The article which makes the link between time and curvature

Here is the article

http://www.m-hikari.com/astp/astp2008/astp5-8-2008/oliviASTP5-8-2008.pdf

Nathalie - I read your paper and, with due respect, found it somewhat lacking: I do not believe you would have been able to publish that in any mainstream astrophysical journal. But perhaps it is a good place to start exploring the Universe.

Perhaps you are unaware of the vast literature on this - the bibliography of your article is very seriously lacking (2 text books, the most recent of which dates from 1973).

As a starter you might like to read the (old) book "The Early Universe" by Kolb and Turner (Addison Wesley, 1994) which deals with such issues in considerable detail. More recent is the highly technical book "Cosmological Inflation and Large Scale Structure" by Liddle and Lyth (Cambridge University Press, 2000).

thanks for the references. I will try to read them. but, as a matter of fact, my approach is new and I did not find any similar approach: this is why the bibliography of my article is so tiny. Did you find any fundamental error in my paper? Anyway, thanks for your remarks!

Nathalie - The equations you present are OK, except that, for models that have a singularity in the finite past, the equation of state (the relationsip between pressure and density) has to be replaced by the properties of a quantum field that is appropriate to the conditions near to the singularity. In that sense your last few paragraphs on "Heisenberg" are somewhat naive. The books i referred to discuss this issue at great length - that's why I recommended those among the great number of fine books on cosmology.

I should also remark that the diversity of Lambda non-zero models is very great - some do not even have singularities but "bounce" at some finite time in the past. Those "bouncers" however are ruled out by the measurements of the expansion of the universe and in particular by the supernova Hubble diagrams that won last year's Nobel prize for physics. Modern cosmology is in part concerned with pinning down the variety of such "dark energy" models.

Incidentally, one of my favourite books for teaching cosmology is Barbara Ryden's "Introduction to Cosmology" (Addison Wesley 2003). It is not as advanced as the previous books I mentioned, but it is pedagogically superb and thoroughly readable. I wish I could write a book like that!

OK! but I do not use that equation of state to discuss about Heisenberg's principle.

About the acceleration of the expansion of universe, my model accounts very simply for that, see:

http://www.m-hikari.com/astp/astp2011/astp13-16-2011/oliviASTP13-16-2011.pdf

Time may not be a fundamental parameter (property) of the universe, however it is NOT by any means a function of space dimensions. This just does not make any sens.

Gerard, why not?

There just are no such indications.

Gerard, please read the paper above and also:

http://www.m-hikari.com/astp/astp2009/astp1-4-2009/oliviASTP1-4-2009.pdf

Nathalie, thank you for the references. However, there is no way to determine if the rate of propagation of time is not constant, in some absolute sense. There would not be any perceived change on our part as humans.

Now, time may not be a fundamental property of universal laws, but may very well be a consequence of other underlying properties which we perceive as time. There is of course time dilation in relativity. However, unless I missed something very profound in your references, I do not recognize any evidence that time is in any way dependent on space.

Gerard, the dimensional analysis of Einstein's field equations leads to time=length.

It is very simple to verify: if you don't want to make the analysis, read the paper (the link just above)

Treating time as space or space as time is common practice in using a metric (proper time and proper distance), it's just a sign difference. If you are interested in properties for time you can start with the arrow of time, which suggests that time progresses into the future and not into the past. There are indications that, since entropy increases and the special conditions in entropy of the very early universe provide insight into the direction of time. But, I don't see how a dimensional analysis leads to a fundamental law.

It's a dimensional analysis of a fundamental equation. I agree that time is treated as space and inversely, but why time would not be related to a space dimension? (as it's commonly used as a space dimension why would it not be one?). The fact that one can not go reverse in time (space) is because the universe is expanding (see the paper on the top of this thread), and of course time has a direction as the expansion has one. it is not because time has a direction that it is not related to a space dimension.

Nathalie, I return to this discussion because I see that you are a respected scientist in a respected institution and I realize that we are diverting from the original question, but maybe that is what such a discussion forum should accomplish. Let's just take your argument step by step:

"Einstein's field equations leads to time=length", well, through dimensional analysis Einstein's field equations lead to what is known as "Proper Time = - Proper Distance", that is what we use on the "opposite sides of curvature" of whatever it is we are generating Metrics and Tensors for. And I have left cues along the way for you, which you have chosen to ignore, all you respond with is something like: "Please read my references". I have read your references and I would prefer not to comment on them. You have not explained any of your references in words, again all you say is "read my papers". I'm sorry, but your papers consist of a few simple equations.

Let's consider another example: Max Plank performed dimensional analysis in order to come up with a value for what we now call Plank's constant. This dimensional analysis is not what determined the fundamental meaning of "h", it only gives us a way to represent the measure of "h" in some ambiguous units we now call the metric system.

And another example, we can define units where "c", the speed of light is equal to 1, then:

E = m (kin of like proper time = - proper distance)

Nathalie, to consider that time is a function of space is, well ... ??.

There are of course other theories of time which proclaim that time is multi-dimensional, maybe even having "complex dimensions". Do any of these theories last?

As scientists, we need to be flexible and adapt to new thing we learn. I tried to point your interest in time in a direction which has a basis to it, however it is up to you to free yourself from your single mindedness.

String theory is beautiful mathematics and Witten was appropriately awarded the Fileds Medal - the Nobel Prize of mathematics - for that. Whether it is relevant to cosmolgy or any other branch of physics is a serious debate. It is up to the proponents of that idea to promote it. It is certainly not insane, and indeed it is not good of you to say that without offering up serious arguments. Merely proposing a so-called alternative is not an argument against string theory.

I am not an expert on string theory, but I have studied Zwiebach's fabuulous book "String Theory" and so I do understand a bit about it. However, I am far from competent to judge the value of string theory to cosmology and so would not presume to do so. I leave that to those who do have that competence and I eagerly await their verdict. I suggest you do the same.

Sorry but I did not intend to judge the mathematics of string theory. I just think that these theories make very many hypotheses (more than 14 dimensions) which will undergo a long time to check.

I was saying 'insane' as a joke: just humor...

The Standard Model for particle physics has evolved over several decades to present a unified model of electromagnetic, weak and strong interactions. During that period it was frequently regarded as having "many hypotheses", as you put it. But slowly with a lot of hard work by hundreds, if not thousands, or scientists this has now become a cornerstone of modern physics. It has made predictions that have been verified and won Nobel Prizes, and perhaps the ultimate was the discovery of the Higgs boson this year (which still needs to be confirmed). In the end this is a triumph for Quantum Field Theory - which you may with some justificatino regard as no less abtruse than string theory!

There are still gaps in the standard model. The biggest of all is perhaps that of bringing in gravitational forces within th framework. Maybe that's what string theory will do, maybe not. However it is one of several paths that we must follow and test - it might take decades or even longer. During that time some brilliant person might come up with a totally different viable and testable alternative and then win their Nobel Prize. But you can bet that such an alternative may will be as abtruse as its predecessors! Like what happened in 1916 with Einstein's theory of General Relativity - deep, complex, radical and totally brilliant.

Nathalie,

You wrote: "proper time=-proper distance, it is exactly what I tried to show"

Yes, know and now you have explained it. I suppose this a finer point of the English language. English provides us with the luxury of different words for "Space", "Distance ( a scalar quantity ) and "Displacement" ( a vector quantity ), all with different meanings. Some languages have little, if any distinction between "space" and "distance" , where terminology may be ambiguous. I was just trying to get you to make that distinction.

I totally agree with your presentation on the relation between time and distance.