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Natural Science Forum / Physics / Relativity / May 2005How long is a muon when at rest?
Whenever we measure small objects such as muons (or fast moving electrons or protons) they always seem to be moving at nearly the speed of light. According to SR, this contracts their length, so I was wondering how long they would be when at rest with respect to the observer. 4.273e-17 cm How come? from the head to tail That didn't answer my question | That didn't answer my question Your original question makes no sense. Restate it so that it does. FrediFizzx How simple can it be? A moving object is Lorentz-contracted when it is moving, so how long is it when it isn't moving? Obviously it has to be longer when standing still than it does when it is moving. > [...] A moving object is Lorentz-contracted when it is >moving, so how long is it when it isn't moving? Obviously it has to be >longer when standing still than it does when it is moving. Unless its length is zero in either case, of course. Multiplying zero by any number gives you zero.  SignatureJon Bell <jtbell@presby.edu> Presbyterian College Dept. of Physics and Computer Science Clinton, South Carolina USA I thought muons were massive objects. Certainly protons are. Why would a massive object have zero length? Arthur Dent. > I thought muons were massive objects. Certainly protons are. Why would > a massive object have zero length? > Arthur Dent. Bearing mass does not necessarily demand bearing volume (or extent). There is only a connection between the two for substances for which density is a well-defined concept. Density is only a well-defined concept for *composites*, as far as I know. Most stuff we know is composites: sand is made of silica is made of atoms is made of protons, neutrons, electrons... Even a proton is a composite (quarks and gluons). However, there are some things that do not appear to be composites -- fundamental particles -- and for these, density is not an appropriate concept, and for these mass does not imply volume. PD Moral: Do not let the familiar drive your conclusions of the necessary. Arthur Dent: >I thought muons were massive objects. Certainly protons are. Why would >a massive object have zero length? Muons are point particles. If you want to know how that can be, then you are entering the realm of relativistic quantum field theory, in which case it doesn't make sense to talk about velocities at all other than as a classical limit in which the muon is a point particle. If you want to begin with the quantum mechanical picture, then you have to begin by noting that the eigenvalues of the dirac equation are +/-c and that velocities less than `c' are the result of zitterbewegung. I think this is more complex than you assumed in your question, but unfortunately that is the way it is. No classical theory can properly describe particles like muons, electrons, etc., so no classical concept of size makes any sense. >No classical theory >can properly describe particles like >muons, electrons, etc., so no >classical concept of size makes any >sense. they don't elongate? parallelepiped: >>No classical theory >>can properly describe particles like >muons, electrons, etc., so no >>classical concept of size makes any >sense. > >they don't elongate? How long is a point? is depends on the space consisting it, overhere it is 4.273e-17 cm long > is depends on the space consisting it, overhere it is 4.273e-17 cm > long A point by definition has position but no size. Bill Massive objects are point particles, it makes no sense to talk about velocities, and there is no classical concept of size. Got it. Thank you. Curious that we are supposed to accept Lorentz contraction when it makes no sense to talk about size. Have a nice day. Arthur Dent Arthur Dent: >Massive objects are point particles, it makes no sense to talk about >velocities, and there is no classical concept of size. Got it. That isn't quite what I said. If you want a one or two sentence summary, then it's that your question doesn't make physical sense. You are trying to use classical concepts in a realm where classical mechanics fails. >Thank >you. Curious that we are supposed to accept Lorentz contraction when it >makes no sense to talk about size. Have a nice day. If you aren't willing to accept the compexities which follow from your question, then you can accept whatever you want, regardless of whether what you accept is physically viable as an answer. Let's see now. You claim that objects are points (i.e. have no spatial dimension) but have mass. Therefore you claim they have infinite density, and ask that I "accept complexity". A Moebius strip has one edge and one face mathematically, but physically a Moebius strip is a torus. The thickness is real. Whilst I am willing to accept the mathematical construct of an idea such as a Moebius strip or a Klein bottle and indeed do find such mathematical ideas somewhat fascinating and beautiful, it would be delusional to assign such an object to physical reality. Mathematics may well be the language of physics, but it is also the language of make-believe when we pretend the Moebius strip (or the massive object) has no physical thickness. If my question doesn't make physical sense, it is because infinitely dense particles make no physical sense. If you are not willing to accept that physically a real moebius strip has thickness (as does a massive particle), then inevitably you'll become bogged down in a world of complex mathematical make-believe of your own manufacture. It is not classical physics that has failed, but rather your inability to accept reality, it is your point particles that are not physically viable. Arthur Dent: >Let's see now. You claim that objects are points (i.e. have no spatial >dimension) but have mass. Therefore you claim they have infinite >density, No, I don't claim that. Reread what I wrote. I'm not buying into the strawman you set up by misreading what I what I wrote. >and ask that I "accept complexity". A Moebius strip has one >edge and one face mathematically, but physically a Moebius strip is a [quoted text clipped - 12 lines] >classical physics that has failed, but rather your inability to accept >reality, it is your point particles that are not physically viable. > Massive objects are point particles, it makes no sense to talk about > velocities, and there is no classical concept of size. Got it. Thank > you. Curious that we are supposed to accept Lorentz contraction when it > makes no sense to talk about size. Have a nice day. > Arthur Dent Lorentz contraction applies to things that have size. It does not apply to things that have no extent. Now, the *path* of a muon has extent, even though the muon itself does not, as I've been trying to explain to you. PD >| That didn't answer my question > >Your original question makes no sense. Restate it so that it does. > >FrediFizzx Yes it did. Now answer the man. | >| That didn't answer my question | > | >Your original question makes no sense. Restate it so that it does. | > | >FrediFizzx | Yes it did. Now answer the man. Perhaps you can explain why it did and make my day, punk. ;-) FrediFizzx http://www.vacuum-physics.com/QVC/quantum_vacuum_charge.pdf or postscript http://www.vacuum-physics.com/QVC/quantum_vacuum_charge.ps > Whenever we measure small objects such as muons (or fast moving > electrons or protons) they always seem to be moving at nearly the speed > of light. According to SR, this contracts their length, so I was > wondering how long they would be when at rest with respect to the > observer. As far as we know, a muon is a point particle, both moving and at rest. PD A muon originates in the upper atmosphere and arrives at sea level, doesn't it? Simultaneously, light from the sun will catch up with and pass the back end of the muon, gradually overtaking the muon as it goes (in our frame of reference), reflect at sea level (which is where the front of muon now is, since it has been hurtling down at near light speed) and then takes the same amount of time to travel upwards from the front of the muon to the back of the muon because the speed of light in the muon's frame of reference is invariant. Doesn't this imply that the muon's length in its own frame of reference is very nearly from upper atmosphere to ground level? > A muon originates in the upper atmosphere and arrives at sea level, > doesn't it? Simultaneously, light from the sun will catch up with and [quoted text clipped - 6 lines] > that the muon's length in its own frame of reference is very nearly > from upper atmosphere to ground level? How far a car travels is not the length of the car. What gets contracted is the path length of the muon, not the muon itself. Instead of words, which are confusing you, draw a series of pictures. In each, draw a line marking the top of the atmosphere and a line marking the earth's surface. Then, in sequence, draw little dots for: 1. Muon at top of atmosphere, light blip behind it and catching up. 2. Light blip catches the muon. Where is the muon now? 3. Light blip reaches the earth. Where is the muon now? 4. Light blip reflected catches the muon, still coming down. Where is the muon now? 5. Muon reaches the earth. Where is the light blip now? Now look at this set of drawings and ask yourself what is contracted, in what frame of reference, and so on. PD How far a car travels is not the length of the car. What gets contracted is the path length of the muon, not the muon itself. Instead of words, which are confusing you, draw a series of pictures. In each, draw a line marking the top of the atmosphere and a line marking the earth's surface. Then, in sequence, draw little dots for: 1. Muon at top of atmosphere, light blip behind it and catching up. 2. Light blip catches the muon. Where is the muon now? AD: At the top of the atmophere. PD: 3. Light blip reaches the earth. Where is the muon now? AD: At ground level. The light wins the race by a nose. PD: Light blip reflected catches the muon, still coming down. Where is the muon now? AD: The tail end of the muon is still at the top of the atmosphere. The head of the moun is at ground level. PD: 5. Muon reaches the earth. Where is the light blip now? AD: On its way back toward the tail of the muon, it will take the same time to reach the tail as it took to reach the head. You've used common sense when you stated that the length of a car isn't the distance it travels. In relativity, the length of a car IS the distance it travels. > How far a car travels is not the length of the car. What gets > contracted is the path length of the muon, not the muon itself. [quoted text clipped - 6 lines] > AD: > At the top of the atmophere. It hasn't moved from picture 1? > PD: > 3. Light blip reaches the earth. Where is the muon now? > > AD: > At ground level. The light wins the race by a nose. Then go back to picture 1 and draw another light blip ahead of your first light blip but still behind the muon. This one is traveling just as fast as the other light blip and will therefore hit the ground *before* the muon does. > PD: > Light blip reflected catches the muon, still coming down. Where is > the muon now? > > AD: The tail end of the muon is still at the top of the atmosphere. The > head of the moun is at ground level. Muons are the length of the atmosphere? How do you know? Why is it a long stretched out thing? What happens if a muon hits Jupiter, where the atmosphere is thicker? What happens if it hits the moon where there is no atmosphere? What's special about the Earth's atmosphere? You think the atmosphere is responsible for relativistic contraction? > PD: > 5. Muon reaches the earth. Where is the light blip now? [quoted text clipped - 5 lines] > the distance it travels. In relativity, the length of a car IS the > distance it travels. Uh, no it isn't. I have no idea where you got that notion about relativity. PD Arthur Dent wrote: > PD wrote: > How far a car travels is not the length of the car. What gets > contracted is the path length of the muon, not the muon itself. > Instead of words, which are confusing you, draw a series of pictures. > In each, draw a line marking the top of the atmosphere and a line > marking the earth's surface. Then, in sequence, draw little dots for: > 1. Muon at top of atmosphere, light blip behind it and catching up. > 2. Light blip catches the muon. Where is the muon now? > AD: > At the top of the atmophere. PD: It hasn't moved from picture 1? A Arthur Dent wrote: > PD wrote: > How far a car travels is not the length of the car. What gets > contracted is the path length of the muon, not the muon itself. > Instead of words, which are confusing you, draw a series of pictures. > In each, draw a line marking the top of the atmosphere and a line > marking the earth's surface. Then, in sequence, draw little dots for: > 1. Muon at top of atmosphere, light blip behind it and catching up. > 2. Light blip catches the muon. Where is the muon now? > AD: > At the top of the atmophere. It hasn't moved from picture 1? > PD: > 3. Light blip reaches the earth. Where is the muon now? > AD: > At ground level. The light wins the race by a nose. Then go back to picture 1 and draw another light blip ahead of your first light blip but still behind the muon. This one is traveling just as fast as the other light blip and will therefore hit the ground *before* the muon does. > PD: > Light blip reflected catches the muon, still coming down. Where is > the muon now? > AD: The tail end of the muon is still at the top of the atmosphere. The > head of the moun is at ground level. Muons are the length of the atmosphere? How do you know? Why is it a long stretched out thing? What happens if a muon hits Jupiter, where the atmosphere is thicker? What happens if it hits the moon where there is no atmosphere? What's special about the Earth's atmosphere? You think the atmosphere is responsible for relativistic contraction? > PD: > 5. Muon reaches the earth. Where is the light blip now? > AD: > On its way back toward the tail of the muon, it will take the same time > to reach the tail as it took to reach the head. > You've used common sense when you stated that the length of a car isn't > the distance it travels. In relativity, the length of a car IS the > distance it travels. Uh, no it isn't. I have no idea where you got that notion about relativity. PD AD: This IS picture one. The light has reached the tail of the muon. The muon is at the top of the atmosphere. > PD: > 3. Light blip reaches the earth. Where is the muon now? > AD: > At ground level. The light wins the race by a nose. PD: Then go back to picture 1 and draw another light blip ahead of your first light blip but still behind the muon. This one is traveling just as fast as the other light blip and will therefore hit the ground *before* the muon does. AD No, I will not. Picture 1 is the light blip at the tail of the muon. Both are at the top of the atmosphere. If you want to use your car analogy, the bullet is at the tailpipe of the car. > PD: > Light blip reflected catches the muon, still coming down. Where is > the muon now? > AD: The tail end of the muon is still at the top of the atmosphere. The > head of the moun is at ground level. PD: Muons are the length of the atmosphere? AD: That's what we are ryng to discover. PD: How do you know? AD. I don't. PD: Why is it a long stretched out thing? AD: I don't know, that's what I'm asking. PD: What happens if a muon hits Jupiter, where the atmosphere is thicker? AD: Who cares? Your question is irrelevant. PD: What happens if it hits the moon where there is no atmosphere? AD: Who cares? Your question is irrelevant. What's special about the Earth's atmosphere? You think the atmosphere is responsible for relativistic contraction? AD:Not at all. > PD: > 5. Muon reaches the earth. Where is the light blip now? > AD: > On its way back toward the tail of the muon, it will take the same time > to reach the tail as it took to reach the head. > You've used common sense when you stated that the length of a car isn't > the distance it travels. In relativity, the length of a car IS the > distance it travels. PD: Uh, no it isn't. I have no idea where you got that notion about relativity. PD AD: I got it from Einstein of course, he says it will take light the same time to travel the length of the object in both directions. It takes time for the light to travel from the top of the atmosphere to ground level. It takes the same amount for time to travel back up. In the frame of the muon, it travels from the back of muon to the front and then back again. Now even though muon time differs from Earth time, never-the-less it takes the same time one way as it does the other. Since the speed of light is invariant, it logically follows that the tail of the moun is still at the upper atmosphere when the returning light reaches it. Arthur Dent. > Arthur Dent wrote: > > PD wrote: [quoted text clipped - 77 lines] > AD: This IS picture one. The light has reached the tail of the muon. > The muon is at the top of the atmosphere. And where is the front of the muon at this instant? At the top of atmosphere or at the ground? > > PD: > > 3. Light blip reaches the earth. Where is the muon now? [quoted text clipped - 12 lines] > If you want to use your car analogy, the bullet is at the tailpipe of > the car. And the front bumper is where, at this instant? > > PD: > > Light blip reflected catches the muon, still coming down. Where is [quoted text clipped - 12 lines] > PD: Why is it a long stretched out thing? > AD: I don't know, that's what I'm asking. Ah, then would it surprise you if I told you its length is at least very, very short compared to the atmosphere? That doesn't mean that it won't MAKE IT to the ground, any more than it means that just because a car is only 12' feet long it won't make it from Duluth to Iowa City. > PD: What happens if a muon hits Jupiter, where > the atmosphere is thicker? > AD: Who cares? Your question is irrelevant. Well, you seem to think that the muon's length is the thickness of the atmosphere, and I want to know why? > PD: What happens if it hits the moon where there > is no atmosphere? [quoted text clipped - 25 lines] > AD: I got it from Einstein of course, he says it will take light the > same time to travel the length of the object in both directions. OK, for the moment. That doesn't mean that then length of an object is the distance the object travels. > It takes time for the light to travel from the top of the atmosphere to > ground level. [quoted text clipped - 6 lines] > light reaches it. > Arthur Dent. Look, this is really very, very simple. I'll use your car analogy, ok? A bullet (analagous to light) catches up to the back bumper of a car, passes the car, bounces off the front bumper and passes the back bumper once again. It travels at constant speed in both directions, and the car travels at a constant speed. It takes the same amount of time to travel the length of the car, bumper to bumper, each way. Now, just how simple can that be? Do try to concentrate, please.There is no need to get confused about Jupiter's atmosphere, or ask what happens on the moon. Dear Arthur Dent: >A muon originates in the upper atmosphere and arrives > at sea level, doesn't it? A trip it sees as tens of feet in length. > Simultaneously, light from the sun will catch up with > and pass the back end of the muon, gradually [quoted text clipped - 5 lines] > muon to the back of the muon because the speed of > light in the muon's frame of reference is invariant. Can't happen as you've set it up, since the muon is already in contact with muon's "target" when it is reflected. > Doesn't this imply > that the muon's length in its own frame of reference > is very nearly from upper atmosphere to ground level? Orders of magnitude less than you think. And PD told you what the experimentally determined size of the muon is, so the answer is still "no". David A. Smith Thank you, David. The question was "How long is a muon when at rest?" Your reply is "no". Have a nice day. Arthur Dent. Dear Arthur Dent: > Thank you, David. > The question was "How long is a muon when at rest?" > Your reply is "no". Actually, my reply was "PD pointed out the experimetnally determined length was zero", or words to that effect. The "no" you replied to were various parts of your misunderstanding in your constructed scenario. > Have a nice day. You too. Remember your towel, Mr. Dent. And stay away from Vogons with poetry books. David A. Smith DS: Actually, my reply was "PD pointed out the experimetnally determined length was zero", or words to that effect. The "no" you replied to were various parts of your misunderstanding in your constructed scenario. PD did nothing of the kind, sir. Perhaps you'd care to cite ANY physical experiment capable of determining a zero dimension and subsequent infinite density, and if you find error in my construct, be so good as to point it out instead of saying "the answer is no". Arthur Dent. nobody can "see" or detect the size of small things, the bedst one can do is to consider them as points, because observations tell us that they must exists you want to give them a "size" as property, fine, but dont come back with questions when you get into a trouble because your gave them "size" as property Perhaps you are unaware of such experiments as Michelson-Morley having "size" as a property and the Lorentz contraction being given as reason for the null result obtained. I, sir, am not "in trouble" as you put it for asking how the Lorentz contraction would apply to a small particle of finite mass travelling at near light speed, Whereas you and your fellow group members appear to be unable to discuss the issue. So far the responses have been: 1) 4.273e-17 cm qwerty 2) Your original question makes no sense. FreddiFrizz 3) Unless its length is zero in either case, of course. Multiplying zero by any number gives you zero. Jon Bell 4) density is not an appropriate concept PD 5) no classical concept of size makes any sense. Bilge 6) Lorentz contraction applies to things that have size. PD 7)As far as we know, a muon is a point particle, both moving and at rest. PD, who at least has the grace to add the caveat "as far as we know". 8) "PD told you what the experimentally determined size of the muon is" David Smith. Not one of you is prepared to discuss Lorentz contraction in a sensible manner, and you sir, seem to think I am in trouble for asking a question. > Perhaps you are unaware of such experiments as Michelson-Morley having > "size" as a property and the Lorentz contraction being given as reason > for the null result obtained. Lorentz contraction does not give the reason for the null result. Lorentz contraction is a consequence of a model that is compatible with the null result. Dirk Vdm Very well. Are there any other models which are compatible with such a result, since Lorentz contraction is not compatible with light taking the same time to turn to a muon after reflection? AD. Arthur Dent: >Very well. Are there any other models which are compatible with such a >result, since Lorentz contraction is not compatible with light taking >the same time to turn to a muon after reflection? No, you're out of luck. You'll have to think of something else to use in mis-attributing replies. > Very well. Are there any other models which are compatible with such a > result, since Lorentz contraction is not compatible with light taking > the same time to turn to a muon after reflection? Yes, John, there is another model that is compatible with that result. Your mental condition. Dirk Vdm Arthur Dent: >Perhaps you are unaware of such experiments as Michelson-Morley having Do you make a habit of stating exactly the opposite of what someone has posted and then attributing your misstatement to the person you misquoted? >"size" as a property and the Lorentz contraction being given as reason >for the null result obtained. I, sir, am not "in trouble" as you put it [quoted text clipped - 32 lines] >manner, and you sir, seem to think I am in trouble for asking a >question. > Perhaps you are unaware of such experiments as Michelson-Morley having > "size" as a property and the Lorentz contraction being given as reason > for the null result obtained. I, sir, am not "in trouble" as you put it > for asking how the Lorentz contraction would apply to a small particle > of finite mass travelling at near light speed, Whereas you and your > fellow group members appear to be unable to discuss the issue. then maybe you should wait for an answer from some other guy, becus I'm not a sir > So far the responses have been: > 1) 4.273e-17 cm [quoted text clipped - 27 lines] > manner, and you sir, seem to think I am in trouble for asking a > question. My apologies. I was hoping for a reasoned discussion from physicists and mathematicians, but alas they do not contribute here. Arthur Dent: >My apologies. I was hoping for a reasoned discussion from physicists >and mathematicians, but alas they do not contribute here. What gave you the idea that a ``reasoned discussion,'' would follow from your trolls? I fail to see how asking a reasonable question is a "troll". Have a nice day. Arthur Dent: >I fail to see how asking a reasonable question is a "troll". Have a >nice day. I gave you a reasonable answer to your reasonable question. You then misquoted me and used your own misrepresentation of what I wrote to set up a strawman, which was apparently your intent all along. That is called a troll. I do not understand your hostility. Accepting your response as reasonable, I've rephrased the question. You'll find it in the thread "Lorentz contraction". Arthur Dent: >I do not understand your hostility. It never occured to you that making something up and attributing your own invention to someone else and/or misquoting people might result in a less than gracious reply? >Accepting your response as >reasonable, I've rephrased the question. >You'll find it in the thread "Lorentz contraction". I didn't find anything related to my response in that thread. All I saw was a statement that you didn't believe something that was completely ridiculous. While that's a good start, it's hard to imagine how you came up with that ridiculous statement you don't believe in the first place. I'd suggest continuing not to believe a muon is 29 meters long. No one else believes it. I do not believe that muons are 29 meters long, and so I accept your suggestion. However, I do accept the definition speed = distance/time as a definition. This is contradictory to Einstein's definition of time, i.e. the time for light to travel from A to B is equal to time it travels from B to A. As you correctly point out, one of these statements is ridiculous. The event of the light leaving A, the event of the light reflecting at B and the event of light arriving back at A are four events, not three, surely, since we are unable to determine the location of A in the stationary frame and in the moving frame. It is this difficulty that I was hoping someone would resolve. I'm sorry that I have not said anything in response to your original reply, but unfortunately your original reply did not address my orginal and perhaps poorly phrased question. > I do not believe that muons are 29 meters long, and so I accept your > suggestion. However, I do accept the definition speed = distance/time > as a definition. This is contradictory to Einstein's definition of > time, i.e. the time for light to travel from A to B is equal to time it > travels from B to A. Aha! It *is* Androcles. > As you correctly point out, one of these > statements is ridiculous. [quoted text clipped - 7 lines] > unfortunately your original reply did not address my orginal and > perhaps poorly phrased question. Arthur Dent: >I do not believe that muons are 29 meters long, and so I accept your >suggestion. Then what's the problem? >However, I do accept the definition speed = distance/time >as a definition. So what? That is a rather commonly accepted definition. >This is contradictory to Einstein's definition of >time, i.e. the time for light to travel from A to B is equal to time it >travels from B to A. As you correctly point out, one of these >statements is ridiculous. There's no contradiction, so the only thing which is ridiculous is trying to argue that there's a contradiction. If you want to argue that there's a contradiction, then you need to go to a math newsgroup and argue that there's no such thing as the slope of a line. >The event of the light leaving A, >the event of the light reflecting at B and >the event of light arriving back at A >are four events, not three, surely, since we are unable to determine >the location of A in the stationary frame and in the moving frame. It >is this difficulty that I was hoping someone would resolve. If you were hoping someone would resolve it, then why do you misconstrue what people write and why do you take every opportunity to be contrary for the sake of being contrary? >I'm sorry that I have not said anything in response to your original >reply, but unfortunately your original reply did not address my >orginal and perhaps poorly phrased question. You asked how ``long'' a muon is and I answered that question. You made something up that bore no relation to anything I said and then attributed what you made up to me. I did not "make up" Einstein's definition of an interval of time. Einstein made it up. Do you accept the definition he gives? If so, how do you reconcile the length of a unit of distance when that unit of distance is in motion? Arthur Dent: >I did not "make up" Einstein's definition of an interval of time. I didn't say you did. I said you made up something and attributed it to me. >Einstein made it up. Do you accept the definition he gives? If so, how >do you reconcile the length of a unit of distance when that unit of >distance is in motion? I have no intention of addressing anything until you stop misrepresenting what I write. You said muons were point particles. I attribute that to you. That is not a mispresentation. Infinite density is a conclusion I drew for a point particles having mass. Now you ask me to "stop" misrepresenting what you write. What else have I "made up" and attributed to you? > You said muons were point particles. I attribute that to you. That is > not a mispresentation. > Infinite density is a conclusion I drew for a point particles having > mass. It's an improper conclusion, as I posted elsewhere. Density is a concept that applies to composite objects only. Bearing mass does not imply having density and therefore does not imply bearing volume. PD > Now you ask me to "stop" misrepresenting what you write. > What else have I "made up" and attributed to you? I was actually addressing Bilge, but I am surprised to learn that having mass does not imply having density since density is defined as mass/volume. When I went to school, division by zero was undefined and you seem to accept a zero volume for a finite mass, or, as some would put it, a singularity. It is, however, immaterial to the original question, since I have now replaced the "length" of the muon with two comoving point-like muons a fixed distance apart, tagged as A and B, and am asking if Einstein's definition of time, to wit, the time for light to travel from A to B is equal to the time it takes to travel from B back to A. Perhaps you could be kind enough to address the real problem instead of skirting around it, or trying to make it into fault on my part, as others have tried to do. Or perhaps you cannot. There seems to be a paradox here, somewhat akin to the Twins Paradox, in that light must traverse the length of the "spaceship" in the same time as it takes to traverse from the Earth to the turnaround point, the ship having raced the light and lost by a length. In the non-accelerative twin paradox, the issue is resolved by the ship instantaneously reversing direction and once again racing the light Earthward, again losing by a length. As far as I know, muons do not exhibit this behaviour. > I was actually addressing Bilge, but I am surprised to learn that > having mass does not imply having density since density is defined as > mass/volume. When I went to school, division by zero was undefined and > you seem to accept a zero volume for a finite mass, Physics doesn't insist that elementary particles have a volume even though they might have a mass. What you learned in school doesn't apply to elementary particles. It does apply to composite objects made of them. John Anderson Thank you Mr Anderson, but I have to point out that your reply is irrelevant since it did not address the main issue, Einstein's definition of time. As with so many others, you seem to wish to skirt around that and would prefer to discuss to properties of particles rather than the properties of time. To Bilge, John Anderson and PD. "Thanks for ignoring the rest of the post and focusing on the one thing of least importance." - PD Couldn't have said it better myself > To Bilge, John Anderson and PD. > > "Thanks for ignoring the rest of the post and focusing on the one thing > of least importance." - PD > > Couldn't have said it better myself You could: http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/SnipCrap.html Dirk Vdm > To Bilge, John Anderson and PD. > > "Thanks for ignoring the rest of the post and focusing on the one thing > of least importance." - PD > > Couldn't have said it better myself Then I suggest you make a new post stating exactly what it is you want to ask, rather than couching it in terms of an irrelevant question. See subject line. PD Arthur Dent: >Thank you Mr Anderson, but I have to point out that your reply is >irrelevant since it did not address the main issue, Einstein's >definition of time. As with so many others, you seem to wish to skirt >around that and would prefer to discuss to properties of particles >rather than the properties of time. If you didn't want to discuss the properties of particles, why did you insist on arguing about the ``size'' of a muon even after you were told that (1) it didn't make sense to talk about it's size, and (2) that ``size'' was irrelevant? If you didn't want to discuss the properties of particles, why did you misquote what I said about particles rather than respond to what I did write so that you could rephrase your question to discuss ``the properties of time'' as you are claiming above? The simplest way to discuss what you say you wanted to discuss would have been to discuss it rather than misquoting replies and arguing about the properties of particles. Now, you are arguing about the argument. What you claim you wanted to discuss and what you are doing to acheive your goal are mutually exclusive. Arthur Dent: >I was actually addressing Bilge, but I am surprised to learn that If you're addressing me and you expect a reasonable response, you'll need to write a reasonable question. I've already addressed what you've listed below as objections. You saw fit to misquote me. You claimed that you dodn't want to discuss particle properties. If that is true, then stop discussing particle properties. If you want to discuss particle properties, then I've already told you what needs to be discussed - relativistic quantum field theory. Whichever you want to do is fine with me. You decide which. I'm not going to go along with some hidden agenda in which you set up a strawman where you pretend not to discuss something until you see a good opportunity to try and create a contradiction where none exists. >having mass does not imply having density since density is defined as >mass/volume. When I went to school, division by zero was undefined and >you seem to accept a zero volume for a finite mass, or, as some would >put it, a singularity. When you went to school, did they also tell you that your division by zero objection applies to classical theories and one of the reasons that relativistic quantum field theories exist is to solve the problems with classical theories? >It is, however, immaterial to the original question, So, why do you keep bringing it up? Just to keep saying something that is incorrect and has been answered by repeating that it's irrelevant? >since I have now replaced the "length" of the muon with two >comoving point-like muons a fixed distance apart, tagged as A and B, Why are you making this so obtuse? What is it you want to know? If you aren't trying to set up some strawman as a troll, why all of the legerdemain? Is there some reason you can't just ask the question you want answered without creating a rube goldberg scenario? >and am asking if Einstein's definition of time, to wit, the time for >light to travel from A to B is equal to the time it takes to travel >from B back to A. Perhaps you could be kind enough to address the real What's the problem? A and B are separated by a fixed distance. You just said so above. The distance from A to B is the same as the distance from B to A. Is there some reason that it should take more time one way than the other given that the velocity of light is the same in both directions? >problem instead of skirting around it, or trying to make it into fault >on my part, as others have tried to do. Or perhaps you cannot. There [...] This is straight forward. Take out a piece of paper and a pen. Draw a horizonal axis and label it `x'. Now, draw a vertical axis and label it `y'. Pick a point along the `y' axis. Obviously, the distance from the origin to the point y is, d^2 = (0-0)^2 + (y-0)^2 = y^2 Now draw a curve from the origin that intersects the same point, but isn't a straight line. Is that line the same length as the vertical line I just described? Is it conceptually difficult to understand how those two paths between the origin and the point, (0, y) can be different lengths? How long is the second path? Well, it's: d = \integral sqrt(dx^2 + dy^2) = \integral sqrt(1 + (dy/dx)^2) dx Now erase the letter `y' and write `t'. Does changing the letters make the difference in the lengths of those two paths any more mysterious? I hope not. The only difference is now there is a minus sign in the expression for the arc length, d = \integral sqrt(dt^2 - dx^2) = \integral sqrt(1 - ((dx/dt)^2) dt Above, dy/dx = tan(A). Here, dx/dt = tanh(A). If you know how to parameterize the curve you drew, then you can solve for the length of the second path. Now just put the one twin on each path. Bilge: This is straight forward. Take out a piece of paper and a pen. Draw a horizonal axis and label it `x'. Now, draw a vertical axis and label it `y'. Pick a point along the `y' axis. Obviously, the distance from the origin to the point y is, d^2 = (0-0)^2 + (y-0)^2 = y^2 Now draw a curve from the origin that intersects the same point, but isn't a straight line. Is that line the same length as the vertical line I just described? Is it conceptually difficult to understand how those two paths between the origin and the point, (0, y) can be different lengths? How long is the second path? Well, it's: d = \integral sqrt(dx^2 + dy^2) = \integral sqrt(1 + (dy/dx)^2) dx Now erase the letter `y' and write `t'. Does changing the letters make the difference in the lengths of those two paths any more mysterious? AD: Yes, I'm afraid it does. I have three points on the x-axis, Ax, A'x and Bx. I have three points on the t-axis - At, Bt and A't. Light travels from (Ax,At) to (Bx,Bt) and returns to (A'x, A't) t A' o | \ | \ B o | / | / [quoted text clipped - 6 lines] | / |/ A------A'-B---------x AB (on the t-axis) does not appear to be BA' as Einstein claims in his definition, the time for light to travel from A to B is equal to the time is takes to travel from B to A. > Bilge: > This is straight forward. Take out a piece of paper and a pen. [quoted text clipped - 39 lines] > definition, the time for light to travel from A to B is equal to the > time is takes to travel from B to A. Hey Androfart, who claimed that lengths are time intervals? Dirk Vdm Arthur Dent: >Bilge: > This is straight forward. Take out a piece of paper and a pen. [quoted text clipped - 14 lines] >mysterious? >AD: Yes, I'm afraid it does. Then, I'm sorry. Your problem is in understanding simple geometry. >I have three points on the x-axis, Ax, A'x and Bx. I have three I didn't ask you to draw three points, nor did I say draw them on the x-axis. Do you have any questions regarding the example _I_ gave you? If not, I'll assume you now understand the twins paradox. Bilge: I didn't ask you to draw three points, nor did I say draw them on the x-axis. Do you have any questions regarding the example _I_ gave you? If not, I'll assume you now understand the twins paradox. AD: I didn't ask about the twins paradox. I'm asking about Einstein's definition of time. There are three points involved, 1) Light leaving A, an event in both the stationary frame and the moving frame. 2) Light arriving at B, an event in both the stationary frame and the moving frame. 3) The light returning to A, which is not an event in the stationary frame as the diagram clearly shows. I am therefore compelled to draw three points. Where do I have a problem? Arthur Dent: >Bilge: >I didn't ask you to draw three points, nor did I say draw them [quoted text clipped - 6 lines] > I'm asking about Einstein's definition of time. There are three points >involved, You don't need to draw three points. Einstein's definition of time is the same as yours. You look at your watch and see how much time has elapsed. >1) Light leaving A, an event in both the stationary frame and the >moving frame. [quoted text clipped - 5 lines] >I am therefore compelled to draw three points. >Where do I have a problem? In trying to turn a simple concept like reading the time from a clock into a convoluted morass. >Arthur Dent May 26, 9:16 am show options >You said muons were point particles. I attribute that to you. That is [quoted text clipped - 3 lines] >Now you ask me to "stop" misrepresenting what you write. >What else have I "made up" and attributed to you? atoms / molecules have size but not density as property you stoopid fock, get lost moren wrote: > >Arthur Dent May 26, 9:16 am show options > >You said muons were point particles. I attribute that to you. That is [quoted text clipped - 7 lines] > fock, > get lost moren Sure, atoms and molecules have an average density. They're composite objects. They also have soft edges, so the answer you get will depend on where you draw the boundary, but that's not unusual. (What's the density of a cirrus cloud, for example?) PD >Sure, atoms and molecules have an average density. They're composite >objects. They also have soft edges, so the answer you get will depend >on where you draw the boundary, but that's not unusual. (What's the >density of a cirrus cloud, for example?) >PD I ment that atoms and molecules dont have that type of density he ment, a lot of morons do that mistake Arthur Dent: Either include the context from the post to which you reply or put up with the replies you receive as a result. Sheeeesh... >You said muons were point particles. I attribute that to you. That is >not a mispresentation. >Infinite density is a conclusion I drew for a point particles having >mass. >Now you ask me to "stop" misrepresenting what you write. And? Is that a problem for you? Do you have some pathological condition that forces you to misrepresent what anyone tells you? >What else have I "made up" and attributed to you? In your post, message-id:<1116697297.404399.202180@o13g2000cwo.googlegroups.com> you wrote: ``5) no classical concept of size makes any sense. Bilge'' You deleted the first part of that sentence, which refers to quantum mechanics and it changes the meaning entirely. Had you bothered to read what I actually wrote, the only way you could have paraphrased me accurately would be to say, ``no classical concept of size makes any sense IN QUANTUM MECHANICS.'' However, you are too lazy to include any context from the responses you receive and instead just write some sort of condensed version of the reply which totally misrepresents the original. Do you understand how to include some context from an article when replying? If you have no interest in posting articles which will help you get what you want, then you'll have to settle for what you get. If you attribute something to me (or anyone else for that matter), copy it _exactly_. Otherwise, you are misquoting them. If you're too lazy to write complete sentences, then expect to get responses that don't contain complete answers. To Bilge Ok, ``no classical concept of size makes any sense IN QUANTUM MECHANICS.'' Now, does size (length) make any sense in relativity? Arthur Dent: >To Bilge > Ok, ``no classical >concept of size makes any sense IN QUANTUM MECHANICS.'' >Now, does size (length) make any sense in relativity? I already told you. It's a point particle. You can either accept that at face value or study quantum field theory, by which time you will have long since answered your question. You accuse me of misrepresenting what you say. I don't want to do that, so I will quite literally repeat the question and your answer to it. AD: "Does size (length) make any sense in relativity?" Bilge: "Its a point particle." At face value, then, you didn't answer the question, but answered a previous one. Arthur Dent: >You accuse me of misrepresenting what you say. I don't want to do that, >so I will quite literally repeat the question and your answer to it. [quoted text clipped - 4 lines] >At face value, then, you didn't answer the question, but answered a >previous one. As far as I can tell, we were still talking about the muon. Of course size makes sense in relativity. Why wouldn't it make sense in relativity? Is there some reason you can't include the _relevant_ context with the proper indent levels? Bilge May 29, 4:35 pm show options Newsgroups: sci.physics.relativity From: dubi...@radioactivex.lebesque-al.net (Bilge) - Find messages by this author Date: Sun, 29 May 2005 15:35:03 GMT Local: Sun,May 29 2005 4:35 pm Subject: Re: How long is a muon when at rest? Reply | Reply to Author | Forward | Print | Individual Message | Show original | Report Abuse Arthur Dent: You accuse me of misrepresenting what you say. I don't want to do that, >so I will quite literally repeat the question and your answer to it. >AD: "Does size (length) make any sense in relativity?" >Bilge: "Its a point particle." >At face value, then, you didn't answer the question, but answered a >previous one . As far as I can tell, we were still talking about the muon. Of course size makes sense in relativity. Why wouldn't it make sense in relativity? Is there some reason you can't include the _relevant_ context with the proper indent levels? Reply Google groups beta doesn't seem to provide the functionality you refer to. I've used copy/paste above as the best compromise I can find. As far as I can tell, the size of an object, x', is the time it takes light to traverse across it and back again, divided by two. Referring to the diagram: t-axis t2 A'' | / | / t1 A'---x'---B' | / | / | / |/ A----------B------- x-axis at t0 <----x'---> At t = 0, A = 0 (origin) light leaves A and travels to B', a length of x', And there it reflects and travels back to A'' again. A, A' and A'' are three positions of the moving rod of length x'. It travels from A to B' at c-v. It travels from B' to A'' at c+v. This gives the time to travel the length x' as x'/(c-v) one way and x'(c+v) for the return, when measured in the stationary frame. Adding these and dividing by two gives, in the moving frame, x' = ct, but [x'/(c+v) + x'(c-v)]/2 in the moving frame. Although Einstein's definition of time seems to work in the moving frame, in the stationary frame t1 isn't half of t2. I find this curious to say the least. | Perhaps you are unaware of such experiments as Michelson-Morley having | "size" as a property and the Lorentz contraction being given as reason [quoted text clipped - 8 lines] | 2) Your original question makes no sense. | FrediFizzx Perhaps your original question might be more suited to an atom or group of atoms instead of a muon? Atoms are known to have a particular approximate size. FrediFizzx http://www.vacuum-physics.com/QVC/quantum_vacuum_charge.pdf or postscript http://www.vacuum-physics.com/QVC/quantum_vacuum_charge.ps FF: Perhaps your original question might be more suited to an atom or group of atoms instead of a muon? Atoms are known to have a particular approximate size. AD: Maybe, although that doesn't change the gist of it. We could take a 3 meter ruler as the "group of atoms", or two muons as the end points of 3 meters. The light passes the back of the ruler at a height of 30,000 meters and reaches the front of the ruler (or the leading muon) at ground level, because the ruler is also travelling at near light speed. According to PD, the length of the ruler is not the distance it travels, which is of course "common sense". In the frame of the earth, it will take 3.0 E+4 meters / c = 1.0 E-4 seconds for light to transit 30,000 meters. In the frame of the ruler, it will take 3.0 meters / c = 1.0 E-8 seconds, and so time dilation is satisfied. Less time has elapsed for the ruler frame than for the Earth frame. The difficulty arises when the light is reflected at ground level, because it takes the same amount of time to travel to the back of the ruler. In the frame of the ruler, this is once again 1.0 E-8 seconds, so that's ok, but in the frame of the earth the light reaches the back end of the ruler at about 1.5 meters above the ground. If it takes the same time to reach the back of the ruler in the earth frame, the back of the ruler is still at 30,000 meters above the ground. You say it is my question that makes no sense. Ok, so you don't understand the question, but that isn't my fault. Certainly something doesn't make sense, so what is it? ... > Perhaps you are unaware of such experiments as Michelson-Morley > having [quoted text clipped - 8 lines] > fellow group members appear to be unable to discuss the issue. > So far the responses have been: All this only to be shown as a troll. What a waste of sperm. <plonk> David A. Smith |
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