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RECENT POSTS IN THIS TOPIC

**S Halayka**: *on* 11/4/12 at 20:01pm UTC, wrote Hi Mike, Have you read Communication in the presence of noise by Shannon? ...

**basudeba**: *on* 3/20/11 at 6:10am UTC, wrote Sub: Possibility of manipulation in judging criteria – suggestions for...

**Mike Bradley**: *on* 3/3/11 at 13:37pm UTC, wrote Hi Tobias, OK great-- thanks! -Cheers, Mike B.

**Tobias Fritz**: *on* 3/1/11 at 18:10pm UTC, wrote Hi Mike, unfortunately, I'm having trouble finding a good...

**Mike Bradley**: *on* 3/1/11 at 16:31pm UTC, wrote Hi Tobias, Thanks for your comments and glad you enjoyed the historical...

**Tobias Fritz**: *on* 3/1/11 at 15:50pm UTC, wrote It's great for a change to read an essay staying with the facts and not...

**Mike Bradley**: *on* 2/22/11 at 10:08am UTC, wrote Hi Tom, Thanks for your comments, and glad you enjoyed the essay. Re:...

**Mike Bradley**: *on* 2/22/11 at 10:02am UTC, wrote Hi Armin, Thanks very much for the comment. I'm glad you found the ideas...

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FQXi FORUM

October 23, 2019

CATEGORY:
Is Reality Digital or Analog? Essay Contest (2010-2011)
[back]

TOPIC: Reality is Digital, with a Quantum-Mechanical Phase by Michael Patrick Bradley [refresh]

TOPIC: Reality is Digital, with a Quantum-Mechanical Phase by Michael Patrick Bradley [refresh]

What is the fundamental nature of reality ? After the development of the atomic theory of matter and nearly 100 years of quantum mechanics, we know that all objects in our world are made up of discrete units, namely atoms and molecules. Experiments in atomic, nuclear, and particle physics have shown that this discreteness (i.e. digital character) is replicated at shorter and shorter distance scales, to dazzlingly short ranges and almost unimaginably high energies. Thus, despite the superficial appearance of continuity at the macroscopic length scales on which we live and breathe, at its core reality is discrete in character, that is to say, digital. However the fact that this discreteness is correctly described by quantum mechanics means that it is a special kind of “digitalness” which we can express in the following way: we live in a world made of digital objects with the added complexity of a continuous quantum-mechanical phase. In this essay I address this idea and show how the historical development of first discrete and then continuous mathematics led to a classical physics which was based on untested assumptions of the continuity of matter. Ultimately these assumptions were unphysical, and had to be rejected in the face of experimental evidence from chemistry and atomic spectroscopy. The resulting development of quantum mechanics led to the correct modern digital description of matter but with the crucial addition of a quantum-mechanical phase factor.

Michael P. Bradley was born in Victoria, BC, Canada, in 1971. He received the B.Sc. (Honours) degree in Applied Physics from the University of New Brunswick in 1992, and the Ph.D. degree in Physics from MIT in 2000. From 2000 to 2003, he was a research scientist at Axcelis Technologies. In July 2003, he became a professor in the Department of Physics & Engineering Physics at the University of Saskatchewan. Dr. Bradley is currently a Research Fellow at the Bureau International des Poids et Mesures (BIPM), in Sèvres, France, working on BIPM’s planned superconducting watt balance.

Hi Michael, I found your style of writing very easy to read and liked your explanation of a 'special kind of digitalness'. Thanks and nicely explained. Alan.

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Hi Alan,

Thanks very much! Glad you enjoyed the essay.

-Cheers,

Mike Bradley

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Thanks very much! Glad you enjoyed the essay.

-Cheers,

Mike Bradley

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Hi Mike, I've been asking a few authors about a new idea in foundational physics which I'd like you to consider please. At the time of Newton, why didn't anyone think about an Archimedes screw as a model for the graviton, a particle responsible for his force of attraction or spooky action at a distance?

Best wishes, Alan

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Best wishes, Alan

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Hi Alan,

That is an interesting idea which I have not heard of before, I will have to look into it before I could comment intelligently.

Thanks for the comment!

-Cheers,

Mike Bradley

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That is an interesting idea which I have not heard of before, I will have to look into it before I could comment intelligently.

Thanks for the comment!

-Cheers,

Mike Bradley

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Michael,

I find that your essay was one of the few advocating a 'digital AND analog' answer that made a serious effort to explain exactly in what way reality could be characterized by these two seemingly contradictory descriptions. It seems to me that your suggestion can be summarized as follows: our description of anything that exists in space must be digital because below a certain limit it loses its essential character, but because it is (by quantum mechanics) associated with a phase it gains a 'continuous' aspect. If I misunderstood, I'd appreciate a correction.

Yours is the only paper (other than mine) that I have read so far which draws special attention to the quantum phase. You may find my effort to explicate its physical origin of interest.

Armin

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I find that your essay was one of the few advocating a 'digital AND analog' answer that made a serious effort to explain exactly in what way reality could be characterized by these two seemingly contradictory descriptions. It seems to me that your suggestion can be summarized as follows: our description of anything that exists in space must be digital because below a certain limit it loses its essential character, but because it is (by quantum mechanics) associated with a phase it gains a 'continuous' aspect. If I misunderstood, I'd appreciate a correction.

Yours is the only paper (other than mine) that I have read so far which draws special attention to the quantum phase. You may find my effort to explicate its physical origin of interest.

Armin

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Hi Armin,

Thanks very much for the comment. I'm glad you found the ideas interesting; I think your summary basically agrees with the point I was trying to make.

I will indeed look at your paper on the quantum phase and its physical origins; that sounds really interesting!

-Cheers,

Mike Bradley

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Thanks very much for the comment. I'm glad you found the ideas interesting; I think your summary basically agrees with the point I was trying to make.

I will indeed look at your paper on the quantum phase and its physical origins; that sounds really interesting!

-Cheers,

Mike Bradley

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Michael,

Thanks for the fine essay, which makes some very good points about how continuity is non-physical in many ways.

Below is some feedback on a few details of your essay which are admittedly minor.

In your definitions you write,

"Continuous entities are non-countable, and in this way they are like the real numbers; there are always more real numbers (in fact, infinitely many more) to be found between any two real numbers on a number line, whereas for countable digital entities like the integers this is not the case."

This seems not quite correct. The rational numbers are countable, yet they also have the property, like the reals, that between any two rational numbers there are an infinite number of rationals. The distinction between the countable and uncountable numbers is more subtle than this property.

Later on, you write,

"continuous mathematics was first developed in the form of geometry, which however remained utterly disconnected from the mathematics of countable objects until Descartes"

While geometry and algebra were not synthesized until Descartes developed analytic geometry, it does not seem accurate to say that geometry was 'utterly disconnected' from countable arithmetic before then. For example, the ancient Greeks certainly were able to count the sides of a polygon, and they studied Pythagorean triples (i.e., integers satisfying the Pythagorean theorem).

But I do appreciate how you put the rise of continuity in physics in historical context, and enjoyed the essay!

Regards,

Tom

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Thanks for the fine essay, which makes some very good points about how continuity is non-physical in many ways.

Below is some feedback on a few details of your essay which are admittedly minor.

In your definitions you write,

"Continuous entities are non-countable, and in this way they are like the real numbers; there are always more real numbers (in fact, infinitely many more) to be found between any two real numbers on a number line, whereas for countable digital entities like the integers this is not the case."

This seems not quite correct. The rational numbers are countable, yet they also have the property, like the reals, that between any two rational numbers there are an infinite number of rationals. The distinction between the countable and uncountable numbers is more subtle than this property.

Later on, you write,

"continuous mathematics was first developed in the form of geometry, which however remained utterly disconnected from the mathematics of countable objects until Descartes"

While geometry and algebra were not synthesized until Descartes developed analytic geometry, it does not seem accurate to say that geometry was 'utterly disconnected' from countable arithmetic before then. For example, the ancient Greeks certainly were able to count the sides of a polygon, and they studied Pythagorean triples (i.e., integers satisfying the Pythagorean theorem).

But I do appreciate how you put the rise of continuity in physics in historical context, and enjoyed the essay!

Regards,

Tom

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Hi Tom,

Thanks for your comments, and glad you enjoyed the essay.

Re: your points:

(1) Yes you are absolutely right about the rational numbers being countable and yet there being arbitrarily many between any two points on a number line.

So although there was a good point to be made my explanation is not exaclty correct.

(2) Yes I was perhaps too theatrical in my contention that there was an "utter disconnect" between continuous and discrete mathematcis until Descartes. Nonetheless I think the real synthesis of the two only happened at that time, and was hugely important for future developments.

Thanks for these useful comments!

-Cheers,

Mike Bradley

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Thanks for your comments, and glad you enjoyed the essay.

Re: your points:

(1) Yes you are absolutely right about the rational numbers being countable and yet there being arbitrarily many between any two points on a number line.

So although there was a good point to be made my explanation is not exaclty correct.

(2) Yes I was perhaps too theatrical in my contention that there was an "utter disconnect" between continuous and discrete mathematcis until Descartes. Nonetheless I think the real synthesis of the two only happened at that time, and was hugely important for future developments.

Thanks for these useful comments!

-Cheers,

Mike Bradley

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It's great for a change to read an essay staying with the facts and not drifting off into wild speculation. The historical perspective has been enlightening! One thought I've had while reading the essay is this: while matter is made of atoms, atoms are made of a nucleus and electrons, the nucleus contains nucleons, which in turn are composed out of quarks... what if this hierarchy would just continue without end? Then at each level, the world would be discrete. But however, there would be no most fundamental discrete level, so in this sense the world would not be discrete. Surely philosophers have thought about this option...

A small fine print about the issue of complex phase: in principle, complex numbers are not inevitable in quantum theory. While being physically unrealistic, quantum mechanics with purely real numbers is a mathematical possibility having many phenomena in common with ordinary complex QM, in particular interference.

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A small fine print about the issue of complex phase: in principle, complex numbers are not inevitable in quantum theory. While being physically unrealistic, quantum mechanics with purely real numbers is a mathematical possibility having many phenomena in common with ordinary complex QM, in particular interference.

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Hi Tobias,

Thanks for your comments and glad you enjoyed the historical narrative, I do think it is useful to consider these questions in that context.

Re: your first question, if there are infinitely many layers of discrete buliding blocks, then yes we have the philosophical problem you posed. In that sense you then have to impose a cutoff or coarse-graining to get a truly discrete "fundamental" description.

RE: your second comment, that is interesting, I didn't know about purely real QM-- can you provide a reference for that ?

-Cheers,

Mike Bradley

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Thanks for your comments and glad you enjoyed the historical narrative, I do think it is useful to consider these questions in that context.

Re: your first question, if there are infinitely many layers of discrete buliding blocks, then yes we have the philosophical problem you posed. In that sense you then have to impose a cutoff or coarse-graining to get a truly discrete "fundamental" description.

RE: your second comment, that is interesting, I didn't know about purely real QM-- can you provide a reference for that ?

-Cheers,

Mike Bradley

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Hi Mike,

unfortunately, I'm having trouble finding a good reference--there's more literature about "quaternionic quantum mechanics", which goes beyond even the complex numbers. The original work seem to be contained in here:

Ernst Stueckelberg, "Quantum Theory in Real Hilbert space", Helv. Phys. Acta 33, 727 (1960).

but this paper I couldn't find online.

You can think of wavefunctions in real quantum mechanics as analogous to water waves. A water wave is described by a single real number at each point, but nevertheless there is interference between water waves.

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unfortunately, I'm having trouble finding a good reference--there's more literature about "quaternionic quantum mechanics", which goes beyond even the complex numbers. The original work seem to be contained in here:

Ernst Stueckelberg, "Quantum Theory in Real Hilbert space", Helv. Phys. Acta 33, 727 (1960).

but this paper I couldn't find online.

You can think of wavefunctions in real quantum mechanics as analogous to water waves. A water wave is described by a single real number at each point, but nevertheless there is interference between water waves.

report post as inappropriate

Sub: Possibility of manipulation in judging criteria – suggestions for improvement.

Sir,

We had filed a complaint to FQXi and Scienticfic American regarding Possibility of manipulation in judging criteria and giving some suggestions for improvement. Acopy of our letter is enclosed for your kind information.

“We are a non-professional and non-academic entrant to the Essay...

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Sir,

We had filed a complaint to FQXi and Scienticfic American regarding Possibility of manipulation in judging criteria and giving some suggestions for improvement. Acopy of our letter is enclosed for your kind information.

“We are a non-professional and non-academic entrant to the Essay...

view entire post

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Hi Mike,

Have you read Communication in the presence of noise by Shannon?

- Shawn (s'toon)

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Have you read Communication in the presence of noise by Shannon?

- Shawn (s'toon)

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