# A question about general relativity ?

1. Apr 17, 2007

### ngkamsengpeter

In general relativity , gravity and acceleration can cause time dilation and curvature of spacetime . But I only read about the gravity in the general relativity , so I wondered is it every force can also cause time dilation and curvature of spacetime since every force also has an acceleration

2. Apr 17, 2007

### pervect

Staff Emeritus
If you work a physics problem wholly in an inertial frame, there will be no time dilation or space-time curvature ever.

Note also that the space-time in Einstein's "elevator experiment" is not really curved, at least not in the sense of having a non-zero curvature tensor. One basically has a flat space-time, which is the inertial frame in which the elevator takes place, using non-linear coordinates.

The issue is a bit like using polar coordinates on a flat sheet of paper. The paper is not actually curved by the usage of a different coordinate system- it's still flat. In some sense, though, one can losely call the polar coordinates "curved" (technically speaking, for instance, they have non-zero Christoffel symbols).

Note that the actual gravity of a mass cannot be described exactly in an inertial frame. (In some instances, it's an acceptable approximation, however).

3. Apr 19, 2007

### phyti

another view

SR concerns constant motion relative to a light source which produces
a real time dilation. Real in the sense that the physical system in motion,
space ship, clock, observer, any part that depends on the exchange of light
signals, functions at a slower rate.
Because the observers biological clock is also running slower
there is no awareness of the effect.
This causes the observer to interpret the arrival time at known distances
along the path as earlier than predicted.The perception of the observer is:
space in the direction of motion has contracted. In other words,
events are occurring faster in the world passing in the opposite direction.
than if the motion had not been initiated.
Every system has its own local frame of reference for space and time.

Acceleration can be viewed as a sequence of transfers to frames with
increasing speeds.
Even though GR proposes the equivalence of inertial acceleration and
gravitational force in a small region of space, the slowing of a clock at rest
on the surface of a massive object cannot be explained in terms of relative
motion since there is none (excluding rotation). I cannot offer any insight
regarding this, it is one of my own questions.

Specific to your question, any force that causes a change in speed
will alter the frame of reference.

4. Apr 19, 2007

### Mentz114

Electromagnetism can be combined with GR in a 5D space-time ( Kaluza-Klein) in which case the EM forces are also geometrized.

5. Apr 23, 2007

### MeJennifer

The amount of (proper) time an inertial observer accumulates between two events depends on the geodesic he travels on. When he applies a (non gravitational) force, he "kicks" himself out of this geodesic and continues to travel on a different one. It is hypothesized that the "kicking" part, by itself, does not influence the accumulation of proper time. This is often called the "clock hypothesis". No experiment has, as of yet, contradicted this hypothesis.

Last edited: Apr 23, 2007
6. Apr 23, 2007

### pmb_phy

Why not? The first calculation of time dilation was in Einstein's 1905 paper on sr.

Best wishes

Pete

7. Apr 23, 2007

### pervect

Staff Emeritus
Ooops - a thinko. There will never be any space-time curvature, but you can have ordinary SR time dilation.