It is clear that when it comes to solving numerical search problems like Integer Factorization, quantum computers allow us to find the solution(s) instantly.

We just setup the problem (multiply two unknown integers and get an unknown integer result, set the unknown result to a result we want) and instantly the input integers become known.

So quantum computers are infinitely more powerful than regular computers for solving numerical search problems.

But we use regular computers also for symbolic calculation.

(CAS (Computer Algebra System) software like Mathematica, Maple etc.) What more quantum computers could provide when it comes to symbolic calculation?

I think they could provide the same benefit as for numerical calculation. Meaning instantly solving symbolic search problems.

Imagine if we could just setup an equation expression string as input, then quantum computer sets the output string (with unknown value) to a general solution expression (known value), if such solution really exists/possible.

For example:

1)

Input string: "a*x^0+b*x^1=0"

String value search problem: "x=?"

Output string: "-a/b"

2)

Input string: "a*x^0+b*x^1+c*x^2=0"

String value search problem: "x=?"

Output string: "(-b+(b^2-4*a*c)^(1/2))/(2*a)"

I think using quantum computers for symbolic calculation should allow us solving many important such problems which we cannot solve with regular computers in a practical time.

I am guessing those would even include some Millenium Prize Problems like finding (all) general solution expressions for Navier-Stokes equations (and proving Riemann Hypothesis?).

I think, assuming we will have a general purpose suitable quantum computer someday, only issue is figuring out exactly how to express and solve symbolic calculation problems like the two examples above.

Let's try to solve the first problem using a quantum computer:

Assuming quantum computer symbolic calculated the solution (expression string E), how we could test it to be correct or not?

How about creating an equation that would be true only if E is a valid solution, which is the input equation itself, then:

"a*E^0+b*E^1=0" or "a+b*E=0"

Then I think the solution algorithm for the quantum computer would be:

Start with unknown values E, a, b.

Calculate a+b*E (not numerical calculation but symbolic expression calculation, using an expression tree).

Set the unknown calculation result to 0.

Unknown string E collapses to the answer: "-a/b"

And if we consider how we could do the symbolic calculation step above using a regular computer, which requires manipulating an expression tree using stack(s), then we need figure out how to create a quantum stack using a quantum computer.

(Imagine a stack that can do any number of push/pop operations instantly, to collapse into its final known state instantly.)

(If we could do quantum stacks, then we also could do quantum queues.)

(And then quantum versions of other standard programming data structures would also be possible.)

What could be the most practical way to build a large scale quantum computer?

I think currently building a quantum computer is really hard because our physical world is highly noisy at quantum scale.

Imagine using single atoms/molecules as qubits.

Imagine cooling them close to absolute zero in vacuum environment that needs to be perfectly maintained.

Could there be a better way?

What if we create a quantum computer in a different level of reality, which does not have noise?

Think about our regular digital computers.

Could we think of the bit values in memory of a working regular computer, like a different level of reality of quasiparticles, which does not have noise?

Can we create an extrinsic-semiconductor-based quantum computer chip, that creates and processes qubits as quasiparticles?

(And the quantum computer designed and operated like a Cellular Automata, similar to Wireworld?)

https://en.wikipedia.org/wiki/Quasiparticle

https://en.wikipedia.org/wiki/Electron_hole

https://en.wikipedia.org/wiki/Extrinsic_semiconductor

https://en.wikipedia.org/wiki/Cellular_automaton

https://en.wikipedia.org/wiki/Wireworld

# FB36 Blog

## Thursday, September 14, 2017

### Continuum Hypothesis is False

Continuum hypothesis states "There is no set whose cardinality is strictly between that of the integers and the real numbers".

Resolution:

Express each set in question, as a set of points on (ND) Euclidean space,

and calculate their fractal dimension to compare their cardinality =>

Set of all integers => Fractal Dimension=0

Set of all real numbers => Fractal Dimension=1

Set of all complex numbers => Fractal Dimension=2

Set of all quaternion numbers => Fractal Dimension=4

Set of all octonion numbers => Fractal Dimension=8

Set of all sedenion numbers => Fractal Dimension=16

Set of all points of a certain fractal => Fractal Dimension:

Cantor set: 0.6309

Koch curve: 1.2619

Sierpinski triangle: 1.5849

Sierpinski carpet: 1.8928

Pentaflake: 1.8617

Hexaflake: 1.7712

Hilbert curve: 2

Resolution:

Express each set in question, as a set of points on (ND) Euclidean space,

and calculate their fractal dimension to compare their cardinality =>

Set of all integers => Fractal Dimension=0

Set of all real numbers => Fractal Dimension=1

Set of all complex numbers => Fractal Dimension=2

Set of all quaternion numbers => Fractal Dimension=4

Set of all octonion numbers => Fractal Dimension=8

Set of all sedenion numbers => Fractal Dimension=16

Set of all points of a certain fractal => Fractal Dimension:

Cantor set: 0.6309

Koch curve: 1.2619

Sierpinski triangle: 1.5849

Sierpinski carpet: 1.8928

Pentaflake: 1.8617

Hexaflake: 1.7712

Hilbert curve: 2

## Tuesday, September 5, 2017

### EXPLAINING DARK ENERGY AND DARK MATTER

If Universe/Reality (U/R) is a Cellular Automata (CA) (Quantum Computer (QC)), operating at Planck Scale (PS), then how it could explain Dark Energy (DE) and Dark Matter (DM)?

Assume Quantum Physics (QP) is its first Macro Scale (MS) Emergent Property (EP), assume Relativity Physics (RP) is its second MS EP,

then Dark (Energy & Matter) Physics (DP) could be its third MS EP!

(Just like for example, Newton (Navier-Stokes) Physics (NP) is the first Macro Scale (MS) Emergent Property (EP) of some CA, like FHP and LBM.)

Is the ratio of DM to Matter (DM/M) is always (everywhere and everywhen) constant in the Universe?

Is the ratio of DE to Vacuum Energy (DE/VE) is always (everywhere and everywhen) constant in the Universe?

(If so, could they be a consequence of DP being what is said above?)

Is every EP has a finite scale range?

(Are fluid simulation CA (like FHP/LBM) have a second layer of EP at super-macro scale (where NP no longer apply)?)

Assume Quantum Physics (QP) is its first Macro Scale (MS) Emergent Property (EP), assume Relativity Physics (RP) is its second MS EP,

then Dark (Energy & Matter) Physics (DP) could be its third MS EP!

(Just like for example, Newton (Navier-Stokes) Physics (NP) is the first Macro Scale (MS) Emergent Property (EP) of some CA, like FHP and LBM.)

Is the ratio of DM to Matter (DM/M) is always (everywhere and everywhen) constant in the Universe?

Is the ratio of DE to Vacuum Energy (DE/VE) is always (everywhere and everywhen) constant in the Universe?

(If so, could they be a consequence of DP being what is said above?)

Is every EP has a finite scale range?

(Are fluid simulation CA (like FHP/LBM) have a second layer of EP at super-macro scale (where NP no longer apply)?)

## Wednesday, August 16, 2017

### NATURE OF TIME

Concept of “now” being relative implies unchanging 4D “Block Universe” (so future is predictable) and it comes from Relativity.

But QM says the opposite (future is unpredictable (only there is a certain probability for any future event)).

As we look at the Universe/reality starting at microscale (particle size) and go to macroscale, future events become more and more certain.

For example, think of how certain things you plan to do tomorrow: Can’t we say they are not perfectly certain but close?

But also think of how certain motion of Earth in its orbit tomorrow. Isn’t it much more certain (but still not perfectly certain)?

Future being unpredictable in microscale and later becoming more and more predictable at higher and higher scales also happens in Cellular Automata (which used for fluid simulation).

I think one clear implication of future becoming more and more predictable at higher and higher scales is that, time must be an emergent property.

Which in turn implies spacetime must be an emergent property.

Which in turn implies Relativity must be an emergent property.

I think I had read somewhere that equations of GR is similar to equations of some kind of (non-viscous?) fluid.

If so it would make sense considering Cellular Automata used for fluid simulation shows similar behavior to GR.

I just came across a part of an article from Scientific American September 2015 that says something very similar to what I had said about nature of time:

“Whenever people talk about a dichotomy, though, they usually aim to expose it as false. Indeed, many philosophers think it is meaningless to say whether the universe is deterministic or indeterministic. It can be either, depending on how big or complex your object of study is: particles, atoms, molecules, cells, organisms, minds, communities. “The distinction between determinism and indeterminism is a level-specific distinction,” says Christian List, a philosopher at the London School of Economics and Political Science. “If you have determinism at one particular level, it is fully compatible with indeterminism, both at higher levels and at lower levels.” The atoms in our brain can behave in a completely deterministic way while still giving us freedom of action because atoms and agency operate on different levels. Likewise, Einstein sought a deterministic subquantum level without denying that the quantum level was probabilistic.”

(All my comments above also published here:

http://scienceblogs.com/startswithabang/2017/08/13/comments-of-the-week-172-from-sodium-and-water-to-the-most-dangerous-comet-of-all/)

If the future (time) becomes more and more certain as we go from microscale to macroscale, here is a thought experiment for determining how exactly that happens:

Imagine in a vacuum chamber we dropped a single neutral Carbon atom from a certain height so many times and measured/determined how close it will hit the center of the target (circular) area with how much probability. And later we repeated the experiment with C60 molecules. And later we repeated the experiment with solid balls of 60 C60 molecules. And later we repeated the experiment with solid balls of 3600 C60 molecules. ...

I think what would happen is bigger and bigger solid balls would hit closer and closer to the center with higher and higher probabilities. And general graph (an exponential curve?) of the results would tell us how exactly future (time) becomes more and more certain.

A more advanced version of the thought experiment could be this:

Imagine we started the experiment with micro balls and with a very small drop height. And as the radius of the solid balls gets bigger and bigger, we increased the drop distance with the same size increase ratio as radius.

But QM says the opposite (future is unpredictable (only there is a certain probability for any future event)).

As we look at the Universe/reality starting at microscale (particle size) and go to macroscale, future events become more and more certain.

For example, think of how certain things you plan to do tomorrow: Can’t we say they are not perfectly certain but close?

But also think of how certain motion of Earth in its orbit tomorrow. Isn’t it much more certain (but still not perfectly certain)?

Future being unpredictable in microscale and later becoming more and more predictable at higher and higher scales also happens in Cellular Automata (which used for fluid simulation).

I think one clear implication of future becoming more and more predictable at higher and higher scales is that, time must be an emergent property.

Which in turn implies spacetime must be an emergent property.

Which in turn implies Relativity must be an emergent property.

I think I had read somewhere that equations of GR is similar to equations of some kind of (non-viscous?) fluid.

If so it would make sense considering Cellular Automata used for fluid simulation shows similar behavior to GR.

I just came across a part of an article from Scientific American September 2015 that says something very similar to what I had said about nature of time:

“Whenever people talk about a dichotomy, though, they usually aim to expose it as false. Indeed, many philosophers think it is meaningless to say whether the universe is deterministic or indeterministic. It can be either, depending on how big or complex your object of study is: particles, atoms, molecules, cells, organisms, minds, communities. “The distinction between determinism and indeterminism is a level-specific distinction,” says Christian List, a philosopher at the London School of Economics and Political Science. “If you have determinism at one particular level, it is fully compatible with indeterminism, both at higher levels and at lower levels.” The atoms in our brain can behave in a completely deterministic way while still giving us freedom of action because atoms and agency operate on different levels. Likewise, Einstein sought a deterministic subquantum level without denying that the quantum level was probabilistic.”

(All my comments above also published here:

http://scienceblogs.com/startswithabang/2017/08/13/comments-of-the-week-172-from-sodium-and-water-to-the-most-dangerous-comet-of-all/)

If the future (time) becomes more and more certain as we go from microscale to macroscale, here is a thought experiment for determining how exactly that happens:

Imagine in a vacuum chamber we dropped a single neutral Carbon atom from a certain height so many times and measured/determined how close it will hit the center of the target (circular) area with how much probability. And later we repeated the experiment with C60 molecules. And later we repeated the experiment with solid balls of 60 C60 molecules. And later we repeated the experiment with solid balls of 3600 C60 molecules. ...

I think what would happen is bigger and bigger solid balls would hit closer and closer to the center with higher and higher probabilities. And general graph (an exponential curve?) of the results would tell us how exactly future (time) becomes more and more certain.

A more advanced version of the thought experiment could be this:

Imagine we started the experiment with micro balls and with a very small drop height. And as the radius of the solid balls gets bigger and bigger, we increased the drop distance with the same size increase ratio as radius.

## Monday, August 7, 2017

### FUTURE OF PHYSICS

If we look at history of physics, is there a clear trend to allow us to guess its future?

What are the major milestones in physics history?

I think it could be said:

1) Ancient Greece (level) Physics

2) Galileo (level) Physics

3) Newton (level) Physics

4) Einstein (level) Physics

5) TOE (level) Physics(?)

I think there is indeed a clear trend if you think about it.

Each new revolution in physics brings something like an order of magnitude increase in complexity of math (calculations), not just a new theory.

So I would guess doing calculations to solve physics problems using TOE will be practically impossible using pen and paper only.

I think it will require a (quantum) computer.

(Realize that all physics problems (where answer is possible) can be solved today using non-quantum (super) computers/calculators/pen&paper.)

I think if Universe (or Reality) turns out to be a Cellular Automata design running on an ND matrix qubit (register) quantum computer (with Planck scale cells)

then it would fit into above guess about future of physics (TOE) perfectly.

What are the major milestones in physics history?

I think it could be said:

1) Ancient Greece (level) Physics

2) Galileo (level) Physics

3) Newton (level) Physics

4) Einstein (level) Physics

5) TOE (level) Physics(?)

I think there is indeed a clear trend if you think about it.

Each new revolution in physics brings something like an order of magnitude increase in complexity of math (calculations), not just a new theory.

So I would guess doing calculations to solve physics problems using TOE will be practically impossible using pen and paper only.

I think it will require a (quantum) computer.

(Realize that all physics problems (where answer is possible) can be solved today using non-quantum (super) computers/calculators/pen&paper.)

I think if Universe (or Reality) turns out to be a Cellular Automata design running on an ND matrix qubit (register) quantum computer (with Planck scale cells)

then it would fit into above guess about future of physics (TOE) perfectly.

## Monday, July 31, 2017

### Physics Of Star Trek

I saw maybe all Star Trek TV show episodes and movies.

Below I will try to provide more plausible ways of realizing similar technologies according to known laws of physics of our Universe.

I do not know if similar explanations were provided by anyone before.

Super Energy Sources:

They could be portable fusion reactors which are almost perfectly efficient.

They could provide continuous power (similar to DC) or as repeating pulses (similar to AC).

There maybe super batteries that store a dense cloud of electron gas in vacuum (or as a BEC?)?

Stun guns:

Imagine a super powerful gun creates conductive paths in air using UV pulse/continuous lasers, momentarily.

It sends a powerful electroshock to the target from those conductive paths.

(I think this tech is already developing currently.)

Teleportation:

Imagine two teleportation machines (chambers).

The sender machine creates some kind of quantum shock wave that instantly destroys the target object into gamma photons that carry the same quantum information.

That information sent to the receiver machine which has a giant BEC (that is made of same kind of atoms/molecules with same proportions as the target object?).

When the information is applied to the BEC (instantly, like a quantum shock wave), it somehow instantly quantum mechanically collapses into an exact copy of the object.

Phasers:

Instantly destroys the target object using similar quantum shock wave that used in teleportation.

(Target object instantly gets destroyed similar to teleportation, but there is no receiver for its quantum information.)

Artificial Gravity:

Imagine if we had small coils that can create high level positive/negative spacetime curvatures around them (spherical/cylindrical).

We could place a grid of those coils under floors etc to create artificial gravity.

Force Fields:

Imagine if we created spherical/cylindrical spaceships that covered by a dense grid of (+/-) gravity coils,

and also a dense grid of (superconductor) coils that can create (+/-) electric/magnetic fields.

Would not be possible to use them to create "force fields" all around the spaceships to deflect any (atom/particle/photon) kind of attack?

Cloaking Fields:

Imagine if we created spherical/cylindrical spaceships that covered by a dense grid of (+/-) gravity coils.

Would not be possible to use them to create a photon deflection field all around the spaceships?

Warp Speed:

Imagine if we created spherical/cylindrical spaceships that covered by a dense grid of (+/-) gravity coils.

Would not be possible to use them to create a warp bubble all around the spaceships to act like an Alcubierre Drive?

Sub-space Communication:

(Since we assume we have ability to manipulate the curvature of spacetime)

Imagine we have tech to create micro worm holes as twins and able to trap them indefinitely.

A communication signal enters to either one and instantly comes out of the other one.

Each time we create a new set of twin micro worm holes, we keep one in a central hub on Earth,

and the other carried by a spaceship or placed on a different planet/moon/space station.

(The same tech could also be useful to create and trap micro Black Holes, which maybe useful as compact batteries.)

Electronic Dampening Field:

Imagine EMP created like a standing wave using a grid of phased array EMP generators.

Spaceships with hulls that can withstand against almost any kind of attacks at least for a while if necessary:

How about metallic hydrogen or another solid material that we created using ultrapressure (and temperature)?

I think it is also clear that Star Trek Physics require devices with ability to create strong positive and negative spacetime curvatures for sure.

How could it work according to laws and limitations of known physics, assuming they are always must be obeyed?

According to General Relativity, spacetime bends in the presence of positive or negative mass/energy(/pressure/acceleration).

What if we destroyed a small amount of matter/antimatter in a spot (as pulses)?

(Could there be an economical way to create as much as antimatter as we need? Think about how we could easily induce a permanent magnet to permanently switch its N and S sides, by momentarily creating a strong enough reverse magnetic field using an electromagnet.

Could there be any way to create a special quantum field/shockwave (using an electric and/or magnetic field generator or a laser?)

that when it passes thru a sample of matter (trapped in mid-vacuum), it induces that matter to instantly switch to antimatter (so that instantly all electrons switch to positrons, all protons to anti-protons, all neutrons to anti-neutrons)?)

What if we created an arbitrarily strong volume/spot of magnetic and/or electric field(s)?

What if we created a spot of ultrapressure using a tech way beyond any diamond anvil?

What if we created a spot of negative ultrapressure (by using pulling force)?

(Imagine if we had or created a (solid?) material that is ultrastrong against pulling force (even for a moment)?)

What if we had or created an ultrastrong (solid?) disk/sphere/ring and trapped it in mid-vacuum.

Later we created an ultrapowerful rotational force on it (even for a moment) using ultrapowerful magnetic field.

So that the object gained (even for a moment) an ultrahigh speed and/or positive/negative acceleration?

Below I will try to provide more plausible ways of realizing similar technologies according to known laws of physics of our Universe.

I do not know if similar explanations were provided by anyone before.

Super Energy Sources:

They could be portable fusion reactors which are almost perfectly efficient.

They could provide continuous power (similar to DC) or as repeating pulses (similar to AC).

There maybe super batteries that store a dense cloud of electron gas in vacuum (or as a BEC?)?

Stun guns:

Imagine a super powerful gun creates conductive paths in air using UV pulse/continuous lasers, momentarily.

It sends a powerful electroshock to the target from those conductive paths.

(I think this tech is already developing currently.)

Teleportation:

Imagine two teleportation machines (chambers).

The sender machine creates some kind of quantum shock wave that instantly destroys the target object into gamma photons that carry the same quantum information.

That information sent to the receiver machine which has a giant BEC (that is made of same kind of atoms/molecules with same proportions as the target object?).

When the information is applied to the BEC (instantly, like a quantum shock wave), it somehow instantly quantum mechanically collapses into an exact copy of the object.

Phasers:

Instantly destroys the target object using similar quantum shock wave that used in teleportation.

(Target object instantly gets destroyed similar to teleportation, but there is no receiver for its quantum information.)

Artificial Gravity:

Imagine if we had small coils that can create high level positive/negative spacetime curvatures around them (spherical/cylindrical).

We could place a grid of those coils under floors etc to create artificial gravity.

Force Fields:

Imagine if we created spherical/cylindrical spaceships that covered by a dense grid of (+/-) gravity coils,

and also a dense grid of (superconductor) coils that can create (+/-) electric/magnetic fields.

Would not be possible to use them to create "force fields" all around the spaceships to deflect any (atom/particle/photon) kind of attack?

Cloaking Fields:

Imagine if we created spherical/cylindrical spaceships that covered by a dense grid of (+/-) gravity coils.

Would not be possible to use them to create a photon deflection field all around the spaceships?

Warp Speed:

Imagine if we created spherical/cylindrical spaceships that covered by a dense grid of (+/-) gravity coils.

Would not be possible to use them to create a warp bubble all around the spaceships to act like an Alcubierre Drive?

Sub-space Communication:

(Since we assume we have ability to manipulate the curvature of spacetime)

Imagine we have tech to create micro worm holes as twins and able to trap them indefinitely.

A communication signal enters to either one and instantly comes out of the other one.

Each time we create a new set of twin micro worm holes, we keep one in a central hub on Earth,

and the other carried by a spaceship or placed on a different planet/moon/space station.

(The same tech could also be useful to create and trap micro Black Holes, which maybe useful as compact batteries.)

Electronic Dampening Field:

Imagine EMP created like a standing wave using a grid of phased array EMP generators.

Spaceships with hulls that can withstand against almost any kind of attacks at least for a while if necessary:

How about metallic hydrogen or another solid material that we created using ultrapressure (and temperature)?

I think it is also clear that Star Trek Physics require devices with ability to create strong positive and negative spacetime curvatures for sure.

How could it work according to laws and limitations of known physics, assuming they are always must be obeyed?

According to General Relativity, spacetime bends in the presence of positive or negative mass/energy(/pressure/acceleration).

What if we destroyed a small amount of matter/antimatter in a spot (as pulses)?

(Could there be an economical way to create as much as antimatter as we need? Think about how we could easily induce a permanent magnet to permanently switch its N and S sides, by momentarily creating a strong enough reverse magnetic field using an electromagnet.

Could there be any way to create a special quantum field/shockwave (using an electric and/or magnetic field generator or a laser?)

that when it passes thru a sample of matter (trapped in mid-vacuum), it induces that matter to instantly switch to antimatter (so that instantly all electrons switch to positrons, all protons to anti-protons, all neutrons to anti-neutrons)?)

What if we created an arbitrarily strong volume/spot of magnetic and/or electric field(s)?

What if we created a spot of ultrapressure using a tech way beyond any diamond anvil?

What if we created a spot of negative ultrapressure (by using pulling force)?

(Imagine if we had or created a (solid?) material that is ultrastrong against pulling force (even for a moment)?)

What if we had or created an ultrastrong (solid?) disk/sphere/ring and trapped it in mid-vacuum.

Later we created an ultrapowerful rotational force on it (even for a moment) using ultrapowerful magnetic field.

So that the object gained (even for a moment) an ultrahigh speed and/or positive/negative acceleration?

## Sunday, July 30, 2017

### 3D VOLUME SCANNER IDEA

I recently learned about an innovative method to get 3D scans of objects. It overcomes line of sight problem and captures the inner shape of the object also. It looks like a robot arm dips the object into water in different orientations. Each time how water level changed over time gets measured and from these measurements 3d object shape is calculated like a CAT scan.

I think these method can be improved upon greatly as follows:

Imagine we put a tight metal wire ring around the object we want to scan, maybe using a separate machine.

It could be a bendable but rigid, steel wire ring, or maybe bicycle wire ring, could be even a suitable kind of plastic.

The object could be in any orientation, hold tight by the ring.

Imagine we have an aquarium tank filled with liquid mercury

(which would keep the object dry unlike water, and also tank walls so that measurements would be more precise).

(Also mercury is conductive which would also make measurements easier using electronic sensor(s).)

(It could also be a cylindrical tank.)

Imagine inside of the tank we have a vertical bar that can move up and down a horizontal bar using electronic control.

Imagine that horizontal bar at its middle (down side) has a hook/lock for the wire ring (around the object).

That hook/lock has an electronically controlled motor that can rotate the wire ring (so the object) to any (vertical) angle.

(To prevent the ring/object moving like a pendulum when it is dipped into liquid (fast) each time, we could add a second horizontal bar with adjustable height, that has a hook/lock for the wire ring at its middle (up side). So the ring would be hold in place from its top and bottom points by two horizontal bars.)

Now imagine to take new measurements each time, we rotate the object a small and equal angular amount (within 360 degrees).

Then we dip the object fully inside the liquid (at constant speed) and take it out fully back (at constant speed).

Every time as we dip the object we record the changes in the liquid level in the tank over time.

(While the object fully dipped we could rotate it again and then record liquid level changes while we take the object fully out back

to get two sets of measurements at each cycle, instead of one.)

Of course mercury is highly toxic and reacts with some metals.

So it would be best to find a better liquid.

The liquid would need to be non-stick to keep scanned objects, tank walls dry. Minimal viscosity and density as possible, maximal temperature range with linear volume change based on temperature, constant volume under common different air pressures would be better. Stable (non-chemically active) and non-toxic are must.

Also electric conductivity would be a plus.

References:

https://www.sciencedaily.com/releases/2017/07/170721131954.htm

http://www.fabbaloo.com/blog/2017/7/25/water-displacement-3d-scanning-will-this-work

https://3dprintingindustry.com/news/3d-scanning-objects-dipping-water-118886/

I think these method can be improved upon greatly as follows:

Imagine we put a tight metal wire ring around the object we want to scan, maybe using a separate machine.

It could be a bendable but rigid, steel wire ring, or maybe bicycle wire ring, could be even a suitable kind of plastic.

The object could be in any orientation, hold tight by the ring.

Imagine we have an aquarium tank filled with liquid mercury

(which would keep the object dry unlike water, and also tank walls so that measurements would be more precise).

(Also mercury is conductive which would also make measurements easier using electronic sensor(s).)

(It could also be a cylindrical tank.)

Imagine inside of the tank we have a vertical bar that can move up and down a horizontal bar using electronic control.

Imagine that horizontal bar at its middle (down side) has a hook/lock for the wire ring (around the object).

That hook/lock has an electronically controlled motor that can rotate the wire ring (so the object) to any (vertical) angle.

(To prevent the ring/object moving like a pendulum when it is dipped into liquid (fast) each time, we could add a second horizontal bar with adjustable height, that has a hook/lock for the wire ring at its middle (up side). So the ring would be hold in place from its top and bottom points by two horizontal bars.)

Now imagine to take new measurements each time, we rotate the object a small and equal angular amount (within 360 degrees).

Then we dip the object fully inside the liquid (at constant speed) and take it out fully back (at constant speed).

Every time as we dip the object we record the changes in the liquid level in the tank over time.

(While the object fully dipped we could rotate it again and then record liquid level changes while we take the object fully out back

to get two sets of measurements at each cycle, instead of one.)

Of course mercury is highly toxic and reacts with some metals.

So it would be best to find a better liquid.

The liquid would need to be non-stick to keep scanned objects, tank walls dry. Minimal viscosity and density as possible, maximal temperature range with linear volume change based on temperature, constant volume under common different air pressures would be better. Stable (non-chemically active) and non-toxic are must.

Also electric conductivity would be a plus.

References:

https://www.sciencedaily.com/releases/2017/07/170721131954.htm

http://www.fabbaloo.com/blog/2017/7/25/water-displacement-3d-scanning-will-this-work

https://3dprintingindustry.com/news/3d-scanning-objects-dipping-water-118886/

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