Hi, all
I’ve always wondered why Einstein struggled with the idea that geometry shouldn’t be a fixed stage, but something linked together with matter and energy. It has always felt real to me since I got more acquainted with physics - like spacetime is not a rigid container, but something that grows out of the universe’s own activity.

/chron44

20 minutes ago, chron44 said:

Einstein struggled with the idea that geometry shouldn’t be a fixed stage

Did he?

46 minutes ago, Genady said:

Einstein struggled with the idea that geometry shouldn’t be a fixed stage

Did he?

Quoted from "Britannica", Einstein's own words in his later years:

“Formerly we thought everything—yes, everything; nowadays we think—nothing. Already the distance‑concept is logically arbitrary; there need be no things that correspond to it, even approximately.”

What Einstein was figuring on here isn't all that clear, still there are some indications for this thread's quest. This may be a late start for him admitting that geometry might be a convenient fiction. One may add this way of "interpreting" Einstein's later ideas "Physics may be built from a non‑geometric fundament".

Edited March 7Mar 7 by chron44
understandable reasoning objectives

15 minutes ago, chron44 said:

Quoted from "Britannica", Einstein's own words in his later years:

“Formerly we thought everything—yes, everything; nowadays we think—nothing. Already the distance‑concept is logically arbitrary; there need be no things that correspond to it, even approximately.”

What Einstein was figuring on here isn't all that clear, still there are some indications for this thread's quest. This may the late start for him admitting that geometry might be a convenient fiction.

This out of context quote does not tell me that "Einstein struggled with the idea that geometry shouldn’t be a fixed stage."

10 minutes ago, Genady said:

This out of context quote does not tell me that "Einstein struggled with the idea that geometry shouldn’t be a fixed stage."

Yes, he although did. By fair reasons also. He was smart, this is my approach for this thread. He wasn't imagining this problem.

Of course 1 meter exist, as 1 cubic of it. Still Einstein did struggle with his own spacetime concept. My own approach, or issue, is if "geometry is fixed or emergent". Okay, now i declared my thread in an fair question form.

Edited March 7Mar 7 by chron44

The opening post wouldn't be useful to answer the question "if geometry is fixed or emergent. Under SR and GR no coordinate system is privileged one can arbitrarily change to any coordinate system and the physics remain the same. This is where one can apply for common example Pythagorous theorem as any curved spacetime the angles will not equal 180 degrees. Positive curvature the angles of an equilateral triangle will be greater than 180 degrees while negative curvature it will be less than 180 degrees. However in each case there is a method to define a small region where it is spatially flat.

It is likely this consideration that Einstein worked with others such as Minkowskii to help resolve.

Emergent properties has rather specific requirements so clarity on what you understand as emergent will be needed

as a visual aid to help understand the above see

http://cosmology101.wikidot.com/geometry-flrw-metric/

Not only "emergent geometry" requires definition, but "fixed geometry" as well. It is not clear without definitions that these two properties are exclusive.

3 hours ago, chron44 said:

Hi, all
I’ve always wondered why Einstein struggled with the idea that geometry shouldn’t be a fixed stage, but something linked together with matter and energy. It has always felt real to me since I got more acquainted with physics - like spacetime is not a rigid container, but something that grows out of the universe’s own activity.

/chron44

Spacetime?

You’re referencing a concept that did not exist in 1905. Perhaps you don’t struggle with concepts that you’re repeatedly exposed to and are accepted as valid, rather than having to confront a new concept.

In the Newtonian universe that covered all of physics at that time, space and time were absolute.

I'm sorry if I made my issue a bit unclear. Still, we all know how GR works. Geometry bends, and rods follow. No one here doubts that. What I’m trying to point at is something else: the difference between measuring a length and the geometric "entity" that gives those lengths their relations.

A meter is a meter — that’s simple. But geometry, in Einstein’s sense, is not the meter itself. It is the rule that tells every meter how to behave. So my question isn’t about rods or volumes at all. It’s about the deeper thing underneath: what geometry is, not what it does. Is it something given, or something that grows from more primitive ingredients?

That’s the only distinction I’m trying to explore.

Well in physics an emergent property is a characteristic of any complex system. They arise from the collective interactions of the systems components and are not additive.

There are some theories that ask the question is spacetime emergent if so then what properties . A decent listing can be found here

https://arxiv.org/pdf/0711.4416

so given the above how would you determine the collective interactions leading to the meter ?

Essentially, we are, or at least I am, trying to:

1. Understand what Einstein himself found, thought or sensed "problematic" with his own spacetime/ GR/ SR "inventions" and ideas.
2. Go beyond and further in this issue of spacetime/ GR /SR. What lies beneath it "all"?
(3. It's not always "easy to "understand" physics giants and follow their thinking. Is Einstein's own later sense, found in arguments in real time physics? Did he sense something, not wrong, but maybe something not finished here? )

Ar you with me in these distinctions?

8 minutes ago, Mordred said:

so given the above how would you determine the collective interactions leading to the meter ?

Well, time is one manner to measure 1 meter. The "length" relates to the time light in free space travel a specific amount of "time". One collective manner here for meter is c and a specific amount of time, t_c_1m.

Edited March 7Mar 7 by chron44

Sounds like we may be on the same page or similar enough that distinctions will become apparent in the discussion. SR and GR uses the interval (ct) to give time dimensionality of length. However length can have several meanings in SR and GR example conformal length and proper length so better clarity which specific length is being examined will be needed.

As far as curvature terms I would consider the amount of curvature as emergent as the stress energy momentum tensor that tells spacetime how to curve contains emergent properties such as the pressure term. Subsequently the ds^2 separation distance between observer and emitter would also be emergent

Edited March 7Mar 7 by Mordred

18 minutes ago, Mordred said:

Sounds like we may be on the same page or similar enough that distinctions will become apparent in the discussion. SR and GR uses the interval (ct) to give time dimensionality of length. However length can have several meanings in SR and GR example conformal length and proper length so better clarity which specific length is being examined will be needed.

Fair, enough. So here we may stumble on one discrepancy Einstein sensed "problematic". Meter is ct derived. A constant, c, and a duration, t. SR argues of c as a cornerstone, and GR has a similar measured empiric value, G. Somewhere here I imagine Einstein on his later days saw only empirical data of measured values and constants. What was it Einstein saw to be the problem?

28 minutes ago, Mordred said:

As far as curvature terms I would consider the amount of curvature as emergent as the stress energy momentum tensor that tells spacetime how to curve contains emergent properties such as the pressure term. Subsequently the ds^2 separation distance between observer and emitter would also be emergent

This is GR math as I can notice. Was it here Einstein saw a discrepancy with some sense of his? What are the emergent combinations, and what are the fixed constants? In spacetime/ GR/ SR. I cannot dive into hard math, I respect and honour people that have this for work. I can only listen to the edge of physicists who some of them, like a late Einstein, today begin to dissect physics in a bit unorthodox manner. Einstein had hard days with the modern and growing QM, this I know. He was never fully settled with probabilistic terms and non-local mysteries. Why? -My own answer is: GR and QM should not be divided, if so, there is an unsolved part.

Edited March 7Mar 7 by chron44

Well I don't really go into the various struggles Einstein had nor what his thoughts were and much of the information one can find on the internet is often misleading. However I have seen numerous papers suggesting he struggled with Minkowskii 4d treatment in that he preferred to keep space and time distinct. I also saw various papers involving Mach principle which suggests that space should not exist independently but has a dependency on matter distribution. There are others relating to Block universe etc.

example here

https://www.sciencedirect.com/science/article/abs/pii/0039368194900566

for the Mach case

Edited March 7Mar 7 by Mordred

6 minutes ago, Mordred said:

Well I don't really go into the various struggles Einstein had nor what his thoughts were and much of the information one can find on the internet is often misleading. However I have seen numerous papers suggesting he struggled with Minkowskii 4d treatment in that he preferred to keep space and time distinct. I also saw various papers involving Mach principle which suggests that space should not exist independently but has a dependency on matter distribution. There are others relating to Block universe etc.

Thanks for discussing in a general manner. Not only hard math. ; ) I'll return in some day or days.

your welcome

The title on this post is: "Einstein and an issue if geometry is a fixed entity"

Yes, I see, I did mix the emergent combined outcome in "geometry" (GR), with the fixed G. -The gravitational constant involved. Sorry.
So, I ask for some indulgence with my math/ geometry/ GR/ G confusion from an interested layman in physics.

Looking over the www is probably not all that secure for getting traces for his reasoning here.
What I have understood, from the www info, where my own altered cited version becomes to:
“Einstein had hard days with the modern and growing quantum mechanics, he was never fully settled with its
probabilistic nature or its non‑local mysteries. Why? My own, LeoK's, answer is this: Einstein’s stance suggests
that if general relativity and quantum mechanics remain divided, then something essential is still unsolved.”

Can we go from here in this thread?

Maybe discussing if: Einstein’s intuition, that the two frameworks must ultimately be unified,
is relevant in theoretical physics today?

Edited March 8Mar 8 by chron44

19 hours ago, chron44 said:

Quoted from "Britannica", Einstein's own words in his later years:

“Formerly we thought everything—yes, everything; nowadays we think—nothing. Already the distance‑concept is logically arbitrary; there need be no things that correspond to it, even approximately.”

What Einstein was figuring on here isn't all that clear, still there are some indications for this thread's quest. This may be a late start for him admitting that geometry might be a convenient fiction. One may add this way of "interpreting" Einstein's later ideas "Physics may be built from a non‑geometric fundament".

This quote sounds a bit odd. Can you provide a link to where you got it from, to help us understand the context?

1 hour ago, chron44 said:

Einstein’s intuition, that the two frameworks must ultimately be unified,
is relevant in theoretical physics today?

The goal is relevant; the intuition is not.

58 minutes ago, exchemist said:

Quoted from "Britannica", Einstein's own words in his later years:

“Formerly we thought everything—yes, everything; nowadays we think—nothing. Already the distance‑concept is logically arbitrary; there need be no things that correspond to it, even approximately.”

What Einstein was figuring on here isn't all that clear, still there are some indications for this thread's quest. This may be a late start for him admitting that geometry might be a convenient fiction. One may add this way of "interpreting" Einstein's later ideas "Physics may be built from a non‑geometric fundament".

This quote sounds a bit odd. Can you provide a link to where you got it from, to help us understand the context?

Yes, the quote and my own writing is a mishmash of ideas. Can we continue from what we know in average stances what Einstein sensed from confirmed "quotes" and writings from him. This is although a serious quest with edge physics involved. I'm really trying to comprehend all distinctions, constants and emerged physics.

2 minutes ago, Genady said:

Einstein’s intuition, that the two frameworks must ultimately be unified,
is relevant in theoretical physics today?

The goal is relevant; the intuition is not.

Yes. quite right. Thanks for the correction. Although I am relying on Einstein's sense of intuition, he did sort of a way anticipate the cosmological constant problem of today.
A common myth is that Einstein “didn’t understand” quantum mechanics. This is historically false. He understood it deeply - he helped create it. His objections were conceptual, not technical:

Edited March 8Mar 8 by chron44

@chron44 I believe the quote that you looking for is this one:

---

"There is no such thing as an empty space, i.e., a space without field. . . . Space-time does not claim existence on its own, but only as a structural quality of the field."

--- Albert Einstein, Relativity: The Special and the General Theory} (Appendix V: ``Relativity and the Problem of Space''), 1952 edition, Methuen (London), p.~155; based on earlier 1920 additions.}

---

Also I have to worn you, my experience on this forum I can describe as "Fundamental Church of container space and its holy trinity (x,y,z)) ".

Einstein was deeply inspired by Mach's relational ideas and couldn't come to terms with postulated manifold in GR as form of background that preexists interactions and relations of mass and energy.

4 minutes ago, Anton Rize said:

Einstein was deeply inspired by Mach's relational ideas and couldn't come to terms with postulated manifold in GR as form of background that preexists interactions and relations of mass and energy.

Maybe have to read about Mach's universal ideas. Heard that these are about energy/ mass in universal uneven distribution, or something like that.

28 minutes ago, chron44 said:

he did sort of a way anticipate the cosmological constant problem of today

This is another common myth though.

2 minutes ago, chron44 said:

energy/ mass in universal uneven distribution, or something like that.

We can boil down the idea to a single question:
If the Universe consists only from one single object - would this object "poses" parameters like mass, energy, position, velocity, etc... and if then this object would vanish what would left of this Universe?

20 minutes ago, Anton Rize said:

Also I have to worn you, my experience on this forum I can describe as "Fundamental Church of container space and its holy trinity (x,y,z)) ".

Still, don't forget that physics in essence are measurements, always done by math (x, y and z). ; )

9 minutes ago, Anton Rize said:

We can boil down the idea to a single question:
If the Universe consists only from one single object - would this object "poses" parameters like mass, energy, position, velocity, etc... and if then this object would vanish what would left of this Universe?

Right on track, you are.

15 minutes ago, Genady said:

he did sort of a way anticipate the cosmological constant problem of today

This is another common myth though.

Let's skip all myths and rumors with Einstein. I know that SM the base for CCP wasn't present first during the 60-70's. Einstein died in 1955. The QFT was present in an early form his latest years, though. And as I can see: "A common myth is that Einstein “didn’t understand” quantum mechanics. This is historically false. He understood it deeply - he helped create it. His objections were conceptual, not technical."

Edited March 8Mar 8 by chron44