Do superluminal worldlines constitute closed time-like curves under the right conditions?What does a closed...
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Do superluminal worldlines constitute closed time-like curves under the right conditions?
What does a closed time-like curve look like?Distance and time measurement in the famous Superluminal Neutrinos ExperimentThe Alcubierre drive and closed timelike curvesFaster than light signals and the price to be paid if we accept them : a very simple protocolClosed timelike curves in the spin-2 gravity formalismClosed timelike curves in the Kerr metricProving the sum of null and time-like four-vectorsWormholes and Closed Time-like Curves
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A closed time-like curve is defined as a word-line that returns to its starting point, in the $x$, $y$, $z$, $t$ coordinates. So, for a chronology respecting observer, an object traversing a closed time-like curve would appear to violate causality. Under certain conditions (Tolman et al.), superluminal propagation of signals also appears to violate causality.
Does this indicate that for a tachyonic anti-telephone situation, the worldline of a superluminal tachyon could be considered as a closed time-like curve?
special-relativity relativity faster-than-light tachyon closed-timelike-curve
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A closed time-like curve is defined as a word-line that returns to its starting point, in the $x$, $y$, $z$, $t$ coordinates. So, for a chronology respecting observer, an object traversing a closed time-like curve would appear to violate causality. Under certain conditions (Tolman et al.), superluminal propagation of signals also appears to violate causality.
Does this indicate that for a tachyonic anti-telephone situation, the worldline of a superluminal tachyon could be considered as a closed time-like curve?
special-relativity relativity faster-than-light tachyon closed-timelike-curve
edited 1 hour ago
SuperCiocia
6,9697 gold badges40 silver badges96 bronze badges
asked 9 hours ago
CuriousDroidCuriousDroid
256 bronze badges
$endgroup$
add a comment |
$begingroup$
A closed time-like curve is defined as a word-line that returns to its starting point, in the $x$, $y$, $z$, $t$ coordinates. So, for a chronology respecting observer, an object traversing a closed time-like curve would appear to violate causality. Under certain conditions (Tolman et al.), superluminal propagation of signals also appears to violate causality.
Does this indicate that for a tachyonic anti-telephone situation, the worldline of a superluminal tachyon could be considered as a closed time-like curve?
special-relativity relativity faster-than-light tachyon closed-timelike-curve
edited 1 hour ago
SuperCiocia
6,9697 gold badges40 silver badges96 bronze badges
asked 9 hours ago
CuriousDroidCuriousDroid
256 bronze badges
$endgroup$
A closed time-like curve is defined as a word-line that returns to its starting point, in the $x$, $y$, $z$, $t$ coordinates. So, for a chronology respecting observer, an object traversing a closed time-like curve would appear to violate causality. Under certain conditions (Tolman et al.), superluminal propagation of signals also appears to violate causality.
Does this indicate that for a tachyonic anti-telephone situation, the worldline of a superluminal tachyon could be considered as a closed time-like curve?
special-relativity relativity faster-than-light tachyon closed-timelike-curve
special-relativity relativity faster-than-light tachyon closed-timelike-curve
edited 1 hour ago
SuperCiocia
6,9697 gold badges40 silver badges96 bronze badges
asked 9 hours ago
CuriousDroidCuriousDroid
256 bronze badges
edited 1 hour ago
SuperCiocia
6,9697 gold badges40 silver badges96 bronze badges
asked 9 hours ago
CuriousDroidCuriousDroid
256 bronze badges
edited 1 hour ago
SuperCiocia
6,9697 gold badges40 silver badges96 bronze badges
edited 1 hour ago
SuperCiocia
6,9697 gold badges40 silver badges96 bronze badges
edited 1 hour ago
SuperCiocia
6,9697 gold badges40 silver badges96 bronze badges
6,9697 gold badges40 silver badges96 bronze badges
asked 9 hours ago
CuriousDroidCuriousDroid
256 bronze badges
asked 9 hours ago
CuriousDroidCuriousDroid
256 bronze badges
asked 9 hours ago
CuriousDroidCuriousDroid
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256 bronze badges
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No. The world-line of a tachyon is spacelike. That's the definition of a tachyon. That means it can't be a closed timelike curve.
The existence of CTCs is a property of the spacetime, not of the particles inhabiting it. Minkowski space simply doesn't have CTCs.
answered 8 hours ago
Ben CrowellBen Crowell
60.5k6 gold badges178 silver badges341 bronze badges
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I see. And does the same logic apply to other methods of apparent superluminal motions, like wormholes?
$endgroup$
– CuriousDroid
8 hours ago
1
$begingroup$
@CuriousDroid: No, in a traversable wormhole, there really can be CTCs. That is a different property of that spacetime.
$endgroup$
– Ben Crowell
7 hours ago
$begingroup$
I see. So a wormhole that allows for superluminal motion relative to an outside observer, but that does not have a relative time shift between the mouths, that would NOT produce a CTC, but still allow for an apparent causality violation?
$endgroup$
– CuriousDroid
6 hours ago
add a comment |
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1 Answer
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1 Answer
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$begingroup$
No. The world-line of a tachyon is spacelike. That's the definition of a tachyon. That means it can't be a closed timelike curve.
The existence of CTCs is a property of the spacetime, not of the particles inhabiting it. Minkowski space simply doesn't have CTCs.
answered 8 hours ago
Ben CrowellBen Crowell
60.5k6 gold badges178 silver badges341 bronze badges
$endgroup$
$begingroup$
I see. And does the same logic apply to other methods of apparent superluminal motions, like wormholes?
$endgroup$
– CuriousDroid
8 hours ago
1
$begingroup$
@CuriousDroid: No, in a traversable wormhole, there really can be CTCs. That is a different property of that spacetime.
$endgroup$
– Ben Crowell
7 hours ago
$begingroup$
I see. So a wormhole that allows for superluminal motion relative to an outside observer, but that does not have a relative time shift between the mouths, that would NOT produce a CTC, but still allow for an apparent causality violation?
$endgroup$
– CuriousDroid
6 hours ago
add a comment |
$begingroup$
No. The world-line of a tachyon is spacelike. That's the definition of a tachyon. That means it can't be a closed timelike curve.
The existence of CTCs is a property of the spacetime, not of the particles inhabiting it. Minkowski space simply doesn't have CTCs.
answered 8 hours ago
Ben CrowellBen Crowell
60.5k6 gold badges178 silver badges341 bronze badges
$endgroup$
$begingroup$
I see. And does the same logic apply to other methods of apparent superluminal motions, like wormholes?
$endgroup$
– CuriousDroid
8 hours ago
1
$begingroup$
@CuriousDroid: No, in a traversable wormhole, there really can be CTCs. That is a different property of that spacetime.
$endgroup$
– Ben Crowell
7 hours ago
$begingroup$
I see. So a wormhole that allows for superluminal motion relative to an outside observer, but that does not have a relative time shift between the mouths, that would NOT produce a CTC, but still allow for an apparent causality violation?
$endgroup$
– CuriousDroid
6 hours ago
add a comment |
$begingroup$
No. The world-line of a tachyon is spacelike. That's the definition of a tachyon. That means it can't be a closed timelike curve.
The existence of CTCs is a property of the spacetime, not of the particles inhabiting it. Minkowski space simply doesn't have CTCs.
answered 8 hours ago
Ben CrowellBen Crowell
60.5k6 gold badges178 silver badges341 bronze badges
$endgroup$
No. The world-line of a tachyon is spacelike. That's the definition of a tachyon. That means it can't be a closed timelike curve.
The existence of CTCs is a property of the spacetime, not of the particles inhabiting it. Minkowski space simply doesn't have CTCs.
answered 8 hours ago
Ben CrowellBen Crowell
60.5k6 gold badges178 silver badges341 bronze badges
answered 8 hours ago
Ben CrowellBen Crowell
60.5k6 gold badges178 silver badges341 bronze badges
answered 8 hours ago
Ben CrowellBen Crowell
60.5k6 gold badges178 silver badges341 bronze badges
answered 8 hours ago
Ben CrowellBen Crowell
60.5k6 gold badges178 silver badges341 bronze badges
60.5k6 gold badges178 silver badges341 bronze badges
$begingroup$
I see. And does the same logic apply to other methods of apparent superluminal motions, like wormholes?
$endgroup$
– CuriousDroid
8 hours ago
1
$begingroup$
@CuriousDroid: No, in a traversable wormhole, there really can be CTCs. That is a different property of that spacetime.
$endgroup$
– Ben Crowell
7 hours ago
$begingroup$
I see. So a wormhole that allows for superluminal motion relative to an outside observer, but that does not have a relative time shift between the mouths, that would NOT produce a CTC, but still allow for an apparent causality violation?
$endgroup$
– CuriousDroid
6 hours ago
add a comment |
$begingroup$
I see. And does the same logic apply to other methods of apparent superluminal motions, like wormholes?
$endgroup$
– CuriousDroid
8 hours ago
1
$begingroup$
@CuriousDroid: No, in a traversable wormhole, there really can be CTCs. That is a different property of that spacetime.
$endgroup$
– Ben Crowell
7 hours ago
$begingroup$
I see. So a wormhole that allows for superluminal motion relative to an outside observer, but that does not have a relative time shift between the mouths, that would NOT produce a CTC, but still allow for an apparent causality violation?
$endgroup$
– CuriousDroid
6 hours ago
$begingroup$
I see. And does the same logic apply to other methods of apparent superluminal motions, like wormholes?
$endgroup$
– CuriousDroid
8 hours ago
$begingroup$
I see. And does the same logic apply to other methods of apparent superluminal motions, like wormholes?
$endgroup$
– CuriousDroid
8 hours ago
1
1
$begingroup$
@CuriousDroid: No, in a traversable wormhole, there really can be CTCs. That is a different property of that spacetime.
$endgroup$
– Ben Crowell
7 hours ago
$begingroup$
@CuriousDroid: No, in a traversable wormhole, there really can be CTCs. That is a different property of that spacetime.
$endgroup$
– Ben Crowell
7 hours ago
$begingroup$
I see. So a wormhole that allows for superluminal motion relative to an outside observer, but that does not have a relative time shift between the mouths, that would NOT produce a CTC, but still allow for an apparent causality violation?
$endgroup$
– CuriousDroid
6 hours ago
$begingroup$
I see. So a wormhole that allows for superluminal motion relative to an outside observer, but that does not have a relative time shift between the mouths, that would NOT produce a CTC, but still allow for an apparent causality violation?
$endgroup$
– CuriousDroid
6 hours ago
add a comment |
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