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Natural Science Forum / Physics / Relativity / June 2005Proof that HUP is wrong
We fill a box with a radioactive material which randomly emits radiation. The box has a shutter, which is opened and immediately thereafter shut by a clock at a precise time, thereby allowing some radiation to escape. So the time is already known with precision. We still want to measure the conjugate variable energy precisely. We measure the energy by weighing the box before and after. The equivalence between mass and energy from special relativity will allow us to determine precisely how much energy was left in the box. The experiment allows us to determine the exact energy of the box at the exact time, violating quantum uncertainty with extreme prejudice. :-) even without entering to your detailes in your example (which i didnt ) i know from my resarch work on nuclear structure that : the HUP can be *bypasses* byother data acumulation!! it seems that the 'scollars of pysics' didnt imagine it (may be because thety were to much methematics minsed!!) Y.Porat --------------------- > We fill a box with a radioactive material which randomly emits > radiation. The box has a shutter, which is opened and immediately > thereafter shut by a clock at a precise time, thereby allowing some > radiation to escape. So the time is already known with precision. Really? How do you know where the shutter is with "precision"? > We fill a box with a radioactive material which randomly emits > radiation. The box has a shutter, which is opened and immediately [quoted text clipped - 9 lines] > the exact time, violating quantum uncertainty with extreme prejudice. > :-) Hey dude, You forgot how Bohr refuted Einstein "light box" experiment. Bohr said to Einstein: "When the photon is released, there will be a recoil, causing an uncertainty in the position of the clock in the earth's gravitational field. This will produce a corresponding uncertainty in the time recording due to - believe it or not - your own general theory of relativity". Want to outsmart Einstein? Try again. Make your description clearer. p6 > > We fill a box with a radioactive material which randomly emits > > radiation. The box has a shutter, which is opened and immediately [quoted text clipped - 13 lines] > > You forgot how Bohr refuted Einstein "light box" experiment. Bohr didn't win the argument. He only shewed that Einstein didn't either. > Bohr said to Einstein: "When the photon is released, there will > be a recoil, So ? Release two photons in opposite directions at the same time. > causing an uncertainty in the position of the > clock in the earth's gravitational field. This will produce a [quoted text clipped - 3 lines] > Want to outsmart Einstein? Try again. Make your description > clearer. [snip] > So ? Release two photons in opposite directions at the same time. Wee! This chestnut again. And, you know accurately that the two are released in the same direction how exactly? The HUP is a mathematical theorm guy. You can't get around it. All you can do is choose situations that don't satisfy the theorm's inputs and conditions. This does not get you around it. Socks > [snip] > > So ? Release two photons in opposite directions at the same time. > > Wee! This chestnut again. And, you know accurately that the two > are released in the same direction how exactly? he dint say the same direction he saied in opposite direction! you ask how ? you can chose a known case in which photons are emmitied in opposite direction.! dont forget that all that is still a thought experiment!1 all the best Y.Porat ---------------- > The HUP is a mathematical theorm guy. You can't get around it. > All you can do is choose situations that don't satisfy the > theorm's inputs and conditions. This does not get you around it. > Socks > We fill a box with a radioactive material which randomly emits > radiation. The box has a shutter, which is opened and immediately [quoted text clipped - 8 lines] > The experiment allows us to determine the exact energy of the box at > the exact time, violating quantum uncertainty with extreme prejudice. No, it does not -- you simply did not apply it to the situation you described, and essentially assumed it away. Specifically, focus on weighing the box: doing so will take a finite time duration (which you forgot to mention), and it is that duration that applies, not any shutter opening. Each of your two weighings will have an associated uncertainty, which you forgot to mention, and _that_ is the effect of the uncertainty principle. This is supposed to be quantum mechanics, and you cannot assume that the energy contained in the box is fixed -- it will radiate, and there is a non-zero probability for its contents to escape. In addition, your scale will have internal fluctuations (e.g. its spring will not have a precisely constant tension, there is noise in its readout, etc.). You'll find that at the level of the uncertainty principle all of these are important (even though in everyday life they are utterly negligible). So the weight will fluctuate during the time you are weighing it, as expected from the uncertainty principle. Tom Roberts tjroberts@lucent.com > > We fill a box with a radioactive material which randomly emits > > radiation. The box has a shutter, which is opened and immediately [quoted text clipped - 16 lines] > uncertainty, which you forgot to mention, and _that_ is the effect of > the uncertainty principle. Wrong. > This is supposed to be quantum mechanics, and you cannot assume that the > energy contained in the box is fixed -- it will radiate, and there is a [quoted text clipped - 5 lines] > the weight will fluctuate during the time you are weighing it, as > expected from the uncertainty principle. Wrong. 1. You are applying the uncertainty principle to this thought experiment *a priori*, which is insufficient to show that it cannot violate HUP. 2. The simple error here is that when the light leaves the box, the box moves on the scale and this acceleration causes the box to deviate from the observers stationary-frame which introduces uncertainty into the time variable. In fact, if you do the calculations the measurement dispersions end up in concise agreement with Heisenberg's relation. 3. What I posted was Einsteins rebuttal of HUP to Neils Bohr, word for word. Pretty stupid isn't it? I'm glad you agree. > Tom Roberts tjroberts@lucent.com Schoenfeld: >3. What I posted was Einsteins rebuttal of HUP to Neils Bohr, word for >word. Pretty stupid isn't it? I'm glad you agree. That's funny. You didn't give credit to einstein for writing it. Didn't you just accuse uncleal of plagiarism in another thread? You need professional help before you end up as a one of the comical anecdotes in a humor article about the world's dumbest criminals. Eventually your inferiority complex will lead you to do more than merely plagiarize and libel people. > Schoenfeld: > > > >3. What I posted was Einsteins rebuttal of HUP to Neils Bohr, word for > >word. Pretty stupid isn't it? I'm glad you agree. > > That's funny. You didn't give credit to einstein for writing it. Yes I did, I just did it several hours after the fact. Stupid David Semon gurgler from the fountain of knowledge, does the crackpottery of the content of that post suddenly change now that you know it came from Einstein, stupid David Semon spitter of that knowledge? > Didn't you just accuse uncleal of plagiarism in another thread? > You need professional help before you end up as a one of the comical > anecdotes in a humor article about the world's dumbest criminals. > Eventually your inferiority complex but my mom says i'm cool > will lead you to do more than > merely plagiarize and libel people. No, I don't libel or plagiarize. I simply retaliate exponentially. *You* are get what you give * 10. Schoenfeld: >> Schoenfeld: >> > [quoted text clipped - 7 lines] >the content of that post suddenly change now that you know it came from >Einstein, stupid David Semon spitter of that knowledge? Huh? It's still plagiarism regardless of what you did after the fact and none of that has bearing on the fact that you're a crackpot. You can interpret that however you like. >> Didn't you just accuse uncleal of plagiarism in another thread? >> You need professional help before you end up as a one of the comical [quoted text clipped - 3 lines] > >but my mom says i'm cool Then why don't you tell her all of the bullshit you post here? You'll have someone tell you that you're cool and you won't be littering usenet with your idiotic posts. It's a win-win situation for everyone but your mom. >> will lead you to do more than >> merely plagiarize and libel people. > >No, I don't libel or plagiarize. You are also pathologically dishonest. Obviously, you do plagiarize as this very thread demonstrates. While the failure to attribute quoted text might not be such a big deal in many cases, you've gone out of your way to not only accuse others of plagiarism, but you offer no proof that your accusation has any merit. You're worse than the typical televangelist who has at least enough common sense not step in his own crap. >I simply retaliate exponentially. >*You* are get what you give * 10. In otherwords, you find it more productive to be an a.shole and abuse anyone who points out that you're posting a lot of bullshit, than to actually go learn something and avoid the problem altogether. What a surprise. Seek psychological help. >> > We fill a box with a radioactive material which randomly emits >> > radiation. The box has a shutter, which is opened and immediately [quoted text clipped - 18 lines] > > Wrong. No. How can it be wrong ? Schoenfeld dikiberately ommited mention of the weight sampling time. >> This is supposed to be quantum mechanics, and you cannot assume that the >> energy contained in the box is fixed -- it will radiate, and there is a [quoted text clipped - 7 lines] > > Wrong. Illiterate mono-syllable responce to a paragraph of sound physics. > 1. You are applying the uncertainty principle to this thought > experiment *a priori*, which is insufficient to show that it cannot > violate HUP. Schoenfeld's "thought experiment" is a priori. Lacking contrary empirical evidence, It must be consistent with HUP. The correctness of HUP isn't in doubt. Rather, the completeness of QM is under fire. Schoenfeld has made incorrect inferences from HUP. Total energy is always observed to be conserved. The Hamiltonian and it's associated Eigen value gaurentees it. HUP applies to the uncertainty in the partition of energy WRT time. > 2. The simple error here is that when the light leaves the box, the box > moves on the scale and this acceleration causes the box to deviate from > the observers stationary-frame which introduces uncertainty into the > time variable. In fact, if you do the calculations the measurement > dispersions end up in concise agreement with Heisenberg's relation. Erroeous parrot. Old Man doubts that Schoenfeld is capable of performing or even of understanding the calculation. There is no physical cause for HUP. It's intrinsic to QM. > 3. What I posted was Einsteins rebuttal of HUP to Neils Bohr, > word for word. Doubt it. Schoenfeld is an erroneous parrot. Clear and concise, Einstein was never evasive. Trick questions weren't his style. > Pretty stupid isn't it? I'm glad you agree. Schoenfeld is stupid. Bohr and Einstein were brilliant. Einstein argued that QM was incomplete, but not that HUP was empirically falsified. [Old Man] >> Tom Roberts tjroberts@lucent.com > >> > We fill a box with a radioactive material which randomly emits > >> > radiation. The box has a shutter, which is opened and immediately [quoted text clipped - 21 lines] > No. How can it be wrong ? Schoenfeld dikiberately ommited > mention of the weight sampling time. No I didn't. > >> This is supposed to be quantum mechanics, and you cannot assume that the > >> energy contained in the box is fixed -- it will radiate, and there is a [quoted text clipped - 10 lines] > Illiterate mono-syllable responce to a paragraph of sound > physics. Actually silly Old Man, had you improved reading comprehension you would've noticed more than that word for my response. > > 1. You are applying the uncertainty principle to this thought > > experiment *a priori*, which is insufficient to show that it cannot [quoted text clipped - 6 lines] > > Schoenfeld has made incorrect inferences from HUP. Is that why you can't show such an inference? > Total energy is always observed to be conserved. Irrelevant to this thread (but thanks for the tip). > The > Hamiltonian and it's associated Eigen value gaurentees > it. Irrelevant to this thread (but thanks for the tip). > HUP applies to the uncertainty in the partition of > energy WRT time. I don't know what that means. How do you partition energy? > > 2. The simple error here is that when the light leaves the box, the box > > moves on the scale and this acceleration causes the box to deviate from [quoted text clipped - 4 lines] > Erroeous parrot. Old Man doubts that Schoenfeld is capable > of performing or even of understanding the calculation. If you apologize for your baseless and unwarranted insults, I will consider tutoring you and consider providing you those calculations (whether using gravitational or inertial mass, you choose). > There > is no physical cause for HUP. It's intrinsic to QM. Did I say that the inverse proportionality of uncertainty between conjugate variables' is somehow causually related? Why are you bringing this up? Everything you have said thus far is either completely unrelated or corrections for mistakes I did not make. Is this how you normally post on usenet or is this a special occasion? > > 3. What I posted was Einsteins rebuttal of HUP to Neils Bohr, > > word for word. [quoted text clipped - 6 lines] > > Schoenfeld is stupid. Bohr and Einstein were brilliant. Perhaps, but that was Einsteins argument whether you like it or not. > Einstein argued that QM was incomplete, but not that > HUP was empirically falsified. Wrong. In that argument, Einstein tried to devise a theoretical way to measure the energy and time of a system more accurately than allowed by HUP. This was his goal, plain and simple. Einstein in all his genius did not realize that this is like trying to measure the frequency spectrum of a wave at a precise point in time - conceptual nonsense. > [Old Man] > > >> Tom Roberts tjroberts@lucent.com >> .... HUP applies to the uncertainty in the partition of >> energy WRT time. > > I don't know what that means. How do you partition energy? Between potential and kinetic energy. Between components of kinetic energy. Between radiated energy, and that of the emitter. Total energy is conserved. Simple math, elegant physics: E = E1 + E2 delta_E = 0 delta_E1 * delta_t1 = hbar / 2 delta_E1 = - delta_E2 >> .... Einstein argued that QM was incomplete, but not that >> HUP was empirically falsified. > > Wrong. In that argument, Einstein tried to devise a theoretical way to > measure the energy and time of a system more accurately than allowed by > HUP. This was his goal, plain and simple .... Cockeyed. EPR is clear and concise. No more than undergraduate QM is required. Either Schoenfeld has never read EPR, or he's stupid, or he's blinded by prejudice. Probably all three. [Old Man] >> [Old Man] >> >> >> Tom Roberts tjroberts@lucent.com > >> .... HUP applies to the uncertainty in the partition of > >> energy WRT time. [quoted text clipped - 12 lines] > > delta_E1 = - delta_E2 Hey pops, http://mathworld.wolfram.com/Partition.html. Please don't use words you don't understand in contexts they do not belong. > >> .... Einstein argued that QM was incomplete, but not that > >> HUP was empirically falsified. [quoted text clipped - 6 lines] > QM is required. Either Schoenfeld has never read EPR, or he's stupid, > or he's blinded by prejudice. Probably all three. Do you normally selectively quote and write pointless responses or is your senility getting the better of you? Time for a pill refill pops. > [Old Man] > > >> [Old Man] > >> > >> >> Tom Roberts tjroberts@lucent.com Old Man says... >Schoenfeld is stupid. Bohr and Einstein were brilliant. >Einstein argued that QM was incomplete, but not that >HUP was empirically falsified. Actually, Einstein *did* start out arguing that the uncertainty principle was wrong, but Bohr gave a convincing rebuttal to all his thought experiments attempting to show this. Einstein later retreated to the more modest position that QM was incomplete. To quote from this paper http://homepages.paradise.net.nz/rochelle.f/Bohr-v-Einstein.html The debate between Bohr and Einstein over the interpretation of quantum theory began in 1927 at the fifth Solvay Conference of physicists and ended at Einstein’s death in 1955. The most active phase of the debate ran from 1927 to 1936 when Bohr replied to the EPR paper written by Einstein and two colleagues. The debate took the form of various thought experiments invented by Einstein in which it would be theoretically possible to measure complementary properties such as the position and momentum of a particle or its energy at a certain point in time. If these measurements were possible it would show that Bohr’s idea of complementarity and Heisenburg’s uncertainty principle were wrong and that the quantum theory proposed by Bohr, called the Copenhagen Interpretation, was wrong. Later Einstein also attempted to disprove quantum theory at the sixth Solvay Conference in 1930 with the “Clock in the Box Experiment”. This involved a box with a hole in one wall covered by a shutter which could be opened and closed by a clock mechanism inside the box. The box also contained radiation which would add to the weight of the box. The box would be weighed and then at a given moment the clock would open the shutter allowing a single photon of radiation to escape. The box could then be re-weighed, the difference between the two weights telling us the amount of energy that escaped using the formula e=mc2. Under the uncertainty principle it is not possible to obtain an exact measurement of the energy of the released photon and the time at which it was released. Einstein’s experiment was designed to show such exact measurements were possible, the clock measuring the time of release of the energy and the weighing of the box disclosing the amount of energy involved. Bohr’s reply involved looking at the practicalities involved in making the required measurements. The box had to be weighed so it had to be suspended by a spring in a gravitational field. To weigh the box it is necessary to compare a pointer attached to the box against a scale. After the photon had left the box weights can be added to the box to restore the pointer to the same position against the scale as it had been before the photon escaped. The weight added to the box gives the weight of the escaped photon. However this involves a measurement of the box to ensure the pointer is back at its original position. This measurement is subject to the uncertainty principle concerning the position and momentum of the box which brings uncertainty into the measurement of the weight of the box. If there is uncertainty in the weight of the box, then there will be an uncertainty in the energy of the released photon. There will also be uncertainty in the time of the released energy as the speed of time depends upon the position of a clock in a gravitational field. This position is uncertain then the time of the release of the photon will also be uncertain. This means both the time and the amount of energy released will be uncertain so Einstein’s thought experiment did not contradict the uncertainty principle. -- Daryl McCullough Ithaca, NY yet how many loafs of bread did that principle borough along its existance?? 2 and to what theoretical acheivements it was leading?? TIA Y.Porat ---------------------------- >> > We fill a box with a radioactive material which randomly emits >> > radiation. The box has a shutter, which is opened and immediately [quoted text clipped - 18 lines] > > Wrong. No. How can it be wrong ? Schoenfeld dikiberately ommited mention of the weight sampling time. >> This is supposed to be quantum mechanics, and you cannot assume that the >> energy contained in the box is fixed -- it will radiate, and there is a [quoted text clipped - 7 lines] > > Wrong. Illiterate mono-syllable responce to a paragraph of sound physics. > 1. You are applying the uncertainty principle to this thought > experiment *a priori*, which is insufficient to show that it cannot > violate HUP. Schoenfeld's "thought experiment" is a priori. Lacking contrary empirical evidence, It must be consistent with HUP. The correctness of HUP isn't in doubt. Rather, the completeness of QM is under fire. Schoenfeld has made incorrect inferences from HUP. Total energy is always observed to be conserved. The Hamiltonian and it's associated Eigen value gaurentees it. HUP applies to the uncertainty in the partition of energy WRT time. > 2. The simple error here is that when the light leaves the box, the box > moves on the scale and this acceleration causes the box to deviate from > the observers stationary-frame which introduces uncertainty into the > time variable. In fact, if you do the calculations the measurement > dispersions end up in concise agreement with Heisenberg's relation. Erroeous parrot. Old Man doubts that Schoenfeld is capable of performing or even of understanding the calculation. There is no physical cause for HUP. It's intrinsic to QM. > 3. What I posted was Einsteins rebuttal of HUP to Neils Bohr, > word for word. Doubt it. Schoenfeld is an erroneous parrot. Clear and concise, Einstein was never evasive. Trick questions weren't his style. > Pretty stupid isn't it? I'm glad you agree. Schoenfeld is stupid. Bohr and Einstein were brilliant. Einstein argued that QM was incomplete, but not that HUP was empirically falsified. [Old Man] >> Tom Roberts tjroberts@lucent.com > We fill a box with a radioactive material which randomly emits > radiation. The box has a shutter, which is opened and immediately [quoted text clipped - 5 lines] > us to > determine precisely how much energy was left in the box. Schoenfeld, you are an idiot both on paper and in the lab. > The experiment allows us to determine the exact energy of the box at > the exact time, violating quantum uncertainty with extreme prejudice. > :-) Idiot. How accurately can you weigh? How accurately can you tell time? How fast can you drop a shutter - faster than a foot/nanosecond? Hey stooopid Schoenfeld, can you spell "adiabatic?" Hey stooopid Schoenfeld, track the loss in weight of a cooling object Planck time by Planck time. Idiot.  SignatureUncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/qz.pdf > > We fill a box with a radioactive material which randomly emits > > radiation. The box has a shutter, which is opened and immediately [quoted text clipped - 18 lines] > Hey stooopid Schoenfeld, track the loss in weight of a cooling object > Planck time by Planck time. Idiot. Stupid Schwartz should realize I merely quoted Einstein. Do wall-wailers get spanked when they insult their own brethren, stupid Schwarz? Stick to stealing others work coz u ain't got nothing new. > -- > Uncle Al > http://www.mazepath.com/uncleal/ > (Toxic URL! Unsafe for children and most mammals) > http://www.mazepath.com/uncleal/qz.pdf <snip> > Stupid Schwartz should realize I merely quoted Einstein. I saw no quotes in your post. Where *should* they have been? Tom Davidson Richmond, VA >> > We fill a box with a radioactive material which randomly emits >> > radiation. The box has a shutter, which is opened and immediately [quoted text clipped - 22 lines] >wall-wailers get spanked when they insult their own brethren, stupid >Schwarz? Stick to stealing others work coz u ain't got nothing new. If you merely quoted Einstein, you should already know why the HUP still has nothing wrong with it. Einstein tried that argument decades ago, did you think it would work better today? Signature"We've all heard that a million monkeys banging on a million typewriters will eventually reproduce the entire works of Shakespeare. Now, thanks to the Internet, we know this is not true." -- Robert Wilensky > We fill a box with a radioactive material which randomly emits > radiation. The box has a shutter, which is opened and immediately [quoted text clipped - 9 lines] > the exact time, violating quantum uncertainty with extreme prejudice. > :-) QM is logically self-consistent. Do the experiment. Don't forget to record the time spent in weighing the box. If delta_t is the time spent in weighing the box, W = M * g = E ( g / c^2) then ( delta_W ) * ( delta_t ) = hbar * g / 2 * c^2 [Old man] > We fill a box with a radioactive material which randomly emits > radiation. The box has a shutter, which is opened and immediately [quoted text clipped - 9 lines] > the exact time, violating quantum uncertainty with extreme prejudice. > :-) Trick questions and physics don't mix. Schoenfeld has made two measurements of the box's weight. One from t = - infinity to t = 0. The other, from t = delta_t to t = + infinity, where delta_t is the time interval over which the shutter is open. By HUP, each weight determination, W1, and, W2, is precise. delta_t can also be known precisely. Where's the HUP violation ? The measurements of W1, W2, and delta_t were performed over orthogonal time intervals. Now repeat the experiment: is delta_W = W1 - W2 = constant ? [Old Man] > Schoenfeld has made two measurements of the box's weight. > One from t = - infinity to t = 0. The other, from t = delta_t > to t = + infinity, where delta_t is the time interval over which > the shutter is open. [...] _IF_ he could do that, then his claims might be able to hold up. But he cannot possibly make any measurement of infinite duration. The finite duration of the measurement is related to its finite accuracy (but there are also noise, etc. as I said before). His basic fallacy is assuming infinite accuracy in his measurements. He is essentially ignoring the HUP and its effects on his measurements, and then claiming he has "proven" that the HUP isn't valid.... Tom Roberts tjroberts@lucent.com >> Schoenfeld has made two measurements of the box's weight. >> One from t = - infinity to t = 0. The other, from t = delta_t [quoted text clipped - 9 lines] > essentially ignoring the HUP and its effects on his measurements, and then > claiming he has "proven" that the HUP isn't valid.... The trick part of Schoenfeld's question is that delta_t is non sequitur. No matter the value of delta_t, total energy is observed to be conserved. The point here isn't over the separate measurability of delta_t or of W1 or of W2. They're measured sequentially in time. However, there's no guarantee that the determination of W2 isn't effected by the measurements of W1 and delta_t. Let delta_E be the measured release of radiation during time interval, delta_t. Then, conservation of energy for each event: delta_E = ( c^2 / g ) ( W1 - W2 ) Note the absence of delta_t in the above. However, over many measurements, Std_Dev{ delta_E } = hbar / 2 * delta_t . Std_Dev{ W1 - W2 } = ( g / c^2 ) ( hbar / 2 * delta_t ) This is exactly how one determines the energy width and / or the lifetime of a nuclear state. (W1, W2) from particle kinematics and / or delta_E from gamma energy. For each event, they add up via conservation of energy. No HUP. Delta_t isn't involved in kinematics. Get delta_t via HUP. [Old man] > Tom Roberts tjroberts@lucent.com > >> Schoenfeld has made two measurements of the box's weight. > >> One from t = - infinity to t = 0. The other, from t = delta_t [quoted text clipped - 18 lines] > time. However, there's no guarantee that the determination > of W2 isn't effected by the measurements of W1 and delta_t. ------------- W2 is not affected by measuring W1 - in case that two photons in opposite direction were *leaving* the W1 iow the moment they left W1 with no recoil they have no more any connection to W1 Y.Porat ------------------ Schoenfeld: Still fails to bullshit his way to a nobel prize, >We fill a box with a radioactive material which randomly emits >radiation. The box has a shutter, which is opened and immediately >thereafter shut by a clock at a precise time, thereby allowing some >radiation to escape. Let's see if I understand this. You plan to use radioactive decays, which have measured decay rates in agreement with quantum mechanical calculations to try and refute quantu mechanics? Doesn't that seem a bit illogical? Wouldn't it be simpler just to find a radioactive decay that violates the uncertainty principle and save the work involved in creating a rube goldberg experiment that relies on delusional handwaving rather than hard numbers from an experiment that can be performed, in principle? >So the time is already known with precision. It's always useful to begin a string of handwaving platitudes with a statement that assumes the result by virtue of not limiting yourself to a real physical process. >We still want to measure the conjugate variable energy precisely. >We measure the energy by weighing the box before and after. The uncertainty in the energy due to only classical thermodynamic fluctuations (no quantum mechanics involved) is, \Delta E = sqrt(kC_v) T, C_v = heat capcity at constant volume The mass if the box before and after a shutter click is given by m_f = m_i - \Delta m. The change in mass has to exceed the classical fluctuations in order to determine the mass has changed, so \Delta m > sqrt(kC_v) T/c^2 The termperature of the box must be greater than the surrounding environment, or else radiation will enter the box with equal probability that it leaves the box. So take T to be some T > 300 K, like 1000 K. For C_v, an order of magnitude estimate is sufficient and for a monatomic ideal gas, C_v = (3/2)nR. If n is 1 mol, then C_v = R/a_avag = k, where a_avag is the avagadro constant. sqrt(kC_v) T/c^2 = sqrt(3k^2 a_avag/2) T/c^2 The smallest energy you you can measure in any shutter click that could differentiate between a change in mass and a fluctuation from just classical considerations in 1 mol of gas is, \Delta E of about 81 GeV or a mass of about 1.5 x 10^-25 kg To violate the uncertainty principle, you therefore need shutter speeds that violate the uncertainty principle which is easy to determine: \Delta t < hbar/(\Delta E) Meaning you have to make measurements of \Delta E = 81 GeV for intervals of \Delta t < 10^-26 sec. So, what does that mean in terms of the power being dissipated by the box? Well, P = dE/dt, so P = 1.3 x 10^19 watts for 1 mol of nuclei in your box. That's a rather substantial rate for electromagnetic radiation and since that won't happen for a mol of gas at 1000 K, you are out of luck for E&M radiation. But you can always try alpha decay so that the 81 GeV is in the form of low energy alpha particles. 20 each 10^-26 seconds to be precise for 1 mol of pure radon gas. You can also drop the temperature back down, but that doesn't help a lot. How many radon decays occur each 10^-26 seconds, on average for 1 mol of pure radon gas? The half-life of radon is 3.8 days. When you're through doing it the hard way, see if you can figure out why this should have been obvious from the start. Unfortunately, regardless of how you do it, you'll need a detector that violates the uncertainty principle to count the alpha particles. Violating the uncertainty principle with apparatus borrowed from a universe with different physical laws doesn't count, unless you can demonstrate that you borrowed such equipment and it works in this universe. In sci.physics.relativity Schoenfeld <schoenfeld1@gmail.com> wrote: > We fill a box with a radioactive material which randomly emits > radiation. The box has a shutter, which is opened and immediately [quoted text clipped - 4 lines] > equivalence between mass and energy from special relativity will allow > us to determine precisely how much energy was left in the box. This was the experiment proposed by Einstein at the 1930 Solvay Conference. You knew that, right? So you also knew Bohr's reply, which analyzed in detail the uncertainty in the "precise time" caused by the change of the energy of the box and the consequent gravitational red shift. Bohr's answer is reprinted in _Quantum Theory and Measurement_, ed. Wheeler and Zurek, p. 32-36. Steve Carlip > This was the experiment proposed by Einstein at the 1930 Solvay > Conference. ... Bohr's answer is reprinted in _Quantum > Theory and Measurement_, ed. Wheeler and Zurek, p. 32-36. You can find this on the web at http://www.marxists.org/reference/subject/philosophy/works/dk/bohr.htm Tom S. |
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