Phi And C And The Values Of Universal Constants

[A-wal]

I've heard it said the the universe is 'fine tuned' so that the 'dials' are set to exactly what they need to be for it to work the way it does. This assumes that the values of things like the gravitational constant are arbitrary rater than self-determined and could be set to something else. I don't believe that's the case.

 

 

Phi is a very special ratio that can be found throughout the universe and biology. I doubt I'm the first to spot this but just in case, this is why the phi ratio has the exact value it does:

 

1/01.618033988749895 = 0.1618033988749895

 

Dividing 1 by phi just shifts the decimal point one to the left.

 

 

The value of the speed of light must be what it is for a reason. Special relativity doesn't need it to be what it is, it would work the same regardless of lights speed as long as it's constant for inertial observers. But it can't be arbitrary and it can't be due to some mechanical process of the light itself.

 

The trouble with measuring velocity is that any unit of distance and time is arbitrary, except for the Plank length. The Plank length should apply equally to time so could the speed of light be one Plank length of distance per Plank length of time?

[CraigD]

Phi is a very special ratio that can be found throughout the universe and biology. I doubt I'm the first to spot this but just in case, this is why the phi ratio has the exact value it does:

1/01.618033988749895 = 0.1618033988749895

You’ve made an arithmetic mistake, A-wall, inserting a stray “1”

 

[math]\frac{1}{1.618033988749895} \not= 0.1618033988749895[/math]

[math]\frac{1}{1.618033988749895} \dot= 0.618033988749895[/math]

 

Written exactly,

[math]\frac{1}{\phi} \not= \frac{\phi}{10}[/math]

[math]\frac{1}{\phi} = \phi - 1[/math]

 

There are many ways to derive [math]\phi[/math], but my favorite is I think, the most obvious and traditional way, by asking the “golden ratio” geometric question “what is the reciprocal of the length of the side of a rectangle that, if added to the side of a unit square to create a rectangle, is similar to it?”. Sketched in ASCII art,

+-1-+-Phi-+

|   |     |

Phi |     |

|   |     |

+---+-----+

 

To which some quick and easy algebra give the answer “[math]\frac{1+\sqrt{5}}{2}[/math]”.

 

The value of the speed of light must be what it is for a reason. Special relativity doesn't need it to be what it is, it would work the same regardless of lights speed as long as it's constant for inertial observers. But it can't be arbitrary and it can't be due to some mechanical process of the light itself.

I agree that SR works for any value of c, but the claim that there’s a reason for it, or any other fundamental constant of nature, to have the value it does is, I think, philosophically suspect. The anthropological principle – that if the fundamental constants weren’t very close to what they are, the universe wouldn’t be a place where wonderful meat-based minds like us could wonder about them - seem sensible to me, but the bolder philosophies I’ve heard seem emotional and essentially religious.

 

Though mainstream physics holds c to have and always will have its present value, some alternative theories, especially alternatives to Big Bang cosmology, describe it and other fundamental constants as changing with time. The literature of such alternative theories is large and often low quality, but bears some thought-provoking ideas – the Wikipedia article “variable speed of light” is a decent jumping-in point for them

 

The trouble with measuring velocity is that any unit of distance and time is arbitrary, except for the Plank length.

What’s the problem with measuring velocity using arbitrarily defined units of distance an time, so long as those units are well defined, and the measurement precise enough for the application?

 

Planck units are neat because they are based on fundamental physical constants (most sources give 5, c, G, K_e, [math]\hbar[/math] and k_B, but I’m reluctant to include k_B, because I suspect it can be derived from the others, and I find [math]\hbar[/math] a sneaky constant, as it contains a [math]2\pi[/math] term) rather than the more mundane ones of more common systems (such as the span of a humans arms, the duration of a heartbeat, etc.), but I think the main effect of this is to shorten and simplify the mathematical mechanics of physics, not anything more profound. The physics could be done in any well-defined unit systems – it would just take more characters to write.

 

The base constants of Planck units aren’t for the intuitive ones of conventional dimensional analysis, Length, Mass, Time, and Charge. In particular, notice that a unit for length isn’t among them The Planck length [math]\ell_\mathrm{P}[/math] is derived from 3 constants – [math]\hbar[/math], G, c, (or arguably 4, because [math]\pi[/math] (because [math]\hbar = \frac{h}{2\pi}[/math]). By everyday intuition, that’s pretty weird – there’s no well-defined thing you can measure the length of to get [math]\ell_\mathrm{P}[/math], nor even a well-defined speed you can divide by a well defined duration – you’ve got to derive it from the speed of light, the constant relating the energy of a photon to its wavelike behavior, and the one relating mass to gravitation.

 

The Plank length should apply equally to time so could the speed of light be one Plank length of distance per Plank length of time?

Units of Length can’t, by definition, apply to time, but the as with [math]\ell_\mathrm{P}[/math], you can derive the Planck unit of time, [math]t_\mathrm{P}[/math] from h, G, c, and [math]\pi[/math], giving

[math]c = \frac{\ell_\mathrm{P}}{t_\mathrm{P}} = 1[/math]

 

This seems to me needlessly roundabout, though, as c is one of the Planck units’ base constants, so is by definition 1.

 

This assumes that the values of things like the gravitational constant are arbitrary rater than self-determined and could be set to something else. I don't believe that's the case.

But the gravitational constant G is a base constant for Planck units, so by definition can’t be derived from the others, only taken to be its observed value.

 

How do you propose to derive it from something more fundamental, like [math]\phi[/math]?

[A-wal]

Thanks for the reply.

 

You’ve made an arithmetic mistake, A-wall, inserting a stray “1”

[math]\frac{1}{1.618033988749895} \not= 0.1618033988749895[/math]
[math]\frac{1}{1.618033988749895} \dot= 0.618033988749895[/math]

So I did. From a more practical standpoint, it's the most efficient spiraling ratio for leaves so that the lower ones aren't blocked from getting sun light by the ones above and it's creates the most densely packed region for patterns like on a sun flower. Phi is absolutely fascinating. I can't believe I was never taught it in school!

 

I agree that SR works for any value of c, but the claim that there’s a reason for it, or any other fundamental constant of nature, to have the value it does is, I think, philosophically suspect. The anthropological principle – that if the fundamental constants weren’t very close to what they are, the universe wouldn’t be a place where wonderful meat-based minds like us could wonder about them - seem sensible to me, but the bolder philosophies I’ve heard seem emotional and essentially religious.

That logic works if you believe in the many worlds theory. If 99.999999% of planets can't support life then it's not weird that we're on one of the others because where else could we be, if 99.999999% of universes can't support life then it's not weird that we're in one of the others because where else could we be. I don't think that argument is needed. I'm sure (I strongly intuitively feel) that the interconnected nature of the universe precludes other values for the constants so that if were to alter one of the dials, it would have a knock on effect that would alter the others and relatively, everything would stay exactly the same, making the values effectively fixed.

 

The base constants of Planck units aren’t for the intuitive ones of conventional dimensional analysis, Length, Mass, Time, and Charge. In particular, notice that a unit for length isn’t among them The Planck length [math]\ell_\mathrm{P}[/math] is derived from 3 constants – [math]\hbar[/math], G, c, (or arguably 4, because [math]\Pi[/math] (because [math]\hbar = \frac{h}{2\pi}[/math]). By everyday intuition, that’s pretty weird – there’s no well-defined thing you can measure the length of to get [math]\ell_\mathrm{P}[/math], nor even a well-defined speed you can divide by a well defined duration – you’ve got to derive it from the speed of light, the constant relating the energy of a photon to its wavelike behavior, and the one relating mass to gravitation.

Bummer. I thought Plank lengths did have an actual length and they would remain the same regardless of length contraction and time dilation, making the speed of light constant in every inertial frame?

 

Units of Length can’t, by definition, apply to time, but the as with [math]\ell_\mathrm{P}[/math], you can derive the Planck unit of time, [math]t_\mathrm{P}[/math] from h, G, c, and [math]\Pi[/math], giving
[math]c = \frac{\ell_\mathrm{P}}{t_\mathrm{P}} = 1[/math]

This seems to me needlessly roundabout, though, as c is one of the Planck units’ base constants, so is by definition 1.

I think of a Plank unit of time as one 'frame' (as in a film). Thinking four dimensionally, a Plank length should apply in exactly the same to time as it does in the other dimensions. Information is transferred to the next unit of space for every unit of time. That would give a definite velocity that would have a very good reason for having the value it does and not changing due to a change of inertial frame of reference.

 

But the gravitational constant G is a base constant for Planck units, so by definition can’t be derived from the others, only taken to be its observed value.

How do you propose to derive it from something more fundamental, like [math]\phi[/math]?

Ah so that shows that altering one would alter the others. I don't know how to derive them from each other because I don't know how exactly they relate to each other or the maths involved. I just think that they have to be what they are and the universe isn't 'fine tuned', it's what it has to be.

[A-wal]

Units of Length can’t, by definition, apply to time, but the as with [math]\ell_\mathrm{P}[/math], you can derive the Planck unit of time, [math]t_\mathrm{P}[/math] from h, G, c, and [math]\pi[/math], giving

[math]c = \frac{\ell_\mathrm{P}}{t_\mathrm{P}} = 1[/math]

If you do this and scale up one Plank length of space over one Plank length of time do you get the speed of light? I bet you do. Plank lengths wouldn't be affected by time dilation and length contraction so you'd get a constant velocity regardless of inertial frame. :)

 

 

Btw, the golden ratio isn't just used for obvious practical reasons through natural selection, like the previous two examples. The patterns on some snakes is an example of something that can't be a direct result of natural selection. It's for camouflage but why would that ratio be favoured over something more random? This proves that it exists right at the core of life and DNA. Snakes developed coloured patterns through natural selection but life chose phi as a default go to. Why is something that's fundamental to not just life but all through nature not taught as an introduction to science in schools? What better way to inspire interest?

[CraigD]

Btw, the golden ratio isn't just used for obvious practical reasons through natural selection, like the previous two examples. The patterns on some snakes is an example of something that can't be a direct result of natural selection. It's for camouflage but why would that ratio be favoured over something more random?

I don’t know the specifics of the snake species you’re writing about, but the golden ratio can emerge from processes involving growth and geometric self-similarity, so it makes sense that many animals exhibit it, or other logarithmic and close to logarithmic spiral patterns.

 

One of my favorite physical realizations of the golden ratio are floors tiled using it. I can’t recall exactly where, but I once played music at a community center where the main floor had in its center a small metal tile with the [math]\phi[/math] symbol and some other writing, which from which square tiles of slightly different color (and when they got too big to be done with individual tiles, collections of same-colored tiles), each [math]\phi[/math] time the size of the previous one (minus a clever allowance from the grouted crack between them), so that it looked like this:

I really need to track that place down, and take a picture!

 

This proves that it exists right at the core of life and DNA. Snakes developed coloured patterns through natural selection but life chose phi as a default go to.

Life, being sloppy, usually goes with ratios slightly different than [math]\phi[/math]. Wikipedia’s “spirals in nature” is a decent jumping in point on the subject.

 

None of this should be taken to suggest that [math]\phi = \frac{1 + \sqr{5}}{2}[/math] isn’t a very special number. One way it’s special is that physical constructions that are only roughtly self similar, such as a “Fibonacci tiling” like this

Approach the ratio of a true golden rectangle tiling.

 

Math and geometry tolerate Life’s (and masons’) sloppiness, easing the ratios of sloppily made things toward perfect constants.

 

Why is something that's fundamental to not just life but all through nature not taught as an introduction to science in schools? What better way to inspire interest?

What indeed?

 

I was taught about the golden ratio and several other inspirational geometric oddities, in the 1960s and ‘70s, in West Virginia’s public school system, which ranked only in the middle of US state school systems.

 

I’ve heard and read many theories explaining why education was better or worse in a given year, state, nations, etc, much of it disagreeing about which years and states were better than which others.

• One compelling theory is that STEM education peaked in the 1950s, because WW II and cold war politics encouraged students to graduate with advanced degrees in physics and engineering, resulting in far more graduates than available specialized jobs, resulting in large numbers of them becoming teachers, and very good STEM ones.
• Another is that “New Math” was very successful, but was removed from the curriculum because political conservative parents considered it suspiciously intellectual and impractical, and part of an attempt to “program” children to hold politically liberal views.
• Another is that STEM education declined after the 1960s because of poor quality of education of teachers – that “education major” became regrettably often synonymous with “mathematically illiterate”. I think this may be an effect of a broader academic trend, which C.P.Snow famously described in his famous 1959 lecture The Two Cultures (image of text available here), in which he expressed alarm at the widening split between mathematical and non-mathematical academics.

 

Units of Length can’t, by definition, apply to time, but the as with [math]\ell_\mathrm{P}[/math], you can derive the Planck unit of time, [math]t_\mathrm{P}[/math] from h, G, c, and [math]\pi[/math], giving

[math]c = \frac{\ell_\mathrm{P}}{t_\mathrm{P}} = 1[/math]

If you do this and scale up one Plank length of space over one Plank length of time do you get the speed of light? I bet you do. Plank lengths wouldn't be affected by time dilation and length contraction so you'd get a constant velocity regardless of inertial frame. :)

 

There’s nothing about using a particular unit system, such as Planck (hey, notice there’s a “c” in Planck!), MKS, or some archaic system like imperial units, that changes the laws of nature of what you’re measuring with it. Planck units, like those of other systems, are constants. Although many of them are defined with formulae to be derived from the system’s 5 base units, they aren’t changed dynamically to behave differently than any other system’s under effects like time dilation and length contraction.

[A-wal]

I don’t know the specifics of the snake species you’re writing about, but the golden ratio can emerge from processes involving growth and geometric self-similarity, so it makes sense that many animals exhibit it, or other logarithmic and close to logarithmic spiral patterns.

Yes but you'd need a snake many miles long for that to be a factor. They way the golden ratio shows up so readily suggests that life uses it as default rather than it appearing separately as isolated instances. DNA itself uses it, and it seems to prefer using it as a solution over more random solutions. If we take that snake for example (can't find the species), if the patterns of coloured scales were completely random then natural selection would have no preference for ordered patterns of scales over messy ones. The fact that the ones that survived long enough to reproduce had ordered patterns shows that the was a preference for that initially, specifically the golden ratio.

 

Life, being sloppy, usually goes with ratios slightly different than [math]\phi[/math]. Wikipedia’s “spirals in nature” is a decent jumping in point on the subject.

I heard that plants use it more than animals, probably because they're much simpler so there's less randomness to mess it up.

 

I was taught about the golden ratio and several other inspirational geometric oddities, in the 1960s and ‘70s, in West Virginia’s public school system, which ranked only in the middle of US state school systems.

Was it part of the curriculum to were you just lucky to get a teacher who showed it to you? It's never been part of the curriculum here in the UK. Seems like anything that could inspire is left out and the whole system is designed to suppress any kind of creativity and create a bunch of soulless drones.

 

There’s nothing about using a particular unit system, such as Planck (hey, notice there’s a “c” in Planck!), MKS, or some archaic system like imperial units, that changes the laws of nature of what you’re measuring with it. Planck units, like those of other systems, are constants. Although many of them are defined with formulae to be derived from the system’s 5 base units, they aren’t changed dynamically to behave differently than any other system’s under effects like time dilation and length contraction.

I think you've misunderstood my point. If you work out a speed using other units of measurement, say 1mm over 1 nanosecond and scale that up then you'd get a velocity that decreases if you move to another inertial frame because of time dilation and length contraction. 1mm will be shortened in your old frame frame from the perspective of your new one and 1 nanosecond will be lengthened, but PanCk lengths are what they are, they can't be lengthened or shortened.

 

Does one Planck length in space every one Planck length in time give 186,000 miles a second if you scale it up?

 

 

acceleration is the absolute

I think you're missing the point of this thread but this is an interesting thought experiment concerning acceleration be relative.

 

Imagine a universe with just one object. Would it be able to accelerate? No because there's no other objects for it to change velocity relative to, there's nothing to accelerate towards or away from. Now imagine everything in this universe accelerating in the same direction so that the distance between every object stays the same. Would that require any energy? No because nothing would change, everything would experience the same amount of time dilation and so they'd be no time dilation so it's just another way of saying nothing accelerates. Acceleration is just as relative as velocity, it's a change in velocity relative to other massive objects.

[CraigD]

They way the golden ratio shows up so readily suggests that life uses it as default rather than it appearing separately as isolated instances.

Biology has many spirals and self-similar polygons, but most are not close to [math]\phi[/math], so I would say [math]\phi[/math] actually does appear in isolated instances. For example, one of the most common examples given for “the golden ratio in biology” is the arrangement of leaves on a plant stem (phyllotaxis). However, repeating angles is 1/2 and 1/3 rotations are common, as are 2/5, 3/8, and 5/13. Remarkable, most of these angles are, in units of rotations (365 deg, [math]2 \pi[/math] radians), the quotients of terms of the Fibonacci sequence [math]\frac{F_n}{F_{n+2}}[/math]. In the same way that [math]\lim_{n \to \infty} \frac{F_{n+1}}{F_n} = \phi[/math], [math]\lim_{n \to \infty} \frac{F_n}{F_{n+2}} = f = \frac{1}{\phi +1} = \frac{1}{\phi^2}[/math], the golden angle, so by this coincidence, if follows that the petals on plant with many small ones, like sunflowers, have them separated by nearly the golden angle.

 

As this paper referenced by the Wikipedia article argues, golden spirals also appear in patterns of cells in the cornea.

 

This and papers like it don’t however, claim that [math]\phi[/math] is somehow encoded genetically in plants and animals, but rather that it arise from the biochemistry that governs how biological cells grow and arrange themselves. Such structures also arise in many-bodies non-biological, like the M51 spiral galaxy.

 

DNA itself uses it ...

I consider this claim to be something between an misunderstanding, exaggeration, and a scientific myth.

 

Consider the page titled “B-DNA has spirals in phi proportions” at the Phi-dedicated site goldennumber.net. Immediately in the article, it explains “It [DNA] measures 34 angstroms long by 21 angstroms wide for each full cycle of its double helix spiral.” 34/21, which is [math]\frac{F_9}{F_8}[/math], evaluates to about 1.6190476, which looks close to [math]\phi[/math]’s about 1.6180340. However, the pitch of the B configuration of DNA (the most common in plants and animals) varies depending on the base pairs and many other chemical influences – the molecule is “springy” – and is more commonly measured to be about 32.2/22, which evaluates to about 1.5090909, which doesn’t look much like it. By fudging these integer up and down less than 1, which, given the amount they actually vary in their springy way, seems permissible, it’s possible to make [math]\phi[/math] look like a unwavering constant of the structure of DNA. But it’s not – this is merely fudging.

 

…and it seems to prefer using it as a solution over more random solutions.

I think all the data we’ve discovered in this thread shows this to simply be false. Biological nature uses many repeating shapes, which leads to many logarithmic spirals, of which the golden spiral, which has a pitch given by [math]\phi[/math], in a special case, but only a minority are near the golden spiral, and those only approximately.

 

Some structures in nature follow other interesting constants, like the silver ratio, [math]\delta_S = 1 + \sqrt{2} \dot= 2.4142136[/math]. The logarithmic spiral of nautilus shells follows it.

 

The silver ratio could also be used to make an interesting floor tile pattern, though I’ve never seen an example. If you take a silver rectangle and add a square to its long side, you get a rectangle with sides [math]\frac{\delta_S+1}{\delta_S} = \sqrt{2}[/math]. If you add a square to this rectangle, you get another silver rectangle. And so on.

 

If we take that snake for example (can't find the species)...

I wish you could find that snake. All the snake scales I’ve seen are pretty regular, usually following a rhomboid tiling pattern, often with beautifully complicated patterns of contrasting colors, but I’ve never seen or heard of one (Even with the help of a web search) that followed a logarithmic spiral or special tiling.

 

... if the patterns of coloured scales were completely random then natural selection would have no preference for ordered patterns of scales over messy ones.

Ordered patterns in animals are usually, I believe, due to the way cells signal one another. Genes code for the biochemistry of this signaling, but don’t actually contain “specifications” for the resulting patterns. You could say the patterns “emerge” from the biochemistry.

[A-wal]

"The DNA molecule measures 34 angstroms long by 21 angstroms wide for each full cycle of its double helix spiral. These numbers, 34 and 21, are numbers in the Fibonacci series, and their ratio 1.6190476 closely approximates Phi, 1.6180339."

 

We've gone into detail about something that really isn't the point.

I've heard it said the the universe is 'fine tuned' so that the 'dials' are set to exactly what they need to be for it to work the way it does. This assumes that the values of things like the gravitational constant are arbitrary rater than self-determined and could be set to something else. I don't believe that's the case.

 

 

Phi is a very special ratio that can be found throughout the universe and biology. I doubt I'm the first to spot this but just in case, this is why the phi ratio has the exact value it does:

 

1/01.618033988749895 = 0.1618033988749895

 

Dividing 1 by phi just shifts the decimal point one to the left.

 

 

The value of the speed of light must be what it is for a reason. Special relativity doesn't need it to be what it is, it would work the same regardless of lights speed as long as it's constant for inertial observers. But it can't be arbitrary and it can't be due to some mechanical process of the light itself.

 

The trouble with measuring velocity is that any unit of distance and time is arbitrary, except for the Plank length. The Plank length should apply equally to time so could the speed of light be one Plank length of distance per Plank length of time?

I'm more interested in your opinion of the initial points.

[exchemist]

"The DNA molecule measures 34 angstroms long by 21 angstroms wide for each full cycle of its double helix spiral. These numbers, 34 and 21, are numbers in the Fibonacci series, and their ratio 1.6190476 closely approximates Phi, 1.6180339."

 

We've gone into detail about something that really isn't the point.

I'm more interested in your opinion of the initial points.

Since the Planck time is defined to be time taken for light in vacuo to travel a distance of the Planck length, the answer to your last question is clearly "yes".

 

I agree with Craig that the explanations for the appearance of various ratios in nature is due to the way natural processes such as growth occur. It is fascinating but I don't think we should over-interpret it.

[A-wal]

Since the Planck time is defined to be time taken for light in vacuo to travel a distance of the Planck length, the answer to your last question is clearly "yes".

Oh, it is. I see. That makes sense. :)

 

I agree with Craig that the explanations for the appearance of various ratios in nature is due to the way natural processes such as growth occur. It is fascinating but I don't think we should over-interpret it.

Maybe you're right, it's just that it's so widespread in nature. 1/01.618033988749895 = 0.618033988749895 is pretty amazing though, especially finding it yourself.

 

I've heard it said the the universe is 'fine tuned' so that the 'dials' are set to exactly what they need to be for it to work the way it does. This assumes that the values of things like the gravitational constant are arbitrary rater than self-determined and could be set to something else. I don't believe that's the case.

I still believe that the so called 'dials' of the universe being exactly what they need to set to is in fact what they have to be set to because changing one would effect the others and relatively everything would stay the same. For example, a slower speed of light would lead to a smaller universe with less energetic atoms and nothing would actually change because proportionally everything would be the same.

[exchemist]

Oh, it is. I see. That makes sense. :)

 

Maybe you're right, it's just that it's so widespread in nature. 1/01.618033988749895 = 0.618033988749895 is pretty amazing though, especially finding it yourself.

 

I still believe that the so called 'dials' of the universe being exactly what they need to set to is in fact what they have to be set to because changing one would effect the others and relatively everything would stay the same. For example, a slower speed of light would lead to a smaller universe with less energetic atoms and nothing would actually change because proportionally everything would be the same.

I've never come across that idea before. That would mean that fundamental constants that appear independent are in fact not independent of each other. Is this based on any theory, or is it a metaphysical speculation of yours? (Nothing wrong with metaphysical speculation, so long as we know that it what it is :) )

[A-wal]

It's just a metaphysical speculation. But one that makes more sense the more I think about it. It might even be provable mathematically.

[exchemist]

It's just a metaphysical speculation. But one that makes more sense the more I think about it. It might even be provable mathematically.

Hmm. Not sure how, if the constants in question are, according to current theory, independent. But it's an attractive idea, I grant you.  

[A-wal]

Yea, at the moment they're treated as independent but in principle it should definitely be mathematically provable.

 

I think the hardest one to tie together with the others would be the gravitational constant.

[A-wal]

Warning: HUGE over simplification!

 

Reduced speed of light = Lower rest mass of quarks and leptons due to E=mc^2 = Reduced Planck constant due to lowered minimum increments of energy = Smaller universe, as it's size is directly determined by it's total energy density, meaning light takes the same amount of time to cross the universe = Lower gravitational constant, as the strength of gravity is determined by the geometry of spacetime = No change what so ever.

 

 

Fine Tuning Problem

1. God did it.

2. If it wasn't the way it was we wouldn't be here to ask the question (debatable whether that's a real answer).

3. There's lots of universes.

4. It couldn't possibly be anything else because they're interdependent.

 

Four! :)

[exchemist]

Warning: HUGE over simplification!

 

Reduced speed of light = Lower rest mass of quarks and leptons due to E=mc^2 = Reduced Planck constant due to lowered minimum increments of energy = Smaller universe, as it's size is directly determined by it's total energy density, meaning light takes the same amount of time to cross the universe = Lower gravitational constant, as the strength of gravity is determined by the geometry of spacetime = No change what so ever.

 

 

Fine Tuning Problem

1. God did it.

2. If it wasn't the way it was we wouldn't be here to ask the question (debatable whether that's a real answer).

3. There's lots of universes.

4. It couldn't possibly be anything else because they're interdependent.

 

Four! :)

I don't think a lower Planck's constant follows, does it? Mass influences energy increments via its appearance in the equations of QM, such as Schroedinger's. And actually in those equations so far as I recall, lower mass tends in increase energy level spacings, not decrease them. So a lower value for h would tend to get you back to where you were, wouldn't it? But I don't see any necessity for h to change. 

[A-wal]

I'm not sure, I don't know QM nearly well enough to do this properly, just thought I'd have a try.

 

This needs someone with better knowledge than me to tie them together properly conceptually and someone with seriously better knowledge to do it empirically as an equation with interdependent variables so that they're no longer variables at all.