Time
Some people are having difficulty understanding Louise, even when she draws very simple Space Time diagrams. Let's use a slightly different diagram. 
We see that an observer at Now looks back to the past, and the infinite future looks back to Now. How much simpler can it be?
We see that an observer at Now looks back to the past, and the infinite future looks back to Now. How much simpler can it be?
posted by Kea | 1:42 PM
7 Comments:
I looked at Louise's blog for
GM= tc^3
and realized that TGD could provide an interpretation for this kind of equation or something analogous to it formulated in terms of mass density in case of Robertson-Walker cosmology and in terms of induced metric of space-time sheet in the general case.
The basic observation is that naximal signal velocity at space-time surface slows down in the sense that the path between points A and B along 4-surface is longer along the space-time sheeet than along lightlike geodesic of imbedding space H=M^4xCP_2. This because space-time surface is curved and warped and it takes longer time to move along space-time surface from point A to B than in H. Thus topologically condensed photons travel slower than free ones.
Using proper time coordinate a of future lightcone as a Lorenz invariant time coordinate for the space-time surface one obtains a Lorentz invariant formulation of this notion. From the expession of the induced line element obtained by projecting the line element
ds^2= h_{kl}d^kdh^l
of the imbedding space to spacetime surface with coordinates (a,x^i) using h^k = h^k(a,x^i) one has
ds^2= g_{aa}c^2da^2+...
and one can identify reduced light velocity as
c1= sqrt(g_{aa})c .
The stronger the curvature of space-time sheet is, the larger the reduction of the maximal signal velocty in this sense is. For Robertson- Walker cosmology one can relate g_{aa) to the density of gravitational mass and one obtains the analog of equation of Louise relating mass density and c1. One prediction is each space-time sheet has its own Hubble constant. This might relate to the long debate about value of Hubble constant.
What is interesting is that it is also possible to have a reduction of light velocity and time dilation also in absence of gravitational field. One can consider warped imbeddings of M^4 for which one CP_2 coordinate, call it s, depends on linear M^4 time t in arbitrary manner. The simplest situation corresponds to s= omega*t. The resulting induced metric is manifestly flat but the time component is given be
g_tt= (1-R^2omega^2)c^2 so that
light velocity is reduced
to
c1= sqrt(1-R^2omega^2)c
There is warping induced time dilation which is observable by a many-sheeted physicist having all the equipment of many-sheeted laboratory. The time dilation by warping might relate to the claim that electrons in graphene behave as massless particles but with reduced light velocity about 10^(-3)c (if I remember correctly).
Best Regards,
Matti
Kea, I enjoy your simple diagrams too. Like Feynman diagrams or the eightfold way, they show great promise. In Planck units "the equation" is just M = t! All this shows that some people are too smart to understand something simple.
Louise, here are some statements from a paper of yours.
(Apparently speaking of "Einstein's Space") "There is no centre in Space... There is a centre in Time, called a 'Big Bang'. Near that initial Singularity, mass was confined to a tiny volume. Though separated from the Big Bang by 13 billion years, we are within its light cone and that mass is pulling on us." And a little later "radius R of the universe is distance from the origin".
This does not sound like Einstein at all to me. It sounds like the common misconception of the Big Bang cosmology, according to which the Big Bang was an explosion which took place in a preexisting space, which was empty except for a concentration of mass around some particular point. But that is not what the standard cosmology says! In the two basic scenarios (infinite spatially open universe, finite spatially closed universe), matter is coextensive with space from the beginning. There is no "origin". Note that I am not criticizing you for being wrong about reality, I am criticizing you for apparently misunderstanding the theory (Einsteinian cosmology) which you are using as the launchpad for your own.
There is also an intrinsic problem in trying to talk about a varying speed of light while purportedly working within the framework of general relativity. "Speed of light" has two connotations. One is just the speed of the physical phenomenon, light. But the other is a geometric concept - you have spacelike, timelike, and lightlike paths. From that perspective, for physical light to slow down, it would have to change from following a lightlike path to a timelike path. Matti describes one way in which this can happen in a general-relativistic framework, namely if physical light is confined to a hypersurface in a larger space. But you do not even mention this as an issue, you just treat c as if it were an ordinary sort of velocity, free to change without upsetting the whole geometric framework.
Kea , you are also right in that even educated people can't get a simple diagram.
M, it will please you to hear that I suffer under neither misconception. This space is better left for comments on Kea's wonderful blog.
"This does not sound like Einstein at all to me. It sounds like the common misconception of the Big Bang cosmology, according to which the Big Bang was an explosion which took place in a preexisting space, which was empty except for a concentration of mass around some particular point. But that is not what the standard cosmology says!"
Science is about finding and using facts, not just about "standard cosmology". That's education which is consensus, regardless of whether there are facts or not.
When you teach something, you may have to conform to consensus so that your students know the same as other students taught by other people, and will therefore be able to take the same exams and pass.
Science is different to consensus, and this has created problems.
Until quantum gravity and general relativity are combined, you have to stick to facts, not speculations such as the standard application of general relativity with cosmological constant (lambda-CDM) to the data. That's an ad hoc theory which can't be explained by quantum field theory.
For one thing, your definition of "space" is probably the fault. The big bang could in theory be simulated by a 10^55 megatons matter-antimatter explosion.
This would not be an explosion in some "pre-existing space".
What exactly do you mean by pre-existing space?
It's a meaningless concept! The standard model of cosmology has a singularity at time zero, which creates problems (infinite energy density), and will require quantum gravity of some sort to resolve.
Until then, nobody can say what happened or existed (if anything) "before" the big bang.
It's simply incorrect for you to claim that the standard science has resolved the singularity problem and has proved that the big bang definitely created the Dirac sea and the spacetime fabric.
General relativity can give no answer. Today's consensus on a topic dependent on quantum gravity, which is controversial, is meaningless.
As regards the problems with c change, I agree. Take E=Mc^2. If c is varying (Louise has analysed the case where c falls as the inverse cube-root of time), then is M also varying to keep E constant, or does "E" vary? It's not too nice, because if energy isn't constant or conserved, where does it go? To explain this, you could maybe argue that cosmic expansion and associated redshift causes a loss of energy to radiation. As frequencies are redshifted to lower levels, the energy of quanta decrease because of Planck's law, E=hf. I not however too concerned with the idea that GM= tc^3 implies that tc^2 is a constant, and have been investigating the situation where M and c are constant, so G is proportional to t.
Correction. The last sentence in the previous comment should read:
"I not however too concerned with the idea that GM= tc^3 implies that tc^3 is a constant, and have been investigating the situation where M and c are constant, so G is proportional to t."
Nige, I do not say anywhere that "existing science has resolved the singularity problem", or any problem at all. And as for what I mean by "pre-existing space", I just mean the idea that space was there before the Big Bang. Again, I am not saying that is how it was, I am paraphrasing a way of thinking.
Louise is using concepts ripped out of context in a highly suspect fashion. Witness her latest "discovery" that hbar is a variable too! It gets harder and harder to believe that she does know what she's doing, and that I just fail to appreciate the subtleties. She resembles a programmer who has borrowed some code and "improved" it without understanding it first. She got a lot of error messages (angry frustrated response from minions of scientific orthodoxy) and now she's debugging, only she thinks the problem is in the operating system (orthodoxy) and not in the way she modified the application. Well, operating systems do have their problems, but they also are the way they are for reasons. You don't just jump on the developers' list and say, 'Hey guys, why don't you make that system variable SPEEDOFLIGHT time-dependent? Everything will go much more smoothly!' Especially if, a little while later, you have to amend your proposal by making HBAR time-dependent in a compensating fashion! It implies that you didn't know what you were suggesting in the first place.
But enough. Louise, you are in a fix, because (if I am right) you are enacting in a highly public way something that happens on a physics forum somewhere every week: someone has a bright idea (that photons are made of neutrinos, let us say), posts confidently about it, and then discovers that for some strange reason people are very resistant to it. If they are lucky enough to have patient interlocutors and are themselves open-minded enough to listen, they may eventually discover why. If they last that long, they will actually learn something, even if they do decide that, all things considered, they still like their original idea.
But you are in danger of proceeding down a different path, namely intuitive visionary cosmology bolstered with just enough mathematics to make it concrete. A young hot sun, singularities in every planet - you have a great imagination, but that is only enough for science fiction. The history of science is littered with grand imaginative conceptions which were consistent, compelling, and wrong. You may have no choice but to continue, right or wrong, but you do have the chance to be something more than a Wilhelm Reich, if you do it with a little more sobriety and, yes, a little more respect for orthodoxy than you have now. You have the potential to go on making contributions even if your current ideas are completely wrong, but only if you escape from the Galileo persona, and learn a little more about how the existing operating system of physical thought works before you go on a campaign to change it wholesale. So I hope there are people at JCU who can help in this respect.
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