scattered around the room, which were in turn connected to monitoring and control equipment.
While Carroway hung back, the Arkentons and Shrewsbury examined the device. Kathleen voiced the obvious thought they all entertained: "Why build a telescope in a basement room with no windows?" No one ventured an answer.
In time they each gravitated to a different part of the room. Shrewsbury concentrated on the lens, while Kathleen checked out the electrical equipment, and Jeremiah found and began reading the researcher's notebook. It was Shrewsbury who broke the silence first.
"This is a scrying glass."
"A what?" Carroway asked as the Arkentons looked over at their friend.
"A magical device for viewing scenes from great distances."
Carroway barked an astonished laugh, but Shrewsbury threw him a stern look. "There is nothing amusing about it. This is an extremely dangerous object, unless you know how to handle it. Among other concerns, it can act both ways, so that a being you are observing may observe you as well. And unlike a technological viewing device such a telescope, a being with a sufficiently powerful will may directly affect whatever it views."
Carroway burst out with a genuine horselaugh, which earned him disapproving looks from all present. "Surely you're not serious?"
"I am deadly serious, Theodore." Shrewsbury's tone sounded severe. "I see you haven't changed. You always were a stubborn student, and it would seem you still need to learn your lessons the hard way."
Carroway colored with anger and embarrassment, but before he could respond, Shrewsbury suddenly announced: "I'm afraid I must leave."
"So soon?" Kathleen objected as she walked over to him.
He smiled. "Yes, I have to be back in Arkham this evening and my flight leaves in an hour."
"Jerry and I were hoping to take you to dinner this evening." She sounded disappointed.
"My apologies, but when you come to Arkham next you shall be my guests instead." He took her hand, and she reached up to kiss him lightly on the cheek.
"We'll see you at the conference in July, Laban," Jeremiah said before turning back to the notebook.
Squeezing Kathleen's hand, Shrewsbury then turned towards Carroway as he began to leave. "I leave you in good hands, Theodore; if anyone can determine what happened it is the Arkentons. However, I strongly advise all of you that once you have completed your investigation, you destroy that device immediately. Good luck, and good day." And with that he left the room and headed down the hall.
Carroway waited until he had passed from earshot, then turned back to the Arkentons. "Surely we can disregard that nonsense about magic."
"At our peril," Jeremiah replied without looking up.
Kathleen added, "Laban may not be a scientist, but he is a leading scholar on the philosophy of science and its relationship to metaphysics and epistemology. He is also an acknowledged theorist on the application of abstract mathematics such as hyperdimensional geometry to physical and metaphysical cosmology. Much of his expertise is in what people superstitiously call 'magic', so his warning is to be taken seriously."
Carroway's face purpled with anger again, but for a different reason. "Then Francis may have been using museum funding to perform crackpot experiments?"
Kathleen scowled, but she was interrupted by Jeremiah's even voice: "Perhaps not so crackpot."
Carroway scoffed, but he followed Kathleen as she went over to where her husband was sitting.
"What've you found?" She leaned over him.
Taking a pen from the desk and ripping the top sheet off a legal pad, Jeremiah began scribbling out formulas. "I'm not sure." He sounded distracted. "The math is rather complex; I wish Robert were here."
Kathleen looked up at Carroway. "Robert is our son; he's currently doing postdoctoral work at Harvard on developing new methods of calculus."
"However," Jeremiah said, sounding more focused, "it would appear that your researcher had a rather unique theory to explain how a scrying glass worked."
"Oh, please, I need you to conduct a serious investigation. If you're going to waste my time on a wild goose chase--"
"Keep still and listen!" Kathleen spat, her Irish temper aroused.
Jeremiah tossed the pen onto the pad. "Based on what I've read, your researcher speculates that scrying glasses use tachyons the way a cathode ray tube uses electrons, to paint pictures on a specially prepared screen. He then attempted to construct a 'tachyon television' as he called it using science instead of sorcery." He paused as a faint smile cracked his lips. "Your researcher seems to have a rather wry sense of humor; he abbreviated his invention as the 'tacky-TV' in his notes."
"What in the name of Beelzebub is a tachyon?" Carroway sounded sarcastic.
"All particles," Kathleen said, "can be divided into three groups: tardyons, which always travel slower than the speed of light; luxons, which always travel right at the speed of light; and tachyons, which always travel faster than light."
Carroway spoke in a smug manner. "Nothing can travel faster than light."
"Actually," Jeremiah said, "any particle traveling through glass can travel superluminally."
"How?"
"You know what happens when you toss a rock into a pool of water, don't you?" Kathleen asked. "It creates a wave in the shape of a ring that expands through the water from the point of impact. That ring is actually made up of a series of ripples that push it forward; they appear at the back of the ring, cross it, then disappear again when they reach the front. As such, any wave of water can be described by two velocities: the velocity of the ripples propelling it, called the 'phase velocity', and the velocity of the wave itself, called the 'group velocity'. The phase velocity is always faster than the group velocity, usually twice as fast.
"Light can be thought of as a wave traveling through a vacuum. Normally, the phase and group velocities of a beam of light are equal, but as that beam travels through matter, those velocities diverge. The group velocity remains unchanged, but the phase velocity slows down; this causes the refraction effect: the slower the phase velocity, the greater the refraction. A side effect is that a particle such as an electron traveling with the beam is itself unaffected, so it doesn't slow down as it passes through the glass. If the phase velocity slows down enough, the electron can actually travel faster than the light beam itself."
Carroway dismissed that notion with a wave of his hand. "Theoretical trickery; an optical illusion."
"No, it's quite real. A particle whose speed exceeds that of the phase velocity of light experiences a Doppler shift similar to that of an aircraft traveling faster than the speed of sound, only instead of producing a sonic boom it gives off a burst of light. This is known as Cerenkov radiation, and it is an observable phenomenon."
Carroway looked chagrined but not yet convinced. "All right, but this phase velocity sounds like it's a special case. According to relativity, no particle can go faster than light because of the mass increase barrier."
"You are partly correct," Jeremiah said. "Special relativity states that as a particle gains energy, it gains mass as well as speed, but the mass increases faster, until the particle would have infinite mass at the speed of light. Since infinite mass requires infinite energy, which is impossible, no tardyon can ever become a luxon. However, this does not preclude the existence of particles that are always superluminal. In fact, tachyons were first predicted around the turn of the century, from Maxwell's electromagnetic theory. They are otherwise identical to tardyons, but they lose speed as they gain energy and mass, so they would need infinite mass to slow down to luminal velocity. Relativistic mass is just as much a barrier for tachyons as it is for tardyons, so special relativity is not violated. It does make sound theoretical and philosophical sense when you think about it. The principle of symmetry demands that if there are tardyons and luxons, there must be tachyons as well."
"But how is it possible for a particle to slow down instead of speed up as it gets more energy?"
"Tachyons have an imag
inary rest mass; that is, the squares of their masses are negative numbers. Again, though, this makes sense in light of symmetry: tardyons have real rest mass and luxons have zero rest mass, so there should be a particle that has an imaginary rest mass."
"Oh, please, now you're being absurd."
"No, not really," Kathleen said. "What is the square root of negative four?"
"There is no answer, because no one knows what the square root of negative one is."
"No one knows the value of the square root of negative one, but mathematicians have created a solution; it's called 'i', short for 'imaginary'. The square root of negative four is 2i."
"But such a number has no meaning."
"Not in ordinary arithmetic, no," Jeremiah said, "but it becomes both necessary and meaningful when doing any form of higher math, including algebra. In any event, a tachyon's rest mass cannot be measured because it can never be brought to full rest; therefore it is experimentally meaningless and does not need to be a real number. However, a tachyon's energy content and momentum are represented by real numbers, so these quantities are measurable and therefore meaningful. The point is, having an imaginary mass means that a tachyon acts oppositely from a tardyon. Whereas a tardyon slows down as it looses energy, a tachyon speeds up; a tardyon with zero energy is at rest, while a tachyon with zero energy is at infinite speed. Such a tachyon is said to be 'transcendent'."
Carroway seemed to become intrigued
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