Talk:Planck force

The original article was a very brief analysis (or definition) of Planck force in terms of Planck energy and Planck length. Planck force is not exclusively related to the Planck scale and this had to be pointed out. Lucretius 01:50, 13 January 2006 (UTC)


 * in any unit system, force is the deriviative w.r.t. time of momentum. in any unit system, the unit of force is always the unit momentum divided by the unit of time. that's where the definition belongs.  this other stuff you added may or may not be accurate (you need to cite verifiable links and define other terms in the article otherwise it original research) but the definition of the Planck force is no different than the definition of the unit force in any other system of units. r b-j 20:48, 14 January 2006 (UTC)

Yes, you can express force as momentum/time. You can also express it as Kg.m/s^2 or J/m or simply Newtons. I don't understand why you think the definition belongs only with momentum/time and surely you don't expect me to provide links to these common dimensions of force. I should also point out that the original article included the definition Planck energy/Planck length, ("Planck energy divided by Planck length") which is of course Joules/metres. There is nothing original in the observations I made - these are basic relations. I'll add that the expression of force as m^2c^3/hbar is simply a rephrasing of Joules/metres, as indicated by the = sign in the article. When m is the electron, the force is associated with the Schwinger Effect, and Schwinger acceleration is mc^3/hbar. As I said, there is nothing original here. There is nothing original in the observation that Planck length is both a Compton wavelength and a G radius. The final equation isn't mine either - it's a well-known relation. What on Earth is original here?! Please point this out to me so that I might either laugh at your ignorance or blush at my own.

Regarding 'format' and 'convention' errors you mentioned, please let me know what these were as everything looked fine to me. Lucretius 03:57, 15 January 2006 (UTC)


 * "I don't understand why you think the definition belongs only with momentum/time." the reason is pedagogical within the physics discipline.  it would be a tautology to define the Joule as the amount of energy required to move a body against a force of 1 Newton the distance of 1 meter, then at the same time, define the Newton as 1 Joule per meter.  it's true but it says nothing about the quantities of the Joule or of the Newton (nor anything about their dimesion).  it is not like the chicken and egg, we know which one comes first (meter, kg, second come first, then the Newton before the Joule). the Planck force is a derived unit and will have to be the Planck unit of momentum divided by the Planck unit of time.  the fact that it comes out to be the basic tension in string theory or in, general relativity, the force that is the conversion factor between spacetime curvature and the energy density giving rise to it or, if multiplied by the fourth power of the (dimensionless) circular orbit speed some distance from a central body that it tells what the body would weigh at that distance, all these are fine and good, but they are the result of working out hypothesized physics problems, they are not the definition .  what if you worked out some other basic physics problem (say the basic tension of a string) and it came out to be 2 FP? or 4 &pi; FP?  would you say that the force solutions to such are the definition of the Planck force?  it doesn't matter what the system of units are, once you have those 5 base units defined, there is no freedom left to define the others.  their definitions are purely consequential.
 * i think you need to word things according to the most common terminology. i fixed it a little more.  i inserted edit notes (invisible) that ask what does it mean to "distribute energy over a gravitational radius"? and what does it mean to "distribute energy over the Compton wavelength"?  unless you expect your encylopediac readers to know, even vaguely, when or where or how or why such distribution of energy is being done (thus defining the rate of such distribution), why say these words?  also, there still is no citation other than Schwartzchild radius, which i did.  so a reader does not think that this was all just made up, you might want to include references to other stuff.
 * i fixed the convention errors and format errors (some just now). do a diff comparison to see what i did. r b-j 04:27, 15 January 2006 (UTC)

This is a much better answer than I anticipated. My responses:

1) it isn't true that Planck force is simply a force derived from Planck units. Have a look at the following link, where the argument is that Planck units can in fact be derived from Planck force. You'll also find there this quote: ""Planck force is, along with the speed of light, the Planck quantity existing most plainly and simply in nature." To argue, as you seem to do, that Planck force should be explained only in Planckian terms is like arguing that the speed of light should also be defined primarily in Planck terms. The link:

You might also consider this other link where it mentions the relation between energy, Planck force and 'gravitational length':. Also this relation energy/length was in the original article.

2) I provided the equation for 'gravitational radius' so that people would not confuse it with the Schwartzchild radius. The gravitational radius is like the electromagnetic radius - Ke^2/mc^2 and Gm^2/mc^2, though I have cancelled out a bit for convenience.

3) Yes, joules/metres can look like a tautology. I used it because it was already in the original article ("Planck energy divided by Planck time"), and because that seemed to me in the circumstances the best way of relating Planck force both to Compton wavelength and 'gravitational radius'. I might be able to find a reference for force expressed as Joules/metres but I hardly think it needs one, being such an obviously implied relation that you call it a 'tautology'.

Thanks for giving my earlier reply a good answer. Lucretius 05:03, 15 January 2006 (UTC)


 * i see you made some references to www.planck.com. Leonard Cottrell is a good guy, i've had some email chats with him very long ago.  i'm glad he's doing the web page, but be careful with using that as an authoritive reference.
 * you say I provided the equation for 'gravitational radius' so that people would not confuse it with the Schwartzchild radius. are they not the same?  they link to the same page here and have the same definition (that's why i changed it to rs).
 * "Planck energy divided by Planck time" is Planck power. "I might be able to find a reference for force expressed as Joules/metres but I hardly think it needs one, being such an obviously implied relation that you call it a 'tautology'." but the point is you need to define one before the other, and pedagogically force comes before energy.  also, you are often confusing units of physical quantity with dimension of physical quantity.  they are not the same.  r b-j 05:19, 15 January 2006 (UTC)

No, the Schwarzschild radius is not the same as the gravitational radius, though there is a tendency to confuse the two. Don't take my word - go to the following link and look at the notes down the bottom of that page, where it says "in actuality the quantity 2GM/c^2 is not the gravitational radius, rather it is the Schwarzschild radius, which is twice the gravitational mass Rs=2Rg." .


 * this link does not help you. they use the term "gravitational radius" but they define it to be the same as Schwarzschild: "gravitational radius of R_g=2GM/(c*c) ~10**15 cm."

(The note I referred to is a comment on the quote you have just given me - it is a correction of the other position. Lucretius 00:57, 16 January 2006 (UTC))

In fact you can find many websites where the gravitational radius is shown to be half the Schwarzschild radius. I've now edited the Schwarz page to point out that a Schwarz radius is not synonymous with a grav radius, and I've included there a link to the hyperphysics website.


 * neither does this link. it does not define the expression you call "gravitational radius" to have any name, but notes that the Schwarzschild radius is twice as big.  Britannica says that "gravitational radius" and "Schwarzschild radius" are the same thing as did Wikipedia before you changed it.  you are not supporting your usage of terminology.  my 30 year old astrophysics text doesn't even have the term ("gravitational radius") at all, and i did not recognize it as having anything to do with Schwarzschild radius until later.  the event horizon of a black hole is the Schwarzschild radius (with the "2" in it), so what is this "gravitational radius" and where are you drawing its definition?

(The Hyperphysics article defines the radius I refer to but I concede that it does not call it a 'gravitational radius'. It mentions that this is not the same as the "Schwarzschild calculated gravitational radius" - I understand the implication to be that this is a different kind of gravitational radius, and I think that is a fair inference. However, you are right to think an inference is not good enough. I spent many hours looking for an appropriate link until I came inevitably to the same conclusion as you did - there is no clear support for my use of 'gravitational radius'. Lucretius 00:57, 16 January 2006 (UTC))

Your changes to the equation simply make the equation wrong and meaningless and I have therefore edited those changes out of the Planck force article. I concede however that 'distribution of energy over radius' is not scientific phrasing - it's simply a mathematical statement and it's a bit confusing if it is somehow thought to refer to a physical process. I've now changed the phrasing with that criticism in mind. However, I've also added a link which uses the same phrasing energy/length in terms of the Schwinger Effect - the link is good also to demonstrate that I have not invented a new way of expressing force. By the way, I'm perfectly happy with your new intro to the article, which is better than the original.

Please don't give me 'pedagogically force comes before energy' - pedagogy is teaching method and it's not necessarily a criterion about content. This article is about force and you can hardly explain it in terms of itself.


 * it's an encyclopedia. besides being self-consistent in the ideal, what else is its purpose?  you can define force as energy per length, but you don't have a concept of energy, at least not a quantitative concept.  how do you think they get E = mc2 or KE = 1/2 mv2?  why would energy take on such dimension as mass•length2•time-2?  from existing concepts, you have to define energy.
 * even if you were to yank out the fact that these articles are meant to be teaching someone who doesn't know Planck force about Planck force (or someone who doesn't know force about force), but if this were a purely scientific endevour, pedagogical principles have application (this is one reason a decent scholar recognizes him/her self as a lifelong student). the need for concept flow, where one concept is defined and developed before going to the next remains necessary.  there is no way that you'll be able to conceptualize "energy" into a physical quantity having dimension of mass•length2•time-2, without first conceptualizing force.  that is how a system of physical units has to do it.

(The fact that force comes before energy does not mean you can't express force in terms of energy. I followed the intentions of the original author, who chose to express force as energy/length. I built on that. If you want to start with momentum/time, that's fine. I don't care either way, just so long as Planck force is explained in a number of different ways. That variety of ways should include a derivation that isn't in Planck units, whereas you seem insistent that Planck units is the only way it can be explained. The radius referred to in the Hyperphysics link is another way of explaining Planck force - a mass undergoes gravitational collapse to the point where its gravitational potential energy is equal to its electromagnetic energy, and at that point the force is Planck force.Lucretius 00:57, 16 January 2006 (UTC))

Also please give me a specific example of how I am confusing units with dimensions.


 * "Since the dimensions of force, Newtons, can be rephrased as Joules/metres, ..." the dimension of force is "force", or if you want it more specific, the dimension of force is mass•length•time-2.  or, if the concept of energy is already defined or is a base physical quantity (it's not) the dimension of force is energy•length-1.

'''(How does this prove that I confused units with dimensions? The dimension of force can be phrased in several ways, as you just pointed out. Also the concept of energy does not have to be defined in this article except as mc^2, which I have done.Lucretius 00:57, 16 January 2006 (UTC))


 * Newton is a unit of force. so is Dyne or pound.  but the dimension is "force" or equivalently mass•length•time-2.  likewise Joule is a unit of energy whereas the dimension is "energy" or force•length or mass•length2•time-2.  metre or "meter" is a unit of length and the dimension is "length" and is a base or primary dimension of physical quantity (but some physicists do not concede that, they say that time and length are the same thing) so it cannot be expressed in terms of other base quantities.  a good system of units will have exactly the same number of base units as there are base dimensions.  these units are a specific anthropometric creations (except for Natural units, be they Planck or Stoney or whomever), the dimension of physical quantity is something considered by most phyicists to be more transcendent. the intelligent aliens on the planet Zog for sure will have no idea what a Joule is, but they will likely know what the physical quantity we call "energy" is.

''Thanks for taking this further. However I still don't quite understand the objection you are making. I say that Joules/metres is one way of phrasing the dimension of force, even though Joules and metres separately are units. When I use energy/length here in the discussion page, I was following your usage - it was the usage you used in revising my edit when you referred to 'energy per length'. That was not my wording. Are you saying it is alright to use energy/length but it is wrong to use Joules/metres? I really would like to understand your argument but the way you express it makes me think you don't really understand it yourself. You'll need to be clearer and to phrase it more carefully.''Lucretius 05:52, 16 January 2006 (UTC)

Regarding my mental slip (energy/time), of course I meant length rather than time, as the context and previous references should have made clear (why insert Planck power, unless of course you are a school teacher?). I might add that you have mispelt Schwarzschild. Because I am a school teacher :) Lucretius 06:31, 15 January 2006 (UTC)


 * in the article?? i copied the link and it is not a red link.  did they misspell it??? r b-j 20:02, 15 January 2006 (UTC)

'''No, you got it right there - you mispelt it here on the discussion page. See my insertions above for other answers to your comments.'''

Now for some humble pie: I have to revise my position on some things after some more research of my own. Firstly, after hours trying to find where I got the term 'gravitational radius', I have to admit there is no clear, authoritative reference to it (I could only come up with a 'note' by a professional physicist and an implication in the Hyperphysics website, and obviously that is not enough). There is overwhelming support within the science community for the Schwarzchild radius to be known as the 'gravitational radius', which means I will have to undo the change I made to the Schwarzchild article. In fact I have already undone it. It also means I can't use the term 'gravitational radius' in the Planck force article. I have to agree with you about that. In other words, the article on Planck force will need to be revised again. It is still important to include in it the fact that Planck force is not exclusively derived from Planck units. The links I provided are proof of that much at least. To insist that it can only be explained in Planck units is pure dogmatism on your part.

Again, sorry I caused you some initial confusion regarding 'gravitational radius'. Thanks again for the time you have given to answers and questions. I enjoy a debate even when I am shown to have got something wrong, as is the case with 'gravitational radius'. Debating is the best way to test out knowledge. In spite of that error, I was right to edit the Planck force article and I am right in believing that we need to go beyond a simple definition in terms of Planck units. Cheers Lucretius 23:39, 15 January 2006 (UTC)


 * there are two things,... no three: 1. pedagogy is salient. we need to present concepts in the order in which they are best conceived. 2. consistency with other related WP articles is salient, that includes style, nomenclature, and notation (math symbols).  3. accuracy: i don't write something up here in the articles (talk pages are different) unless i'm real confident that i know precisely what i am talking about.  and even so, i still get in fights.  dunno why. :-)  r b-j 02:45, 16 January 2006 (UTC)

I just re-edited the Planck force article substituting 'half the Schwarz radius' for 'grav radius'. Regarding the points you made, I agree with point 2, though I'm worried that 'consistency' might translate to the domination of a particular perspective that isn't necessarily the only perspective (e.g., as far as I can tell you give a preponderant emphasis to natural units, which is the brainchild of theoretical physics, while blokes who subscribe to such things as variable c tend to emphasize the importance of experimental physics and are not really all that interested in theoretical edicts, as shocking as that might seem to you). Regarding point 3, you have my sympathy (there is this bloke here at Wiki called Rbj and he always gives me a hard time). Regarding point 1, I agree so long as you don't become dogmatic about it. The fact is we can't in every article present concepts in the order in which they are best conceived, and this is even assuming that we all agree about the right order and that we all interpret it in exactly the same way. Otherwise, first beginnings would have to repeated over and over and over again. Secondly, I still don't understand why you think I have broken some profound law simply because I define force in terms of energy/length. This is a perfectly acceptable definition and I don't have to arrive at it from first principles when those principles are covered elsewhere. Also I said I'm happy with your intro, which I assume you consider to be a good foundation for the whole article. My belief is you are using this 'right order' notion simply to justify your opinion that Planck force can only be derived from Planck units, and this seems to me like an attempt to stifle other perspectives under the mask of 'pedagogical orthodoxy'. I've given you links showing that Planck force is not exclusively understood in Planck terms. It is a force that would be understood to exist even if Planck units had never been conceived. It refers in fact to a particular strength of the gravitational force, which has physical explanations that don't require Planck units.

Anyway, I luv you heaps but i still aint convinced you've fully understood your own arguments. If you did, and if they were valid, you would have convinced me by now. I listen to reason and I am not too stupid to understand a well-reasoned argument. I only have to look at your invariant scaling article on the Planck Units page to know that you don't always practise what you preach here. That article looks to me like a pedagogical nightmare. The fact that Sdedeo messed it up further only proves that it looks like a draft and it invites indiscriminate editing. But I do respect you for your willingness to argue and I do concede that you were absolutely right to question my use of 'gravitational radius'. I'd be happy to be proved wrong in future also. Just for the record, your arguments against my edits on the Gravitational constant page are good and I accept that I could have expressed that better. By which I mean I can eat humble pie without choking. Lucretius 05:30, 16 January 2006 (UTC)


 * "I still don't understand why you think I have broken some profound law simply because I define force in terms of energy/length." because, as you say, you are defining force.  that means what you're calling it is a definition.  but one of the terms you use to define force is, itself, defined by use of the concept of force.


 * "This is a perfectly acceptable definition and I don't have to arrive at it from first principles when those principles are covered elsewhere." the only problem, besides that it is not a definition (what you are doing is solving a physics problems whose answer is a quantity of force), if the result of your derivation of this "Planck force" came out to be quantitatively different than one Planck unit of momentum divided by the Planck time, a whole bunch of equations of physical law would have to be rewritten with some dimensionless (and extraneous) conversion factors tossed in.  like F = 2ma.


 * "I listen to reason and I am not too stupid to understand a well-reasoned argument. I should add that I could say the same about your mate Duff - he just doesn't seem to understand that people would not disagree with him if he was demonstrably right and if he explained his meaning clearly. The fact that he hasn't convinced a lot of very intelligent people is proof that the argument he puts forward is debatable." first of all, in the trenches, i don't think that very many physicists dispute Duff (in favor of Moffat, Davies, or Magueijo even if they get more attention in the popular press).  go to sci.phyics.research and ask those guys questions and find out.  5 or 6 years ago, i thought that G sorta defined the "strength of gravity" and, even if it is dimensionful, was somehow set by Nature or God (whatever your philosophy) until i was set straight by John Baez, Jan Lodder, Ted Bunn, and others there.


 * The reason Duff (who is really not the main partisan in this VSL debate, but is the most vocal about it in the lit) is "demonstrably right" (over Moffat, Davies, or Magueijo) is that even a dummy engineer like me know that we never measure any dimensionful physical quantity directly. we always measure such a quantity against a like dimensioned standard (as a ratio).  so we end up always measuring things as dimensionless numbers.  and these technological instruments are just extensions of our basic perception of how big or heavy or old something is.  we perceive everything as anthropometric ratios.  it is those dimensionless numbers that count.  if you say "the speed of light has changed", i can find upon investigation what the actual dimensionless number that you perceived has changed (likely to be &alpha;) and that dimensionless number remains the only salient quantity that has changed in our perception.  if you say "that's just our perception, not necessarily reality" i say that every quantitative equations of physical law you can find in any textbook or paper in the lit can be nondimensionalized, expressed in a form that all of these quantities are normalized against some set of natural units and those dimensionful constants of nature just go away.  they're not around anymore (they've been changed to 1) to change.  there can't be a VSL if there is no c.  there can't be a "varying-G" if there is no G.


 * These dimensionful numbers come out to be what they are because there are about 1025 lP in the size of an atom, and there are about 105 atoms across the diameter of a biological cell, and there are about 105 cells in the length of beings like us (and we define the meter or the foot or whatever to be about as big as we are). a similar argument can be made that there are about 1044 tP in a second.  since, by definition, c = 1 lP per tP, it's just a matter of arithmetic to work out that c = 299792458 m/s, but rather than ask "why is c = 299792458 m/s?", the salient question to ask is why there are about 1025 lP in the size of an atom or why there are 1044 tP in a second, as well as the other dimensionless numbers.  if you answer those more fundamental questions, then you answer why c is perceived or measured to be what it is perceived or measured to be.  That is an argument this 5 decade old electrical engineer can understand and i cannot see how Moffat, Davies, or Magueijo or the New York Times can ever dispute it.  BTW, i had been reading John Barrow The Constants of Nature (2002) and he agrees with Duff on p 49.  He might not even think of it as "agreeing with Duff" but more of a fundamental principle.  Duff just happens to be the one taking on Moffat, Davies, or Magueijo most vocally. IMHO, what Duff (or Barrow or Baez) is saying is very conservative.r b-j 05:42, 16 January 2006 (UTC)

Rbj thanks again for trying to set me straight. But can we do it one thing at a time? I've replied to an earlier insert you made and I copy my response here. If you can answer this lucidly, we'll be on the first step of mutual understanding (I hope). The stuff about Duff (there's a rhyme in there somewhere) can be dealt with later and probably isn't really necessary (I raised that subject and I accept the blame for going outside the limits of this page). My response is here:

''Thanks for taking this further. However I still don't quite understand the objection you are making. I say that Joules/metres is one way of phrasing the dimension of force, even though Joules and metres separately are units. When I use energy/length here in the discussion page, I was following your usage - it was the usage you used in revising my edit when you referred to 'energy per length'. That was not my wording. Are you saying it is alright to use energy/length but it is wrong to use Joules/metres? I really would like to understand your argument but the way you express it makes me think you don't really understand it yourself. You'll need to be clearer and to phrase it more carefully.'' Lucretius 06:02, 16 January 2006 (UTC)

By the way, I noticed on the history page you say that the Planck Compton wavelength is the Schwarzschild radius. That isn't right - it's half the Schwarzschild radius. Do the calculation yourself - Planck length is equal to GM/c^2 not 2Gm/c^2.Lucretius 06:17, 16 January 2006 (UTC)


 * yes, L, for the umpteenth time, Joules/meter is a quantity of force that is equal to the unit of force we call a "Newton". "Energy" is a (derived) dimension, "length" is a (base) dimension. "energy per length" is a dimension equivalent to the dimension of quantity we call "force". r b-j 06:19, 16 January 2006 (UTC)

This is clearer and it's a good starting point. I accept this. Now I'd like to know exactly which parts of my edit you wish to undo and could you please explain why you think they need to be undone (I mean changes you intend to make and not those you have already made). Also in the history page you mention that there is a certain roughness in Planck values. That's true but its only due to experimental uncertainties. Choose any particular value for G, and a particular value for Planck mass emerges in terms of the known values for c and hbar. Use those values to prove to yourself that the Planck length is half the Schwarz radius. Or maybe you already understand this, though your comment on the history page suggests not.Lucretius 06:40, 16 January 2006 (UTC)

I looked at your recent edits, Rbj, and I think r_s/2 does help with clarity. However, I simply can't agree that "the force is roughly Planck force for the Planck mass." It is exactly Planck force - experimental uncertainties in the value of G don't matter because these are offset by corresponding uncertainties in Planck mass. Consider this relation: Gm^2=chbar. We know the precise experimental values on the RHS, so any change you might want to make to G is offset by an inverse change in the value of m^2. Divide both sides by mc^2 and you get Gm/c^2=hbar/mc. Divide mc^2 by either of these lengths and you get Planck force exactly (C^4/G=m^2c^3/hbar). There is nothing roughly about it. You can phrase it in terms of natural units but the result is still Planck force exactly. In fact that's probably the easiest way to get a handle on the issue: G=c=hbar=1, therefore Planck mass=1, Planck energy=1 and Planck length=1, therefore Planck energy divided by Planck length is 1 and c^4/G=1. It isn't roughly 1 but exactly 1. Also I notice that the word 'half' has disappeared from the last reference to the Schwarz radius.

I've already eaten a big piece of humble pie and deservedly so. I hope you'll consent to nibble it a bit yourself. It doesn't taste all that bad once you get used to it [:)] Lucretius 09:27, 16 January 2006 (UTC)


 * i moved the word "roughly" to where it belongs:"... the Compton wavelength of the Planck mass is roughly equal to the Schwarzschild radius of the Planck mass." And the problem has to do with a missing factor  of π from the Compton wavelength not a factor of 2 from the Schwarzschild radius nor of the relative sloppy measure of G.   this, BTW, illustrates another reason i believe that Planck missed a little (i think he should have normalized 4 π G, instead of just G).  but it's all in the same ballpark anyway and the meaning or effect of the Compton wavelength  doesn't kick in precisely at the Compton wavelength, but gradually and in the ballpark of the Compton wavelength.   r b-j 18:00, 16 January 2006 (UTC)

This article now looks like a finished product to me and thanks for your help with it. I am aware that there are quantum uncertainties in these relations but I also know that the mathematical definition of Planck force is exact and this was not obvious in your previous draft. I noticed on the history page you advised me to read up on Planck mass. If you've seen an error in my discussion of Planck mass here, I hope you'll point it out here. That gives me an opportunity to learn from my mistake or to correct anything you have misunderstood. I'm no expert on Planck mass, I admit, but if you are in the business of correcting Planck himself, I guess I got off lightly.Lucretius 00:15, 17 January 2006 (UTC)

Actually, I've just had another look at the article and spotted a problem. I use the word 'Compton wavelength' to refer to the hbar form, whereas your inclusion of Pi clearly refers to the unreduced form. That inconsistency should be tidied up, either by removing your Pi comment or by rephrasing my use of 'Compton wavelength' (eg we could call it the crossed-Compton wavelength, or hbar-Compton wavelength, or maybe reduced Compton wavelength. Personally I think it's more consistent to delete the Pi as it just doesn't fit the context established by the equations, where the hbar form is used.Lucretius 00:32, 17 January 2006 (UTC)

I just noticed something else. In my external link 2, I advised the reader to 'see page 3' because the Schwinger Effect is mentioned in a particular part of the text. You've deleted this, which means the reader now needs to wade through the text to find the relevant part. I think we need to include the page number, preferably without citing the text title as that would take up unnecessary space.Lucretius


 * you can do what you want to the article. i removed the "page 3" note because i haven't noticed that style of reference elsewhere here at WP.  People can look for this "Schwinger effect" and find it in less than a minute, in my estimation.  the &pi; issue has to do with the definition of Compton wavelength as it is and the definition of Planck mass as it is.  The Planck mass is not precisely the mass that makes the Compton wavelength and Schwartzchild radius equal.  But it's roughly that. r b-j 01:11, 17 January 2006 (UTC)

Thanks for this. I'll make the changes. It's a good article due to our co-operation. Cheers. Lucretius 01:43, 17 January 2006 (UTC)


 * L, the Schwartzchild radius:
 * $$r_s = \frac{2Gm}{c^2} \ $$


 * the Compton wavelength
 * $$ \lambda = 2 \pi \frac{\hbar}{m c} \ $$


 * equate the two, substitute $$ m_P \ $$ in for $$ m \ $$ and solve for $$ m_P \ $$. do you get the correct expression for the Planck mass?


 * try it again, but this time with half of the Schwartzchild radius:


 * $$\frac{r_s}{2} = \frac{Gm}{c^2} \ $$
 * $$ \lambda = 2 \pi \frac{\hbar}{m c} \ $$


 * equate the two, substitute $$ m_P \ $$ in for $$ m \ $$ and solve for $$ m_P \ $$. what do you get?  the correct expression for the Planck mass? r b-j 05:13, 17 January 2006 (UTC)

Obviously the Schwarzschild radius is not the equivalent of the Planck Compton length (using either the h or hbar form) and the equations you've given me therefore are obviously wrong. The article does not equate Planck length with Schwarzschild radius, but equates it with half the Schwarz radius. Possibly my use of 'Compton wavelength' for the hbar form has led to some confusion here - you seem here to be assuming that I am equating Gm/c^2 with h/mc. But the equations in the article clearly show that I am equating Gm/c^2 with hbar/mc. If this is the problem, then it can be addressed by referring to the Compton wavelength as the 'reduced' or 'crossed' Compton wavelength.

By the way, I've recently corrected the Schwarz=Compton stuff on the Planck mass page. The Planck length page also needs correcting for the same reason - do you want to fix that? Otherwise I'll get around to fixing it myself. Lucretius 06:28, 17 January 2006 (UTC)

I've just looked at your latest edit of the Pforce page and it convinces me that my use of the words 'Compton wavelength' for hbar/mc is the source of the misunderstanding. I was hoping not to have to put in added words to define my use of 'Compton wavelength', thinking the equations were self-explanatory, but if this has confused you it might confuse others also. I'll do another edit to fix the phrasing and please get back to me on that. Lucretius 06:37, 17 January 2006 (UTC)

I've now done the new edit to remove any possible source of misunderstanding. I also restored the 'see page 3 here' clause because to me this is a simple courtesy to the reader, who might not want to sift through an entire text for a specific reference. It might not be convention but it should be. In fact I'm pretty sure I've seen it today on another page. I've also taken into account a comment you inserted invisibly within the text, which actually refers to some sloppy phrasing on my part. That also is now fixed. By the way, this is how you should be working on the invariant scaling article - I mean you should be working with someone else to fine-tune that article also. Anyhow, let me know how you feel about this new edit. Thanks. Lucretius 07:03, 17 January 2006 (UTC)

Finally, I decided to squeeze in a reference to the Einstein field equations since it is in this context that Planck force seems most relevant to contemporary physics.[;)] Lucretius 10:42, 17 January 2006 (UTC)