Lattices and Lorentz invariance

No you can't. Think about it: do you just "will" that you move, and then you magically move? No. You can move, but there are certain definite ways you need to interact with your environment in order to accomplish that, and the environment needs to provide you with the means to do it. The rules aren't even the same in different environments. Just ask anyone who's gone swimming or done external maintenance on the international space station. You are certainly not free to move as you wish in the vacuum of outer space for instance.

By the way I'm mostly making a sort of sub-point here that in physics, where we're trying to get a fundamental grasp of what's going on, it is not very useful or helpful to just fold your arms and say "I can move freely in space but not in time". It's a vague statement that doesn't really get a good handle on the problem and has lots of irrelevant stuff about how humans happen to perceive themselves ("free will") and the world all mixed up in there. It obviously contains a nugget of truth hidden in there somewhere, but you leave a physicist the job of having to dig it out for you.

Another point: motion is normally defined as a change in (spatial) position over time - i.e. motion is defined in a way that does not refer to space and time the same way. You are not likely to get useful insights about how similar or different space and time are if you reason in terms of quantities that have asymmetries between space and time defined into them. I think this single point applies to a lot of your post.

This is a good reason to talk about worldlines by the way: they're a way of describing things that does not priviledge space over time in any way or vice versa. So if I describe things in terms of worldlines, and some difference between space and time still appears, I know it's a real difference and not just an artefact of the language I'm using. Neat, huh?

Actually the point I was making was that, in the sense there's a real difference between space and time with regard to motion, you can largely derive it from that sign difference in the metric. It's not a separate difference.

I think it's rather you here who hasn't grasped just how much of a difference that innocuous looking sign difference makes in the end. It's not just there for show, you know.

And...? Yes, worldines are an abstract way of describing things - i.e. a notation - that we happen to find convenient for many purposes. But their properties - the things that worldlines can and can't do - are not just a matter of notation.

Your argument is a bit like me pointing to a timeline of events of World War II, and you telling me that the concept of a "timeline" is an abstraction invented by humans. That's true, but almost certainly irrelevant: I was probably trying to tell you something interesting about World War II, or about the progression of wars in general, and probably not that I thought timelines were "real".

Instead of focusing on the fact I'm describing things in terms of worldlines, you should really be focusing on what I'm saying in terms of worldlines.

And...? Are you now going to tell me that the exact equation I posted isn't what it is because you think you own everything that has ever had the word "motion" applied to it? That equation is what it is. At worst, you could debate whether "equation of motion" was really the most accurate phrase to describe it.

No, not necessarily. I could imagine building a clock based on muon decay for instance. Muons decay with a certain half life. As far as we know they have no internal structure, and relativity does not require or imply that they do.

I think you're taking too much from the fact that many introductions to relativity use the light clock to derive time dilation. It's only used because it is easy to calculate from the invariance of c, and the logic behind it is that the principle of relativity implies that if a light clock dilates, all other clocks must dilate regardless of their internal architecture. Rather than this you seem to have somehow gotten the idea that relativity is about everything being a light clock. It really isn't.

 

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przyk, that was a cheap shot and misrepresentation of what was meant by moving through space at will. I have a hard time believing that you do not understand that context plays some role in the meaning of words. When a post starts off with a statement like this I often just shine the whole thing on as argumentative.

 

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Er, no, I was making two points I consider rather important: 1) Farsight's characterisation of things is vague and not very helpful, and 2) motion through "space", just like "motion" through time, is subject to physical laws and it's how similarly those laws treat space and time that really needs to be compared. Far from attempting to dodge the issue, I gave an example of how to better characterise what Farsight was attempting to say, and addressed that, in post #78. So from that perspective, I did a better job of making Farsight's case than Farsight did.

Please learn to read people's posts before giving knee-jerk responses to them. You didn't understand post #78 either: it had nothing specifically to do with the relationship between physics and mathematics.

 

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It sometimes seems to me that the difference between mathematics and physics has become almost lost today, but there is a great deal of mathematics that has nothing to do with physics.

The above post was not a comment on your post as a whole, only on an aspect or interpretation of that portion quoted. From the general context, comparing the perception of space and time, to the "fundamental level", suggests that the fundamental level, which I understood to be expressed as a mathematical model/theory, is of greater significance than, the experience time and space itself.

While mathematics is a very useful and powerful tool when describing physics, observation and experience, it is not itself physics.., any more than English, German or French is physics.

I added Farsight's comment to the above quote for purposes of context.

Whether, you walk, drive a car, fly in a plane or a spaceship.., you or we can move through space at will... The meaning of the word or phrase "at will" here, is very different than suggesting that one wills oneself to move through space.

You seem to be a smart fella and it is difficult for me to believe that you did not understand the original contextual meaning. That makes the reinterpretation a cheap shot. If I am wrong and you did not see the difference.., I stand corrected. Farsight could also come to your rescue and correct my misunderstanding, by confirming your understanding of his intent.

I should perhaps have also made it clear that in calling that part of your post a cheap shot, was in essence also saying I thought it was beneath you. I'm pretty sure you could make your point without, what I read as a misrepresentation of Farsight's intent.

I understand the discussion. I did not just drop in. I can see some merit in both perspectives.

Sometimes a knee-jerk reaction is what is required to highlight a misinterpretation, accidental or intentional. (Too often it seems to me in these discussions.., misinterpretation and/or misrepresentation are not a constructive aspect, of the discussion.)

My comment on the two sentences quoted from post #78 were obviously at this point inadequate to convey the point I intended. I should have spent more time and explanation. In retrospect, what seemed obvious, was anything but obvious. Still my original point, restated here.., that while all or almost all of physics can be accurately expressed mathematically, not all mathematics describes physics. The mathematical argument of theory and hypothesis says nothing of physics without, the support or proof of experience or experimental observation. The mathematics on its own does not rise to the level of experience and observation.

 

No it hasn't. Of course there's a thriving relationship between the two: physics is both heavily dependent on and a source of inspiration for mathematics. But the difference is the same as it has always been: mathematics is the study of patterns and abstractions, and physics is a quantitative, mathematically refined natural science.

*sigh*

This is really getting silly. Speaking of context, I didn't just say "No you can't. Think about it: do you just "will" that you move, and then you magically move?". I said that in the much larger context of the points I was making in posts #78 and #81. Read those. Does it really look like I'm trying to dress Farsight up as someone who believes we all float around with the power of thought alone? No, of course not - but I still think it's an important point to articulate. Establishing that Farsight would not say that we just "will" ourselves to move and then magically move invites him to think more carefully about what he does mean, and its relevance to the physics of space and time, when he says we can move around "at will" through space.

 

Przyk, you are right, this is getting silly.

My original mention of the relationship between mathematics and physics was not intended to initiate and separate discussion. It was just an observation, generally about physics today.

My orginal post suggesting a, cheap shot, should really be taken more as, how a single phrase can affect the interpretaion of one's comments. This seems to happen over and over on these forums.

I have been following the discussion, between you and Farsight, with interest and will continue to.

This sidetrack deserves no further attention.

 

Yes I can. Come on pryzk. We have freedom of motion through space, but not through time.

There's no magic to it. I'm essentially a machine, I receive stimuli, I process them with my "consciousness" feedback loop that provides more stimuli, and I plan a course of action. I send commands to my muscles, and I hop back a metre. I moved. I changed my x coordinate. It's that simple.

Yes I am. I throw my spanner that way, and I go this way. Come on pryzk.

It isn't vague at all. It's crystal clear. I just hopped back a metre. I can show you this. We do have freedom of motion in space. It's cut and dried.

Bang. I thumped the nugget down in front of you, it's the size of a basketball and your desk is caved in. The truth is right there in plain view, you don't have to dig it out.

You can move, and you can see things moving. That isn't anything to do with the way motion is defined. If you decide you want to hop back a metre in the x direction, you can. You can't do this in the t "direction". That's the important difference between space and time. It isn't just a minus sign.

I reason in terms of the patent evidence. And the insights are very useful. Really. Time is the key that unlocks all the doors in physics.

Not as neat as getting up off your chair and hopping backwards a metre. Then having a shot at hopping backwards a second. Remember that people do talk about CTCs and time travel. I shall name no names. But some should know better.

I told you about this. The minus sign is there on the t because you use your parallel-mirror light clock to measure local motion, and the total motion is limited to c. If you move in the x direction your local motion is of necessity reduced. If you could move at c in the x direction there's no local motion left, your light is moving like this → so there's no t and your spacetime interval is just the light-path length. If you don't move in the x y or z directions your local motion is going at c and it's all t, your light is moving like this ↑↓, and the spacetime interval is still the light-path length. It's the same for anything in between these two extremes. In a gravity free world of course.

I know. I know why it's there.

OK.

I was happy with that means that a worldline can't do something like start going up and then looping around and going back in time. But point taken. I'll pay more attention next time.

Just put a bit more emphasis on motion. Accept that it's an equation of motion. And look at what clocks actually do. Note that you can see things moving, but you can't see time flowing. And in order to be able to see them, and think about them, your human "machinery" has to be in motion too.

But they are spin ½ particles and they do have a magnetic moment. And the Einstein de-Haas effect tells us that spin angular momentum is indeed of the same nature as the angular momentum of rotating bodies as conceived in classical mechanics.

It's the same for a muon.

I haven't. But light is very important in relativity.

 

I forgot about the tail end of your previous post:

OK. We could maybe get on to gravity and black holes here, but best leave that for another day.

OK noted. Thanks. I learn something new every day.

 

I just explained why it was vague. And I don't see where the problem is, because I'm not using this to ignore your point. I clarified it in language that I find makes the issue easier to get a handle on, and you apparently agree:

That is a clear difference between space and time where the worldlines of massive objects are concerned. Nobody is denying that.

Are you making a point here that's really different from what I said about a worldline not being able to loop back in time? If so, what's the difference? If not, isn't that covered by my explanation of how that follows from the sign difference?

No it isn't. The minus sign essentially makes the invariance of the Minkowski metric the same thing as the invariance of c postulate in relativity, and ends up defining the causal structure (notions of past and future light cones) I mentioned in post #78. This is well known to anyone who has spent any time studying the properties of Lorentz transformations (which are defined as the transformations that leave the Minkowski metric invariant). It's got nothing directly to do with how we measure time, and in the end has implications for any way we might try to measure time.

Again, you sound like you're taking derivations of time dilation based on light clocks to mean that everything experiences time dilation for the same reason a light clock does. That isn't the point of such derivations.

What's an "equation of motion" to you? Because I know what the equation I posted is, and depending on what you say I'll be able to tell you whether your version of the label "equation of motion" applies to it or not.

Only in the sense that spin contributes to total angular momentum. Basically it's a term in the angular momentum conservation law. None of that implies the muon (or the electron for that matter) has any internal structure.

 

OK. Let's move on.

Whilst we approach "travelling back in time" from different viewpoints, we agree that it's out of the question, so let's also agree that this point is not different.

There's a difference in approach in that my explanation describes why the sign difference follows from real-world phenomena. This different approach was what OnlyMe was referring to: let's not get sidetracked by that.

What I'm trying to get across to you here is why Lorentz symmetry applies and why we always measure c to be the same. It concerns physical evidence, which IMHO is better than relying upon a postulate.

It has everything to do with how we measure time. That's the mother lode I broke your desk with. You seem unable to see it, as if it's hidden in plain view. To see it you have to forget everything you think you know and focus your attention on a clock, any clock, and ask yourself this: What does a clock really do?

Noted.

An expression that allows you to calculate how an object will move in some given situation.

But it does imply that the muon has some internal rotational motion. So draw a circle instead of an up-and-down line, and a helix instead of a zigzag, then reason that a muon lifetime is circa x rotations. A fast-moving muon lives longer.

 

I don't see that you've done that without assuming something basically equivalent to it to start with.

From various things you've said, you seem to be under the impression that Lorentz invariance can somehow be derived from the idea that everything is made of waves. This is absolutely not true: I can readily give you an example of a wave equation that is not Lorentz symmetric, and I can readily give you an example of an equation of motion that is Lorentz symmetric while having nothing in particular to do with waves. In fact I'm sure I've shown you both in past threads.

I don't know what point you're trying to make here, because the postulates of relativity, or simply the postulate of Lorentz symmetry, are well supported experimentally. When we call something a postulate in physics, it does not necessarily mean we just plucked it out of thin air. The invariance of c is axiomatic as far as certain formulations of relativity are concerned, but it is also an observation that has been confirmed experimentally many times. As the basis of a theory, it has ample support.

No it doesn't. Relativity, despite the way it might seem from the way some introductory texts like to present it, is not fundamentally a theory about clocks. It just happens that, being a theory about a symmetry, you can extract a few generic and straightforward predictions about the behaviour of clocks moving clocks.

In fact it isn't really accurate to call relativity a theory in the first place, as it does not attempt to model any particular physical system. It's really a "theory" about other theories in physics: relativity asserts that the laws of physics, whatever they might be, are Lorentz symmetric. This is completely analogous to the "theory" that all the laws of physics possess rotational symmetry, and in fact the Lorentz group is a generalisation of the rotation group.

Then \(f^{\mu} = m \frac{\mathrm{d}^{2}x^{\mu}}{\mathrm{d}\tau^{2}}\) is an equation of motion by your own definition, as it has implications for how material objects will move. But it is also an equation that, apart from the sign difference hidden away in the definition of \(\tau\), treats space and time symmetrically. Solutions to that equation come in the form of worldlines.

No it doesn't. Just that it has a form of intrinsic angular momentum.

 

I haven't assumed it, the wave nature of matter is supported by experiment.

I said Lorentz symmetry can be, that being the idea that "the laws of physics" don't change when you move fast, and crucially that you don't measure the local speed of light to change. When everything is made of waves, you always measure wave speed to be the same. Because when you move fast, your clock rate changes, because your clock is made of waves. Then you use that clock to measure wave speed.

Please give the examples and I'll give you my comments.

No it hasn't. The experiments demonstrate that the measured speed of light is always the same. And think on this: two optical clocks at different elevations lose synchronisation. They're optical clocks, and you know that two parallel-mirror light clocks will do the same. And for that to be happening, the light beams have to be moving like this:

|------------------|
|------------------|

Forget about "time flowing at different rates", or about defining something you can see using something you can't. Put the emphasis on motion, and look at the evidence.

It doesn't actually have any. If you're subjected to time dilation you know that your seconds are altered, so you know that one 299,798,452 m/s is not the same as another. You might resort to definitions to assert that they are, but actually, they aren't. They only seem to be because you are a part of the world you measure.

I didn't say it was fundamentally a theory about clocks. SR is fundamentally a theory about space and time, and how our motion alters the measurements we make with our rods and clocks, but preserves "the laws of physics".

IMHO this is an overly mathematical view. You're talking about the laws of physics as if they're tangible things that exist, with tangible properties. They don't, they're merely a codification of how real things behave.

That minus sign makes all the difference.

Yes it does. The experimental evidence is there. I'm sorry pryzk, but with respect, you claimed that we have no freedom of motion in space, despite the patent evidence that we do. You are similarly dismissing other experimental evidence and direct observation here. You probably won't agree with me about that, so maybe we should wrap this up and agree to differ.

 

The quantum nature of matter is supported by experiment. The idea that "everything is made of waves" is not. I pointed out some important differences between quantum physics and the physics of (especially classical) waves [POST=2852519]here[/POST]. And even if everything was "made of waves", even that wouldn't automatically get you Lorentz symmetry.

Why should this be true? This is completely unsupported. Your only hint at a justification is:

but that doesn't follow. In fact, if you're referring to derivations of time dilation like the "parallel mirror light clock" one, they only work because they make a plethora of assumptions, including invariance of c, to begin with. You wouldn't get time dilation if the speed of light could depend on the speed of the emitter for example.

The obvious example of a non-relativistic wave equation is the non-relativistic Schrödinger equation, which for a single free particle is

\( - \frac{\hbar^{2}}{2m} \triangle \psi \,=\, i \hbar \partial_{t} \psi \,. \)​

For an example of a Lorentz-symmetric equation of motion that doesn't apply to waves, just take the relativistic version of Newton's second law I already gave you:

\( f^{\mu} \,=\, m \frac{\mathrm{d}^{2} x^{\mu}}{\mathrm{d} \tau^{2}} \,. \)​

Relativistic fluid dynamics would make for another example. The point is, we can do physics with non-relativistic waves, and we can do relativistic physics without waves.

That is exactly what I meant, and what the invariance of c postulate refers to.

I don't see that there's much point in making a distinction, since all we can say about time is what we measure. If all moving clocks slow down by the same factor, then for all practical purposes we may as well say "time" slows down. I have no idea what the phrase "time flowing at different rates" is even supposed to mean otherwise.

But space and time are really just there in SR and aren't really attributed any intrinsic properties. All we can say about them is what we measure, and as I think you like to point out, measurement devices are themselves physical systems governed by physical laws. So to my mind that squarely makes relativity a theory about physical laws in general.

I never said otherwise. SR is a theory about the laws of physics having a certain symmetry. That means it is a theory that asserts real things can only behave in a way that preserve this symmetry. It's an abstract formulation but you can get some powerful conclusions out of it when you supply some context, especially when you start applying relativity to quantum physics. Probably the most famous example is Dirac's prediction of the existence of the positron. Other good examples include the spin-statistics theorem and the fact that relativity severely restricts the allowable interactions in quantum field theory (there are literally only a handful of allowable interaction terms in QFT that preserve Lorentz symmetry and satisfy a few other conditions, and some of the best evidence for relativity in my opinion is that precisely these interaction terms are enough to account for all the interactions we have so far observed in nature).

That is exactly the point I was making: we can understand why worldlines can't loop back in time, even though they can loop around in space, purely from that sign difference.

Er, what? Where is the experimental evidence that muons have internal structure? You seem to be concluding that they must have internal structure because it fits in with your worldview (in order for them to have angular momentum for instance), and not because you have direct evidence that they do.

I said that we have no freedom of motion in space in a sense that I explained. I was actually being deliberately argumentative in response to you using vague language. The thing is, I know what you mean, but I don't know how to discuss it with you in a language we'd both agree on. If I wanted to talk about motion "in time", the way I'd want to do it would be to consider a worldline parameterised with something like proper time, and discuss motion in time in terms of \(\mathrm{d}t/\mathrm{d}\tau\), \(\tau\) being a parameter such as time measured by an observer travelling along the worldline, and \(t\) being a measure of time defined by an external inertial observer. So I ask you: how would you hypothetically describe the idea of "moving" in time in a language that, were I to use it, you wouldn't try to dismiss it as "abstract"?

 

The rate at which any particular clock ticks, is an observation of change. When we change the external conditions that any particular clock is exposed to, we note a change in the rate of observed change, for that particular clock. It is certain that clocks function differently under different conditions. We cannot associate this directly with any real change in the rate at which time progresses. We can only associate the change in rate with the change in external conditions.

An example: An athlete runs a mile in 4 minutes. This is timed repeatedly, on a clay track, at the Olympics. The same athlete is then asked to run a mile, on a sandy beach and his time comes in at 8 minutes. Does this represent a slowing down of time?.., or just that the athlete performs differently under different conditions?

We can say with some certainty, that a clock ticks at different rates under different conditions. We can predict that change in rate with a degree of accuracy. That change in rate does affect our perception of the passage of time, as our perception of time is tied to an of observed change and the clock is our reference for that change.

While SR did not directly address any intrinsic properties of space (what it says about time is a different matter), since it incorporates the Lorentz Transformations and leads to the famous equation, \(E = mc^{2}\), it does imply some intrinsic property of space, associated with inertia. Whether one approaches that, from a Machian perspective or as one that involves and object's interaction with the virtual particles of QM, it can be associated with an intrinsic property of space, that results in an exponentially increasing inertial resistance to the acceleration of an object, as it approaches \(c\)

To some extent this is dealt with within the context of GR. From the context of GR space must be considered to be not only dynamic, but to have some intrinsic substance, which allows for the interaction between matter and space.., and the propagation of light (EM). However, GR provide little or no insight into what the substance of space is or how it interacts with matter and light. For answers to these questions QM may be on the verge of providing answers. Or at least some framework from which to explore possible answers.

Here are a couple of links to a press release and the associated preprint, of a paper dealing with the detection/observation of virtual particles, Scientists create light from vacuum and Observation of the Dynamical Casimir Effect in a Superconducting Circuit. (The content of these references has been raised for discussion in another thread, Light reated from vacuum.)

While photons have no mass they do have momentum. If the above references hold up and are confirmed, any relativistically moving object would also have to be affected by the opposing momentum of the virtual particles it encounters.

Again, though SR did not address this directly, it is implied and has played a significant role in the underlying science that has led us to where we are today.

 

There's an important difference between this example and relativistic time dilation: making an athlete run a mile is not the only possible clock one can imagine, and not all clocks will dilate in sand by the same factor, compared with a clay track, that a running athlete does. Most of them wouldn't be affected much at all, while one clock might get sand stuck in it and stop altogether. Contrast this with the fact that all systems (and therefore every conceivable measure of time) slow down by exactly the same factor when moving at some given velocity.

No, I wouldn't say SR says anything about time beyond what we can measure - i.e. time "slows down" in SR in the sense that any system we could conceivably use to measure the passage of time slows down when in motion.

Er, no, I'd consider inertia a property of objects moving in space, and not space itself.

First of all, GR attributes the property of curvature to the whole of spacetime, and not just space. And even there it's debatable whether that's really necessary. In GR, curvature in practice implies the impossibility of constructing globally inertial coordinate systems. Since inertial coordinate systems are ultimately defined in terms of physical laws taking a particular form in them, even curvature in GR could be considered a property of physical laws rather than of spacetime itself.

Er, just to be clear, "vacuum" in those references doesn't mean "empty space". It refers to what are called "vacuum states" in quantum field theory. They're ground energy states that a quantum field (or a number of interacting quantum fields) can be in.

 

There's no thing as an empty space, might I add.

 

It's been quite a while since I managed to post on this thread. Sorry about this, I've been rather busy with real life stuff.

I never said time travel was a possibility, but it's kind of a tautology that cumulative motion cannot be reduced.

So you would assert that at absolute zero there is no perception of the flow of time? As I said before, time ticks on regardless of whether there is any motion or not.

This has been covered quite extensively with przyk, but the Lorentz transformations tell us that you are free to a certain extent to move through time by acquiring a velocity, the same way you control your motion through space.

It's more fundamental than that: The second law of thermodynamics states that entropy (what you picture as particles moving slowly or quickly) must increase or stay the same as a function of time. Note you can also have changes in entropy for adiabatic processes (adiabatic means no heat transfer) so your simple model is too simple again.

You can't point to a wavefunction, or an S-matrix, but they are the correct descriptions of nature. To quote a rather famous film, "If you're talking about what you can feel, what you can smell, taste and see, then "real" is simply electrical signals interpreted by your brain."

Moving relative to what? The whole universe? I'm not sure I understand what your point is.

Tach asked you a simple question that you didn't really answer (in a rude way, but that's Tach...) Why does the sign of the time component of the metric mean you can't travel backwards in time?

This is an awful attitude. Essentially you're making an appeal to authority which is a logical fallacy in itself, but it's not even as good as that because you're ascribing an opinion to someone who never expressed such an opinion in their lifetime and now that their lifetime is over they cannot be asked whether they agree or not. It's sloppy, fallacious and presumptuous and I will not tolerate it.

If you are trying to tell me that you agree with quantum mechanics and quantum field theory and particles (included in everything) are made of waves then you are simply wrong, because that is not what QFT implies.

I don't think that's what a photon is. A photon is a quantum excitation of a vector field.

You're fixating on a classical spinning ball which I keep saying is not the same thing as quantum mechanical spin. In your example of the football I can kick the ball with different forces in different positions so it I repeat this many times, by the time it gets to the goal it has the potential to be anywhere along the transverse axis (the goal line). It is not the same quantum mechanically. If the ball behaved like a quantum particle with spin the goal keeper would have an easy job, because the ball is only allowed to be measured on the goal line at a finite number of points. In the case of spin 1/2 it has the potential to be measured in 2 places.

This is what I've been trying to explain over this entire thread: Lorentz symmetry does not "boil down to it doesn't matter how fast you're moving the laws of physics don't change." That is one aspect of Lorentz invariance, but there is a great deal more to it than that.

Recapitulation: You can think of boosts (the type of Lorentz transformation as a rotation in one space and the time direction) but the rest of the Lorentz group consists of rotations in two spatial directions. How can you use a lattice of points to illustrate rotations in two spatial directions.

How on earth can a particle travel through itself? It makes no sense.

 

I know the feeling. I hope you're finding this thread interesting and thought-provoking.

It goes a bit deeper than that: there's no such thing as negative motion. This is like old "negative carpet" thing I've mentioned before. If you need 16 square metres of carpet, one solution is to buy a carpet measuring -4m by -4m, but this isn't a real solution.

No. Temperature is a measure of the vibrational or translatory motion of say atoms, at zero degrees Kelvin there isn't any, but the magnetic moment of the electrons protons and neutrons hasn't gone away.

I'm sorry prometheus, but if you take all the motion away there are no ticks any more.

You really don't "move" through time. If I stay on earth and you take a fast round trip through space I can watch you all the way, and when you come back we can see that you've aged less than me. But you don't end up living in my past.

That's a bit circular. All that's actually happening here is that particles move. You can see them move, but you can't see any time. That's because time is derived from motion. Clocks really do clock up motion rather than time flowing or motion through time. Just look hard at what clocks do. Keep at it, focus on what you can see and resist the urge to refer to abstract things you can't see, and it'll click.

No problem.

I've seen The Matrix. It's a good film, but it's science fiction. And people have used weak measurement to map out wavefunction, or at least "the wave-like behaviour of photons", see http://physicsworld.com/cws/article/news/46193

Nevermind. You just asked me if I meant relative motion, and I said yes.

The guy is an abusive troll, you should do something about it. What else is a moderator for?

Think about the parallel-mirror light clock. It's because time is derived from local motion through space, and if you move fast through the universe your local motion is of necessity reduced because the overall rate of motion is c. Look closely at what you've got there and you should be able to work out that the invariant interval is based on the light-path length.

It's not sloppy or fallacious or an opinion as far as Einstein is concerned. Go and look at A World Without Time: The Forgotten Legacy of Godel and Einstein.

That takes us back to In QFT photons are not thought of as 'little billiard balls', they are considered to be field quanta – necessarily chunked ripples in a field. I thought we were past that because you said I do accept the wave nature of matter.

And it moves at c, and we can diffract it. That should be enough.

I'd rather talk about spherical waves, I don't actually like using balls as analogy, but it's the only common-life thing people have experience of. Yes you can vary your kick, but to take that out of the scenario shoot the balls from a uniform cannon. When you load the cannon with a spinning ball (with some uniform rate of rotation), the place the ball ends up depends on the orientation of the spin axis. However when you load a ball that has two orthogonal spins, there's only two places where it ends up, depending on whether the spins are opposed or not. Think it through.

Wikipedia says "In standard physics, Lorentz symmetry is "the feature of nature that says experimental results are independent of the orientation or the boost velocity of the laboratory through space".[1] Lorentz covariance is a related concept, covariance being a measure of how much two variables change together". Here's another example: http://www.physics.mcgill.ca/~guymoore/research/lorentz.html

What it really is, is a change of speed. There isn't any actual rotation going on. The "rotation" of your measurements of time and space is something abstract.

You reach into the lattice with your right hand, grab it, and turn your hand. Then you reach in sideways with your left hand, grab it, and turn your hand. But I suspect you didn't mean literal spatial rotations, so please rephrase the question.

It makes sense when it's a wave. Start with a photon, then put it through pair production.

 

You've got it, OnlyMe.

Exactly. Replace the athlete with a beam of light and vary the vacuum impedance Z[sub]0[/sub] = √(μ[sub]0[/sub]/ε[sub]0[/sub]), remembering that c = √(1/ε[sub]0[/sub]μ[sub]0[/sub]).

Yes, we don't notice it because the thing that affects the clock affects us too.

Actually I think it's talking about an intrinsic property of matter. You know how I was talking to pryzk about the muon, and I said draw a circle instead of an up-and-down line, and a helix instead of a zigzag. Think about stretching a helical spring.

There's interesting quote here.

I read that. It was interesting, but IMHO the article puts too much emphasis on virtual particles. They're rapidly altering the evanescent wave. Whilst they're not actually vibrating the mirror, the effect is the same, and thus photons are generated. In that respect it isn't hugely different to a conventional light bulb. But in another respect there are no moving parts even at the subatomic level, so I think it could turn out to be more important than people appreciate.

 

pryzk: apologies to reply out of turn, and apologies again because I have to go now.