Theoretically, can perfectly flat spacetime exist in the Universe?

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• John Constantine
John Constantine
TL;DR Summary
Can perfectly flat spacetime exist in the universe?
According to general relativity, mass and energy cause the curvature of spacetime. To have perfectly flat spacetime, there must be a completely empty vacuum state with no mass or energy. Does this mean that perfectly flat spacetime cannot exist if mass and energy are present?

Let's assume that mass and energy are present in space. Theoretically, is it possible to create perfectly flat spacetime, even locally, by precisely arranging mass and energy in the universe?

I am not a physics major nor have I studied physics in depth; I am an ordinary person.

John Constantine said:
Does this mean that perfectly flat spacetime cannot exist if mass and energy are present?
Except for special cases, yes. See further comments below.

John Constantine said:
is it possible to create perfectly flat spacetime, even locally, by precisely arranging mass and energy in the universe?
There is one known way to do it: create a perfectly spherical shell of matter with vacuum inside. The spacetime inside the shell will be flat. (But spacetime outside the shell will not.)

John Constantine
PeterDonis said:
There is one known way to do it: create a perfectly spherical shell of matter with vacuum inside. The spacetime inside the shell will be flat. (But spacetime outside the shell will not.)
I think that only works on an already flat or spherically symmetric background. I don’t think a spherical shell gives you any “curvature shielding”

Nik_2213
Dale said:
I think that only works on an already flat or spherically symmetric background.
Yes, spherical symmetry is required for the spacetime inside the shell to be exactly flat.

Dale
This sounds more philosophical than physical: a variation on trees falling in empty forests making sounds or not.

If I cannot bring in any rulers or clocks, how do I know if that region of spacetime is perfectly flat?

jbriggs444
John Constantine said:
Theoretically, is it possible to create perfectly flat spacetime, even locally, by precisely arranging mass and energy in the universe?

I am not a physics major nor have I studied physics in depth; I am an ordinary person.
Infinite precsion is ruled out by the Heisenberg Uncertainty Principle, if nothing else. Even excluding QM, with a classical theory of matter, you cannot achieve absolute zero and cannot infinitely precisely control a large number of particles. Even an electron moving in a classical orbit about the nucleus makes the mass distribution time dependent.

Perfection is only to be found in mathematics.

At the risk of nit picking, I see no reason a spherical mass shell wouldn’t be nearly transparent to gravitational waves. Any actual region of space will have some level of curvature.

John Constantine
Paul Colby said:
I see no reason a spherical mass shell wouldn’t be nearly transparent to gravitational waves.
Just as spherical mass shells are all transparent to electromagnetic waves?

John Constantine
Just as spherical mass shells are all transparent to electromagnetic waves?
Well, there are no earthly materials that shield gravitational waves. In the weak field limit it’s pretty easy to calculate the gravitational refractive index of a material given its stiffness. For any earthly material it’s one followed by many zeros. Likewise energy loss is also negligible.

John Constantine
Of course, if we add “theoretically” to “perfectly flat”, then I think the answer is yes.

John Constantine
If your position is "a spherical mass shell is almost transparent to gravitational waves" because "everything is almost transparent to gravitational waves", well, I guess. Not sure how that's helpful.

John Constantine
It’s helpful to point out there are no gravitational shielding materials like there are for electric, magnetic and electromagnetic fields. The spherical solution only works in spherically symmetric space-times with flat space time as a special case. I suppose if one knew the curvature in advance, one could arrange masses so as to cancel curvature over a given region to some order. But then some random gravitational wave could blow on through and disrupt your flatness.

John Constantine and Dale
Paul Colby said:
It’s helpful to point out there are no gravitational shielding materials like there are for electric, magnetic and electromagnetic fields.
Even if that were true, how is it helpful?

Furthermore, I don't think it is true. Energy can be extracted from gravitational waves, so these waves can be attenuated. Same as for EM.

PeroK and ergospherical
Even if that were true, how is it helpful?
Well, the one example given, a spherical mass shell, is not an example of gravitational shielding. While this may be obvious to many it’s likely not obvious to all.

Furthermore, I don't think it is true. Energy can be extracted from gravitational waves, so these waves can be attenuated. Same as for EM.
Yes, but keep the numbers in mind. The gravitational power incident on LIGO for a detected event is measured in kW per square meter. It’s huge. The power converted into the optical side bands of LIGO is measured in femto Watts. It’s so small it took a good fraction of the physics community 40 years to build a system capable of measuring it. Not much attenuating is happening.

Dale and fresh_42
Paul Colby said:
The power converted into the optical side bands of LIGO is measured in femto Watts.
There would also be some power that was absorbed from the wave that was wasted and not converted into a signal. But still it is small. Matter is largely transparent to gravitational waves in my understanding too.

It would be interesting to know what configurations of matter would be most and least transparent to GW's. I would assume something that was very deformable and that deformed plastically would be the most opaque, but that is just an assumption

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Dale said:
There would also be some power that was absorbed from the wave that was wasted and not converted into a signal. But still it is small. Matter is largely transparent to gravitational waves in my understanding too.

It would be interesting to know what configurations of matter would be most and least transparent to GW's. I would assume something that was very deformable and that deformed plastically would be the most opaque, but that is just an assumption

Damping of gravitational waves by matter
Gordon Baym, Subodh P. Patil, and C. J. Pethick
https://journals.aps.org/prd/abstract/10.1103/PhysRevD.96.084033

Nugatory and Dale
Paul Colby said:
Well, the one example given, a spherical mass shell, is
A physical object can only approximate a sphere, even theoretically. You could, of course, theorise that mass is continuous and can be smeared into a shell. This seems to me more fundamental than debating the nature of gravitational waves. There is no such thing as a perfect sphere in the first place. The rest is moot.

Dale said:
It would be interesting to know what configurations of matter would be most and least transparent to GW's.
Sticky beads would be the classical example, but any damped oscillator will do.

Dale
Paul Colby said:
I see no reason a spherical mass shell wouldn’t be nearly transparent to gravitational waves.
A perfectly spherical shell cannot transmit gravitational waves. Any gravitational wave requires a violation of spherical symmetry. Even if a gravitational wave ends up perfectly transmitted, it still requires the shell to not be spherically symmetric while it is transmitting the wave: the atoms in the shell have to move with perfect elasticity in a non-spherically-symmetric manner while the wave is passing.

So, I think the position is:

You can have exactly flat spacetime if the matter (or stress-energy, more precisely) distribution across the whole spacetime is exactly spherically symmetric (note that such a solution doesn't allow gravitational waves in the first place) and has an exactly spherically symmetric cavity at its center of symmetry. Spacetime is flat in this cavity. The cavity may be infinite in size, and this is Minkowski spacetime.

You can't have this for any number of reasons in our universe. It's possible to describe the parameters needed for a flat region, but canot have one in our universe.

If "flat enough" is what you're after then head for deep space.

Dale and PeterDonis
PeterDonis said:
A perfectly spherical shell cannot transmit gravitational waves. Any gravitational wave requires a violation of spherical symmetry. Even if a gravitational wave ends up perfectly transmitted, it still requires the shell to not be spherically symmetric while it is transmitting the wave: the atoms in the shell have to move with perfect elasticity in a non-spherically-symmetric manner while the wave is passing.
But even a perfect sphere wouldn’t have uniform fields within if other masses are present outside the sphere. This of course would break spherical symmetry you’ve specified. The framing of the OP I read as could one construct a uniform space. In our universe I think the answer is no.

Paul Colby said:
even a perfect sphere wouldn’t have uniform fields within if other masses are present outside the sphere. This of course would break spherical symmetry you’ve specified.
Yes, exactly. If you break spherical symmetry then the shell theorem no longer holds.

Paul Colby said:
The framing of the OP I read as could one construct a uniform space.
I don't know what you mean by "uniform space". The OP used the precise term "flat spacetime".

Sorry, replace flat for uniform.

Dale said:
It would be interesting to know what configurations of matter would be most and least transparent to GW's. I would assume something that was very deformable and that deformed plastically would be the most opaque, but that is just an assumption
A somewhat related question is could one rethink the Weber Bar detectors? These convert gravitational wave energy into vibrational energy in the bar. For Webers design, only the residual tidal forces on the bar ends drive mechanical vibration. Could changing the surface design increase the coupling or broaden the bandwidth? Non isotopic materials might also increase coupling. Mechanical vibrations even in isotopic materials is a complicated subject.

ergospherical said:

Damping of gravitational waves by matter
Gordon Baym, Subodh P. Patil, and C. J. Pethick
https://journals.aps.org/prd/abstract/10.1103/PhysRevD.96.084033
That is pretty interesting. I thought it would be an unstudied concept, but from the article it makes sense why it was studied. That places limits on how early they could get GW signals. The collisional damping appears to prevent GW’s from the first moments of the universe

Dale said:
It would be interesting to know what configurations of matter would be most and least transparent to GW's. I would assume something that was very deformable and that deformed plastically would be the most opaque, but that is just an assumption

Paul Colby said:
A somewhat related question is could one rethink the Weber Bar detectors? These convert gravitational wave energy into vibrational energy in the bar. For Webers design, only the residual tidal forces on the bar ends drive mechanical vibration. Could changing the surface design increase the coupling or broaden the bandwidth? Non isotopic materials might also increase coupling. Mechanical vibrations even in isotopic materials is a complicated subject.
I recall this interesting remembrance of Joseph Weber at Maryland. He was subject to some intense criticism as I remember.

Um, would there not be a persistent 'crinkling' of space/time due 'zero point energy' and fleeting virtual particles ?? That sets a limit --Of sorts--on 'flatness'...

However, by analogy with how laser beams may be 'squeezed' to trade-off various properties for enhanced measurements, there's possible potential for canny enhancements.

Nik_2213 said:
Um, would there not be a persistent 'crinkling' of space/time due 'zero point energy' and fleeting virtual particles ??
We don't understand what gravitational fields of quantum objects look like - that's what we need quantum gravity for. So the answer to your question is that we'll get back to you when we have a working theoretical framework in which to answer it.

This whole discussion is purely classical.

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hutchphd, Dale and PeterDonis
hutchphd said:
He was subject to some intense criticism as I remember.
Yes. Weber’s war time experience was in the detection of submarines. He spent much time looking for signals in high noise environments. His gravitational detector work was impressive but his system just wasn’t sensitive enough to detect events that are seen by LIGO. Problems arose when he claimed detection of events on the order of ##10^{-18}##. Thorn pointed out these event were just too large not to be ruled out other cosmological data.

hutchphd

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