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| In physics, a '''world tube''' is the path of an object which occupies a nonzero region of space (nonzero ]) at every moment in time, as it travels through 4-]al ]. That is, as it propagates in ], a world tube traces out a three-dimensional ] for every moment in time.<ref>Malcolm Ludvigsen: ''General relativity: a geometric approach'', Cambridge University Press, 1999, {{ISBN|0-521-63019-3}}, </ref> The world tube is analogous to the one-dimensional ] in that it describes the time evolution of an object in space, with the difference that a world line represents the path of a ] (of nonzero volume), whereas a world tube occupies finite space at all moments in time. | In physics, a '''world tube''' is the path of an object which occupies a nonzero region of space (nonzero ]) at every moment in time, as it travels through 4-]al ]. That is, as it propagates in ], a world tube traces out a three-dimensional ] for every moment in time.<ref>Malcolm Ludvigsen: ''General relativity: a geometric approach'', Cambridge University Press, 1999, {{ISBN|0-521-63019-3}}, </ref> The world tube is analogous to the one-dimensional ] in that it describes the time evolution of an object in space, with the difference that a world line represents the path of a ] (of nonzero volume), whereas a world tube occupies finite space at all moments in time. | ||
| A world tube extends beyond the observer in every direction, as it travels from one point to another, allowing to view it as a 4-dimensional map, and a sphere in the 4 dimensions can be described by representing its path in 3-dimensional space. An important difference between two 3-D, one-dimensional world lines is their ] boundaries. If there are infinite worlds, a non-zero boundary must exist for every time point between its two corners while none exist for a non-zero one-dimensional world line, since there is a finite distance between each corner of a world line.<ref>Hamilton, J. C. (2003), The Relativity of Physics, Princeton University Press, ISBN |
A world tube extends beyond the observer in every direction, as it travels from one point to another, allowing to view it as a 4-dimensional map, and a sphere in the 4 dimensions can be described by representing its path in 3-dimensional space. An important difference between two 3-D, one-dimensional world lines is their ] boundaries. If there are infinite worlds, a non-zero boundary must exist for every time point between its two corners while none exist for a non-zero one-dimensional world line, since there is a finite distance between each corner of a world line.<ref>Hamilton, J. C. (2003), The Relativity of Physics, Princeton University Press, {{ISBN|0-89501-022-6}}</ref> At that moment in time, the object has been created by a set of events or "unions", corresponding to certain mathematical relations whose expression can be represented within the object's world space. It is thus analogous to the two-dimensional sphere in that they both describe a three-dimensional volume, which is the boundary of an object between the four-dimensional space to which it has been added and the four-dimensional space the object does not have a corresponding space-velocity along on.<ref>Hamilton, J. C. (2003), The Relativity of Physics, Princeton University Press, {{ISBN|0-89501-022-6}}</ref> | ||
| The concept of world tube is particularly relevant for ], where a world tube is embedded in ]. | The concept of world tube is particularly relevant for ], where a world tube is embedded in ]. | ||
Revision as of 16:09, 8 July 2019
In physics, a world tube is the path of an object which occupies a nonzero region of space (nonzero volume) at every moment in time, as it travels through 4-dimensional spacetime. That is, as it propagates in spacetime, a world tube traces out a three-dimensional volume for every moment in time. The world tube is analogous to the one-dimensional world line in that it describes the time evolution of an object in space, with the difference that a world line represents the path of a point particle (of nonzero volume), whereas a world tube occupies finite space at all moments in time.
A world tube extends beyond the observer in every direction, as it travels from one point to another, allowing to view it as a 4-dimensional map, and a sphere in the 4 dimensions can be described by representing its path in 3-dimensional space. An important difference between two 3-D, one-dimensional world lines is their non-zero boundaries. If there are infinite worlds, a non-zero boundary must exist for every time point between its two corners while none exist for a non-zero one-dimensional world line, since there is a finite distance between each corner of a world line. At that moment in time, the object has been created by a set of events or "unions", corresponding to certain mathematical relations whose expression can be represented within the object's world space. It is thus analogous to the two-dimensional sphere in that they both describe a three-dimensional volume, which is the boundary of an object between the four-dimensional space to which it has been added and the four-dimensional space the object does not have a corresponding space-velocity along on.
The concept of world tube is particularly relevant for special relativity, where a world tube is embedded in Minkowski space.
See also
References
- Malcolm Ludvigsen: General relativity: a geometric approach, Cambridge University Press, 1999, ISBN 0-521-63019-3, p. 74
- Hamilton, J. C. (2003), The Relativity of Physics, Princeton University Press, ISBN 0-89501-022-6 Parameter error in {{ISBN}}: checksum
- Hamilton, J. C. (2003), The Relativity of Physics, Princeton University Press, ISBN 0-89501-022-6 Parameter error in {{ISBN}}: checksum
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