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Art
Would it be possible to adjust for the curvature of space between 2 points and so by taking the shortcut (a true straight line) beat a light source in a race between the 2 points whilst traveling at less than light speed?
Art said:Would it be possible to adjust for the curvature of space between 2 points and so by taking the shortcut (a true straight line) beat a light source in a race between the 2 points whilst traveling at less than light speed?
Do you really mean the curvature of space? Or do you mean the curvature of space-time? They are different things, each having a particular meaning.Art said:Would it be possible to adjust for the curvature of space between 2 points and so by taking the shortcut (a true straight line) beat a light source in a race between the 2 points whilst traveling at less than light speed?
As the choice of a time co-ordinate would seem to be largely arbitary in this example I thought the underlying space curvature was the significant aspect but I stand open to correction.pmb_phy said:Do you really mean the curvature of space? Or do you mean the curvature of space-time? They are different things, each having a particular meaning.
In GR it is possible that there could be two worldlines between the same two events, which are widely spaced in space-time (i.e. two events which are located a places which are "far", i.e. in the Euclidean sense, from each other). Each of which might possibly correspond to two different (coordinate) times of travel.
Pete
Since light can orbit a massive object it is certainly possible to construct such a case: Send a photon on an orbit, and move a bit in the opposite direction. If the photon hits you after one round, you can say: "I was here first!"Art said:The essential point of my question was is it possible for a sub-lightspeed particle to reach a destination sooner than light by taking a 'shorter' route by by plotting a course which compensated for curvature?
Excellant point Rob, excellant!robphy said:You don't need local curvature...
Consider a cylindrical universe (with periodicity in the spatial x-direction).
A.T. said:Since light can orbit a massive object it is certainly possible to construct such a case: Send a photon on an orbit, and move a bit in the opposite direction. If the photon hits you after one round, you can say: "I was here first!"
In my example the light is sent on a detour, while you take a shortcut. If you assume that light takes the quickest way too, then it will be always faster than sub-c information.Art said:I meant more in the sense of is it possible to send information faster to a point than light can carry the same information whilst obeying the rule of not traveling faster than light can traveling at it's max speed whilst not deliberately constraining the speed of light.
Art said:I meant more in the sense of is it possible to send information faster to a point than light can carry the same information whilst obeying the rule of not traveling faster than light can traveling at it's max speed whilst not deliberately constraining the speed of light.
I'm just curious if one could theoretically pilot a sub-LS craft along an arc rather than follow the grand circle light has to follow. A little like how a sailing boat can sail slightly into the wind to maintain a straight heading.pervect said:Whew. Are you trying to ask "Are shortcuts like wormholes possible"? The answer to whether or not wormholes are possible is a qualified yes - there is currently no proof they are impossible, which is not quite the same thing as demonstrating that they are possible.
Art said:I'm just curious if one could theoretically pilot a sub-LS craft along an arc rather than follow the grand circle light has to follow. A little like how a sailing boat can sail slightly into the wind to maintain a straight heading.
I was responding to other people's posts who posted after you.Chris Hillman said:Assuming that by "follow the grand circle light has to follow" you mean that in gtr, the world line of a laser pulse (or a photon, if you prefer) is a null geodesic, did you read [post=1506991]my earlier post in this thread[/post]? Didn't I answer your question?
Art said:Would it be possible to adjust for the curvature of space between 2 points and so by taking the shortcut (a true straight line) beat a light source in a race between the 2 points whilst traveling at less than light speed?
Art said:I understand you correctly the inference seems to be that you can send information from Point A to B (effectively) faster than light.
Art said:My question then was could this be achieved by simply steering a course to nullify the effect of the curvature?
Art said:I ask this as it would appear to avoid the necessity for exotic matter etc for wormholes whilst achieving the same result?
Art said:Would there be any causality consequences if this were done?
The curvature of space refers to the bending or warping of the fabric of space due to the presence of mass and energy. It is a fundamental concept in the theory of general relativity and helps explain the behavior of gravity.
The curvature of space is measured by calculating the curvature of spacetime, which is a mathematical representation of the fabric of space. This can be done using mathematical equations and tools such as tensors and curvature tensors.
The presence of mass and energy causes curvature of space. This is because mass and energy are related to spacetime through the equation E=mc², and they create a distortion in the fabric of spacetime, resulting in the curvature of space.
The curvature of space has several effects, the most significant being the behavior of gravity. The curvature of space determines the path that objects will take when moving through space, and it also affects the passage of time. Additionally, the curvature of space can also cause gravitational lensing, where light is bent as it passes through a curved region of space.
Yes, curvature of space can be observed through various phenomena, such as the bending of light around massive objects, the orbit of planets around the sun, and the gravitational waves detected by LIGO. Additionally, the effects of curvature of space can also be observed through experiments and observations in space and on Earth.