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I'm intrigued to know why you involve Planck's constant at all. Any reduction in c must, at least, have the same units as velocity. Planck's constant (6.626068 × 10-34 m2 kg / s) does not. Anyway, the point about the limit of c is that you don't actually get any infinities in practice because you can't get the non-zero rest mass particles to actually get there; it needs infinite energy.
Hi Graham, DrB, I did say _if_ there's no limit... I agree that there is probably not infinite energy in the universe, so it would be impossible in practice to simply keep pumping in more energy. Heh, in practical terms, I think the fact that there isn't infinite energy to draw upon would be the least of our worries, but the problem with what DrB is thinking about, as I see it, is the discontinuity in the curve that must happen when a hypothetical upper sub-lightspeed limit is reached.It does seem intuitive that (c - one of the small planck units) should give a speed that is the maximum sub-lightspeed possible but because we're dealing with speed we have to use both the Planck length and time units, which gives us c. If you try to use only one of them i.e. length, the time factor can be anything, and likewise, if you try to use the Planck time the length can be any value.I'm afraid that c-(c*1.6 x 10-35) won't work because you're trying to subtract a distance from a speed - it's like asking how fast is 10 m.p.h - 3 feet. Similarly, you can't ask how fast is 10 m.p.h - 3 seconds.
Particles in accelerators can reach near lightspeed and I've been putting my little beaver brain to work again pondering their highest possible velocity. I appreciate that particles with non-zero mass cannot attain c; but would I be right in thinking that the highest velocity they can acheive is c-Planck's constant?My reasoning is that I can't accept that they can acheive a velocity that is an infinitely small fraction less than c (I cringe whenever infinite values occur as I consider them a cop-out). So, my rodentiate grey matter thinks there must be some finite upper limit. The Plancky thingy seems to crop up everywhere, so why not here?I know that's not very scientific and lots of physics is counter-intuitive; but, for some reason, it just feels right to me. I've never seen it written anywhere so it is pure supposition on my part.
OK... c-(c*1.6 x 10-35mps)
Beaver there are limits. There is a maximum photon energy where if you exceed it it effectively becomes a black hole this could also apply to particle energies. these are related to the Planck scales but I can't remember them at the moment. they are way beyond any levels to be expected at any time other than the planck times associated with a simple big bang.
How the quarks and gluon's are rearranged within a proton I do not know but I have always thought that protons were to some degree compressible at high energies.
I have always believed that a highly accelerated particle becomes fore shortened into a disk and have seen many illustrations of this effect in articles on accelerator's.How the quarks and gluon's are rearranged within a proton I do not know but I have always thought that protons were to some degree compressable at high energies.
I am fairly sure that it not is right to consider an object foreshortened through Lorentz contraction as in any way in compression. To an observer moving close to light-speed all objects in the universe are Lorentz contracted, but there is no energy transfer to the object concerned to distort it physically in its own frame in any way. In its own frame of reference it is unchanged. By you moving very fast cannot cause a star somewhere in the universe to collapse as far as I know.
Interestingly, someone wrote a paper, years ago, on how fast moving objects of different shapes would appear. A sphere still looks like a sphere but rotated so that you can see its far side, maybe by 90 degrees (I don't remember). It is the effect of Lorentz contraction and the time of flight of light from the object.
syhprum - I'm aware of all that. That's why I thought something like a proton can be compressed.I don't know - what with colours, flavours & families it's beginning to sound like an Italian ice-cream parlour! 
Quote from: DoctorBeaver on 29/05/2008 17:14:06syhprum - I'm aware of all that. That's why I thought something like a proton can be compressed.I don't know - what with colours, flavours & families it's beginning to sound like an Italian ice-cream parlour! Does it mean that we are inside the very basic elements of matter? 
Quote from: lightarrow on 29/05/2008 21:00:12Quote from: DoctorBeaver on 29/05/2008 17:14:06syhprum - I'm aware of all that. That's why I thought something like a proton can be compressed.I don't know - what with colours, flavours & families it's beginning to sound like an Italian ice-cream parlour! Does it mean that we are inside the very basic elements of matter? Are Italian ice-cream parlours "the very basic elements of matter"? 
LeeE - I did think about the aspects you mentioned but I came to the conclusion that only time dilation & mass increase would affect an electron or photon. I wasn't sure that a fundamental particle could suffer foreshortening.I can see that maybe a composite particle could be foreshortened, but a fundamental particle cannot be compressed. Or can it?
But then if we think about particles as wave functions, where/how then does foreshortening fit in? Is it simply wavelength/frequency? It seems to me that somewhere along the line we should see deviations from the planck units, although I think the deviations will be > than and not < than, but even so, an intermediate value between one and two Planck units is still a problem: 1.5 - 1 = 0.5
But seriously, if you can get fractions of a Planck unit, won't that throw QM into total confusion?