Altering the speed of light, implications

[xlovenuggetx]

i was watching sixty symbols today, and i learned about refractive indexes. light travels at 40% of its normal speed c when traveling through glass. after i watched that video i attended my summer class (engineering physics II, covering circuitry, optics and EM waves) and i started asking about what happens beyond what is normally shown in textbooks on the high-energy portion of the EM spectrum. my professor is Da-Zhu (levitated mouse using magnetic fields) and he said that the spectrum continues beyond 10^22 Hz and less than pm λ. he said it gets technical though. so, after some thinking (mind you I'm a chemistry major, whatever that means), i then asked if it was possible to increase the frequency while holding λ constant. he directed me to this equation: fλ=c . he said that would break the rules since the value of c is constant and f and λ are proportional.

now, consider what would happen if the entire universe was composed of a solid chunk of molecularly uniform glass (sio2, not important i don't think). this would change the value of c in the equation c=fλ. c would then be equal to 120,000 km/s. my first question is, how would this affect frequency and wavelength in such a universe? would the spectrum in that universe be shorter, or confined to one end of our spectrum?

my second question is this: would it be possible to construct a material such that as an EM wave traveled through it, it would slow down to some value, then slowly speed back up? because if indeed you could do that, then c=fλ would stop making sense (at least to me). that would allow the relationship between frequency and wavelength to fluctuate allowing for example, 10^22 Hz frequency with a wavelength of a meter. what don't i understand?

since i don't know a whole lot about physics, i started to let my mind wander (but i was really just learning) and began wildly speculating which is a lot of fun. i'll tell you what i was thinking, and i'd appreciate it if someone could direct me to a topic that explains my wild, erroneous conclusion: on the high-energy side of the spectrum, frequency is increasing as wavelength decreases. if you continued to lower the wavelength down beyond the diameter of a proton (measured at 1.6 fm), it's possible for the frequency to be so high and the wavelength be so low, that it escapes through the long-sought-after *third* right angle (perpendicular to a 3-D coordinate axis, also violating conservation of energy principle, possibly black-hole related?). i understand this topic is highly time-dependent, since, for example, frequency can only infinitely approach, but never reach, f->∞. I've thought an inordinate amount about time today.

thank you for reading. i want to be prepared with better questions to ask tomorrow.

 

[Khashishi]

Light travels at about 66% speed in glass, not 40%. But that's just a minor detail. Inside a medium with $n \neq 1$, it isn't true that $c=f\lambda$. Rather, you should use $\frac{c}{n}=f\lambda$.

$c$ is always the speed of light in vacuum. If the universe were flooded with some other medium like glass, then light would travel at the speed $c/n$. Ok, maybe you are thinking, what if what we think is vacuum isn't really vacuum, but actually a medium which slows down light?. In that case, it should be possible to travel faster than what we think is the speed of light. There have been a lot of experimental confirmations of special relativity, which indicate that this is not the case.

Sure, it's possible to construct a material with a varying index of refraction. Light waves passing through such a medium will be refracted inside the material. The frequency won't change, but the wavelength changes as $\lambda = \frac{\lambda_0}{n}$ where $\lambda_0$ is the vacuum wavelength.
Check out the graded index fibers in http://www.fiberoptics4sale.com/Merchant2/multimode-fiber.php

Fourth paragraph sounds like utter BS. Where did you come across such an idea?

 

[xlovenuggetx]

Light travels at about 66% speed in glass, not 40%. But that's just a minor detail. Inside a medium with $n \neq 1$, it isn't true that $c=f\lambda$. Rather, you should use $\frac{c}{n}=f\lambda$.

$c$ is always the speed of light in vacuum. If the universe were flooded with some other medium like glass, then light would travel at the speed $c/n$. Ok, maybe you are thinking, what if what we think is vacuum isn't really vacuum, but actually a medium which slows down light?. In that case, it should be possible to travel faster than what we think is the speed of light. There have been a lot of experimental confirmations of special relativity, which indicate that this is not the case.

Sure, it's possible to construct a material with a varying index of refraction. Light waves passing through such a medium will be refracted inside the material. The frequency won't change, but the wavelength changes as $\lambda = \frac{\lambda_0}{n}$ where $\lambda_0$ is the vacuum wavelength.
Check out the graded index fibers in http://www.fiberoptics4sale.com/Merchant2/multimode-fiber.php

Fourth paragraph sounds like utter BS. Where did you come across such an idea?

Khashishi, thanks for responding and for being frank. i would have been better off wording the last paragraph less... nonsensically. i didn't get the idea from anywhere, i just remember watching sagan's flatland and the shadows of hypercubes, etc. and should have worded my question/speculation differently: when the wavelength gets infinitesimally small, the frequency must increase. with the increase in frequency comes higher energy. if somehow you were able to shorten the wavelength infinitely, a type of singularity event (should?) occur. i can only imagine this much energy being confined to such a small space when a black hole forms, or two black holes collide, etc. -- so instead of being clear, i jumped ahead to attempt to wildly speculate about the cause of the singularity occurrence (black holes have zero volume and thus infinite density). sorry for being so broad.

i do have a follow-up question: if you continue moving along the high-energy side of the EM spectrum, what happens beyond 10^22 Hz (which would correspond to picometer wavelengths)? is it possible to have a wavelength smaller than, say, a quark? it seems like you should approach some impossible limit or barrier, and i don't know whether it has to do more with space limitation (i.e. the Planck length) or time limitation (what's the maximum value of frequency possible?). thanks.

 

[xlovenuggetx]

shortest wavelength / highest frequency possible?

>this thread was moved from general physics and edited for clarification.

<< Moderator Note -- 2 threads merged >>

i was watching sixty symbols today, and i learned about refractive indexes. light travels at 60% of its normal speed c when traveling through glass. after i watched that video i attended my summer class (engineering physics II, covering circuitry, optics and EM waves) and i started asking about what happens beyond what is normally shown in textbooks on the high-energy portion of the EM spectrum. my professor is Da-Zhu (levitated mouse using magnetic fields) and he said that the spectrum continues beyond 10^22 Hz and less than pm λ. he said it gets technical though. so, after some thinking (mind you I'm a chemistry major, whatever that means), i then asked if it was possible to increase the frequency while holding λ constant. he directed me to this equation: fλ=c . he said that would break the rules since the value of c is constant and f and λ are proportional.

now, consider what would happen if the entire universe was composed of a solid chunk of molecularly uniform glass (sio2, not important i don't think). this would change the value of c in the equation c=fλ. c would then be equal to 180,000 km/s. my first question is, how would this affect frequency and wavelength in such a universe? would the spectrum in that universe be shorter, or confined to one end of our spectrum?

second question: if you continue moving along the high-energy side of the EM spectrum, what happens beyond 10^22 Hz (which would correspond to picometer wavelengths)? is it possible to have a wavelength smaller than, say, a quark? it seems like you should approach some impossible limit or barrier (singularity), and i don't know whether it has to do more with space limitation (i.e. the Planck length) or time limitation (what's the maximum value of frequency possible?) or neither.

thanks. and sorry for posting in the wrong board.

 

[Khashishi]

There is no known limit to frequency and wavelength.

 

[king vitamin]

Classically, the frequency of light can be increased without bound. However, if we include quantum effects, the classical theory breaks down for very short wavelengths. Specifically, once hf = 2mc^2 where m is the mass of an electron, there is the possibility for electron-positron pairs to be created out of the vacuum. If I'm still capable of basic arithmetic, I think this corresponds to a frequency of about 10^21 Hz.

Note that this energy is far, far below the Planck scale, so I wouldn't worry about black holes.

 

[omega_minus]

Xlovenuggetx you might be interested in the fast light research being done at Duke University. A google search on "fast light" will bring it up. They're making materials that exhibit negative values of group velocity meaning light travels backward in them. They are able to send a pulse of light toward the material and it exits the other side apparently before it enters the material from the front. It's a bit too much for me to try to explain here but you can check it out on the web.

 

[Drakkith]

Specifically, once hf = 2mc^2 where m is the mass of an electron, there is the possibility for electron-positron pairs to be created out of the vacuum.

Not true. A photon cannot conserve momentum and energy simultaneously if it does not have another particle to interact with when it decays.

 

[king vitamin]

Not true. A photon cannot conserve momentum and energy simultaneously if it does not have another particle to interact with when it decays.

I was making no assumptions on photon number. In accordance with how the question was phrased, I was picturing light at a definite frequency, such as in a laser. Such sources should result (ideally) in a coherent state. Such a state should have overlap with multiparticle electron-positron states if energetic enough.