Paul Dirac on Dimensionless Numbers

[@douglasstrother6584]

"Electromagnetic Fields and Waves" by Lorrain & Corson (2nd Edition) contains two problems relating Electrodynamics and Cosmology. Problem 4-22 starts with: "In 1959 Lyttelton and Bondi [Proc. Roy. Soc. (London) A, vol. 232, p.313] suggested that the expansion of the Universe could be explained on the basis of Newtonian Mechanics if matter contained a [tiny] net electric charge." A follow-on problem, Problem 10-11, mentions that correction terms to curlB and divE due to the creation of this charge should be on the order of R^-2 where R is on the order of the radius of the Universe, so that the new terms would be negligible at all length scales but cosmological situations. This hypothesis is consistent with the linear velocity-distance observations. Rather thought-provoking questions from an Undergraduate E&M textbook!

[@KevTheImpaler]

So it wasn't 42. It was either 137 or 10^39

[@gaulindidier5995]

Dirac, might not been as well known as Einstein but to me he’s made of the same ilk. I guess this is what happens when you don’t have the easiest of personalities, but his mind is just as beautiful.

[@Lk_boca]

Agreed! Dirac was the worthy successor of Einstein in the later devolopment in Quantum Physics. No doubt we hold him to such high standards.

[@annaclarafenyo8185]

Dirac was NOT like Einstein! He was an independent type of person of a different style. Einstein was great in his way, Dirac in his completely different way. Einstein was a physical thinker, and always thought in terms of mechanical devices. Dirac thought in mathematical structures. My favorite quote about Dirac is by Einstein: "Why does he walk on a tightrope hung between genius and madness"?. I believe this quote came because of what I consider Dirac's greatest paper: the 1943 paper introducing negative probability.

[@dan5626]

I believe that Paul Dirac was superior to Einstein in terms of achievements....one can say even that modern particle physics would not exist without him at all. Einstein derived from concepts already established by Lorentz, Poincaré and De Preto (down to the formulation) while Dirac originally provided concepts like the antielectron (positron), the "Dirac Sea" and matter/antimatter, far more impacting on Physics. In summary, Einstein explained problems dating back to Galileo and which other physicists had mostly paved the way, expanding on it abd basically turning physics upside-down. Dirac turned physics upside-down and inside-out.

[@annaclarafenyo8185]

@@dan5626 Suffice it to say, this wasn't Dirac's opinion of Einstein and himself.

[@dan5626]

@@annaclarafenyo8185 of course not, he was an well-educated academic and a gentleman. To state this would appear to be of poor character and below his status, as would be for any person of the same pedigree. Also, there are rules in life and career, and there is a pecking order with anything....I believe you can understand that.

[@sixpooI]

the grandmaster himself speaks to us!

[@samuell4775]

...FYI....Dirac predicted antimatter...the Dirac Equation is engraved in the floor of Westminster Abbey...he made fundamental contributions to Quantum Mechanics and Quantum Electrodynamics....

[@pgknippel]

I think this might be the longest clip of the man talking I’ve ever seen, thank you!

[@cdorman11]

kzbin.info/www/bejne/gJvNqJ13o7lgqNE

[@0cgw]

Dirac's large number hypothesis was an interesting proposal (and his idea that it not a coincidence is correct). However, today the numerical coincidence has been explained. The requirement that stars are currently burning their fuel imposes a constraint on the ratio of the large numbers and fixes the time of observation (i.e., the age of the universe). Ignoring factors of order unity gives the sort of relationships between Dirac's large numbers that Dirac wanted to explain.

[@philcarter2362]

How wonderful to hear Dirac speak while looking at his image.

[@gilliebrand]

Thanks so much for sharing...it's the first time I have heard his voice even though I've read his words.

[@edwardedward7974]

A person worthy of great respect !

[@Jabber_Wock]

Curious to know about when this was recorded. Indeed Dirac was a genius. Like the slow and deliberate manner of talking. Quite in contrast to Feynman’s way of talking.

[@Theineluctable_SOME_CANT]

Dick was Paul on speed...

[@v.sandrone4268]

Feynman was talking slow ...for how fast his mind operated.

[@Theineluctable_SOME_CANT]

@@v.sandrone4268 both were amazing geniuses, imho.

[@GundamnWing]

The Dirac Equation made me get into physics. He is my idol.

[@channalbert]

Dirac, making 10:01 youtube videos since 1902.

[@liamroche1473]

When was this originally recorded?

[@campbellmorrison8540]

Very interesting, I've never heard this before thank you

[@fig7047]

The irony is that we no longer think matter is constantly created, but space is.

[@hipposlapper]

Isn't the energy density of the universe constant, so energy is constantly being created? And isn't mass just another form of energy?

[@brandonlewis2599]

citation needed, both of you.

[@andrewz2854]

@@hipposlapper Mass is essentially extremely condensed, cooled down energy. And energy as far as we know is not being created. Mass is being converted into radiation by black holes all over the universe, thus increasing the sum quantity of energy relative to mass.

[@jimroth7927]

I notice that his explanation of why the most distant nebulae are receding fastest seems to be wrong. I thought it was because of the expansion of space, not because "the objects that were shot out fastest are furthest away"? Maybe I am misunderstanding?

[@stoferb876]

You understood correct. He was wrong. Partly because cosmology/astronomy wasn't his specialty, and partly because the big bang theory hadn't yet been clarified and really worked out the way it later became. Also because he evidently wasn't quite onboard with the theory of relativity, and the expansion (or any other kind of bending/shrinking/distortion of space itself) is a feature of Einsteins theory of gravity. Note also that he had a very outdated estimate of the age of the universe too.

[@fanbasealpha292]

A fundamental insight at least hundred years ahead of his time.

[@davidwilkie9551]

The first Steam Engine for pumping water out of a mine worked by condensation and contraction of steam to water. You can identify the same mechanism of Cosmology in which the wave-packaging is like a linear-transverse spring matrix such that what appears to be accelerating expansion of Black-body "hot space" is counter balanced by accelerating Black Hole contraction in "Aidiabatic isolation" be-cause-effect in/of "it's always NOW". Students who have excellent memories and acceptance of lessons tend to have an aptitude to recite brilliantly assembled narratives such as those proposed by precision observation that Dirac's Number Theoretical approach has established as conventional knowledge.

[@greese007]

If gravity is decreasing with time, then it was stronger in the past. Could this explain the high rotational velocities in ancient galaxies, as an alternative to dark matter? If true, then the oldest galaxies should appear to contain the most dark matter, but I don't know if that is true.

[@mito88]

I didn't understand this part. is it gravity as a universal force that is decreasing? or is it the strength of gravitational attraction between two objects that begins to decrease as they move away from each other?

[@matteoserafini7704]

@@mito88 G=G(t). The gravitation "constant" is decreasing with time, so the interaction between two bodies becomes weaker as the univers ages

[@subjekt5577]

Instead of gravity decreasing in power, could it be the electromagnetic force increasing in power? Also I wonder how/if the hypothesis of complexity-action-duality plays into this

[@JonErikNordstrand]

It has been asked here, but I didn´t see any answer. Anyone knows when the recording was done?

[@RoyMustang.]

Truly a beautiful Man with the great ideas

[@jswets5007]

Speculation, or hypothetical proposal, or hypothesis, whichever makes you feel as though it is the most accurate description of the action or event, is the beginnig of discovery and not the answer itself. "Dimensionless" numbers are ratios, and ratios exist because the only true, or real, or complete unit is unity; everything else is only a ratio thereof.

[@2tehnik]

Why assume a cap size? He just says it and doesn’t elaborate on it or justify it whatsoever.

[@snowpants2212]

is there still hope of being able to check in the near future whether G varies as predicted by his hypothesis?

[@pauldirc..]

Any updates

[@mito88]

​@Paul Dirac not any updates, but the pertinent ones....

[@acr08807]

Dirac's hypothesis was tested and rejected 70 years ago.

[@stoyanfurdzhev]

Leave all hope to overcome scientific delusion, and engage instead in administration of Einstein geniality, not at least for his contribution for the modern rediscovery of Parmenides' account of ultimate reality, to which Dirac quite consistently with Einstein's conceptual framework predicted the existence of antimatter.

[@norseko]

Dirac must of worn a hat in the midday sun.

[@edwardjones2202]

Just receded past his youthful hairline

[@Barley150]

Is pi a dimensionless number?

[@paulerickson3553]

Pi is dimensionless (ratio of two lengths - so dimensions cancel).

[@MiniLuv-1984]

Imagine the world had we ignored such gifted individual. Now image the world had we not ignored many, many more gifted individuals.

[@NicleT]

That’s a fantastic document!! Too bad for the hissing in the audio of his voice.

[@stoyanfurdzhev]

Proportionless nonsense.

[@Sandsteine]

His voice is so cute

[@GeorgeTodd]

It’s like bingo, imagine a dumb guy, me lets say. I’m in a gameshow and the top phrase is “Familiarity breeds BLANK” and I say “Pigeons”.

[@pukaman2000]

Gravity keeps us from collapsing to the forth dimension.

[@danieloblinger1199]

Volume is much too low.

[@superioropinion7116]

No dimensions?

[@blitzer2062]

He talks about the number of particles in the universe as 10^78, but this isn't fixed because the size of the observable universe is getting larger all of the time. So I must be missing some aspect of what he is saying.

[@tomlavelle8340]

I tried his method of mathematics and I had……. Problems. 😮

[@coulombejonathan]

Thanks!

[@quarkgluonplasma3614]

damn

[@MikeWiest]

Wow! Far out!

[@charanjeetsingh2598]

First I thought he will start with π

[@lunam7249]

ohhhh come on!! of course it was going to be the alpha constant

[@MrNibiru2112]

Me tooo

[@sentientblob1381]

Pi is not a physical constant though. It's a number that shows up in math. Though I have to agree i don't understand why G has to be constant. If gravity is a change of spacetime and we see that that universe is indeed expanding fast at cosmic scales, why do we assume the proportionality factor of curvature due to matter/energy should stay constant when even space is not constant.

[@lunam7249]

@@sentientblob1381 at the highest levels no one knows what gravity is, however it is known that it travels at lightspeed

[@luisfabricio6439]

Ratios by nature have no dimensions, all ratios

[@werdnarotcorp8991]

Not true. The numerator and denominator must have identical units so they cancel out. Thus speed being distance/time is a ratio but the result is not dimensionaless.

[@luisfabricio6439]

@@werdnarotcorp8991 Yhea that’s true

[@kshred3043]

@@werdnarotcorp8991 I think it is true. Speed is a rate, not ratio.

[@drdca8263]

@@kshred3043 I think you are defining “ratio” in an odd way if you don’t include things like “12 kilograms per 5 meters”

[@kshred3043]

​@@drdca8263 OK, you forced me to look up the definitions. Per Merriam-Webster: RATE - 'A quantity, amount, or degree of something measured per unit of SOMETHING ELSE'. RATIO - (a) 'The indicated quotient of two mathematical expressions' (b): 'The relationship in quantity, amount, or size between two or more things' Per Wikipedia: 'In mathematics, a RATE is the RATIO between two related quantities in DIFFERENT units.' (Emphasis mine)' 'When two quantities are measured with the same unit, as is often the case, their RATIO is a dimensionless number. A quotient of two quantities that are measured with different units is called a RATE.' So, I think it is more specific and and certainly more appropriate to call your example of “12 kilograms per 5 meters” a rate rather than a ratio. However, I will concede (reluctantly 🙂) that, because rate is apparently a special case of a ratio, your example is also ratio.

[@ivanpoljic1790]

Intresting , unfathomable...

[@noonewn]

the best example of a dimensionless number is pi. You can use feet or meters. Use one or the other but not both at once.

[@1invag]

So a dimensionless number is also what's referred to as a transcendental number? Like infinity, or zero?

[@richardfredlund8846]

@@1invag no a dimensionless number might also be just a whole number like 3 or 5, the key feature is that it doesn't matter what units you make the measurements in.

[@1invag]

@@richardfredlund8846 so essentially 3 is 3 doesn't matter wether it's 3cm or 3 metres will still be 3. What about shifting between systems, such as imperial vs metric. Does the same apply, would 3 miles still equate to 3 kilometres as an example? Or to complicate matters further how about things that aren't measures of distance? Like memory capacity on a hard drive? Here's a thought how can something that's proported to be dimensionless be used to measure spatial dimensions? See now I'm thinking aren't all numbers dimensionless anyway ffs lol

[@richardfredlund8846]

@@1invag distance isn't dimensionless, so it would make a difference if you measured in imperial vs metric. But if you are measuring the ratio of two distances then it wouldn't matter if you used imperial or metric you would still get the same answer.

[@richardfredlund8846]

the number of spatial dimensions is a bit more of an interesting example than the ratio of two distances. I'm not a physicist, so to me there are 3 spatial dimensions. That doesn't depend on what units we use either, so is probably dimensionless. (ironically).

[@WesFanMan]

Tom Hanks anyone?

[@nymoldinrui7117]

I didnt get the concept of dimensionless numbers. In my interpretation ,any ratio that is found on the nature is dimensionless.For example a table ,its width and length.No matter of what width/length will be dimensionless. Then why are dimensionless numbers so special?

[@Leberteich]

'Dimension' is a generalised concept of unit- of- measurement. For example, there are different units of length (metre, yard, or whatever), but all units of length are considered to have the same 'dimension', L, because they can be converted into each other. But a unit of length can never be converted into a unit of time or mass, which therefore are assigned different dimensions (T and M). So, say, your table's density, given by the ratio of its mass to its volume, has dimension M/L**3. There are different units of density, most commonly kg/m**3 or g/cm**3, but all conceivable units of density must have dimensions M/L**3, otherwise they aren't a unit of density. But the numerical value of density can and will be different in different units, e.g. 1 g/cm**3 = 1000 kg/m**3. On the other hand, width and length of your table both have dimension L, so can be converted into the same units. The units (and the dimesnions) then cancel in the width/length ratio. This ratio therefore is the same (dimensionless) number whatever units of length you use, and also independent of the somewhat arbitrary definitions of our units of measurement. Unlike the numerical value of density, which would be different had we chosen to define, say, the same kilogram, but a different metre. And that's why dimensionless numbers are special. Although I agree that the term 'dimensionless number' is confusing. All numbers are dimensionless. If a number had a dimension, it wouldn't be a number. 3 is a number, 3 kg or 3 m are not. 3 kg and 3 m are physical quantities, which are the combination of numbers and units. To make matters worse, there is a so- called 'number' in Physics that isn't a number because it has a dimension, that is the wave 'number' k with dimension 1/L, and units 1/m or 1/cm, whichever you like better. 🤮

[@davidhowe6905]

I think the point is that correspondences between quantities measured in particular human-made units can easily be put down to coincidence, as they would be unnoticed if one used a different unit system; but if they are dimensionless, they would be the same even for e.g. an extra terrestrial scientist, which might suggest a more fundamental origin.

[@drdca8263]

Specifically he is talking about dimensionless numbers which at least appear to be physical constants.

[@jamesdolan4042]

Well the observations from the James Webb Space Telescope (JWST) is throwing doubt on the origin of the Universe and the Big Bang theory in particular. The JWST has observed at least one completely formed galaxy so far, much too soon after the so called Big Bang.

[@nxtlightdesign7440]

continuous creation is > 6,000 years, right?

[@JoeKoOhNo]

Theoretically, yes.

[@ophello]

All numbers are dimensionless.

[@johnsolo123456]

no silly. 5 feet, for instance, is by definition a dimensional number. 5 is a dimensionless number.

[@longcours]

What about PI ?

[@johnsolo123456]

dimensionless. all pure numbers are dimensionless.

[@zdenkonovak7209]

Richard Feynman stile of talking and mind set, thank you, next...

[@MediaFilter]

Nice connection there... Spot on... Must have been the explicative style of that time for mathematicians and physicists

[@stevegreen3716]

Mark 10:39: Whoever finds their life will lose it, and whoever loses their life for my sake will find it. Like Newton, maybe the arch athetist could see further than normal mortals

[@liamthompson9090]

FYI, Newton was a deeply religious man. He spent more time studying the Bible than he spent studying Nature.

[@johnbuggy9121]

@@liamthompson9090 Was Dirac an Atheist?

[@easterntechartists]

Is it perhaps related to fractals and some sort of scaling?

[@JoeKoOhNo]

Consider Pi. Regardless of the size of the circle, Pi is constant.

[@Martinit0]

@@JoeKoOhNo Only on a flat surface aka Euclidean geometry. On a curved surface, i.e. a large enough circle on the surface of Earth the ratio between circumference and radius is no longer 2 Pi (of course, we define Pi as that number in Euclidean geometry).

[@JoeKoOhNo]

@@Martinit0 Sorry, but your explanation is incomprehensible.

[@dannygjk]

It sounds like what he means is "unitless" numbers.

[@cancel1913]

That's what is meant by dimensionless.

[@LucVignolles]

One dimension can be expressed in multiple units. e.g. lenght is a dimension and it can be expressed in any unit we created to describe that dimension. Same with Time, Electrical charge, etc. In order to get a dimensionless number though, you need to compare two quantities that represent the same dimension and are in the same unit

[@patpat5135]

There are plenty numbers that are weird : pi , e ,

[@dannygjk]

@@cancel1913 not necessarily. A number could be multidimensional but unitless.

[@cancel1913]

@@dannygjk Well now I'm confused and searching for clarification is not helping. LOL

[@chelmano0]

Einstein, Dirac and Maxwell. The greatest geniuses ever to ever live. No, Tesla's woowoo doesn't make him great. His contribution to physics is definitely huge though.

[@bailahie4235]

You forget Newton and probably Leibniz... ! If it is about physics. From math we also have some other geniuses at the same level.

[@bailahie4235]

It may be that Leibniz was in a sense already on his way towards the theory of relativity, way before Newton, although he didn't know how to formalise it adequately.

[@maxqubit]

For that big number 10^39 you need all numbers in between, 1, 2, 3, 4, ..., 10^39 To 'create' a next number it takes 1 time, thus to have the 10^39 number it took 10^39 time (atomic) ... therefor they are PER DEF the same (no coincidence) Now, the length between 4 and 5 is 1, as is the lenght between 1033 and 1034, etc but the lenght of the string of numbers is again 10^39 Felectric vs Fgravitation is this fraction. Now all numbers are not only in a string but also connected to each other. 1034 implies all previous numbers (connected) so thete are 10^39^2 'connections' ... this 10^78 number is the same as the Mass of the Universe divided by the Mass of a proton 👍

[@nschulz5698]

< | LIKE | >

[@archonphilosopher8221]

I am just about finished my second book, which outlines metaphysical fields including those ratios of dimensionless numbers. These metaphysical fields also include Attractors, and other organizing features of our world such as Fibonacci Sequence, Pi, Euler's Number, and the like. Ultimately, these are interplays among the Laws of Physical Nature that I have outlined as providing the structure for our universe. As a philosopher, I would contend that at 2:01, "provided by nature and that we should expect theory some day would provide a reason for this number" is against the observation of David Hume, that we may continue this "provide a reason" ever further and further. Coming to see that the universe contains structure unfinalizability is one step, but understanding that the reason for this is due to the equiprimordial nature of the metaphysical Laws of Physical Nature is another step.

[@Brice23]

I wonder if there is a limit to what can be deduced through the human intellectual process. Perhaps somehow there are features of nature that are interdependent but which occur beyond the limits of the methods at our disposal for interpretation. It smacks of irreducible complexity in my thoughts.. not that I fully understand the ultimate limits of human intellect. I am merely an average man..

[@aalexjohna]

Why don't you shove it up your hairy hole.

[@allmorrisvideos]

Woo woo

[@LokeyeMC]

The dimensionless number I'm most curious with is the ratio of 5:1. It seems to pop up everywhere and I have no idea why. It appears to apply at least at a physiological level in many aspects. For example, John and Julie Gottman discovered (first revealed in their book The Relationship Cure) that when good things happen 85% of the time we feel like it's 100% but when bad things happen 15% of the time, it feels like all the time. These percentages were chosen as close approximations to the 5:1 ratio, which is also what they identified is the ratio at which couples should turn towards each other's bids for connection instead of turning away, in terms of what separates a healthy relationship from those that end in separation. But when I look at the spectrum of ego development from the early 1900s (persona shadow, health ego, centaur, transpersonal, unitive consciousness) I can see that those states can be visited on occasion but don't become a trait until they are inhabited at a 5:1 ratio. Beyond that, I assume the 5:1 ratio appears in many other ways. But I do wonder if it is beyond social physiology related matters or if it's simply something within our mammalian brain structures. If anyone has insight please let me know. Thanks!

[@rikku6065]

Dimensionless numbers are ratio of two measurements of same dimensions thus doesn't depend on unit and if you change the object or situation of the measurement you can get another dimensionless number which would also be a constant. The importance of the constant, as in why only that number, comes from the pair of objects or situations we took for ratio. If we change those we would get another equally special constant.

[@sanjarcode]

You didn't understand the examples, he's talking about fundamental measurements, in the examples. The reading would be the same for any electron/proton, for example - be it an alien civilization in our universe. The mystery is why it's that number only, why not something else.

[@mito88]

​@@sanjarcode is Pi a dimensionless #?

[@sanjarcode]

@@mito88 Yes, it's literally as a ratio of lengths. But I don't think it's the thing Dirac is talking about, Pi is kind of abstract but something like e/m is physical.

[@JoeKoOhNo]

@@sanjarcode Pi is definitely a dimensionless number because it does not vary no matter what size the circle. It is exactly what Dirac is talking about. Furthermore, it isn't abstract. It's a commonly found ratio occurring in the physical realm. It also occurs in other contexts not involving geometry.

[@drdca8263]

@@JoeKoOhNo yeah, but it arises from math, in a way we understand, rather than being something we measure about the universe but have not yet found a mathematical explanation for

[@poon999able]

Um ok. I'm sure this is terribly and embarrassingly wrong. Sounds like old age got em.

[@evilotis01]

nooooooope

[@drdca8263]

I think it is more likely that this was a reasonable guess at the time, and just now seems unlikely?