(December 3, 2019 at 10:55 am)John 6IX Breezy Wrote: 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.
(December 3, 2019 at 1:54 pm)John 6IX Breezy Wrote: 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.
(December 3, 2019 at 2:18 pm)John 6IX Breezy Wrote: 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.
