explain xkcd - User contributions [en]

2646: Minkowski Space

2022-07-16T04:23:30Z

Minkoswki: /* Explanation */

{{comic
| number = 2646
| date = July 15, 2022
| title = Minkowski Space
| image = minkowski_space.png
| titletext = My liege, we were able to follow the ship into Minkowski space, but now they've jumped to Hilbert space and they could honestly be anywhere.
}}

==Explanation==
{{incomplete|Created by A RELATIVISTIC QUANTUM STATE - Please change this comment when editing this page. Do NOT delete this tag too soon.}}

A spaceship is being pursued by an enemy ship. Much like in [[2577: Sea Chase]], it attempts to escape by changing the nature of the space. In this case, it goes into {{w|Minkowski space}}, a mathematical formulation of three dimensional space combined with the dimension of time to form a {{w|manifold}} originally intended to describe {{w|electromagnetism}} in terms of {{w|special relativity}}, and which is also used in {{w|general relativity}}.

Minkowski space is no different than ordinary spatiotemporal physical reality, so the idea of traveling from regular space into Minkowski space is meaningless, providing the humor of the comic's absurdist joke. The visual depiction of the spaceships skewed diagonally is based on graphical {{w|Minkowski diagram}} representation of objects in Minkowski space, where the {{w|world line}} of matter is bounded inside its diagonal {{w|light cone}}. The mention of distance depending on the observer's {{w|frame of reference}} refers to distances changing when measured in different inertial frames of reference, a concept called the {{w|relativity of simultaneity}}.

The title text implies hiding in {{w|Hilbert space}} is much easier. This is because Hilbert spaces can have an infinite number of dimensions, and thus are much more complicated than four-dimensional Minkowski space. However, Hilbert space is used to describe mathematical objects such as functions of various parameters and complexity, not physical spatiotemporal reality, so it is very unusual for a physical object to be represented in Hilbert space. The reference to Hilbert space could also refer to the {{w|Uncertainty principle}}, as quantum states can be represented as vectors in a Hilbert space.

=== Apparent distance ===

Whether the two spaceships are getting closer to each other does not depend on frame of reference if both the ships are moving at constant velocity.
Though if they are accelerating then depending on frame of reference they may be getting further apart or they may be getting closer.
If the ship giving chase has higher velocity than the ship being chased but ship being chased is accelerating faster , then from the perspective of ship being chased the other ship is getting closer to it . While from perspective of something a few light years away which is moving towards both of the ships the ship being chased is getting more distant from the other ship.

This is because from perspective of something a few light years away which is moving towards the ships the ship being chased has already accelerated and is faster from the other ship so the distance between them is increasing.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}
:{A spaceship is being pursued.}
:Voice 1: The enemy ship is right behind us! Prepare to jump to Minowski space on my mark.

:Voice 1: Three... two... one... MARK!
:SFX: Click

:{The panel distorts.}

:{The panel distorts further.}
:Voice 1: Are they still getting closer?
:Voice 2: I can't tell.
:Voice 3: I think it depends on your frame of reference.

{{comic discussion}}

2646: Minkowski Space

2022-07-16T04:21:33Z

Minkoswki: /* Explanation */

{{comic
| number = 2646
| date = July 15, 2022
| title = Minkowski Space
| image = minkowski_space.png
| titletext = My liege, we were able to follow the ship into Minkowski space, but now they've jumped to Hilbert space and they could honestly be anywhere.
}}

==Explanation==
{{incomplete|Created by A RELATIVISTIC QUANTUM STATE - Please change this comment when editing this page. Do NOT delete this tag too soon.}}

A spaceship is being pursued by an enemy ship. Much like in [[2577: Sea Chase]], it attempts to escape by changing the nature of the space. In this case, it goes into {{w|Minkowski space}}, a mathematical formulation of three dimensional space combined with the dimension of time to form a {{w|manifold}} originally intended to describe {{w|electromagnetism}} in terms of {{w|special relativity}}, and which is also used in {{w|general relativity}}.

Minkowski space is no different than ordinary spatiotemporal physical reality, so the idea of traveling from regular space into Minkowski space is meaningless, providing the humor of the comic's absurdist joke. The visual depiction of the spaceships skewed diagonally is based on graphical {{w|Minkowski diagram}} representation of objects in Minkowski space, where the {{w|world line}} of matter is bounded inside its diagonal {{w|light cone}}. The mention of distance depending on the observer's {{w|frame of reference}} refers to distances changing when measured in different inertial frames of reference, a concept called the {{w|relativity of simultaneity}}.

The title text implies hiding in {{w|Hilbert space}} is much easier. This is because Hilbert spaces can have an infinite number of dimensions, and thus are much more complicated than four-dimensional Minkowski space. However, Hilbert space is used to describe mathematical objects such as functions of various parameters and complexity, not physical spatiotemporal reality, so it is very unusual for a physical object to be represented in Hilbert space. The reference to Hilbert space could also refer to the {{w|Uncertainty principle}}, as quantum states can be represented as vectors in a Hilbert space.

=== Apparent distance ===

Whether the two spaceships are getting closer to each other does not depend on frame of reference if both the ships are moving at constant velocity.
Though if they are accelerating then depending on frame of reference they may be getting further apart or they may be getting closer.
If the ship giving chase has higher velocity than the ship being chased but ship being chased is accelerating faster , then from the perspective of ship being chased the other ship is getting closer to it . While from perspective of something a few light years away which is moving towards both of the ships the ship being chased is getting more distant from the other ship.

This is because from perspective of something a few light years away which is moving towards the ships the ship being chased has already accelrated and is faster from the other ship so the distance between them is increasing.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}
:{A spaceship is being pursued.}
:Voice 1: The enemy ship is right behind us! Prepare to jump to Minowski space on my mark.

:Voice 1: Three... two... one... MARK!
:SFX: Click

:{The panel distorts.}

:{The panel distorts further.}
:Voice 1: Are they still getting closer?
:Voice 2: I can't tell.
:Voice 3: I think it depends on your frame of reference.

{{comic discussion}}

2646: Minkowski Space

2022-07-16T04:20:15Z

Minkoswki: /* Explanation */

{{comic
| number = 2646
| date = July 15, 2022
| title = Minkowski Space
| image = minkowski_space.png
| titletext = My liege, we were able to follow the ship into Minkowski space, but now they've jumped to Hilbert space and they could honestly be anywhere.
}}

==Explanation==
{{incomplete|Created by A RELATIVISTIC QUANTUM STATE - Please change this comment when editing this page. Do NOT delete this tag too soon.}}

A spaceship is being pursued by an enemy ship. Much like in [[2577: Sea Chase]], it attempts to escape by changing the nature of the space. In this case, it goes into {{w|Minkowski space}}, a mathematical formulation of three dimensional space combined with the dimension of time to form a {{w|manifold}} originally intended to describe {{w|electromagnetism}} in terms of {{w|special relativity}}, and which is also used in {{w|general relativity}}.

Minkowski space is no different than ordinary spatiotemporal physical reality, so the idea of traveling from regular space into Minkowski space is meaningless, providing the humor of the comic's absurdist joke. The visual depiction of the spaceships skewed diagonally is based on graphical {{w|Minkowski diagram}} representation of objects in Minkowski space, where the {{w|world line}} of matter is bounded inside its diagonal {{w|light cone}}. The mention of distance depending on the observer's {{w|frame of reference}} refers to distances changing when measured in different inertial frames of reference, a concept called the {{w|relativity of simultaneity}}.

The title text implies hiding in {{w|Hilbert space}} is much easier. This is because Hilbert spaces can have an infinite number of dimensions, and thus are much more complicated than four-dimensional Minkowski space. However, Hilbert space is used to describe mathematical objects such as functions of various parameters and complexity, not physical spatiotemporal reality, so it is very unusual for a physical object to be represented in Hilbert space. The reference to Hilbert space could also refer to the {{w|Uncertainty principle}}, as quantum states can be represented as vectors in a Hilbert space.

Whether the two spaceships are getting closer to each other does not depend on frame of reference if both the ships are moving at constant velocity.
Though if they are accelerating then depending on frame of reference they may be getting further apart or they may be getting closer.
If the ship giving chase has higher velocity than the ship being chased but ship being chased is accelerating faster then from the perspective of ship being chased the other ship is getting closer to it . While from perspective of something a few light years away which is moving towards both of the ships the ship being chased is getting more distant from the other ship.

This is because from perspective of something a few light years away which is moving towards the ships the ship being chased has already accelrated and is faster from the other ship so the distance between them is increasing.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}
:{A spaceship is being pursued.}
:Voice 1: The enemy ship is right behind us! Prepare to jump to Minowski space on my mark.

:Voice 1: Three... two... one... MARK!
:SFX: Click

:{The panel distorts.}

:{The panel distorts further.}
:Voice 1: Are they still getting closer?
:Voice 2: I can't tell.
:Voice 3: I think it depends on your frame of reference.

{{comic discussion}}

2646: Minkowski Space

2022-07-16T04:16:46Z

Minkoswki: /* Explanation */

{{comic
| number = 2646
| date = July 15, 2022
| title = Minkowski Space
| image = minkowski_space.png
| titletext = My liege, we were able to follow the ship into Minkowski space, but now they've jumped to Hilbert space and they could honestly be anywhere.
}}

==Explanation==
{{incomplete|Created by A RELATIVISTIC QUANTUM STATE - Please change this comment when editing this page. Do NOT delete this tag too soon.}}
A spaceship is being pursued by an enemy ship. Much like in [[2577: Sea Chase]], it attempts to escape by changing the nature of the space. In this case, it goes into {{w|Minkowski space}}, a mathematical formulation of three dimensional space combined with the dimension of time to form a {{w|manifold}} originally devised to describe {{w|electromagnetism}} in terms of {{w|special relativity}} but which is also used in {{w|general relativity}}.

Minkowski space is no different than ordinary spatiotemporal physical reality, so the idea of traveling from regular space into Minkowski space is meaningless, providing the humor of the comic's absurdist joke. The visual depiction of the spaceships as skewed diagonally is based on graphical {{w|Minkowski diagram}} representation of objects in Minkowski space, where the {{w|world line}}s of physical matter are bounded inside its diagonal {{w|light cone}}s. The mention of distance depending on the observer's {{w|frame of reference}} refers to distances changing when measured in different inertial frames of reference, a concept called the {{w|relativity of simultaneity}}.

The title text implies hiding in {{w|Hilbert space}} is much easier. This is because Hilbert spaces can have an infinite number of dimensions, and thus are much more complicated than four-dimensional Minkowski space. Hilbert space is used to describe mathematical objects such as functions of various parameters and complexity, not physical spatiotemporal reality, so it is very unusual for a physical object to be represented in Hilbert space. The reference to Hilbert space could also refer to the {{w|Uncertainty principle}}, as quantum states can be represented as vectors in a Hilbert space.

Weather the two spaceships are getting closer to each other does not depend on frame of reference if both the ships are moving at constant velocity.
Though if they are accelerating then depending on frame of reference they may be getting further apart or they may be getting closer.
If the ship giving chase has higher velocity than the ship being chased but ship being chased is accelerating faster then from the perspective of ship being chased the other ship is getting closer to it but from perspective of something a few light years away which is moving towards both of the ships the ship being chased is getting more distant from the other ship.

This is because from perspective of something a few light years away which is moving towards the ships the ship being chased has already accelrated and is faster from the other ship so the distance between them is increasing.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}
:{A spaceship is being pursued.}
:Voice 1: The enemy ship is right behind us! Prepare to jump to Minowski space on my mark.

:Voice 1: Three... two... one... MARK!
:SFX: Click

:{The panel distorts.}

:{The panel distorts further.}
:Voice 1: Are they still getting closer?
:Voice 2: I can't tell.
:Voice 3: I think it depends on your frame of reference.

{{comic discussion}}

2646: Minkowski Space

2022-07-16T04:15:03Z

Minkoswki: /* Explanation */

{{comic
| number = 2646
| date = July 15, 2022
| title = Minkowski Space
| image = minkowski_space.png
| titletext = My liege, we were able to follow the ship into Minkowski space, but now they've jumped to Hilbert space and they could honestly be anywhere.
}}

==Explanation==
{{incomplete|Created by A RELATIVISTIC QUANTUM STATE - Please change this comment when editing this page. Do NOT delete this tag too soon.}}
A spaceship is being pursued by an enemy ship. Much like in [[2577: Sea Chase]], it attempts to escape by changing the nature of the space. In this case, it goes into {{w|Minkowski space}}, a mathematical formulation of three dimensional space combined with the dimension of time to form a {{w|manifold}} originally devised to describe {{w|electromagnetism}} in terms of {{w|special relativity}} but which is also used in {{w|general relativity}}.

Minkowski space is no different than ordinary spatiotemporal physical reality, so the idea of traveling from regular space into Minkowski space is meaningless, providing the humor of the comic's absurdist joke. The visual depiction of the spaceships as skewed diagonally is based on graphical {{w|Minkowski diagram}} representation of objects in Minkowski space, where the {{w|world line}}s of physical matter are bounded inside its diagonal {{w|light cone}}s. The mention of distance depending on the observer's {{w|frame of reference}} refers to distances changing when measured in different inertial frames of reference, a concept called the {{w|relativity of simultaneity}}.

The title text implies hiding in {{w|Hilbert space}} is much easier. This is because Hilbert spaces can have an infinite number of dimensions, and thus are much more complicated than four-dimensional Minkowski space. Hilbert space is used to describe mathematical objects such as functions of various parameters and complexity, not physical spatiotemporal reality, so it is very unusual for a physical object to be represented in Hilbert space. The reference to Hilbert space could also refer to the {{w|Uncertainty principle}}, as quantum states can be represented as vectors in a Hilbert space.

Weather the two spaceships are getting closer to each other does not depend on frame of reference if both the ships are moving at constant velocity.
Though if they are accelerating then depending on frame of reference they may be getting further apart or they may be getting closer.
If the ship giving chase has higher velocity than the ship being chased but ship being chased is accelerating faster then from the perspective of ship being chased the other ship is getting closer to it but from perspective of something a few light years away which is moving towards both of the ships the ship being chased is getting more distant from the other ship.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}
:{A spaceship is being pursued.}
:Voice 1: The enemy ship is right behind us! Prepare to jump to Minowski space on my mark.

:Voice 1: Three... two... one... MARK!
:SFX: Click

:{The panel distorts.}

:{The panel distorts further.}
:Voice 1: Are they still getting closer?
:Voice 2: I can't tell.
:Voice 3: I think it depends on your frame of reference.

{{comic discussion}}

2646: Minkowski Space

2022-07-16T04:13:16Z

Minkoswki:

{{comic
| number = 2646
| date = July 15, 2022
| title = Minkowski Space
| image = minkowski_space.png
| titletext = My liege, we were able to follow the ship into Minkowski space, but now they've jumped to Hilbert space and they could honestly be anywhere.
}}

==Explanation==
{{incomplete|Created by A RELATIVISTIC QUANTUM STATE - Please change this comment when editing this page. Do NOT delete this tag too soon.}}
A spaceship is being pursued by an enemy ship. Much like in [[2577: Sea Chase]], it attempts to escape by changing the nature of the space. In this case, it goes into {{w|Minkowski space}}, a mathematical formulation of three dimensional space combined with the dimension of time to form a {{w|manifold}} originally intended to describe {{w|electromagnetism}} in terms of {{w|special relativity}} but which is also used in {{w|general relativity}}.

Minkowski space is no different than ordinary spatiotemporal physical reality, so the idea of traveling from regular space into Minkowski space is meaningless, providing the humor of the comic's absurdist joke. The visual depiction of the spaceships as skewed diagonally is based on graphical {{w|Minkowski diagram}} representation of objects in Minkowski space, where the {{w|world line}}s of physical matter are bounded inside its diagonal {{w|light cone}}s. The mention of distance depending on the observer's {{w|frame of reference}} refers to distances changing when measured in different inertial frames of reference, a concept called the {{w|relativity of simultaneity}}.

The title text implies hiding in {{w|Hilbert space}} is much easier. This is because Hilbert spaces can have an infinite number of dimensions, and thus are much more complicated than four-dimensional Minkowski space. Hilbert space is used to describe mathematical objects such as functions of various parameters and complexity, not physical spatiotemporal reality, so it is very unusual for a physical object to be represented in Hilbert space. The reference to Hilbert space could also refer to the {{w|Uncertainty principle}}, as quantum states can be represented as vectors in a Hilbert space.

Weather the two spaceships are getting closer to each other does not depend on frame of reference if both the ships are moving at constant velocity.
Though if they are accelerating then depending on frame of reference they may be getting further apart or they may be getting closer.
If the ship giving chase is has higher velocity than the ship being chased but ship being chased is accelerating faster then from the perspective of ship being chased the other ship is getting closer to it but from perspective of something a few light years away which is moving towards both of the ships the ship being chased is getting more distant from the other ship.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}
:{A spaceship is being pursued.}
:Voice 1: The enemy ship is right behind us! Prepare to jump to Minowski space on my mark.

:Voice 1: Three... two... one... MARK!
:SFX: Click

:{The panel distorts.}

:{The panel distorts further.}
:Voice 1: Are they still getting closer?
:Voice 2: I can't tell.
:Voice 3: I think it depends on your frame of reference.

{{comic discussion}}

2646: Minkowski Space

2022-07-16T04:12:12Z

Minkoswki:

{{comic
| number = 2646
| date = July 15, 2022
| title = Minkowski Space
| image = minkowski_space.png
| titletext = My liege, we were able to follow the ship into Minkowski space, but now they've jumped to Hilbert space and they could honestly be anywhere.
}}

==Explanation==
{{incomplete|Created by A RELATIVISTIC QUANTUM STATE - Please change this comment when editing this page. Do NOT delete this tag too soon.}}
A spaceship is being pursued by an enemy ship. Much like in [[2577: Sea Chase]], it attempts to escape by changing the nature of the space. In this case, it goes into {{w|Minkowski space}}, a mathematical formulation of three dimensional space combined with the dimension of time to form a {{w|manifold}} originally intended to describe {{w|electromagnetism}} in terms of {{w|special relativity}}, and which is also used in {{w|general relativity}}.

Minkowski space is no different than ordinary spatiotemporal physical reality, so the idea of traveling from regular space into Minkowski space is meaningless, providing the humor of the comic's absurdist joke. The visual depiction of the spaceships skewed diagonally is based on graphical {{w|Minkowski diagram}} representation of objects in Minkowski space, where the {{w|world line}} of matter is bounded inside its diagonal {{w|light cone}}. The mention of distance depending on the observer's {{w|frame of reference}} refers to distances changing when measured in different inertial frames of reference, a concept called the {{w|relativity of simultaneity}}.

The title text implies hiding in {{w|Hilbert space}} is much easier. This is because Hilbert spaces can have an infinite number of dimensions, and thus are much more complicated than four-dimensional Minkowski space. However, Hilbert space is used to describe mathematical objects such as functions of various parameters and complexity, not physical spatiotemporal reality, so it is very unusual for a physical object to be represented in Hilbert space. The reference to Hilbert space could also refer to the {{w|Uncertainty principle}}, as quantum states can be represented as vectors in a Hilbert space.

Weather the two spaceships are getting closer to each other does not depend on frame of reference if both the ships are moving at constant velocity.
Though if they are accelerating then depending on frame of reference they may be getting further apart or they may be getting closer.
If the ship giving chase is has higher velocity than the ship being chased but ship being chased is accelerating faster then from the perspective of ship being chased the other ship is getting closer to it but from perspective of something a few light years away which is moving towards both of the ships. The ship being chased is getting more distant from the other ship.
the ship being chased
==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}
:{A spaceship is being pursued.}
:Voice 1: The enemy ship is right behind us! Prepare to jump to Minowski space on my mark.

:Voice 1: Three... two... one... MARK!
:SFX: Click

:{The panel distorts.}

:{The panel distorts further.}
:Voice 1: Are they still getting closer?
:Voice 2: I can't tell.
:Voice 3: I think it depends on your frame of reference.

{{comic discussion}}