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RichP714

Visualizing four dimensions

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Hard to think about projecting from 4D into 3D.  Object gets spontaneously bigger in 3D as it's rotated in 4D.

In graphics a 4x4 matrix is used for what's called a projective transformation where a 3D object is projected onto a 2D plane which is your CRT screen.   There's an implicit scaling divide by the W term in the matrix, and that's what gives perspective correction.  Without that, you would have a simple affine transformation.  The apex of the projection is supposed to be the viewer's eye.  Painting with perspective correction was not discovered until the Renaissance.  Before then, images were in flat profile.

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17 hours ago, jvandyke_texas said:

Hard to think about projecting from 4D into 3D.  Object gets spontaneously bigger in 3D as it's rotated in 4D.

In graphics a 4x4 matrix is used for what's called a projective transformation where a 3D object is projected onto a 2D plane which is your CRT screen.   There's an implicit scaling divide by the W term in the matrix, and that's what gives perspective correction.  Without that, you would have a simple affine transformation.  The apex of the projection is supposed to be the viewer's eye.  Painting with perspective correction was not discovered until the Renaissance.  Before then, images were in flat profile.

 

Yes, and the title of this video being 'a beginners guide' it doesn't go that deep.  Higher than 3 dimensional objects can appear, in certain orientations, to occupy more volume than seems logical, but that's because we as observers exist in only three dimensions.  In a way, perspective correction is normalizing for three dimensional experience.

It's a common phrase around here that (or something similar) 'in reality, it only matters what it sounds like to you'.........,well, actually, 'reality doesn't care what you think' is more appropriate.  In that context, I prefer to attempt to visualize what is, rather than what is filtered to make sense to my existence.

 

For more (and a visualization technique I haven't seen since sick bay on the enterprise) I'll post a companion piece at the outer rim:  

 

 

Edited by RichP714

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17 hours ago, Mopardamo said:

4th dimension is time.  I see 3D object all the time move in time. lol  Easy to visualize:-)

 

 

The video is talking about spacial dimensions; a condition in which there are four spacial axes that are all perpendicular to each other, and which is a bit hard to imagine to a three dimensional being.

 

You might be thinking of space-time, a construct in which there are three spacial dimensions and one temporal 'dimension'; here they've given the duration axis the name 'dimension', but it is not strictly.

 

https://www.learner.org/courses/mathilluminated/units/5/textbook/03.php

Edited by RichP714

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4 hours ago, Mopardamo said:

I didn't watch the video but I get it.  Just thinking about my sub driver pounding away in realtime 3D:-)

 

Well, a three dimensional object existing within a duration is not a four dimensional object; that's probably the part that you missed in not having watched

Edited by RichP714

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Think about how you would handle occlusion from a 4D space onto a 3D.  An object moves in front of another in 4D into our projected 3D line of sight, and in 3D the old object suddenly appears engulfed or replaced by the occluding one!

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6 minutes ago, jvandyke_texas said:

Think about how you would handle occlusion from a 4D space onto a 3D.  An object moves in front of another in 4D into our projected 3D line of sight, and in 3D the old object suddenly appears engulfed or replaced by the occluding one!

Okay, my head hurts...

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53 minutes ago, jvandyke_texas said:

Think about how you would handle occlusion from a 4D space onto a 3D.  An object moves in front of another in 4D into our projected 3D line of sight, and in 3D the old object suddenly appears engulfed or replaced by the occluding one!

 

Pretty neat eh? and in some orientations you can 'see' inside four dimensional projections onto 3D space.  Robert A. Heinline takes this idea into words in his novel "Job".  One of the characters is taken from his 3 dimensional reality temporarily, and watching the geometry changes and scale shifts so abruptly and un-intuitively gives him vertigo.

 

RAH liked to explore tesseracts, higher dimensions, gyroscopic precession, etc.

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Hmm,  this is beginning to sound like string theory.

 

I love Dr. Michio Kaku here:

 

 

Oh and, listen for an um...  Anywhere, ever;  Doesn't happen, this guy's a machine.

Edited by Turbo
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20 hours ago, jvandyke_texas said:

Maybe this is related to vacuum energy and spontaneous generation and destruction of virtual particles.  They are really entering and exiting into our dimension.

 

Like quantum tunneling and zeropoint energy?  Interesting conjecture.  afaik, quantum tunneling is the result of wave function collapse, not a higher dimension folding down into ours.  afaik, zeropoint energy is the frothy 'foam' of sub-planck length quantum fields that, by law. are allowed to exist for very short and spurious periods; kind of the 'noise floor' of space-time.

 

It's a neat idea, especially considering your other idea of 4space projections spontaneously occluding each other from certain orientations.  AFAIK, however, that would require folding one dimension onto another, which would require energy that doesn't seem to be there 

Edited by RichP714

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The way tunnelling works is there is a particle in a quantum energy well.  The sides are steep, and the particle occupies all possibles modes and energy states within the well subject to boundary constraints and normalization of all states to total energy of the particle.  Higher energy states are less occupied.  So there's this situation where arbitrarily close to the wall of the well, there are wave equation solutions where the particle can exist.  But the wave state is continuous across the boundary.  So there is a solution on the forbidden side with only the alpha or real part of the eigenvalue.  This is an exponential decay in the forbidden energy zone.  So there is a probability the particle can exist there.  Suppose the wall of the well was thin, and on the other side of the energy barrier is a low energy permissible region.  Then the particle will penetrate the barrier with some probability and be sucked onto the other side and remain there.  That is quantum tunnelling.

 

You can imagine these vacuum energy particles crossing a thin barrier between our dimension and another.  But not by much.  If there is nearby matter on our side, that makes coming over here energy prohibitive because the particles are repelled.  So there is no occluding or merging going on over here.  Just very small particles appearing and going back to the other side in a vacuum.

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17 hours ago, jvandyke_texas said:

The way tunnelling works is there is a particle in a quantum energy well.  The sides are steep, and the particle occupies all possibles modes and energy states within the well subject to boundary constraints and normalization of all states to total energy of the particle.  Higher energy states are less occupied.  So there's this situation where arbitrarily close to the wall of the well, there are wave equation solutions where the particle can exist.  But the wave state is continuous across the boundary.  So there is a solution on the forbidden side with only the alpha or real part of the eigenvalue.  This is an exponential decay in the forbidden energy zone.  So there is a probability the particle can exist there.  Suppose the wall of the well was thin, and on the other side of the energy barrier is a low energy permissible region.  Then the particle will penetrate the barrier with some probability and be sucked onto the other side and remain there.  That is quantum tunnelling.

 

You can imagine these vacuum energy particles crossing a thin barrier between our dimension and another.  But not by much.  If there is nearby matter on our side, that makes coming over here energy prohibitive because the particles are repelled.  So there is no occluding or merging going on over here.  Just very small particles appearing and going back to the other side in a vacuum.

 

That's an upcoming video I was going to post to the outer rim.  Yes, our reality has the shakes, and even solid materials are leaky down in the planck lengths.  It's my understanding that proximity to a boundary (within the wavelength of a particle) allows one to 'select' the energy states for the collapse of that wave into a particle that are beyond the boundary; I don't remember this being worked as a dimensional energy transfer though

Edited by RichP714

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It's because I'm conjecturing.  Making it up.  Usually I'm wrong because I have limited understanding.  I don't believe waves collapse into particles.  We just don't know the wave until measured.  Haven't read much about that.  I don't think anybody really knows.

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4 minutes ago, jvandyke_texas said:

It's because I'm conjecturing.  Making it up.  Usually I'm wrong because I have limited understanding.  I don't believe waves collapse into particles.  We just don't know the wave until measured.  Haven't read much about that.  I don't think anybody really knows.

 

Part of why I'm so interested in these things (apart from my attraction to weird things) is that, when I was younger, I was so busy learning the math, and the instruction of the day was more 'shut up and calculate' than a comprehensive picture, that I missed details, and some of the knowledge was unsorted.  Looking back a few decades, I can see how the QED and QCD that I was familiar with has become QFT; how some ideas have merged, and an umbrella of understanding seems to indicate a somewhat generally 'correct' heading.

 

Wave particle duality is a good example.  Nobody might really know, but things have moved closer since I've been alive

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Posted (edited)
On 2/18/2019 at 12:20 PM, jvandyke_texas said:

 I don't believe waves collapse into particles.  We just don't know the wave until measured.  Haven't read much about that.  I don't think anybody really knows.

 

Have you heard of pilot wave theory?  It seems similar to what you are saying.

 

 

Now, back in my day, they talked about the 'collapse' of a wave function into a particle, the math worked and that was that.  Now, the math hasn't changed, but the interpretation of what's happening has changed quite a bit.  e.g.  the 'collapse' of the wave function is now regarded as a sharpening of the Q (if you think about it, Pauli's exclusion and Heisenberg's uncertainty principles don't really describe particles, but rather a narrow bandwidth pulse).  THe particle is never really a particle.

 

 

 

Edited by RichP714

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Pilot waves were a deBroglie concept.  Obsolete.  I ask phD physicists, and they never have an answer.

What is the meaning of the transverse wave of light?  There's an energy density that has mass.

Light is moving forward in direction of Poynting vector but the E and B fields are transverse.  So what is their perpendicular extent,

and at what speed?  Speed of light?  Nobody knows.  It's this perpendicular extent that causes interference

between slits with only one photon.  There's a Nobel prize in there somewhere.

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Posted (edited)
27 minutes ago, jvandyke_texas said:

Pilot waves were a deBroglie concept.  Obsolete. 

 

Yes, I thought that might be what you were referring to in your disbelief that the wave function collapses; you are in good company there.

 

 

27 minutes ago, jvandyke_texas said:

It's this perpendicular extent that causes interference

between slits with only one photon.

 

Interesting; imlu the propagation time differences between the e and b fields would preclude this; do you have a reference? 

 

http://www.pas.rochester.edu/~cline/P114/chapter15.pdf

 

Edited by RichP714

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