Special Relativity. Lifetime.

[John 6IX Breezy]

Nah, thanks to quantum theory, there is no fundamental difference between light and other particles, it's applicable universally. The frequency and time for a cycle are just the reciprocal of each other: 5 Hz means 1/5th of a second etc.

Hmm then again, perhaps frequency means different things depending on what it's describing. 5 Hz in neurons means they've fired 5 action potentials in the span of a second, but it does not mean each action potential lasts 1/5th of a second. To increase the frequency the time between cycles decreases, but not how long each cycle lasts.

If sawtooth and square waves decompose into sine waves then I retract what I said about them.

[Alex K]

Nah, thanks to quantum theory, there is no fundamental difference between light and other particles, it's applicable universally. The frequency and time for a cycle are just the reciprocal of each other: 5 Hz means 1/5th of a second etc.

Hmm then again, perhaps frequency means different things depending on what it's describing. 5 Hz in neurons means they've fired 5 action potentials in the span of a second, but it does not mean each action potential lasts 1/5th of a second. To increase the frequency the time between firing decreases, but not how long each firing lasts.

Exactly, the frequency of 5 Hz would refer to the 5 times repetition of the entire cycle, not the length of any feature within this 0.2 second cycle. If you'd fourier decompose such a time dependent potential, what you'd find is a fundamental frequency of 5 Hz which takes care of the overall repetition ebery 1/5th of a second, and higher harmonics determining the shape of the potential. If the firing last much less than the 0.2 seconds of the overall cycle repetition, that just means that there are  lot of multiples of 5 Hz present in the spectrum shaping the signal.

Look:
your example would be the first picture, with f=5 Hz but relatively short pulses. Note how it therefore has some stronger and more higher harmonics at 10 Hz, 15 Hz etc. than the regular square wave in the second picture. The cosine wave has no higher components at all.

[John 6IX Breezy]

Exactly, the frequency of 5 Hz would refer to the 5 times repetition of the entire cycle, not the length of any feature within this 0.2 second cycle. If you'd fourier decompose such a time dependent potential, what you'd find is a fundamental frequency of 5 Hz which takes care of the overall repetition ebery 1/5th of a second, and higher harmonics determining the shape of the potential. If the firing last much less than the 0.2 seconds of the overall cycle repetition, that just means that there are  lot of multiples of 5 Hz present in the spectrum shaping the signal.

Look:
your example would be the first picture, with f=5 Hz but relatively short pulses. Note how it therefore has some stronger and more higher harmonics at 10 Hz, 15 Hz etc. than the regular square wave in the second picture. The cosine wave has no higher components at all.

The idea of action potentials having harmonics is certainly new to me. I'm familiar with harmonics in music because I produce my own as well as edit audio. You can audibly hear individual harmonics, which leads me to believe you can physically identify harmonics in action potentials if they exist. I just don't know what portion of the action potential would correspond to a harmonic.

(Coincidentally, it was because synthesizers often offer saw waves and square waves in conjunction with sine waves as the basis of what the instrument does, that I thought these waveforms were perhaps unique and irreducible from one another)

[Paleophyte]

They both appear to measure the amount of something over a specified time. Thus why the adjectives fast and slow can be used to describe both. My question, more properly, asks if both types of fastness have a function in SR.

Perhaps I should have initially asked if Hz functions as a type of "fastness" instead of a type of velocity; either way the vocabulary seems limited to properly state the question.

Language commonly uses a number of words to describe similar concepts that, when you get down to nuts and bolts, are fundamentally different. "Fast" can be used to describe how fast your heart is beating, how fast your car is driving, whether your boat is moored fast to the dock, and if you have broken your fast. Clearly we're talking about a few different concepts there.

Frequency describes the number of occurrences of an event per unit time. Strictly speaking, those should be nice periodic events that have regular, predictable waveforms or something similar. If you use frequency to describe non-periodic events like shots on net or neuron firings then you can find yourself in a messy situation where an event may not actually occur during a given period and may occur multiple times in another period.

Velocity describes the distance that you can travel in a specific direction over a specified amount of time. It can appear similar to frequency because both are rate measurements. Frequency measures the rate of occurrence while velocity measures the rate of travel. Occurrences don't require motion, so you can measure the frequency at which a quarts crystal pulses without that crystal ever acquiring a velocity. There are other rate measurements including water flow and power.

Special Relativity is very specific about what it does and does not apply to and it requires velocity. Not just speed, but velocity (speed plus direction). If you try and use frequency the units don't cancel and you simply can't calculate your Lorentz transformations. Its like asking "A train leaves Philadelphia travelling at 40 km/s and a clock is ticking at 17 Hz in Boston. If it's a 600 km long trip, where on the tracks do they meet?" The answer is that if it's on the tracks the train runs over the clock in Boston station 15 hours later because it have a velocity of sweet bugger all regardless of its frequency.

The term frequency, seems to me, applicable to very different types of phenomenon. The frequency of a neuron is similar to the pulsation of a heart; they are individual entities with a limit to how fast pulsations can be produced. But the frequency of light or sound seems different, it appears continuous or connected; it makes more sense to talk about "how many" as opposed to "how fast" when it comes to these waves. (Assuming an increase in wave frequency corresponds to more waves fitting into the same space, not waves traveling faster through that space).

So I think the lack of an upper limit, or its relatedness to energy, depends on what frequency is in reference to.

Both measure an occurrence per unit time. In the case of the heartbeat it's beats per minute. In the case of light it's the number of waves that pass per second. Both translate to Hertz pretty nicely.

There actually is an upper limit to frequency but it's enormous and tied into Planck time, which gets messy.

I thought frequency was more about how many cycles in a given time frame, not how much time to complete a cycle. Perhaps the difference is arbitrary however.

You're looking at the complimentary and inverse concepts of frequency and period here. Frequency is occurrences per unit time, whereas period is units of time per occurrence. 1/f = T and 1/T = f where f is the frequency and T is the period. Period is measured simply in units of time (e.g. seconds) so frequency is measured in the inverse (per second).

So if you try and plug frequency into a Lorenz transformation to try and determine your time dilation you get:

1/sqrt(1-((((2,450,000,000 /s)^2/(299,792,458 m/s)^2)))) This is the operating frequency of my CPU.
1/sqrt(1-66.8 /m^2) 66.8 what per meter squared? These units make no sense! And how do I subtract that from 1?!? And then take the square root?!?!?
1/Baby Jesus cries because your units don't cancel and you can't math like that.

[John 6IX Breezy]

Special Relativity is very specific about what it does and does not apply to and it requires velocity. Not just speed, but velocity (speed plus direction). If you try and use frequency the units don't cancel and you simply can't calculate your Lorentz transformations. Its like asking "A train leaves Philadelphia travelling at 40 km/s and a clock is ticking at 17 Hz in Boston. If it's a 600 km long trip, where on the tracks do they meet?" The answer is that if it's on the tracks the train runs over the clock in Boston station 15 hours later because it have a velocity of sweet bugger all regardless of its frequency.

When I began reading your train/clock question I thought you were going to make a point on relativity. Many examples of time dilation for the non-specialist begin with some kind of moving object (train) and a clock. Of course, I understood you were just demonstrating the clock's lack of velocity. However, I found it interesting you described the clock as ticking at 17 Hz. I don't necessarily know what that means, but a constant rate of any kind be it the ticking of a clock or firing of a neuron, can be used to keep time. Isn't this rate or fequency what gets affected by velocity in relativity? In other words, there still seems to be something that ties frequency and velocity together, if not categorically, then at least causally, within relativity.

(I should mention that my views on time are influenced by psychology; as such I view time as an abstraction derived from the perception of change, not an actual space in which change occurs. I'm ignorant of how physicists view or define time)

[Alex K]

@Breezy

The relation is precisely this: if f is the frequency in the rest frame of the system, then when it has relative velocity v to you, you observe the frequency

f(moving) = f * sqrt(1-v^2/c^2)

This does not include doppler effects, just the way time runs.

[John 6IX Breezy]

@Breezy

The relation is precisely this: if f is the frequency in the rest frame of the system, then when it has relative velocity v to you, you observe the frequency  

f(moving) = f * sqrt(1-v^2/c^2)

This does not include doppler effects, just the way time runs.

Assuming I understood, which is questionable, you are just treating frequency as if it were any other moving object, correct? I don't think thats the type of relationship I'm asking about.

All three variables, f, v, and c, have time embedded in them as if time were a separate entity. In fact, time appears to be an ingredient in their composition, as opposed to an abstraction derived from them. I don't exactly know what I'm asking, or how to phrase it. Its just that coming from the cognitive sciences, relativity seems to me as if it were the psychology of physics, rather than physics itself. Terms such as observer, frames of reference, perception are psychological terms which are only possible if there is a subject with a mind that can experience movement, velocity, etc.

If that's the case, then what happens to these equations when time is treated as a complete psychological abstraction derived from the perception of motion and change? Because it seems to me, and I could be wrong, that physicists treat time as if it were an actual entity in which things occur, which is the reverse of how psychologists view it (I don't know much about the composition of spacetime, however, or if its different from time by itself).

Both fields tend to look down on each other. Physicists view psychology as barely a science, and psychologists view physics as low on the totem pole of complexity. So I doubt theres been much crosstalk between the two fields, and I have often wondered what happens if they collaborated more.

[Alex K]

@Breezy,
Frequency is tied to some physical process occuring at this rate. The base time is determined using some reference process such as caesium oscillstions.

All these things come with precise prescriptions how they can be observed. These aren't vague philosophical statements, you can put an atomic clock on a fast plane and compare the counters with resting clocks, and you'll see exactly the discrepancy between them as given by the formula above (plus some gravity effects) with as many digit precision as the equipment can manage. This so-called relativistic time dilation affects every physical system you can think of the same, and with it the frequencies at which any process occurs.

[Paleophyte]

When I began reading your train/clock question I thought you were going to make a point on relativity. Many examples of time dilation for the non-specialist begin with some kind of moving object (train) and a clock. Of course, I understood you were just demonstrating the clock's lack of velocity. However, I found it interesting you described the clock as ticking at 17 Hz. I don't necessarily know what that means, but a constant rate of any kind be it the ticking of a clock or firing of a neuron, can be used to keep time. Isn't this rate or fequency what gets affected by velocity in relativity? In other words, there still seems to be something that ties frequency and velocity together, if not categorically, then at least causally, within relativity.

Yes, frequency is affected by SR as Alex has already mentioned. Everything is affected including your mass and colour.

Time pops up a lot in any physics discussion because it's one of the basic dimensions in which we exist. It's exceptionally difficult to describe our universe without bringing time into it, so yes, it pops up a lot in physics.

[John 6IX Breezy]

Time pops up a lot in any physics discussion because it's one of the basic dimensions in which we exist. It's exceptionally difficult to describe our universe without bringing time into it, so yes, it pops up a lot in physics.

I question whether time exists independent of a mind, but I suppose I don't know enough about the physicists view to argue against it at the moment.