Lattices and Lorentz invariance

I didn't say this. The three dimensional lattice is dynamical, it has waves running through it. Minkowski spacetime is four-dimensional, it's static, and it doesn't have waves running through it. Thus Minkowski spacetime is not a good mental model to think about the underlying reason behind Lorentz symmetry.

Not much. I might quibble and say the lattice line-elements are important and the nodes aren't in space because the lattice is space, but it's not a material issue.

No problem.

They aren't quite the same thing. Lorentz symmetry is a postulate that says the laws of physics are same regardless of your uniform motion. It emerged from various contributors after Maxwell and the Michelson-Morley experiment. Lorentz invariance is mathematical attribute relating to transformations in Minkowski spacetime, a mathematical model where space and time are treated in a similar fashion, but where the concept of the wave nature of matter is missing as far as I know.

 

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Without making any direct comment or specific connection, as the discussion in the last link above begins, mentioning what Einstein might think (paraphrased).., it reminded me of a lecture David Gross once gave in which during the lecture he invoked Einstein's approval of his conclusions. That single lecture took him down several notches in my estimation. If a Nobel Prize winner must invoke Einstein's approval as support of his ideas, they are not worth much on their own.

It is one thing to quote Einstein or anyone for that matter and connect that quote with your ideas. It is a completely different thing to use a name like Einstein's projecting what they might have thought or agreed with, in support of something Einstein had no way of knowing anything about.

It is one thing to say Eistein said or wrote.., and quite another to claim that Eistein would have liked or approved of my.....

I cannot say that I have never been guilty of anything similar, only that we would be better served if we keep ourselves to quotes, rather than projections...

 

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It isn't because of any history we've had. I just thought I ought to respond to people you seem to take a lead from, and stop them leading you astray. I'll look at your posts now.

 

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Are you serious?! I have a PhD in theoretical physics so my opinions on the subject are reasonably well formed on their own without others "leading me astray."

I'm wondering if you could actually be more patronising...

 

Yes it's true. It's just space and motion through it. You assign a t coordinate derived from the motion measured by your clock, and away you go.

You effectively started this thread by jettisoning tetration. Look at the initial posts. It's all about "the whole spacetime vs space thing". You still don't seem to understand the distinction. But OK, if you don't want to talk about it just lock the thread. I won't be offended.

Sure, it isn't a compelling reference, but it is a reference, and you should have been interested in the mention of topological charge. But nevermind. Let's move on.

I didn't say that. I said this:

See my post above re Lorentz symmetry and Lorentz invariance.

I do my best to make things easy to understand.

I know the difference. You're suggesting this because I said you just move. In another thread we were talking about a boost when the charge moves. And yet here you are trying to suggest that I meant you change location. Drop it prometheus, you're wasting everybody's time.

Stop digging.

I said The time "direction" isn't the same thing as space directions. You have freedom of motion in space but not time. The important thing about it is that it's an abstract direction. You can't move or point in that direction, or away from it. It isn't a literal direction, hence the quotes.

Consider dynamical Euclidean space with waves moving through it. Consider your clock to be a wave moving in a circular path in front of you, and yourself as being some more complex aggregation of the same. Now think it through.

If you're not questioning electron diffraction and the wave nature of electrons, then what are you quibbling about? Go look at pair production and annihilation and electron spin and magnetic dipole moment and the Einstein-de Haas effect. Get your calculator out and work out λ = 4π / c^1½. Think for yourself.

Not good enough, it would seem. Go and do some research. Go look at things like neutron optics.

Anyway, I hope you're getting something out of this. If not, just lock the thread. It's your thread, not mine. I'm going to bed.

 

That doesn't mean it isn't poor, even incorrect, phrasing.

I'm sorry that you're only able to parrot back things you read in pop science books rather than engage in an informed discussion based on experience and wider reading but that isn't my fault.

I did say ever. Pay attention.

And do you really think I'm unfamiliar with space-time manifolds? More than once I've had to explain things about them to you. The separation of space and time in space-time, curvature, symmetries etc. That behaviour might fly with friends and family but no one here buys it.

It isn't abuse, it's a statement of fact. If you spent less time thinking reading a pop science book makes you informed and more time actually gaining a working understanding of this stuff maybe people would think you spend your time a little more wisely. Have you ever done any calculation with manifolds, metrics, tensors? I doubt it, yet they form the central core of what we're talking about. I saw you mention line bundle curvature in another thread. Do you think anyone here believes you have a working understanding of that?

It's produced more physically relevant stuff than your work has. Managed to come up with a single physical model yet? Thought not.

Me.

Bear in mind Farsight that the behaviour of asserting knowledge when you're demonstrably uninformed is not exactly good behaviour. The other people in this thread all have working familiarity with relativity and you do not. You simply believe you have some insight. Your posts are generally not quite trolling but certainly you aren't as forth coming and intellectually honest as you could be.

If any of us challenged you to show working understanding of this stuff, rather than you just waving your arms, would you be able to do so? If the discussion went much more formal then it would certainly be more scientific so if everyone in the discussion has the capability there's no reason not to.

And the majority of Americans think God is real and a non-insignificant proportion think the Earth is 6000 years old and Jesus is coming soon. Does that mean science should be providing those answers because the public demands it?

You also failed to understand what I said (unsurprisingly). Why should the labels 'wave' and 'particle', concepts developed from our experience of the everyday world, exactly square up with things outside of our experience? What is wrong with developing new concepts to describe new things? To think everything in the universe should be interpretable in a simple way in terms of things we experience in our day to day lives is a mixture of naive and ignorant.

Yes and you're doing so well in your crusade to right the wrongs of physics. How many books you sold now? How many journals have you been rejected from? Honestly, what's your next step? It's been 5 years and you've accomplished nothing but get banned from huge numbers of forums.

I like how you throw in spherical waves and spinors, as if they are somehow two sides of something, like particles/waves. Once again you show you're not above just throwing out concepts you have only heard the names of but you don't understand the details of. If you disagree with this then I'm more than willing to have a formal, quantitative discussion with you about spinors and their role in physics.

Actually he spent considerable time trying to correct your misunderstanding in a thread with 'inflation' in the title not so long ago. You demonstrated you didn't understand it, nor do you understand curvature.

No, you'll explain what you think clocks 'actually measure' but you won't have any formalism to show how you derived such a result via clear, precise logic (ie mathematics). You'll just wave your arms and proclaim conclusions. Much like Sylwester does, he's over in the alternative theories forum claiming to have subsumed string theory into his work. Hasn't got a jot of mathematics to show it. When asked to provide justification he just asserts things again and again. Much like yourself.

When you can actually derive your conclusions in a precise sequence of logic from clearly stated principles then you'll have a justifiable case for saying you have hypothesises an explanation/model for something. Until then you're even less viable than string theory (I phrase it like that since you dislike it so much but your work is inferior to it in every way).

What do you mean 'do they'? Don't you know? Haven't you come across it in your learning of relativity? Haven't you seen how the Schwarzchild metric is derived? Haven't you looked at any quantitative material which uses any general relativity?

This just illustrates my point. You're always so damn sure you've got understanding yet you are ignorant of things so fundamental to a working understanding of the associated physics that it's amazing you don't realise you really need to do some learning.

So when do you plan to make any of your work precise? When are you going to provide any logical derivations from postulates? When are you going to provide any quantitative models? When are you going to be able to precisely describe anything?

Are we back to your 'Time explained' thing?

No matter how much you assert something as if it's a fore gone conclusion you're certain of you have yet to provide actual evidence for your claims beyond assertions and alternatively interpretable points of view.

Which doesn't have anything to do with what I said. Did you read what I said and just spew out a talking point you wanted to say or did you simply not understand?

You've had 5 years and spent huge amounts of time on pretty much every physics forum you could find advertising your work. You've appeared on terrible television. You've self published a book. You've paid for adverts in physics magazines. You clearly have the time and the resources. The problem is you don't have the ability or the results.

In 5 years, even working in your spare time, you could have covered much, even all (if you're motivated enough) of a physics degree. Instead you have learnt nothing of any detail. I'm sure you couldn't pass a 1st year exam in mechanics, relativity, quantum mechanics or mathematical methods.

See above. You clearly have the time and money. Personally I think the fact you've wasted significant amounts of money on self advertising your nonsense when you have a 3 year old child is disgraceful. More than once I've suggested you spend that money on your family instead. Now you're playing the "Oh I wouldn't be a very good father". Sorry but how is spending huge amounts of time on almost every physics forum Google can find advertising your work, claiming to be worth multiple Nobel prizes and after being rejected from every journal you tried refusing to accept it and self publishing using your own money 'being a good father and husband'?

Is this your version of having a mid-life crisis and buying a sports car? You proclaimed you're the new Einstein, deserving of multiple Nobel Prizes and ignored all evidence to the contrary?

I find your choice of words interesting. Are you implying you're not a 'regular guy'? Is this your "I deserve multiple Nobel Prizes" ego showing again?

What does authority have to do with it? Was Einstein in a position of authority when he published special relativity? No. 't Hooft and Josephson were PhD students when they did their Nobel prize winning work. Physics isn't just advanced by heads of department. But perhaps this is a continuation of your 'regular guys' comment, where you see yourself deserving of significant reputation and acclaim and working up from the bottom like everyone else doesn't appeal to your inflated ego.

I really do wonder if it's some kind of midlife crisis you're having (though it'd be a long one). Clearly you've never been competent at physics or maths but suddenly you decide to tell all and sundry you've explained this, that and the other and when you're retorted, rebutted and rejected you pump money into your endeavours to avoid facing up to it. Even on this forum you sometimes skirt so close to glaring 'double think' it makes me think you're either deliberately trolling or there's some serious motivation behind behaviour.

Here's a suggestion, put the money you're wasting on yourself into a trust fund/child ISA for your 3 year old. It'll do much more good that way.

Well taken literally that's true, as you would never get an academic job (unless it was along side Magneto at a degree mill). But you might be referring to the same thing you've said many times about how 'string theory is dying' (or even dead) and people are leaving it and it'll be gone in a few years and it'll be a black mark on everyone's CV etc etc. The fantasy of all their nay sayers being called to account seems a common one for people who peddle pet theories on forums.

 

They let you use calculators now?

Add that to Mathematica and LaTeX and no wonder I have trouble sometimes.

All we got was a pencil and paper... No wonder I've forgotten so much.

 

It seems like you're taking issue with the whole notion of spacetime. Looking through the history of our discussions on the subject it seems like you would rather talk about space in 3 dimensions and time rather than one four dimensional structure called spacetime (which I quite often refer to as "space" since as AN has explained to you, that is shorthand for "manifold" which is the general relativistic description of spacetime.

Funny that you're pushing for the thread to be closed now that I've started posting equations (which surprisingly, you haven't responded to).

The topic of this thread is your remark that a good way to see why Lorentz symmetry is a symmetry is by considering a lattice, and developments of that. The difference between space and spacetime is something of a tangent to this topic in my opinion.

Seeing as we can't agree on the basics like Lorentz invariance and different types of transformation I think topological charge is something to be avoided on this thread.

It doesn't follow from your setup that Lorentz symmetry applies. If you think it does then you'll have to provide a lot more detail and not just say "follow it through" or "think about it."

This typifies your approach to physics: give a wordy explanation which is fine when you're talking about something basic like Newtonian physics, but when talking about an advanced topic like Lorentz invariance it's very easy to leave things out, as you have done here. One of the crucial ingredients into Lorentz symmetry is invariance under rotations. Granted, the pop science books you read will always talk about Lorentz transformations relating frames where one is moving at a speed v with respect to the other, but that is categorically not all they are. See the more detailed explanation below.

It's usually a big mistake to disagree with rpenner but that is exactly what I am going to do: Lorentz symmetry is a name for the symmetry group which must be obeyed by a relativistic theory. Specifically the Lorentz group is SO(3,1) in 3+1 dimensions. Lorentz invariance is the statement that a particular theory is invariant under Lorentz symmetry transformations which leads to the theory having nice properties like the conservation of the energy momentum tensor.

Actually, I've changed my mind - they basically are the same thing.

Notice I said the Lorentz group is SO(3,1). That means that almost trivially the rotation group in 3 dimensions SO(3) is a subgroup so spatial rotations are part of Lorentz symmetry. I now repeat that your lattice of points in 3 dimensional space is not invariant under rotations so it cannot be used as a model to visualise Lorentz symmetry.

This would be a laudable goal, but it seems that you are trying to use the simple explanation to understand things that are inherently complicated, rather than understanding the complicated explanation first and then giving the simple explanation (based on complicated knowledge) to someone with a passing interest. You have nothing behind the simple knowledge which is a sure fire way to get things wrong.

I really love the way you quote me saying you don't understand something, completely miss out the part of my post where I actually explain the difference and why you didn't understand, and then tell me I'm wasting time. It's another feature of your posting style that the brash faux outrage comes out when you cant keep up with the discussion.

There have been at least 2 examples of your chatbot behaviour. I think it's worth noting.

And as I said, I am aware of the difference between spatial directions and the time direction. Since I have actually studied relativity quite extensively I am aware of the real difference, not simply a wordy description of the perceived difference.

Also, there is a certain freedom of motion in the time direction. Sure, I can't go backwards but I can certainly alter the perception of the passage of time by changing my velocity. Incidentally, changing my velocity is how I exercise my freedom to move in space as well, so time and space really aren't all that different after all.

This doesn't explain anything. How is Euclidean space "dynamical"? How does the wave go in a circular path? What are the waves anyway? It's an endless series of non sequiturs.

I'm quibbling your assertion that electrons are made of waves and saying there are far better ways to describe subatomic particles, specifically using quantum field theory. I can't see any other reason for bringing up the Einstein-De Haas effect other than to throw Einstein's name around again.

What exactly is that formula supposed to be computing? If \(\lambda\) is supposed to be a wavelength then it can't be correct because the right hand side has units \(m^{3/2} s^{-3/2}\)

Quantum field theories predict physical quantities with remarkable accuracy. Does the approach you are advocating come anywhere near that? I don't know anything about neutron optics, but I know that neutrons are composite particles and as such are a lot more complicated than electrons.

As I said above, this thread is serving an important purpose so I won't lock it until I have to.

 

I brought this on myself with my abuse of the equals sign. But it seemed bothersome to expand on the point more when I was trying to get Farsight to expand meaningfully on his "rubbish" comment.


The basics of symmetry is that you have something, and do something, and in a certain sense that first something is unchanged by that second something. Spherical symmetry lets you take a perfect sphere (first something), turn it any which way about its center (second something), and every property of the sphere (certain sense) is unchanged. A cube does not have this symmetry because its shadow changes when the cube is rotated 45 degrees. But if you rotate it 90 degrees about any axis running through the center of two parallel faces again every property of the cube is preserved. Further you can combine any sequence of such rotations and still every property of the cube is preserved. Abstracting somewhat, we call those properties preserved by a symmetric its invariants, we call the combinations of all the operations that preserve the invariants the (representation of a) symmetry group, and we say the thing which is subject to the operations and preserves the invariants has this symmetry.

Minkowski spacetime (a first something) has Poincaré symmetry, with the symmetry group that is a continuously connected subgroup of ISO(3,1) as the usual "second something" that preserves the invariant \(c^2 (\Delta t)^2 - (\Delta \vec{r})^2\) between any two "world-points". Lorentz symmetry is usually a similar continuously connected subgroup of SO(3,1) and not only does it preserve the above invariant based on coordinate differences, but it singles out a coordinate origin and for any single "world-point" it preserves \(c^2 t^2 - \vec{r}^2\).

Electromagentism also has Poincaré symmetry, with every solution preserving the invariants \(\frac{1}{c^2} \vec{E}^2 - \vec{B}^2\) and \(\frac{1}{c} \vec{E} \cdot \vec{B}\) when operated on by ISO(3,1).

Relativistic mechanics also has Poincaré symmetry, with every solution preserving the invariant \(E^2 - c^2 \vec{p}^2\).

Sorry, I forget if it was Guest254 or prometheus who first called out in a thread that SO(3,1) is something like 4 times larger than the usually used continuously connected subgroup used in physical models. The full SO(3,1) is used in discussion of CPT invariance.

So symmetries are strongly associated with invariants and invariants are preserved by groups. Both ISO(3,1) and SO(3,1) preserve the invariants of Poincaré symmetry while SO(3,1) (being "smaller" than ISO(3,1)) also preserves single "world-point" invariant of Lorentz symmetry. SO(3) ("smaller") also preserves \(\vec{r}^2\) and we are back at spherical symmetry.

So SO(3,1) (or the continuously connected subgroup) is the set of operations called the "Lorentz group". And those things which have (Lorentz) invariants under these operations are said to have the Lorentz symmetry.

Whew! Sometimes I express myself idiosyncratically.

 

I didn't notice that, well spotted.

Farsight, Minkowski space-time can be said to be 'static' because the metric is time independent. This is why I asked you about gravitational waves, because they represent deformations to the space-time metric in full GR which are time dependent. Now you're saying Euclidean space is dynamic. You have contradicted yourself. Euclidean space is time independent. The only difference between it and Minkowski space-time is a factor of -1 on some entries. If you consider one to be static then so is the other, you can't have it both ways. Minkowski space-time is to relativity what Euclidean space-time is to Newton. Both are static, stationary, possess the same local and global symmetries and are completely flat (in all senses of curvature).

This is yet another example of you having a shoddy grasp of things because of your lack of quantitative understanding. Both Prom and I have pointed out that your "I'm trying to explain things" condescending attitude is extremely misplaced because you don't have the in-depth understanding necessary to formulate simplified explanations. You're trying to reword other people's wordy explanations, since that's all you understand, but in doing so you introduce errors. Reiku does it all the time, trying to reshuffle equations using little to no understanding of what he's saying and inevitably he screw it up.

Your time (and money) seems fundamentally mismanaged. The time you spend on forums telling people you've 'explained [something]' you should spend reading introductory books on physics and mathematical methods. If you'd started that 5+ years ago you'd be able to understand what we're talking about in this thread on a working level.

Do you plan to be in precisely the same situation in another 5 years time? Except your wallet is even lighter thanks to you pumping more money into vain attempts to convince people who understand physics that you're one of us?

 

I have no issue with that, rpenner.

 

Noted, prometheus. Apologies. I didn't mean to sound patronising. That's just the way it seemed to be.

 

I'm going to skip Alphanumeric's post for now. I did of course know he was a moderator. Prometheus, you might want to have a quite word with him about abuse and thread wrecking!

I'm not taking issue with spacetime. I've been talking about real space and real motion, but you won't find me saying things like relativity is all wrong. The thing to remember is that there's no motion in Minkowski spacetime, it's a static structure. So be careful about referring to it as space, or before long you'll be talking about waves moving through spacetime.

I'm not pushing for it. And the equations you posted are trivial. In \(t'' = \gamma \left(t - \frac{vx}{c^2} \right), \, x'' = \gamma \left(x - vt \right), \, y'' = y, z'' = z\) the Lorentz factor comes straight out of Pythagoras' theorem.

What I actually said was the "wave nature of matter" means you and your clocks are composed of these waves, and as a result you always measure wave speed to be the same. That's essentially why Lorentz symmetry applies. The lattice is only a visualization aid.

Maybe, but it's crucial.

I'm not taking issue with Lorentz invariance.

OK.

I'll talk some more about it.

They aren't exactly the same thing. He dodged the issue. And you should have challenged it.

And I now repeat the "wave nature of matter" means you and your clocks are composed of these waves, and as a result you always measure wave speed to be the same. That's essentially why Lorentz symmetry applies. I guess I need to talk some more about transformations.

It is simple. It isn't inherently complicated.

It's not me being abusive or outraged here.

No comment.

I really don't think you are. Because there is no time direction.

No there isn't. Not at all.

And time doesn't pass. That's just a figure of speech. If you and I are the twins, then when you get into your rocket and come back, we meet up. We agree that I've got more grey hairs and wrinkles, and your clock readings are less than mine, but those clocks have clocked up local motion, that's all. And we meet up at the same time, regardles of those clock readings. You don't miss me by six months and spend the rest of your life living in my past.

I think it's better to focus on motion myself.

It all follows, prometheus.

It demonstrates that spin angular momentum is indeed of the same nature as the angular momentum of rotating bodies as conceived in classical mechanics.

Electron wavelength. I should have said that the c is dimensionless here, it's a bit like using Planck units.

Yes, but it isn't my original work. Try c^½ / 3π.

They are. But you can still diffract them.

Good stuff.

Oo er, the wife is standing over me. Gotta go.

 

If I ever see Alphanumeric doing any of those things you can rest assured that he will be dealt with in the same way as anyone else doing it (and I would hope for the same treatment myself).

Your view on Minkowski spacetime is clear, but are you suggesting that in 3 dimensional space (i.e. only the spatial directions) is not static, as that is what you appear to be saying.

I'm not quite sure I follow your reasoning here. How exactly do the Lorentz transformation equations follow from Pythagoras?

And as I said before, I am taking issue with your statement that particles are made of waves.

I think the matter was clarified very nicely in rpenner's subsequent post (and really it didn't need all that much clarification anyway.).

Yes I think you do, because as far as I can tell your conclusions do not follow from you propositions.

I have to ask at this point why you feel nature shouldn't be complicated, or even make any sense at all? The fact that nature can be described by the standard model of particles physics and general relativity means nature is already vastly more simple than the most general field theoretic possibilities. The fact that global and gauge symmetries exist and make things simpler is not a trivial fact so you're asking a lot if you want nature to be even more simple.

Well, assuming that the twins live long enough they will always coexist at every time after their birth. Suppose I have two identical bombs and I replace the twins with them, if the timer is set so that the bombs would detonate exactly as the twin returns home from the point of view of the one who stays, the stay at home bomb would detonate as the other one arrives home, who would be left wondering how he missed the other one.

The underlying point here is you can't escape time. You can affect it by moving (as shown by the Lorentz transformations) but you cannot vanish from time altogether.

I think everyone would be grateful for a step by step guide at this point.

Ok. Again, I'm not sure I see quite what your point is, but I certainly agree that spin is honest to god angular momentum.

If c is supposed to be dimensionless then there is just as big a problem because the RHS is now dimensionless. Wavelength is just that - a length.

What exactly is this constant?

In summary, I think we would all very much like to see the more extended versions of these statements you have made. I presume they exist somewhere in such a form that it won't be too much trouble to reproduce them here.

 

Noted. I think it's shame how threads, and indeed forums can be wrecked by nastiness and personal abuse. IMHO there's no place for that in physics.

No. If anything it's just a shift in emphasis from you can't have motion without time to you can't have time without motion. Either way you've got dynamical waves moving through 3-dimensional space, and you can define time as a fourth dimension and combine it with the space dimensions to give yourself a 4-dimensional mathematical space. Then you can do useful mathematics.

Sorry if I implied that. I meant to say the Lorentz factor \(\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}\) comes from Pythagoras' theorem. See Simple inference of time dilation due to relative velocity. It depicts a parallel-mirror light clock where the light beam goes straight up and down like this | then zigzags like this /\/\/\/\. Take half a triangle so you've got a right-angled triangle, and the hypotenuse / is the light path, we’re using natural units where c=1, the base _ is your speed as a fraction of c, and the height | is the Lorentz factor. You need a reciprocal in expressions because time “dilation” is the opposite sense to length “contraction”.

I've given you enough to go on, just go with "wavelike" or something so we can get on.

He didn't get to the bottom of it.

They do, and I will.

To be honest: because I think I understand portions of it in outline terms.

Let's just say I think aspects of it can be expressed more simply, particularly when it comes to SR.

He wouldn't be wondering about anything, he's a smart bomb, like in Dark Star. He'd know that the timer employed some form of clock, and he would know what clocks do.

The real underlying point is that clocks, be they pendulum clocks, quartz watches with an oscillating crystal, atomic clocks calibrated on microwaves from hyperfine spin-flips, or optical clocks using visible wavelengths, all clock up some kind of local motion. That's what they actually do. Your macroscopic out-and-back motion is at the cost of this local motion, just as it is in the parallel-mirror light clock.

True enough. Funny old thing is time.

I'll start with the simplest, the spacetime interval, and explain why it's invariant. I've probably given you enough to work it out for yourself, but I will talk about it.

Good. The point is that I need to get you to a position where you can conceive of an electron as something going round and round. Please agree that we can say it's a wave. Keep things simple and say it's going round in a circle like this O, then look at it from the top so it looks like this |. Then move it, and the helical path when viewed from the top is a sinusoidal version of this: /\/\/\/\. Length contraction is a cracker by the way.

Then insert an n = 1 m/s to keep your dimensionality sweet. But get your calculator out.

It's a mass ratio, without the binding energy term.

Yes. I rather think it's more straightforward than you've been thinking. But sadly it's now 10pm and I'm afraid I have to go.

 

Firstry, I got the position with the other midst knowing my style . Secondly, you aren't presenting science but your unjustified assertions about things you have no experience with. Whenever I give lengthy explanations why you are hypocritical you avid relying. That isn't an ad hom but a fact. You complain about string theory while ignoring the fact your work, which you've claimed is worth 4 Nobel prizes, can't model anything. You never respond to that, you complain about abuse. Statint yourself as flighting the good fight ("not on my watch" etc) then you should expect to have your claims examined When your hypocrisy or mistakes are shown suddenly you don't want to play.How many more years will this continue?

 

Yes.. perhaps. Mind you on this occasion, due to the quality of conversation, I'd say it is good on it's own. He had a valid question about the subject, atleast it is being dealt with efficiently.

 

Please elucidate.

 

My general logic, though flawed as it may be, is telling me no one asks a question without knowing the answer.

 

Prometheus: A spacetime interval is usually expressed like this:

\(s^2 = - (\Delta t)^2 + (\Delta x)^2 + (\Delta y)^2 + (\Delta z)^2\)

In our twins example, let's say that you travel in the x direction whilst the light bouncing back and forth between your parallel mirrors moves in the x and y directions. That means we can forget about the z direction. So let's say:

\(s^2 = - (\Delta t)^2 + (\Delta x)^2 + (\Delta y)^2 \)

You will recall my explanation of the Lorentz factor in terms of Pythagoras' theorem \(a^2 = b^2 + c^2\), where we trivially work out the height of the triangle: \(\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}\).

So let's ponder why the interval is invariant. What do we actually have in our gedankenexperiment? What's actually there? The flow of time? I can't see any time flowing. I'm just sitting here motionless with the light reflecting up and down between my parallel mirrors like this |. It's moving back and forth on the y axis only. You're on an out and back trip, and as far as I can tell, your light is reflecting between your parallel mirrors like this: /\/\/\/\/\, its motion being on both x and y axes. All we have here is light moving. You don't observe your light following some zigzag pattern, because the waves that comprise you are moving in a related fashion. As far as you're concerned, your light is moving straight up and down.

OK, there's a clue in Simple inference of time dilation due to relative velocity. This is it: Consider a simple clock consisting of two mirrors A and B, between which a light pulse is bouncing. There is no "time flowing". You cannot perceive any such thing as proper time. Just light moving. That's all that's there. That's it. Just waves, moving. Particles have a wavelike nature, and you're made of 'em. Your clock clocks up motion, that's all. And in your frame of reference your clock runs slower because that motion is going slower by a factor of \(\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}\). Yes there's a symmetry; with no external reference you could assert that my motion is going slower. But you turn round and come back, and that breaks the symmetry.

So what's invariant here? It's thin gruel. We don't have much to go on. You probably know already: when we meet up, I find that my light has travelled one light year between my two parallel mirrors. And guess what, so has yours. Your measurement of time and distance has been different to mine during your journey, you enjoyed a "rotation" in your measurements. Your measurement of time, based on light waves bouncing between your mirrors, was altered by your motion through space, as per that Lorentz factor. Ditto for your measurement of space. We separated at time a, which was an event. We met back up again at time b on my clock and time c on your clock. But we did meet up at the same time, we didn't miss each other by a month leaving you to dwell forever in my past. Our meet-up was another event. Despite our different measurements of time and space, the spacetime interval between these two event was invariant. Because our two light paths were the same length.

Are you OK with this so far?