Big bang location

hartlw

Sounds like mysticism to me. You haven't defined x,y,z,t other than as mathematical coordinates, and you purport to describe the universe without even considering mass as a variable.

True, there is the axiomatic approach. Assume undefined variables, call them what you will, and assume a mathematical relation between them. Then associate the result with a physical reality. Depending on your mathematical creativity, you could explain almost any specific physical event that way and then claim the general truth of your "theory.".

cristo

But that's because that's what they are. One can't write down a theory in mathematics, and expect not to use mathematical coordinates! The theory of relativity says that we live in a four dimensional spacetime. This theory has agreed with experiment to an outstanding accuracy, and is currently our best theory. I don't think that your argument of "mysticism" holds up, because it is a personal opinion. Just because you don't understand something, or you don't think it intuitive doesn't automatically void all experimental evidence, or make the theory incorrect. Finally, I don't see anywhere in my post that I went on to describe the universe at all, and I didn't discuss anything to do with mass. Let's not put words into the mouths of others, please.

hartlw

Relativity says something about the speed of light without defining either distance or time. With that kind of flexibility, you can explain anything you want.

Classical physics and science has always started with very specific definitions of space and time. The problem with classical physics was that it exposed the theories to intelligent criticism.

I have a 5D model of the universe. I call the dimensions spatial location x,y,z , time, and color, but do not define them. They satisfy hartl's equation.

I would explain it to you but you would have to be well versed in modern algebra, euclidean and affine geometry, algebraic geometry, covariant and contravariant tensors in n-dimensional space, n-dimensional and infinite dimensional vector space, and advanced calculus.

My equation explains all physical phenomena.

hartlw

And of course, since my equation explains space, time and the physical universe, I am responsible for all material and scientific progress in the twentieth century.

Transistor? me
DNA? me
Space Travel and Satelite Communications? me
Atomic Energy? me
and so on

marcus

Please don't leave us in suspense. What is Hartl's equation? Please write it down for us.

Fredrik

No.

Now you're talking about spacetime, not space, and what you can access in your future is irrelevant to what we're talking about.

No, it isn't. (And I don't). The problem is that you believe that your intuitive ideas about space and time are somehow "better" than any theory. You don't seem to reallize that your intuitive ideas (which are the same as everyone else's intuitive ideas) is just another theory about the real world, which by the way has been thoroughly disproved by experiments.

I can't teach you general relativity here, but I can give you a brief outline of some of the basic ideas. Spacetime is a 4-dimensional manifold M. A coordinate system is a function [itex]x:U\rightarrow\mathbb R^4[/itex], i.e. the coordinate system is the function that assigns coordinates to events:

[tex]x(p)=(x^0(p),x^1(p),x^2(p),x^3(p))[/tex]

If you'd like, you can use the notation (t,x,y,z) for the thing on the right. These are however not the variables in Einstein's equation. The variables are the components of the metric tensor, which contains all the information about the geometric properties of spacetime. Einstein's equation describes the relationship between the metric tensor and the stress-energy tensor, which represents the properties of matter. You asked specifically about mass. Mass enters the equation through the equivalence between mass and energy (E=mc²) because one of the ten independent components of the stress-energy tensor is energy density.

The relevant solutions of this equation are found by first assuming that spacetime can be "sliced" into a one-parameter family of spacelike hypersurfaces [itex]\Sigma_t[/tex] (we can think of each [itex]\Sigma_t[/tex] as "space, at time t"), such that each [itex]\Sigma_t[/tex] is homogeneous and isotropic (according to a precise mathematical definition of those terms). There are only three solutions of Einstein's equation that are consistent with that assumption. (Wikipedia link). These three solutions describe space as a 3-dimensional version of a sphere, a plane and a hyperboloid respectively. Spheres are finite in size. Planes and hyperboloids are not.

It's convenient, but not necessary, to define a coordinate system x that assigns time t to all the points in [itex]\Sigma_t[/tex]. (I.e. [itex]x^0(p)=t[/itex] when [itex]p\in\Sigma_t[/itex]). If we do, we find that t can't be defined for all real t. There exists a t₀ such that t is only defined for t>t₀. It's convenient to choose t₀=0.

The fact that each [itex]\Sigma_t[/itex] looks like a sphere, a plane or a hyperboloid means that there's also a very natural way to assign the spatial coordinates to points on [itex]\Sigma_t[/itex]. This gives us a way to identify a point on [itex]\Sigma_t[/itex] with a point on [itex]\Sigma_s[/itex] when [itex]t\neq s[/itex], and this allows us to define the distance between any two points in space as a function of time. It can be shown that this distance goes to zero as t goes to zero. That's why the limit t→0 is called "the big bang".

DaveC426913

A point of order if I may.

Your original post was asking where the centre of the universe is. You don't have to delve very far into cosmology to dispose of this misconception. We've shown you that the centre of the universe is everywhere. This was shown in the BB model - without resorting to extra dimensions.


Aside from that, you've asked how a volume can be finite yet unbounded, which we're showing you using the notion of extra dimensions. This is what we are now discussing.

Let's just back up.

Are you satisfied that your idea of a centre of the universe was naive?

I am a bit confused as to how you could have - in the same breath - thought there was a centre to the universe and yet argue with confidence that you know about higher-order dimensional space.

Can you clarify you level of understanding of this science field?

hartlw

Since you haven't identified (defined) what you are talking about, I don't understand a word you are saying. You are simply taking symbols, manipulating them mathematically, and calling the result a proof of something.

How can you say your equation says something about the real world when you don't even define the terms of your equation other than giving them a name, which anybody can do. Let's see, space is really time and time is really space, so your results are wrong.

cristo

Is this "hartl theory" published in a peer-reviewed journal? If so, please give a reference. If not, then note as per PF rules, you may not discuss it here: you must take your discussion to the Independent Research forum.

If, however, you're trying to be funny, you're not succeeding. Pack it in.

hartlw

You keep confusing physical space with mathematical space and on that basis draw erroneous conclusions about what you say I said. Obviously a conclusion about mathematical space says nothing about physical space without a clear definition of the variables, and the physical source of the equations. Simply naming a variable is meaningless.

Why is it inappropriate in a physics forum to ask for the meaning of the terms used in physics? If you can't define the terms in your equations then this discussion is meaningless.

Perhaps a new thread is in order: "How many angels can dance on the head of a pin?"

Fredrik

You're not just asking about definitions. You're spending a lot of your time insinuating that physics is all nonsense, and that those who claim to understand it are just "confused". People who keep doing that tend to get banned around here, so you might want to tone it down a little.

No one here is confusing "physical space" with "mathematical space". You're right that a mathematical model by itself doesn't make predictions about the real world (if that's what you're trying to say). My personal opinion is that this isn't emphasized often enough. What you need to turn a mathematical model into a theory of physics is a set of postulates that describe how the things we measure are related to things in the model. Those postulates are usually described as "operational definitions". An example is "time is what you measure with a clock". (A more precise statement is that a clock measures the proper time of the curve in spacetime that represents the clock's motion).

We spend a lot more time discussing the model than the details of its relationship with the real world simply because it's the model that's causing most people difficulties.

hartlw

Frederik,

If it is being said that General Relativity says something about the mathematically defined variables x,y,z,t, or lets say q,r,v,w, fine. I'll accept that. There's really nothing to discuss.

Just saw your latest post. You ascribe to me sweeping statements that I didn't make. But I'll clarify what I was implying: in my opinion, physics without careful definiton of terms is nonsense. I haven't come across any physics books that don't start with a careful definition of what is being discussed. I guess we don't read the same books.

Let's clean this up.
I don't understand General Relativity.
You do.
You win.
Congratulations.

hartlw

I have the answer. Start a mathematics forum. A typical thread might begin:

I have variables u,r,s,t that satisfy the following tensor equation. The solution to this equation says.....

If you don't define u,r,s,t you are not doing physics, in my opinion. So I question the appropriateness of this approach in a physics forum.

hartlw

If you use the result to define your premise you are engaging in circular reasoning.

DaveC426913

This thread has gone off the reservation. Higher-order math aside, are you still asking where the centre of the universe is?

You need to witidraw and restate the question you want answered.

Fredrik

Hartlw,

I really don't understand what you're complaining about. It obviously isn't possible to teach GR from scratch in every thread that has something to do with GR. The definitions you seek are available in any GR book. If you want a definition of some specific thing, then we can probably help you out.

Here's a (partial) definition that you definitely need: A coordinate system is just a function from an open subset of the spacetime manifold into [itex]\mathbb R^4[/itex]. (Yes, there are some technical requirements, but they are irrelevant here).

What else do you feel hasn't been sufficiently defined?

hartlw

In response I get something about the universe being a balloon.