String theory is what?

[oddmanout]

No, the photon adds mass alright. The mirror-box to electron, 'there ain't no box' analogy does not work.

Ah, you were talking about the electron!

OK, so the photon does add mass to "the system". Could you explain this, in layman's terms, please? Light / photons is something that has been confusing me for a while. So, the photon is a massless particle, yet it is also a wave. If you confine "it" (the "wave-particle"?) into a mirror-box it adds to the total mass of the box. What does this mean?

If I'm not mistaken, a common thing is to consider light quantified; light as quanta. But I feel like I'm missing something here, an important part of the puzzle. I'm quite aware that light is "bent" in gravitational fields, but this because of the curved space, is it not? And not because of interactions with (the supposed) gravitons? Or is that two ways of looking at the same thing; from either a GR or a QM point of view?

[newolder]

No, the photon adds mass alright. The mirror-box to electron, 'there ain't no box' analogy does not work.

Ah, you were talking about the electron!

OK, so the photon does add mass to "the system". Could you explain this, in layman's terms, please? Light / photons is something that has been confusing me for a while. So, the photon is a massless particle, yet it is also a wave. If you confine "it" (the "wave-particle"?) into a mirror-box it adds to the total mass of the box. What does this mean?

If I'm not mistaken, a common thing is to consider light quantified; light as quanta. But I feel like I'm missing something here, an important part of the puzzle. I'm quite aware that light is "bent" in gravitational fields, but this because of the curved space, is it not? And not because of interactions with (the supposed) gravitons? Or is that two ways of looking at the same thing; from either a GR or a QM point of view?

In layman's terms boxes that carry surplus or injected wave energy weigh more than utterly dark ones and the bluer the wave being carried, the heavier the box. The gravitational nature of massless entities is described by their effect on local curvature in space-time.

The Weyl curvature represents such gravitational effects as tidal fields and gravitational radiation.

[lpetrich]

Farsight, you're being too literal-minded. The particles are not little billiard balls or whatever, but quantum fields that follow field equations.

Photons and abelian gauge fields in general: Maxwell's equations.
Nonabelian gauge fields: Yang-Mills equations (generalization of Maxwell's equations for the nonabelian case)
Elementary fermions: the Dirac equation
Elementary scalars: the Klein-Gordon equation
Etc.

I'm glad you said that lpetrich. It's something we agree upon. But sadly I have had numerous conversations with people who consider themselves to be educated and knowledgeable in physics, who are utterly convinced that electrons and quarks are pointlike. I wish people like you would attempt to persuade them that this is not the case. Unfortunately the myth persists, such as on the wiki article, see http://en.wikipedia.org/wiki/Electron#F ... properties where it says "The electron has no known substructure.[2][71] Hence, it is defined or assumed to be a point particle with a point charge and no spatial extent."

That's a misunderstanding about particle spin, that it's like some added gyroscope. In reality, it's built into the spatial structure of the particle field. Here goes:

Spin-0: Klein-Gordon equation

Di - partial-differential operator with respect to variable xi.
gij - raised-index space-time metric

A simple space-time wave equation:

Field: f
Potential: V(f)
Equation: gijDiDif = V'(f)

Spin-1: Maxwell's equations

Electromagnetic potential: Ai
Electromagnetic field: Fij = DiAj - DjAi
Raised indices: Fij = gikgjlFkl

Maxwell's equations:
DiFjk + DjFki + DkFij = 0
DjFij = Ji

Spin-1/2: Dirac equation

Dirac matrices gmi:
Time: [I 0; 0 -I]
where I is the 2*2 identity matrix.
Space [0 sg; -sg 0]
where sg is the Pauli matrices.
The gm's have dimension 4*4.

Field: f (dimension 4)
Mass: m
Equation -i * gmiDif + m*f = 0

The particles' spins is a result of their space-time structure. 0: scalar, 1: vector, and 1/2: spinor.

I know this is only wiki, but it says "If an elementary particle truly has no substructure, then it is one of the basic building blocks of the universe from which all other particles are made." This is misleading. The electron does have a structure, that's why it exhibits charge, and it isn't a "basic building block". You can destroy it via annihilation, and get something more basic. Ditto for the proton. And note that one nanosecond after low-energy proton/antiproton annihilation, the quarks have gone.

All bad arguments against elementariness. Spin is not some sort of gyroscope added to a particle. Decay and annihilation happen because they are permitted by energy conservation and conservation of various quantum numbers and its nonabelian analog.

Demonstrably false.

It isn't. Elementary particles really do work like macroscopic objects. The Stern-Gerlach experiment is a good example.

Don't make me laugh. That's a quantum-mechanical effect without a classical counterpart. A stream of particles with angular momentum j gets split by a magnetic field into (2j+1) equally-spaced streams around where the original stream would be in the absence of a magnetic field.

It happens because the angular-momentum operator J projected onto any direction will have eigenvalues -j, -j+1, ..., j-1, j.

Try explaining relativity to your grandmother some time and see how successful you are. Especially general relativity.

I have. I'm the relativity+ guy. I wouldn't say I've set the world on fire yet, but I'm off to a TV studio for a documentary in a couple of weeks.

Why not try to take it to the mainstream scientific community?

Whoever said it, I hope you agree that if one is unable to give a simplified explanation, there is an issue.

I don't.

[lpetrich]

This is a good illustration of why a solid understanding of maths is needed to discuss these topics for more than illustration. As Paul Dirac said "I understand an equation when I have a good idea of the results it will produce before performing the calculation". Much can be lost in the translation from a mathematically forumalated idea into English, and the process of communicating it is typically one way. There is not much point in attacking an explanation of a theory with linguistic tricks - all it usually identifies are a weakness in the explanation, or a failure to understand the explanation.

That's so true. The mathematics is there for a reason - not necessarily to produce grandiose qualitative claims but testable quantitative claims -- and sometimes very precisely testable quantitative claims at that.

[hackenslash]

And what of Einstein, whose understanding was visceral, and whose mathematics was poor?

[Twiglet]

And what of Einstein, whose understanding was visceral, and whose mathematics was poor?

It's a rather relative point that his maths was poor... he still formulated general relativity, the maths of which is hardly trivial. Whatever Einsteins shortcomings may have been, he was nonetheless able to put forward his theories mathematically, and subject them to experimental tests which produced results that validate them. Not only that, but they explained results which the prevailing ideas of the day could not.

I strongly agree that conceptual understaning is extremely important in science, and even that many science graduates can achieve pretty good results by just learning by wrote how to solve the kind of problems which come up on tests, but that really isn't the point at issue here.

It's pretty trivial to come up with an "explain it all theory" - Fairies do everything. There - I just did (Feynmann uses this example to very amusing effect in his biographies). But where do we go from there? How are we any better off?

If I invent something couched in scientific jargon, the effect is still much the same: "The resonance of electromagnetic waves exhibits certain stabilities which describe the elementary particles. Quarks are stable resonances which pattern up in groups of threes through the exchange of gluons, but in fact the elementary nature of quarks can be challenged in very high energy collisions where more fundamental stabilities occur due to the higher energy densities involved".

The above piece of mumbo-jumbo has the virtue of being testable, and predicting something (it's very unclear what, beyond the existence of particles we haven't found yet) - so in that sense, it's a good concept, despite being mumbo-jumbo. It's also a good concept because it validates existing experimental data, just as special relativity reduces to Newtonian mechanics at zero velocity. Newtonian mechanics is simply relativistic mechanics at zero velocity. How?

E=mc^2= m0c^2/(1-v^2/c^2) 1/2 Performing a binomial expansion and applying the assumption v<<c yields E=m0c^2 + 1/2m0v^2 - which is the classical kinetic energy, plus the energy any body possesses by virtue of having a rest mass. This is a good example of how a new theory validates existing ideas with strong experimental evidence supporting them, as well as suggesting where the old theories break down, i.e. where V is of the order c.

[hackenslash]

And what of Einstein, whose understanding was visceral, and whose mathematics was poor?

It's a rather relative point that his maths was poor... he still formulated general relativity, the maths of which is hardly trivial. Whatever Einsteins shortcomings may have been, he was nonetheless able to put forward his theories mathematically, and subject them to experimental tests which produced results that validate them. Not only that, but they explained results which the prevailing ideas of the day could not.

Einstein had a great deal of assistance in couching his ideas in mathematical terms. The math was not Einstein's, though the concepts were.

Take myself. I left school at the age of 12 with a grade 3 trumpet to my name. This is still the only qualification I possess. I had a basic understanding of algebra when I left formal education, and I have done no work to advance that in the interim. However, many will testify that I have a visceral understanding of some pretty esoteric principles, and that I can apply real understanding to real-world circumstances. Indeed, in another thread on this very forum, one member who studied relativity and QM at university level suggested that, of the two of us, I was the more knowledgeable. I'm not actually convinced that that is the case, but the assertion itself gives the lie to the assertion that mathematics is actually necessary to understanding of the principles, if Einstein were not enough.

[Twiglet]

And what of Einstein, whose understanding was visceral, and whose mathematics was poor?

It's a rather relative point that his maths was poor... he still formulated general relativity, the maths of which is hardly trivial. Whatever Einsteins shortcomings may have been, he was nonetheless able to put forward his theories mathematically, and subject them to experimental tests which produced results that validate them. Not only that, but they explained results which the prevailing ideas of the day could not.

Einstein had a great deal of assistance in couching his ideas in mathematical terms. The math was not Einstein's, though the concepts were.

Take myself. I left school at the age of 12 with a grade 3 trumpet to my name. This is still the only qualification I possess. I had a basic understanding of algebra when I left formal education, and I have done no work to advance that in the interim. However, many will testify that I have a visceral understanding of some pretty esoteric principles, and that I can apply real understanding to real-world circumstances. Indeed, in another thread on this very forum, one member who studied relativity and QM at university level suggested that, of the two of us, I was the more knowledgeable. I'm not actually convinced that that is the case, but the assertion itself gives the lie to the assertion that mathematics is actually necessary to understanding of the principles, if Einstein were not enough.

We have heard of Einstein because his ideas were put into a form which allowed for them to be tested. I'm not enough of a historian to debate how much help he had, I know it's attracted some controversy. It's quite possible someones new concept has some hitherto unrecognised truth to it, but the onus is on them to put it into a form where that can be tested, as Einstein did.

Perhaps you do have a better conceptual understanding of QM than your physicist friend - I can't really say, but I do know you can do well enough studying physics by learning hwo to apply formulae to problems without ever once raising a philosophical question about what any of it means. By the way, just about anyone who has studied physics at university in the last 50 years has studied QM & special relativity pretty much by definition.

The controversy in this thread, and in the SR thread are about misrepresentation of existing theory to support a pet theory. There's a pretty radical difference between saying "your understanding of existing theory is flawed, so the conclusions you have drawn from it don't hold up" and "your new theory of everything is bollocks cus I said so".

Citing a wikipedia entry which is mathematically based as if it supports a verbal argument is duplicitous. It's very transparent to anyone who understands the concepts mathematically and conceptually, but to someone trying to understand linguistically they have no way to distinguish if the paper/citation is actually backing the post up or not. If you personally have a good conceptual understanding, I would assume it's because you have read a number of good books by scientists doing their absolute best to explain those concepts without resorting to mathematical hyperbole, and you have taken those explanations at face value and on trust - which is great. By doing so, you certainly could understand the core concepts very deeply. Your ambition is understanding.

The ambition of someone misappropriating bits of maths and misrepresenting existing theories to lionise their pet ideas is a different matter altogether.

[lpetrich]

The controversy in this thread, and in the SR thread are about misrepresentation of existing theory to support a pet theory. There's a pretty radical difference between saying "your understanding of existing theory is flawed, so the conclusions you have drawn from it don't hold up" and "your new theory of everything is bollocks cus I said so".

What's that SR thread?

The mathematics of SR is, if anything, easier than that of QM. If you can understand the mathematics of Newtonian mechanics, you can understand that of SR without much trouble. The main thing you have to worry about is to be careful of time coordinates - time values are relative as well as space-position values.

So I don't see much excuse for not trying to understand it if one already understands the math of Newtonian mechanics.

[oddmanout]

The controversy in this thread, and in the SR thread are about misrepresentation of existing theory to support a pet theory. There's a pretty radical difference between saying "your understanding of existing theory is flawed, so the conclusions you have drawn from it don't hold up" and "your new theory of everything is bollocks cus I said so".

What's that SR thread?

The mathematics of SR is, if anything, easier than that of QM. If you can understand the mathematics of Newtonian mechanics, you can understand that of SR without much trouble. The main thing you have to worry about is to be careful of time coordinates - time values are relative as well as space-position values.

So I don't see much excuse for not trying to understand it if one already understands the math of Newtonian mechanics.

Hi, I have a newbie question on this subject (although on GR): how is it (if I'm not mistaken, which I probably am) that the space-time coordinates in GR can be treated as interchangeable? I.e. it doesn't matter which coordinate is which. This makes sense from the point of view that travelling through the 4-dimensions of space-time is limited by the upper speed limit of c, but is there really no difference between space and time?

[Twiglet]

What's that SR thread?

This is: http://www.rationalia.com/forum/viewtop ... &start=200

[lpetrich]

Thanx, Twiglet.

Hi, I have a newbie question on this subject (although on GR): how is it (if I'm not mistaken, which I probably am) that the space-time coordinates in GR can be treated as interchangeable? I.e. it doesn't matter which coordinate is which. This makes sense from the point of view that travelling through the 4-dimensions of space-time is limited by the upper speed limit of c, but is there really no difference between space and time?

Strictly speaking, coordinates don't have to be well-defined "space" or "time" coordinates. However, timelike, lightlike, and spacelike directions are still well-defined. One has to use the space-time metric to find what a direction is. For a vector u, one finds u.g.u over metric g.

In practice, one selects coordinates that are associated with various symmetries or else make the metric or certain functions of it take certain forms.

Thus, for flat space-time, one may select rectangular space-time coordinates and diagonalize the metric. The four coordinates then become three space ones and one time one.

[Coito ergo sum]

Every time I read this title "String theory is what?" - I wanna say "asphinctorsayswhat?"

[Farsight]

Hey Farsight, oddman from RD.net here.

But anyway: a photon in a mirror-box adds mass to that system. Pair production and electron angular momentum tell us the electron is like a photon in a box, only it's going round and round rather than back and forth. And there ain't no box.

Could you elaborate on this? And, preferably, someone else too? It struck me as important, not sure why.

Hi oddman. Like newolder said, trap a massless photon in a box, and the mass of the system is increased. This is essentially what Einstein said in Does the Inertia of a Body Depend Upon its Energy Content?". That's the paper that introduced E=mc², though Einstein used L instead of E, saying If a body gives off the energy L in the form of radiation, its mass diminishes by L/c².

If you take a look at pair production and annihilation you can see this in extremis. In pair production we create two "bodies" with mass, the electron and the positron, out of a massless photon. (It has to be a pair for conservation of angular momentum etc). In annihilation, each body emits a photon, and then isn't there any more.

The electron has angular momentum, and magnetic dipole moment, so there's something going round and round. See Is the electron a photon with toroidal topology? which essentially says it's a photon. This paper is by John G Williamson and Martin B van der Mark, formerly of CERN, and appeared in the journal Annales de la Fondation Louis de Broglie, volume 22 in 1997. The electron is thus a system like a photon in a box, but without the box.

It's very simple really, but people seem to have difficulty with the symmetry between momentum and inertia. The distinction between these two measures depends on whether you say it's you moving, or something else. If you try to stop a cannonball moving at 5 m/s it's not easy, because it has considerable momentum. If however you're moving at 5 m/s and you're trying to scoop up a motionless cannonball and get it moving, it's not easy because it has considerable inertia. The massless photon exhibits energy/momentum, and it's always moving at c. Pair production contrives things so that whilst it's going round and round at c, it isn't moving in aggregate with respect to you, so the energy/momentum is now expressed as inertia. In other words, mass.

[Farsight]

That's a misunderstanding about particle spin, that it's like some added gyroscope. In reality, it's built into the spatial structure of the particle field.

I'd say that doesn't go far enough. Ever considered a whirlpool? IMHO it's quite a good introductory analogy. It involves fluid dynamics rather than dynamical stress-energy, and the rotation is in one plane visible at a surface, but it still kind of works: a whirlpool isn't like a spinning billiard ball. It's only a whirlpool because the rotation is present. In similar vein the spatial structure of the electron field is only there because of the rotation.

Here goes:

Spin-0: Klein-Gordon equation

Di - partial-differential operator with respect to variable xi.
gij - raised-index space-time metric

A simple space-time wave equation:

Field: f
Potential: V(f)
Equation: gijDiDif = V'(f)

Spin-1: Maxwell's equations

Electromagnetic potential: Ai
Electromagnetic field: Fij = DiAj - DjAi
Raised indices: Fij = gikgjlFkl

Maxwell's equations:
DiFjk + DjFki + DkFij = 0
DjFij = Ji

Spin-1/2: Dirac equation

Dirac matrices gmi:
Time: [I 0; 0 -I]
where I is the 2*2 identity matrix.
Space [0 sg; -sg 0]
where sg is the Pauli matrices.
The gm's have dimension 4*4.

Field: f (dimension 4)
Mass: m
Equation -i * gmiDif + m*f = 0

The particles' spins is a result of their space-time structure. 0: scalar, 1: vector, and 1/2: spinor.

Thanks for going to all that trouble. I see things a little differently because I have a different view of time. I see it as an emergent property of motion through space. Thus I have a different interpretation, which isn't a space-time structure per se, but a dynamical stress-energy structure in space. A spin-zero pion is however an unstable structure, it lasts for less than a microsecond. A spin-1 photon is a stable structure, as is a spin 1/2 electron, which has a moebius aspect to it.

All bad arguments against elementariness. Spin is not some sort of gyroscope added to a particle. Decay and annihilation happen because they are permitted by energy conservation and conservation of various quantum numbers and its nonabelian analog.

The spin is what makes the particle what it is.

Don't make me laugh. That's a quantum-mechanical effect without a classical counterpart. A stream of particles with angular momentum j gets split by a magnetic field into (2j+1) equally-spaced streams around where the original stream would be in the absence of a magnetic field. It happens because the angular-momentum operator J projected onto any direction will have eigenvalues -j, -j+1, ..., j-1, j.

There is a classical counterpart, really. Just think it through for a particle where the spin axis is spinning.

Why not try to take it to the mainstream scientific community?

I've tried, and I'm still trying. The reaction is somewhat mixed. String theorists obviously hate it. Mathematical physicists dismiss it because there's a lack of rigor, and don't understand that I've analysed terms to try to explain what they really mean. The LQG guys are unhappy because I say you can't quantize gravity. The Beyond the Standard Model guys aren't too chuffed because I'm saying understand the electron before you dream up a whole new raft of supersymmetric particles. The HEP guys aren't too keen either because they feel they own a monopoly on this sort of thing, and massive stable particles are knots is somehow threatening. Even some of the relativity guys are unhappy, because I advance the Einstein interpretation rather than the modern interpretation, and say Misner/Thorne/Wheeler is wrong in some respects - see http://arxiv.org/abs/astro-ph/0703751 re George Ellis having a bit of ding-dong with Jo Maguijo re VSL. The people who do like it are the guys involved in photonics, condensed matter physics, and electromagnetics. But they have their own problems getting papers into top-flight journals. It's getting out there slowly, eg via an ad on the Institute of Physics PhysicsWorld website, and I fancy I'm seeing some movement. We'll see how it goes I suppose.

I don't.

You should. Really.