# Space-time curvature and the fabric of space

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## Main Question or Discussion Point

Greetings: I watched several videos describing so-called "empty space" as being permeated with fields (electron field, quark field, etc.). Is it possible that it is actually these fields that curve about large masses and that the trajectory of light and matter curve because they follow the curved fields? That is, the curvature is in the fields and not the emptiness of space-time. I come a bit closer to understanding if the fields curve by interacting with mass/energy. Trying to grasp some intuitive understanding of curved space-time. Thanks.

Rich

megacal

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phinds
Gold Member
2019 Award
Greetings: I watched several videos describing so-called "empty space" as being permeated with fields (electron field, quark field, etc.). Is it possible that it is actually these fields that curve about large masses
They do, due to space-time curvature
and that the trajectory of light and matter curve because they follow the curved fields?
No, I don't think that even makes sense.
That is, the curvature is in the fields and not the emptiness of space-time.
It doesn't MATTER whether you are talking about a relative vacuum or elsewhere, the curvature exist if mass is nearby, BECAUSE the mass is nearby, not because there are fields or not.

Ibix
That is, the curvature is in the fields and not the emptiness of space-time.
As I understand it, quantum field theory assumes the existence of spacetime as a "background" on which these fields exist. So no, in short.

Edit: my understanding is the Fierz-Pauli quantum gravity does use a flat background and explains apparent curvature in terms of the quantised gravitational field. However the theory can't be made to work properly, and in this case there is no curvature anyway.

pervect
Staff Emeritus
Greetings: I watched several videos describing so-called "empty space" as being permeated with fields (electron field, quark field, etc.). Is it possible that it is actually these fields that curve about large masses and that the trajectory of light and matter curve because they follow the curved fields? That is, the curvature is in the fields and not the emptiness of space-time. I come a bit closer to understanding if the fields curve by interacting with mass/energy. Trying to grasp some intuitive understanding of curved space-time. Thanks.

Rich
Einstein has a well known example of how one can model a curved space as a flat space with an auxiliary field, a "temperature field", that causes rulers to expand or contract depending on their temperature.

It's possible to use these sorts of ideas to talk about curves space-time as well. This isn't the usual way of doing things, however. It is likely that there are some difficulties with understanding the event horizon of black holes with these sorts of formulations, but I haven't seen any paper that really talks about the issue.

Some references: Einsein's "heated marble slab" https://www.bartleby.com/173/24.html
Strauman's "reflections on gravity" https://arxiv.org/abs/astro-ph/0006423

nitsuj and megacal
PeterDonis
Mentor
2019 Award
the curvature is in the fields and not the emptiness of space-time
This doesn't make sense, because the fields don't have any property that corresponds to being "flat" or being "curved" to begin with. Only spacetime has such properties.

Dale
Mentor
Is it possible that it is actually these fields that curve about large masses and that the trajectory of light and matter curve because they follow the curved fields?
I am not sure that this question is scientifically meaningful. Let’s suppose unlimited budget and resources. Is there any experiment that could possibly be done that could detect the difference?

nitsuj
FactChecker
Gold Member
Typically, when a force field changes the path of a massive object away from the space-time geodesic, the resulting path depends on the amount of mass and the strength of the field. If the object's path does not depend on mass or any field strength, one must consider that the path is a space-time geodesic.

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Nugatory
Mentor
If the object's path does not depend on mass or any field strength....
Is that not another way of saying "no proper acceleration"?

FactChecker
Gold Member
Is that not another way of saying "no proper acceleration"?
I may have been clumsy in making my point. I interpreted the OP as asking if the curvature of space-time might just be due to curvature in force fields. My point is that the latter would have the usual charactoristics of acceleration -- an object's path would depend on the object's mass and the force field strength. So that is not equivalent to curvature of space-time.

PeterDonis
Mentor
2019 Award
the latter would have the usual charactoristics of acceleration
Huh? "Curvature of force fields" doesn't make any sense. Proper acceleration is path curvature--curvature of the particle's world line. It has nothing to do with "curvature of fields".

PAllen
2019 Award
According to many TV adds in the US, we must presume the fabric of spacetime is cotton.

weirdoguy and Nugatory
nikkor180 asked perfectly reasonable questions, and pervect gave

I hope nikkor180 was not put off by the dismissive posts by some.

nitsuj
Greetings: I watched several videos describing so-called "empty space" as being permeated with fields (electron field, quark field, etc.). Is it possible that it is actually these fields that curve about large masses and that the trajectory of light and matter curve because they follow the curved fields? That is, the curvature is in the fields and not the emptiness of space-time. I come a bit closer to understanding if the fields curve by interacting with mass/energy. Trying to grasp some intuitive understanding of curved space-time. Thanks.

Rich
Ignoring the "poetic physics" stuff and things, #6 Dale's post/reply is spot on imo.

It's just a different "story", description of the physics...atm no physical significance.

Dale