Elsewhere there are answers to a similar qustion about square waves which I am mostly going to ignore. The type of impulse I am interested in ideally travels at the speed of light, is very narrow in the time domain (ideally zero width) and carries (holds?) an amount of energy (ideally one Joule). The replies for square waves rush to Fourier analysis and speak of the bandwidth etc. I want to approximate my impulse with a 14 keV gamma ray (photon) emitted by iron-57 when it transitions to its base state. I'm borrowing this photon from the Pound-Rebka experiment ( see for example https://en.wikipedia.org/wiki/Pound–Rebka_experiment ). The energy of the photon is about 2.243E-15 Joules and the frequency about 3E15 Hertz. In the actual Pound-Rebka experiment they used a filter with a bandwidth of ?? 1Hz or less to detect the effect of gravitational potential. As part of the experiment the gamma rays (photons) are counted. My claim is that these photons are going to behave like impulses when looked at from our nice 1Hz to (say) 2.4 Ghz 'radio' spectrum. Any tuned circuit that gets hit by one of these gamma rays is (ideally) going to absorb the entire energy of the gamma ray and 'ring' at its natural frequency - giving rise to the claim (true or false?) that the gamma ray contained or was made up of or could be decomposed into - the natural frequency response of the tuned (or untuned) circuit that detected it. Yet the Pound-Rebka experiment was pretty conclusive that the frequency of the gamma ray was 3E15 Hertz +- less than 1 Herz. So - can we transmit an impulse through free space and is it made up of simewaves? Rider - are photons (all photons) really impulses? En masse they might not behave like impulses but is that a property of the quantity not the individual.
I don't really understand the question, or the references to the Pound-Rebka experiment. Does the question boil down to "do photons exist"? As to the sine wave part, Fourier analysis tells us that any wave can be decomposed into a superposition of sine waves. Also, the term "impulse" is usually used in physics to refer to a change in momentum, or a force exerted over time. So, to me, the question "are photons impulses" doesn't make much sense. Photons have momentum, certainly, but I don't think that's what you're asking. Perhaps you mean "pulse" rather than "impulse"?
The Pound-Rebka experiment is effectively a spectrum analyser. What it shows (supports) is that the gamma rays (photons) generated are of a single frequency to better than 1 part in 10E15. Without this information I would be making an unsupported claim about the bandwidth of these gamma ray photons. Given that all the photons are of the same frequency we can't later assume any observed effects are the result of a spread in the frequency of the source. There follows an unsupported claim (which may be false) that these photons are a good approximation to an impulse ( https://en.wikipedia.org/wiki/Dirac_delta_function ) "The Dirac delta is used to model a tall narrow spike function (an impulse),". If you are happier calling my impulse a pulse then that isn't a problem as long as we both mean the same thing by it. In the absence of quantum physics a bandwidth of less than (say) 1hz would suggest a rise and fall time in the order of a second which I don't think is the case here (though of course I could be wrong). I'm not sure if it is your intention to suggest big (high energy) photons are made up of lots of smaller (low energy) photons and I'm not sure how to apply a superposition of sinewaves to a single photon - clarification please. So we have a single photon which (I claim) looks pretty much like an impulse [very short pulse] - am I wrong there? If the photon does indeed look like an impulse then where do the sinewaves come into it?
I'm not at all an expert on this, but if these gamma rays are almost monochromatic then then I should have thought their waves would be very far from being spikes indeed, due to the uncertainty principle - they should be very highly spread out in space. But as for the detection of individual photons, it is my understanding that you can't model that interaction in terms of waves, because you are collapsing the wavefunction. But I'll bow to a quantum mechanic here. Please Register or Log in to view the hidden image!
Well, keep in mind that a "sine wave" is just a mathematical tool we use to describe things. Actual EM waves in free space can only be observed when they interact with something - and often that interaction presents with a sine-wave-like magnitude of E or H fields. But the 'thing' itself is made up of photons. Well, they are both, of course.
As billvon suggests - I think I might be (accidentally) rediscovering wave particle duality. Looking at the results of a single photon double slit experiment (example https://wiki.brown.edu/confluence/display/PhysicsLabs/7A55.20 Single Photon Interference ) I'd say there is definitely something 'sinusoidal' going on before the photon is detected (apparently and possibly in reality) at a point. This 'detection at a point' of light already fits my definition of an impulse without the need to go to gamma rays where (I suspect) the sinusoidal 'thing' will still be there. I would be delighted if someone would tackle the relationship (if any) between the 'sinusoidal thing' seen for a single photon and 'electromagnetic waves' but I have to admit the OP probably wasn't a good start. Thanks to all who have taken the time to respond.
I hope Confused2 don't mind me tagging this question on his thread. On the glass of a microwave oven door there is that grid metal mesh thingy. A pop science answer to ''why are the holes in the mesh such a size?'' The pop answer is '' The holes are smaller than the microwaves, so stopping the microwaves from getting out.'' So my cute mental picture of the waves not passing through the mesh holes was because the waves amplitudes were too large to fit through the hole ( I told you it was cute). But, this picture falls apart if the waves are not really sinusoidal and just modelled as such. What is the answer ?
It's not the amplitude but the wavelength/frequency that matters. It determines the "cross-section" of the photons. Simply put, this is a statistical measure of how close a photon can get to to something before it interacts with it. The cross-section is also effected by what the photon is potentially interacting with. (for example, the cross-section for a given photon is smaller for a neutron than it is for an electron.) The cross-section for the microwaves in a microwave oven with the metal grating is roughly the size of a baseball which is much larger than the holes. Now you might be wondering why, if the cross-section is so large, the hole are as small as they are. This goes back to cross-section being a "statistical measure" and not an absolute one. It determines the odds of interaction. So even if the hole is smaller than the cross-section, it doesn't mean that a given photon won't pass through, only that the odds of it doing so have been reduced. The smaller the hole compared to the cross-section, the less the chance of any given photon of that wavelength slipping through. The holes are made small to keep this probability low enough so the the number of microwave photons avoiding the trap is very, very low and not a safety hazard.
If the photon does indeed look like an impulse then where do the sinewaves come into it?[/QUOTE] I am not a physicist or a mathematician but i think vibrating ball can define it.
