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 8 hours ago8 hr 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 7 hours ago7 hr 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 4 hours ago4 hr 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 4 hours ago4 hr 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 3 hours ago3 hr 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 3 hours ago3 hr 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