When can true singularity take place? Was the big bang the only chance

[Maui]

What "physical meaning" are you looking for here? I mean, do you also ask for a physical meaning to, say, Coulomb's law?

Aha, so you do not understand in quantitive terms what a gravitational singularity at the center of a black hole is, but you feel compelled to push your instrumentalism in a philosophy thread?

Do you know the physics of black holes, i.e. beyond just what you read in popscience books? Have you tried asking for a clear understanding of the physics in the Astro forum?

Ad hominems are not a good way to argue. I don't think that at this time even Hawking "understands" the physics of black holes enough to claim so, and you certainly don't either.

I(and probably many others here) don't understand your hate towards poscience books. What's wrong with that? Most of them were written by people way more knowledgeable than you attempting to approach the big philosophical questions from a physicist's viewpoint(even if they don't always manage to get the point across to the whole audience), so why bash them here? Can you offer anything more substantial than instrumentalism?

Shouldn't THAT be the first step before trying to find the "physical meaning" of something.

Zz.

Instrumentalism has never been productive for philosophy or ontology. Would asking the question of gravitational singularities in the Astro forum get "better" personal opinions on this particular question?

 

[Evo]

Aha, so you do not understand in quantitive terms what a gravitational singularity at the center of a black hole is, but you feel compelled to push your instrumentalism in a philosophy thread?

Philosophy here is little more than hand waving by people that don't have a true understanding of the science.

Zz has an understanding of the science. You might want to listen and take advantage of his knowledge.

There will be new rules next month that will require an understanding of the science as well as more structured and defined opening arguments. This forum is way overdue for the new rules. Being a science forum, we will be raising the bar on discussions here.

I think people will appreciate the new higher standards. Stay tuned.

 

[ZapperZ]

Aha, so you do not understand in quantitive terms what a gravitational singularity at the center of a black hole is, but you feel compelled to push your instrumentalism in a philosophy thread?Ad hominems are not a good way to argue. I don't think that at this time even Hawking "understands" the physics of black holes enough to claim so, and you certainly don't either.

I(and probably many others here) don't understand your hate towards poscience books. What's wrong with that? Most of them were written by people way more knowledgeable than you attempting to approach the big philosophical questions from a physicist's viewpoint(even if they don't always manage to get the point across to the whole audience), so why bash them here? Can you offer anything more substantial than instrumentalism?
Instrumentalism has never been productive for philosophy or ontology. Would asking the question of gravitational singularities in the Astro forum get "better" personal opinions on this particular question?

When you talk about an apple, but you actually have NEVER seen one, do you think that is a rational discussion?

So when people talk about "singularity", but they never actually understood the MATHEMATICS of what a singularity is, do you think such a discussion is actually based on valid knowledge? Look at my first post in this thread. I pointed out that in all the discussion that had occurred, not once was there EVER a mention of the mathematical definition of what a singularity is! This is a glaring omission! You won't know what a singularity is without the mathematics, even if it comes up and bites you on the rear end!

And this "understand the quantitative" aspect of a singularity, what is this if it isn't a mathematical description of it? What has been going on here is the hand-waving discussion of singularity based on some pop-science understanding of what it is. Do you think you can actually have a meaningful discussion of it while totally ignorant of the actual physics? Are you people THAT delusional that you think you can talk about something that you have no understanding of?

If you think that you have the ability to understand "in quantitative terms" what a gravitational singularity is WITHOUT invoking mathematics, then prove it! I'd like to see that.

Zz.

 

[JaredJames]

Are you people THAT delusional that you think you can talk about something that you have no understanding of?

Welcome to 99% of modern 'philosophy'.

I detest philosophy because of this. I'm all for an interesting thought debate, but some of the threads in this forum have ridiculous content.

 

[Pythagorean]

Philosophy here is little more than hand waving by people that don't have a true understanding of the science.

Zz has an understanding of the science. You might want to listen and take advantage of his knowledge.

There will be new rules next month that will require an understanding of the science as well as more structured and defined opening arguments. This forum is way overdue for the new rules. Being a science forum, we will be raising the bar on discussions here.

I think people will appreciate the new higher standards. Stay tuned.

OMG, we're going to approach a singularity?!?

(Q = 1/s)

where Q is quality of discussion in philosophy forums and s is the amount of rampant speculation.

 

[Maui]

When you talk about an apple, but you actually have NEVER seen one, do you think that is a rational discussion?

So when people talk about "singularity", but they never actually understood the MATHEMATICS of what a singularity is, do you think such a discussion is actually based on valid knowledge? Look at my first post in this thread. I pointed out that in all the discussion that had occurred, not once was there EVER a mention of the mathematical definition of what a singularity is!

I did state in this thread that Einstein's field equations lead to an infinite gravity and infinite density of matter. Since there is no practical difference between 0.999999(...)=1 and 0.0000000(...)=0, the volume of a spacetime singularity is considered to be zero. I did state earlier that some don't believe the volume of a gravitational singularity is zero because GR is not a theory of QG and what it says about singularities is likely either wrong or incomplete. All these points are factual and provide a basic understanding that the OP was seeking.

And this "understand the quantitative" aspect of a singularity, what is this if it isn't a mathematical description of it?

We understand in classical 'pictures', if i may borrow Einstein's ontological phrasing. At some point gravitational singularities will be described in better terms than infinite gravity and infinite densities.

What has been going on here is the hand-waving discussion of singularity based on some pop-science understanding of what it is. Do you think you can actually have a meaningful discussion of it while totally ignorant of the actual physics? Are you people THAT delusional that you think you can talk about something that you have no understanding of?

If you think that you have the ability to understand "in quantitative terms" what a gravitational singularity is WITHOUT invoking mathematics, then prove it! I'd like to see that.

Zz.

Prove to me how it's possible to 'understand'(whatever that means) the breakdown of mathematics at the center of a black hole. A description of its breakdown is by far not the same as understanding it.

 

[JaredJames]

Prove to me how it's possible to 'understand'(whatever that means) the breakdown of mathematics at the center of a black hole. A description of its breakdown is by far not the same as understanding it.

But to come up with a description you need to understand the mathematics. If no one here understands the maths then they cannot hope to come up with a valid description other than something purely speculative.

Simply repeating the descriptions of others without understanding the work behind them doesn't mean anything, especially when trying to debate the issue.

 

[Maui]

Welcome to 99% of modern 'philosophy'.

Now go post this message in the Quantum and Beyond the Standard Model forums as most of what you read there are opinions.

I detest philosophy because of this. I'm all for an interesting thought debate, but some of the threads in this forum have ridiculous content.

Sadly they do. But new regulations are coming, and you need to sort out the opinions from established facts in the other forums as well.

 

[Maui]

But to come up with a description you need to understand the mathematics. If no one here understands the maths then they cannot hope to come up with a valid description other than something purely speculative.

What are you talking about?

There is no math describing a gravitational singularity. Did you just pull that out of thin air like that?

And ironically you should detest philosophy, while making totally unsupported claims.

 

[ZapperZ]

When you talk about an apple, but you actually have NEVER seen one, do you think that is a rational discussion?

So when people talk about "singularity", but they never actually understood the PHYSICS of what a singularity is, do you think such a discussion is actually based on valid knowledge? Look at my first post in this thread. I pointed out that in all the discussion that had occurred, not once was there EVER a mention of the mathematical definition of what a singularity is!

I did state in this thread that Einstein's field equations lead to an infinite gravity and infinite density of matter. Since there is no practical difference between 0.999999(...)=1 and 0.0000000(...)=0, the volume of a spacetime singularity is considered to be zero. I did state earlier that some don't believe the volume of a gravitational singularity is zero because GR is not a theory of QG and what it says about singularities is likely either wrong or incomplete. All these points are factual and provide a basic understanding that the OP was seeking.

And you think the people who were doing all the discussion on here actually UNDERSTOOD what you just said? Really?!

We understand in classical 'pictures', if i may borrow Einstein's ontological phrasing. At some point gravitational singularities will be described in better terms than infinite gravity and infinite densities.

Prove to me how it's possible to 'understand'(whatever that means) the breakdown of mathematics at the center of a black hole. A description of its breakdown is by far not the same as understanding it.

I'm sorry, but you are barking up the wrong tree. You have completely misunderstood my intention in this thread.

I'm not here to discussion Einstein's field equation. If want to discuss that, the LAST place I would go is the philosophy forum. Discussing the validity of some aspect of physics here is a futile effort. But discussing physics with NO understanding of the actual physics, and then trying to get some "meaning" out of it, as an even greater waste of time. You keep coming back with some other rhetoric, but you have not been able to counter anything on this point, which is what I've been trying to get across. Talking about "singularity", without knowing what a singularity is, leads to a meaningless discussion. Now, which part of that did you have a problem with?

Zz.

 

[Pythagorean]

There is no math describing a gravitational singularity.

Whatever slippery way you try to defend that statement is not going to work.

There is bad philosophy and good philosophy... I think he meant he detested bad philosophy.

 

[JaredJames]

Now go post this message in the Quantum and Beyond the Standard Model forums as most of what you read there are opinions.

Opinion, or personal theory that can't be substantiated isn't allowed there as per every other part of the site. You are still discussing published (or to be published in this sub-forums case) papers. Read the guidelines, you can just spout a load of rubbish. It needs backing up.

Sadly they do. But new regulations are coming, and you need to sort out the opinions from established facts in the other forums.

Again, all claims need to be backed up, and most of the time you get called out if you are just making things up or giving opinion that isn't backed by fact. (Some good debates arise because of this).

The problem in philosophy is people do mainly give some form of opinion and when asked to back it up with fact they tell you "ah well this is philosophy and that doesn't apply", which is nonsense.

 

[JaredJames]

I think he meant he detested bad philosophy.

Correct.

 

[jackmell]

. . . I'd like to get mine in before the new rules apply:

Personally I believe this entire thread can be better approached from the perspective of Catastrophe Theory. This deals with "critical points" of phenomena when the dynamics changes qualitatively and often abruptly. Once these points are breached, descriptions describing the phenomena before the critical point are often insufficient to adequately explain the qualitatively new dynamics occurring beyond the critical point. I believe it is precisely these critical points that are being referred to as "singularities" in this thread. The Universe is filled with such dynamics at all scales from nuclear fission to collapsing stars. For example take dying. That is a critical point as the dynamics of life are suddenly replaced by qualitatively new dynamics of non-living. What happens to the concept of swimming in water at the critical point of freezing? Swimming reaches a singularity at that point as the phenomenon no longer applies to ice. Take conflicting nations. The peaceful conflict can escalates until the critical point of war is reached. Suddenly, a qualitatively new dynamics is reached at the nations reach this singular point in social contracts.

The dynamics of nature are not always smooth. There are points where it changes abruptly and qualitatively and often at these points new descriptions are needed to describe this new behavior. That is the case in my opinion to what we call the "singularity" at the Big Bang, and likewise, the singularity at the center of a black hole. Both of these represent a sudden and qualitative change in dynamics which renders our descriptions of the phenomena before the critical point, inadequate.

Also, I'm interested in Complex Analysis. We call discontinuities in complex analytic functions "singularities" because our descriptions of a finite derivative, suddenly and abruptly loose meaning at the point it becomes infinite, that is, it has no (finite) derivative at the singular point. At that point we use a qualitatively new description and say the derivative is "infinite".

 

[Maui]

Whatever slippery way you try to defend that statement is not going to work.

Meaning what?

There is bad philosophy and good philosophy... I think he meant he detested bad philosophy.

Then 99% is bad philosophy in his words, to which number he greatly contributed with his statement about mathematics describing spacetime singularities.

 

[Pythagorean]

. . . I'd like to get mine in before the new rules apply:

Personally I believe this entire thread can be better approached from the perspective of Catastrophe Theory. This deals with "critical points" of phenomena when the dynamics changes qualitatively and often abruptly. Once these points are breached, descriptions describing the phenomena before the critical point are often insufficient to adequately explain the qualitatively new dynamics occurring beyond the critical point. I believe it is precisely these critical points that are being referred to as "singularities" in this thread. The Universe is filled with such dynamics at all scales from nuclear fission to collapsing stars. For example take dying. That is a critical point as the dynamics of life are suddenly replaced by qualitatively new dynamics of non-living. What happens to the concept of swimming in water at the critical point of freezing? Swimming reaches a singularity at that point as the phenomenon no longer applies to ice. Take conflicting nations. The peaceful conflict can escalates until the critical point of war is reached. Suddenly, a qualitatively new dynamics is reached at the nations reach this singular point in social contracts.

The dynamics of nature are not always smooth. There are points where it changes abruptly and qualitatively and often at these points new descriptions are needed to describe this new behavior. That is the case in my opinion to what we call the "singularity" at the Big Bang, and likewise, the singularity at the center of a black hole. Both of these represent a sudden and qualitative change in dynamics which renders our descriptions of the phenomena before the critical point, inadequate.

Good post =) (dynamical systems bias)

I'm curious though, have we ever actually observed a singularity in nature? Wouldn't that require measuring some value to be infinite?

 

[ZapperZ]

. . . I'd like to get mine in before the new rules apply:

Personally I believe this entire thread can be better approached from the perspective of Catastrophe Theory. This deals with "critical points" of phenomena when the dynamics changes qualitatively and often abruptly. Once these points are breached, descriptions describing the phenomena before the critical point are often insufficient to adequately explain the qualitatively new dynamics occurring beyond the critical point. I believe it is precisely these critical points that are being referred to as "singularities" in this thread. The Universe is filled with such dynamics at all scales from nuclear fission to collapsing stars. For example take dying. That is a critical point as the dynamics of life are suddenly replaced by qualitatively new dynamics of non-living. What happens to the concept of swimming in water at the critical point of freezing? Swimming reaches a singularity at that point as the phenomenon no longer applies to ice. Take conflicting nations. The peaceful conflict can escalates until the critical point of war is reached. Suddenly, a qualitatively new dynamics is reached at the nations reach this singular point in social contracts.

The dynamics of nature are not always smooth. There are points where it changes abruptly and qualitatively and often at these points new descriptions are needed to describe this new behavior. That is the case in my opinion to what we call the "singularity" at the Big Bang, and likewise, the singularity at the center of a black hole. Both of these represent a sudden and qualitative change in dynamics which renders our descriptions of the phenomena before the critical point, inadequate.

This is not new. What you're describing is a first-order phase transition, where certain state variables become discontinuous at the phase boundary.

But you will note that that is a GENERIC description of singularity, where you actually HAVE to know the quantitative aspect of the description, i.e. you have to know how the state variables evolve when you change certain parameters, and then realize that the discontinuity will result in a pole in, say, the first derivative of that state variable. In other words, you will NOT know that when water turns into ice, there are some singularities in some of the state variable simply by looking at it! You have to be able to know the mathematics and actually know the physics of what is being measured! This is what I meant earlier by what I was trying to say that people here talk about "singularity" as if it is something you could see, etc. That's bogus! Without the mathematics, you won't know it!

But if you notice, the earlier discussion on here were focusing really on the so-called "space-time singularity", while using the generic phrase "singularity". That is also another severe misinformation/misunderstanding.

Zz.

 

[Pythagorean]

Meaning what?

It's a loaded challenge. Many aspects of gravitational singularity are described mathematically (even the wiki authors know that). "There is no math describing a gravitational singularity" may be true if you spin it the right way, but then it would be a meaningless and irrelevant statement.

So there's really no defending it.

 

[jackmell]

\Without the mathematics, you won't know it!Zz.

Jesus dude, like I'm skiing. Suddenly and abruptly and I mean in a split second, the whole side of the mountain fractures into a very, very large avalanche. They ask about actually seeing a singularity in here. That's one in my opinion: the dynamics of the snow pack have suddenly and abruptly changed in a qualitative manner and I didn't have to know the mathematics to know it happened.

 

[Pythagorean]

Jesus dude, like I'm skiing. Suddenly and abruptly and I mean in a split second, the whole side of the mountain fractures into a very, very large avalanche. They ask about actually seeing a singularity in here. That's one in my opinion: the dynamics of the snow pack have suddenly and abruptly changed in a qualitative manner and I didn't have to know the mathematics to know it happened.

But don't you think deep philosophical conversation about singularities should be grounded in the mathematics? That the three of us (you, zapperz, and I) recognize the connection between singularities and bifurcation is probably deeply rooted in our mathematical understanding.

I think it makes definitions more lucid, personally. And it avoids wiggle room in ambiguous uses of the word that waste poster's time and PFs bandwidth.

edit: It's not that I don't think we can communicate in natural language once we've learned the math, you have perfectly demonstrated that in your big post. But I think it's the people that have had long-term exposure to mathematics that really understand your post.

 

[jackmell]

But don't you think deep philosophical conversation about singularities should be grounded in the mathematics? That the three of us (you, zapperz, and I) recognize the connection between singularities and bifurcation is probably deeply rooted in our mathematical understanding.

I'm afraid I can't be in the same category as Zapper. I know he's very knowledgeable in physics. Very much so I believe. I myself am not. See, I wouldn't say this stuff in a physics forum. I know better but philosophy, well ok but I was hesitant to post in here but I am interested in the subject of critical points, catastrophe, and bifurcation, nevertheless and view much of Nature from that perspective. I don't know your background though Pythagorean except that you are interested in brain science.

 

[Pythagorean]

I'm afraid I can't be in the same category as Zapper. I know he's very knowledgeable in physics. Very much so I believe. I myself am not and was hesitant to post in here because of that but I am interested in the subject of critical points, catastrophe, and bifurcation, nevertheless and view much of Nature from that perspective. I don't know your background though Pythagorean except that you are interested in brain science.

My undergraduate degree was in physics. I designed my current interdisciplinary degree. My advisor studies dynamical systems, and so there was mutual benefit for study neuron systems from the dynamical perspective. Once I was introduced to that perspective (in the context of transient chaos in nature) I became very interested in the general framework of dynamical systems and it's applications to biology in general (cell cycles, epigenetics and "junk" DNA) but continue to focus academically in dynamical systems and neuroscience.

I actually read about Lorenz's chaos before my physics education and was quite infatuated with it (always had chaos in my screen name). I had forgotten about that until I was reintroduced to it more formally (still currently learning a lot of the mathematics formally).

Anyway, I think the math is important. I think it has positively influenced the way I think about things I observe. I believe in the theory of linguistic relativity, that language influences how you think, and to some extent, who you are: and I believe mathematics is a language. So to my mind, it stands to reason that topics born in mathematics are elusive (even when using the proper english equivalents) to someone who doesn't have that innate, subconscious understanding that comes from years of exposure to mathematics.

Once you're five analogies into describing complex theory, each person is taking home their own story, over-applying the analogies that hit home with them the most.

 

[jackmell]

My undergraduate degree was in physics. I designed my current interdisciplinary degree. My advisor studies dynamical systems, and so there was mutual benefit for study neuron systems from the dynamical perspective. Once I was introduced to that perspective (in the context of transient chaos in nature) I became very interested in the general framework of dynamical systems and it's applications to biology in general (cell cycles, epigenetics and "junk" DNA) but continue to focus academically in dynamical systems and neuroscience.

I actually read about Lorenz's chaos before my physics education and was quite infatuated with it (always had chaos in my screen name). I had forgotten about that until I was reintroduced to it more formally (still currently learning a lot of the mathematics formally).

Anyway, I think the math is important. I think it has positively influenced the way I think about things I observe. I believe in the theory of linguistic relativity, that language influences how you think, and to some extent, who you are: and I believe mathematics is a language. So to my mind, it stands to reason that topics born in mathematics are elusive (even when using the proper english equivalents) to someone who doesn't have that innate, subconscious understanding that comes from years of exposure to mathematics.

Once you're five analogies into describing complex theory, each person is taking home their own story, over-applying the analogies that hit home with them the most.

Ok. Thanks for that. I'm interested in non-linear math too. You didn't see that brusselator thing we've been working on in the DE sub-forum huh? Anyway, I think it's fascinating that we can start with a purely random mixture of chemicals (like the primeval earth), and by the intrinsic dynamics alone, create ordered structures. And they wonder how complex life forms can emerge from scratch. What happens when we couple not two but two-hundred? :)

Anyway, it's singularities here. I think the "Big Bang singularity" gets a lot of people. They think linearly and then wonder what can exists before existence because they're thinking "more of the same". But that causes the problem I believe. Once jump-discontinuities, bifurcations, catastrophe, phase-transitions, and critical-points are added to the equation, then it's not too difficult to suppose maybe the reason we believe it's a "singular" point is because it's really a "critical point" and by virtue of the qualitative change that is often associated with critical points, our current (incomplete) laws of physics cannot apply. The same I believe can be said of black holes and other "singular" phenomena in nature: the singularity is a consequence of applying a (smooth) description of phenomenon across a critical point where the dynamics may not change smoothly but rather abruptly and discontinuously.

Just my opinion guys and again, it's philosophy and not the (empirical) physics sub-forums and I'm gettin' mine before the rules change. :)

 

[ZapperZ]

Jesus dude, like I'm skiing. Suddenly and abruptly and I mean in a split second, the whole side of the mountain fractures into a very, very large avalanche. They ask about actually seeing a singularity in here. That's one in my opinion: the dynamics of the snow pack have suddenly and abruptly changed in a qualitative manner and I didn't have to know the mathematics to know it happened.

So? You saw something. How does that relate to the fact that the description of it involves a singularity? I already gave you an example of water turning into ice. Would you have known that a mathematical description of that process has a singularity?

Just because you saw something doesn't mean you can recognize the mathematical description of it.

Zz.

 

[Pythagorean]

Ok. Thanks for that. I'm interested in non-linear math too. You didn't see that brusselator thing we've been working on in the DE sub-forum huh? Anyway, I think it's fascinating that we can start with a purely random mixture of chemicals (like the primeval earth), and by the intrinsic dynamics alone, create ordered structures. And they wonder how complex life forms can emerge from scratch. What happens when we couple not two but two-hundred? :)

I will occasionally wander to the DE forum, but I really prefer discussion to be motivated from science and observation. I checked out that thread though now that you mentioned it, and it looks like something I'll have to check out in-depth.

Anyway, it's singularities here. I think the "Big Bang singularity" gets a lot of people. They think linearly and then wonder what can exists before existence because they're thinking "more of the same". But that causes the problem I believe. Once jump-discontinuities, bifurcations, catastrophe, phase-transitions, and critical-points are added to the equation, then it's not too difficult to suppose maybe the reason we believe it's a "singular" point is because it's really a "critical point" and by virtue of the qualitative change that is often associated with critical points, our current (incomplete) laws of physics cannot apply. The same I believe can be said of black holes and other "singular" phenomena in nature: the singularity is a consequence of applying a (smooth) description of phenomenon across a critical point where the dynamics may not change smoothly but rather abruptly and discontinuously.

This is close to my opinion. To me, it seems several different behaviors can be represented by one system of equations if you construct the mathematics with nonlinearities in mind. So I guess the only difference really is that I speak of our models of reality only and their closeness to reality, but not reality itself.

Just my opinion guys and again, it's philosophy and not the (empirical) physics sub-forums and I'm gettin' mine before the rules change. :)

I don't know; to me, your posts don't seem like the target of the coming policy change. You may need to define things more carefully for non-dynamical peoples, but to me you are arguing from mathematics, even if you're not showing it mathematically.

 

[Maui]

It's a loaded challenge. Many aspects of gravitational singularity are described mathematically (even the wiki authors know that).

What aspects specifically are you referring to? I haven't read the wiki but my usual reference - Penrose's "the Road to reality" say no such thing.

"There is no math describing a gravitational singularity" may be true if you spin it the right way, but then it would be a meaningless and irrelevant statement.

No, i meant what i said. There is no math describing spacetime singularities.

So there's really no defending it.

I try to stay on the safe side, hence my statements are usually much stronger when I am perfectly aware that there is no empirical way to test the veracity of a theory that lies very very far in the future. Maybe you should explain in more detail what you meant so that i know what to reply to. I am completely in the dark as to what your above statements were supposed to mean.

 

[Pythagorean]

Maui:

http://en.wikipedia.org/wiki/Penrose-Hawking_singularity_theorems
http://en.wikipedia.org/wiki/Raychaudhuri_equation

 

[ZapperZ]

No, i meant what i said. There is no math describing spacetime singularities.

R. Geroch, Annals of Phys. v.48, p.526 (1968).
D. Christodoulou, Annals of Mathematics v.140, p.607 (1994).
etc...

Zz.

 

[Maui]

We won't know for quite sometime, if someone's arguing a certain point through proposed mathematical structures, depict spacetime singularities(or something quite fictitious) without some sort of empirical verification. Kind of leans towards the absurdly complex mathematics in ST that still has no empirical verification whatsoever. But there is nothing fundamenta lly wrong in being hopeful.

 

[ZapperZ]

We won't know for quite sometime, if someone's arguing a certain point through proposed mathematical structures, depict spacetime singularities(or something quite fictitious) without some sort of empirical verification. Kind of leans towards the absurdly complex mathematics in ST that still has no empirical verification whatsoever. But there is nothing fundamenta lly wrong in being hopeful.

But this is beside the point. You're arguing that there is NO gravitational/spacetime singularity of any kind. That in itself has no "empirical verification" either. I merely pointed out that there are plenty of theoretical papers that would counter your assertion.

Again, this is more suited to be done in the SR/GR forum where people who are more familiar with this area hang out. This is not a philosophy topic anymore.

Zz.

 

[Math Is Hard]

I agree with Zapper on this. Why speculate when there are experts in another part of Physics Forums.