# Funics Lesson #1 - Frequency

This is an offshoot of the Crackpot Index thread. There are some misconceptions about a very simple concept in that thread: frequency.

This is probably somewhat esoteric, but I’m trying to be as plain as possible. If anyone has any questions or corrections let me know.

Frequency is the reciprocal of the period of a cyclical process.

The period is measured in seconds (the amount of time of time between one cyclical event and the next), and the frequency is one over the seconds, or s^-1, otherwise known as hertz (Hz). That’s where your computer’s ‘hertz’ rating comes from. I think our family’s first brand-new computer was 127 megahertz (it also had a 1.6 gigabyte hard drive ). Computers now operate in the realm of multiple gigahertz. My wife is the computer engineer, but the layman’s definition of this number is it tells you how many times a second your computer can turn its transistors on and off.

One of the cool things nobody really talks about in geometry class is how important the geometric functions of sine, cosine, tangent, and their inverses and reciprocals are. Yes, they’re great for finding the length of the unknown side or the unknown angle of a triangle, but that’s probably their least important application. Among their many other uses, sinusoidal functions are used to model periodic functions like waves and exponential decay. Here’s an example of some light waves:

The above waves all have about the same amplitude (vertical distance from the peak or trough is one way to measure it), but their wavelength changes (horizontal distance from peak to peak or trough to trough). The decreasing wavelengths increases the measured hertz (frequency), as can be seen in this gif:

And here’s an example of exponential decay of a spring-mass-damper system. The graph isn’t made for that animation, but it’s a good visual approximation of a graph of the vertical motion of the mass over time:

The point is all kinds of stuff can be modeled with sinusoidal functions which are ways of describing, among other things, the period and frequency of the thing to be modeled. Frequency is important and fun. Just don’t ask me to do a Fourier Transform.

All the above images came from Almighty Wikipedia.

Now for the not so good images. They’re rough and not to scale, but hey, I made them at great personal expense of time so back off.

Here’s the discussion on the misconception from the other thread. It’s about how an atomic clock works. There’s a theory out there that the speed of light is actually variable…okay, whatever. Let’s assume that’s true.

The misconception is that if there is a change in the speed of light then there is an effect on the length of the second because the length of time it takes to travel between the atoms emitting radiation and the sensor is longer. This is wrong.

I’ve created an imaginary atomic clock that ticks three times every second. Here are two identical clocks, one where the speed of light is slower than the other. Here they are starting at the same time:

At first glance, then, this seems to confirm the theory that the actual speed of the radiation changes the second. But watch what happens if we start them at different times:

You can see that the length of time between when the first signal enters the receiver and when the last enters the receiver is the exact same for both clocks. Here it is shown a different way. One receiver is put further away from the other:

So you see, the speed of the radiation doesn’t matter. Only the frequency at which the radiation is emitted matters in the definition of the second.

Now let’s change the frequency of the clocks themselves and leave the speed of the radiation constant:

You can see the varied frequency of the emission creates a time difference between the two clocks. This could be caused by a variable speed of light, but the relationship would be very complicated and it would look slightly different from this. It would be a combination of the first gif and the last gif.

So…any questions?

Yeah it assumes that emission/absorption potentials are deterministic not probabilistic. Other than that no for a high school---->college level text its quite informative well done.

Farsight’s contention is that the time/distance model is based on only time really rather than motion and so inherently prone to error.

Since time is relative it’s metric only applies in one frame of reference. All he’s saying is there is no spoon. Gravity weirdly is different yet and its metric is relativistically complicated. Take the box falling to Earth, from the inside what happens to time and is the difference semantic or real?

Try looking at the non quantum model of electron orbitals written laboriously out in maths jargon by me.

Wilson-Sommerfield quantisation rules.

Now ask yourself why we need a quantised model at all?

Have you studied General Relativity yet?

These use cosh and sinh in a matrix commonly referred to as mass/energy tensor. Hyperbolic geometry.

Farsight has a contention with the maths that is philosophical ie there is no space bend just co-ordinate distribution is effected by the scalar of mass/energy. Thus in order to measure time you have to ignore the idea of bent space and substitute it with treacle space of differential potential treacles with differing amounts of sugar in them, think more Navier -Stokes than Swartzschild.

Anthem has totally dodged the issue. The atomic clock involves a hyperfine transition which emits microwave radiation. Then you sit there counting 9,192,631,770 microwave peaks coming past you, and then you say a second has elapsed:

“Since 1967, the second has been defined to be the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom”.

For those peaks to come past you, the light has to move. If your second is different, the rate of motion is different. Saying “no, the emitted frequency is different” just doesn’t cut it, because frequency is the number of occurrences of a repeating event per unit time. And you’re counting 9,192,631,770 events to define your unit of time. So once you’ve done that, the frequency is… 9,192,631,770 Hz. It doesn’t matter where you are, or how big your second is, that’s what you say the frequency of the microwave radiation emitted by the caesium atom is.

So, Anthem. You’re going to have to try again.

Sidhe - You’re getting really hung up on quantum theory and probability. I’ve told you a couple times we’re being ideal. Honestly, I don’t see the problem with that even in real life with the atomic clock. Aren’t we ‘collapsing the wave function’ when we observe these atoms emitting at regular intervals? We already have experimental error in the clock, we don’t need any more probability functions. Unless I’m missing something. I’m not a physicist, I’m a mechanical engineer by trade.

farsight - I’m not going to draw a gif with nine billion dots just because you are unable to comprehend a model. I’m sticking with three.

The frequency is always the same for you, quite right. The receiver will always count the same number of pulses and call it a second. But someone not in your frame of reference might have counted a whole second by the time you’ve only counted a fraction of a second. That’s the point of the last gif:

The frequency associated with the second doesn’t change, but the frequency to an outside observer has changed. In both cases, the receiver thinks a second has passed. But the top receiver gets to a second well before the bottom receiver.

The top receiver counts and says 3 Hz…that’s one second.

The bottom receiver counts and says 3 Hz…that’s one second.

The top receiver looks at the bottom receiver and says, 3 Hz? Wtf are you talking about? You’re only at 2Hz! You’ve got to wait another third of a second.

The bottom receiver look at the top receiver and says, 3 Hz? Wtf are you talking about? You’re at 5 Hz! You’ve counted 140% of a second.

All that matters is the amount of time that has elapsed from when the first signal enters the receiver and the last signal enters the receiver. This is completely independent of the speed of the radiation. I’m getting tired of restating this.

Farsights right your dodging the issue if you don’t provide a model that reflects what is.

I think he’s wrong but atm it looks like you are are more wrong. You can’t just show classical models and expect them to gel with GR and SR. You have to have gone to university learnt the maths and at least try to unify gravity with QM.

Now let’s make this clear getting hung up on what is accurate is the difference between Newtonian celestial mechanics and Einstein’s Schwartzschild metrics.

No offence but just looking at a particle model is not even wrong.

Error number one the frequency is based on QM, not on emission in a particle model, to say it is means that the clocks are accurate beyond the Planck scale and we know they are not.

Whether his motional issues are right or not, you can’t duck under the wire by appealing to classical mechanics, neither can you wave away the concerns of a gravitational issue even if G is 1 and it seldom is.

I t makes no difference if the two measures are dependant or independent, we know that a three body model of SR is likely to be right but a three body model of GR is wrong and has been since the start of this issue.

There is no integral that will calculate both SR and GR in a gravitational and electromagnetic model.

I know you both think you are right that is ok, but you are both wrong to some extent.

How can I explain that field theory has no regard for quantum gravity without you understanding that classic em models are little more than true under very definite integral circumstances.

i isn’t a number as such it’s a number that has to be removed only if to make it i for real.

Sidhe. I am only talking about frequency. Not unifying gravity and quantum mechanics.

Yes, the frequency arises from interactions at the quantum level. So what?

The atomic clocks work on the principle that the frequency appears on a macro scale to be constant. I know this is not the case, but I don’t care. That’s why they have experimental error, or at least one of the reasons.

If it makes you feel better you can pretend my model is a quartz oscillator. It doesn’t matter. The different reference frame will effect any type of clock the exact same way.

In fact, forget that it’s a real clock at all. It’s an imaginary clock. Are you going to pick apart Einstein’s thought experiments using fictional clocks? Pretend it’s one of his clocks. A beam of light between two mirrors or something.

It. Does. Not. Matter.

You don’t need the math to say that. I have had the math, by the way. I threw that in about being a mechanical engineer as a way of saying that I don’t frequently practice higher level math and that it’s not applied to the realm of theory in my world very often.

OK if all you are trying to say is that Bohmian mechanics is the whole story then you are right, QM is non local but has hidden variables.

We can’t disagree on that but we can say that Bohmian mechanics is not Copenhagen at least and thus the loser.

Anthem before we proceed what level of kung fu mastery are you at if it’s at the degree level then fair enough…

I know that resort to authority or even education is bad at even that level but in science education trumps philosophy every time.

I have a bachelor’s degree in mechanical engineering. I’ve been through Calc I, II, and III, linear algebra, differential equations, mechanics, electricity and magnetism, waves, statistics, vibrations, fluid flow, thermo, statics, dynamics, materials science, chemistry, mechanics of materials…you know, the regulars.

I’m not even saying that. I don’t care about the interpretation of quantum mechanics. This is a thought experiment about the effect on a clock where there is a variable speed of light.

I could have used a grandfather clock (and would have preferred it) but farsight is completely hung up on repeating the definition of a second using an atomic clock. So I just went with that.

My above clocks are imaginary. Pretend they’re reasonably analogous to any real clock out there. Atomic, grandfather, pocket, or wrist. I don’t care. The mechanism is unimportant to the discussion.

My entire point is that the frequency standard doesn’t change, i.e three ticks is still a second, but the frequency appears to change to an outside observer. That’s it.

In his theory, the variable speed of light would result in this frequency change to an outside observer.

By the by, this frequency change also explains the time dilation in a moving, inertial reference frame. The speed of light doesn’t change, but the frequency of light can change.

Ok I agree but that doesn’t change the fact that what you are saying is not precise, and doesn’t reflect what really happens.

I’m not disagreeing with just you, but with the whole premise of frequency being determinate.

Of course we both know it isn’t if it was the integral of the gaussian function would be renormalisable under a simple mechanical system and it isn’t.

Thus my only contention is this isn’t QED it’s not.

You didn’t answer the question what level are you at?

It’s not bad to admit that like me you aren’t a professor of physics or even a post graduate.

The frequency standard is not a constant thus QM.

I wasn’t refraining form answer, we’re just talking past each other because of our post times. Check the top of my last post. It has the information you wanted. I edited it after reading the post before that after I posted it. If that makes sense.

I don’t feel bad about it, I’ll be back for my graduate work as soon as I can. Even if I didn’t I’m capable of teaching myself the basics on this.

If at any time you’re thinking of disagreeing with me, just think ‘thought experiment’ and everything will be better.

Just thinking of Bell’s inequalities leaves me weak at the knees.

Dude we’re on the same page but you’re going to have to explain at what point you unified all the forces or we are going to be fighting in the car park.

This is a philosophical issue, it’s in the right forum I suggest we take it to a proper physics from so that neutral ground will give us the best arbiters. I suggest this one.

And don’t forget the loser buys a pint. And that we can’t lose.

physicsforums.com/

Just because we’re on a philosophy board it doesn’t make everything here philosophical.

If he wants to get derided he can take his theory there himself. The theory isn’t necessarily the problem but his juvenile understanding of the most basic physics concepts is.

Well you don’t seem to understand that what he says isn’t devoid of fundamentals it’s devoid of something.

Ok let’s take it to the judge and that judge is the professors on Physicsforums.com

We can’t resolve this amongst peers but only by appealing to authorities.

I feel strong in my judgement, you feel strong, Farsight feels strong, but let’s get an adjudication from experts.

As long as we’re only talking about frequency. What do you want to ask?

Ah but we’re not are we, I’ve already said that as a model that’s ok, but it’s missing the renormalisation.

I don’t care about quantum mechanics in this thread. I’ll let you know if I start talking about photons and such.

For the last time, quantum mechanics is not a part of this discussion. I know you think it is, but get it through your thick skull that I’m pointing out an error in farsight’s logic about frequency and speed.

Go away, you’re getting annoying.

I know what you are doing, that’s because you don’t understand his point.

It’s like the difference between the planck model of atoms, The Bohr model and the Dirac model. Acoustics, electromagnetism, gravity nothing you have said fits a quantum model so you really can’t disagree that Farsight is wrong when you’re both talking about two different things.

Frequency of acoustic wave

Frequency of general wave

Frequency of a quantum system:

en.wikipedia.org/wiki/Template:Quantum_Frequency

That’s because you are wrong and you know it. Stop saying this is how it works then if it doesn’t really work like this, that’s just bad information.

Go away little boy. You’re in way over your head. As far as I’m concerned, you’re no longer a part of this thread. farsight will tell me what he thinks. You clearly have no clue and are giving him too much credit.

By the by, there is no prize for having the most posts in the month of November.

dp