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Author Topic: How fast can non-zero mass particles travel?  (Read 10147 times)

Offline DoctorBeaver

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How fast can non-zero mass particles travel?
« on: 25/05/2008 10:16:12 »
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.

???
« Last Edit: 25/05/2008 10:27:54 by DoctorBeaver »


 

Offline graham.d

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How fast can non-zero mass particles travel?
« Reply #1 on: 25/05/2008 11:30:00 »
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.
 

Offline LeeE

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How fast can non-zero mass particles travel?
« Reply #2 on: 25/05/2008 16:18:08 »
I don't like infinities either, at least not when applied to the real world.  It seems to me that they only work iteratively, when a time component is present i.e. in dynamic systems, but not in static systems.

But anyway...  If there's no limit to the energy you can pump into the system, there appears to be nothing stopping the velocity from continually approaching, but never reaching c.  Put another way, after getting your particle up to this hypothetical speed limit, what happens to additional energy pumped into the system?  Sure, putting more energy into it also increases the mass, but if the speed curve becomes discontinuous, so must the mass curve.

I think I understand what you're getting at regarding c-Planck's constant - the Planck length and the Plank time are both applicable to speed but I can't see how you could use them to get a speed constant just below c.
 

Offline graham.d

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How fast can non-zero mass particles travel?
« Reply #3 on: 25/05/2008 20:10:04 »
Lee, there is an energy limit which would be the total energy in the universe which is largely accepted as not infinite. You could think of the infinities as the boundaries of the equations rather than a physical limit as it can never be achieved.

I see the point DrB is getting at but it is the speed and position that trade in uncertainty. I am unsure how to do this trade (or what it means) at the very very high velocities and high energies under consideration. This is a bit like trying to guess at the outcome of equations (yet to be determined) that unify general relativity with quantum mechanics. Even then, this may be at the edge of any such theory, being so extreme. I suppose it is amusing to speculate though:-)
 

Offline DoctorBeaver

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How fast can non-zero mass particles travel?
« Reply #4 on: 25/05/2008 21:15:10 »
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.

Maybe I was wrong saying Planck's constant. I was getting at the smallest number you can have without reaching zero. I believe that number is a Plancky thingy. Something like c-(c*1.6 x 10-35) as being the maximum allowable velocity.

As I said previously, it just seems to me that a Plancky thingy comes into it somewhere.
 

Offline LeeE

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How fast can non-zero mass particles travel?
« Reply #5 on: 26/05/2008 22:43:48 »
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.
 

Offline DoctorBeaver

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How fast can non-zero mass particles travel?
« Reply #6 on: 27/05/2008 00:10:42 »
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.


OK... c-(c*1.6 x 10-35mps)
 

Offline syhprum

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How fast can non-zero mass particles travel?
« Reply #7 on: 27/05/2008 12:36:39 »
I read an account of the velocity of the most energetic cosmic ray particles, apparently the particle only lags behind a photon by one microsecond after travelling 200 million light years.
 

Offline lightarrow

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How fast can non-zero mass particles travel?
« Reply #8 on: 27/05/2008 12:52:47 »
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.

???
If you tell me how large is the universe, then we could try to find a limit for the speed from a limit on the centripetal acceleration an object would have revolving around the entire universe before auto-disintegration. [:0]
 

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How fast can non-zero mass particles travel?
« Reply #9 on: 27/05/2008 13:05:17 »
Quote
OK... c-(c*1.6 x 10-35mps)
Why would you think that an arbitrary formula like that would work?
I have a feeling that the limit to the speed of any particle with mass that you could find is imposed by statistics and thermodynamics; you need more an more energy to accelerate a particle and that energy would have to come from some process involving a lot of other particles - such as in a Supernova. The probability of getting a large mass of material together in one spot decreases as the mass increases.
You don't have to involve the word 'infinity' - you can just say it gets less and less likely -without  limit - as a fraction of c, of course.
« Last Edit: 27/05/2008 13:31:10 by sophiecentaur »
 

Offline DoctorBeaver

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How fast can non-zero mass particles travel?
« Reply #10 on: 28/05/2008 09:04:50 »
Sophie - I'm not actually putting that forward as a formula that may work. I merely used it as an example.

As I said, I just have this gut feeling that there should be an upper limit without resorting to infinitely small fractions. It seems to me that some connection with the Planck scale could be the answer as that crops up so often.
« Last Edit: 28/05/2008 09:07:05 by DoctorBeaver »
 

Offline Soul Surfer

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How fast can non-zero mass particles travel?
« Reply #11 on: 28/05/2008 09:43:38 »
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.
 

Offline DoctorBeaver

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How fast can non-zero mass particles travel?
« Reply #12 on: 28/05/2008 11:57:45 »
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.

Does that mean I'm sort-of right(ish)?  [:0]
 

Offline lightarrow

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How fast can non-zero mass particles travel?
« Reply #13 on: 28/05/2008 12:51:40 »
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.
But he was talking about limits on an object' speed not on the photon's energy.
 

Offline LeeE

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« Reply #14 on: 28/05/2008 15:54:50 »
I think a similar thing should happen with objects too.  According to GR, as I understand it, when an object is accelerated it experiences time dilation, mass increase and foreshortening, and there appear to be no limits to any of these changes.

If the mass increases without a corresponding increase in volume the density will increase, leading to a steeper grav gradient and eventually to a BH.  At the same time, foreshortening also leads to higher density as it results in an effective reduction of volume and so too, could lead to a BH (might be a very strange shaped one though - the cross-section wouldn't change so the gradient perpendicular to the direction of tavel shouldn't change either - not at all sure about this though).

Anyway, if you consider that both mass increase _and_ foreshortening occurs it would seem that an accelerated object might well become a BH.
 

Offline DoctorBeaver

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« Reply #15 on: 28/05/2008 18:14:01 »
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?
 

Offline syhprum

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« Reply #16 on: 28/05/2008 19:47:02 »
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. 
 

Offline hurricane221

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How fast can non-zero mass particles travel?
« Reply #17 on: 29/05/2008 04:14:39 »
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. 

why wouldn't they be compressible if they are made of multiple quarks.this seems logical if atoms made of smaller things (than atoms) can be compressed

about the speed limit thing cant we say if there is inf energy, we can get infinitely close to the speed of light, but if there is... say 10 energy then our speed limit is exactly how fast that 10 energies will get us?

--sorry its kind of confusing  ;D
 

Offline DoctorBeaver

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« Reply #18 on: 29/05/2008 12:52:00 »
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. 

That's what I was saying. Protons are not fundamental, they are composite. I don't see that quarks, gluons, etc. can be compressed. If it were possible, that would imply there is space inside them which would itself imply that they are not fundamental but are composed of even smaller particles.
 

Offline graham.d

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How fast can non-zero mass particles travel?
« Reply #19 on: 29/05/2008 13:27:06 »
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.
 

Offline DoctorBeaver

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« Reply #20 on: 29/05/2008 16:54:09 »
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.

Ah, my mistake. I've obviously been reading too many sci-fi novels.  [:I]

Quote
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.

That sounds familiar. Now you've mentioned it, I'm sure I remember seeing that bit about a sphere somewhere before.
 

Offline syhprum

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« Reply #21 on: 29/05/2008 17:06:16 »
The Quarks and Gluon's with in a Hadron are by no means locked together in a solid mass but are whizzing about with much energy making a substantial contribution to the rest mass hence the possibility that they can be pushed closer together.

QCD is the name of the game, see this 1993 Scientific American article.

QED for QCD; July 1993; Scientific American Magazine; by Philip Yam; 2 Page(s)

It's a good thing machines don't get overtime. Researchers at the IBM Thomas J. Watson Research Center have recently completed a set of calculations on a supercomputer that ran continuously for approximately an entire year. More than an exercise in patience, the task may have provided the strongest con firmation yet of a current theory of elementary particles. In particular, the IBM team calculated the masses of eight hadrons, a family of particles that includes the proton and neutron, and showed that the values obtained are consistent with the masses measured in the laboratory.

The theory of quantum chromodynamics, or QCD for short, was postulated in the 1970s to describe how the fundamental particle known as the quark builds the various hadrons. Two "up" quarks and a "down" quark, for example, create a proton. A so-called chromoelectric field (based on a property of quarks called color) holds the quarks together; the chromoelectric field is carried by particles called gluon's. The QCD theory was highly successful in enunciating the properties of hadrons in certain kinds of experiments and became part of the so-called Standard Model, which unites all the forces of nature except for gravity.

 

Offline DoctorBeaver

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« Reply #22 on: 29/05/2008 17:14:06 »
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!  :D
 

Offline syhprum

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« Reply #23 on: 29/05/2008 19:19:19 »
I have re read the views of correspondents on the compressability of Hadrons and have been pleased to note that more people are in agreement than I had first thought.
When I made the suggestion that beyond the event horizon of a blackhole there lurked not a singularity but merely a more compressed form of matter than a Neutron star the idea was not well received.
 

Offline lightarrow

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« Reply #24 on: 29/05/2008 21:00:12 »
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!  :D
Does it mean that we are inside the very basic elements of matter?  ;)

Ah! But you already knew I would have answered something like this, isnt'it?  :) :o
« Last Edit: 29/05/2008 21:02:37 by lightarrow »
 

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How fast can non-zero mass particles travel?
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