Despite the probabilities in the rules, the interference pattern doesn't look like something that would result from dice being cast.

I agree the interference pattern is not the result of chance at all, but a product of the 'fixed geometry' of a particular setup. But any particular photon's arrival somewhere/sometime in the pattern is probabilistic.

Quote:

But whatever form the particle (or atom or molecule) is in while 'non-local', somehow nothing more than a photon is required to 'localize' it ... I'm stumped at the moment, but can't help thinking that the speed of light seems very slow, considering the range of velocities between zero and instantaneous, the speed of light it far closer to the former ... that, and isn't there also a probability (amplitude) for a photon to go faster than c?

edit: Would there necessarily be any limit to how fast a virtual photon could propagate?

As it so happens, I was just listening to Stephen Hawking last night ( Audible.com audio book of A Brief History .... ) and he mentioned [ in the setting of black hole horizon radiation, wave functions, information 'loss' and time machines ] of Feynman sums-over-histories involving exactly that sort of thing. Also time-backward travelling particles aka anti-particles. So some of the integral components may be like that, which are then folded in together with the 'standard' particle behaviours to yield a measurable 'real' result. It goes back to the earlier point about not constraining non-observables.

Heck he was even talking about imaginary time co-ordinates ie.

it

where i = sqrt[-1] and t is a real number. Naturally I'm at a loss to understand what that means physically.

One certainly does get the feeling of faster-than-light goings on behind the 'curtain of measurement'. I still like the concept of some extra dimension(s) involved - like cutting across through the park to shortcut the go 'round along the footpath! :-)

Cheers, Mike.

I have made this letter longer than usual because I lack the time to make it shorter.Blaise Pascal

As it so happens, I was just listening to Stephen Hawking last night ( Audible.com audio book of A Brief History .... ) and he mentioned [ in the setting of black hole horizon radiation, wave functions, information 'loss' and time machines ] of Feynman sums-over-histories involving exactly that sort of thing. Also time-backward travelling particles aka anti-particles. So some of the integral components may be like that, which are then folded in together with the 'standard' particle behaviours to yield a measurable 'real' result. It goes back to the earlier point about not constraining non-observables.

Heck he was even talking about imaginary time co-ordinates ie.

it

where i = sqrt[-1] and t is a real number. Naturally I'm at a loss to understand what that means physically.

One certainly does get the feeling of faster-than-light goings on behind the 'curtain of measurement'. I still like the concept of some extra dimension(s) involved - like cutting across through the park to shortcut the go 'round along the footpath! :-)

Cheers, Mike.

Ahhh, see Wick rotation.
Imaginary time (from Quantum theory) is a way to apply the laws of physics to singularities in a way that allows calculations without breakdown of the laws â€“ and general relativity predicts singularities whenever a sufficient amount of mass is present in a region. The implications are that the universe is finite, but without any boundary, and also that it has sufficient mass to eventually collapse again.

I read (from here) where Hawking mentions that the expanding universe is similar to the time reverse of a collapsing star. Could there be an oscillation between matter and antimatter occurring - e.g., spin-up electrons are positrons moving backwards through time while spin-down electrons are moving forwards...?

Insofar as the question of why more matter than antimatter, I did experience a mild Eureka! moment:

Equal amounts of matter and antimatter were created, in the conversion of energy from radiation to matter. This process is evidently not different from two equal things being created (e.g., two electrons), which not only go off in different directions in space, but also go off in opposite directions in time. So then, if half of the matter that was originally created had the opposite sign for the time variable (negative vs. positive), and the same were true for the antimatter that was created at the that time (half of it with opposite sign for the time), then the result would be annihilation of only some fraction of the total matter/antimatter that was created, while the rest would enter a stable configuration by virtue of the underlying symmetries (which I don't understand, but the direction of time is evidently central to the symmetry of an electron and its antiparticle, the positron).

Further, why isn't spin simply positive (as with mass)? What symmetry is it that gives spin its up/down quality? Would attributing the direction of time to a particle with spin simplify things, or are there specific reasons why this would be an invalid physical interpretation?

Gee Chipper, thanks for the heads up on the Wick rotation! :-)
Never heard of it before, and what parallels it opens up on stuff! So here was I saying earlier that that:

Quote:

type of statistics used is not that of 'ordinary large numbers' of things ................ aren't using the statistical/stochastic/randomness methods that we apply to a can of gas molecules say.

but clearly there's a deeper channel here.

Quote:

that the expanding universe is similar to the time reverse of a collapsing star

In fact we are/could all be within a cosmic black hole in the sense that we can't escape and the light paths always return back ( closed ).

Quote:

Further, why isn't spin simply positive (as with mass)? What symmetry is it that gives spin its up/down quality?

Now the spin business has generally of two sorts of ways to think about it:

One is a particle tooling along and the direction of motion defines an axis about which you can have either clockwise or anticlockwise 'rotation' or 'spin'. Now what is rotating here? Hmmmm .... but you can call the spins left/right, up/down or some other suitable language opposites.

The second is that, plus some external field which defines an axis. Typical example is a magnetic field in which some intrinsic spin particle as above is located. If there is a magnetic moment associated with the spin then 'space quantization' occurs so that only certain directions of the spin vector ( which is some vector cross product or "axial vector" ) with respect to that external field are allowed. Those configurations where that intrinsic spin are within 90 degrees of the field are 'up'/'toward', contra-wise are those greater than 90 degrees which are 'down'/'away'.

The Stern-Gerlach experiment many moons ago threw some atoms with a nett spin in between magnet poles. With not only a field orientation/axis in space but also a gradient in strength then this deflects/sorts the atom stream into distinct groups depending on the spin/field geometry. Now if you then take any one of those groups and put it through another similiar apparatus there is no further splitting of the group. So the selection/detection/measurement of spin this way is quite real, and as you'd guess subject to the usual QM rules, uncertainty etc. I can't remember right now what the exact conjugate to spin is though ..... :-)

Quote:

Would attributing the direction of time to a particle with spin simplify things, or are there specific reasons why this would be an invalid physical interpretation?

This is the CPT symmetry business. P == Parity == mirror image will flip a left/right, up/down OR run the particle backwards along it's path ( ie. T == time reverse ) gets you ditto, OR flip the charge sign and the magnetic moment will too ........ this gets you onto tricky ground. This is the

Quote:

deep explanations, which have some surprising convolutions

that I alluded to earlier. But it is why an antiparticle can be considered as the corresponding particle going backwards in time. One of Feynman's lectures explains this well, culminating in a humorous story about left-handed handshakes with aliens! :-)

Cheers, Mike.

I have made this letter longer than usual because I lack the time to make it shorter.Blaise Pascal

Equal amounts of matter and antimatter were created, in the conversion of energy from radiation to matter. This process is evidently not different from two equal things being created (e.g., two electrons), which not only go off in different directions in space, but also go off in opposite directions in time. So then, if half of the matter that was originally created had the opposite sign for the time variable (negative vs. positive), and the same were true for the antimatter that was created at the that time (half of it with opposite sign for the time), then the result would be annihilation of only some fraction of the total matter/antimatter that was created, while the rest would enter a stable configuration by virtue of the underlying symmetries (which I don't understand, but the direction of time is evidently central to the symmetry of an electron and its antiparticle, the positron).

Well the backwards-in-time particle being interpreted as anti-matter really means the particle coming from the future to the point of 'creation'. Here it gets fiddly terminologically ( recall the 'Campaign For Real Time' in the Hitch-Hiker's Guide to the Galaxy series ), but bear with me.

Call some point in time t0, this is when ( on the time axis ) a reaction vertex occurs that say represents a photon splitting into an electron and a positron - when we progress from low time co-ordinate values to higher ones. Suppose I now view life as the positron then : I'm really an electron born in the future at some time t1 ( where t1 > t0, or t1 is to the right on the time axis which increases numerically to the right ) but I travel back in time to t0. I absorb a photon there and then reverse my direction of travel in time so I will be seen as an electron by those that also travel in that direction along the time axis.

Or I could, by symmetry, be a positron which is born at some future time t2 ( t2 > t0 ) and travelling backward in time ( toward lower t axis values ). I will look like my anti-particle, the electron, from the point of view of other 'forward' travellers ( those proceeding to higher t values ). I absorb a photon at t0 and reversing my direction of time travel look like a positron! Whew! :-)

Tricky, huh? You could think of the photon as flicking the gearstick to reverse the direction of time travel on the electron/positron. A bit like the lever on my ride-on mower which ( belt driven ) will just hop back and forth by slamming the gear lever through neutral. [ Yes, the owner's manual does say stop before reversing direction! ]. From its 'personal' point of view it is always the one particle type ( matter or anti-matter ), but just looks different to others depending on whether it is proceeding to higher or lower t values.

As for the electric charge sign flip with antimatter? It is really just conservation of charge. From the forward time moving observer's frame a photon with zero charge becomes two particles with opposite charges, thus nett zero. From our particle's personal viewpoint it has never changed it's charge when coming from 'the future' ( higher than t0 ), going through the reaction vertex to change it's time direction, and returning to 'the future' ( higher than t0 values ).

I think you were describing an interaction vertex where, say, a photon at t0 converts to a ( forward time travelling ) electron going to t values above t0, and a ( backward time travelling ) electron going to t values less than t0.

Oh, my brain hurts! :-)

Cheers, Mike.

I have made this letter longer than usual because I lack the time to make it shorter.Blaise Pascal

There's quite a lively discussion on there also. Make sure that you have a long lunch-break clear. (If you happen to be taking your lunch break in the HHGTTG, then all the better! Say "Hi!" to Zarniwoop...)

That includes my earlier idea/question about quantised space-time volume. Does that also suggest quantised physical states in time and space...?

Is time itself consequently in effect quantised by this? That is, even if time is continuous, that smooth continuity can never be experienced due to the quantised nature of everything else that is in the time of "space-time"...

I'm following the threads but just a little short on lunch breaks :-(

Briefly, re: time reversal:

Can we still have causality AND reversed time?

Are the time reversal ideas just being used as an analogy from forward-time non-antiparticles? Or is there really any evidence for time reversal?

(Or is time reversal a physicist's pun on history and Steve Hawkin's book?... :-p )

Are the time reversal ideas just being used as an analogy from forward-time non-antiparticles? Or is there really any evidence for time reversal?

When the equation has a squared term, then for that term there exists both a positive and negative root (e.g., if x^2 = 4, then x can be +2 or it can be -2). This is exactly the type of interpretation Dirac considered with his equation, and from it he predicted that it must mean that for every particle there exists a corresponding 'antiparticle' ... Wow, reading that Wikipedia article for the first time, I see that's also where the 'sea of electrons' idea comes from â€“ along with the idea of 'negative energy'. But I don't think negative energy implies negative mass or negative temperature (below absolute zero). Indeed, it turned out that the antiparticle for the electron had the same (positive) mass as the electron, and I'm guessing it has positive temperature also. I think negative energy eigenstates correspond to the 'hidden variables' simply running their wheels (or strings or loops or branes?) in opposite directions with respect to the positive energy eigenstates.

Furthermore, the product of the interaction between an electron and positron does not result in â€œcancellationâ€? of energy (as with the dark areas in an interference pattern), rather the result is â€œconservationâ€? of energy, with all of it as positive as the mass and temperature. But then, why would something that's running backwards in time still not have a definite (â€œpositiveâ€??) location (i.e., occupy some real coordinates in spacetime) in any forward-running frame of reference? If the particle is a positron running backwards in time, the question is, could it find stability, for example, sharing the s-orbital of a helium atom that's running forward in time with an electron that's also running forward in time? And if so, does that then account for the missing antimatter?

When I asked earlier about symmetry, spin, and time, it looks like Dirac worked out the answer back in 1928! But I'm going to have to reread that page a few more times (and learn more basics) â€“ not sure what it means that there are four components to the wave function yet only two choices for the form of the metric - I had recalled the conventions of using (-,+,+,+) or (+,-,-,-) for (t,x,y,z), and I'm getting to understand it all a little better - right now it seems to me that it's perfectly acceptable for something that's propagating backward in time to have any velocity (less than light) through any locations in any inertial reference frame that's relative to a particle moving forward in time. In fact, it's interesting to note that the exclusion principle doesn't apply to two electrons when they're moving in opposite directions through time - they'll both be attracted to the same location in spacetime! It's almost like forward/backward through time makes as much sense as up/down in space. Does a photon, then, propagate in either, both, or neither direction through time?

As for the causality, I don't think it's a problem. The easiest way to explain why would be to use the example of a gas in thermal equilibrium where a movie is made of the molecules bouncing off each other and flying in all directions at slightly different velocities. Then that movie is played back in both forward and reverse directions â€“ and for those watching it, there's no way to know when the movie's running forward or when it's running backward (short of asking the person who made the movie). It has everything to do with symmetry and physical laws being the same in all inertial frames. And everything to do with the nature of mathematics, as with a squared term in an equation: it will have both positive and negative roots.

The Wick rotation is new to me too, Mike â€“ got to it from checking on imaginary time, and I need to reread/study it a few more times - it was easy to see from the examples how it can provide additional insights - so, thanks again! :)

Martin, looking forward to checking out LQC. I recall that Ben Owen mentioned Loop Quantum Gravity (about 3 years ago, iirc) and I took one look at it and understood almost nothing. Fortunately I've learned a few things since then â€“ hopefully enough to at least make some intelligent comments :)

When the equation has a squared term, then for that term there exists both a positive and negative root (e.g., if x^2 = 4, then x can be +2 or it can be -2). This is exactly the type of interpretation Dirac considered with his equation, and from it he predicted that it must mean that for every particle there exists a corresponding 'antiparticle' ... Wow, reading that Wikipedia article for the first time ...

Quoting the Wikipedia lead-in:

These matrices, and the form of the wavefunction, have a deep mathematical significance. The algebraic structure represented by the Dirac matrices had been created some 50 years earlier by the English mathematician W. K. Clifford, which in turn had been based on the mid-19th century work of the German mathematician Hermann Grassmann in his "Lineare Ausdehnungslehre" (Theory of Linear Extensions). The latter had been regarded as well-nigh incomprehensible by most of his contemporaries. The appearance of something so seemingly abstract, at such a late date, in such a direct physical manner, amounts to one of the most remarkable chapters in the history of physics.

The "deep mathematical significance" sums it up rather briefly!

Puns and headaches aside...

Looks like various flavours of quantums were spun off from his formulation. The 4x4 matrix also complicates what a negative root might be or mean... Which comes to the aspect of how mathematical abstractions and processes map onto physics and reality... Just because you can have a -ve root, there doesn't necessarily have to be a correspondence to reality, only that you have another 'what if'.

Quote:

I see that's also where the 'sea of electrons' idea comes from â€“ along with the idea of 'negative energy'. But I don't think negative energy implies negative mass or negative temperature (below absolute zero).

More a question of negative potential?

An interesting aspect for calculating gravitational potential wrt to open space is that you assume space to be at zero potential and that you move to a lower potential as you approach any object mass. (And adding more mass to the already established mass increases/concentrates that negative potential yet further!)

Are there any formulae that suggest there could be a positive gravitational potential wrt open space? (Negative roots...?)

Quote:

... I think negative energy eigenstates correspond to the 'hidden variables' simply running their wheels (or strings or loops or branes?) in opposite directions with respect to the positive energy eigenstates.

Possibly so if there are physical effects that are (partly) described by the matrix values...

Quote:

If the particle is a positron running backwards in time, the question is, could it find stability, for example, sharing the s-orbital of a helium atom that's running forward in time with an electron that's also running forward in time? And if so, does that then account for the missing antimatter?

... In fact, it's interesting to note that the exclusion principle doesn't apply to two electrons when they're moving in opposite directions through time - they'll both be attracted to the same location in spacetime! It's almost like forward/backward through time makes as much sense as up/down in space. Does a photon, then, propagate in either, both, or neither direction through time?

The question in all that lot is consistency of the flow of time locally. We assume time is consistent at least 'locally'. Hence your backwards time particle would be 'seen' for an infinitesimal moment as its existence moves from the local future through the present to then explore into the past.

Or do you assume some 'interface' between a 'volume' of 'reverse' time in our assumed 'forward' world of time?

Can we have particles oscillating in time around an 'approximate' time point. A Heisenberg uncertainty of local time?

Quote:

As for the causality, I don't think it's a problem. ... gas in thermal equilibrium where a movie is made of the molecules bouncing off each other ... played back in both forward and reverse directions â€“ and for those watching it, there's no way to know when the movie's running forward or when it's running backward ... everything to do with symmetry and physical laws being the same in all inertial frames. And everything to do with the nature of mathematics, as with a squared term in an equation: it will have both positive and negative roots.

Indeed so and a very good analogy described there. Perhaps the clues are still yet to be found in the symmetries and for where there are discrepancies rather than symmetry.

Quote:

The Wick rotation ...

Martin, looking forward to checking out LQC. I recall that Ben Owen mentioned Loop Quantum Gravity (about 3 years ago, iirc) and I took one look at it and understood almost nothing. Fortunately I've learned a few things since then â€“ hopefully enough to at least make some intelligent comments :)

Likewise here. Some more reading required! Not sure about gaining inspiration whilst staring into the fire but a beer or two may help. Some Christmas cheer may well be very inspirational... ;-)

From other meandering thoughts...

There must be a suspicious connection between evanescence, tunneling, and interference.

For the Young's Slits experiment, are there any interesting effects on the interference pattern that are dependant on the material used for the physical obstruction?

Can any insight be gained from the pattern from single electrons/photons and an inverse Young's Slits? (Open space instead of barrier and material instead of slits.)

(I'll catch up with the cosmological stuff eventually! :-p )

Because the equation is second order in the time derivative, one must specify both the initial value of \partial_t \phi\, and not just \,\phi\,. This is normal for classical water waves, the initial conditions are the position and velocity, but in quantum mechanics the wavefunction is supposed to be the complete description, just knowing the wavefunction should determine the future.

... So...

Do we have positional uncertainty merely because initial position is excluded from the initial assumptions?

Or rather, rephrased, do we have the Heisenberg Uncertainty Principle due to the assumptions and the mathematical tools that we are working with?

Or rather, rephrased, do we have the Heisenberg Uncertainty Principle due to the assumptions and the mathematical tools that we are working with?

I guess the tools flow from the assumptions, with feedback from reality! :-)

It's primarily because we're not using point models for our objects, but functions that have some extension in their domains. Thus one can ( Fourier etc ) decompose into sums of primitives ( sines etc ). Each primitive represents a 'pure' sinusoid of a single frequency ( with regard to the units of the domain ) and is correlated with a particular physical meaning via p ~ h * k or E ~ h * f ( where p = momentum, E = energy, ~ means 'goes like', h = Planck's constant, k and f are spatial and time frequencies respectively ).

One way to think of uncertainty is to view a measurement as a selection of one of those primitives - the phrase "collapse of the wave function" comes to mind. Each instance of measurement/selection of a given functional form yields ( likely ) a different primitive, but in a way that after many selections you get a distribution that reflects the underlying function that represents the 'particle'. Now the Heisenberg uncertainty is a result of the inverse-ness of function specification in one domain ( say distance ) with the corresponding domain ( say momentum ) of the decomposition - it's a Fourier thing.

The fact is that in practice you don't get a nice ordered, sequential sampling of functional values. So if the function f(x) has domain x = [a,b] then one doesn't get a neat readout of f(x) for x = a progressing monotonically to x = b, in the fashion that one would go about forming a visual graph of it, say.

Quote:

[aside]
[=blue]Thus the probability aspect is such that if x = c is the measured value, then the likelihood of obtaining that is proportional to |f(c)| ( NB. absolute value ). Or more precisely is proportional to the 'area under the curve' between two domain values near x = c : so one is using the behaviour of f(x) in the chunk of domain x = [x1, x2] where x1 = 0 ( NOT equal ), then looking at how/whether a value exists to converge to as a -> 0. See improper integrals.

is finite, but the sequence S(n) as n -> infinity is unbounded, then the integral(1/r) is not defined either ( or infinite if you like ).

So f(r) = 1/r cannot be normalised, and thus no denominator for probability purposes is available. You can't have wave functions of this character to represent physical situations.

( edit ) ..... aargh, just tell me to stop! :-)

One of Feynman's, and others, contribution was to 'renormalise' which is a clever way of accounting for all those spacetime paths/histories in a particular way. Suppose you had a big accounting ledger with an infinite number of separate accounts with non-zero balances. If you just added them all up in 'any old way' then you'd likely not get a helpful finite result. However if you noted some regularity in the characteristics of the figures so that a given debit was matched with a corresponding credit then alot would cancel ie. not contribute to a nett non-zero sum. This gives some helpful finite answer. The analogy is that the Feynman diagrams are the accounts, and the ledger is the total set of them.

I have made this letter longer than usual because I lack the time to make it shorter.Blaise Pascal

## RE: Despite the

)

I agree the interference pattern is not the result of chance at all, but a product of the 'fixed geometry' of a particular setup. But any particular photon's arrival somewhere/sometime in the pattern is probabilistic.

As it so happens, I was just listening to Stephen Hawking last night ( Audible.com audio book of A Brief History .... ) and he mentioned [ in the setting of black hole horizon radiation, wave functions, information 'loss' and time machines ] of Feynman sums-over-histories involving exactly that sort of thing. Also time-backward travelling particles aka anti-particles. So some of the integral components may be like that, which are then folded in together with the 'standard' particle behaviours to yield a measurable 'real' result. It goes back to the earlier point about not constraining non-observables.

Heck he was even talking about imaginary time co-ordinates ie.

it

where i = sqrt[-1] and t is a real number. Naturally I'm at a loss to understand what that means physically.

One certainly does get the feeling of faster-than-light goings on behind the 'curtain of measurement'. I still like the concept of some extra dimension(s) involved - like cutting across through the park to shortcut the go 'round along the footpath! :-)

Cheers, Mike.

I have made this letter longer than usual because I lack the time to make it shorter. Blaise Pascal

## RE: As it so happens, I was

)

Ahhh, see Wick rotation.

Imaginary time (from Quantum theory) is a way to apply the laws of physics to singularities in a way that allows calculations without breakdown of the laws â€“ and general relativity predicts singularities whenever a sufficient amount of mass is present in a region. The implications are that the universe is finite, but without any boundary, and also that it has sufficient mass to eventually collapse again.

I read (from here) where Hawking mentions that the expanding universe is similar to the time reverse of a collapsing star. Could there be an oscillation between matter and antimatter occurring - e.g., spin-up electrons are positrons moving backwards through time while spin-down electrons are moving forwards...?

## Insofar as the question of

)

Insofar as the question of why more matter than antimatter, I did experience a mild Eureka! moment:

Equal amounts of matter and antimatter were created, in the conversion of energy from radiation to matter. This process is evidently not different from two equal things being created (e.g., two electrons), which not only go off in different directions in space, but also go off in opposite directions in time. So then, if half of the matter that was originally created had the opposite sign for the time variable (negative vs. positive), and the same were true for the antimatter that was created at the that time (half of it with opposite sign for the time), then the result would be annihilation of only some fraction of the total matter/antimatter that was created, while the rest would enter a stable configuration by virtue of the underlying symmetries (which I don't understand, but the direction of time is evidently central to the symmetry of an electron and its antiparticle, the positron).

Further, why isn't spin simply positive (as with mass)? What symmetry is it that gives spin its up/down quality? Would attributing the direction of time to a particle with spin simplify things, or are there specific reasons why this would be an invalid physical interpretation?

## Gee Chipper, thanks for the

)

Gee Chipper, thanks for the heads up on the Wick rotation! :-)

Never heard of it before, and what parallels it opens up on stuff! So here was I saying earlier that that:

but clearly there's a deeper channel here.

In fact we are/could all be within a cosmic black hole in the sense that we can't escape and the light paths always return back ( closed ).

Now the spin business has generally of two sorts of ways to think about it:

One is a particle tooling along and the direction of motion defines an axis about which you can have either clockwise or anticlockwise 'rotation' or 'spin'. Now what is rotating here? Hmmmm .... but you can call the spins left/right, up/down or some other suitable language opposites.

The second is that, plus some external field which defines an axis. Typical example is a magnetic field in which some intrinsic spin particle as above is located. If there is a magnetic moment associated with the spin then 'space quantization' occurs so that only certain directions of the spin vector ( which is some vector cross product or "axial vector" ) with respect to that external field are allowed. Those configurations where that intrinsic spin are within 90 degrees of the field are 'up'/'toward', contra-wise are those greater than 90 degrees which are 'down'/'away'.

The Stern-Gerlach experiment many moons ago threw some atoms with a nett spin in between magnet poles. With not only a field orientation/axis in space but also a gradient in strength then this deflects/sorts the atom stream into distinct groups depending on the spin/field geometry. Now if you then take any one of those groups and put it through another similiar apparatus there is no further splitting of the group. So the selection/detection/measurement of spin this way is quite real, and as you'd guess subject to the usual QM rules, uncertainty etc. I can't remember right now what the exact conjugate to spin is though ..... :-)

This is the CPT symmetry business. P == Parity == mirror image will flip a left/right, up/down OR run the particle backwards along it's path ( ie. T == time reverse ) gets you ditto, OR flip the charge sign and the magnetic moment will too ........ this gets you onto tricky ground. This is the

that I alluded to earlier. But it is why an antiparticle can be considered as the corresponding particle going backwards in time. One of Feynman's lectures explains this well, culminating in a humorous story about left-handed handshakes with aliens! :-)

Cheers, Mike.

I have made this letter longer than usual because I lack the time to make it shorter. Blaise Pascal

## As for: RE: Equal

)

As for:

Well the backwards-in-time particle being interpreted as anti-matter really means the particle coming from the future to the point of 'creation'. Here it gets fiddly terminologically ( recall the 'Campaign For Real Time' in the Hitch-Hiker's Guide to the Galaxy series ), but bear with me.

Call some point in time t0, this is when ( on the time axis ) a reaction vertex occurs that say represents a photon splitting into an electron and a positron - when we progress from low time co-ordinate values to higher ones. Suppose I now view life as the positron then : I'm really an electron born in the future at some time t1 ( where t1 > t0, or t1 is to the right on the time axis which increases numerically to the right ) but I travel back in time to t0. I absorb a photon there and then reverse my direction of travel in time so I will be seen as an electron by those that also travel in that direction along the time axis.

Or I could, by symmetry, be a positron which is born at some future time t2 ( t2 > t0 ) and travelling backward in time ( toward lower t axis values ). I will look like my anti-particle, the electron, from the point of view of other 'forward' travellers ( those proceeding to higher t values ). I absorb a photon at t0 and reversing my direction of time travel look like a positron! Whew! :-)

Tricky, huh? You could think of the photon as flicking the gearstick to reverse the direction of time travel on the electron/positron. A bit like the lever on my ride-on mower which ( belt driven ) will just hop back and forth by slamming the gear lever through neutral. [ Yes, the owner's manual does say stop before reversing direction! ]. From its 'personal' point of view it is always the one particle type ( matter or anti-matter ), but just looks different to others depending on whether it is proceeding to higher or lower t values.

As for the electric charge sign flip with antimatter? It is really just conservation of charge. From the forward time moving observer's frame a photon with zero charge becomes two particles with opposite charges, thus nett zero. From our particle's personal viewpoint it has never changed it's charge when coming from 'the future' ( higher than t0 ), going through the reaction vertex to change it's time direction, and returning to 'the future' ( higher than t0 values ).

I think you were describing an interaction vertex where, say, a photon at t0 converts to a ( forward time travelling ) electron going to t values above t0, and a ( backward time travelling ) electron going to t values less than t0.

Oh, my brain hurts! :-)

Cheers, Mike.

I have made this letter longer than usual because I lack the time to make it shorter. Blaise Pascal

## RE: As for: ... Oh, my

)

Try:

loop quantum cosmology (LQC)

There's quite a lively discussion on there also. Make sure that you have a long lunch-break clear. (If you happen to be taking your lunch break in the HHGTTG, then all the better! Say "Hi!" to Zarniwoop...)

That includes my earlier idea/question about quantised space-time volume. Does that also suggest quantised physical states in time and space...?

Is time itself consequently in effect quantised by this? That is, even if time is continuous, that smooth continuity can never be experienced due to the quantised nature of everything else that is in the time of "space-time"...

I'm following the threads but just a little short on lunch breaks :-(

Briefly, re: time reversal:

Can we still have causality AND reversed time?

Are the time reversal ideas just being used as an analogy from forward-time non-antiparticles? Or is there really any evidence for time reversal?

(Or is time reversal a physicist's pun on history and Steve Hawkin's book?... :-p )

More later,

Cheers,

Martin

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## RE: Briefly, re: time

)

When the equation has a squared term, then for that term there exists both a positive and negative root (e.g., if x^2 = 4, then x can be +2 or it can be -2). This is exactly the type of interpretation Dirac considered with his equation, and from it he predicted that it must mean that for every particle there exists a corresponding 'antiparticle' ... Wow, reading that Wikipedia article for the first time, I see that's also where the 'sea of electrons' idea comes from â€“ along with the idea of 'negative energy'. But I don't think negative energy implies negative mass or negative temperature (below absolute zero). Indeed, it turned out that the antiparticle for the electron had the same (positive) mass as the electron, and I'm guessing it has positive temperature also. I think negative energy eigenstates correspond to the 'hidden variables' simply running their wheels (or strings or loops or branes?) in opposite directions with respect to the positive energy eigenstates.

Furthermore, the product of the interaction between an electron and positron does not result in â€œcancellationâ€? of energy (as with the dark areas in an interference pattern), rather the result is â€œconservationâ€? of energy, with all of it as positive as the mass and temperature. But then, why would something that's running backwards in time still not have a definite (â€œpositiveâ€??) location (i.e., occupy some real coordinates in spacetime) in any forward-running frame of reference? If the particle is a positron running backwards in time, the question is, could it find stability, for example, sharing the s-orbital of a helium atom that's running forward in time with an electron that's also running forward in time? And if so, does that then account for the missing antimatter?

When I asked earlier about symmetry, spin, and time, it looks like Dirac worked out the answer back in 1928! But I'm going to have to reread that page a few more times (and learn more basics) â€“ not sure what it means that there are four components to the wave function yet only two choices for the form of the metric - I had recalled the conventions of using (-,+,+,+) or (+,-,-,-) for (t,x,y,z), and I'm getting to understand it all a little better - right now it seems to me that it's perfectly acceptable for something that's propagating backward in time to have any velocity (less than light) through any locations in any inertial reference frame that's relative to a particle moving forward in time. In fact, it's interesting to note that the exclusion principle doesn't apply to two electrons when they're moving in opposite directions through time - they'll both be attracted to the same location in spacetime! It's almost like forward/backward through time makes as much sense as up/down in space. Does a photon, then, propagate in either, both, or neither direction through time?

As for the causality, I don't think it's a problem. The easiest way to explain why would be to use the example of a gas in thermal equilibrium where a movie is made of the molecules bouncing off each other and flying in all directions at slightly different velocities. Then that movie is played back in both forward and reverse directions â€“ and for those watching it, there's no way to know when the movie's running forward or when it's running backward (short of asking the person who made the movie). It has everything to do with symmetry and physical laws being the same in all inertial frames. And everything to do with the nature of mathematics, as with a squared term in an equation: it will have both positive and negative roots.

The Wick rotation is new to me too, Mike â€“ got to it from checking on imaginary time, and I need to reread/study it a few more times - it was easy to see from the examples how it can provide additional insights - so, thanks again! :)

Martin, looking forward to checking out LQC. I recall that Ben Owen mentioned Loop Quantum Gravity (about 3 years ago, iirc) and I took one look at it and understood almost nothing. Fortunately I've learned a few things since then â€“ hopefully enough to at least make some intelligent comments :)

## RE: When the equation has a

)

Quoting the Wikipedia lead-in:

These matrices, and the form of the wavefunction, have a deep mathematical significance. The algebraic structure represented by the Dirac matrices had been created some 50 years earlier by the English mathematician W. K. Clifford, which in turn had been based on the mid-19th century work of the German mathematician Hermann Grassmann in his "Lineare Ausdehnungslehre" (Theory of Linear Extensions). The latter had been regarded as well-nigh incomprehensible by most of his contemporaries. The appearance of something so seemingly abstract, at such a late date, in such a direct physical manner, amounts to one of the most remarkable chapters in the history of physics.

The "deep mathematical significance" sums it up rather briefly!

Puns and headaches aside...

Looks like various flavours of quantums were spun off from his formulation. The 4x4 matrix also complicates what a negative root might be or mean... Which comes to the aspect of how mathematical abstractions and processes map onto physics and reality... Just because you can have a -ve root, there doesn't necessarily have to be a correspondence to reality, only that you have another 'what if'.

More a question of negative potential?

An interesting aspect for calculating gravitational potential wrt to open space is that you assume space to be at zero potential and that you move to a lower potential as you approach any object mass. (And adding more mass to the already established mass increases/concentrates that negative potential yet further!)

Are there any formulae that suggest there could be a positive gravitational potential wrt open space? (Negative roots...?)

Possibly so if there are physical effects that are (partly) described by the matrix values...

The question in all that lot is consistency of the flow of time locally. We assume time is consistent at least 'locally'. Hence your backwards time particle would be 'seen' for an infinitesimal moment as its existence moves from the local future through the present to then explore into the past.

Or do you assume some 'interface' between a 'volume' of 'reverse' time in our assumed 'forward' world of time?

Can we have particles oscillating in time around an 'approximate' time point. A Heisenberg uncertainty of local time?

Indeed so and a very good analogy described there. Perhaps the clues are still yet to be found in the symmetries and for where there are discrepancies rather than symmetry.

Likewise here. Some more reading required! Not sure about gaining inspiration whilst staring into the fire but a beer or two may help. Some Christmas cheer may well be very inspirational... ;-)

From other meandering thoughts...

There must be a suspicious connection between evanescence, tunneling, and interference.

For the Young's Slits experiment, are there any interesting effects on the interference pattern that are dependant on the material used for the physical obstruction?

Can any insight be gained from the pattern from single electrons/photons and an inverse Young's Slits? (Open space instead of barrier and material instead of slits.)

(I'll catch up with the cosmological stuff eventually! :-p )

Regards,

Martin

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## RE: ... Dirac considered

)

From that article:

Because the equation is second order in the time derivative, one must specify both the initial value of \partial_t \phi\, and not just \,\phi\,. This is normal for classical water waves, the initial conditions are the position and velocity, but in quantum mechanics the wavefunction is supposed to be the complete description, just knowing the wavefunction should determine the future.

... So...

Do we have positional uncertainty merely because initial position is excluded from the initial assumptions?

Or rather, rephrased, do we have the Heisenberg Uncertainty Principle due to the assumptions and the mathematical tools that we are working with?

(Awaits the meow of Schrodingers cat!)

Cheers,

Martin

[edit] Amazing where bits of TeX show up! [/edit]

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## RE: Or rather, rephrased,

)

I guess the tools flow from the assumptions, with feedback from reality! :-)

It's primarily because we're not using point models for our objects, but functions that have some extension in their domains. Thus one can ( Fourier etc ) decompose into sums of primitives ( sines etc ). Each primitive represents a 'pure' sinusoid of a single frequency ( with regard to the units of the domain ) and is correlated with a particular physical meaning via p ~ h * k or E ~ h * f ( where p = momentum, E = energy, ~ means 'goes like', h = Planck's constant, k and f are spatial and time frequencies respectively ).

One way to think of uncertainty is to view a measurement as a selection of one of those primitives - the phrase "collapse of the wave function" comes to mind. Each instance of measurement/selection of a given functional form yields ( likely ) a different primitive, but in a way that after many selections you get a distribution that reflects the underlying function that represents the 'particle'. Now the Heisenberg uncertainty is a result of the inverse-ness of function specification in one domain ( say distance ) with the corresponding domain ( say momentum ) of the decomposition - it's a Fourier thing.

The fact is that in practice you don't get a nice ordered, sequential sampling of functional values. So if the function f(x) has domain x = [a,b] then one doesn't get a neat readout of f(x) for x = a progressing monotonically to x = b, in the fashion that one would go about forming a visual graph of it, say.

I have made this letter longer than usual because I lack the time to make it shorter. Blaise Pascal