/sci/ - Science & Math

>>8162952
You know. The sad thing is many textbook authors have actually said similarly retarded things.

>>8162952
I take it you're an engineer.

>>8162956
why is it retarded?
>>8162959
I could be anything

>>8162952
sorry for being dumb but i dont catch everything

So, are you meaning that by fourier analisis on reality u get a discrete number of sinusoidal waves and not inifinte, but there is an error, so that leads to heisenberg relation?

Or is it the contrary?

>>8162965
there are three "worlds".

A base universe (1) where all the particles and waves live, continuous.
A fourier domain (2) associated to that world, discrete. This causes aliasing in the sampling.
The world we experience, where the objects are inverse discrete fourier transform of the objects in (2). The aliasing in (2) leads to uncertainty in (3).

Notice that the finer the discretization in (2), the smaller the distortion, and in other words the uncertainty. Which is exactly the same as the uncertainty principle.

>>8162952
As the universe is either infinite or multiply connected [only geometries which allow flatness], the Fourier domain of spacetime is continuous.

>>8163044
>is either infinite or multiply connected
why can't it be finite?
Why does an infinite universe imply a continuous fourier domain?

>>8163072
>why can't it be finite?
...did you hit 'infinite' and just stop reading?
>Why does an infinite universe imply a continuous fourier domain?
To get a discrete Fourier domain, you must require either quantization of space [something no theory I am aware of seriously supports, including all the quantum gravitys] or open boundary conditions. An infinite universe eliminates the possibility of open boundary conditions.

>>8163095
I should correct my last answer. In the limit of an infinite universe with discrete spacetime, the Fourier domain remains continuous, but has an upper/lower bound based upon the quantization of spacetime. If space is quantized, periodic boundary conditions would not be sufficient to recover a continuous Fourier domain, but, once again, nothing supports a quantized spacetime.

>>8163095
>to get a discrete Fourier domain, you must require either quantization of space or open boundary conditions.

then what's the matter?
open boundary conditions seems acceptable. Couldn't that be the case as far as we know?

>>8163147
You can't have open boundary conditions and a macroscopically flat universe. Hence why I said that infinite or multiply connected topologies are the only ones which allow for flatness.

>>8163236
is there any reason why open boundary conditons (or no boundary at all) prevents flatness?

>>8162952
>realize the fourier domain associated to our spacetime is discrete

No. The Fourier transform of a low pass filter is sinc(x). If we model the Fourier transform of a finite universe as one that is infinite multiplied by the step function around finite volume we get a continuous FT.

>>8163245
Sorry I might not have been clear.
This is not a mathematical conclusion, this is a postulate:
the first universe (1) is analyzed through a discrete fourier space (2). Just like you can sample a continuous signal and analyze it, even if the signal itself is continuous.


the universe that we observe (3) is the inverse dft of what is in (2).
(3) is different from (1) because of aliasing.

>>8163269
Sounds to me like you have discarded math literalism better than most physicists, so kudos for that.

>>8163244
You will get odd curvatures from the Einstein field equations as a result of the boundaries. [You should also get some ridiculously obvious resonance effects in the CMB that are absent, but that is another matter.]

>>8163308
thanks for taking the time to give me all this information