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My question -- pardon if not asked in the most incisive scientific prose

Do all observers see the same curved-space time?

Let me clarify:

Given that objects traveling at different relative speeds will be found to have different mass i.e. inertial mass due to the relative speeds -- does it follow that for each observer the curved space-time will be different?

We know that for some particles -- for example particles that have short half-lives that should not be found in parts of the atmosphere because they would otherwise not exist long enough for them to travel the distance -- the relativistic explanation is that from the ground observer stand-point the particle cannot be where it is, but from the particle's viewpoint it can exist long enough to be there

Similarly -- take any large mass that obviously could curve space-time ( the Sun for example). Various bodies in space are in motion relative to the Sun -- nearby and also light-years away. Given the relative nature of motion, that is the same as the objects seeing the Sun in relative motion to themselves. An object that sees the Sun traveling at speed X would see a certain curved space-time due to the Sun. An object that sees the Sun traveling at speed 5X would see a different curved-space time (as the Sun would be more massive (i.e. inertial mass)). An object approaching the speed of light -- would be the same as seeing the Sun traveling at near the speed of light i.e. incredibly massive. As such, the curved space-time would be dramatic.

Do you see the crux of my question? If we say that mass curves space-time...and we say that relative motion increases apparent mass -- then the same object for different observers can be seen as inducing different curved space-time frames.

In fact we could say that objects jump from one display of curved space-time to another curved space-time (even if just by the smallest amounts) as they change relative speeds -- relative to each other.

Is this the right way to think about curved space-time? It seems that in every instance it is mentioned, it is described as static -- caused by static, unchanging super large masses. But any mass will curve space-time...and relative motion approaching the speed of light...increases apparent mass.

This leads to my question -- do all observers see the same curved space-time from all vantage points? I would think not, as it would seem to violate relativity and create a preferred inertial frame.

But it creates the paradox that the same object would be seen -- by different observers-- to have different relative motion/mass curving effects on space-time. In effect, space-time, rather than being the back-ground for action -- becomes very individualized and fractured.

You can see why I am having trouble with this.

Thoughts?

Qmechanic
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chesspride
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  • You are using an outdated definition of mass. All modern physics uses the invariant mass, defined by the equation $m^2=E^2-p^2,$ where $E$ is the particle energy and $p$ the momentum. All inertial observers agree on $m,$ regardless of their motion. The reason a particle can't go beyond $v=c$ should not be understood as "as $v\to c,$ also $m\to\infty,$ so $F=ma$ gives $a\to0,$" but should rather be understood as "$F=ma$ is incorrect for $v\sim c,$ and the correct formula shows that $a\to0$ as $v\to c.$" We shouldn't use nonrelativistic physics as a crutch for relativistic physics. – HTNW Jun 15 '23 at 20:03

2 Answers2

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I believe that all observers experience the same curved spacetime because a perturbation metric depends only on the gravitational mass which by the equivalence principle is equal to the rest mass of a object which in turn doesn't depend on a reference frame.

  • I like your answer that it depends on rest mass. Even though "rest" is relative, it means that at least there is one common measure. – chesspride Jun 15 '23 at 18:56
  • "Rest mass" isnt the appropriate term it was given this name due to relativity because people were trying to understand why a object cannot exceed the speed of light."Rest mass" is the inherent mass of a object with classical mechanics.What changes during Lorentz boosts is not mass but inertia ,in a reference frame where the object is at rest the inertial mass is equal to the rest mass, when the object starts moving relative to the reference frame the inertial mass grows while the rest mass stays the same. –  Jun 15 '23 at 20:37
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Different patches of the same curved spacetime are covered by different neighborhoods of events. Each such patch has its own coordinate system, which could be adapted to the motion of a certain observer in that neighborhood.

A simple example: suppose you have rockets leaving you static outside a black hole, and your friend is freely falling towards the center. From your perspective, you will see your friend snag at some point and using your frame, you will predict that they will never enter the black hole. From the perspective of your friend, there is no event horizon and they fall helplessly towards the singularity in finite proper time. Both descriptions are valid yet they predict different phenomena. The resolution is that they are related by a coordinate transformation.

QuantumFieldMedalist
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