When did spacetime form?

[geordief]

I understand that the model we have goes back to T+10^-43secs.

Did spacetime form then ,at that (those?) moment or did it happen  when the Higgs field was created? (or emerged?)

Since the  time it did form ,has it evolved into what we now measure in a continuous fashion?

[Mordred]

That answer depends on the model of how the universe started which we do not know. For example if the universe started from nothing then it stayed immediately after T=0. If our universe was due to a bounce from a previous universe then you would have the spacetime from the previous universe  ( the portion of the previous universe that bounced to form out universe.)

In short we do not know previous to 10^{-43} seconds. We can only accurately extrapolate to that time. Any process prior we can only speculate.

[geordief]

1 hour ago, Mordred said:

That answer depends on the model of how the universe started which we do not know. For example if the universe started from nothing then it stayed immediately after T=0. If our universe was due to a bounce from a previous universe then you would have the spacetime from the previous universe  ( the portion of the previous universe that bounced to form out universe.)

In short we do not know previous to 10^{-43} seconds. We can only accurately extrapolate to that time. Any process prior we can only speculate.

So spacetime existed before the Higgs field came  to become a  dominant force?

Does spacetime  work the same way if there are no sources of curvature?

Or do the other fields provide sources of curvature even if  there is no mass present ?(I understand ,probably naively that the Higgs field is reponsible at least in part for gravity)

[Mordred]

A common misconception spacetime isn't really something that forms spacetime has no fabric like substance. It's simply a geometric volume with time having dimensionality of length via the ct interval. So in order to have fields you require a volume for the fields to reside in.

All forms of mass energy contribute to spacetime curvature. If there is no curvature spacetime is still just the 4d volume.

 

[geordief]

4 hours ago, Mordred said:

A common misconception spacetime isn't really something that forms spacetime has no fabric like substance. It's simply a geometric volume with time having dimensionality of length via the ct interval. So in order to have fields you require a volume for the fields to reside in.

 

 

Ah yes, I must have a blind spot.I thought I understood that spacetime was just a mathematical construct but my question showed that I didn't.

I think I was  also probably equating in my head  curved spacetime with spacetime itself -as if flat spacetime wasn't "proper" spacetime.

 

[Mordred]

 

No problem it's easy to forget details when thinking of GR QFT etc lol.

 It may help to recall that it is the stress energy momentum tensor that spacetime how to curve and that spacetime curvature describes particle paths (geodesics).  Hence the use of the (ct) interval is incredibly useful.

[MigL]

I would say that, since GR is geometric, and GR fails on approach to Planck time, any notion of geometry ( spatial or temporal )  is similarly not applicable.

Fields have an energy density; any field will contribute to the stress-energy-momentum tensor, and curvature.

[geordief]

1 hour ago, MigL said:

I would say that, since GR is geometric, and GR fails on approach to Planck time, any notion of geometry ( spatial or temporal )  is similarly not applicable.

Fields have an energy density; any field will contribute to the stress-energy-momentum tensor, and curvature.

Do you mean there could be no quantifiable relationships between  distinct  objects ?

[Genady]

GR assumes geometry. Geometry does not assume GR. Thus, failure of GR does not necessitate failure of geometry.

[joigus]

10 hours ago, geordief said:

Do you mean there could be no quantifiable relationships between  distinct  objects ?

I suppose what @MigL means is that differential geometry is no longer applicable.

There is no point closer, and closer, and closer still to a given point.

There might be "quantifiable relationships between distinct objects" but not of a geometric nature. Or there might be no distinction of objects. Or...

I suppose when you say "objects" you mean points?

Maybe the quantifiable relationships are something like entanglement, but that's not really geometry.

[Genady]

Differential geometry requires a manifold structure. Defined neighborhoods do not require that.

[geordief]

48 minutes ago, joigus said:

I suppose what @MigL means is that differential geometry is no longer applicable.

There is no point closer, and closer, and closer still to a given point.

There might be "quantifiable relationships between distinct objects" but not of a geometric nature. Or there might be no distinction of objects. Or...

I suppose when you say "objects" you mean points?

Maybe the quantifiable relationships are something like entanglement, but that's not really geometry.

No I meant objects (interactions?) .The points ,to my mind are (relative) attributes  of the objects.

I understand what you said (avoiding using the word "point" ,as in "your point") about differential geometry breaking down but did I read somewhere something about  some attempt at building a maths based on  a "discontinuous number system?)

 

Maybe the "objects" I had in mind would be  fields.

 

Better not ask any more questions here  and get even further out of my depth..

[MigL]

2 hours ago, dimreepr said:

The stage doesn't assume the actor can act...

GR has no stage to act on ...

[joigus]

24 minutes ago, geordief said:

Better not ask any more questions here  and get even further out of my depth..

On my part, it's OK. Those aren't bad questions necessarily. Any imprecision is understandable on account of the difficulty of the subject. IMO Mordred's answer was spot on and succinct. I have little to add to what he said.

You seem to be bothered by the presence of fields in the geometry though, and that's fair enough. In pure geometry we don't have this arrowy structure we call fields. On top of that they have an algebra of creation and annihilation, and they are complex (have an imaginary part). Those are quantum fields and they seem to go beyond the scope of geometry. Does space-time emanate from the field, or is it the other way? Nobody knows. Maybe there was an eternal inflation scenario, as some models say, and scalar fields gave shape to everything else. It's, as Mordred said, speculation. Highly educated, yes, but speculation after all.

[Mordred]

Well in terms of emergent there are numerous papers of emergent spacetime as well as emergent quantum fields. However how emergence is typically treated is from other field geometries example Calibi Yau spacetime from string theory.

The more typical papers for emergent spacetime are typically string theory or ADS/CFT formalism  

We have to be careful here as emergent doesn't necessarily mean come into existence but rather specific relations and dimensionality ie 5d or higher dimension models leading to emerging 4d spacetime relations. The same can result from lower dimension theories emerging to higher dimension relations.

I should add a field can be any collection of values (mathematical or physical) under a geometric treatment.

In QFT for example the creation/annihilation operators employ the field as an operator. In a sense the field can propagate the creation/annihilation operators. The operators operate on the propogators.

(An operator is has a minimal of 1 quanta of action ) this is the minimum energy level for an operator. (A propogator can have any value but can be below a quanta of action ) example virtual photons and gauge bosons. Aka the internal wavy lines of Feymann path integrals. The operators would be the external lines.

Edited June 2 by Mordred

[MigL]

On 6/2/2024 at 8:07 AM, Genady said:

ailure of GR does not necessitate failure of geometry.

GR defines space-time using its geometry; if there is any 'geometry', GR can use it to describe the space-time.
For GR to not be applicable there has to be an absence of 'geometry', such as geometry becoming infinitely curved.
Or can you show me an example of GR describing a space-time without 'geometry' ( does that even make sense ? ).

Edited June 6 by MigL

[Genady]

1 hour ago, MigL said:

GR defines space-time using its geometry; if there is any 'geometry', GR can use it to describe the space-time.
For GR to not be applicable there has to be an absence of 'geometry', such as geometry becoming infinitely curved.
Or can you show me an example of GR describing a space-time without 'geometry' ( does that even make sense ? ).

"Failure of GR does not necessitate failure of geometry" implies geometry without GR. Why would I try to show an example of GR without geometry? 

[iNow]

On 6/1/2024 at 8:40 AM, geordief said:

When did spacetime form?

On a Tuesday

[Airbrush]

On 6/1/2024 at 9:25 AM, geordief said:

So spacetime existed before the Higgs field came  to become a  dominant force?

Does spacetime  work the same way if there are no sources of curvature?

Or do the other fields provide sources of curvature even if  there is no mass present ?(I understand ,probably naively that the Higgs field is reponsible at least in part for gravity)

"Matter acquired its mass during the electroweak epoch, through electroweak symmetry breaking, when the universe cooled to a temperature where the Higgs field could spontaneously break the electroweak symmetry. The timeline for this event is around 10^(−12) seconds after the Big Bang." 

I don't understand this, but does this help answer your questions?

Cosmic inflation happened before the universe started to "pull" on matter through gravity?  That's how it expanded so fast because there was no gravity to slow it down?

Edited June 7 by Airbrush

[MigL]

6 hours ago, Genady said:

Why would I try to show an example of GR without geometry? 

GR is a geometric theory.
Any geometry can be used by ( a version of ) GR to define that space-time.
For example, a specific 5dimensional version of GR can be used to describe space-time with EM fields ( see Kaluza-Klein ).
Absence of ( or undefined ) geometry makes GR fail.

But if you don't wish to provide an example of GR without geometry, you don't have to.
 

 

1 hour ago, Airbrush said:

Cosmic inflation happened before the universe started to "pull" on matter through gravity?  That's how it expanded so fast because there was no gravity to slow it down?

Any field will have an associated energy density, and any energy, be it in the form of mass, stress, or momentum, will be a source of gravity. Even the gravitational field itself, is a source of gravity.
The symmetry break that precipitated the decoupling of electromagnetism from the weak interaction, and the acquisition of mass for leptons, quarks and some bosons, was due to a false zero energy level.
It was the slow roll down from this false zero level that provided the impetus for inflation, which I thought happened between 10^-35 and 10^-32sec.

Edited June 7 by MigL

[Genady]

11 minutes ago, MigL said:

But if you don't wish to provide an example of GR without geometry, you don't have to.

I guess I was not clear enough.

My claim is that geometry can exist without GR, but GR cannot exist without geometry.

Thus, there cannot be an example of GR without geometry. 

15 minutes ago, MigL said:

Absence of ( or undefined ) geometry makes GR fail.

As I said earlier, GR can fail for a reason other than absence of geometry.

[geordief]

20 minutes ago, MigL said:

GR is a geometric theory.
Any geometry can be used by ( a version of ) GR to define that space-time.
For example, a specific 5dimensional version of GR can be used to describe space-time with EM fields ( see Kaluza-Klein ).
Absence of ( or undefined ) geometry makes GR fail.

But if you don't wish to provide an example of GR without geometry, you don't have to.
 

 

Any field will have an associated energy density, and any energy, be it in the form of mass, stress, or momentum, will be a source of gravity. Even the gravitational field itself, is a source of gravity.
The symmetry break that precipitated the decoupling of electromagnetism from the weak interaction, and the acquisition of mass for leptons, quarks and some bosons, was due to a false zero energy level.
It was the slow roll down from this false zero level that provided the impetus for inflation, which I thought happened between 10^-35 and 10^-32sec.

Was spacetime curved even before the Higgs field formed?

There were sources of gravitation then  separate  from mass?

1 hour ago, Airbrush said:

"Matter acquired its mass during the electroweak epoch, through electroweak symmetry breaking, when the universe cooled to a temperature where the Higgs field could spontaneously break the electroweak symmetry. The timeline for this event is around 10^(−12) seconds after the Big Bang." 

I don't understand this, but does this help answer your questions?

Cosmic inflation happened before the universe started to "pull" on matter through gravity?  That's how it expanded so fast because there was no gravity to slow it down?

 I was confused in the OP and imagined that spacetime came into being  around the same time as the  Higgs field.

I now think that spacetime existed as far back as the BB(T+ 10^-43 seconds ) and that it was curved ,although I have no idea how curved it would have been-possibly  indistinguishable  from flat spacetime or possibly  extremely  curved.I don't know.

[Genady]

29 minutes ago, MigL said:

Any geometry can be used by ( a version of ) GR to define that space-time.

This is incorrect. GR requires geometry with certain smoothness. It fails if the geometry is not sufficiently smooth.

[MigL]

As I said 

25 minutes ago, MigL said:

Any field will have an associated energy density, and any energy, be it in the form of mass, stress, or momentum, will be a source of gravity. Even the gravitational field itself, is a source of gravity.

It may, however,  have been global, as local would require a specific field configuration, not a homogeneous isotropic energy distribution.

1 minute ago, Genady said:

It fails if the geometry is not sufficiently smooth.

Exactly.
As happens when geometric curvature goes to infinite at a singularity.

[Genady]

3 minutes ago, MigL said:

Exactly.
As happens when geometric curvature goes to infinite at a singularity.

Right. But when this happens what fails is GR together with its framework, differential geometry. Not geometry. Geometry is fine with such singularities. Differential geometry has a problem.