Curved spacetime and measurement direction

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In summary, "Curved spacetime and measurement direction" explores how the curvature of spacetime, influenced by mass and energy, affects the way measurements are taken in physics. It highlights the relationship between spacetime geometry and the direction of measurements, emphasizing that the presence of curvature can alter the perceived trajectory of objects and the flow of time. This interplay is crucial for understanding fundamental concepts in general relativity and has implications for both theoretical and experimental physics.
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How are parallel directions for measurements of entangled particles defined in locations which are far from each other?
To be specific, let's say that two photons in EPR entangled state were sent to Alice and Bob separated by billions of light years. We know that if they measure their photon polarizations in the same direction, they certainly get the same result. My question is, what is the same direction in their case?
I assume that this is determined by the parallel transport in curved spacetime and depends on trajectories of the photons between their origin and Alice and Bob respectively. Is this assumption correct?
 
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FAQ: Curved spacetime and measurement direction

What is curved spacetime?

Curved spacetime is a concept from Einstein's General Theory of Relativity, which describes how mass and energy influence the geometry of space and time. Instead of being a flat, unchanging backdrop, spacetime can be curved by the presence of mass and energy, affecting the motion of objects and the flow of time.

How does curved spacetime affect measurements?

Curved spacetime affects measurements by altering distances and the passage of time. For example, the presence of a massive object like a planet or star can warp spacetime, causing nearby objects to move along curved paths. This curvature also affects the measurement of time, leading to phenomena such as time dilation where time passes differently depending on the gravitational field's strength.

What is the significance of measurement direction in curved spacetime?

Measurement direction in curved spacetime is significant because the curvature can cause different measurements depending on the path taken. For instance, the distance measured between two points can vary if you take different routes through a curved spacetime. This is due to the non-Euclidean geometry where straight lines (geodesics) are curved by the presence of mass and energy.

How do we measure distances and angles in curved spacetime?

In curved spacetime, distances and angles are measured using the metric tensor, which encodes information about the curvature. The metric tensor allows us to calculate the proper distance and proper time between events, taking into account the curvature of spacetime. This involves integrating along the path taken through spacetime, using the metric to account for the curvature.

Can curved spacetime be directly observed?

Curved spacetime itself cannot be directly observed, but its effects can be. For example, the bending of light around massive objects (gravitational lensing) and the precise orbits of planets are both consequences of curved spacetime. Additionally, experiments such as the observation of gravitational waves provide indirect evidence of spacetime curvature.

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