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Small to Large? [Split from What determined the inital state of the universe?]

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44 minutes ago, studiot said:

In particular there is no such thing as a quantum curve, since a curve is continuous.
But no one knows the answer to the question is the physical universe continuous or granular (discrete) ?

1 hour ago, Mordred said:

The Langrangian in QM and QFT or even GR applies the same principle. 

A good example is in GR if you take  a curve you can find infinitisimal portions of that curve that is approximately flat. 

A curve must be continuous if you want to use calculus and all the useful and accurate predictions it can make, but why must it not be granular?

Going back to small things cause big things.   If there is a principle of bigwards, then it would suggest that quantum mechanics "causes" GR, and not vice versa.  Perhaps, one reason why they havent been reconciled is the mathematics of GR is entirely founded upon a continuous functions and continuous manifolds, and (I'm guessing here) QM isnt entirely (though i am looking up Lagrangian).   The fundamental theorem of calculus is real-valued continuous functions.  Surely it has complications if the function is discrete or made of quanta.

Perhaps that is the problem... if you take infinitesimal portions of a quantum curve deltaY/deltaX, why should it be flat?  Correct me if I'm wrong, a quantum universe suggests at infinitesimal size, you get a quanta that has a curved property.  A big curve is made of infinitesimally small curves each with a unique curve value.

If there is a principle of bigwards, it would suggest granular should explain continuity.

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A good tool is calculus of variations to understanding the Langrangian.

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Edit my above post...

A quantum curve when divided into infinitesimal portions, will deliver a single quanta where the X and Y values are in super position.  You cannot be simultaneously certain of both the X and Y values.  Therefore, it cannot be flat!

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1 hour ago, AbstractDreamer said:

A curve must be continuous if you want to use calculus and all the useful and accurate predictions it can make, but why must it not be granular?

 

 

Because continuity is destroyed at every grain boundary. The curve is only 'piecewise continuous, and one condition that such a curve fits into the math of continuous functions is that there are a finite number of discontinuities.

1 hour ago, AbstractDreamer said:

 

Going back to small things cause big things.   If there is a principle of bigwards, then it would suggest that quantum mechanics "causes" GR, and not vice versa.  Perhaps, one reason why they havent been reconciled is the mathematics of GR is entirely founded upon a continuous functions and continuous manifolds, and (I'm guessing here) QM isnt entirely (though i am looking up Lagrangian).   The fundamental theorem of calculus is real-valued continuous functions.  Surely it has complications if the function is discrete or made of quanta.

 

 

Yes SR and GR pay no respect to discrete mathematics.

But the quantum solution to a totally free (ie isolated) particle is continuous.

When we introduce the boundary conditions (usually zero at the boundary) we are looking for specific solutions that have zeros.
We may also have to match first derivatives (this is one of the things Dirac did with his relativistic equation).

1 hour ago, AbstractDreamer said:

Perhaps that is the problem... if you take infinitesimal portions of a quantum curve deltaY/deltaX, why should it be flat?  Correct me if I'm wrong, a quantum universe suggests at infinitesimal size, you get a quanta that has a curved property.  A big curve is made of infinitesimally small curves each with a unique curve value.

If there is a principle of bigwards, it would suggest granular should explain continuity.

 

It is granularity or continuity.

This last bit is a bit of Physics or Engineering hand waving to make an approximation as close as desired.

But, as any proper school of numerical maths teaches, the higher order the collocating function the more the function squiggles in between match/calibration points.

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1 hour ago, studiot said:

 

Because continuity is destroyed at every grain boundary. The curve is only 'piecewise continuous, and one condition that such a curve fits into the math of continuous functions is that there are a finite number of discontinuities.

 

Yes SR and GR pay no respect to discrete mathematics.

But the quantum solution to a totally free (ie isolated) particle is continuous.

When we introduce the boundary conditions (usually zero at the boundary) we are looking for specific solutions that have zeros.
We may also have to match first derivatives (this is one of the things Dirac did with his relativistic equation).

 

It is granularity or continuity.

This last bit is a bit of Physics or Engineering hand waving to make an approximation as close as desired.

But, as any proper school of numerical maths teaches, the higher order the collocating function the more the function squiggles in between match/calibration points.

Bingo

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Cool paper but off topic to this thread.

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6 hours ago, AbstractDreamer said:

Here's a cool paper on X-ray anisotropies found within the universe, albeit with unidentified causes.

https://arxiv.org/pdf/2004.03305.pdf

If space expansion is anisotropic, then the distance coordinate axes are not uniform at all scales.

I think the authors may have fallen foul of what I call the 'ley lines argument.'

But there is already a thread on this document. Perhaps someone can link to it, as Modred says, it is off topic here.

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Posted (edited)

dcd1744eb08d6c1e941df020d79831796aa3f773

On 5/19/2020 at 12:27 AM, studiot said:

[...]

But, as any proper school of numerical maths teaches, the higher order the collocating function the more the function squiggles in between match/calibration points.

Sorry, I think you may be making a very interesting point here. Just terminology, what do you mean by "collocating function"? By "squiggles" as synonymous of, or implying, "zeros of the function" or the derivative? And calibration points: Fixed points in your approx.?

The zeros of solutions to physical problems or their derivatives are another old interest of mine.

As to granularity vs continuity, I see an interesting possibility in the fact that an intermediate cardinality between dcd1744eb08d6c1e941df020d79831796aa3f773  cannot be reached by logic.

Edited by joigus
image rendering

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1 hour ago, joigus said:

dcd1744eb08d6c1e941df020d79831796aa3f773

Sorry, I think you may be making a very interesting point here. Just terminology, what do you mean by "collocating function"? By "squiggles" as synonymous of, or implying, "zeros of the function" or the derivative? And calibration points: Fixed points in your approx.?

The zeros of solutions to physical problems or their derivatives are another old interest of mine.

As to granularity vs continuity, I see an interesting possibility in the fact that an intermediate cardinality between dcd1744eb08d6c1e941df020d79831796aa3f773  cannot be reached by logic.

I will dig out some actual plots for you.

Meanwhile your last line didn't come out properly for me can you have another go at it please?

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1 hour ago, studiot said:

Meanwhile your last line didn't come out properly for me can you have another go at it please?

Sure. It's,

\[\aleph_{0}<\left|S\right|<2^{\aleph_{0}}=\aleph_{1}\]

The possibility of a cardinality between the discrete and the continuous. It's one of Hilbert's 23 problems.

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2 hours ago, joigus said:

The possibility of a cardinality between the discrete and the continuous. It's one of Hilbert's 23 problems.

 |S| is the cardinality of such hypothetical set sandwiched between aleph naught and aleph one.

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On 5/18/2020 at 9:24 PM, AbstractDreamer said:

Well unfortunately for me, I have tried to "truly" learn some physics previously, but I came across unscalable walls and bottomless pits.

The biggest obstacle for me was the mathematics.  I simply don't understand them.  I can follow instructions.  I can find the area bounded by two hyperbolic functions.  I can follow matrix calculus operations.  But I can't understand them.  They have no "meaning".  There are mathematical techniques and tricks that are used that I can accept are true, but I cannot logically comprehend them and cannot apply logical proof to the equations once they are added.    In addition I have questions about the legitimate use of some mathematics.  There are some assumptions that are taken for granted, or at least rarely mentioned, but these assumptions underlay ALL the conclusions that are drawn from the results the mathematics give.  Just for example, off the top of my head, integration relies on a coordinate system that is "uniform", that is the gap between integers are consistent, but what if it isnt?  That throws integration out of the window.  Any integration with respect to Time from zero to infinity, assumes that it is uniform and consistent from the beginning and  forever  What evidence do we have this is so?  Sure you can calculate the area under a curve...but only if you assume your axes are consistent and uniform.  What if the gap between 2 and 3 was larger than the gap between 1 and 2, such that 1 +2 =/= 3?  We already know space expands, that is, the axes are stretched.  Are they stretched evenly everywhere at the same time?  Do two volumes of space mutually exclusive from each other's observable universe and future universe stretch at the same rate?  How does space expansion reconcile with an isotropic universe?

The second biggest obstacle for me was the scope.  If you want to "truly" know one thing, you have to know ten other things first, the rabbit hole never ends.  I am truly awestruck by how vast the scope of physics is.  It is like running up a mountain of infinite size, and everytime you summit a local maxima, there's ten more summits behind.

The third problem was time and attention.  I don't have the time or the attention or even the ability to learn all the things I need to know to answer my own questions.

The bottom line is, I am resigned to forever never truly understanding anything, and forever asking questions like a child.

Nice post.

On 5/16/2020 at 1:43 PM, AbstractDreamer said:

(...).

The direction of time is forwards?

The direction of cause is bigwards?

 

 

On the same stance:

Inside versus Outside: a past light cone spreads always outside. The past is always far away from the observer (The galaxies are several million years in the past) and the more you get closer the more you reach present time (our Moon is only a few seconds in the past. Ultimately, the present will be reached when contacting the observer.

The direction of time is from the outside (Past) to the inside (Present)

 

Now maybe you can equate "big" with "outside", I'll have to think about it.

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On 5/25/2020 at 7:54 AM, joigus said:

dcd1744eb08d6c1e941df020d79831796aa3f773

Sorry, I think you may be making a very interesting point here. Just terminology, what do you mean by "collocating function"? By "squiggles" as synonymous of, or implying, "zeros of the function" or the derivative? And calibration points: Fixed points in your approx.?

The zeros of solutions to physical problems or their derivatives are another old interest of mine.

As to granularity vs continuity, I see an interesting possibility in the fact that an intermediate cardinality between dcd1744eb08d6c1e941df020d79831796aa3f773  cannot be reached by logic.

'Collocating' comes from co - location or co located ie in the same place or better places.

There is no reason for these places to be zeros, though they could be.

Collocating points are simple a set of points where the collocating function's values (or perhaps slopes for differential equations) exactly match (pass through) the known points either form a curve we are trying to fit or a set of individual data points.

Here are some examples which show the effect of higher order functions 'wiggling' more.

This is why when we do finite element analysis, low order approximating functions are preferred bwtween the mesh points.

 

collocate1.jpg.84755e5224a08e3b82b9bbc1876ff049.jpgcollocate2.jpg.266beb87832f60b41e7dce6b9546e533.jpg

 

collocate3.jpg.62acfdd16eb12e54fbabf1ad7e2666d5.jpg

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Aaah. Thanks. That clarifies it for me. +1

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On 5/26/2020 at 11:02 AM, michel123456 said:

On the same stance:

Inside versus Outside: a past light cone spreads always outside. The past is always far away from the observer (The galaxies are several million years in the past) and the more you get closer the more you reach present time (our Moon is only a few seconds in the past. Ultimately, the present will be reached when contacting the observer.

The direction of time is from the outside (Past) to the inside (Present)

 

Now maybe you can equate "big" with "outside", I'll have to think about it.

This almost exactly parallels the way I tend to think about the OP's initial question.

  

On 5/16/2020 at 4:24 PM, joigus said:

I think it's to do with the arrow of time. When you try to solve the wave equation in spherical coordinates, there are solutions that go inwards that must be discarded just because you know that there is an arrow of time, as the inward-going solutions can be obtained by taking the negative radius. Waves only propagate outwards; never inwards. That's very mysterious. A definite direction of time is closely related with a definite orientation inside-outside. But I'm just guessing. I think it's an interesting question.

That's because, when you try to solve the wave eq. in spherical coordinates (choice of variables only motivated by the presence of point sources,) you're faced with,

\[\varphi=\frac{1}{r}f_{\textrm{ret}}\left(t-\frac{r}{c}\right)+\frac{1}{r}f_{\textrm{adv}}\left(t+\frac{r}{c}\right)\]

In naive (unrenormalized) classical electrodynamics of point particles, you must decree the advanced solution to be zero. In the Wheeler-Feynman version of electrodynamics on the other hand, which AFAIK is consistent, you must assume an asymmetry between radial directions in that you must place a perfect absorber at spatial infinity. No matter what level of treatment, you must suppress the ingoing waves.

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