Minkowski Space Time Briefly Revisited

I do understand it. Thanks.

 

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Nicely done, all.

For those interested in the Cadillac relativity problem, a Java applet simulation of the calculated "rotation" appears here:

http://webphysics.davidson.edu/applets/Minkowski/Minkowski_FEL.html

Minkowski rotation has limits and mathematical peculiarities that Euclidean rotation does not. You can decide for yourselves if this is really a rotation. As far as I can determine, it has no bearing whatsoever on the application I was most interested in.

The math for Minkowski rotation does find various application in certain technologies I deliberately avoided, both as an undergraduate and today. It's bad enough that part of my engineering career included A-10 military avionics, and that was enough to give me nightmares. The nuclear warhead arming devices were being tested in an adjacent room.

 

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Minkowski Rotation and the Arrow of Time

Now that I'm certain everyone is up to speed on what Minkowski rotation, I'd like to divert a little to a discussion of exactly why that rotation looks so odd, even for something traveling at c that is without contours other than a beginning and an end (of the two pulses), each propagating in its own straight line.

One possible explanation is the arrow of time. Although it is possible to rotate the observer of the two pulses (separated by an arbitrarily small distance d) and thereby change the perception of which pulse was emitted first, and even though this provides some (but not all) of the missing range of rotation as compared to rotation in Euclidean space, this does not entirely explain the asymmetry observed. Some here will also notice similarities between this thought experiment and a double slit interference setup, but for the purposes of this one, interference between the pulses is neglected, as this further complicates a discussion of the arrow of time.

The 'proper' FoR here, of course, is the frame from which the two pulses were emitted simultaneously. This will also be evident for a moving observer that is oriented and traveling in a plane at right angles to a line joining the beginning of the two pulses, provided that line also appears to be at right angles with respect to the propagation of the pulses. For an observer approaching either side of the pair of pulses however, it is possible to make one or the other pulse appear as though it was emitted first. But although the ordering of events may appear different, this is not the same as reversing the arrow of time.

Reversal of the arrow of time is not possible even in this simple pair of events, no matter which way you observe them. You can make the pulses appear Doppler shifted either to the red or the blue if you are traveling in a path parallel to their direction of propagation, but under no circumstances will either of the pulses appear to be propagating in a backward direction once they have been emitted. We will stipulate there are no mirrors to effect such a reversal, and even if there were, mirrors also are not time machines.

We have now completely characterized Minkowski rotation of the two pulses in terms of 4* pi * r Euclidean Steradians. Just because a rotation is hyperbolic is no reason not to observe what happens from every conceivable angle we can. We are not constrained by planar or any other geometry to observe things as though we had tunnel vision.

The simple relation I had proposed for relating space to time by means of the speed of light c fails only because it lacks compensation for of the arrow of time. Also, it does not adequately explain why if time has an arrow, space apparently does not. Or does it?

For energy that is bound, as it is in matter, essentially there is no time, unless that matter decays in a finite amount of it. Stable matter remains matter for a very long time, particularly on quantum scales. For energy that is not bound such as in this example, time is represented by a direction of propagation and the rate at which it proceeds, limited only by the speed of light or interaction with other bound or unbound energy.

 

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Needless to say, the idea that length contraction / time dilation were somehow connected by this '4D rotation' has always rubbed me the wrong way. An asymmetrical hyperbolic 4D rotation doing this really makes no sense if you look at the physical details from more than just one physical angle.

 

You really don't understand, do you?

You have a description of reality, the math.., mixed up with the fundamental origins which remain undiscovered.., or at least not yet fully discovered/undrstood. I think you are also confused by the seemingly contradictory perspectives associated with frames of reference...

Sinse you admittedly reject GR and even at least some aspects of SR, perhaps you should leave these things to others.., and focus on just getting through the day before you.

 

I'm actually onboard with GR, OnlyMe, up to a certain point, and that would be the point at which curved space becomes a mathematical study in topology, like it would for solid objects. If it turns out that the dynamics of gravitation comes from the superfluid that is vacuum fields and energy, then the topological description of curved space will need to be jettisoned and replaced with a better set of descriptive dynamics more in tune with what is observed, not something unjustifiably anchored in absolute space and time.

"Not fully understood" is exactly what this is all about. When something is not completely understood, we should be trying to understand it, not make our math more incomprehensible and pretend that because we are using that language, that we understand any better what we are talking about. It really, really doesn't work that way. Complex numbers with no real parts are just as comprehensible as any real number with no imaginary parts. Potential energy in a compressed spring or in a gravitational field are just as comprehensible as playing catch, if you know which balls (particles, waves) are in play. The "multiverse", parallel universes, and block universes are all bunk. They are about as real as the ideas of young Earth creationists that fossils older than about 5000 years don't exist, or are some sort of scam. If you can't directly observe something or its effects, it might as well not exist. Don't tell me a fairy story with supporting math unless you can back it up with a prediction that actually pans out.

Notice that in the last post, this two pulse Minkowski thought experiment of mine, unlike ones done using Cadillacs or other material objects to demonstrate the rotation, has no difficulty whatsoever in sorting out what part of the experiment pertains to the arrow of time and which part pertains to Lorentz simultaneity ideas.

The flow of time is the excitations of electric, magnetic fields in the vacuum, and it doesn't even matter whether the photons are virtual or 'real'. In any FoR in which it appears that one of the pulses is emitted before the other one, the other one becomes "virtual" for a time. Virtual photons (or other kinds of energy) are just as real as real ones.

 

I looked back at where I thought that last sentence came from and found it an error on my part. Since edit is no longer available it is struck out below.

How you arrived at superfluid as a description of vacuum energy, is suspect... Meaning it comes across here as a biased opinion, not a reasoned conclusion. In its purest form vacuum energy is virtual.., and not universally accepted as real... In the limited context, speculation might attach to the idea, when considering only the EM spectrum, of vacuum energy.., there may exist some underlying reallity, but by being limited to the cumulative affect of EM radiation from all sources (including some remaining hypothetical at present).., it would not be self interacting, thus a stretch to arrive at anything even resembling a fluid/super fluid.

And all of this is diverging from the discussion of geometries, though I am sure geometries could be descriptive of any associated dynamics....

 

See the Baez Preliminaries GR article and note this:

"Similarly, in general relativity gravity is not really a `force', but just a manifestation of the curvature of spacetime. Note: not the curvature of space, but of spacetime. The distinction is crucial."

 

Well, it's good to see that Farsight has finally learned to identify gravity in GR with spacetime curvature!

 

Dan: space isn't curved where a gravitational field is. Instead it's inhomogeneous. See Einstein talking about it here and see this for something more recent. Spacetime curvature relates to the tidal force, which is the second derivative of potential. The force of gravity relates to the first derivative of potential which is the spacetime "tilt". In the bowling-ball analogy the slope determines how fast the marble falls, not the curvature.

 

Please demonstrate this with an example.

 

I am having trouble reconciling this....

....with this

Tell us, Farsight, which of these seemingly incompatible assertions (do you believe) is true?

 

And can you show us how a sample physics application with these concepts works with an example?

 

The Higgs boson is real, and apparently part of the vacuum, and gives certain particles inertia. I'm just anticipating what's coming next. As far as I can tell, the dynamics that will be needed to take on the problems ahead are not there yet.

Yes, we have diverged a little from the brief discussion of Minkowsi space time I wanted to finish here, but it has been done in much greater detail this time, and I'm very happy with the result. I learned a lot from everyone here, and from thinking about their responses. The Minkowski math definitely has practical value, but the simulation in Javascript I found is pretty typical of how far people take the analysis, and I for one don't think it's quite far enough, for a number of reasons. It does not, for example, provide any motivation to conclude that length contraction and time dilation are by any means bound dimensionally the way some discussions of Minkowski space-time would suggest. The pulse example demonstrates the folly of this idea.

On other forums, I have sometimes given folks the impression that I have an axe to grind with math, ANY math. Actually, I do not. Math for its own sake is every bit as important as doing physics for its own sake, and they play well off each other, for the most part.

I think we're now finished here unless some other part of the thread needs resolution.

 

The efficacy of the math of GR is undeniable. But I really want to see it re-unified with particle physics.

 

Skip to 5:15:

 

I did not watch the whole thing yet. I did skip to the part you pointed out.., and I disagree, at least in principle or context???

In stating that space-time has to be thrown out (my words), I believe only applies to that modern interpretation I keep mentioning, which is itself mostly a conceptualization. The underlying descriptive model may require some modification, but no more so than Newton's work was modified by Einstein's.., and yet remains valid.

 

How about this one?

 

I don't believe that has been demonstrated. I don't even remember seeing anything that confirms the Higgs mechanism, though a short lived boson in one of many energy ranges consistent with what might be expected of a Higgs boson, has been detected.., in the lab.

Zero point or vacuum energy is still really pretty much theoretical, other than as I mentioned earlier for the EM spectrum which could be a real component.., note I did not say is a real component of vacuum or zero point energy, just could be!

Beyond that even if the Higgs mechanism were confirmed, it would account for only a small fraction of the mass of matter.., which seems to account for only a small fraction of the mass necessary to explain cosmological observations associated with dark matter.

I still don't see anything more than wishful thinking in the sentence quoted above.

 

Tashja, I'll have to try and watch these later. Not sure when. It is getting late now and I have several irons in the fire right now, so to speak.