Wikipedia:Reference desk/Archives/Science/2024 August 10

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August 10

Since gravity is formed by the stress–energy tensor, which apparently depends on the reference frame, does gravity depend on the reference frame?

HOTmag (talk) 17:38, 10 August 2024 (UTC)

Suppose we have a planet in a circular orbit around a star, using a reference frame in which the star is stationary and the rest of the universe doesn't spin around it. This is an ordinary, Keplerian orbit, as predicted by classical physics.

Now suppose a spaceship passes at high speed (0.8c or thereabouts) through this planetary system, in the plane of the planet's orbit. We switch to the reference frame of that spaceship. Special relativity tells us there's length contraction. The orbit of the planet turns into an ellipse with the star in the centre – not at one of the focal points. This is not a Keplerian orbit, so gravity must have done something funny.

Theoretically, it should be possible to apply the Lorentz transformation to the stress-energy tensor and solve the Einstein field equations for the orbit of the planet, which should give the same result as the Lorentz transformation of the Keplerian orbit, but I won't do the maths for you. PiusImpavidus (talk) 18:39, 10 August 2024 (UTC)

You have a wrong premise here, or at least one not aligned with the current way of looking at these things.

The stress–energy tensor does not in fact depend on the frame of reference. The components of the tensor depend on the frame of reference.

But the tensor is not its components. The tensor (field) is the underlying Platonic entity that can be viewed in any local coordinate system and its components extracted with respect to those coordinates, but the underlying thing remains the same.

This is the coordinate-free approach, which has been the preferred one since the mid-20th century. You don't necessarily have to agree with it; it's not the kind of thing that's subject to scientific confirmation or disconfirmation. But you probably ought to be aware that it's the dominant approach. --Trovatore (talk) 21:35, 10 August 2024 (UTC)

To be clear, this approach predicts the same outcomes for observations as approaches in which the tensor is identified with its (frame-of-reference dependent) representation. It is preferred because it gives one fewer headaches.  --Lambiam 01:41, 11 August 2024 (UTC)