# "Artificially" time dilated photons

If you bang on the table you create a single thump, but if you keep doing so with shorter and shorter intervals, eventually it'll start to sound like a note with a particular pitch.

Now, if I used a stationary device to emit a blue photon towards a stationary detector every 1 millisecond, and if I start to increase the interval, say emit a blue photon every 1 second, the detector wouldn't see it as redder light now would it? But wouldn't this be kind of like "time being dilated" and thus we can say the "photon" should be "redshifted" and thus appear redder? (I'm thinking of the shifting of single photon energy/frequency due to moving source time dilation in the Doppler effect.)

• I'll note that even in your acoustic example, emitting a tone at increasingly small intervals does not change the frequency of the tone. The frequency depends on the natural frequency of the thing vibrating Commented Jun 22, 2023 at 21:38
• Your thumping example involves two frequencies: that of the resonant frequency of the table and that of the thumping frequency. This can lead to what are known as beat frequencies, which IIRC are the sum and difference of the two frequencies. This can also be measured in the EM spectrum when you have two superimposed or overlapping waves, but I don't think you get this effect when you emit single photons. In fact, I think it is the absence of any waves when the emitter is off that precludes the formation of beat frequencies. Commented Jun 23, 2023 at 1:08

The electromagnetic field in your example has several different timescales going on: $$p_1$$ - The period of the photon wavepackets ($$1/f$$ for $$f$$ the frequency of photons corresponding to blue light). This determines the colour of the photon.

$$p_2$$ - The time-length of the individual wavepackets. This depends on the process used to generate the photons. In the diagram (which I stole and adapted from RC_23's answer) this is the length of each pulse. Where as (1) refers to the time-length of the individual wiggles inside the pulses. While $$p_1$$ determined the average colour of the photon $$p_2$$ determines the spread of colours. So if you took that traditional glass prism (Dark side of the moon), and put this light into it $$p_1$$ sets the angle in the middle of the light beam coming out, with $$p_2$$ deciding how wide or narrow that beam is.

$$p_3$$ - The time-length between the middle of one wavepackets and the middle of the next wavepacket.

Now we can rephrase the question. You are asking whether $$p_1$$ changes as we make $$p_3$$ smaller and smaller. The answer is not really.

Their are some important rules connecting these timescales. First, you have said your device emits a blue photon every $$p_3$$ seconds. We will assume its a single-photon source (1 photon every time) clocked to fire like a machine gun at that rate. If the photons overlap then we sometimes have 2 photons arriving at the same time (in the overlap), and its not single photon source any more, but more of a beam. When its a beam the whole concept of $$p_3$$ doesn't really make much sense any more and so the question doesn't work. So we will assume we have the spacing between the photons is bigger than the photon packets themselves: $$p_3 > p_2$$.

Now, looking at the picture it is also clear that $$p_2 > p_1$$. The pulse can't have wiggles inside it that are bigger than the pulse itself.

So $$p_3 > p_1$$, meaning if you want to fire photons one-at-a-time there is a closest distance you can put them together, which is determined by their colour. (If you are happy to have them overlap, like in a laser, then no-such restriction applies, and you can fit as many as you like. But in this case the question doesn't really make sense any more.)

This is a great question, and it shows you are struggling under the false picture of what a photon is. Pop culture science creates this bad picture.

In brief, a the frequency of light is not the interval between two photon detections. Each individual photon is a wave packet with an innate frequency.

If you want a picture in your head of photons, it's better to envision something like this

(source: https://youtu.be/rYLzxcU6ROM)

Also here's a good overview with visuals:

https://youtu.be/Q2OlsMblugo

• Thanks for the visual. I agree each photon is described as a little packet. I guess I'm alluding to the shift in doppler effect, where the derivation uses the fact as the source is moving time is dilated, and each individual photo is shifted to lower energy (if source is moving away). Why doesn't that occur here? Commented Jun 22, 2023 at 18:09
• @Cosmo You said the source and receiver were stationary in your question. Why would you expect a Doppler effect?
– HTNW
Commented Jun 22, 2023 at 20:32

Blue light is about 450 nm wavelength, meaning its period is $$T = \frac{\lambda}{c} \approx 7fs$$.

So you can't make a "blue light photon" in 1 ms, the shortest interval you can make one in is about 7 fs. Thus you could make blue light at any interval up until 7 fs, then any less time than that and you'll have to make a higher frequency of light.

• Check your magnitudes. $(450\,\mathrm{nm})/c\approx1.5\,\mathrm{fs},$ where a femtosecond (fs) is a trillion ($10^{12}$) times shorter than a millisecond.
– HTNW
Commented Jun 22, 2023 at 5:28
• @HTNW thanks, multiplied instead of divided =X Commented Jun 22, 2023 at 5:33