BOB LAZAR: FROZEN CANDLE
Bob tells a story about how they lit a candle and when they pointed the reactor output on it — candle flame remained luminous and stopped moving.
Bob described that the time slowed down at the area where they put the candle. The rate of slowing down (see chapter 1) is expressed in (Z+1), where Z called redshift. Let’s say it slowed down 101 times (could be any, should be measured at the site). So, if Bob stood right next to the candle, both for him and the candle, the time slowed down 101 times, so he would not notice anything weird about the candle flame, because time flow is the same for him and the candle. But when he stood outside, for 1 second passed inside the circle — 101 sec > 1 min passed for him. That is why candle flame does not flicker from his perspective — watching the candle is like watching video at a hundred times slower speed. But the most puzzling in this story, both for him and for myself (look at chapter 12 to see why), was that he could see the candle. Our expectation was — it should be screened from us, turned out it is not true, or to be exact — not always true.
By now you should be familiar with Snell’s refraction (page 6 of the book)
Let’s notice that for a large number Z, 100 for example, if angle B is not close to 0, for example B > 1° (B of 0°-90° range), (1+Z)*Sin(B) will become greater than 1 — and that cannot be, because on other side it is Sin(R). Only light that is almost perpendicular to the timezones border can cross it. What happens to the light that reaches the border at the angle far from a perpendicular — it bounces back = reflects. And reflection law states that light bounces back symmetrically under the same angle, here is proof:
For the light inside circle
only very close to a radius (that is always perpendicular to the circle) light can get out. And the light that is reflected back, will continue reflecting again and again, because of the property of the circle — angle to the radius remains same:
Now, regarding visibility of the candle we will have several cases.
Visible
We can see the candle on the “screen” where it is marked in orange:
In this position of the candle and the observer candle flame is visible on the screen, and its image is a bit enlarged and a bit shifted.
Mirrored
There are positions at which the candle is still visible, but its image is flipped and is seen faraway from the actual position:
Glowing screen
If the center of the screen is inside the candle flame — we won’t see the candle, but we’ll see a glowing sphere. Luminosity will be low compared to the candle luminosity — because light is dissipated over the screen — the orange arc is huge:
Invisible
And there are two areas of invisibility in white:
But in still can be seen at a different angle — from another position:
Wavelength and Visibility
Another aspect of visibility is wavelength — our eye can see only a certain range of wavelengths, usually at wavelengths from 380 to 700 nanometers. Visible light, when redshifted or blueshifted, can become invisible. If 380–700 nm wavelength doubles, then 760+ nm light is invisible to a naked eye, and if it is blueshifted to a half of wavelength 350- nm, then it is invisible too. And on the contrary, some light spectrum which was invisible can become visible after redshift or blueshift.
In the story with the candle, we shall wonder why the candle light is still visible after strong redshift (caused by time dilation). Candle light is produced from chemical reaction between candle wax molecules and the oxygen — from electron interactions of C and H atoms of the wax and O atoms from the air. Atomic time is autonomous / independent from the time of the environment / space. So, change to the wavelength of the light emitted by the candle flame occurs twice (from point A to point B, and from point B to point C):
From point A to point B wavelength decreases (Z+1) times, and from point B to point C it increases (Z+1) times. So, to the eye (point D) it arrives unchanged at a visible range for the eye — in a usual spectrum at which candles glow. I simplified the explanation (actually, time in the candle A could be different from normal time at C, and normal time at C could be different from time in the eye D), but point is: adding layer B between A and C does not change A-to-C wavelength ratio, because it is divided by Z+1 between A and B, and then it is multiplied by Z+1 between B and C. Intermediate redshifts cancel out:
(wavelength(B) / wavelength(A)) * (wavelength(C) / wavelength(B)) *
(wavelength(D) / wavelength(C)) = wavelength(D) / wavelength(A)
And wavelength ~ 1/Second — is in reverse proportion to time (faster time corresponds to “shorter” second and “longer” wave):
wavelength(D) / wavelength(A) = Second(A) / Second(D)
Thus, visibility depends on time speed at the beginning and at the end.
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