time dimension. One has to understand a dimension under physics  is an independent variable. This is any function that can change without affecting any other function. These include each spatial dimension and under GR the dimension of time. However one can add other variable to describe how an object evolves. Under symmetry we can classify how systems/objects/states/fields evolve under translations under three distinct categories. Spatial, rotational and time translations. Take for example a rotor blade, if we move the blade from one location to another without changing its orientation, the object (blade) does not change only its location. This is a spatial translation. Now take that same blade and change its orientation to any of the principle axis. This is a rotational translation. Translations in time are  rotational translations however under time transformations between reference frames. When [latex]\acute{t}\neq t[/latex]. One can arbitrarily break any object into smaller slices and apply a geometry and translations to those smaller slices. For example a 3 dimensional volume can be broken down into two planes. [latex]\mathcal{R}^3=\mathcal{R}^2\otimes\mathcal{R}^2[/latex]. These treatments add variables that can independently change. Which is an added dimension. For example in Kaluzu-Klein we have the 4D coordinates (3 spatial, 1 time) then we add charge with two polarities. We can describe charge via a binary function, which becomes a degree of freedom. We now went from 4d to 5d.

 

Scalar Fields :     A scalar quantity is a quantity that is not a vector, a vector is composed of a magnitude and direction. A scalar is a quantity that can be described by a single real number.

https://www.encyclopediaofmath.org/index.php/Scalaral

also see definition of quantity under mathematics.

https://www.encyclopediaofmath.org/index.php/Quantity

 Recall earlier that a field can be assigned any function, one can assign any scalar function however complex provided its resultant returns a scalar quantity. One such example is the gradient of a scalar field such as used in temperature of the Earths atmosphere. Scalar fields can also be used with curvature, an example being the temperature or pressure scalar mappings of the Earths atmosphere. The function assigned to all coordinates to the metric mapping return a scalar quantity. Prime example being [latex]\rho[/latex] for energy/mass density.

Vector Fields

diverging curl

converging divident

rotating curl

 

Galilean relativity.

[latex](\acute{t}=t), (\acute{x}=x-vt), (\acute{y}=y),(\acute{z}=z)[/latex]

Edited May 5, 2018 by Mordred

[MikeAL]

11 minutes ago, Mordred said:

Also keep in mind all fields are an abstract device, where one assigns a collection of functions or values to a geometric basis. One can mathematically equate any collection of functions or values to any geometric space and even stack any arbitrary number of overlapping fields.

My feeling was that fields are not abstract devices for the purpose of calculation, but rather actual intangible properties of our universe. It seems there is one big field, teased apart for the purpose of measurement and because of its predictable independent behaviours into smaller threads of fields such as gravitational or electromagnetic or strong or weak forces or any one of the tiny particle ones. 

Looking for the moment at a field as an actual rather than abstract entity and applying the definitions set by science, and I will just quote you here for a second: 

15 minutes ago, Mordred said:

Energy the ability to perform work

mass resistance to inertia change. 

Could we not suggest that, when a magnet bends the magnetic field, that the magnetic field itself is doing work on the magnet? (Newtonian) or that because different strength magnets are capable of bending the magnetic field to different extents that the field itself is resistive of the change (inertial implies mass and velocity and so we enter into a loop with too strict a definition) - and that this resistance to change of form (I want to now call it inertial) therefore suggests mass. Under such a definition, mass thus would stand independent of the particles of the field and reside as a property of the field itself.

 

[Mordred]

Ok so lets go with your feelings for a moment answer this question.

"What is a scalar, vector, Spinor or tensor field made of"?

These are major types of fields how would you answer the above question ? Is it not valid that I can accurately describe any volume as a scalar, vector, spinor or tensor field ? or any combination of multiple overlapping fields some with embedding connections with other fields thus generating its own field. Such examples include numerous types of manifolds, fibre bundles, branes etc.

What about different types of spaces such as phase space, vector space etc ?

What about subfields and rings?

 What is energy or mass made of would be another unanswerable question as both are properties.

 Another very common misconception question relates to spacetime which is a type of field.

" How does spacetime curve or stretch, what is is made of that bends or stretch?"

see the problem of trying to apply substance to a mathematical methodology or a property?

 Trust me if you stick to the proper definitions you will have a far easier time understanding any physics related topic. Every physics model etc String theory, relativity, QFT, QM etc all follow those definitions precisely.

Lol there would be far less misconception posts as well on topics such as ADS/CFT, the holographic universe etc.

Here is a quote from a 5 second google lookup.

"Abstract field theory emerged from three theories, which we would now call Galois theory, algebraic number theory and algebraic geometry.
Field theoretic notions appeared, even though still implicitly, in the modern theory of solvability of polynomial equations, as introduced by Abel and Galois in the early nineteenth century. Galois had a good insight into fields obtained
by adjoining roots of polynomials, and he proved what we call now the Primitive Element Theorem."

Field Theory chapter 3.

https://www.google.com/url?sa=t&source=web&rct=j&url=http://www1.spms.ntu.edu.sg/~frederique/chap3.pdf&ved=2ahUKEwjs2MTF9e3aAhXix4MKHZ9BB0YQFjACegQIBxAB&usg=AOvVaw3LVo_kAXPwmAPDZPpyMLJ4

For subfields and rings see the following.

https://www.google.com/url?sa=t&source=web&rct=j&url=http://www.jmilne.org/math/CourseNotes/FT.pdf&ved=2ahUKEwjo743i9u3aAhWO3oMKHT7uDI8QFjAgegQIAxAB&usg=AOvVaw0WfWUT1gvKuvX_NIwdqbRk

 

How do you apply tangibility to the field definitions in those two articles?

Edited May 5, 2018 by Mordred

[Strange]

7 hours ago, MikeAL said:

It is not an alternative to GR at all. GR tell us that at the time of the Big Bang there must have been infinite density in a tiny space, and that it is the point that time started.

GR tells use the relationship between mass-energy and the curvature of space-time. You seem to reclaiming it is wrong.

[MikeAL]

1 hour ago, Mordred said:

How do you apply tangibility to the field definitions in those two articles?

You obviously know what you are talking about much better than I do,  so it's going to take me a little while to get back to you with the specificity of answer I think you are after. But let me take a shot at it for now anyway.

1 hour ago, Mordred said:

see the problem of trying to apply substance to a mathematical methodology or a property?

The universe can be described mathematically and therein lies the dilemma. We don't live in mathematics. We live in a world in which material objects materialise out of a mathematical orchestra. But they do not materialize out of a void. We limit our truths, and perhaps rightly so, to what is at some level tangible and testable, and what what is mathematically plausible. 

1 hour ago, Mordred said:

What is a scalar, vector, Spinor or tensor field made of

These are descriptors of reality. Not reality. It is like looking at a sonar image and asking what the image you are observing is made of. The answer can only be found by beginning with the material properties of the objects themselves. 

We know that there is matter and there is energy. We know for example that the mass of an atom cannot be accurately accounted for without including the binding energies.

1 hour ago, Mordred said:

see the problem of trying to apply substance to a mathematical methodology or a property?

So back to this one, I would describe it as the problem of applying mathematical methodology to a substance.

What precisely it is made of is anybody's guess and maybe one day we will know. However, it does manifest itself in the material from time to time, and in its observable effects (DM and DE) from time to time. A layer of reality, describable by mathematics, underlays our universe - but that layer is not mathematics. 

Mass does not bend spacetime because mathematics says so. Mathematics describes the fact that mass bends spacetime. But something is being bent for the effect to occur, otherwise it makes no sense. 

That's my take on it.

 

 

1 hour ago, Strange said:

GR tells use the relationship between mass-energy and the curvature of space-time. You seem to reclaiming it is wrong.

No, Strange, I'm not claiming anything. I'm just pursuing a line of reasoning that originates from conventional wisdom. If that line of reasoning contradicts Einstein, then that is very interesting, but it is by no means my assertion that GR is wrong.

[Strange]

38 minutes ago, MikeAL said:

But something is being bent for the effect to occur, otherwise it makes no sense. 

 I would say that what is being curved is the geometry; a mathematical description of how our measurements of time and distance relate to one another. 

[MikeAL]

24 minutes ago, Strange said:

 I would say that what is being curved is the geometry; a mathematical description of how our measurements of time and distance relate to one another. 

Good answer.

For this to occur then we must assume one of two conditions:

1. That time and distance themselves have extra-mathematical properties attributable to them that is causing the physical effect.

2. That the interaction is occurring in a medium of some sort. Perhaps not a PB and J medium, but something.

 

[Strange]

14 minutes ago, MikeAL said:

Good answer.

For this to occur then we must assume one of two conditions:

1. That time and distance themselves have extra-mathematical properties attributable to them that is causing the physical effect.

2. That the interaction is occurring in a medium of some sort. Perhaps not a PB and J medium, but something.

 

I don't see why we should have to assume either of this things. Do you need to assume them if geometry is Euclidean (as we used to think)?

It turns out that the geometry of space and time measurements is non-Euclidean. I don't see why that implies a medium of some sort.

[studiot]

11 hours ago, MikeAL said:

You haven't told me the direction of expansion of the hole, only the outer walls. 

 

That is what I asked you. (except that the edges of the block are not outer walls)

 

 

11 hours ago, geordief said:

All right,if I take a 2d plane at rt angles to the walls I want to populate the block with  equally spaced /sized  spherical  objects. 

With expansion the distance between the spherical objects increases and  the object (discounting the hole) gets larger uniformly.

As for the hole it also increases if we say that the distances between opposite walls increase.

I can build the 3d block up from these 2d planes.

Am I close?

 

This apparantly innocuous question seems to be causing a deal of difficulty.

Perhaps that is because expansion and contraction is more complicated than at first meets the eye.

 

Let me ask again.

 

Suppose you were to printout my sketch and then photocopy it on the 100% enlargement setting.

Would the hole get bigger or smaller?

Would every point in the solid part of the block be further from its neighbours than before?

 

To save time:

Yes, of course the hole would get bigger.

Yes every point would be further from its neighbours.

 

Now there is a point to all this because the expansion of the universe is not like my example (with or without the hole)

The expansion of the Universe is an entirely different sort of expansion.

And you need to understand this difference before trying to discuss the expansion of the Universe.

 

Interestingly this difference has to do with curvature and another dimension, which everyone seems anxious to discuss.

Edited May 5, 2018 by studiot

[geordief]

53 minutes ago, studiot said:

the expansion of the Universe is an entirely different sort of expansion.

And you need to understand this difference before trying to discuss the expansion of the Universe.

 

Interestingly this difference has to do with curvature and another dimension, which everyone seems anxious to discuss.

Please expand on this

seriously (I do struggle with expansion /inflation in the global context) and would like to get over a hurdle or two.)

 

I am familiar with the idea that every point (outside zones held by gravity) separate  from each other in a homogeneous way.

And of course that there was no centre at the origin of the expansion (it is everywhere)

Edited May 5, 2018 by geordief

[swansont]

10 hours ago, MikeAL said:

Some other factor, but not gravity? How can you be so sure? 

Because when we modify gravity to account for observations, it breaks in situations where it was working. When we add dark energy, we don't have that problem.

10 hours ago, MikeAL said:

I'm not looking at just one piece of data.

It's not clear you are looking at any data.

10 hours ago, MikeAL said:

The gravity is a field (no pun intended) that you chose to explore when discussing a potential diminuition of fields in general, which seems reasonable based on simple extrapolations of the physics. The fact is our current understanding of gravity is not complete and seems to be showing a lot of problems. We keep adding bits to the existing theory to try and make it better (dark energy, dark matter),  but at some point, the theory simply needs to be gutted and reworked. The same site, NASA, also suggests: 

A last possibility is that Einstein's theory of gravity is not correct. That would not only affect the expansion of the universe, but it would also affect the way that normal matter in galaxies and clusters of galaxies behaved. This fact would provide a way to decide if the solution to the dark energy problem is a new gravity theory or not: we could observe how galaxies come together in clusters. But if it does turn out that a new theory of gravity is needed, what kind of theory would it be? How could it correctly describe the motion of the bodies in the Solar System, as Einstein's theory is known to do, and still give us the different prediction for the universe that we need? There are candidate theories, but none are compelling. So the mystery continues.

No, that's not what "a last possibility" implies (or anything else; you really should provide a link when you quote things). They  are not saying that there is any kind of solid conclusion that relativity needs to be replaced. Simply that it can't be ruled out.

 

[Mordred]

8 hours ago, MikeAL said:

You obviously know what you are talking about much better than I do,  so it's going to take me a little while to get back to you with the specificity of answer I think you are after. But let me take a shot at it for now anyway.

The universe can be described mathematically and therein lies the dilemma. We don't live in mathematics. We live in a world in which material objects materialise out of a mathematical orchestra. But they do not materialize out of a void. We limit our truths, and perhaps rightly so, to what is at some level tangible and testable, and what what is mathematically plausible. 

These are descriptors of reality. Not reality. It is like looking at a sonar image and asking what the image you are observing is made of. The answer can only be found by beginning with the material properties of the objects themselves. 

We know that there is matter and there is energy. We know for example that the mass of an atom cannot be accurately accounted for without including the binding energies.

So back to this one, I would describe it as the problem of applying mathematical methodology to a substance.

What precisely it is made of is anybody's guess and maybe one day we will know. However, it does manifest itself in the material from time to time, and in its observable effects (DM and DE) from time to time. A layer of reality, describable by mathematics, underlays our universe - but that layer is not mathematics. 

Mass does not bend spacetime because mathematics says so. Mathematics

 

Everything described, defined or modelled by physics involves mathematics. It is a requirement of any model to make testable predictions of how a affects b.

You cannot describe every possibility of how a affects b without involving math.

Lol even the the term mass involves mathematics. Ie Newtons laws of inertia

Edited May 5, 2018 by Mordred