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(Probably related to this one, and probably should be CW.)

A very long time ago, I had the good fortune to read George Gamow's excellent series of Mr. Tompkins books. That introduced me to the idea of a world where the usual physical constants (e.g. the speed of light and Planck's constant) were changed such that "paradoxical" effects became apparent in the macroworld.

My memory is hazy now, but I do recall the concepts of relativity (e.g. dilation) becoming more pronounced when the speed of light is reduced to "human-sized" speeds.

In this vein, I ask this: assuming all other physical constants being fixed, what exactly can be expected to happen if (physical constant of your choice) is increased/or decreased?

One physical constant per answer, please.

Community
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    I suppose that you realize that books such Mr. Tompkins are not physical at all. In them it is supposed that speed of light is decreased but that people are still the same old people which is inconsistent because people are made of elementary particles that would also need to obey new speed limit and so life (and probably also any composite matter) would cease to be possible. So are you asking for real physical effects (which usually imply that life becomes impossible) or unphysical magnified effects for better illustration of the phenomena (as in Mr. Tompkins)? – Marek Dec 03 '10 at 14:08
  • @Marek: I meant the question in a speculative spirit; that is to say, what would we be observing if we increase or decrease a certain physical constant? –  Dec 03 '10 at 14:11
  • I cannot answer your question since I am not a physicist, but João Magueijo has worked on the theory of variable speed of light (VSL) in a vacuum. – Jaime Soto Dec 03 '10 at 15:00
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    M.: it all depends on how precise you want to be. If you want to be very precise you can't really say anything because we don't know anything about complex structures in any other universe than our own. If you don't want to be precise, you are really just asking for personification of some natural effect (like Doppler shifts, length contraction, time dilation, etc.). So please answer which question are you asking: complete implication for real physics, or just personified explanation of some individual effects? – Marek Dec 03 '10 at 16:07
  • As a side note, I think a much more interesting/entertaining question is "what if the physical constants were allowed to change very slowly over space-time"? – Sklivvz Dec 04 '10 at 13:52
  • Increasing the speed of light is meaningless in itself. Marek's comment is half-accurate, the actual answer is that if you change the speed of light, keeping all else equal, nothing changes and you just redefine the meter. To keep the meter and second constant, while changing the speed of light, is the intended effect, and it is better thought of as making us really super-strong and relativistic. – Ron Maimon Mar 22 '12 at 03:05

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See Smolin's book "The Life of the Cosmos", here and here, wherein he suggests common descent and Darwinian selection amongst multiverses for peturbed physical constants maximizing black hole formation in that universe. His most recent paper on arxiv on this topic is http://arxiv.org/abs/hep-th/0612185, where he argues that this is still a live hypothesis, which has already survived several experimental tests.

sigoldberg1
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Increasing the value of $\hbar$ significantly would be pretty interesting, as matter has a wavelength proportional to it. Walking through a doorway might become a new experience as you get diffracted into a wall.

However, this is all backwards thinking. The physical constants calibrate our mathematical models of the universe, like $\lambda = h/p$, not the other way around. So it is better to say that if you got diffracted every time you walked through a doorway, you would need a large $\hbar$ to model that.

Additionally, since constants like $\hbar$ have units, their value is somewhat arbitrary anyway. Which brings us to dimensionless constants... here's a good one:

$F_{\rm{grav}} / F_{\rm{em}} \propto \frac{\frac{G m m}{r^2}}{\frac{K q q }{ r^2}} \propto \frac{G}{K}$

the ratio of the gravitational to electromagnetic force for a unit charge and mass at a unit distance.

Currently the electromagnetic force kicks gravity's butt, but I wonder what life would be like if that weren't the case.

Pete
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    Value of dimensionful constants is not really arbitrary. This is because there exist various scales in the nature. That is, speed of light is big with respect to normal velocities we observe around us (and SI system reflects this in the concept of second and meter). It's true that these are arbitrary scales of human beings but it's precisely they what allows Gamow to talk about small speed of light. Problem is, once you redefine some constant the matter will not able to form compounds and you'll lose all scales needed to talk about the change in (dimensionful) constants anyway. – Marek Dec 03 '10 at 16:02
  • The existence of scales does not negate the fact that you can make dimensionful constants whatever you want. "speed of light is big with respect to normal velocities we observe around us". That's a dimensionless constant $c/v_{\rm{normal}}$. Can't I find units where c = hbar = e = G = K = ... = 1? – Pete Dec 03 '10 at 16:32
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    @Pete: oh, if you meant your statements in this way then I completely agree with you. Scales are what enables us to define dimensionless constants and then it's indeed true that only those are really physical. – Marek Dec 03 '10 at 20:35
  • I wonder, can I really define units where all the physical constants are 1? Or do I run out of degrees of freedom at some point? – Pete Dec 03 '10 at 20:51
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    @Pete, you run out way before that. It's one of the most important problems in modern physics. E.g. the standard model has a big bunch of finely tuned constants whose measured value is unexplained at the moment. – Sklivvz Dec 03 '10 at 21:06
  • @Pete: I didn't notice the question mark at the end of your answer and thought you were talking about Planck units. @Sklivvz: this is a different question. I believe Pete was asking about setting dimensionful constants to 1. You are talking about dimensionless constants (e.g. fine structure, etc.). – Marek Dec 04 '10 at 12:17
  • I just realized that comparison of classical electrostatic and gravitational force says more about the size of the unit charge and mass than anything else. It is not a fair comparison of the strength of the forces. – Pete Dec 04 '10 at 18:05