Exploring Zero and Infinity in Physics

[Antonio Lao]

Zero and Infinity

In mathematics, we see these two numbers appear almost always as the end points of some limiting processes. We see zero in the definition of a derivative in calculus. We see infinity in the math of infinite series. In this discussion, we will try to see these extreme numbers in physics. These will be used to give some insights into the following statements: (1) The mass is zero, (2) the mass is infinite, (3) the time is zero, and (4) the time is infinite.

The mass is zero. Since mass is equivalent to energy, the statement is same as “the energy is zero.” Zero energy does have a meaning in quantum mechanics. It is the energy of the vacuum equals half a quantum (Planck’s constant over 4 pi). This is associated to a point particle at the absolute temperature of zero. Because of Heisenberg’s uncertainty principle, this energy can never be exactly zero. This gives meaning to the quantum vacuum as a complex structure. This structure was verified by experiments to detect the Casimir effect.

This structure of the quantum must necessarily give meaning to an infinitesimal volume. In mathematics, we can define volume in any given dimension of space. And if the geometries are that of a sphere or a cube, there exist formulae to calculate their volumes.
It can be shown that the volume of 1-sphere is equal to the volume of a 1-cube. The different in volume becomes worse and worse at higher dimensions. This volume is static. In order to make the volume dynamic, it must be associated with a vector, in this case, an infinitesimal vector. This is called a local infinitesimal motion (LIM). For volumes to have any physical meaning, it must be a closed volume. The closure of one-dimensional volumes forms closed one-dim loops. And there are two distinct types. The LIMs are all conserved and there is infinite number of them. Here again we have reached infinity by not going as far as the next LIM. In mathematics, a line segment or a loop (closed line segment) contains in itself infinite number of points. We can take away the end points of a line segment, and still there remain an infinite number of points. It is useless to keep removing end point, the number of points will never be less than infinity.
But in the loop, the LIMs have started from a begin point and have passed infinity and back to the same begin point without really knowing it, just in the blink of an eye. And it continue to cycle through these infinite points forever and ever holding on to the same bearing of travel. This is the principle of a directional invariance.

If we attempt to visualize this volume in two-dimension, we get the limiting problem resulting in a Sierpinski carpet, which area is zero, and while the total perimeter of the loop is infinite. In three dimensions, we get the Menger sponge, whose volume is zero, while its surrounding area is infinite. Only in one dimension does the volume of the loop make any little sense. And it is in this one-dim that we can justifiably defined eight invariant properties for the principle of directional invariance.

The time is zero. This is just to give a linear definition for time. Taking the line segment again, zero time is surely at one end. The other end might be when time equals infinity. But in a closed loop, time just keeps flowing, from time zero, passes infinity and back to zero, on and on. Since in principle, there are two distinct types of closed loops from a 360 degrees twist of a Moebius strip, there are two directions of time. These two directions can only make any sense if viewed in one dimension. If we attempt to view time in three dimensions, we get the senseless image of Escher’s Waterfall. The validity of most of Escher’s images is true only if we live in the one dimension. For the one dimensional Waterfall, it is logical to have two directions of flow. In three dimensions, the water (time) has to flow uphill fighting against the forces of gravity making it only natural for water (time) to flow downhill.

We have discussed the concepts of 1-dim volume and the possibility of two directions of time. By so doing, without even realizing what we have done, we have actually separated the space-time structure of special and general relativity and came up with a bonus of an extra time’s direction than can most benefit the description of antimatter, which was not part of relativity but is a big equal participant in quantum field theories.

 

[8LPF16]

Antonio,

This thread deserves more life.

On the point of a closed loop, you could still have the beginning at 1 (or any other small number) rather than "absolute" zero. Such as I've mentioned before - .0618033..., which is "less than zero" in loose terms. I think that sometimes, we need to think in loose terms because the numbers that we use are our invention. Nature just deals in quantities - and sometimes this appears loose to our rigid math.

LPF

 

[Antonio Lao]

Agreed

8LPF16,

I agree with you 100%. The zero that I am driving at is the zero of time. This zero time is called the temporal intersect of two mirror worlds. One world is contracting in space and one is expanding in space. The total energy of both worlds is conserved. The zero time is the connection or bridge between these mirror world. The flow of time for each world is opposite in "direction" as that of the other. This different direction of time flow becomes my justification for the existence of antimatter and consequently also justified the CPT Theorem of physics.

Antonio

 

[Organic]

And if we have 3 connected worlds?

 

[Antonio Lao]

Not at the same Time Intersect

Organic,

The temporal intersect only takes two worlds at a time (time=0). This does not mean that there is only one temporal intersection, there can be many and in fact infinitely many. Each intersect takes two mirror worlds at a time in order for conservation of the CPT Theorem (total energy cannot be destroyed or created).

Antonio

 

[Mr. Robin Parsons]

Didn't have time yet to digest all of what you have written, but...

Originally posted by Antonio Lao
(SNIP) This is associated to a point particle at the absolute temperature of zero. Because of Heisenberg’s uncertainty principle, this energy can never be exactly zero. (SNoP)

Heisenberg's principal speaks (Only!) of our inability to measure, (at atomic scales..) it does NOT dictate, in any way, shape, or form, how the universe (or atoms) operate(s)

 

[8LPF16]

Just think, we can't measure the atomicly small, or the Universely big. Personally, I think we are a millenium from knowing when/where the Universe started. We will have to travel the far reaches, and gather vast data to even begin. I don't really care how old the planet is or our Universe, it doesn't have relevancy in my everyday life. Until we have a better grip on when/where we came from, and how our world works (and how to work in harmony with it), I think it's energy spent in the wrong direction.

I thought Heisenburg was more of a ratio of uncertainty - knowing place and time simultaneously. Which, I will add, if you know the path an object takes then this Herculean task becomes rather simple.
(ask a detective)

The reason I still shy from zero - even with time ... I look at the expansion/contraction of the Universe to be analogous with my lungs. They are never empty, even as a fetus, there were fluids inside, and at some point, exchanged with oxygen from Mom's blood.
All things are cyclical, a "breathing" Universe needs no beginning or end.

LPF

 

[Antonio Lao]

Time Zero

8LPF16 and Mr. Robin Parsons,

Time zero is not a quantitative thing that I can measure.
It is just another name for the qualtitative directional meaning of time. Time zero means that there is no way we can measure or determine which directions time will take, growing older or growing younger.

But in Heisenberg's uncertainty principle, time is measureable but only if it is related to the energy of the vacuum. Energy can be borrowed from the vacuum but the more energy you borrow the shorter time that you can keep this energy to useful purpose. If you borrow infinite amount of energy from the vacuum it can only keep it for zero time which is no time at all. If you borrow zero energy then you can keep it forever.

Antonio

 

[russ_watters]

Originally posted by Mr. Robin Parsons
Didn't have time yet to digest all of what you have written, but...

Heisenberg's principal speaks (Only!) of our inability to measure, (at atomic scales..) it does NOT dictate, in any way, shape, or form, how the universe (or atoms) operate(s)

That's a common misinterpretation (due largely to laymans' descriptions like that found in "A Brief History of Time"). It was actually first proposed by Heisenberg himself. It is not correct. http://en.wikipedia.org/wiki/Uncertainty_Principle

The uncertainty principle is sometimes erroneously explained by claiming that the measurement of position necessarily disturbs a particle's momentum. Heisenberg himself offered this explanation initially. Disturbance plays no part, however, since the principle even applies if position is measured in one copy of the system and momentum is measured in another, identical one. It is more accurate to say that the particle is a wave, not a point-like object, and does not have a well-defined simultaneous position and momentum.

 

[Organic]

Hi Antonio Lao,

I am talkin about any odd number of worlds where their time balance = 0

 

[Antonio Lao]

How many World?

Organic,

Is infinity an odd or even number? If I assume that there are infinite number of universes, is this number odd or even?

But we don't have to answer the question if all we wanted is to say something about the connection between two worlds, by doing some kinds of binary operations such as addition and multiplication.

So we just taking two things at a time, do some analyses, and then go ahead and make generalization. It might turn out that all these worldly connections might be just relative and where the absolutes is at zero and infinity. These two extremes can only be approached but never be reached exactly. So we all have our journey to follow but we can never say that we have finally at the destination (the end of eternity). To think about our average lifespans and compare to infinity, our lifespans are just zeros, as if we never existed at all.
Our awareness of our existence is a gift given by higher collective awareness that at the moment I don't have any answer.

Antonio

 

[matt grime]

Originally posted by russ_watters
That's a common misinterpretation (due largely to laymans' descriptions like that found in "A Brief History of Time"). It was actually first proposed by Heisenberg himself. It is not correct. http://en.wikipedia.org/wiki/Uncertainty_Principle

I don't see how your correction corrects what was posted. Heisenberg's principle is *just* a manifestation of a fairly straightfoward result of some integration you might come across in, say, an advanced course on Fourier Analysis.

The post by Mr Robin Parsons didn't mention anything about *disturbances* by measurement, but merely talks of our inability to simultaneously measure these two quantities. It doesn't state any reason for this inability.

 

[Antonio Lao]

Question for Who?

Matt Grime,

Are you addressing your post to me or other? Maybe i did not understood what was the question.

As far as Heisenberg's Uncertainty Principle goes, there are most likely many interpretations. For me, I am not an authority on it, I am just using it to say something about zero time and infinite energy.
Time and energy are conjugated into another form of the principle. The other is momentum and position.

Antonio

 

[8LPF16]

Also to Matt,

It seems logical to me that, depending on what your using to measure, that at the atomic scale, the tool would disturb the thing being measured. Is this not accepted now?

LPF

 

[Antonio Lao]

Never Questioned

8LPF16,

The disturbance of the obsevers was never questioned by the authorities of quantum physics. So you are correct. They were trying to come up with a good explanation for the double slits experiment of interference patterns. Feynman was able to resolve this mystery with his sum of histories - path integral methods.

Antonio

 

[8LPF16]

Antonio,

My idea on the double slit experiment: the slit disturbs the normal path of the wave of potentials, they are at first scattered about, but will eventually regroup. The difference (from Feynman) is I don't think they travel all potential paths simultaneously, I think they know them all previous to going through the slit, and the experiment does not allow them enough distance to regroup into one slit. Given enough distance, the image on the back wall would be what is predicted by particle definition - 1 slit.

What is the standard distance from the slit to the back wall in this experiment?

Any record of someone doing a sideways slit experiment?

As I stated before, when doing even the simple prismatic experiment that Newton did, if you change the distance, you get different results. If you change position (I call it anti-slit, in which, the color is examined before it hits the wall, not after), then you will get different results as well. I thought scientific experiments were supposed to eliminate these discrepancies by testing other locations, conditions, etc.?

It is my very strong belief, after doing these tests, that the slit itself throws the results. It creates a dark-light-dark condition that forces a change to the natural dark to light flow (vector forward in time).

LPF

 

[Antonio Lao]

Least Action

8LPF16,

Feynman used the principle of least action. This principle states that nature will never waste time or energy on purpose. For every possible path, nature will always choose the path that takes the least amount of time and the least amount of energy. On an Euclidean plane, this is the straight line. On a spherical surface, this is the geodesic curve. The standard distance should be the same for both surface. What is summed are the probability amplitudes, which is the normalized product of the wave function and its conjugate.

Distance for the slit experiment is arbitrary. It can be any distance you want as long as the apparatus can be fitted into the room.
Another thing I need to mention is that the width of the slit cannot be larger than the wavelength of the radiation going into the slit.
The radiation can be light, or x-ray (use crystal lattice as slit), or a stream of electrons, or a stream of apples.

Antonio

 

[8LPF16]

Antonio,

The path of least resistance dominates all my ideas. This is why I say the photon would never travel all paths, because it knows the paths already, through color memory. The gamma portion of the wave acts as a "scout", and directs the wave like a laser sight on a gun. So, it "knows" what is on the other side before the "visible" portion comes through.

I understand the need for contol of the width of the slit, how could they possibly have missed the need to control and record different distances?

Here is the slit through prism:

[DARK]red/yellow..[LIGHT]..cyan/violet[DARK]

the "cone" extending from the controlled slit to the wall is mediated by the distance. Only when it is "squeezed", through improper distance, do you see:

[DARK]red/orange/yellow..GREEN..cyan/blue/violet[DARK]

what they missed is the constant of attraction of red and violet to darkness, and yellow and cyan(turquoise) to lightness. This is critical to unifying electro-weak and gravitio-strong.

This is confirmed by the anti-slit experiment. You will see:

[LIGHT]yellow/red..[DARK]..violet/cyan[LIGHT]

upon final calibration for distance you will see:

[LIGHT]yellow..magenta..cyan[LIGHT] (magenta has maximum attraction to darkness, and apparently, optimal communication with gamma)

By decreasing the distance, magenta is "squeezed" apart into red and violet. You can watch this happen as you change distance.

The rainbow can be more easily explained this way. The Earth =[DARK]..clear area=[LIGHT]..rain cloud=[DARK], the long distance "squeezing" green (and other tertiary colors) into the picture.

My theory puts the primaries at C-M-Y, and R-G-B as secondary. A fairly minor change, with major ramifications.

LPF

 

[Mr. Robin Parsons]

Originally posted by Antonio Lao
(SNIP) Time zero is not a quantitative thing that I can measure.
It is just another name for the qualtitative directional meaning of time. Time zero means that there is no way we can measure or determine which directions time will take, growing older or growing younger.
(SNoP)

Time, equalling zero, equalls infinity, respective of energy, not a new, or unknown, thought.

Heisenbergs uncertainty principal as I learned of it tells of 'light' being 'shined' on the outer valence shells of electron orbitals, to make measurements, it is the act of shining the light (EMR probe of any kind/type of EMR) that excites the electron, and therefore we cannot determine it's position, prior to our investigative light shining having adulterated the event we are attempting to observe.

This DOES NOT imply, nor state, that the electron is not observable, nor that its position and momentum are NOT, Both, simultaneously knowable, just that we have not a method to achieve that outcome, due to the constraints that the physical reality imposes upon us, by it's very nature, and makeup/arrangement.

 

[Antonio Lao]

Symmetry

Mr Robin Parsons,

The nature that limits us from knowing the quantum world is the inherent symmetry of the structure.

A point looks the same from any angle, any distance, any time.

Antonio

 

[Mr. Robin Parsons]

Originally posted by Antonio Lao
Mr Robin Parsons,
The nature that limits us from knowing the quantum world is the inherent symmetry of the structure.
A point looks the same from any angle, any distance, any time.
Antonio

Are you referring to the work of Emmy Noether as per your reference to symmetry?

 

[8LPF16]

Antonio,

I forgot to ask - do you have a prism?

LPF

 

[Antonio Lao]

8LPF16,

I do have a prism.

Antonio

 

[Organic]

Antonio,

You wrote:

Our awareness of our existence is a gift given by higher collective awareness that at the moment I don't have any answer.

If 0 is the balance of infinitely many worlds, then each awareness is limited to some world, but when we try to be aware to more then one world at a time, we get 0.

Form 0 point of view infinitely many worlds become one.

So, through this point of view, we have:

1) 0 aware to global 1.

2) Local 1 aware to 0.

By (1) we get infinitely many worlds that never destroy each other.

By (2) each world gets its possibility to fulfill its own uniqueness.


The hidden divinity is 0 aware to 0.

 

[Antonio Lao]

Organic,

I could never have said it better than you. Thanks.

Antonio

 

[Mr. Robin Parsons]

Once again Mr. Robin Parsons ASKS...
Are you referring to the work of Emmy Noether as per your reference to symmetry?

If you would prefer NOT to respond, fine, but it ends the discussion for me...

 

[Mr. Robin Parsons]

Originally posted by Organic
Antonio, You wrote: If 0 is the balance of infinitely many worlds, then each awareness is limited to some world, but when we try to be aware to more then one world at a time, we get 0.
Form 0 point of view infinitely many worlds become one.
So, through this point of view, we have:
1) 0 aware to global 1.
2) Local 1 aware to 0.
By (1) we get infinitely many worlds that never destroy each other.
By (2) each world gets its possibility to fulfill its own uniqueness.
The hidden divinity is 0 aware to 0.

Humm could it just be that 'zero' is simply the distinguishing/distinguishment between 1 and -1 AKA that which separates them as to allow us to see 1 and -1, otherwise we have no distinction between negative values and positive values, no midpoint...

 

[matt grime]

Originally posted by 8LPF16
Also to Matt,

It seems logical to me that, depending on what your using to measure, that at the atomic scale, the tool would disturb the thing being measured. Is this not accepted now?

LPF

Ask a physicist. my post was merely to point out that robin was being misrepresented.

 

[Mr. Robin Parsons]

Originally posted by matt grime
Ask a physicist. my post was merely to point out that robin was being misrepresented.

How, please...

 

[matt grime]

I seem to recall russ watters claiming you had misrepresented heisnberg's principle in respect of 'disturbing' things when measured. I pointed out that you hadn't used the word disturbed, or even alluded to it.

 

[Mr. Robin Parsons]

Thank you, for the clarification...

 

[Antonio Lao]

Addendum to this Thread

To anyone who still wants to know the purpose of this thread,

Maybe I wasn't clear at the beginning, but the point I am trying to get across is that zero and infinity are ordinal numbers. They could not really be used to do any calculation.

But in actual calculations they become the limits to be approached.
This is how differential calculus is built that some argument of the domain approaches zero but the range of that function is never zero or infinite.

In integral calculus, the limits of integration usually start from negative infinity to positive infinity but the actual result is in between.

The key to understanding zero and infinity is the theory of limits.
How we can use mathematical arguments to show the logical existence of a limit at zero and at infinity hence show that a series will converge to a limiting value. If the series diverge then it not useful and nobody wants it. Nobody wants infinity.

The theory of infinite series can very well shed some light on the meaning of zero and infinity.

I think I can now rest my case.

Antonio

 

[Antonio Lao]

Belated Reply

Mr. Robin Parsons,

This is a belated reply to your post about Emmy Noether. Yes, I am referring to her symmetry theorem. But the one that bothers me is the symmetry in time for conservation of energy. This symmetry says that energy does not depend on the progress of time. But in real life, we know it does, increase of entropy, thermodynamics tells us that energy does depend on time. So the CPT theorem cannot be true for our universe. The other problem is that these symmetries hold only for a closed system but there is no way at this point of our knowledge in science to show that out universe is closed. The big bang theory says it can go on expanding forever unless we can find the dark matter (energy) to hold back the expansion. We have not found this dark matter. There are many hypotheses but no consensus agreements just yet. To make matter worse, cosmologists are now saying the expansion is accelerating.

Antonio

 

[Mr. Robin Parsons]

Originally posted by Antonio Lao
(SNIP) This is a belated reply to your post about Emmy Noether. Yes, I am referring to her symmetry theorem. Antonio (SNoP)

O.K. Thank you...and, it is wrong!

 

[matt grime]

Originally posted by Antonio Lao
To anyone who still wants to know the purpose of this thread,

Maybe I wasn't clear at the beginning, but the point I am trying to get across is that zero and infinity are ordinal numbers. They could not really be used to do any calculation.

But in actual calculations they become the limits to be approached.
This is how differential calculus is built that some argument of the domain approaches zero but the range of that function is never zero or infinite.

In integral calculus, the limits of integration usually start from negative infinity to positive infinity but the actual result is in between.

The key to understanding zero and infinity is the theory of limits.
How we can use mathematical arguments to show the logical existence of a limit at zero and at infinity hence show that a series will converge to a limiting value. If the series diverge then it not useful and nobody wants it. Nobody wants infinity.

The theory of infinite series can very well shed some light on the meaning of zero and infinity.

I think I can now rest my case.

Antonio

You should not talk of infinity as either a cardinal or an ordinal. There are obviously infinite cardinals and infinite ordinals but there are many such and to imply some uniqueness is incorrect. This seems to be a common misconception in this forum: the difference between infinite and infinity.

In particular, there seems to be this idea that there is this unique object we call infinity. That that infinity is what we mean in a sequence tending to infinity, and for it to be the cardinality of the Natual numbers.