Markus Hanke Posted September 10, 2021 Share Posted September 10, 2021 22 hours ago, Intoscience said: So, its the physical interaction between mass and space that causes the warping thus producing the gravity. It’s more the other way around, in a sense. What we ordinarily experience as gravity in a scenario like being ‘attracted’ to the earth is almost exclusively due to time dilation, which can be considered ‘warping of time’. Curvature of space then produces tidal effects. Ultimately though you can’t neatly separate these. Link to comment Share on other sites More sharing options...

Intoscience Posted September 10, 2021 Share Posted September 10, 2021 1 hour ago, Markus Hanke said: It’s more the other way around, in a sense. What we ordinarily experience as gravity in a scenario like being ‘attracted’ to the earth is almost exclusively due to time dilation, which can be considered ‘warping of time’. Curvature of space then produces tidal effects. Ultimately though you can’t neatly separate these. This is interesting, how is it so that it is almost exclusively time dilation? My understanding is that objects follow a curved path in space. Link to comment Share on other sites More sharing options...

Markus Hanke Posted September 10, 2021 Share Posted September 10, 2021 27 minutes ago, Intoscience said: This is interesting, how is it so that it is almost exclusively time dilation? My understanding is that objects follow a curved path in space. They follow paths in space-time, not just space. That’s a crucial difference. When in free fall, they will follow precisely that path which maximises proper time; so they tend to follow the longest possible path through space-time (‘geodesic’), which is also that path for which acceleration vanishes everywhere (hence free fall). This is called the principle of extremal ageing. Writing this mathematically gives an equation the solution to which is precisely the path followed by the falling body. Very simply put, the mathematical description for simple cases like the Earth (but not in more complicated cases!) ultimately depends on just two terms - one for time, and one for the radial coordinate. The former carries an additional factor of c^2, so it is much larger than any spatial effects. In that sense, time is the crucial thing here. Note that this is not necessarily true in more complicated spacetimes - just for some simple cases. 2 Link to comment Share on other sites More sharing options...

Intoscience Posted September 10, 2021 Share Posted September 10, 2021 37 minutes ago, Markus Hanke said: They follow paths in space-time, not just space. That’s a crucial difference. When in free fall, they will follow precisely that path which maximises proper time; so they tend to follow the longest possible path through space-time (‘geodesic’), which is also that path for which acceleration vanishes everywhere (hence free fall). This is called the principle of extremal ageing. Writing this mathematically gives an equation the solution to which is precisely the path followed by the falling body. Very simply put, the mathematical description for simple cases like the Earth (but not in more complicated cases!) ultimately depends on just two terms - one for time, and one for the radial coordinate. The former carries an additional factor of c^2, so it is much larger than any spatial effects. In that sense, time is the crucial thing here. Note that this is not necessarily true in more complicated spacetimes - just for some simple cases. Interesting, thanks for the insight. Link to comment Share on other sites More sharing options...

studiot Posted September 10, 2021 Share Posted September 10, 2021 40 minutes ago, Markus Hanke said: They follow paths in space-time, not just space. That’s a crucial difference. When in free fall, they will follow precisely that path which maximises proper time; so they tend to follow the longest possible path through space-time (‘geodesic’), which is also that path for which acceleration vanishes everywhere (hence free fall). This is called the principle of extremal ageing. Writing this mathematically gives an equation the solution to which is precisely the path followed by the falling body. Very simply put, the mathematical description for simple cases like the Earth (but not in more complicated cases!) ultimately depends on just two terms - one for time, and one for the radial coordinate. The former carries an additional factor of c^2, so it is much larger than any spatial effects. In that sense, time is the crucial thing here. Note that this is not necessarily true in more complicated spacetimes - just for some simple cases. +1 30 minutes ago, Markus Hanke said: When in free fall, they will follow precisely that path which maximises proper time; so they tend to follow the longest possible path through space-time (‘geodesic’), which is also that path for which acceleration vanishes everywhere (hence free fall). Just a note of additional explanation to add here. In many (if not most) presentations of relativity/gravitation (particularly Physics ones) it is stated that a geodesic is the shortest line. This is actually only half the story because a geodesic is a line of extremal values. And extremal values may be maximum or minimum (as Markus has here). Applied Mathematicians have therefore started to use the term extremal or state both maximum and minimum. This is further complicated in that the standard calculus technique to indentify such points and lines also identifies 'points of inflection' which are neither a maximum or a minimum. 1 Link to comment Share on other sites More sharing options...

Markus Hanke Posted September 10, 2021 Share Posted September 10, 2021 1 hour ago, studiot said: This is actually only half the story because a geodesic is a line of extremal values. And extremal values may be maximum or minimum (as Markus has here). Yes, true indeed. The concept of ‘extremum’ is much more precise. Whether it is the longest or shortest path is simply a matter of which convention one chooses. I’ve seen both used in various books, but personally prefer ‘longest’ since the concept of ‘time dilation’ then takes on a nicely intuitive geometric meaning. Link to comment Share on other sites More sharing options...

koti Posted September 14, 2021 Share Posted September 14, 2021 Gravity not only looks like it's not a force but it also looks like its not a basic concept, it looks like it's an aproximation of something underlying. Interestingly, time seems to fill the same rough definition - time seems to be an aproximation and not a basic concept and it too seems to be a part of something underlying. Link to comment Share on other sites More sharing options...

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