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Just curious if the possibility exists (not necessarily spontaneously) for a photon with a wavelength greater than the distance component of c to be emitted, and would this inherently violate the scalar c?

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In addition to the answers you've been given, keep in mind that a speed does not have distance and time "components." It's just a speed. Given any time it allows you to find a distance, and vice versa, but just because the speed is special doesn't make any particular distance or time special. –  David Z Feb 8 '12 at 18:01
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The concept of a wavelength and frequency can be operationally defined only for classical electromagnetic waves, they cannot be defined for photons. –  Revo Feb 8 '12 at 19:12
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That's the number of meters light travels in one second. The length of "one second" was arbitrarily decided by humans, so passing that arbitrary boundary (causing the frequency to be <1Hz) shouldn't be anything special. –  BlueRaja - Danny Pflughoeft Feb 8 '12 at 20:57
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3 Answers

up vote 5 down vote accepted

$$c=\nu\lambda$$ The waves will still travel at $c$. Changing $\lambda$ changes $\nu$, not $c$.

If, in SI units, $c<\lambda$, then $\nu<1 \text{ Hz}$. These can exist, though we don't come across them often. Ultra-redshifted light coming from sources near a black hole have such frequencies (A source just entering the event horizon gets redshifted all the way to $\nu=0,\lambda=\infty$).

Update: As leftaroundabout pointed out, such low frequency waves are possible when dealing with the transmission of electromagnetic fields. So shaking a charged balloon or any small current can give such photons.

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Actually, we come across them all the time; like when you shake a statically charged balloon, or when a lighning strikes. It's just not very useful to treat such kind of EMF as photons. –  leftaroundabout Feb 8 '12 at 16:53
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The expression $c<\lambda$ is meaningless since $c$ and $\lambda$ have different units. –  Jan Feb 8 '12 at 20:39
    
Ive specified SI units to avoid exactly this discrepancy. The OPs question demands it anyways.. –  Manishearth Feb 9 '12 at 0:14
    
Even when SI units are specified, strictly speaking one cannot compare. I'm implying comparison of magnitudes. –  Manishearth Feb 9 '12 at 0:56
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See http://en.wikipedia.org/wiki/Ultra_low_frequency

EM frequencies below 1Hz, and therefore with a wavelength longer than c meters can be observed in nature. This does not violate relativity since those waves still propagate with velocity c (in vacuum).

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Ah, ok. I get it. Regardless of the frequency or wavelength(cycle?) the entire quantum of EM will move at c. So even if the wavelength was greater than the distance component of c, the speed the quantum propagates at is still just c. I was confused. –  DestressedData Feb 8 '12 at 16:51
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@DestressedData: There would have to be something magical about 1 second for the wavelength you note to be special, but a second is just a convenient time scale for humans---not something that the universe gives special meaning to. –  dmckee Feb 8 '12 at 17:10
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@dmckee: That seems like an answer to me! –  Jefromi Feb 8 '12 at 17:35
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It's probably best not to think of wavelength as anything to do with the size of the photon but more as a convenient way to think about frequency.

Imagine a police car with a flashing light going at constant speed. If it's doing 36kph and the light flashes 1/second then the flash will appear every 10m along the road - you could think of this as a 10m wavelength. But really it's just a way of describing the speed and frequency.

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Thank you, that helps me understand wavelength a little better. –  DestressedData Feb 8 '12 at 16:51
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