nishri (01/13/83)
"An electrical signal in a conductor, under suitable conditions of very low L and C values, can be made to pass through a conductor at a velocity considerably greater than that of light." So concludes Harold W. Milnes, Ph.D, in the January 1983 issue of "Radio-Electronics" in an article that begins on page 55. I found I did not agree with parts of the article. I would be interested in comments from others who have read the article. Please mail comments to : decvax!utzoo!utcsrgv!utcsstat!nishri Informational replies of general interest should be posted to net.physics
ltn (01/14/83)
Under certain propagation conditions (not necessarily in a conductor; the same thing can happen to a wave propagating in a plasma), an electrical signal *can* travel at a velocity greater than light. *But* that is only true for the phase velocity. The phase velocity is the velocity of a wave of a single frequency, which means that signal has a constant amplitude for all time. The key point is that the group velocity *cannot* exceed the speed of light. The group velocity is the velocity that a modulation envelope (whether amplitude modulation, on-off cw pulses, or whatever) will travel at. The difference arrises because modulation involves propagating signals of many different frequencies (remember Fourier) which travel with different velocities (the faster-than-light phenomenon only occurs in dispersive media). Thus *information* still cannot travel faster than light, and information propagation is what relativity is concerned with. Les Niles, Bell Labs Murray Hill (aluxz!ltn)
jis (01/14/83)
Although the phase velocity of an elctromagnetic disturbance can be greater
than the speed of light in dispersive media, it strikes me as improper or
misleading to claim that an "electric signal" can travel faster than light.
The concept of a signal is intimately related to communication, and a
"electric signal" travelling at the phase velocity (whatever that might mean)
cannot be used to relly send a "signal" (as is normally connoted by the word)
to anyone at a velocity greater than that of light.
Jishnu Mukerji
ABI Holmdel 1B-425
{vax135, harpo, allegra}!hocsd!jisKANorman.ES@PARC-MAXC (01/16/83)
The following statemant is true, yet it is not possible to physically construct such a structure: "An electrical signal in a conductor, under suitable conditions of very low L and C values, can be made to pass through a conductor at a velocity considerably greater than that of light." The real difficulty is designing such a wave guide. The propogation delay in an homogeneous medium is Tpd= (L0 * C0))**0.5 = (<mu>0 * <mu>r * <epsilon>0 * <epsilon>r )**0.5 Where <mu>0 = 4*<pi>*10**-7 Henry/meter <epsilon>0= 8.85*10**-12 Farad/meter and both <mu>r and <epsilon>r are both necessarily greater than 1. Thus where both are 1, the minimum value of 3.33*10**-9 seconds/ meter which is also known as 3*10**8 meters/second. One may claim to find materials with <mu>r less than one, or those with <epsilon>r less than one, but this exceedingly unlikely in this physical universe. If you can find one or both, please send a sample to me, I'll pay the postage! Kevin Norman Xerox Corp.
faustus (01/22/83)
A recent article mentioned a gas jet from a quasar (wasn't it a galaxy,
though?) as an example of faster than light transmission of signals.
This example is not necessarily a case of something actually moving
faster than c (a signal, or whatever). On possible explanation that
I have seen for this phenomenon is analogous to what happens when you
shine a flashlight on clouds and move it quickly from one side of the
sky to another. The apperant velocity of the spot is very high, but
the actual movement that takes place is really quite small. Well, I
don't know if this is useful, but I just thought I'd mention it.
-Wayne Christopher
faustus@berkeley
ucbvax!faustusBillW@SRI-KL (01/23/83)
From: William "Chops" Westfield <BillW @ SRI-KL> using wave partical duality (If I remember this correctly), the phase velocity of the waveform of a baseball is something like C^2/V... Of course the signal, which is the group velocity of the wave packet, turns out to be just V, the velocity of the baseball... BillW
gwyn@Brl-Bmd.ARPA (01/23/83)
From: Doug Gwyn <gwyn@Brl-Bmd.ARPA> c^2 / v is also the true speed of a so-called "tachyon" of nominal velocity v > c. I worked this out in 1970 and am sorry to see tachyons still considered something special.
Marshall.WBST (01/24/83)
Could you send me a reference to the slow speed of tachyons? --Sidney Marshall
gwyn%brl-vld@sri-unix.UUCP (06/02/83)
From: Doug Gwyn VLD/VMB <gwyn@brl-vld> There is no way to send useful signals faster than light even in quantum theory. Some of the abstract entities in the theory can "propagate" faster than light but that is not the same thing as practical signaling. Also note that classical quantum theory is non-relativistic and a more careful theory must be used when investigating such matters. My understanding of the Bell inequalities is that they demonstrate the incompatibility of simplistic superposition (linear) quantum theory and relativity. In the above I have not bothered to take into account the demonstrable isomorphism between subluminal and superluminal speeds explained some time back in this mailing list.
guy@rlgvax.UUCP (06/03/83)
No, if I remember correctly, Bell's Theorem merely states that no theory which
is:
1) local - i.e., if any thing happening at point A is to affect something at
point B, any "signal" must pass through all the intermediate points at a
finite speed.
2) realistic - i.e., says that the underlying variables of the theory (position,
momentum, field strengths, etc.) must have values independent of the observer.
can NOT exactly reproduce the predictions of quantum mechanics. Therefore,
if somebody concocts a local, realistic theory, there must be an experimental
test to tell whether it or quantum mechanics is correct. In fact, there have
been several such tests; all but one validated quantum mechanics, and the
other one is in doubt.
This does NOT mean that "nature is not local", i.e. you can send "signals"
at infinite speed or via "action at a distance". It merely says "nature is
either local or realistic, not both". I'm not familiar with the mechanics
of the theorem, so I'm sure I'm leaving out other conditions (i.e., "nature
is not local, realistic, and ... all together").
Guy Harris
RLG Corporation
{seismo,mcnc,we13,brl-bmd,allegra}!rlgvax!guymarkb@sdcrdcf.UUCP (06/04/83)
Bell's theorm syas that due to weird quantum effects an event can cause changes in another event via what appears to be faster-then-light messages. But, due to the random nature of the changes the only way to determine the what actually happened to to compare the sequence of events at one place with the sequence of events at the other which need non-random messages which must travel slower then light. This is the same problem observed in the famous twin paradox where as long a constant velocities are maintained the you can never get the twins together to compare there aging and determine which is really older. Mark Biggar
AI.Mayank@MCC.ARPA (06/26/85)
From: Mayank Prakash <AI.Mayank@MCC.ARPA> > I just read "In Search Of Schrodinger's Cat," a book by John Gribbin, > intended to introduce laymen to the subject of quantum mechanics. Does > anybody have any comments on the following excerpt, with respect to > info. travelling faster than the speed of light? The first (long) > paragraph gives technical details on how the experiment works, the > second (short) paragraph gives the results of the experiment: that > information was transmitted instantaneously, i.e., faster than the speed > of light. There is nothing wrong with faster than light speeds, as long as no information is transmitted at those speeds. In this particular experiment, there is no paradox for the following reason - this setup cannot be used to communicate at super-luminal speeds. To see this, imagine two people sitting at opposite sides of the ring. Let's call them John and Mary. Suppose they use the different states of the system as the letters of an alphabet. For simplicity, assume that the system has two states, denoted by 0 and 1. To send the message,say 11001, to John, Mary would have to successively put the system in the states 1, 1, 0, 0, 1. Let us assume that the system starts out in the state 0. Then, Mary has to change the state of the system to 1. To do this, she will have to apply an external influence to the system for a certain duration. However, due to uncertainty principle, she cannot be certain that the system is an the state 1 at the end of this duration. She can only be sure that it is in state 1 with probability, say 98%, and in state 0 with probability 2%. To decipher this message, John will now have to make a measurement on the system, and he will find it in state 1 with probability 98%, and in state 0 with probability 2%. But, no matter which state he finds the system in, he does not know what the probabilities are (if he did, he wouldn't have to make the measurement, as he already knows what state Mary INTENDED the system to be in, i.e., what she was trying to communicate). Therefore, from John's point of view, the measurement of the state of the system does not tell him anything at all. Result: no meaningful messages can be transmitted between John and Mary using this system at ANY speed, let alone faster than light. This experiment reminds me of the so-called EPR (Einstien-Podolsky-Rosen) paradox - imagine a bound system of two spin half particles with net spin zero. We hit it with a spin zero particle to seperate the two particles, so that they start moving in opposite directions. The net spin of the system was zero when we started, so due to conservation of angular momentum, it will remain zero. Suppose after the two particles have been seperated by a large distance, we make a measurement of the spin of one of the particles. Before the measurement was made, the spin state of each particle was inderminate. After the measurement is made, the spin state of the measured particle is determined (say it is up). Since the total spin must be zero, the other particle is now forced to chang its state from an inderminate state to one with spin down. This must happen instantaneously, no matter how far apart the two particles are. The important thing here is that no information can actually be transferred in this manner, since what state the first particle will be found cannot be determined in advance. This famous paradox caused a big debate between Einstein and Niels Bohr in the early 30's, as Einstein did not believe in the probabilistic interpretation of QM. - mayank. -------
knutsen@sri-unix.ARPA (06/26/85)
From: knutsen (Andrew Knutsen) > To do this, she will have to apply an > external influence to the system for a certain duration. However, due to > uncertainty principle, she cannot be certain that the system is an the state 1 > at the end of this duration. She can only be sure that it is in state 1 with > probability, say 98%, and in state 0 with probability 2%. To decipher this > message, John will now have to make a measurement on the system, and he will > find it in state 1 with probability 98%, and in state 0 with probability 2%. > But, no matter which state he finds the system in, he does not know what the > probabilities are (if he did, he wouldn't have to make the measurement, as he > already knows what state Mary INTENDED the system to be in, i.e., what she was > trying to communicate). Can't John and Mary decide beforehand what the duration of influence is, and therefore the probabilities are? And using those probabilities come up with a suitable ECC? There is a certain probability of mistake in any medium. > This experiment reminds me of the so-called EPR (Einstien-Podolsky-Rosen) > paradox Its long been agreed that no info can be transmitted via EPR (well by most people anyway)... The people receiving the particles cannot influence their state, only measure them. The "paradox" is due to the undecided correlation, not superluminal info transfer. Andrew
MJackson.Wbst@Xerox.ARPA (06/26/85)
I believe that your explanation of why the "superconducting ring" experiment does not violate the "speed-of-light limit" for information transfer is wrong. Information need not be guaranteed error-free to be information, and (meaningful) messages are sent over non-error-free (noisy) channels all the time. All that is required is that the signal sent and received not be random. Contrast this with your remarks on the EPR "paradox", where you correctly state that "no information can actually be transferred in this manner, since [in] what state the first particle will be found cannot be determined in advance." Here one has a 50-50 proposition; the signal "sent" is random, and the signal "received" is indistinguishable from random since it is *determined* (in some sense) by a random input. There is an excellent, and quite accessible, introduction to EPR, Bell's inequality, and the Aspect experiments in /Physics Today/ of a couple of months ago. Mark
gwyn@BRL.ARPA (06/26/85)
From: Doug Gwyn (VLD/VMB) <gwyn@BRL.ARPA> Re: EPR paradox It's even worse than that -- spatially separated particles CANNOT be such that a happening at one of them causes a related happening INSTANTANEOUSLY at the other. This is because simultaneity is a relative concept, devoid of absolute physical meaning. This is the root of Einstein's objection.
mikes@AMES-NAS.ARPA (06/26/85)
From: mikes@AMES-NAS.ARPA (Peter Mikes)
That (relativity of simultaneity) IS NOT root or related to EPR
problem. Imagine an photon as spherical wave origaniting at North Star.
The moment you detect (absorb) that one photon here, on Earth. the whole
big sphere collapses 'instananeously)'. T%hat is the root of problem.AI.Mayank@MCC.ARPA (06/27/85)
From: Mayank Prakash <AI.Mayank@MCC.ARPA> First of all, please, please D O N O T send messages both to the bboard and me. If I am corresponding on the bboard, I read the bboard. If I don't, I will say so in the message. So please reply only to the bboard. Thanx. Now for the objections raised to my earlier message - 1. (Knutsen, Jackson) John and Mary have to decide to beforehand the duration of the influence in order to communicate. The problem here is not whether they can use this setup as a communication device (as in a telephone), but rather can they use it to produce a contradiction with the theory of relativity. Unless the communication is 100% reliable, a contradiction will not result. To improve the reliability, one will have to detect errors and retransmit, and in that case, I am willing to bet that the effective speed will have to be less than that of light (although I have not done any calculations on this yet.) 2. (Gwyn) There are really two issues here - the theory of relativity, and the quantum theory of measurement. The first is well understood and empirically confirmed to as high an accuracy as is possible with the current technology. The second has been a painful thorn in the otherwise perfect Copenhagen interpretation of quantum mechanics ever since its beginning, and despite many attempts to date, has not been satisfactorily expounded. The point of the original message by McNelly however was if the superconducting ring was in contradiction to relativity, the answer to which is no, as I explained. Let me now take up your objection - essentially that a spatially distributed wave function collapses instantaneously upon measurement, and this seems to contradict relativity. Well, yes and no. Yes because how does the wave function communicate its collapse information to points far apart instaneously? No because that still does not lead to a contradiction. Consider your photon from North Pole example. It has a spherical wave function until the point it is detected on Earth, at which time it is localized, say within your eye. Now suppose another observer is moving along say in a spaceship on the other side of the North Pole, and is also trying to detect the same photon. True, simultaneity is relative, and what appears to us as a simultaneous collapse of the wave function cannot appear simultaneous to our friend, and indeed, it does not appear to him at all. Once the photon has been seen by you, it is gone, our friend wouldn't even know it existed. So he doesn't have to worry about simultaneity. Only the wave function of the photon needs to carry out its collapse in such a way that if it is observed at a point A, then it may not be observed at a different point B, independent of the time difference between the two observations, and the states (of motion) of the two observers. Admittedly not a very satisfactory situation, but at least free of contradictions. At any rate, this is the best that can be done until we really understand the quantum theory of measurement. - mayank. ========================================================================== II Mayank Prakash AI.Mayank@MCC.ARPA (512) 834-3441 II II 9430 Research Blvd., Echelon 1, Austin, TX 78759. II ========================================================================== -------
MJackson.Wbst@Xerox.ARPA (06/27/85)
[To: Mayank Prakash <AI.Mayank@MCC.ARPA>] No, you're *still* wrong about faster-than-light information transfer and uncertainty. Suppose one had the situation you describe, Mary trying to send signals by "apply[ing] an external influence to the system for a certain duration". I assert that in order for Mary's "influence" to raise the probability of a state transition *above what it would be in the absence of the influence* (i.e. above random) either: - the influence must be applied over the entire system, or - the duration of the influence must be > L/c, where L is the distance to the other side of the system. In neither case is superluminal communication at issue. If this were not the case, an external observer would conclude *unambiguously* that Mary's actions were *causing* an effect (albeit perhaps a probabilistic effect) outside of Mary's light cone. Then some relatively moving observer would see the order of these events (cause and effect) reversed, a contradiction which would identify a preferred frame contrary to relativity. Note that in the EPR situation there is a symmetry between detection-at-A and detection-at-B which is missing in your John-and-Mary case. Point A may be closer to the source (so the stationary observer says "detection at A 'causes' the particle approaching B to change state", but since A and B are outside each other's light cones there are moving observers who can equally say that the particle at B arrived first, and conclude the reverse. It is the *lack* of causal influence, not a 2% uncertainty in it, which prevents a contradiction. Mark
AI.Mayank@MCC.ARPA (06/28/85)
From: Mayank Prakash <AI.Mayank@MCC.ARPA> >I assert that in order for Mary's "influence" to raise the probability >of a state transition *above what it would be in the absence of the >influence* (i.e. above random) either: > - the influence must be applied over the entire system, or > - the duration of the influence must be > L/c, where L is > the distance to the other side of the system. Mark, That's correct and is the reason why they cannot communicate faster than light using this setup. I don't see what you are complaining about. Let me backtrack a little - the whole thing started when McNelly wondered how could information be transferred faster than light in the superconducting ring, and I attempted to explain why that is not a contradiction (at least not an empirical one). You can either agree with my explanation, in which case we have no quarrel, or you can disagree, in which case you must at least explain why my explanation is wrong, and perhaps, in addition, also supply an exlpanation of your own, and we will have something to talk about. - mayank. ========================================================================== II Mayank Prakash AI.Mayank@MCC.ARPA (512) 834-3441 II II 9430 Research Blvd., Echelon 1, Austin, TX 78759. II ========================================================================== -------
brooks@lll-crg.ARPA (Eugene D. Brooks III) (06/30/85)
> Let me now take up your objection - essentially that a spatially distributed > wave function collapses instantaneously upon measurement, and this seems to > contradict relativity. Well, yes and no. Yes because how does the wave The wave function is not physical matter or an energy field. It is a computational entity used to predict the results of experiments. When you solve the equations of motion, you are solving for the motion of a computational entity which can then be used to predict the results of experiment. It won't predict results that are in violation with relativity, ie that the photon gets absorbed sooner than the speed of light would allow for. The wave function itself is just a computational device and is not some real physical thing that is distributed over space. The wave function "collapse" is simply the statement that there was one photon and if it gets absorbed in a given detector then no other detectors will absorb it. This is about as simple and intuitive as you can get.
MJackson.Wbst@Xerox.ARPA (07/01/85)
[To: Mayank Prakash <AI.Mayank@MCC.ARPA> BTW, you can raise the probability that others will reply "only to the bboard" by including a Reply-To field, as above] If you agree with the referenced statement then we have no disagreement. Apparently I did not read one or more of your previous statements as having the meaning you intended. Mark
fred@mnetor.UUCP (Fred Williams) (07/03/85)
In article <315@sri-arpa.ARPA> AI.Mayank@MCC.ARPA writes: >... This famous paradox caused a big debate between Einstein and Niels >Bohr in the early 30's, as Einstein did not believe in the probabilistic >interpretation of QM. > >- mayank. >------- If this is the same arguement I am thinking of, it went on for quite some time. I don't really think there is much of a paradox. Bohr always used to win this arguement whenever Einstein came up with a new objection... not because he was more brilliant than Einstein, but because he was right! (As far as we know.) Cheers, Fred Williams
AI.Mayank@MCC.ARPA (07/04/85)
From: Mayank Prakash <AI.Mayank@MCC.ARPA> >The wave function is not physical matter or an energy field. It is a >computational entity used to predict the results of experiments. When you >solve the equations of motion, you are solving for the motion of a computational >entity which can then be used to predict the results of experiment. It won't >predict results that are in violation with relativity, ie that the photon >gets absorbed sooner than the speed of light would allow for. > >The wave function itself is just a computational device and is not some real >physical thing that is distributed over space. The wave function "collapse" >is simply the statement that there was one photon and if it gets absorbed in >a given detector then no other detectors will absorb it. This is about as >simple and intuitive as you can get. The wave function is more than just a computational device - it is the actual probability amplitude, whose mod-squared gives the probability density of seeing a photon at a given point. The wave function collapse is the stronger statement that the probability amplitude, which was spread out over a (possibly) large region of space, is now localized within a small volume in which the photon was seen. Before the observation was made, the probability distribution was ACTUALLY spread out, and after the photon is detected at some point, it "collapses" to within that volume. So there is a change in the ACTUAL porbability density of seeing that photon at other spots in space once it has been detected at earth. Note that you are confusing two issues here - the photon does not get absorbed sooner that the speed of light would allow for because the wave function does not expand faster than the speed of light, thereby ensuring that the PROBABILITY of its being seen is zero before that time, but once that time has elapsed, and an observation made, it collapses "instanteneously." That is the only way contradictions can be avoided. The situation with regards to relativity is tolerable (not completely satisfactory) only because this will lead to no observable contradictions as long as the wave function (i.e., the actual probability distribution, not just a mathematical entity) collapses instantaneously. - mayank ========================================================================== II Mayank Prakash AI.Mayank@MCC.ARPA (512) 834-3441 II II 9430 Research Blvd., Echelon 1, Austin, TX 78759. II ========================================================================== -------
brooks@lll-crg.ARPA (Eugene D. Brooks III) (07/05/85)
> The wave function is more than just a computational device - it is the actual > probability amplitude, whose mod-squared gives the probability density of > seeing a photon at a given point. The wave function collapse is the stronger I certainly agree that the wavefunction is a probability amplitude which mathematically propagates according to a set of equations of motion. It is not however real physical entity like for instance an electric field. It is just a probability amplitude that you square to get the probability of various results. People get unhappy with the idea of it "collapsing instantanously" because they think of it as a real physical object. This causes them to think that someting is moving faster than light when it "collapses". Nothing is moving! There wasn't anything there in the first place. The only real things that happend were the release of a photon at one place and its later capture somewhere else. Nothing happens in between. You conjure the wavefunction up in your head to explain the probability distribution of the results and it works, I will be the last to argue with that, but the wave function is in your head. The only real physical happenings are the release and detection of the photon. Only the "event", ie the firing of a phototube is real. Insisting on believing that the wavefunction is a real physical object will only keep you from developing an intuition that removes any headaches over the EPR paradox and the like. There is no such thing as a wave function meter, you can't measure it directly. You can only see the phototube fire and that it all there is to it. If you don't repeat the experiment many times you can't even find out anything about the supposed "wave function". You can only know that the phototube fired. Physics is what happens on the experimental table, theorists should not get their backs up about this statement as I am a theorist, theory is what goes on in your head. The wave function which is a figment of ones imagination is a computational tool. Can you loan me a cup of wavefunction just like a cup of sugar?
gwyn@brl-tgr.ARPA (Doug Gwyn <gwyn>) (07/05/85)
> > The wave function is more than just a computational device - it is the actual > > probability amplitude, whose mod-squared gives the probability density of > > seeing a photon at a given point. The wave function collapse is the stronger > > I certainly agree that the wavefunction is a probability amplitude which > mathematically propagates according to a set of equations of motion. It > is not however real physical entity like for instance an electric field. (followed by a discussion about how the wave function isn't real) Everything you say about the QM wave function could also be said about the electric field. What makes the electric field any more real than the QM wave function?
g-rh@cca.UUCP (Richard Harter) (07/06/85)
FOR SALE: One (1) probability wavemeter, slightly used, still under factory warranty. Meter reading instantaneously drops to zero during electron phototube measurements, otherwise works perfectly. Manufacturer claims that the problem can be fixed but that it is too bohring to work one. Their slogan, "The only physically real things are the nonobservables." Best offer accepted, preferably in the form of non-negotiable bearer bonds.
brooks@lll-crg.ARPA (Eugene D. Brooks III) (07/08/85)
> > is not however real physical entity like for instance an electric field. > > (followed by a discussion about how the wave function isn't real) > > Everything you say about the QM wave function could also be said about > the electric field. What makes the electric field any more real than > the QM wave function? The wave function and the electric field have one fundamental difference. The electric field is observable in a single experiment. The wave function is not. When an electric field collapses the stored energy density has to go somewhere and there are measureable physical consequences. The electric field certainly did have its beginnings as a computational device. And I think that this is the root of your your comment. I in fact won't argue with anyone about whether or not it is real. It is likely that you can have it both ways. The wave function is a different sort of animal. It is used to describe the probabilistic results of a large number of identical experiments. It can be measured only by repeating the identical experiment. When it "collapses" there are no measureable consequences of the "motion". The "collapase" is only there to explain the fact that when the particle is detected at one place it is not going to be detected elsewhere. The wave function (squared) gives the probability of one of several choices. It is inherently not measureable in the context of a single experiment. Reality, like beauty, is in the eye of the beholder. I will not further harass anyone who wants to think of the wavefunction as a real thing that is distributed in space and moving around. When using the Schrodinger picture (See QM by Messiah for discussion on this) I tend to think of the wave function as a 'real' field that is distributed over space and is moving around. Consider, however, the Heisenberg picture where the wavefunction is a constant vector and its the operators that move around. You can of course have if anywhere in between. A case in point is the Interaction picture. When someone wants want to worry about the wavefunction's "instantaneous collapse" as being in potential violation of relativity or unasthetic he/she is thinking that the wavefunction is a bit more real than it really is. This is something that is not in the eye of the beholder and can clearly labeled as a misinterpretation of the facts.
mikes@AMES-NAS.ARPA (07/09/85)
From: mikes@AMES-NAS.ARPA (Peter Mikes)
The vawe function in the Schrodinger Equation differs from the
Amplitude of the electromagnetic field (E and H or F(n,m)) of the Max-
vell equations in the assumption of the existence of a discrete particle.
If concept of photon is considered together with Maxwell's eq., then
same problem and same paradoxes appear. As remarked recently, this is
indeed the same discussion which Bohr had with Einstein, but contrary
to the conclusion stated in that remark, it far from being is over.
Some people believe that Einstein was right, rather then Bohr. I suggest
that we do accept the fact that there is indeed a division of opinion
concerning the interpretation of psi function of QM and concerning the
queastion whether QM is paradox free and logicaly consistent. Some people
prefer not to see or face the problems - that's fine - but lets stop pa-
rroting the statement that 'all is fine and there is no paradox'. Some
people believe that there are serious problems in the foundations of Q.M.
and that's fine too. Thye discussion should proceed by examination of the
(alleged) problems and paradoxes - not just by stating that there is/ or
is not a problem.
Peter Mdgary@ecsvax.UUCP (D Gary Grady) (07/09/85)
> From brooks@lll-crg.ARPA (Eugene D. Brooks III) Wed Dec 31 19:00:00 1969 > When someone wants want to worry about the wavefunction's "instantaneous > collapse" as being in potential violation of relativity or unasthetic he/she > is thinking that the wavefunction is a bit more real than it really is. I don't think the wavefunction is a completely imaginary construct. Many experiments indicate the wave structure of light, with Young's slit experiment jumping to mind. -- D Gary Grady Duke U Comp Center, Durham, NC 27706 (919) 684-3695 USENET: {seismo,decvax,ihnp4,akgua,etc.}!mcnc!ecsvax!dgary
AI.Mayank@MCC.ARPA (07/09/85)
From: Mayank Prakash <AI.Mayank@MCC.ARPA>
>Please define "instantaneously" in a generally-invariant way.
Instantaneity cannot be defined even in a specially invariant way, forget a
generally invariant definition.
You are missing the point entirely and we are getting on a tangential
discussion. Perhaps my inability to express myself clearly is at least
partially to blame, but let me make another attempt to clarify my position.
All I am claiming is that QM does not give rise to any *observable*
contradictions with SR. Logically, there are problems and I am not claiming
that a good solution exists. For sake of concreteness, let us consider your
earlier example of a photon starting from the north star. Its wave function
expands at the velocity of light, (in ANY inertial frame). The important
property of the wave-function to remember is that the wave-function of a *given
photon* in a *given state* cannot be observed (measured). We can only measure
the wave-function corresponding to a *given state* of photons. The reason of
course is the uncertainty principle - any attempt to measure it at one
space-time point alters it irreversibly at all other points, and hence a
measurement at one point makes a measurement at other points meaningless.
(Footnote1: The probability distribution corresponding to a given state of
photons can be measured by preparing a large number of photons in that state,
and then recording the distribution of these photons. This gives us the
mod-squared of the wave-function. To get its phase, one could do interference
experiments).
Now consider an observer at Earth. As soon as she sees the photon, the wave
function collapses to within a small region (the speck on a photographic plate,
a cell in her retina or whatever) **instantaneously in her frame**. In
particular, the wave-function at the point diametrically opposite from her on
the pther side of the north star suddenly reduces to zero as soon as the
observation is made. Suppose another person is moving along in, say a
spaceship. In the moving frame, the wave function at the same diametrically
opposite point would collapse to zero either before or after the photon is
observed on Earth. Does this mean we have a contradiction? Logically, yes;
empirical, no. The reason there is no empirical paradox is simply that the wave
function is not itself observable. Therefore, the collapse of the wavae
function cannot be observed by any other observer. A real contradiction with SR
arises only if *information* can be transmitted faster than light, for in that
case, causality can be violated. I:n this situation, *WE* cannot use this setup
to transmit information faster than light, and hence cannot *observe* causality
violations. However, the wave function does receive a signal to collapse
instantaneously (in some frame), and therefore, in some frames it would
collapse before the observation was made, and this is far from a satisfactory
situation. However, since the wave function is not an observable entity itself,
no *empirical* contradictions arise in conventional QM, making the situation
*tolerable*, at least pending a better understanding of the measurement process
in QM.
That was the whole point I was trying to make, and I would welcome criticisms
or comments on this issue, but please do not send me any more messages on the
meaning of simultaneity etc.
- mayank.
==========================================================================
II Mayank Prakash AI.Mayank@MCC.ARPA (512) 834-3441 II
II 9430 Research Blvd., Echelon 1, Austin, TX 78759. II
==========================================================================
-------AI.Mayank@MCC.ARPA (07/09/85)
From: Mayank Prakash <AI.Mayank@MCC.ARPA> > Mayank, I think that some people might ascribe too much meaning to the >wave function from your discription. After all, a wave function is >fundamentally different from an electromagnetic wave in that the EM wave >has physical reality (i.e. physical energy density = mass) at every >point of the wave all the time independently of any observer. The QM >wave function only has "reality" when it is observed. Not true. Let us not confuse between the classical and quantum electromagnetic fields. The quantum EM fields are as much unobservable as the wave function. The classical EM field, on the other hand, is just the average of a large number of photons. The quantum EM field does not have any physical energy density. The energy density of the classical EM field at any point is the average energy density of the photons at that point = energy of a photon * mod-squared of the wave function of the photon at that point. It is hard for me to see how one can ascribe *more reality* (what does it mean anyway) to the EM field than the wave function of the photons. > Apropo of your discussion on simultaneity. Consider two observers >with synchronized perfect clocks starting out, in a relativistic way, from >the same spot on the equator, in opposite directions, parallel to the >equator, at the same instant that your photon leaves the north pole. From >symmetry, the photon reaches each at the "same time". Each makes a >measurement at that "instant". However, from each observer's point of >view, the other observer's clock is running slow. So although each agrees >that each made her measurement when her own clock read time T, each also >insists that she made her measurement before the other did, since she >observed that the other's clock was running slow. Hence the wave function >"instantaneously" collapsed with the "first" measurement and the other >observer couldn't have made the measurement because the wave funtion had >collapsed prior to time T on the other observer's clock. But since the >situation is completely symmetric each observer makes the same argument >that it is impossible for the other to make the measurement! > How can this be??? Please be advised that making a measurement is not the same as seeing the photon. The measurement in this case can have two outcomes - either you find the photon, or you don't. Secondly, the photon does not reach the two observers at the same time, only the wave function does. Only one of them can *see* the photon, not both, despite the symmetry. The only catch here is that no matter who makes the measurement first in whatever frame, the collapse of the wave function in each frame is consistent, i.e., that it collapses to the same region (which may be different from the positions of both observers, or may coincide with the position of one of them). This is the sticking point - how does the wave function know how to collapse. As I have stated before, as long as it does know however, there will not be any observable contradictions. - mayank. ========================================================================== II Mayank Prakash AI.Mayank@MCC.ARPA (512) 834-3441 II II 9430 Research Blvd., Echelon 1, Austin, TX 78759. II ========================================================================== -------
DANTE@EDWARDS-2060.ARPA (07/09/85)
1
AI.Mayank@MCC.ARPA (07/10/85)
From: Mayank Prakash <AI.Mayank@MCC.ARPA> >> The wave function is more than just a computational device - it is the actual >> probability amplitude, whose mod-squared gives the probability density of >> seeing a photon at a given point. The wave function collapse is the stronger >I certainly agree that the wavefunction is a probability amplitude which >mathematically propagates according to a set of equations of motion. It >is not however real physical entity like for instance an electric field. >It is just a probability amplitude that you square to get the probability >of various results. People get unhappy with the idea of it "collapsing >instantanously" because they think of it as a real physical object. This >causes them to think that someting is moving faster than light when it >"collapses"...... cup of sugar? Why is the electric field any more real? Isn't it just something in my mind as well? Can you pass me a cup of electric field please? If you do, I will give you two cups of wave function. How's that for a bargain? The point is, whether *real* or not (whatever that means in this context), the probability of finding a photon actually changed as a result of the measurement. If I understand you correctly, then your position is based on a misunderstanding of QM. For, let us imagine two situations as follows -(1) I am shooting bullets from an aperture in random directions. That is, the direction of the next bullet is unpredictable, all you know in advance is the probability of the bullet going in any given direction, i.e., its probability distribution. You place detectors all around to detect each bullet. Let us assume that we cannot see the bullets before they are detected by the detectors. Now, I fire my next bullet. Before it reaches a detector, you cannot tell me which direction it is travelling in, except the probability o f its actually going in any direction. As soon as it is detected, however, the whole probability distribution collapses to a point, and you now know exactly where the bullet is. Why is there no problem here? Because the whole probability distribution was used by us simply to express our ignorance of the bullet's direction. It did not represent the bullet in any sense - the bullet was moving in a fixed direction, even if we did not know that direction. Its detection simply fills the gap in our knowledge, and in this sense the probability distribution is something in our minds, and nothing really moved when it collapsed. In particular, no information was transferred by any one in the process. Now let us look at situation (2) I am preparing photons in identical states, and firing them from an aperture. Again, you know the statea I am preparing them in, and hence the wave function of each photon in advance. This wave function gives you the probability of finding the photon in any given direction. As before, you have detectors placed around the aperture to detect these photons. Now, I shoot the next photon. Before it is detected by a detector, all you can tell me is the probability that it will be found to be in a given direction. Why is there a problem here? Because it is not actually moving in any given direction *before* the detection takes place. In the classical case, the bullets were actually being in different states each time, and our ignorance of the state of each bullet forced us to resort the probability description. In the quantum case, we are shooting photon in identical states, and it is not our ignorance of its state that forces us to use probabilitiesm but because that is all there is. The wave function is as complete a description of the state o fthe photon as anyone has (including the photon), and therefore, when the photon decides to be found in one detector, it has changed its state across all space. In other words, it is not true that the photon was actually moving in given direction, and it got observed there etc., as we did in the previous case. THe photon was living a spread out existence, with a probability of being detected anywhere being given by its wave function, and before the measurement was made, it was not movving in any given direction. that is the root off the problem - how does it change its spread out out state to a localised one *instantaneousy*? And yes, don't forget the cup of electric field. - mayank. -------
mikes@AMES-NAS.ARPA (07/10/85)
From: mikes@AMES-NAS.ARPA (Peter Mikes)
I by and large agree with your description of the collapse of the vawe
function. The only thing I do not see (naturaly) is why I am missing the
point 'entirely'. Let's leave it at that.
Peterbrooks@lll-crg.ARPA (Eugene D. Brooks III) (07/11/85)
> From: Mayank Prakash <AI.Mayank@MCC.ARPA> > > > >> The wave function is more than just a computational device - it is the actual > >> probability amplitude, whose mod-squared gives the probability density of > >> seeing a photon at a given point. The wave function collapse is the stronger > > >I certainly agree that the wavefunction is a probability amplitude which > >mathematically propagates according to a set of equations of motion. It > >is not however real physical entity like for instance an electric field. > >It is just a probability amplitude that you square to get the probability > >of various results. People get unhappy with the idea of it "collapsing > >instantanously" because they think of it as a real physical object. This > >causes them to think that someting is moving faster than light when it > >"collapses"...... cup of sugar? > > Why is the electric field any more real? Isn't it just something in my mind as > well? Can you pass me a cup of electric field please? If you do, I will give > you two cups of wave function. How's that for a bargain? I can actually pass you a cup of electic field! A sealed box with niobium inner walls at an appropo low temperature. Put any desired EM field in there you like, or any arbitrary number of photons you like. If you define the field you can't deternine the number of photons and vice versa. The QM wavefunction is not in there however. Thats still in your head. Seriously Mayank, If you read my recent posing on QM and Quantum Field theory and don't yet see the light I suggest that you observe a 10 megaton airburst at close range as a blindness test. When you are ready for the eye test it can be arranged! We don't do bursts in the open air these days but we a few tens of kilotons in tunnel shot is still definite possibility. 1/2 a :-)
mikes@AMES-NAS.ARPA (07/12/85)
From: mikes@AMES-NAS.ARPA (Peter Mikes)
How real is the wave function?
Psi function does two things - none of them too well:1) It serves as a
'state of the system' and in this role is 'objective and real'.
2) It also 'describes information which observer X has about the system'
and in this role it is 'just a computational device'.
So far we have talked about widely separated events (astronomical distances)
in which the function 2 (information) dominates - so we were told that it is
not 'real' and should not worry about FTL.
Now, when you have introduced the interference phenomena, we will be
told that we are 'forgetting' function 1. Just watch the sleight of
hand! It has been done before - so many times that it gets boring. It was to
avoid this kind of ambiguity that DeBroglie introduced the "theory of
double solution" in which both the particle and wave are real and inte-
ract (vawe is guiding the particle). Naturally - a typical hard core po-
sitivist - always ready with Occam's ax - will not entertain a notion just
becouse it removes a logical absurdity ( we can always invent a new logic!).
.
How many people would agree with this?? P.M..gwyn@BRL.ARPA (07/15/85)
From: Doug Gwyn (VLD/VMB) <gwyn@BRL.ARPA> I agree that there is a logical problem. I was pointing out that the instantaneous collapse of the wave function in a special frame was indicative of the logical problem. I too think we need a better quantum theory of measurement. The logical relativistic problem is perhaps best seen by considering the following slight modification of the passing spaceship scenario: observer A E observer B spaceship --> E is an emitter of two particles in exactly opposite directions with exactly correlated spin. Due to the quantum nature of the particle emission, nothing is known about the spins except that they are correlated so that if one measures a spin component of one of them, the statistical distribution (call this D1) of a tilted component measurement of the other one will be different (involves cosine of the relative component tilt angle) than it would have been if the first measurement had not been done (call this distribution D2). Now, observer A measures a spin component of a particle sent in his direction, and shortly thereafter (separated by a spacelike interval w.r.t. the frame in which A, B, & E are all at rest) observer B, who is slightly farther away from E, measures the tilted spin component of the other correlated particle. According to QM, the result of an ensemble of such experiments is that B measures statistical distribution D1. The state of B's particle is supposed to be established "instantaneously" when A makes his measurement. There is no real paradox so long as we think in the rest frame. Now consider the situation from the viewpoint of a passing spaceship traveling at very high speed in the direction shown. If the collapse of the wave function is "instantaneous" as seen by the spaceship, and if B is not too much farther from E than A, then B will measure the spin "before" A does. QM says that B will find statistical distribution D2 (and A something like D1) in this case. Now, we all know that the statistics at B will really still be D1, not D2 (since the spaceship is irrelevant to the quantum phenomenon going on here). Surely there is something fundamentally wrong with the idea that the wave function collapses "instantaneously". What is a correct replacement for this bogus idea? This is more or less the thinking of Einstein that led him to reject the conventional formulation of quantum theory. (He also did not like the idea that there was a fundamental randomness, but that is a separate issue.)
MJackson.Wbst@Xerox.ARPA (07/15/85)
I think your discussion of the spin-experiment might confuse some
readers into thinking that there is a *real* paradox (in the sense that
properly applied QM would give conflicting predictions in the two
frames). Of course, that is not the case.
Referring to your example:
observer A E observer B
spaceship -->
Assume for definiteness that E is emitting unpolarized spin-1/2
particles. Then D2 (what you call the distribution when the other
measurement has not been done) is just 50% up, 50% down.
In general, D1 (the distribution to be expected when A PARTICULAR SPIN
has been measured by the other observer) will depend on the angle
between the detectors. Note that since there are two possible outcomes
of the other observer's measurement, there are TWO distributions, call
them D1up and D1down. Let us assume (again, for definiteness) that D1up
is 25% up, 75% down and that D1down is 75% up, 25% down.
Now in the stationary frame one can say that A receives his particle
first, the wave function collapses "instantaneously," and B's
measurement is thereby affected. We predict, and would observe
experimentally, that for the set of all cases where A receives a spin-up
particle, B receives 75% down and 25% up; similarly for the cases where
A receives a spin-down particle. Speaking loosely, one might say that
the measurement at A "caused" the shift in B's distribution.
In the moving frame, B receives his particle first. Now we expect his
distribution to be D2. But that was his total distribution before!
(Note that D2 = .5*D1up + .5*D1down.) And for those events in which B
receives a spin-up particle, it is found that A's distribution is 25% up
and 75% down, and similarly. Now it *seems* more natural to say that
the measurement at B "caused" the shift in A's distribution, but since
the experimentally measureable facts are the same, who's to tell?.
All that has happened, of course, is that we have chosen two different
ways of looking at the fundamental relationship:
A = up A = down
B = up .125 .375
B = down .375 .125
There is *no* paradox. There *is* a difficulty in putting together an
intuitively acceptable combination of causality, induction, and
speed-of-light limit. Let me recommend again the recent /Physics Today/
article on Bell's inequality; I am willing to summarize it if there is
interest, although I might not have the time to key it in for a couple
of weeks.
Markdgary%mcnc.csnet@csnet-relay.arpa (07/15/85)
I don't really follow you. The point of my posting was that Young's slit (and other experiments) indicate that there is something going on more than particles flying along - something is interfering with something to produce an interference pattern. This does indeed reflect the state of the system. A "measurement" (in the quantum sense - this does not require an observer but what Bohr called an irreversible quantum event, I think) either results in the "collapse" of the wave equation if you're a fan of the Copenhagen view or something else (switching into one of the available time-tracks in the many-worlds view, say). I certainly agree that's ambiguous, but so what? Nobody claims we know all there is to know about physics. Objecting to a successful (if perhaps unappealing) scheme like quantum mechanics is just pointless griping unless something better is being offered as an alternative.
gwyn@BRL.ARPA (07/15/85)
From: Doug Gwyn (VLD/VMB) <gwyn@BRL.ARPA> What I really had in mind in the (A E B spaceship) thought experiment was that observer A would be doing something nonsymmetric with respect to the two spin states, so that there would be a way of telling whether he had "interfered" with what is going on at observer B. Perhaps this is not possible, which would save the situation in the way you describe, but offhand it is hard to see why not..
AI.Mayank@MCC.ARPA (07/16/85)
From: Mayank Prakash <AI.Mayank@MCC.ARPA> > >I agree that there is a logical problem. I was pointing out that >the instantaneous collapse of the wave function in a special frame >was indicative of the logical problem. I too think we need a better >quantum theory of measurement. > >The logical relativistic problem is perhaps best seen by considering >the following slight modification of the passing spaceship scenario: > > observer A E observer B > > spaceship --> > . . . . . >This is more or less the thinking of Einstein that led him to reject >the conventional formulation of quantum theory. (He also did not >like the idea that there was a fundamental randomness, but that is a >separate issue.) -------- >I think your discussion of the spin-experiment might confuse some >readers into thinking that there is a *real* paradox (in the sense that >properly applied QM would give conflicting predictions in the two >frames). Of course, that is not the case. > >Referring to your example: > > observer A E observer B > > spaceship --> > . . . . >Mark ------- >What I really had in mind in the (A E B spaceship) thought experiment >was that observer A would be doing something nonsymmetric with >respect to the two spin states, so that there would be a way of >telling whether he had "interfered" with what is going on at >observer B. Perhaps this is not possible, which would save the >situation in the way you describe, but offhand it is hard to see >why not.. The argument of Mark can be generalized easily to any system that will be correlated in the way you describe. Let us suppose you are trying to measure the operator Q. Let us label the two particles 1 (A) and 2 (B) respectively. Q must satisfy the following conditions - (1) It must be measurable on both particles seperately, (2) It must be additive, i.e., its value on the whole system must be the sum of its values on each particle individually, and (3) It must be a constant of motion (for otherwise, the correlation between its values on the two particles will be lost in time). Now, suppose that its eigenstates on particle 1 are u(p), and on particle 2 are v(q), where p and q are the corresponding eigenvalues respectively. Then, u(p)v(q) is the state in which particle 1 has value p, particle 2 has value q, and the entire system has value p+q for the observable Q. A general state of the system is a linear superposition of these states. However, we are interested in a state in which the system as a whole has a fixed value, say, P. Such a state is a linear superposition of those products u(p)v(q), for which p+q = P. Let us say the coefficient of u(p)v(q) in this state is a(p,q). Rest of the argument is a repeatition of Mark's argument. So really there is no paradox here. - mayank. ========================================================================== II Mayank Prakash AI.Mayank@MCC.ARPA (512) 834-3441 II II 9430 Research Blvd., Echelon 1, Austin, TX 78759. II ========================================================================== -------
AI.Mayank@MCC.ARPA (07/17/85)
From: Mayank Prakash <AI.Mayank@MCC.ARPA> It seems that thi smessage got garbled somewhere in the system. At least, I only got half of it. So, here's another attempt at it - -------