Indeed, I would not want to delve into the deeper mathematics, even if I could.
I do appreciate the effort thou and your courage in that regard. But find the explanation too basic.
Panda has already said this, but this isn't really sensible. You don't want the proper mathematics, but you don't want explanations which are too basic. What do you want? Should I explain exactly what Energy is in General Relativity and then explain why you can say that it both is and isn't conserved.
My statement rests on the notion that the materialist must provide a complete description of a creation apart from God; even though these mechanisms are often ad-hoc and resemble philosophy to the point of being a religion. As a Christian, I believe that God is very much in the totality of the universe description, but also admit that the human mind is probably incapable of attaining such a holistic description of the universe as to be complete.
The materialist makes no such admissions and pushes on with the pretense of scientific truths that are often not scientific at all; they are at best philosophical. As a Christian, I trust the real science and especially promote the reproducible and the provable.
Personally, I accept that Einstein’s General relativity theory has met a very high standard of scientific proofs and contains very fundamental truths of nature even though it is not by definition holistic. Please do not be offended by me stating that quantum mechanics is a theory of fundamental compromise although it also has recognizable achievements (a view held by Einstein).
To sum this denunciation up, FLRW is a unworthy trophy to the holistic description of the universe apart from God.
This seems to be about holistic worldviews. I asked a specific question however, namely: How a lack of energy conservation defies the materialistic rationalist view of the universe?
Then provide the proper mathematics, if you must, because a Newtonian treatment is simply insufficient.
Why? What I showed above is the proof that in the FLRW Big Bang spacetime momentum is conserved. There isn't another "more advanced proof", it's actually the proof. Plus even if there was, a proof is a proof.
For a proof of conservation of energy I will need to discuss the notion of Energy in General Relativity, but I will deal with this post first.
Any accepted principle that violates basic laws of physics is not scientific and must be considered philosophical (if not religious).
The "Laws of Physics" do not operate the way you think.
In the 17th century Newton and others, noticed that in all collisions between objects a number, which was called Energy, was always conserved. That is, a certain combination of the momenta of the particles in a collision never changed.
Later, violations to this principle were found, in electric interactions. However it was then realised that you could consider the particle to have a certain energy coming from its position relative to the object causing the Force. As when you hold pen some distance from the Earth (Earth causing the force of gravity), the pen is said to have Potential energy, even though it isn't moving.
In truth, this potential energy is just another number, it's only called energy because the sum of it with what Newton called energy originally (which we now call kinetic energy) is always conserved. So now we have a number that is always conserved.
Later Hamilton and Lagrange came to a deeper understanding of what was going on. Energy was simply temporal momentum. Just as momentum moves you through space, energy moves you through time. As momentum is conserved because different points in space are no different, Energy is conserved because different points in time are no different. Hamilton and Lagrange couldn't answer why Energy/Temporal momentum wasn't free to be any value it wanted, like spatial momentum, but instead was a specific function of spatial momentum.
Einstein answered this in Special Relativity. Space and time were now spacetime. So instead of having temporal and spatial momenta you just had spacetime momenta, or four-momenta as it is known.
The total amount of four-momenta an object has is always equal to its mass. Four-momenta is a vector with four components:
The first term is energy, the rest momenta in the various x, y and z directions. Since this whole thing is fixed to be of size m=mass, energy cannot be whatever value it wants. The square of the size is given by the formula:
This has to equal :
So you can see that Energy has to adjust to the values of the spatial momenta in order to keep the entire four-momenta of size m.
So the answer to Lagrange and Hamilton's question lay in the unification of space and time. (Note that creationists who reject special relativity have no explanation for why energy is fixed by spatial momenta).
Finally Einstein then came up with General Relativity. Here spacetime can curve, so different points in time are different, so you don't expect Energy/Temporal momenta to be conserved. What happens mathematically is that four-momentum still has to have size "m = mass", but how you calculate size is different, because the geometry is different
In the FLRW spacetime of the Big Bang, the size of vectors is calculated by a different formula. This gives the following for the size of the four-momentum:
which has to equal "m":
Now not only does energy have to adjust to the changing values of the spatial momenta, but also the scale factor describing the current size of the universe.
When the universe is large, is large, so the Energy has to be large to compensate for it, it will also have to get larger as gets larger. So Energy is not really conserved, but the length of four momenta is.
Hopefully I have conveyed two things:
1. A lot of physics is just pure geometry in General Relativity.
2. Rather than "Laws of physics" that cannot be violated, you should think in terms of an increasing understanding of the universe. Energy used to be a fundamental concept, but we now see it is just the temporal part of our spacetime momentum or four-momentum. There is no reason that we should be super-glued to 17th century notions when faced with a universe where space and time are just aspects of spacetime, where spacetime itself can bend and where matter is a probabilistic soup. We should, of course, be able to explain the previous laws, but we can move on.
Edited by Son Goku, : Error in a formula, some typos.
There is so much wrong with this model that it is difficult to know where to start.
First of all, let me explain something about General Relativity. The main equation for the General Relativity is Einstein's Field Equations:
The term is purely geometric, by which I mean it tells you about the geometry of spacetime. Specifically it tells you how much a ball of particles will shrink as time (time being measured by the centre of the ball) passes due to the curvature of spacetime.
is measure of the energy and pressure of matter. It's basically the energy density of the matter added to the total amount of momentum flowing through a point in each of the three directions.
So Einstein's equation basically says that at every point in spacetime the part of the curvature of spacetime which will cause a ball of matter to shrink over time is equal to times the sum of energy density at that point and the amount of momentum flowing through that point.
So basically you figure out for a piece of matter, how much energy density and momentum flow a piece of matter causes at a point and this (through Einstein's equations) gives you the volume shrinking part of the curvature of spacetime. Once you now that you basically know what the spacetime is like.
For example put in for a homogeneous gas of particles (basically like the universe on the largest scales) and the spacetime you get out is an expanding universe.
Now the equations are normally used with the assumption that spacetime is four-dimensional, three space and one time, although technically they can be used in general, but the results have no relation to reality. Carmeli uses them with five dimensions, one time, three space and one velocity. He uses velocity as a dimension and then applies the equations.
What is wrong with this? Velocity is not a dimension! Even if you pretend the idea makes sense the equations have no sensible solutions, they feature 5D universes being blown apart by gravitational radiation.
What do you mean practically by being at rest relative to the universal fluid? Who or what can be said to answer that description?
On large scales the universe appears as a homogenous fluid. This fluid would have an average momentum in a given direction in any reference frame. Somebody at rest with respect to this fluid is an observer who would perceive it to have no average motion.
God resting outside the universe may. Or is God moving at the average speed of the universe? Have you got a figure for that speed? Is the Universe a finite object in relative motion God is moving along with, my friend?
Characters from Bronze Age Western Semitic literature don't have a speed that can be compared with the average motion of matter in the universe.
The universe appears as even fluid on such scales to whom exactly? If I look now out my window would I catch that appearance?
Water is a collection of widely separated molecules on the scale of the molecules, however zoom out far enough and it effectively becomes a fluid. It is the same with the universe, zoom out far enough and on those scales it behaves like a continuous fluid.
Did Friedmann personally observe the fluid or did he hatch the idea in his head?
He made a reasonable assumption that the universe would be homogeneous and isotropic on the largest scales. Turns out he was right as the WMAP studies have shown.
You may not respect the actual characters of the Semitic literature but you seem to honour the principles of its cosmogony.
There is no issue of respect or disrespect, it's simply that your question was nonsensical. For analogy let us take another God and another physical variable. So could you tell me the approximate entropy of Zeus?
The linear time following a creation event and suchlike.
I have no idea what you mean by linear time in this context, could you explain and also what is the "suchlike".
The average speed of motion of matter could logically be only that of causality
No, as that makes no sense. Speed is measured in meters per second, causality is a general concept. All the matter in the universe typically has some relative velocity with respect to other pieces of matter. The FLRW description of spacetime is written down from the perspective of somebody for whom all these velocities average out to zero. We do this simply because calculations are easier in this reference frame.
that is expressed in the speed of light
This makes absolutely no sense. Causality is not a speed (think about it!).
The problem with your interpretation is that in real life any speed has a vector and that points every which way relative to an observer and is called velocity.
Do you honestly believe you are going to find a flaw in the Big Bang model by pointing out that velocity has magnitude and direction, i.e. is a vector?
So, no sorry, no universal time is possible as per the Copernican principle and the rest of post-geocentric relativity.
Who spoke of universal time?
Also, again, how do you think the principle of Relativity can contradict a model of the universe generated by General Relativity.
It means what I said, Inadequate. No universal Greenwich Mean Time is possible. That's a notion strictly for the birds. Extremely silly of the best professionals in the field to entertain such a primitive notion. Simultaneity is relative and the relation depends on distance measured in light units. No shared birthday for the whole of existence is remotely possible. Not a slightest chance in eternity. The Universe has no possible age.
There is no universal time in the Big Bang model of cosmology.
Please think about what you are saying. You are not going to be able to use Relativistic ideas to disprove General Relativity.
My point is that Son Goku was referencing the homogenous fluidity of the earth as witnessed from a non-moving observer perspective
I certainly wasn't, if the Earth was a homogeneous fluid, me and you wouldn't be having this conversation.
and I disagree with the whole notion of measuring or quantifying things from one perspective within the universe,
When you do a mechanics problem, you commonly solve it in the rest frame of the object. For example when working out the stress on a bridge, you commonly work in the rest frame of the bridge and not the frame of a plane passing by. You could if you wanted to, but it would simply be more difficult.
Hence, when we use the coordinates of an observer to whom the average velocity of the universe is zero, we do so to make calculations simpler.
This involves no mention of anything outside the universe.
There must be a concrete mechanism of translation. I don't make vain hypotheses but it is obvious that all matter is interconnected through radiation. The space between "gravitating" bodies is not empty. This is the invisible touch of all matter on all other matter. One idea I liked is imagining this radiation as electromagnetic ropes with torque. This is better than space warped by mass or aether though still it has its conceptual difficulties. The task is to explain how the ropes pass through each other and do not get entangled. Still, that is a start as the observation tells that this is strangely enough the case with light. Light beams don't clash and bounce off each other though are material enough as anyone can feel the pressure of the beating sun.
This cannot possibly work. Light is made of Photons, which carry a spin (intrinsic angular momentum) of 1 unit. Gravity couples to mass, the relativistic generalisation of mass is Stress-Energy. Stress-Energy is a spin-2 quantity of matter, so photons cannot directly couple to it. (Only quantities of equal spin can couple directly.)
The only spin-2 quantity associated with photons is electromagnetic flux. However coupling electromagnetic flux to Stress-Energy results in a theory which falls apart into infinities. (There are also serious conceptual issues with the theory, but I won't mention them for now.)
My friend, by relativity I mean the deepest underlying principle of relativity which is that everything is related to everything else and that the relation is following strict ratios and not a particular doctrine such as GR.
Strict ratios instead of doctrines? Sounds interesting, what value does it give for the Quadrupole moment of the Cosmic Microwave Background(CMB)?
No, photons are particles which have been detected and manipulated on an individual basis.
The strongest proof is the photon correlation experiments of the 1980s, the best of which is the classic: Grangier, P.; Roger, G.; Aspect, A. "Experimental Evidence for a Photon Anticorrelation Effect on a Beam Splitter: A New Light on Single-Photon Interferences". Europhysics Letters 1 (4): p. 173–179.
In this paper photon beams were observed to exhibit effects that cannot possibly be explained in any classical theory of light. Any theory in which light has real determined properties can be shown (mathematically) to be incapable of producing the anti-correlation effects in the beams of light.
Your idea has been totally experimentally refuted.
Photons are waves dead on arrival in the theory if you forgot that.
What do you mean?
My point is simply as there is only one existence, hence there is one motion only possible and therefore one and the same energy is spent for every action and reaction. The division into four forces is a convenient artefact.
Yes, energy is involved in motion, but that tells you nothing. You want to know what causes the motion and it would seem thus far that there is four forces.
Remember people have tried to unify the forces, but all such theories are experimentally refuted. It is conceivable that there really are four forces and not one or two (some think that all the non-gravitational forces might unify, but that gravity is different).
That division is nothing to be proud about and a good future theory will certainly scrap it.
You seem to be convinced that raw logic can trump experimental evidence. There is no evidence thus far that the forces are unified. We think they might be, but that's it. We certainly just can't decide that they are, because it seems nicer.
If the current theories fall apart into infinities is the fault of the theories and not any concern of Mother Nature.
I never said that the theories used by scientists at present have infinities, in fact there are proofs that they don't (J. Feldman, T. Kurd, L. Rosen, J. Wright, QED: A Proof of Renormalizability).
I said that the idea of having gravity being caused by electromagnetism does. All such theories have infinities.
Is it forceless geometry as per Einstein or is it the force carried by gravitons as per QM? It can't be both, you know.
I don't know who this is directed at, but the current evidence suggests and the widely accepted theory is that gravity is a forceless effect which results from geometry.
Many people have suggested that, if gravity is in some way quantum mechanical, then one of the first pieces of evidence would be that gravitational waves would come in particle like lumps. (this is not "per QM", but from separate theories.)