daerengD Time Paradigm by Brian Beverly

Eckard,

Either way I am correct because if the universe is deranged then I would be deranged too. If the universe does not involve derangements then that makes me a crackpot which means I am still deranged. Both could be true! You bring up a good point about "all" and infinities which requires one final proof by induction. I think I will leave the inductive proofs for the readers.

I agree with your point because physicists are in love with differential equations yet none of them seem to care about real or complex analysis and they completely ignore combinatorics.

Newton knew a lot of geometry and from this geometric approach he deduced calculus. Calculus allowed Newton to understand physics using the infinitesimal time, dt. Einstein used a geometric approach for time he created space-time and the gamma factor. Quantum physics at its heart is probability theory. I am willing to bet the final theory will be about combinatorics.

I believe the universe is discrete and you believe the universe is continuous. I think we should agree to disagree :)

Brian,

You got me wrong several times.

I do not believe anything. I found out that discrete models of reality and continuous ones can be shown to be mathematically equivalent via cosine transform. It is a matter of chosen point of view which one you prefer.

While I do not consider differential equations the primary relations, I nonetheless love differential equations too.

My point includes that physical quantities do not need a sign, and consequently transformation into a complex domain might be indispensable for the sake of feasible calculation but not for general reasons.

Huge electric circuits with lumped resistors, capacitors and inductances can only be calculated with complex calculus instead of differential equations.

Newton's (1642-1727) geometry has perhaps its roots mainly via Descartes (1596-1650) in ancient geometry. Descartes hesitated to introduce coordinates between -oo and +oo.

Incidentally, matrices with Hermitian symmetry are equivalent to complex representation.

Infinite quantities means: Abstract models without limits of size. There is no infinite value of a quantity. Infinity is a property, not a quantum.

Eckard

Eckard,

Sorry for the miscommunication. I thought by infinity you were asking if my reasoning held for n = 0,1,2,....infinity which it does. How much of an approximation is the continuous cosine transform relative to the discrete model?

Brian,

Someone who may or may not approve our post was perhaps unhappy when I wrote:

My point is: One has to use [complex calculus] not blindly but correctly. Heisenberg and Schroedinger frankly uttered that they did not always understood what they did.

I pointed to some cases elsewhere, and I could give further examples.

Continuous cosine transform does not specify a restricted n.

Therefore, discrete cosine transform is an approximation to the continuous one, not the other way round.

Eckard

Eckard,

Thank you for the clarification. I see some strengths in your idea for the cosine transform. What ways are you considering to explain the wavefunction collapse and probabilistic coefficients? I know the uncertainty principle comes directly from Fourier analysis. This makes sense because if the momentum is related to wavelength and measuring its position collapses the wavefunction, then it is impossible to know the values of both observables with certainty at the same time.

Brian,

When I was a child, I read that there are quanta of action.

Meanwhile I understand h_bar as a natural constant, a coefficient of proportionality between distance and momentum. Accordingly I do not see any difference in principle between uncertainties for the orthogonal pair distance/momentum and for the likewise orthogonal pair time/frequency. An exact value of frequency precludes exactness of the belonging value of timespan, no matter whether or not one tries to measure the two values.

Heisenberg speculated: "I believe that the existence of the classical path can be formulated as follows: The path comes into existence only if we observe it."

While it would be unfair suspecting Heisenberg stupid just because he failed his exam and he later on failed to correctly calculate the critical mass, we should consider this seemingly logical conclusion a challenge to clearly distinguish between reality and theory. Uncertainty is something mathematical and relates to the tacit switch from continuous to discrete or vice versa. After Cantor managed to create a General-Gouvernement of discrete numbers, after Hilbert, Zermelo, Fraenkel and others tried to save this paradise, nobody in Berlin and Goettingen was ready to abandon this putative treasure just for the sake of a reasonable while godless physics.

Let me anticipate a frequent error: Cosine transform cannot provide a spectrum for sine transform. Doesn't this matter?

No. It is true that one cannot decide how large the angle phi is for a cos(phi) that does not noticeable differs from one. Bicyclist know the dead point, however it does not prevent healthy people from using a bicycle. At first, sinusoidal functions are always approximations to reality in the sense that no oscillation in reality reaches to infinity. Secondly, if we decide to refer to the natural zero of elapsed time between past and future, the sine function would only apply for an infinitely small and therefore irrelevant timespan.

Eckard

Sorry, when I wrote sine transform, I meant sine function.

Happy birthday, Brian!

Cristi

Eckard,

I have been thinking about the cosine function and its only attractive fixed point. I find it interesting that this fixed point is where the cosine function intersects the y = x line. The y = x line is also defined as the speed of light and creates the future and past light cones in a minkowski space.

This makes me wonder if the speed of light looks like a constant because we are observing the attractive cosine fixed point after a large number of iterations.

The cosine function is also identical to f(x) = (A)exp(-x^2) on the interval [-1, 1]. Maybe the speed of light is a direct consequence of the quantum mechanical wavefunction's attractive fixed point.

If this were true then quantum teleportation would not be spooky, because it would be a consequence of the same mathematics which make the speed of light a constant.

Brian,

I am claiming that effectively any one-sided function f(x) can be expanded into an infinite sum of cosine functions rather than sine and cosine functions or sine functions alone.

Since the point f(0) is always of interest and sin(0)=0, one would need a sum of actually infinitely many zeros in order to get f(0)=|=0. This would not work.

I do not understand why you refer to the point cos(x)= x approximately at 0.739.

What about cos(x) = 1 - x^2/2! x^4/4! - x^6/6! ... it looks indeed similar to exp(-x^2) = 1 - x^4/1! x^4/2! - x^6/3! ... Let's check: cos(0.5)=0.87758

while exp(-0.25)=0.7788

The speed of light was perhaps first calculated by Maxwell with reference to Weber and Kohlrausch as the ratio of electrostatic by electromagnetic units. Notice, in the cgs system by Gauss my_zero was equal to one. In the SI, my_zero equals to 4 pi 10^-7 Vs/Am, and c = 1/sqrt(my_zero eps_sero). Impedance of vacuum Z = sqrt(my_zero/eps_sero).

Admittedly, I did not yet understand your ideas. I am just an old electrical engineer.

Regards,

Eckard