The complex frequency domain?
Hopefully that's not too complex! https://en.wikipedia.org/wiki/Frequency_domain
Hopefully that's not too complex! https://en.wikipedia.org/wiki/Frequency_domain
coulomb = 6.241509074 x 10^18 electron charges ---> SI definition
second = duration of 9192631770 cycles of caesium transition frequency ---> SI definition
ampere = coulomb / second --> derived unit
ampere = 6.241509074 x 10^18 electron charges per second
Not Fourier, Laplace! There's a nonzero real part, where s = σ + jω
Otherwise you'd only have boring sine waves, and we wouldn't want that.
Pierre-Simon would be very upset. Heaviside too.
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And, back to the thread title, we have Leonard Susskind, who believes that GR = QM.
If you think about that, it really has to be so. How could it be otherwise?
If you think about that, it really has to be so. How could it be otherwise?
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I guess you could summarise post #2090 as time and energy being fundamentally linked at some deep level in the same way space and time are linked. You cannot have one without the other.
My point is that you can't avoid time as a parameter. FREQUENCY implies time. Tell me how you explain frequency without time!
You mentioned transferring back to the TIME domain. Explain how electronic filters work without time!
I shouldn't have to explain this to a group of engineers.
You avoided the definition of a farad. The definition references time.
Even your definition of ampere references time. You can't avoid it!
I did the calculation a few months ago of the universes expansion rate converted to everyday distances and it’s something like 10^-30 (IIRC) per second per meter. Very very tiny.
I probably need to redo it but in Planck length units.
😳
I probably need to redo it but in Planck length units.
😳
I notice, Bonsai, that while two engineers are having a spat over time, you are getting off scot-free!
So, we are talking about converting (km/s)/Mpc to (m/s)/m.
The SI unit of the Hubble constant would therefore be s^-1.
I cheated and read that 67 (km/s)/Mpc is about equal to 2.2 x 10^-18 s^-1.
There can be little argument that the latter number is a lot harder to remember that 67!
More searching reveals that the 67 (km/s)/Mpc expansion rate can be converted to a percentage growth in a million years.
The conversion gives a rate of expansion of around 0.007 of a percent per million years.
Ah yes - that's more like the number I had.
The problem here is the universe doesn't work in m/s^-1 or km/s^-1 per Mpc. I think it would be good to think about it instead in some sort of natural units. But which one?
Filters can be designed entirely in the complex frequency s domain. It's not necessary to transform to the time domain.
Example of a low pass RC filter:
T(s) = (1/sC) / ( R + (1/sC) )
= 1 / ( 1 + sRC )
Filter has one pole at s = -1 / (RC)
Or if you prefer, one pole at f = 1 / (2π RC )
Wiki has a good article on natural units. But you have to choose your domain.
https://en.wikipedia.org/wiki/Natural_units
Frequency is dependent on time. Capacitance parameters are dependent on time. Every time you invoke frequency or capacitance, you are using time in your equations.
No matter what domain you use, time as a real life parameter is unavoidable.
SI defines time in terms of frequency !!
second = duration of 9192631770 cycles of caesium transition frequency ---> SI definition
So all of the derived units are based on that frequency.
Recall that time depends upon the observer, see relativity.
But the exact 9192631770 cycles of caesium does not depend on the observer,
since the natural numbers are universal, so frequency is regarded as more fundamental than time by SI.
Unfortunately, I'm out of time.
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I know about the SI definition. It is used because radioactive decay is very repeatable and precise.
Frequency is not more fundamental than time. Radioactive decay of cesium is used because of the precision it offers. The most precise and accurate clocks are cesium clocks.
I'm beginning to think you guys are pulling my leg. Are we engineers or are we Devo?
Frequency is not more fundamental than time. Radioactive decay of cesium is used because of the precision it offers. The most precise and accurate clocks are cesium clocks.
I'm beginning to think you guys are pulling my leg. Are we engineers or are we Devo?