Answering Mermin’s Challenge with the Relativity Principle

[RUTA]

If you have a spacetime that meets the conditions of the singularity theorems, and which therefore has an initial singularity, it seems to me that the singularity theorems themselves would provide an adequate nondynamical explanation of the initial singularity, since, as I've said, those theorems are not dynamical, they're geometrical.

So, you tell me, why do I have to past extend beyond $a(0) \neq 0$ to a singularity in a simple Einstein-deSitter model for example?

 

[PeterDonis]

So, you tell me, why do I have to past extend beyond $a(0) \neq 0$ to a singularity in a simple Einstein-deSitter model for example?

I have made no such claim, so I don't see why I should have to justify it.

You don't appear to even be reading what I'm actually saying. I'm just asking which of these two options you are choosing:

(1) You are disputing that the singularity theorems are mathematically correct: you think there can be a model that satisfies all of the premises of the singularity theorems but does not have an initial singularity; or

(2) You are accepting that the models you are interested in, which do not have initial singularities (and I am not in any way disputing that you can have legitimate reasons for being interested in such models), violate at least one of the premises of the singularity theorems (the obvious ones to violate would be the energy conditions, since we already know inflationary models and models with a positive cosmological constant violate them anyway).

I don't see a third option.

 

[PeterDonis]

why do I have to past extend beyond $a(0) \neq 0$ to a singularity in a simple Einstein-deSitter model for example?

Since the Einstein-de Sitter model satisfies the conditions of the singularity theorems (assuming you mean the model described on this Wikipedia page), it must have an initial singularity. Whether you call the point of that initial singularity $a(0) = 0$ or redefine your coordinates so the singularity occurs at some coordinate time before $t = 0$ doesn't make a difference to the global geometry of the solution.

 

[RUTA]

I have made no such claim, so I don't see why I should have to justify it.

You don't appear to even be reading what I'm actually saying. I'm just asking which of these two options you are choosing:

(1) You are disputing that the singularity theorems are mathematically correct: you think there can be a model that satisfies all of the premises of the singularity theorems but does not have an initial singularity; or

(2) You are accepting that the models you are interested in, which do not have initial singularities (and I am not in any way disputing that you can have legitimate reasons for being interested in such models), violate at least one of the premises of the singularity theorems (the obvious ones to violate would be the energy conditions, since we already know inflationary models and models with a positive cosmological constant violate them anyway).

I don't see a third option.

You have to look at what they proved. If you have a copy of Wald, read chapter 9 section 1, "What is a Singularity?" I'm not going to type that entire section here, but you'll find that the notion of a singularity is difficult to define, so the singularity theorems proved "the existence of an incomplete timelike or null geodesic." That such a place is exists is deemed "pathological" because "it is possible for at least one freely falling particle or photon to end its existence within a finite "time" (i.e., affine parameter) or to have begun its existence a finite time ago." So, my choice of $a(0) \neq 0$ would satisfy their definition of a singularity. It's not infinite density or infinite curvature, it's an entirely well-behaved "singularity," so I am not calling it a singularity. Here is the last sentence in that section, "Unfortunately, the singularity theorems give virtually no information about the nature of the singularities of which they prove existence."

 

[DarMM]

Regarding adynamical explanations: I think it would be fine if we said that there is a 4D manifold of events $\mathcal{M}$ with some set of data $\Sigma\left(\mathcal{M}\right)$ at each event but that $\Sigma\left(\mathcal{M}\right)$ must obey some constraint $\delta \Sigma\left(\mathcal{M}\right) = 0$ with $\delta$ intended in some highly symbolic way as I'm not proposing such a constraint.

If we then went out and checked that the physical content of events matched that predicted by the constraint, that would be clearly scientific and sensible. I don't think it is required that the data on each leaf of a foliation of $\mathcal{M}$ must be related to that on any other leaf via some Green's function or other expression of dynamical propogation in order for the theory to be scientific or count as an explanation.

Classical theories were always such that data on later leaves followed from that on earlier leaves via integration against some kernel (or similar), but I don't think this must be true.

 

[PeterDonis]

You have to look at what they proved.

Yes, I know that, strictly speaking, "singularity" means "geodesic incompleteness".

my choice of $a(0) \neq 0$ would satisfy their definition of a singularity.

Why? Since you appear to be saying the spacetime in the model you describe here is extendible past $t = 0$ indefinitely (i.e., to arbitrary negative values of $t$), then geodesics in the model would be similarly extendible. So the spacetime in your model would not be geodesically incomplete, hence would not contain a singularity.

If you think your model would still be geodesically incomplete while still being extendible indefinitely past $t = 0$, then you will have to give quite a bit more detail about your model, because I don't understand how it would be, given what you have said so far and what kind of model you appear to be interested in.

 

[PeterDonis]

you will have to give quite a bit more detail about your model

Or a pointer to a paper or other reference that describes the sort of model you are referring to would be fine.

 

[RUTA]

Why? Since you appear to be saying the spacetime in the model you describe here is extendible past $t = 0$ indefinitely (i.e., to arbitrary negative values of $t$), then geodesics in the model would be similarly extendible. So the spacetime in your model would not be geodesically incomplete, hence would not contain a singularity.

If you think your model would still be geodesically incomplete while still being extendible indefinitely past $t = 0$, then you will have to give quite a bit more detail about your model, because I don't understand how it would be, given what you have said so far and what kind of model you appear to be interested in.

If you choose to have the "beginning" be at $a(0) \neq 0$ in the EdS model, for example, then you have a "singularity" per their definition. It's "pathological" because "it is possible for at least one freely falling particle or photon to ... have begun its existence a finite time ago." That's only pathological from the dynamical perspective, as I explained using the thrown ball example.

 

[PeterDonis]

If you choose to have the "beginning" be at $a(0) \neq 0$ in the EdS model

You can't; the Einstein-de Sitter model is a known exact solution of the EFE and has $a(0) = 0$.

I suppose you could quibble about this by changing coordinates so that the value of $t$ where $a = 0$ is not $t = 0$; but it will have $a = 0$ at some value of $t$. That is a known geometric property of the model.

You seem to be confusing the (true) statement that the singularity theorems by themselves don't tell you very much about the actual properties of the singularities, with the (false) statement that you can just handwave any kind of singularity you want into a specific model. We know a lot more about the EdS model than just what the singularity theorems tell us.

If you want to construct some other model that looks like the EdS model for some range of $t$ (such as, for example, redshifts smaller than $z = 1000$ or so), but then differs at values of $t$ before that, that's fine. If you can show that such a model, while satisfying the premises of the singularity theorems and therefore being geodesically incomplete, nevertheless has $a(0) \neq 0$, that's fine too. But you can't just wave your hands and say "EdS model" to do that; you have to actually construct the other model and show that it has the properties you claim it has.

 

[RUTA]

You can't; the Einstein-de Sitter model is a known exact solution of the EFE and has $a(0) = 0$.

It's a second-order differential equation, of course you can freely choose $a(t)$ at two different times to find a particular solution. There is no quibble, it's a mathematical fact.

 

[PeterDonis]

It's a second-order differential equation

The Einstein Field Equation is a second-order differential equation, for which you can freely choose as you say.

The Einstein-de Sitter model is not; it is a particular solution to that equation, in which there is no more freedom to choose $a(t)$; it's exactly specified for the entire solution.

There is no quibble, it's a mathematical fact.

A mathematical fact about the wrong thing. See above.

 

[RUTA]

The Einstein Field Equation is a second-order differential equation, for which you can freely choose as you say.

The Einstein-de Sitter model is not; it is a particular solution to that equation, in which there is no more freedom to choose $a(t)$; it's exactly specified for the entire solution.

You're arguing semantics now. Call it something else, then. The point is, we have a solution of EE's for the spatially flat, matter-dominated cosmology model without infinities. If this solution bothers you, you need to ask yourself, "Why does this solution bother me?" Wald was clear about why it would bother him, but that is purely dynamical bias.

 

[RUTA]

Again, you're free to have a dynamical bias and ignore adynamical explanation. But, that sentiment does not in any way refute the point I'm making, i.e., adynamical constraint-based thinking avoids the problem caused by dynamical thinking in this case.

 

[PeterDonis]

You're arguing semantics now.

I'm using the same terms you used. I'm just correcting your erroneous usage of them.

The point is, we have a solution of EE's for the spatially flat, matter-dominated cosmology model without infinities.

Then you need to show me one, because the EdS model is not one.

you're free to have a dynamical bias

I have said nothing at all about my personal preferences. If you make statements that are wrong as a pure matter of math, you should expect to have them corrected. Correcting them is not "bias", it's just correcting erroneous statements. Your claim that the EdS model is "without infinities" is wrong as a pure matter of math: the EdS is a specific solution of a specific equation with specific properties, and those properties include $a = 0$ at $t = 0$.

Your claim that there might be some solution of the EFE that is spatially flat, matter-dominated, but without any point at which $a = 0$ might be true; but you can't just wave your hands and claim it. You need to show such a solution, or prove that one exists. You have done neither. My pointing that out is not "bias"; it's just asking you to show your work.

 

[RUTA]

I have said nothing at all about my personal preferences. If you make statements that are wrong as a pure matter of math, you should expect to have them corrected. Correcting them is not "bias", it's just correcting erroneous statements. Your claim that the EdS model is "without infinities" is wrong as a pure matter of math: the EdS is a specific solution of a specific equation with specific properties, and those properties include $a = 0$ at $t = 0$.

Your claim that there might be some solution of the EFE that is spatially flat, matter-dominated, but without any point at which $a = 0$ might be true; but you can't just wave your hands and claim it. You need to show such a solution, or prove that one exists. You have done neither. My pointing that out is not "bias"; it's just asking you to show your work.

Go to this Insight and you'll see the solution I'm talking about. I have not said anything "mathematically incorrect." I assumed you were familiar with the differential equation resulting from the spatially flat, matter-dominated cosmology model called Einstein-deSitter, which is the differential equation I am solving. The only dispute you have raised here is that you claim the EdS solution entails $a(0) = 0$, while I am using the term to mean the spatially flat, matter-dominated model. We can argue semantics if you like, but it doesn't change anything.

 

[PeterDonis]

Go to this Insight and you'll see the solution I'm talking about.

Thank you for the pointer, it's much better to talk about a specific model.

the differential equation I am solving

Do you mean equation (18) in the Insight?

 

[RUTA]

Do you mean equation (18) in the Insight?

Yes

 

[PeterDonis]

Yes

Ok, then yes, I agree you can pick $a(0) \neq 0$ in your solution, and, as far as I can tell, that also makes $\dot{a}$, $\ddot{a}$, and $\rho$ finite at $t = 0$ (basically because you have substituted $t + B$ for $t$, so all of the values at $t = 0$ are proportional to some power of $B$ instead of diverging).

However, this model is obviously extensible to negative values of $t$, and when you reach $t = - B$, your model has $a = 0$ and $\dot{a}$, $\ddot{a}$, and $\rho$ all infinite. So your model is not a different model from the standard one, it's just a shift of the $t$ coordinate by $B$ (strictly speaking there is a rescaling of $t$ as well). Considering the patch $t \ge 0$ in this model is simply equivalent to only considering the patch $t \ge B$ in the standard Einstein-de Sitter model. This is not a model in which the singularity theorems are violated; it's just a model in which you have artificially restricted attention to a particular patch.

 

[RUTA]

Ok, then yes, I agree you can pick $a(0) \neq 0$ in your solution, and, as far as I can tell, that also makes $\dot{a}$, $\ddot{a}$, and $\rho$ finite at $t = 0$ (basically because you have substituted $t + B$ for $t$, so all of the values at $t = 0$ are proportional to some power of $B$ instead of diverging).

However, this model is obviously extensible to negative values of $t$, and when you reach $t = - B$, your model has $a = 0$ and $\dot{a}$, $\ddot{a}$, and $\rho$ all infinite. So your model is not a different model from the standard one, it's just a shift of the $t$ coordinate by $B$ (strictly speaking there is a rescaling of $t$ as well). Considering the patch $t \ge 0$ in this model is simply equivalent to only considering the patch $t \ge B$ in the standard Einstein-de Sitter model. This is not a model in which the singularity theorems are violated; it's just a model in which you have artificially restricted attention to a particular patch.

Right, the singularity theorem is not violated because it is still true that there are timelike and null geodesics with finite affine parameter lengths into the past (finite proper time). But, all the observables and physical parameters are finite (except meaningless ones like the volume of spatial hypersurfaces of homogeneity). It is absolutely "artificial" in that there is no dynamical reason whatsoever for not extending the solution into the past (with negative values of t) all the way to $a = 0$. But, in the 4D global self-consistent view, there is no reason to do that. You only need as much of the spacetime manifold as necessary to account for your observations. I don't foresee a need for $\rho = \infty$, i.e., $a = 0$, but if we ever do need such $\infty$, then you can include it at that point.

 

[PeterDonis]

all the observables and physical parameters are finite

Not at $t = - B$. There the density $\rho$ is infinite.

in the 4D global self-consistent view, there is no reason to do that

Yes, there is, because in the 4D global self-consistent view, the manifold is its maximal analytic extension. Arbitrarily cutting it off at some point prior to that makes no sense on that view. If you think it does because of some "adynamical constraint", what is that constraint? It can't be "because RUTA prefers to cut off the solution at $t = 0$ in his model".

You only need as much of the spacetime manifold as necessary to account for your observations.

Not if you want your model to make testable predictions about observations that haven't been made yet.

 

[RUTA]

Not at $t = - B$. There the density $\rho$ is infinite.

Yes, there is, because in the 4D global self-consistent view, the manifold is its maximal analytic extension. Arbitrarily cutting it off at some point prior to that makes no sense on that view. If you think it does because of some "adynamical constraint", what is that constraint? It can't be "because RUTA prefers to cut off the solution at $t = 0$ in his model".

Not if you want your model to make testable predictions about observations that haven't been made yet.

As I explained in the Insight, EEs of GR constitute the constraint. Any solution of EEs that maps onto what you observe or could conceivably observe is fair game. There is nothing in GR that says you must include extensions of M beyond what maps to empirically verifiable results. But, if you have a prediction based on $a = 0$ and $\rho = \infty$, by all means include that region.

 

[PeterDonis]

As I explained in the Insight, EEs of GR constitute the constraint.

That doesn't explain why you would cut off a solution of the EFE short of its maximal analytic extension.

There is nothing in GR that says you must include extensions of M beyond what maps to empirically verifiable results.

Again, you have to do this if you want your model to make testable predictions about observations that haven't been made yet.

Also, the position you appear to be taking seems highly implausible on your own "blockworld" viewpoint. Why would a "blockworld" just suddenly have an "edge" for no reason? It seems much more reasonable to expect any "blockworld" to extend as far as the math says it can.

 

[RUTA]

That doesn't explain why you would cut off a solution of the EFE short of its maximal analytic extension.

Again, you have to do this if you want your model to make testable predictions about observations that haven't been made yet.

Also, the position you appear to be taking seems highly implausible on your own "blockworld" viewpoint. Why would a "blockworld" just suddenly have an "edge" for no reason? It seems much more reasonable to expect any "blockworld" to extend as far as the math says it can.

Look again at the partial parabola for the trajectory of a ball with $y(0) = 3$. We don’t include the mathematical extension into negative times demanding therefore we must include $y = 0$. Why? Because we don’t believe there can be any empirical evidence of that fact. So, in adynamical thinking the onus is on you to produce a prediction with empirical evidence showing you need to include $a = 0$ with $\rho = \infty$. We can then do the experiment and see if your prediction is verified. If so, according to your theory, we need to include that region. There is no reason to include mathematics in physics unless that mathematics leads to empirically verifiable predictions. So, what is your prediction?

 

[martinbn]

They're looking for past extendability and found it. Why were they looking for that? Because they were thinking dynamically. Here is an analogy.

Set up the differential equations in y(t) and x(t) at the surface of Earth (a = -g, etc.). Then ask for the trajectory of a thrown baseball. You're happy not to past extend the solution beyond the throw or future extend into the ground because you have a causal reason not to do so. But, the solution is nonetheless a solution without those extensions. Same for EEs with no past extension beyond a(0) and a choice of a(0) not equal to zero. Why are you not satisfied with that being the solution describing our universe? There's nothing in the data that would ever force us to choose a(0) = 0 singular. The problem is that the initial condition isn't explained as expected in a dynamical explanation. All we need in 4D is self-consistency, i.e., we only have to set a(0) small enough to account for the data. Maybe someday we'll have gravitational waves from beyond the CMB and we'll be able to push a(0) back to an initial lattice spacing approaching the Planck length. But, we'll never have to go to a singularity.

I am missing something very basic here. Take for example $y''=2$ on the interval $[0,2]$ with $y(1)=1$ and $y(2)=4$. The only solution is $y(x)=x^2$. How do you make $y(0)$ not equal to zero?

 

[RUTA]

I am missing something very basic here. Take for example $y''=2$ on the interval $[0,2]$ with $y(1)=1$ and $y(2)=4$. The only solution is $y(x)=x^2$. How do you make $y(0)$ not equal to zero?

There are any number of reasons you might want to use $y = 0$, but you have to come up the reason to do so. You don’t use the math to dictate the use of $y = 0$. What if I want to use the math for throwing a ball? I don’t use $y = 0$ because I believe it is not possible to find empirical verification of that fact. Again, the empirically verifiable physics drives what you use of the math, not the converse. So, again, what is your prediction requiring I keep $a = 0$ with $\rho = \infty$? Produce that prediction and its empirical verification and we’ll know we have to keep that region.

 

[martinbn]

My point was, that in the given example if I need the value $y(0)$, I don't have the freedom the choose it, it is a consequence of the equation and the other values. It seemed to me that you were saying that in the cosmological model you can just addjast that value?

 

[RUTA]

The key phrase there is "if I need the value of $y = 0$" (the origin of the time parameterization is irrelevant of course). So, what dictates your need? Empirical results, not math results. Same with $a = 0$ with $\rho = \infty$. Do you have an empirically verifiable prediction requiring we keep $a = 0$ with $\rho = \infty$? If so, we'll check it and if you're right, we'll need to keep that region. Otherwise, why would we keep it?

 

[martinbn]

The key phrase there is "if I need the value of $y = 0$" (the origin of the time parameterization is irrelevant of course). So, what dictates your need? Empirical results, not math results. Same with $a = 0$ with $\rho = \infty$. Do you have an empirically verifiable prediction requiring we keep $a = 0$ with $\rho = \infty$? If so, we'll check it and if you're right, we'll need to keep that region. Otherwise, why would we keep it?

I suppose I missunderstood. I thought you were claiming that at $t=0$, the quantity $a$ has to have a value, and since the value zero is problematic you don't use that value, but you use a different value. Of course not using any value and saying that the solution is valid only vor $t>0$ is fine, and that is what is done in GR anyway.

 

[RUTA]

... that is what is done in GR anyway.

Exactly, we’re using $\Lambda\text{CDM}$ successfully to make predictions relying on conditions even before decoupling (anisotropies in CMB power spectrum depend on pre-decoupling oscillations). No one is saying, “Well, if you extrapolate that cosmology model backwards in time far enough, you get $\rho = \infty$, so I guess we have to stop using it otherwise.” That’s silly. Again and again, as I keep showing, adynamical thinking vindicates what we’re doing in modern physics, revealing its coherence and integrity. The Insight here is refuting Smolin et al. who believe “quantum mechanics is wrong because it’s incomplete.” Modern physics isn’t wrong or incomplete, it’s true it isn’t finished (we need to connect quantum and GR), but what we have is totally right. All its mysteries can be attributed to our dynamical bias (you don’t have to attribute them to that, but you can).

 

[Elias1960]

Why were they looking for that? Because they were thinking dynamically. Here is an analogy.

Set up the differential equations in y(t) and x(t) at the surface of Earth (a = -g, etc.). Then ask for the trajectory of a thrown baseball. You're happy not to past extend the solution beyond the throw or future extend into the ground because you have a causal reason not to do so. But, the solution is nonetheless a solution without those extensions.

Why should we be happy with this? Only because we know that before the moment of the throw we have a completely different physical situation, namely a baseball in a hand. There was a physical act of creation of the flying baseball which tells us that it makes no sense to apply the physics valid after the act of creation to the situation before. So, the creationist is happy with the trajectory of the world as described in the Holy Scripture and is happy not to extend the actual laws of physics past the moment of creation.

Same for EEs with no past extension beyond a(0) and a choice of a(0) not equal to zero. Why are you not satisfied with that being the solution describing our universe? There's nothing in the data that would ever force us to choose a(0) = 0 singular.

Because we have no evidence for any act of creation of different physics for any a(0)>0. The creationist has such evidence - in his Holy Book. We don't have. Our Holy Script

The problem is that the initial condition isn't explained as expected in a dynamical explanation. All we need in 4D is self-consistency, i.e., we only have to set a(0) small enough to account for the data.

In this case, your approach is even worse than I thought when I started my creationist analogy. The subset of our FLRW universe restricted to the last 5000 years is (or at least we hope so) self-consistent. There is nothing in the data which forces us to go beyond the 5000 years.

In classical "dynamical thinking", there is a lot that forces us to look into the past. Namely, there is causality, with Reichenbach's common cause principle (the one we have to throw away to save relativity) which forces us to search for common causes for all the correlations we see around us, for all those dinosaur bones and so on. But with the rejection of the common cause, they have to be simply ignored. Is there anything inconsistent with these bones? Not. Thus, there is no problem.

Science is what it is because the scientific method identifies open problems of existing theories. Without trying to solve open problems, scientists could restrict themselves to the teaching of the Holy Scriptures of Euclid or Ptolemaeus, maybe Newton, maybe Einstein, whatever was the actual state of science when scientists no longer cared about the usual problems of "dynamical thinking" and restricted themselves to the consistency of the Scriptures.

Maybe someday we'll have gravitational waves from beyond the CMB and we'll be able to push a(0) back to an initial lattice spacing approaching the Planck length. But, we'll never have to go to a singularity.

This is not how it works. First, we have to compute something nontrivial about those gravitational waves. This initial step already requires to go far beyond what is accessible to data now. Any attempts to build devices that could test that particular theory of the gravitational waves in CMBR would have to be based on this application of GR (together with similar applications of alternatives of GR, or some sort of null hypothesis if there are none).

 

[RUTA]

It's always true, even with dynamical thinking, that reality could have begun 10 min ago with all the signs of a past beyond that. You can choose to model reality that way, but I'm not suggesting we do so. I'm saying we should take the model as far back as necessary to account for our observations. With anisotropies in the CMB that's before decoupling. @Elias1960, you have a strong dynamical bias, so you should pursue a model consistent with that. Again, you're not in any way refuting the point I'm making by simply espousing your dynamical bias.

 

[PeterDonis]

We don’t include the mathematical extension into negative times demanding therefore we must include $y = 0$. Why?

Because we already know there is a constraint: the ball wasn't freely flying at negative times, it was sitting on the ground. So we don't extend the parabolic trajectory to negative times because we know it doesn't apply. Instead, we join that trajectory to a different trajectory for negative times.

Now, suppose that we weren't watching the ball at all at negative times and had no empirical evidence whatever of its trajectory then. But we do know that the surface of the Earth is there and that the parabolic trajectory intersects that surface at $t = 0$. How would we model the ball? Would we just throw up our hands and say, well, we don't have any evidence at negative times so we'll just cut off our model at $t = 0$ and stop there? Or would we exercise common sense and predict that, at negative times, the ball is sitting on the surface of the Earth, and someone threw it upwards at time $t = 0$, and extend our model accordingly?

As far as I can tell, you prefer the first alternative and I (and others, it appears) prefer the second. Can I give you a logical proof that you must use the second alternative? No. But I can tell you that the first alternative makes no sense to me, and I suspect it makes no sense to a lot of other people.

in adynamical thinking the onus is on you to produce a prediction with empirical evidence showing you need to include $a = 0$ with $\rho = \infty$.

I haven't made any such prediction. I don't have a problem with looking for a solution that does not have $\rho = \infty$ at $t = 0$. And we have such solutions: inflationary models do not require $\rho = \infty$ at $t = 0$. Eternal inflation is a possibility. Other possibilities have been suggested as well. If your position is that everybody except you is stuck in a rut thinking we have to have $\rho = \infty$ at $t = 0$, then I think you are ignoring a lot of work being done in cosmology.

OTOH, what I do have a problem with is saying, oh, well, we don't have any empirical evidence for times before the hot, dense, rapidly expanding state that in inflationary models occurs at the end of inflation, so we'll just cut off the model there and pretend nothing existed before that at all, it just suddenly popped into existence for no reason. That, to me, is not valid adynamical thinking. Valid adynamical thinking, to me, would be that the 4-D spacetime geometry, which does not "evolve" but just "is", should extend to wherever its "natural" endpoint is. The most natural thing would be for it to have no boundary at all, which means that if your model has a boundary in it, which it certainly does if you arbitrarily cut off the model the way you are describing, your model is obviously incomplete. Unless you can show some valid adynamical constraint that requires there to be a boundary at that particular place in the 4-D geometry. I have not seen any such argument from you.

I'm saying we should take the model as far back as necessary to account for our observations.

But why should we stop there? Why should our observations be the criterion for where the 4-D spacetime geometry of the universe has a boundary?

There is no reason to include mathematics in physics unless that mathematics leads to empirically verifiable predictions.

Inflationary models, which carry the 4-D spacetime geometry of the universe back past the earliest point we can currently observe directly, do make empirically verifiable predictions. But those models were developed before anyone knew that they would be able to make such predictions. You seem to be saying nobody should bother working on any model unless it covers a domain we already have empirical data from. That doesn't make sense to me; if we did that we would never make any predictions about observations we haven't made yet. But science progresses by making predictions about observations we haven't made yet.

No one is saying, “Well, if you extrapolate that cosmology model backwards in time far enough, you get $\rho = \infty$, so I guess we have to stop using it otherwise.”

You're right that no one is saying that. But that's because no one is extrapolating the model backwards in time to $\rho = \infty$ in the first place. Everyone appears to me to be looking at how to extend our best current model in ways that don't require $\rho = \infty$ anywhere. Nobody appears to me to be saying, "oh, well, we'll just have to arbitrarily cut off the model at the earliest point where we can make observations, and say that adynamical thinking prevents us from going further until we have more evidence".

 

[Elias1960]

It's always true, even with dynamical thinking, that reality could have begun 10 min ago with all the signs of a past beyond that. You can choose to model reality that way, but I'm not suggesting we do so. I'm saying we should take the model as far back as necessary to account for our observations.

What means "to account for our observations"? This is clear and obvious for me, given my "dynamical thinking", and my insistence on Reichenbach's common cause principle which defines what is a reasonable explanation. You reject both and rely on consistency only.

I argue that this restriction to consistency only is inconsistent, and in this particular post in conflict with "we should take the model as far back as necessary to account for our observations", because the consistency of our observation requires essentially nothing of that sort.

 

[RUTA]

Because we already know there is a constraint: the ball wasn't freely flying at negative times, it was sitting on the ground. So we don't extend the parabolic trajectory to negative times because we know it doesn't apply. Instead, we join that trajectory to a different trajectory for negative times.

Now, suppose that we weren't watching the ball at all at negative times and had no empirical evidence whatever of its trajectory then. But we do know that the surface of the Earth is there and that the parabolic trajectory intersects that surface at $t = 0$. How would we model the ball? Would we just throw up our hands and say, well, we don't have any evidence at negative times so we'll just cut off our model at $t = 0$ and stop there? Or would we exercise common sense and predict that, at negative times, the ball is sitting on the surface of the Earth, and someone threw it upwards at time $t = 0$, and extend our model accordingly?

As far as I can tell, you prefer the first alternative and I (and others, it appears) prefer the second. Can I give you a logical proof that you must use the second alternative? No. But I can tell you that the first alternative makes no sense to me, and I suspect it makes no sense to a lot of other people.

The difference here is that there is an external context for the ball's trajectory where there is no such external context for cosmology. You're tacitly using that external context to infer empirical results. Again, in physics there must be some empirical rational for using the mathematics. So, yes, without an external context and a physical motivation otherwise, what would motivate you to include $a = 0$ with $\rho = \infty$ in your model? The burden is on you to motivate the use of the math. That is precisely what we're doing now with $\Lambda\text{CDM}$, i.e., we're using it where it can account for observations. If someone used $a = 0$ with $\rho = \infty$ to make a testable empirical prediction and that prediction was verified, then we would include it in our model. It's that simple. You're just not giving me any empirical reason to include that region, so why would I? There is something that is driving you to believe $a = 0$ with $\rho = \infty$ should be included despite the lack of empirical motivation. Can you articulate that motive?

 

[RUTA]

What means "to account for our observations"? This is clear and obvious for me, given my "dynamical thinking", and my insistence on Reichenbach's common cause principle which defines what is a reasonable explanation. You reject both and rely on consistency only.

To account for the Planck distribution of the CMB or the anisotropies in its power spectrum, for example. The self-consistency I'm talking about is in EEs. Did you read my GR Insight on that? And I do not reject dynamical explanation. I use it all the time.

My claim is that if you view adynamical constraints as fundamental to dynamical laws, then many mysteries of modern physics, such as entanglement per the Bell states, disappear. You have said nothing to refute that point. All you have done is espouse your dynamical bias in response. If I had claimed that you MUST use constraints to dispel the mysteries of modern physics, then your replies would be relevant. But, I never made that claim. To refute my claim, you would have to accept my premise that constraints are explanatory and show how they fail to explain something that I claim they explain. So, for example, show how my constraint, conservation per NPRF, cannot explain conservation per the Bell states, conceding first that constraints are explanatory. I don't see how that's possible, but I'll let you try. You haven't even made an effort wrt cosmology, all you've done is espouse your dynamical bias there.