What are the Consequences of Varying Planck's Constant?

[a.a]

Hi there, we were just introdued to the concept of Plancks theories and his constant and I was just wondering hat would the consequences be if Planck's constant were a higher or lower value than the accepted value of 6.63 * 10^-34? I would think that any change would be very significant but not sure as to how...

 

[a.a]

May be the amount of overal lenergy in the universe would increase...
because of E= hf??

 

[gn0m0n]

I'd have to think about the implications but the immediate consequence is that quantization would be more "apparent"; that is, the smaller "h" is, the closer the available values of energy, etc., are to being continuous; the larger it is, the larger the "chunks" of everything would be... sort of like comparing an old 8-bit Nintendo game to a modern PS3 - they are both ultimately pixelated but it is way more apparent in one than the other.

As to your E=hf conjecture, I'm inclined to think we would just see fewer photons with frequency f, since for the same E we would require a smaller f. Again, the subtle implications I'm not sure of.

 

[a.a]

Surely there must me some other largerscaled implucations of a change in the constant?...

 

[Michael King]

I suppose there are, but provided Planck's constant is just that, a constant, albeit a different number, then everything would still react the same way with respect to one another, just on a larger or smaller scale. The universe in general would be a different place.

It can be seen as the difference between Little-League and Pro. Same game, same rules, just cranked up a notch (or down depending on what you do)

 

[gn0m0n]

I suspect there would be a.a but I'd really have to give it more thought than I've had time to. I figured some others on here would've answered for us by now :)

 

[gn0m0n]

I mean, the peak of the blackbody curve would shift... what could that do?

I would imagine that the Planck time, distance, etc. would also change, and that could have effects...

 

[NYSportsguy]

Hi a.a. -

I think I can answer your question. The basic answer to is if we were to increase Planck's constant to say 6.62 x 10 ^2 (for example)...then a lot of principles we see at the quantum level would be experienced by us in our everyday lives.

For instance - "Wave - Particle duality" would be seen everyday when you hit a tennis ball for instance. Hitting this tennis ball you would see the ball as it hit your racket but as soon as it goes flying back into the air, the ball would become a "wave" and you would no longer be able to see this ball as a solid object again until it made contact with something else. (Similar to how electrons and photons now behave on a quantum level).

Also, similar to the Heisenberg uncertainty principle in quantum physics, if you were to go speeding in a car or a plane at say 100 mph, you wouldn't be able to measure your speed and your exact location at the same time with precision. Basically any movement at any speed (when multiplied together) its error would have to be greater than Planck's constant. Thus your navigation systems and measurement abilities would be severely impaired if you increased Planck's constant to a really high number.

 

[rbj]

there have been similar questions raised regarding if the gravitational constant, G, or the speed of light, c, have changed. you got to remember that we don't measure any dimensionful quantity without respect to another quantity of the same dimension (usually called a "unit"). like G and c, the value of \hbar is a human construct, if we measure everything in terms of Planck units, those 3 quantities become the number 1 and there simply is no G, c, nor \hbar to vary.

so a.a, it's sort of a meaningless question. asking what would happen if a dimensionless constant (such as the fine-structure constant) varied, that is not meaningless.

 

[peter0302]

Right. I like to think of dimensionful constants like h and c as conversaion factors between variables that are equivalent.

c connects space and time. h connects spacetime and energy. etc.

If you changed all of the dimensionful constants proportionally, nothing would happen. But if you changed one without changing the other, we'd live in a very different world.

 

[rbj]

Right. I like to think of dimensionful constants like h and c as conversaion factors between variables that are equivalent.

c connects space and time. h connects spacetime and energy. etc.

If you changed all of the dimensionful constants proportionally, nothing would happen. But if you changed one without changing the other, we'd live in a very different world.

ya got to worry a little bit about "proportionally". some of these dimensionful constants team up and others don't. consider the fine-structure constant

\alpha = \frac{e^2}{\hbar c (4 \pi \epsilon_0 )}

if c and \hbar both changed proportionally, say they decreased somehow with the other factors remaining constant (in terms of the units we use to measure them), then \alpha would increase and, being dimensionless, that would mean that something really is different.

i might word it as: "if some god-like being changed any dimensionful constant yet constraining all 26+ of the dimensionless constants to be the same, nothing would be noticed by mortals. if any of these 26 dimensionless constants were changed, something would be different (since they were measured and would be measured again to be different). depending on which constant gets changed and how much, we could very well be living in a different world if life (or matter) could exist at all."

 

[gn0m0n]

I'm not so sure that changing a constant would be essentially meaningless just because it has units that are chosen by humans. I mean, *how many* of those units describe something is not chosen by humans, and neither is how many of those units are relevant to other physical situations.

The argument seems to rest on something like this (excerpted from that link, which looks interesting, by the way): "...in the grand scheme of things, units are not very important. They are arbitrary human conventions." True, but as in NYSportsguy's argument, the number of those units that go into processes comparable in size, time, and whatever other dimension/scale of interest to those we experience relative to some fundamental building-block such as "h" is not a convention! In other words, it is not a convention that there is a difference between the "macroscopic" world we inhabit and the "quantum" world where the discrete nature of "h" (as opposed to continuous) becomes important. That was never a choice we had to make! It was simply where we found ourselves. The very fact we can talk about a "macroscopic" and "quantum" world is due to the vast multiples of "h" that are relevant to ordinary human affairs. However if h increases then (for instance) the de Broglie wavelength increases, too, so assuming we all stay the same size then the macroscopic world would go wonky.

A femtomenter isn't small because it's 10^-15 meters; it's "small" because WE are about 2 meters!

Or am I totally off base? :)

 

[gn0m0n]

From the same link: "The masses of these quarks, divided by the Planck mass, give 6 dimensionless constants."

Now again this does attribute some significance to the Planck mass; if we keep the units the same and take 100 times the number we'd get a drastically different quotient! The very act of making such a comparison implies that we are getting a number that tells us how many units of the Planks mass go into each quark.

Also "...the "fine structure constant", e2/ hbar c..." if hbar were 20 orders of magnitude greater, would be 1.37*10^-18 instead of 137! But of course if things adjusted proportionally then we wouldn't notice.

It is a very interesting topic. I like that fellow John Baez's stuff, too.

 

[rbj]

The argument seems to rest on something like this (excerpted from that link, which looks interesting, by the way): "...in the grand scheme of things, units are not very important. They are arbitrary human conventions." True, but as in NYSportsguy's argument, the number of those units that go into processes comparable in size, time, and whatever other dimension/scale of interest to those we experience relative to some fundamental building-block such as "h" is not a convention! In other words, it is not a convention that there is a difference between the "macroscopic" world we inhabit and the "quantum" world where the discrete nature of "h" (as opposed to continuous) becomes important. That was never a choice we had to make! It was simply where we found ourselves. The very fact we can talk about a "macroscopic" and "quantum" world is due to the vast multiples of "h" that are relevant to ordinary human affairs. However if h increases then (for instance) the de Broglie wavelength increases, too, so assuming we all stay the same size then the macroscopic world would go wonky.

A femtomenter isn't small because it's 10^-15 meters; it's "small" because WE are about 2 meters!

Or am I totally off base? :)

assuming we all stay the same size in the macroscoping world relative to what standard?

i don't necessarily want to get in a tiff about this, but i have in the past (but it was about either G or c, not \hbar, however i believe the principle is the same).

in my opinion, the salient questions are not why is c equal to 299792458 m/s? nor why is G or \hbar equal to what they are?. we know that the meter is about as big as we are (in the same order of magnitude) and that the second is about as long as a fleeting moment of thought in our experience (again same order of magnitude) and that a kilogram is about as heavy as some typical object we might pick up and hold (same order of magnitude). the salient questions are why are there as many Planck Lengths as there are in a meter? or why are there as many Planck Times as there are in a second? or why are there as many Planck Masses as there are in a kilogram? those are asking about dimensionless quantities.

Now, I don't know why an atom's size is approximately 10²⁵ L_P, but it is (and that seems to me to be a legitimate question for physicists), or why biological cells are about 10⁵ times bigger than atoms, but they are (and that seems to me to be a legitimate question for micro-biologists), or why we sentient human beings are about 10⁵ times bigger (in one dimension) than the cells that make up our bodies, but we are (a good question for biologists) and if any of those dimensionless ratios changed, life would be different. We would know the difference. But if none of those ratios changed, nor any other ratio of like dimensioned physical quantity, we would still be about as big as 10³⁵ L_P , our clocks would tick about once every 10⁴⁴ T_P, and, by definition, we always perceive the speed of light (not just light or E&M but the speed of propagation of all instantaneous interactions, such as gravity) to be c = L_P/ T_P which is the same as how we do now, no matter how some "god-like" manipulator might change it.

This same argument can be made for G and \hbar. c, G and \hbar are not "parameters" of the universe that are measurable according to some absolute scale of length, time, and mass. they are what defines the scaling of the universe. they define, in a universal sense, what the unit length, unit time, and unit mass are. the aliens on the planet Zog will have a common means to measure things with us even if we can't show them how big a meter is or any other human unit. (we might quibble about factors of \sqrt{4 \pi}, but that's not an order of magnitude difference.)

so moral of the story is this, when asking "what would be different if some universal quantity changed?" ask that if we measured everything in terms of Planck Units and remember that Nature doesn't give a rat's ass which units we use to measure things.

 

[gn0m0n]

I certainly don't want to cause any tiffs. I'm totally trying to work this out as I go. I've still not seen a derivation of where the fine structure constant comes from and so I very well might be oblivious to something important. I think I agree with you more than I first thought - I should've said that a femtometer is not small because it's 10^-15 m but because it is significantly closer to (or smaller dimensionless multiples of) the Planck length than a meter; this is an absolute sense, whereas what I was thinking of before was referring to what we as ordinary people (rather than physicists) are inclined to call small. I certainly agree that the Planck units define the scaling; I guess I was (perhaps sloppily) interpreting the original question to be about h being larger relative to us, or to be more precise, life existing on a scale of much smaller dimensionless ratios to the Planck units. But perhaps that ultimately is more a question of biology than physics - is life on such a scale even possible? Again I agree with you: if so, it would be much different.

Tiff averted (?).

 

[Orion1]

The most fundamental definition of Planck constant:
\boxed{\hbar = E_p \cdot t_p}

E_p - Planck energy
t_p - Planck time

The Planck constant is a measurement of the magnitude in which Planck energy is conserved in a Planck time dimension as a harmonic oscillator and is used to describe the sizes of quanta.

Increasing or decreasing the Planck constant changes the Planck energy magnitude conservation in a Planck time dimension as a harmonic oscillator.

\boxed{\alpha = \frac{dE \cdot dt}{\hbar c}}

Increasing the Planck constant magnitude decreases the interaction strength.
Decreasing the Planck constant magnitude increases the interaction strength.

The Planck constant is an immutable fundamental physical constant in the Universe.
[/Color]
Reference:
"[URL constant - Wikipedia[/URL]

 

[gn0m0n]

Read that thread you linked rbj. Again, I think I ultimately agree with you, although I think in this context and that one the question that was *meant* to be asked was the one that occurs intuitively to most people (apparently); still, what you point out seems to be a way around something I got confused about way back when. When I flipped through A Brief History of Time as a youngster I thought the whole notion of an expanding universe didn't make sense because I though *everything* would be expanding equally, not just space, but matter and therefore rulers, etc., as well. I guess to take that further, it would ultimately mean the Planck length getting longer along with space, in my naive conception. Since then I've come to understand cosmic expansion better but that slipperiness still worried me; perhaps these dimensionless constants give some grounding to such questions. Could you offer any mathematics or physical examples on how 1, we might try to measure a change in h but be thwarted by concomitant changes in other constants, or 2, indicate what dimensionless constant or ratios would be relevant ones, the changing of which would indicate a possible change in h? Would it not be possible to narrow down the culprit in a dimensionless constant's change by comparing a variety of them, ie, if the ratio up quark mass/planck mass changed but down quark/planck and others did not we would be inclined to say the up quark mass changed while Planck mass stayed the same I think. Hm... which again seems to indicate that changing a fundamental unit does change things...! Aaahh! Still, I guess there we're changing a ratio, too.

My brain hurts and it's 2:32 am.

 

[NYSportsguy]

The bottom line is if we all stayed the same but Planck's constant was bigger ( ie the size of light quanta and energy were bigger by nature) all the things I said would happen.

I think that is all this guy is asking...most of the rest of you are getting to philosophical with this question right now.

 

[rbj]

The bottom line is if we all stayed the same but Planck's constant was bigger ( ie the size of light quanta and energy were bigger by nature) all the things I said would happen.

call it philosophyzing, but when you speak of changing Planck's constant (or c or G) on one hand, and then qualify that with "if we all stayed the same", you need to be clear about what the meaning of "staying the same" is. stay the same relative to what? if we stayed the same relative to the Planck Units, then there is no change of Planck's constant. it won't happen. if something did change relative to the corresponding Planck unit, then that change of a dimensionless parameter is what is salient, not the fact that it gets reflected in a measurement of some particular dimensionful parameter in terms of our anthropocentric units. if a different basis of units were selected, it would be a different parameter (physical constant) that ostensibly changed. Nature doesn't care which set of units we use. if we use atomic units and it looks like c changed and then consider the very same phenomenon but use Stoney units and it looks like \hbar has changed, then how can you associate fundamental meaning to the values or either? it's the dimensionless values that matter, not the dimensionful since the latter depends on what units you use and Natue doesn't give a rat's ass which units we use.

 

[LowlyPion]

Is the dog chasing the tail or the tail the dog?

If you are not changing the fundamental nature of matter, (if you are preserving the 26 dimensionless variables discussed by the John Baez piece referenced earlier) and you are expecting that a constant that falls out of observation can just be arbitrarily changed, you've got to ask yourself what you are going to do with that tail when you finally catch it? Complain that something is biting it?

Intuitively I'd say that if Planck's constant changed, then one should expect that the dimensions of time, mass, distance would also need to change, in lock step, preserving the same relationship expressed now in the current Planck's constant. Net sum zero gain. Reprint the table of fundamental physical constants and move on.

Similarly if you changed the speed of light to be an arbitrary value of meters per second the practical effect seems to me to be that you would need to change road markers throughout the world. And good luck with that.

 

[rbj]

Is the dog chasing the tail or the tail the dog?

If you are not changing the fundamental nature of matter, (if you are preserving the 26 dimensionless variables discussed by the John Baez piece referenced earlier) and you are expecting that a constant that falls out of observation can just be arbitrarily changed, you've got to ask yourself what you are going to do with that tail when you finally catch it?

welcome to PF, Lowly. i like your PF name.

i think that we "catch it" right away. because in any observation, any physical experiment with quantitative results, the net raw results are dimensionless numbers. if either c or h or G is measured to have changed, it was measured to have changed relative to the existing standard quantities tied the the existing unit definitions. that means a dimensionless ratio has changed and rather than just say that Planck's Constant has changed (relative to e^2/(c 4 \pi \epsilon_0) or say that the Speed of Light has changed (relative to e^2/(\hbar 4 \pi \epsilon_0), we should, IMO, just say that the fine-structure constant (the net dimensionless "constant") has changed. if \alpha changed, it could be interpreted as a change in the speed of light or it could be interpreted as a change in Planck's constant, or perhaps the Elementary charge or maybe the permittivity of free space. we could define all but one of those values fixed and blame the change of alpha on whatever value was left un-fixed. but there is no good reason to blame c over \hbar or e. the salient parameter that changed was the fine-structure constant. (i like to blame it on e, but that's because i like Planck Units because what they normalize are parameters of free space and care not about attributes of any prototype, particle, or thing that would have to be arbitrarily selected.)