I Questions regarding traveling speed in time and gravity as a force

[ersmith]

GR is making a statement that is completely unbelievable. And are proven only through math (I'm talking about gravity not being a force and the apple falls down due to spacetime curvature thing).

Wow, I think we need to step back here. "GR" says only two things, which boil down to:

(1) Objects move along geodesics in spacetime ("geodesic" is the generalization of a straight line that applies to any space, even one with intrinsic curvature). This is often summarized as "Spacetime tells matter how to move".
(2) Spacetime is curved, and the curvature is determined by the configuration of energy in that spacetime (including momentum, stress, and pressure). ("Matter tells spacetime how to curve")

These aren't terribly difficult or even unintuitive statements, and millions of people have no trouble believing them. The hard part is seeing how these statements imply that apples fall, planets orbit the sun, and so forth. But that's just a matter of grinding through the math. There are "pop science" attempts to bypass the math and explain how our ordinary experiences of gravity follow from the assumptions. You certainly may find those pop science explanations unconvincing, and that's fair. But the conclusions drawn from the two postulates are not a matter of "belief", they're a matter of mathematics.

Consider flat spacetime (in deep space, away from any large masses). A moving object not subject to any forces traces a straight line in such a spacetime. So the path taken (in both space *and* time) by an inertial object is a "straight" line. This includes a "stationary" object, for which the straight line in spacetime happens to coincide with our choice of time axis. The angle between the various lines taken through spacetime by objects is a function of the relative velocities of those objects.

What's a curved line in spacetime? At each point of such a line there's a straight tangent line. Each tangent line corresponds to a particular velocity. "Curved" means the tangent lines are changing, i.e. the velocity is changing. So a curved line in spacetime corresponds to an accelerating object. This may be linear acceleration (e.g. an object falling straight towards a planet) or centripetal acceleration (e.g. an object in orbit) or both.

So saying "matter curves spacetime" is not too different from saying "matter makes things accelerate", which is a fairly uncontroversial statement. The details of how matter curves spacetime (and thus how things accelerate) are found in Einstein's field equations, and reduce to Newton's equations in the weak field limit (when there isn't very much matter, or it's far away).

 

[Grasshopper]

@Grasshopper Not to travel, to change direction or accelerate. Which is what happens when you change part of time traveling into space traveling.

How are you changing direction if you remain on the same geodesic? Are they not the straightest possible paths in spacetime?

Changing part of time into space traveling, as I understand it, is due to your arbitrarily chosen coordinates. In special relativity this happens simply by virtue of have a relative speed between the observers, and requires no force. E.g.,
$t’ = \frac{t - \frac{vx}{c^2}}{\sqrt{1 - \frac{v^2}{c^2}}}$EDIT — If you mean what someone not next to you sees, if I understand it, reference frames are strictly local in curved spacetime, and you’d have to have some parallel transport convention (I am not familiar with this topic).

 

[Dale]

GR is making a statement that is completely unbelievable. And are proven only through math (I'm talking about gravity not being a force and the apple falls down due to spacetime curvature thing).

This is completely backwards. GR's statement that gravity is not a force is proven experimentally with accelerometers. As you stand on the Earth an accelerometer directly measures that you are accelerating upward and as you free fall an accelerometer directly measures that you are not accelerating.

In contrast it is the traditional Newtonian gravitational treatment that is “proven only through math”. The Newtonian gravitational force cannot be experimentally measured, but only mathematically reconstructed by asserting a specific mathematical reference frame and inferring the force from the motion in that frame.

The equivalence principle comes from taking experimental measurements seriously and not pretending that the math is more “real” than the physical measurements. You have this complaint 100% exactly backwards.

 

[PeterDonis]

When we curve spacetime we are curving both space and time axis.

No. This makes no sense; an axis can't be curved. You have already been told this, repeatedly.

 

[PeterDonis]

I guess all of physics is true until a new, more complete theory comes up or for some reason is proven wrong.

You aren't paying attention. I never said theories are true. I said they are models that make predictions, and we test the modelsby comparing their predictions with experiments.

You need to stop responding to things nobody has said, and start paying attention to what we are actually saying.

 

[PeterDonis]

Since the OP is taking a vacation, this thread is closed.