Minkowski Space Time Briefly Revisited

One of the more lively discussions on this forum since I joined June last was one about Minkowski space-time.

Several misconceptions I previously had about space-time have been wiped clean. One of the first misconceptions to fall was the utility of Minkoski's "light cones". Once a pulse of light is emitted (in every direction) from an ideal point source by an event in Minkowski's version of space-time, it is impossible ever to catch up with the trailing edge of that event starting from the same point some time interval after the event occurred, much less overtake it. Another related misconception is the idea that the entire universe appears as a 2D flat pancake perpendicular to the observed direction of relative motion approaching c. Oh, the length contraction and time dilation effects are real enough by any standard of physical reality, and have been shown to be the case for any number of experiments to test them. Pick any single direction and observe distant objects in our universe receding or approaching us (but not using parallax like a range finder). Yep. They appear to be flat alright. With parallax, whole galaxies actually would appear to be flatter also, and the spaces between them too, no doubt. The images thus obtained will be Doppler shifted as well. The proton pancakes in the LHC are close-up examples that we can actually observe contracting with increasing collider energies. But these are simpler Lorentz effects, not strictly associated with Minkowski's ideas.

So I need to vet a thought experiment that occurred to me that had not been previously discussed. Although the Poynting vector (direction of propagation) of light in a vacuum was discussed in association with Minkowski's thread and others, something has always bothered be about diagrams depicting a propagating wave of linearly polarized monochromatic light, traditionally depicted as phase shifted sine waves (one for E, one for B) oriented as mutually orthogonal components of a traveling wave. If a photon of light had a wave behavior as indicated by such diagrams, it would mean that a time interval delta t would be involved.

But this depiction of a traveling light wave isn't the "real" physical case, is it? For one thing, for something that is presumably moving in a trajectory that is along an ideal straight line, we could, intellectually at least, take this model to the infinitesimal limit (no time interval) in the single dimension it represents, and create a slow motion film, frame by frame. In the 21st century, the sort of high speed photography that led to fame for EG & G has been supplanted by much higher exposure speed experiments like this one:



which demonstrates that pulsed light scattered along the path of a high energy beam through a liquid can indicate its position as a function of time.

So our instrumentality has improved to the point that if there is something wrong with this model, we should already know about it, right? I wish to understand whether there is a limit to the narrowness of the light pulse below which nothing can propagate. I'd also like to see experiments like this one recast for the double slit experiment, and also for simple reflection from a mirror. This video is old now. Does anyone have links to videos of updated and/or more elaborate experiments with light pulses?

 

Log in or Sign up to hide all adverts.

Not quite, but it isn't totally wrong. The important thing to appreciate is that it's an electromagnetic wave. In section 11.10 of Jackson's Classical Electrodynamics he says "one should properly speak of the electromagnetic field Fuv rather than E or B separately". There isn't actually an electric wave E orthogonal to the magnetic wave B, it's an electromagnetic wave. This isn't usually made clear, for example see Wiki :

"Not only are the electric and magnetic field waves in the far-field traveling at the speed of light, but they always have a special restricted orientation and proportional magnitudes,

Please Register or Log in to view the hidden image!

, which can be seen immediately from the Poynting vector. The electric field, magnetic field, and direction of wave propagation are all orthogonal, and the wave propagates in the same direction as

Please Register or Log in to view the hidden image!

. Also, E and B far-fields in free space, which as wave solutions depend primarily on these two Maxwell equations, are always in-phase with each other. This is guaranteed since the generic wave solution is first order in both space and time, and the curl operator on one side of these equations results in first-order spacial derivatives of the wave solution, while the time-derivative on the other side of the equations, which gives the other field, is first order in time, resulting in the same phase shift for both fields in each mathematical operation."

But see where it says spatial derivative and time derivative? The E and B sine waves are the spatial and time derivatives of an electromagnetic pulse of four-potential. To grasp this, imagine you're in a canoe on a flat calm ocean, and a wave comes at you. (This wave has no trough). As you rise up the wave, your canoe tilts. The angle of tilt denotes E, and the rate of tilt denotes B. At the top of the wave your canoe is horizontal and momentarily still, then your canoe tilts down and everything reverses, and then your canoe flattens out.

Please Register or Log in to view the hidden image!

Check out Aharonov Bohm effect where you can read this: Thus the Aharonov–Bohm effect validates the view that forces are an incomplete way to formulate physics, and potential energies must be used instead. In fact Richard Feynman complained[citation needed] that he had been taught electromagnetism from the perspective of electromagnetic fields, and he wished later in life he had been taught to think in terms of the electromagnetic potential instead, as this would be more fundamental. Also have a look at http://arxiv.org/abs/0803.2596/ which talks about the photon as a pulse, and see the lemon-like depiction on physicsworld here. I'm afraid I wasn't clear about the pulsed light in the liquid.

 

Log in or Sign up to hide all adverts.

I would mention that, if memory serves, that coke bottle video is a bit of a cheat. It isn't a single blast of light propagating through the bottle and being filmed but rather a single frame for every pulse of light emitted, which were then strung together to make a smooth video.

Also, if the light were "actually" travelling as a sovereign pulse through that water we wouldn't see anything at all; we are currently seeing reflections of all kinds of photons.

 

Log in or Sign up to hide all adverts.

Farsight: This (Aharonov Bohm effect) is very helpful indeed. I was never very happy with the E and B field representation, and it's also good to know that propagation of EM energy is a good deal more finessed than the simple representation favored by Maxwell.

But isn't the Poynting vector just another one of those stupid conventions like the right hand (thread) rule for magnetic fields, or the idea that current by definition flows from positive to negative (whether positive charges are mobile or not in a wire)? Does it "explain" anything, like why a photon travels in a particular direction when the initial conditions aren't actually known? Why would one direction in space actually be preferred for propagation as compared to any other? What sort of chirality violation is it, and to what field(s) does it happen that makes one direction of propagation preferred over another?

RJBeery: That is more than a little bit of a cheat. Yes, scattering is an underrated effect. It tells us a lot more than it is generally given credit for.

If it hadn't been such a cheat, I'd like to have seen similar experiments done with longer wavelength EM.

A bank of pumped lasers intercepting the beam in sequence should work fast enough to enable photographing the real deal.

 

I think Maxwell is misrepresented actually. When you actually read what he said, it's quite a lot different to what people say he said. For example, see On Physical Lines of Force and note this bit:

""a motion of translation along an axis cannot produce a rotation about that axis unless it meets with some special mechanism, like that of a screw".

You never hear about this "screw" nature of electromagnetism, even though we use the right hand rule for both electromagnetism and screw threads. See wiki and note the two pictures.

Yes. I think it is. However...

The right hand rule isn't stupid at all. It relates to that screw thing, which Minkowski also referred to, in Space and Time:

"In the description of the field caused by the electron itself, then it will appear that the division of the field into electric and magnetic forces is a relative one with respect to the time-axis assumed; the two forces considered together can most vividly be described by a certain analogy to the force-screw in mechanics; the analogy is, however, imperfect".

I think it's a back-to-front thing myself. The photon is going thataway so the displacement current is going up and down orthogonally thisaway, like that ocean wave. But it's misleading to depict a sinusoidal magnetic field variation orthogonal to the electric field variation, because the field concerned is the electromagnetic field, and because potential is more fundamental than field. And then in QFT people talk about the photon field and the electron field, only it's as if they've never done classical electromagnetism.

 

Given that you have now insulted the physicists who work in QFT as ignorant of physics, will you now show us the Farsight-from-the-Mountain correct way to model the electromagnetic field so that we can do away with the photon field and the electromagnetic field and preserve the utility of QFT and electromagnetism? Feel free to use whatever examples you would like.

Or perhaps you can't do this because you are lying about physics?

 

Dan: I'm sorry about the troll ↑. And I'm sorry our "moderators" permit such ad-hominem anonymous abuse. Best put him on ignore.

 

Maybe that's the problem?

 

Really? You call a direct question about your claim about the competence of physicists "trolling"?

You seem to me like a petty liar trying to make your own opinions seem grand. Yet all you do is insult people and offer no evidence.

If you provide evidence, you would seem like less of a liar.

 

Ain't that the truth!

 

PhysBang: I have no axes at all to grind with QFT and much fewer with QCD than I did before I joined this forum, and some of your comments are the reason for that.

I like it that Farsight has gone all the way back to what Maxwell himself said, and I haven't met very many individuals who go to that much trouble to read original works, as I myself have done on occasion. It is usually true that originality doesn't count for much in science when the next better idea (and hopefully, explains something in more detail) comes along.

Maxwell could only guess about the boundary conditions of any field(s) that produce EM radiation. The right hand thread rule, sure enough, comes originally from there. But surely you can tell, this is only an accounting device; a convention. The vector math works that way because it was defined to work that way, and for no other good reason. Can it be claimed that QFT provides a deeper motivation without recycling Maxwell's conventions?

 

It isn't only an accounting device Dan. The important think to remember is that the field is the electromagnetic field. You don't "create" a magnetic field when you change an electric field. The field is the electromagnetic field. What we call an electric field is one aspect of it, what we call a magnetic field is another aspect of it. And like Maxwell and Minkowski said, it has this "screw" nature. Think about a pump-action screwdriver. It converts linear motion into rotational force. That's kind of what you do when you send a current up a wire.

 

Maxwell usually rewards reading, since he was a very smart and careful writer and thought a lot about the foundations of the physics he was presenting and the assumptions that went into crafting it.

Sadly, Farsight has only read those portions of Maxwell that he found through a google search to match terms that he can tie to his personal theory. He is doing only a textual analysis of these few passages.

 

Minkowski was a mathematically sophisticated person talking to an audience of people well-versed in physics and mathematics. Moreover, in context, Minkowski cited the Liénard–Wiechert description of electromagnetism of a moving charged particle in the immediately prior paragraph to make it clear what he was describing by analogy.

All analogies are imperfect. To understand the analogy you have to understand both endpoints and then you can see the similarities highlighted by the analogy and the dissimilarities where the analogy is not reliable.

Farsight misunderstands in post #12 a reference to "force screw" (also called "wrench" ) in Newtonian mechanics of rigid bodies referring to a six-dimensional description of linear force + torque. No "twistyness" of the electromagnetic field† is implied by Liénard and Wiechert and therefore not by Minkowski, either. Thus Minkowski was just saying there was a six-dimensional mathematical object that describes the electromagnetic field at a point in every inertial frame. Today we call that geometric object the electromagnetic tensor.

http://de.wikipedia.org/wiki/Dyname (Notice mention of Kraftschraube)
http://en.wikipedia.org/wiki/Screw_theory
http://www.euclideanspace.com/maths/geometry/affine/screwTheory/index.htm
http://en.wikipedia.org/w/index.php?title=Liénard–Wiechert_potential&oldid=557636754

† The spin of the photon was not necessarily anticipated at this time. That would wait for generalizations of Dirac's equation in the 1920s, sensitive experimentation in the 1930s and for a 1939 paper by Wigner which is foundational for QFT.

 

There does seem to be a "twistyness" of electrons and EM based on spin, and only one spin dimension less than W and Z bosons of the electroweak.

I agree wholeheartedly, extra dimensions are appropriate to EM and are a robust (but not necessarily complete) vindication of QFT formulations. To be successful, I must either explain how each one of these added dimensions derive from something that started out only as energy and time, or else find a better idea somewhere. Time evidently does proceed at different rates for different kinds of particles, starting with neutrinos. This could be a start.

A couple of appropriate John Von Neumann quotes are in order here:

"Young man, in mathematics you don't <really> understand things. You just get used to them."

"If one has really technically penetrated a subject, things that previously seemed in complete contrast, might be purely mathematical transformations of each other." I think he must have been speaking in regard to the current 'E + M', or equivalently 'A and phi' discussion, and this idea has a lot of merit.

Happy Bird Day, all. Guests will be arriving soon. We'll be talking turkey for a change, not physics or math.

 

Dan: rpenner doesn't understand this I'm afraid. AFAIK he's a mathematician, not a physicist. Have a look at this NASA article about gravitomagnetism. It says things like There is a space-time vortex around Earth and space is twisted. It gives this artist's impression:

Please Register or Log in to view the hidden image!

The electromagnetic field isn't totally unlike the gravitomagnetic field in this respect. Gravitomagnetism was initially developed by Oliver Heaviside as an analogy of electromagnetism, see his original paper here. Look again at the Minkowski quote:

"In the description of the field caused by the electron itself, then it will appear that the division of the field into electric and magnetic forces is a relative one with respect to the time-axis assumed; the two forces considered together can most vividly be described by a certain analogy to the force-screw in mechanics; the analogy is, however, imperfect".

The field of the electron is the electromagnetic field Fμv. It's a combination of what think of as electric field E and magnetic field B. See section 11.10 of Jackson's Classical Electrodynamics where he says "one should properly speak of the electromagnetic field Fμv rather than E or B separately". The electric field is usually depicted with radial field lines (or lines of force if you prefer), and the magnetic field is usually depicted with concentric field lines. But you never see any depiction of electromagnetic field lines. I think one can depict them by combining electric and magnetic field lines like this:

Please Register or Log in to view the hidden image!

 

More fingerpaints?

Can you show us how to do a physics problem with your pictures, Farsight?

 

I strongly suspect you are wrong about that, but he can speak for himself

{cut some unintelligible gibberish}

Once again, you reveal your complete ignorance. \(F_{\mu \nu}\) are the scalar components of the (Faraday) field strength tensor, not the tensor itself and not repeat NOT the field itself. (Interestingly - slightly alarmingly - this tensor describes the "curvature" of the field. You won't want to know this, of course, but I have a proof)

Maybe you would care to show the Faraday tensor in component form in its matrix representation, then we can see where to go from there. Or do you want me to do it for you?

 

Physics problem? Why does anybody want to do a physics problem? We want to understand the world, not do puzzles. And these pictures deliver understanding. For example, and electron and positron move towards each other linearly, and they move around one another, as per ortho or para positronium. They don't do this because they're throwing photons back and forth. That's a myth, virtual particles aren't short-lived real particles, they're field quanta. Hydrogen atoms don't twinkle, magnets don't shine. The linear and rotational motion occurs because an electron is a spinor. Electrons and positrons interact and attract like a cyclone and anticyclone. As you are doubtless aware, counter-rotating vortices attract, co-rotating vortices repel. Like this:

Please Register or Log in to view the hidden image!

 

Farsight, the article, a dumbed down lay oriented explanatintion of the GP-B experiment, uses the word space 18 times, 13 including once in the title associated with the word time, as space-time, including 1 occurrence of, time and space. There were then 5 occurrences of the word space, with no associated reference to time, like space craft and going into space...

There was only one use of the word space which could be misinterpreted in your customary manner.., a quote follows,

Looks like the first instance above was a typo, since of the 14 (13+1) references, of the words space and space-time, only one used the word space alone, and that instance was followed in the next sentence with a correct reference to space-time.

Another example of how your cherry picking quotes misrepresents the facts.