Why arent Plancks constant's relative?

1. Dec 14, 2004

The Quark

Just curious as to why Plancks constant's arent relative?

I mean if distance is relative to speed then how can there be a minumum distance? Or do I have a wrong view of the constants altogether. :uhh:

2. Dec 14, 2004

Staff Emeritus
Planck Length in Relativity

PLanck's length is calculated as an algebraic expression in three constants: Newton's constant of gravity, the speed of light, and Planck's constant. Assuming those are really constant, they are invariant in all frames and so is the calculation. Attempts to deal with this lead to Doubly Special Relativity (DSR) which has been discussed on several threads here, with citations to papers on the arxiv. Use the search function.

Afterthought: It's possible that G, Newtons' constant, could have a frame dependence in quantum gravity due to the conceivable running of it in a gauge theory of gravity.

Last edited: Dec 14, 2004
3. Dec 14, 2004

HallsofIvy

Staff Emeritus
Plank's constant is not a "distance". It is a measure of "action" and has very different values. You may mean "Planks length" as selfAdjoint says.

4. Dec 14, 2004

Chronos

If you are asking about Planck units [length, mass, time, etc.], they are all derived from the Planck constant.

5. Dec 23, 2004

yogi

I think the inquiry is with regard to Planck units -

I frequently speak out against the notion that these factors actually represent fundamental limitations. If we choose other things that we believe to be temporally invarient like the electron charge "e" rather than "h" we can combine it with G and c to get a different set of values for the units of length, time and mass. Stoney did this prior to Planck. Why is "h" any better than "e" ?? Moreover, if any of the factors are ultimately shown to be a variable that changes with time, then the whole idea is nonsense. It may be nonsense even if h, c and G are constant - simply cosmological numerology - unless it is founded upon some physics, we are imposing unjustified constraits upon our thinking - anytime some lenght or time emerges from a line of inquiry which is smaller than the Planck length or Planck time, the theory is immediately abandoned -

The liklihood that G, h, c, and e are God given factors that endure for all time in a dynamic expanding universe is small. There are some very strong reasons to suspect that G is a variable proportional to 1/R .. we have no way of measuring G by itself - we only measure MG - the field of the mass M that is used in obtaining the radar ranging of objects in orbit from which we calculate G, however, will change as the universe expands.

6. Dec 23, 2004

Chronos

You are taking on a huge amount of baggage with that premise. It does not work unless the big bang model, Einstein's field equations, and the standard model are seriously flawed. Given the amount of observational support, this appears highly improbable. The universe would appear much different than it does if the fundamental constants have changed over time by any more than a miniscule amount. To contend they conspire to vary proportionately to preserve the dimensionless constants is untestable, hence meaningless.

7. Dec 24, 2004

yogi

What physical principle would wreck the universe if it is shown that Planck units have no significance. You can take your argument up with Dirac if he were alive - or John D Barrow, or some of the others that have concluded for good reason that some "so called" constants may not be constant. The fact that our present techniques are limited to making measurements of ratios does not preclude the possibility that a new technique could reveal individual variability.

8. Dec 24, 2004

Rob Woodside

How big is the Planck mass? Current folklore says that quantum ideas are crucial at Planck scales. The length and time are so tiny that they are well insulated from experiment, but what about the mass? Shouldn't the Planck mass be the fundamental quantum of mass as the folklore suggests? This is just modern Pythagorianism

9. Dec 24, 2004

Chronos

Where to start. There are certain fundamental properties in nature that can only be measured, not derived from first principles [at least not yet]. There are known relationships between these quantities. Even small changes in these relationships over time would be readily detectable [and possibly life threatening] in the observed universe.

Planck's constant describes the scale at which certain physical properties can only occur in discrete [quantized] amounts instead of a smooth continuous range of possible values. The constant h describes relationship between the energy level and frequency of a photon. In this realm, the quantum realm, energy may only change in integer multiples of the Planck constant. Starting with the Planck constant, and a relatively small number of other fundamental constants, it was later found that all other physical properties of particles could be expressed in terms of the relationships between these constants. This led to the system of natural units proposed by Planck. Only five universal physical constants are needed. It is called 'natural' because the value of these five constants is 1 when expressed in units of this system. Given these natural constants occur regularly in quantum equations, the system is quite popular.

Just to be clear, the Planck constant is not some arbitrary number Planck pulled out of thin air. Planck was trying to find an equation for cavity radiancy that many other physicists had attempted without success. After Wien produced an equation that nearly fit the empirical data, Planck made a simple change so that it did. Wien's equation included two constants of proportionality, c1 and c2, whose values Wien had to hand pick to make the equation work. Planck broke the two constants into more basic factors: pi, c, k, and a factor previously unknown. Interestingly enough, the unknown factor turned out to occur in both constants. It later came to be known as Planck's constant, h.

The Planck mass is defined by the formula [(h-bar x c) / G]^1/2. The numerical value is 5.46E-08 kg, which is enormous compared to the other planck units. The reason it is so huge is that gravity is so feeble. I don't think it is accurate to characterize quantum theory as folklore. It works quite nicely.

10. Dec 25, 2004

Rob Woodside

Thanks Chronos. I certainly didn't characterize quantum mechanics as folklore. However, the supposed happenings at Planck length and time scales are, and will remain folklore, until such scales are experimentally accessible. Just as there is nothing fundamental about the Planck mass, so there is nothing fundamental about the length and time scales.

11. Dec 25, 2004

Chronos

Actually, you have. You are effectively claiming the uncertainty principle is fundamentally unsound. The experimental evidence suggests otherwise.

12. Dec 25, 2004

Rob Woodside

What??? Gone are the days when one could doubt the dispersion relations of quantum mechanics. What do the dispersion relations have to do with the current experimental inaccessibility of Planck length scales??? Scattering data suggest that the electron is coulombic and point like down to ~10^-20 m. That's a good 10 orders of magnitude larger than the Planck length. You might as well accuse me of denying evolution or some other irrelevancy!!!

13. Dec 25, 2004

yogi

Its refreshing to find someone else that doesn't blindly accept Planck units as sacrosanct - it may turn out that two of the constants (maybe h and c) are invariant - even though the third G might be proved to be a property of expansion or some other changing attribute of the cosmos. Questioning Planck units has nothing to do with questioning Planck's constant as a foundational element of uncertainty, nor does it mitigate its importance in the quantum scheme of things.

Chronos- If the universe is ultimately found to not be accelerating - the difference in the observed brightness of the 1a SN may turn out to be an effective measure of the variance of G as a separate entity (independent of some mass)

14. Dec 25, 2004

Rob Woodside

Thanks Yogi. When Dirac saw a relief map of the Atlantic Ocean floor, he intrepreted the sea floor spreading as expansion cracks and reasoned that G was getting weaker to permit the expansion. I doubt he was aware at that time that the sea floor was less than 300 million years old. Astronomers have had an unlucky time with standard candles and so when the type 1a SN were suggested I shrugged my shoulders and waited for confirmation. The CMB has provided it with Boomerang and WMAP data. The acceleration appears real ( my criteria for real, that may be wrong, is to have something experimentally verified by at least two credible and independent groups) The explanation for this acceleration may appear obvious to future generations, but it will require significant new physics. It may even require a quantum vacuum that may be the key to uniting gravity and quantum mechanics. Dark energy is just the first stab at this.

15. Dec 26, 2004

yogi

Bob - after Dirac published his LNH (large number hypothesis) in 1937 he came under attack mostly aimed at showing that a variable G would be disasterous for life on earth (Gamow and Teller specifically) - much of the argument(s) turned on the premise that a larger G in the past would have necessarily required the earth to be closer to the Sun. I was not aware that Dirac had relied upon ocean floor topography in support of LHN - I vaguely recall (may have my facts wrong), that some had argued that the cracking observed on the earths surface was evidence of a higher earth temperature in the past,

Some years ago I derived some equations that convinced me (probably no one else however) that it is the MG product that is constant and not G - If correct, as I previously posted, planetary orbits would be temporally unaffected; ergo many of the arguments raised against a varying G are disposed.

Even if h, c and G are invariant, the whole notion of combining them in a contrived manner to eliminate all but one dimension, seems more like metaphysical numerology than science.
So far, I have not seen any explanations of why Planck units are any better than Stoney units - i.e., why is h any more of a fundamental invarient than e?

16. Dec 26, 2004

yogi

One further comment: The Boomerang and WMAP experiments do not directly measure acceleration - it gets inferred from the fact that the data shows the universe to be flat - in consequence the density is critical. It is then reasoned that since only 30% or so of the cosmic energy can be accounted for, the other 70% must be in the form of unknown dark matter negative pressure which is believed to be the root cause of acceleration.