[Bill S (OP)]

John Gribbin says, regarding the tachyon:   “So if a tachyon were created in some violent event in space, it would radiate energy away furiously…..and go faster and faster, until it had zero energy ……and was travelling at infinite speed”. 

“Infinite speed” is a term that trips easily off the tongue, but is not easy to define.  If it means anything, surely, it must mean that a journey from A to be B would take no time.  In other words, one would be at A and B simultaneously. 

If A and B are physically separated, then a situation arises in which an instantaneous response occurs in separated locations.  Relativity must forbid this.

[wolfekeeper]

Not necessarily. However, if it existed you would probably be able to measure the rest frame of the universe, because it would be logically impossible for it to go the same speed relative to all reference frames or even relative to the object that emitted it. There would probably be a special frame in which it had a symmetric superluminal speed. If that wasn't the case then I think in all cases you could build a telephone to call yesterday.

The normal statement is that Relativity 'disproves' the Aether, however electromagnetism only makes it impossible for you to find out which frame is the Aether (if there is one) using electromagnetic experiments, so it gets cut away with Ockham's razor. But the Aether, or something like it, could come back if there was a tachyon that moved at a fixed speed.

But personally, I'm not holding my breath for a tachyon.

[Bill S (OP)]

However, if it existed you would probably be able to measure the rest frame of the universe, because it would be logically impossible for it to go the same speed relative to all reference frames or even relative to the object that emitted it.

For what to travel at “the same speed relative to all reference frames”? 
Speed is d/t.  How could you apply that, or any other measure to “infinite” speed?

There would probably be a special frame in which it had a symmetric superluminal speed.

Relative to what?

I’m unsure of the connection between infinite speed and the aether; other than the strong possibility that neither exists.

[wolfekeeper]

Infinite speed is a timelike interval. It's possible to have a timelike interval relative to one frame of reference, but not all frames of reference.

[Bill S (OP)]

Infinite speed is a timelike interval.

For a time-like interval between 2 events, it is impossible to find an inertial reference frame in which the events occur at the same time.  If the “speed” at which something travelled between A and B were infinite, A and B would have to be synchronous in that RF.  How can infinite speed be timelike? 

[guest4091]

Infinite speed would be

“Infinite speed” is a term that trips easily off the tongue, but is not easy to define.  If it means anything, surely, it must mean that a journey from A to be B would take no time.  In other words, one would be at A and B simultaneously. 

You have it correct. It's a contradiction of terms, and another nonsensical interpretation of x/0. Will it ever end? If the tachyon is serving as a messenger, we would have real time awareness of distant events, a universal time.

[wolfekeeper]

My bad, I meant spacelike. Infinite speed is a spacelike interval. You can only have a spacelike interval relative to one particular reference frame.

[evan_au]

Tachyons (=a particle that only travels faster than light) are not explicitly forbidden by the equations of relativity. Once such a hypothetical particle was formed, it could never gain enough energy to slow down and reach the speed of light.

Such a particle could have real energy, even if some of its other characteristics are bizarre, due to the Lorentz factor of SQRT(1-v²/c²), which is imaginary (in the mathematical sense) for v>c.

Despite various attempts to discover tachyons, none have been detected. One of the search methods was to look for Cerenkov radiation in a vacuum, which is normally emitted by particles traveling faster than the speed of light in a transparent medium. The hypothesis was that Tachyons should emit Cerenkov radiation in a vacuum, losing energy, and thus speeding up even faster.

The idea that Tachyons would emit Cerenkov radiation was rather speculative. But despite various searches, no evidence has been found for Tachyons, and for now, they are regarded as imaginary (in the speculative sense).

See: https://en.wikipedia.org/wiki/Tachyon

[Kryptid]

Can anything have truly zero energy in reality? It sounds more like a limit that can be approached but never reached, much as absolute zero can be approached but never reached. That sounds like a way to avoid the "infinite speed" problem for tachyons.

[Bill S (OP)]

  Will it ever end?

No; it’s infinite! 

[Bill S (OP)]

You can only have a spacelike interval relative to one particular reference frame.

Interpreting space-like events as those that can take place at the same time but not happen at the same location, given an appropriate RF; I would not argue with your statement.  However, it seems to throw little light on the question of infinite speed.  Speed involves movement between locations.  Infinite speed would involve instantaneous “movement”. There is, therefore, no distance or time to measure.  What meaning can speed have in this situation?

[Bill S (OP)]

Evan, that’s some interesting stuff about tachyons, thanks.

I mentioned tachyons only because they were a feature of Gribbin’s introduction of “infinite speed”. 
It’s the concept of infinite speed I’m trying to clarify in my mind.

[Bill S (OP)]

Can anything have truly zero energy in reality? It sounds more like a limit that can be approached but never reached, much as absolute zero can be approached but never reached. That sounds like a way to avoid the "infinite speed" problem for tachyons.

You are, presumably, likening the situation to a hyperbolic curve which, although it never becomes a straight line, at least in theory, does, quite obviously, become increasingly straight, and therefore more like a straight line.  As you point out: this does seem to avoid the infinite speed problem, but the price of that is the introduction of “infinite” acceleration!

[jeffreyH]

Since speed is distance traveled over time taken it is not possible to have an infinite speed. The time taken in this case is zero. The equation becomes undefined at this point, which can also be interpreted as infinite. The true interpretation of this situation is that an object is everywhere at once and so occupies all of spacetime over a zero time interval. As if it exists everywhere and nowhere. That is more like religion than science. Infinity has its uses but should not be taken literally.

[opportunity]

could the objects be in quantum-entanglement?

Quantum-entanglement proposes immediate interaction. That itself suggests space is either everywhere at once or time is a relativity of its own beyond the simple arrow at the speed of light of the observer.

[Bill S (OP)]

Since speed is distance traveled over time taken it is not possible to have an infinite speed.

I certainly agree with that, but one still finds references like that of Gribbin.  I have to wonder why.
Is it sloppy wording, oversimplification, or just another example of unfortunate use/misuse of “infinite”?

Infinity has its uses but should not be taken literally.

I would agree with that as well, except that I see no way to avoid a literal interpretation when considering the “something from nothing” question. 

[Bill S (OP)]

could the objects be in quantum-entanglement?

Quantum-entanglement proposes immediate interaction. That itself suggests space is either everywhere at once or time is a relativity of its own beyond the simple arrow at the speed of light of the observer.

This would not address the problem of the transition from finite to infinite speed.  At one moment it is measurable, then it is not.  Make sense of that!

[opportunity]

could the objects be in quantum-entanglement?

Quantum-entanglement proposes immediate interaction. That itself suggests space is either everywhere at once or time is a relativity of its own beyond the simple arrow at the speed of light of the observer.

This would not address the problem of the transition from finite to infinite speed.  At one moment it is measurable, then it is not.  Make sense of that!

I agree. Maybe time has more granularity to it as opposed to just being one-dimensional?

[Bill S (OP)]

I’d be interested to know what you see as the link between granularity and multi-dimensionality.

[opportunity]

Well, an interesting feature to our reality is how “nature” develops “growth patterns” through time, especially on the quantum level in regard to the uncertainty principal [a link is available], as a process of the development of spatial constructs in time, “time” seeming to weave spatially-related phenomena according to a thing termed the “golden ratio”. This alone could suggest one of two things, namely that the “arrow of time” surely has more granularity to it, granularity that features a “golden-ratio” algorithm, or space is a particular matrix that encodes the golden ratio by its own constitution. I'd prefer to give credence to the idea of “time” being the entity with the golden-ratio feature, not space, as all evidence suggests that the golden ratio is a process of “growth” in time and not an immediate manifestation of space itself all of a sudden (as “all of as sudden” is not possible in considering the golden ratio as a function of the “uncertainty principal”, as observations for the “uncertainty principle” conclude that both features of the golden ratio can’t co-exist at the one time on the quantum scale in the one frame of reference). I'm working on a paper that shows such an algorithm for time can link the four basic field forces.