Mordred

Lets replace complexity with entropy shall we this is in essence what your describing above. Though I will now show that greater complexity arises with lower concentrations of mass/energy. Rather than the opposite that you posted. The second law as you mentioned previous states entropy never decreases, lets assume this is true So lets start with the Big Bang at [latex]10^{43}[/latex] seconds. This is as far back as our understanding reaches, we do not know the origin of energy etc previous to this point. As I'm showing a cosmology example we need a comoving volume (expanding) the entropy in a comoving volume is given by the equation [latex]S=\frac{\rho+p}{T}R^3[/latex] [latex]\rho[/latex] is the energy density, p is the pressure, T the temperature, R the radius. now at this time all particles are in thermal equilibrium, they become indistinguishable with one another, at high enough density they all look and behave like photons. The photon has spin of one which has 2 degrees of freedom. (degree of freedom corresponds to their interactions) loosely put. As the universe expands we get the other particles dropping out of thermal equilibrium. photon= 2 degrees of freedom, w boson=4, z boson= 2, gluons= 16, Higgs =4, For the leptons. electron=4, electron neutrino=2, muon =4,muon neutrino=2,tau=4, Each quark has 12. degrees of freedom. so greater complexity of our system arises as our universe expands, more particles drop out of thermodynamic equilibrium and our system gains a greater number of degrees of freedom ( added complexity).

Judging from the feedback I think this would be a good thread to pin.

You can also apply the field aspects to how Relativity works including 1) time dilation 2) length contraction. 3) redshift/blueshift and their frequency relations. This is one of the reasons why I'm glad Carroll mentions mass from the standpoint of how it works with vibrations. The video will be extremely handy to explain these advanced concepts and others to numerous threads currently ongoing. With literally no background knowledge required by the viewer. I am considering pinning this thread for a time so our regular members can readily go. "here watch this video " However I'd like to see what the OP thinks of it.

Good lecture, definitely handy to keep a link to. I particularly liked how he broke down the descriptive of fields with local neighbor potential. +1 this video covers a lot of the related replies I have been trying to teach here. I wish it was available when I first started studying physics. It took me years to put the pieces together to understand what he described in the first 50 minutes. Some additional information to digest. the portion of every particle field communicates mentioned in the video is forms of constructive/destructive interactions. The constructive interferences can give rise to new particles when the two waves combine to a quanta of energy in confinement. The portion on the above interactions accurately describe spacetime. That being the sum of all field values at a given coordinate. As every particle has a corresponding field, whose interactions can generate additional vibrations both constructive and destructive. To model all the dynamics at each point you use embedded geometries such as Hilbert space etc. The embedded geometries are your overlapping vibrations. String theory is also a collection of embedded geometries. Notice Sean Carroll's reference to string vibrations. In particular his correlation to mass.

Lol I liked that one too

Fair enough, lets play toy model. Lets assume a condition with no Heisenburg uncertainty principle. No field excitations/particles. (lets be 100% clear on below I am not trying to describe how a Universe is created or a Universe from Nothing model) so don't even go there I am strictly describing known physics in a heuristic manner. (specifically space-time under GR) The only thing left is strictly volume. In GR this volume which is assigned coordinates as the volume is 3 dimensional that volume requires 3 coordinates. x,y and z. We can include time as the fourth coordinate t. this is literally Space-time. Space being the three spatial coordinates with time as the fourth coordinate. As we have nothing to interact with the effective energy of this Space-time is literally zero. Now lets include some basic physics definitions. Energy: The ability to perform work. Mass: Resistance to inertia change potential energy: the energy possessed by a body by virtue of its position relative to others, stresses within itself, electric charge, and other factors. Field: An abstract device to describe any collection of objects/coordinates/events. So using the definition of a field I can describe the space-time coordinates as a field. However as I have no interactions involved the field energy is precisely zero. There is literally no stress tensor as coordinates are not moving without an interaction. All I have defined thus far is the metric tensor [latex]g_{\mu\nu}[/latex]. Now as I have no stress tensor, nor any anistropy ( differences in potential energy) Our Space-time is Euclidean (flat) there is no curvature in distribution. [latex]\eta_{\mu\nu}=g_{\mu\nu}[/latex] Now if I add a single particle the particle doesn't interact with coordinates. Coordinates are strictly an abstract construct. So our potential energy still remains zero. Analogy Time: lets use an everyday example. The electromagnetic field. Lets take your Voltmeter and in a vacuum move the + and - prongs onto two points of a bare wire ( assume the wire is a perfect conductor). You will measure zero volts. GR is no different if you have no potential difference {resistance} you have no voltage. A magnet itself however is a charged field. It has an inherent difference between the south and North pole. Think of Space-time itself with no interactions as an Uncharged field. There is no potential difference in any coordinate as we have no particles as of yet. Once I add two or more particles this is where things get interesting. Now I have interactions, I can now assign those coordinates to each particle and call these individual events. As we have interactions between two or more objects I now have potential energy. My space-time field is now charged. However the charge is strictly the interactions between the particles not the geometry itself. In GR however we can assign each particle as an event and assign those event coordinates to the particles. Now the above electromagnetic field is described by the Maxwell equations. Those Maxwell equations also can be described as as tensor (electromagnetic stress tensor) The stress tensor for GR is the exact same principle. In both cases the stress tensor is describing your kinematic vectors. ie flux. curl,div etc. They are identical in principle the only difference lies in the particular differences between gravity and the electromagnetic field ie Gravity only attracts while the electromagnetic field can attract and repel. In essence you stress tensor is a means to organize your different momentum vectors. We can equally assign different coordinates to different points in your electro-magnetic field however that doesn't mean those coordinates gain a medium quality. The electromagnetic field itself not its coordinate field is what exhibit the medium qualities. So Spacetime curvature under GR is the collection of vector relations where we set the geometry as the free-fall motion. A geodesic is describing a free fall motion at every coordinate with the use of vectors via the stress tensor between two points. This is what space-time curvature (under GR) is describing a collection of vectors at each coordinate. In accordance to the Principle of least action (kinematic motion under free fall). This is also why we use inertial frames in SR (key word inertial) Now a medium induces further delays in the kinematic motion of two particles. So if space-time was a medium we would have further delays. It would be the same as placing additional resistance to the electromagnetic example above. Recall the word Impedance in your electromagnetic theory. Mass is a form of impedance it is impedance to kinematic motion. impedance=resistance. Now using the electromagnetic field once again. You may recall that two circuits with two electromagnetic fields can induce impedance upon each other (propogation delay) we can describe these delays via coordinate time if we assign coordinates to each point of each field. See where I am going with in time dilation ? If every particle is a field excitation then time dilation itself is by analogy a form of propagation delay. Just as it is in the electromagnetic field theory. (keep in mind the above is a simpification) A heuristic rudimentary means to understand space-time under familiar terms. I won't try to show that gravity is not a force under GR using kinematic action as I know your not ready for that level of mathematical detail. However it does include everything I described above in particular the principle of least action under space-time curvature

Pretty good your getting the picture now congrats I know how troublesome thats been for you +1

Of course, spacetime is incorperated in very deifinition of a particle itself when you get into the QFT treatment of a particle. You literally cannot describe a particles wavefunction without spacetime

lol very true

Sure you can use those terms. The majority of the textbooks though on GR and Cosmology will use the term fluid to denote the perfect fluid equations. A full study will reveal that that the majority of your advanced equations have a thermodynamic basis. Mike those terms are used once you have a stress tensor. Space by itself with all excitations/particles removed is just your metric tensor. Your geometry . The metric tensor being [latex]g_{\mu\nu}[/latex] in the above conditions there is no active stress tensor [latex]T_{\mu\nu}=0 [/latex] In your other thread you wanted to apply an ether or medium to space itself which is false as that is just your geometry. You have no medium like properties unless you have other fields other than just geometry. This is an incredibly important distinction. ie there is no Div,Grad or Curl if the stress tensor is zero. The key distinction is that space all by itself isn't a medium,fluid or ether. It is just the geometry. Once you add other fields such as force fields/particles you now have a stress tensor involved and can have medium like characteristics.

Feyman has excellent lectures. I would ask any further questions not directly related to "what is space" please start another thread I'll be more than happy to reply there. I don't want this thread to describe the body of physics 😉

Spin is a property but one that is quantized. A VP being "off shell" may or may not exhibit spin. The minimum measurable quantizable value is [latex] E=\hbar w [/latex]. In QFT this defines the creation/annihilation operators (math term). The reason a VP isn't measurable is that they have insufficient energy to cause action to affect even the most ideal detection instrument.

Ok good images I can distinquish the problem using these. The external lines are your excitations (particles) these are termed your real particles. The internal ziggly lines on the right image is your fluctuations (virtual particles) it is those internal lines that is the issue. The external lines are renormalizable the internal lines are not. The external lines can induce effective action. While the internal lines has insufficient energy to do so. This is all described under S-matrix theory. Lattice QCD shows that an external line is really a boundary confined collection of fluctuations(VP) that sum up under confinement to an excitation. (particle) Spots in your eyes are more a biology discussion. I don't know the proper terminology but in essence your receptors are still sending delayed signals

Not at this point the problem with quantum gravity lies within a term called "renormalization" which is a very complex topic. Part of the problem with renormalization lies within the Heisenburg uncertainty principle itself. Just to be clearer there, when you hear the term "the problem is quantization" A quanta is the nimimum energy to cause "observable action". Action is a term to describe kinematic motion. Whats often described as a virtual particle for example cannot perform action as it is less than a quanta. The term particle itself is a classical misnomer as all particles are a field excitation. A field being a collection of excitations in this case. A field deviod of excitations being what is termed your zero point energy in QM. Under Cosmology true vacuum. However the Heisenburg uncertainty principle causes difficulty even after all excitations are removed. An excitation being a quanta, a fluctuation being VP of energies less than a quanta. I'm being a bit heuristic but this is where the problem lies between quantum gravity and relativity for a full blown TOE.

yes mass is resistance to inertia change so your common relation is momentum and factors that affect change in momentum. The stress tensor doesn't identify the cause but describes the influence to momemtum. Energy is "the ability to perform work." This all relates back to your Newton laws of inertia under a collective organization in your stress tensor. Spacetime curvature itself is a geodesic map of freefall motion. Described as the particles worldline. The stress tensor gives us the momentum based components of that map. So literrally any dynamic/interferance or interaction that can induce a resistance to inertia change is a form of mass. These are described under the stress tensor.

Not purely mathematical they are in essence fluid dynamic terms. flux is particles/unit area/unit time) across surfaces of constant x, y and z. Vorticity is a type of motion of those particles often described as the curl component. In essence describing rotational fluids. Classical examples being whirlpools etc. The curl component of the Maxwell equations being another example of vorticity. In essence vorticity is your angular momentum terms. Angular momentum being skew-symmetric

There is three main components to the stress tensor. Momentum, flux and vorticity.

I've always preferred stating the stress tensor instead of mass. Far more accurate but then many wouldn't know what the stress tensor is. @Tom one can apply a numeric description to anything in nature. That does not mean numbers are intrinsic to anything. Numbers are simply another form of language. A method of descriptive. Strange and Stingyjunky already covered the important details to Brownsfan77 post but I will add Any form of field can influence spacetime whether its electromagnetic, a matter field, the strong force etc. Using electromagnetic field to bend light is just one example but not the only one. While its great you showed that an electromagnetic field can bend light. So can other forms of either force or matter fields. With or without the presence of an electromagnetic field such as two asteroids far removed from any magnetic field. Another key distinction between gravity and any other force field is that gravity matches spin 2 statistics (which includes its thermodynamic character via Bose-Einstein statistics) No other known field does. Electromagnetic follows spin 1. So a GW wave is significantly different from an electromagnetic wave. We have now detected GW waves and confirmed the spin 2. Keep in mind a field is a mathematical abstract device to describe any collection of objects/events etc. Then again mass is also an abstract device to describe resistance to inertia change. Mathematics and physics simply describes what we understand as reality or aspects of it. Spacetime curvature is a mathematical geometric description of relations. Space is a description of volume, too often posters seek what it is fundamentally made up of due to trying to understand how it can curve. What curves includes additional relations causing resistance to inertia change.

nice reference and example Studiot. I don't want to add anything just yet. Might add confusion. My explanations often do lol.

Yes I'm familiar with some of Wolframs work. Though certainly not in great detail. Ok so you are simulating Newton gravity along x axis distance. Judging from above. This shows x axis, but what about the y and z axis? I look through your links I'm unclear which is your work or others. you may find these articles helpful. Cell Automata and Physics. http://www.google.ca/url?sa=t&source=web&cd=1&ved=0ahUKEwi0js7IrpzPAhUGy2MKHefsA-8QFggbMAA&url=https%3A%2F%2Farxiv.org%2Fpdf%2Fphysics%2F9907013&usg=AFQjCNHja_3J6NFDSGI3PzKbHvDALS-3mQ&sig2=ymSvYw3QO-umfbRFt5yLKA And "What are the hidden Quantum laws behind Newtons laws" http://www.google.ca/url?sa=t&source=web&cd=2&ved=0ahUKEwi0js7IrpzPAhUGy2MKHefsA-8QFgggMAE&url=http%3A%2F%2Farxiv.org%2Fpdf%2Fphysics%2F9904036&usg=AFQjCNGiDpIcBEmWePTYr-qmDmD_O8qx-g&sig2=n2oIRg0Qj90JeDaINLgbKw both articles gives some excellent examples in Newton gravity. particularly in the 3d regime with CA having 26 neighbors. 2D only 8 ( see second article)

Ok mathematically I have no problem with using math to describe reality. This is essentially done with physics. Without having to search your links is there specific formulas you want to look at? The Newton limit we can already derive using math. So without having to search your links. Can you post the math in your solution? The extension of the Bohr model should also be looked at.

Good point on particles and fields. I was considering a rewrite on that post. Unpinning this thread and replacing the article. It had initially hoped for a more collaborative on its initial writing. A couple of details I wish to add is a decent example of many particle distribution and how it correlates to the metric tensor and geodesics. The problem isn't that I can't derive the necessary equations. It's finding a series of derivitaves that can be readily followed. Specifically thinking the Newtonian limit where [latex]g_{\mu\nu}=\eta_{\mu\nu}+h_{\mu\nu}[/latex] I'm certainly open to other suggestions. However I feel this may be a good way of showing the field aspects of mass only. In a way I've been posting numerous derivitaves along these lines in Speculations and relativity forum to test how well they are understood by others.

I believe the statement" space is filled with the standard model particles and fields" is a better statement than space being some form of ether is more accurate. It is those fields and SM particles that determines the topography. The point being space itself does not have its own unique particles, which would be required for an ether. Unless you accept the graviton neither does gravity... Even twistor theory doesn't state space itself has its own particles. Though I had to confirm that with a PH.d that specialized in string/twistor theory. The metric tensor is determined via SM particle distribution. Thanks for the spelling corrections. I'm curious though why you would post a 1922 translation. The details of that paper is outdated by later research.

Thanks for the catch, gotta love auto corrects. Correction applied.

No you shouldn't think of particle spin as meaning spinning on its axis. I rarely use YouTube vids to answer questions but in this case it will make it easier. http://m.youtube.com/watch?v=v1_-LsQLwkA