- #36

learn.steadfast

- 59

- 2

Ibix said:The only reason you need to accelerate at all is because there's no other way for you to meet your twin again in flat spacetime.

For future reference, if I make statements that something is "like" something else, I do not MEAN they are identical. Carefully note that they are likely Not the same in sense that identical "twins" are meant to be the same. For example, if I say "A duck is like an airplane" please do not jump to the conclusion that I think a duck IS an airplane or that an airpane must have feathers. etc.

In Special Relativity, the idea that light is accelerated by gravity is not yet accounted for. The purpose of using "twins" in special relativity experiments is to simplify the mathematics, for since they are "identical" in how they act, or measure time, etc. we are invoking the scientific method of investigation and attemption to limit what might interfere with a thought experiment; eg: I am trying to isolate what assumptions (false/true) we may be making that we don't realize we are making.

In the twin paradox I linked to by Dr. Don Lincoln, Femilab:

The experiment is broken into a "triplet's" paradox, in order to avoid acceleration. Please watch the video carefully. I think Doc does an admirable job.

The implicit assumption of the show, however, is that calling something an "inertial reference frame" is sufficient to solve the paradox. This is why I tried to call your attention to the doppler effect and measurements of acceleration; I wanted to try and isolate what "acceleration" is.

There are at least two ways I know to measure acceleration. I am not certain they are the same under the assumptions of Special Relativity.

One method is that if two "identical" lasers (twins) are in motion toward (or away) from each other, that they can measure a color change (doppler shift) of each other. Therefore, they can measure acceleration between the two lasers by measuing the time derivative of the laser's color change.

The second method of measuring acceleration is to use two masses (inertias) that are in torsion with each other. We attach one mass rigidly to a "reference" frame, and measure the shear force required to keep the other mass moving rigidly next to the first mass. When I accelerate the reference frame (eg: by shoving a cart with my hand that the accelerometer is attached to) the other mass is "dragged" along with the reference mass by a spring or other energy transfer device. We can therefore measure the amount of force the transfer device uses in order to measure/sense the "acceleration" of the cart.

An inertial accelerometer is the kind of accelerometer that a computer hard disk drive uses to detect when it is dropped or shoved suddenly, to protect the heads from "crashing." A doppler accelerometer is the kind of accelerometer used to measure whether a distant sun of the same spectra as our own, is moving (OR) accelerating toward or away from us.

However, I do not thnk an intertial accelerometer necessarily gives the same measurements in Special Relativity that a doppler shift accelerometer will give. The reason is that "free fall" can not be detected by an inertial accelerometer, but it can be detected by a doppler accelerometer.

When we did the "twin" paradox, using minkowski space, I suspect we are assuming that somehow we can magically tell the difference between inertial acceleration and gravitational acceleration in Special Relativity by the mere labeling of "frames of reference."

But it seems to me that we can always use gravitational acceleration to "hide" acceleration from an inertial accelerometer.

A special television show was aired last week about General Relativy's 100th birthday. At the end of the show they posed a Gedanken "Suppose the Sun disappeared from our solar system, never mind "HOW" it happened, what would be the effect on the earth?"

The television show's point was that it would take 8 minutes for the gravitational wave from the diappearing sun to reach the Earth, and for Earth to stop "curving" around the region where the sun used to be. The Earth would then move in a straight line flying off at a tangent...

The issue I see is that the Earth is normally in "Free" fall around the sun (in Special Relativity) and an inertial accelerometer can not detect the acceleration of the Earth by the sun (accurately). Whether the sun is there (or not), an inertial accelerometer will measure approximately 1g because of the accelerometer's close proximity to Earth's surface. I am unsure what the accelerometer would meausre if it was some-how moved magically to the center of the Earth ... but I suspect it would measure zero.

Both before and after the "sun" went out, the Earth has the same mass , and therefore an inertial accelerometer will still measure 1g if oriented parallel to the Earth's gravitational field at the surface of the Earth, or probably zero if at the center. The inertial accelerometer is not going to measure the same amount of acceleration as a doppler accelerometer will measure because an inertial accelerometer doesnt' "know" the total mass of the entire universe. (Especially if the sun suddenly just "disappeared.).

That leads me back to the assumption I'm trying to explore:

Whenever we do measurments in Minkowski space, for special relativity, we always measure with time of travel via the length "ct", to make the measurement co-variant. But this automatically implies that light is some-how involved in the measurement and acceleration is inherently a doppler measurement.

The second issue is that Minkowski space uses the generalized Pythagorean theorem, which is the same as taking the square root of an absolute value. In every case where a square root is taken, there are mathematically TWO solutions. It's not clear to me that one can't use Newtonian gravity in Special Relativity, to artificially manipulate which soultion applies to path length, or time length, etc.

For example, in the Twin paradox, at the 8 year mark ... what happens if two massive (but tiny) black holes moving in opposite directions were to move approximately perpendicular to both A and B at the "midway" point between them? The inertial accelerometers on A and B are not going to measure much change (if any!) ... But the doppler shift accelerometer is going to suddenly blue shift on both A and B very distinctively. This change will happen under the assumptions of Special Relativity, as well.

Therefore, I think that "inertial reference frames" are a necessary condition to claim that something is not accelrating, but merely being in an inertial reference frame is not a *sufficient* condition to guarantee that measurable acceleration is not happening in Special Relativity.

I realize that General Relativity may come to a different conclusion, but I think General Relativity uses different assumptions.

I have completed my calculations for the orbit of the planet-satellite system based on F=ma. One very important point is that the effective mass is different in different directions for 3 vectors. It goes as gamma in directions perpendicular to the direction of motion, and gamma cubed in the direction of motion. Therefore, the direction of the force vector is only the same as the direction of the acceleration vector when going exactly perpendicular or exactly parallel to the direction of motion. In all other cases, the direction of acceleration is not exactly the same as the direction of the applied force.