I recall reading an SF story years ago, Light of Other Days by Bob Shaw. The srory revolves around the concept of ‘slow glass’, ie glass through which light takes years to pass. The protagonist and his wife, touring in Scotland, decide to buy some of the locally-produced slow glass.
Of course it transpires that Mrs Hagan and her son were killed in a road accident 6 years previously and the bereaved spouse and father spends hours watching them through the pane of slow glass he had installed while they were alive.
Is this scientifically possible? I know photons can be slowed down but could they be brought under such control to produce an image years later?
It also seems to me that if the light which is passing directly through the glass at a right angle is delayed by 1 year, for instance, then if you’re looking through at a 45% angle then you’re seeing light which has taken approx 17 months (12 months times the square root of two.) This would make it hard to get a coherent picture of moving objects, and would even give unusual effects for landscapes (snow around the edges and springtime in the middle of the scene for instance.)
There are so very, very many things against this. I’ll just mention a bit more:
Chromatic aberration. Not all parts of the “scene” are coming in straight (or leaving straight out). The index of refraction for this glass would be phenomenal. While a flat thinnish plane and not a lens, the difference in refraction on entering/leaving the pane would be significant. So the colors would be dispersed to astonishingly different degrees.
In fact, the time delay of the different colors passing thru the plane even ignoring bending would be weird. A waving red and blue flag would be viewed as as red and black waving flag then a black and blue waving flag.
They handwaved the chromatic aberration away by stating that the slow glass had a near infinite index of refraction so that all light was refracted so as to pass through the glass at a ninety degree angle. That way all path lengths were the same and the delay matched up.
Chromatic aberration seems less like a fundamental law of physics, and more like a property of the materials that happen to exist in our present real world. If someone did make “dispersive slow glass”, then you at least could sandwich a narrow bandpass filter to make “monochrome slow glass”, or maybe a few of them with some dichroic beamsplitters for “RGB slow glass”.
The delay vs. angle thing is separate, and seems more fundamental. There’s really just one degree of freedom, the index of refraction, which determines both the angle of the ray in the glass and the “speed” of the glass. Going from vacuum/air to the slow glass, we’ve got sin(theta_air) = nsin(theta), or theta_air = ntheta for small angles, or theta = theta_air/n.
A ray at angle theta from normal sees a path length per unit thickness of 1/cos(theta) = sec(theta) ~ (1 + 0.5theta^2), so a path length delta of 0.5theta^2 = 0.5*(theta_air/n)^2, so a time delta of 0.5*(theta_air/n)^2/(c/n) = 0.5theta_air^2/(nc).
In other words, if you slow the glass down by a factor of two, then you decrease the angle from normal of the refracted ray in the glass by a factor of two. That decreases the path length delta (vs. an exactly normal ray) by a factor of four, so the time delta decreases (not increases) by a factor of two.
So the handwave seems well-founded. Someone should check my math, though.
Transmission mediums have a “velocity factor” which is how slow a wave front propagates. It is easily possible to slow down electromagnetic signals by 50% or 66%: Velocity factor - Wikipedia
Sometimes this effect is used to create an analog delay line which delays a signal. Before the digital era, a long stretch of coax cable was often used to delay an oscilloscope signal and see what happened before the trigger event: Analog delay line - Wikipedia
However delay lines introduced noise and degraded the signal.
A similar approach is possible using a fiber optic cable but the delay would only be milliseconds at most, even for a very long cable. During that delay the image quality would be degrading.
The question is could a physical substance slow down light transmission by millions of times without degrading the image. I don’t think so. Even if it was possible the “slow glass” would not be usable as glass. It would be opaque for several years until the first light passed through.
Photons have zero rest mass, but a system containing photons has mass proportional to the energy.
If the window is 1 square meter and can handle the outdoors, then it must be able to store about 1.5 kW of power during the day. Over 6 years and 12 hour days, that’s 1.4e11 joules. That’s about 1.5 milligrams of mass-energy, which is a lot, but obviously wouldn’t contribute much to the total mass.
Well, they apparently got light down to 38 miles per hour in a Bose-Einstein condensate.
So, the answer to the first part of whether light can be slowed down by millions of times appears to be yes. (On the other hand, a factor of a few millions isn’t really enough for the effect of slow glass, you’d need several more orders of magnitude.) No word on degrading the image, though that sounds like an engineering problem rather than a theoretical impossibility.
This really intrigues me. I can’t think of a fundamental reason why it’s impossible.
But there is another fundamental reason why it would be very difficult. The greater the index of refraction, the greater is the reflection you get at the surfaces of the substance (these reflections are one of the reasons you can see a drinking glass sitting there on the table, for example). An infinite index of refraction would mean the material would be a perfect mirror. I think an index of refraction in the hundreds or thousands would practically make the material only appear to be a mirror and not a window, and increasing the index of refraction by many more orders of magnitude would make it so much the worse.
The required slowdown would be roughly 10^20 (10 to the 20th power), IOW from 186,282 miles per second to about 0.5 mm per year. Slowing to 38 miles per hour is only eight orders of magnitude, out of a required 20 orders of magnitude required.
No physics experiment has ever remotely approached the degree of slowdown required, and even if so it could not be a material property. All the tests to date with delay lines and optical fibers indicate a signal-to-noise degradation on long runs. There is no reason to believe this would somehow go away on delays many orders of magnitude greater, rather would likely be worse.
Also the “slow glass” would essentially be storing in First In First Out fashion six years of optical data so perfect it appeared to be a transparent glass into the scene. We can approximate using known bit rates for encoding for 8k video over that period, which is about 9,500 terabytes. Of course this does not take into account the multiple view angles the window would have to cover, which would likely increase the data requirement many times beyond this.
It’s a good story but is best viewed as a magical property not one founded in physics.
There’s also wavelength to consider, take this form of the Planck-Einstein relation:
E = hc / λ
So if you halve the speed of the medium, you halve the wavelength. (The energy of the photon has to stay the same or else you’re talking about some way of dropping/restoring photon energy.)
Taking a middle visible spectrum wavelength as 550 nm, a “mere” slowdown of a factor of a million leads to a wavelength of 0.55 m. Presumably a lot more than the thickness of the pane. This is in the VHF radio/TV frequency band. “Optics” no longer applies in this world. The behavior of radio frequency photons in regular glass is a whole 'nother matter. The material in the pane in question wouldn’t be considered glass-like at this point.
The “resolution” of such waves is crappy and then some. If you used VHF waves as radar (with a lot of energy), you’d barely be able to tell if something was merely near you. No fine details at all. I don’t think the passing of such waves thru matter would preserve the details of the original image at all.
The Bose-Einstein condensate way of slowing things down has been mentioned. The nature of such of a material and how it relates to mundane materials we are familiar with rules out anything remotely analogous to the world of common optical glass.
A factor of a billion slowdown and you’re in the VLF band, etc.
ftg, You’re multiplying when you should be dividing.
Napier, that only necessarily applies to the reflections within the medium, not from outside of the medium. The critical angle for slow glass would be very close to 90 degrees. But that wouldn’t matter, because the light inside the slow glass got there via refraction in the first place. If light can enter a plane-parallel medium, then it can leave it, too.
I’m not talking about total internal reflection because of the critical angle.
I’m talking about the (usually small) reflection that happens to a ray coming into the medium from outside, the phenomenon that antireflection coatings are for minimizing, the phenomenon that lets you see your reflection in a window.
Of course, you could simulate the appearance of slow glass by storing the information of those photons and projecting it later as if on a glass wall. I reckon that continuous HD video recording for 6 years (the buffer size) using current compression technology requires ~1Gb/hour, thus around 50 TB for 6 years. This without considering night time and the extreme image redundancy of a static camera over long periods.
My home server has over 50 TB storage, so this is trivially possible.
It is just that slow glass is not the right tool for the effect.
