"Light is frame-dependent in PF, but constant in SR"

Trying to elicit a useful and constructive reply seems a very reasonable action. I find your complaining about Maxilla "goading and trolling" in itself. I usually find Maxilla's post really educational so I am being a little protective when I see you are trying desperately to attract attention to his words.
OK the maths and arguments here are beyond me but the tone of your posts seems to be out of the ordinary.

 

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Great post AN. I say something like this. Some folks probably wonder what I'm talking about. Special relativity is the special case of a more general theory of gravity where the effects of gravity, on empirical measurements, can generally be ignored. IE there exists a local segment of an objects path through the gravitational manifold where the spacetime approximates SR. It's essentially flat. AN said it like a mathematical physicist when he said "The Lorentz transforms are not defined by their action on coordinates of a manifold but by their action on the tangent space of a manifold." That's the segment of the path I'm referring to. It defines the local coordinate frame and the local proper frame where spacetime events occur, and empirical measurements, are invariant.

 

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The problem is that if you lean too much on your intuiton and don't get into the habit of formalising your workings then you're going to inevitably dig yourself into a hole. After all, how do you know what you've done is the right answer? Without the formalisation you're just assuming.

Calculating gamma is nothing more than putting a number into a basic formula, please don't think that your ability to do the most basic algebra and use a calculator implies a grasp of Lorentz transforms.

And, as I explained, you didn't show a relationship between frames. You threw in factor of gamma without any real justification. The additional factor of gamma comes from comparing Newtonian and relativistic points of view. Then the "Frame A sees slower clock, Frame B sees shorter distance" alternative views is something anyone who has ever studied relativity would have come across very early on. And, as I explained, the naive insertion of the gamma factor is not rigorous nor does it actually compare two different frames. The different frames are related by a Lorentz transform, giving a new representation of a system, while the 2 alternative views I just mentioned amounts to just how you wish to factorise the same expression, ie abc = (ab)c = a(bc).

You went from \(\frac{x}{t}\) to \(\frac{x}{t}\frac{1}{\gamma}\), which has nothing to do with how you change from one frame to another, that is not represented by a Lorentz transform, so your comments about how the muons see 1/5 of the ground c (which is in itself a gibberish statement) are baseless.

The gamma comes into an arm wavy discussion when you're trying to explain why more muons reach the Earth than Newton predicts. The increase is related to relativistic effects, which are quantified by gamma, so in an arm wavy way it is as if the muons experience slower time or shorter distance. But this doesn't mean you get to throw in a random factor of gamma and say "Ta da! I've explained it!".

Clearly your reasoning is wrong since if the speed of light worked like that then a variety of phenomena involving high speed charged particles would behave differently. A charged particle, by definition, interacts with light. If a muon, which has the same charge as the electron, were somehow experiencing a different speed of light due to its relative motion then its interactions with the EM field is produces would be altered. We understand very very well how electrons and muons interact with light at high velocity because it is the dominating issue when building circular particle accelerators. An accelerated charge emits braking radiation known as bremstrahlung. So bad is this (it goes like the fourth power of speed) that CERN replaced its electron/positron collider, LEP, (which gives nice 'clean' collisions) with a hadron collider, the LHC, whose collisions involve a huge amount of debris noise (protons are more massive so move slower than electrons for the same amount of energy). Similarly Cherenkov radiation is the visual version of a sonic boom, where charged particles move faster than the speed of light in a medium (light moves at about 0.7c in water). We use this effect to detect neutrinos, often ones formed by muon decays in the upper atmosphere. If the speed of light for a muon or any other charged particle were different in a significant way we'd have detected it, as it is pretty much the main way in which we probe particle phenomena.

This is illustrating your lack of knowledge about special relativity, which makes some of your previous comments to others all the more hypocritical.

The reason ct appears in expressions, ie \(ds^{2} = -(c\,dt)^{2} + dx^{2}\) is that each term in the sum must have the same units, you cannot add 4 seconds to 2 metres for instance. As such if ds has units of length and so does dx then we need a conversion factor in front of dt to give it units of length, ie something with units of velocity.

Notice how I keep putting 'd' in front of everything. This is because all of these properties are not defined on coordinates but on vectors. The above expression is about an infinitesimal line element (a concept from geometry), ie the line element in space-time is a weighted combination of line elements in each different direction in the space-time. GR says the weights can be variable, ie functions of position and time etc, as these weights are the metric components. As you should remember from school velocity is change in distance over change in time. The calculus formalisation is \(v = \frac{dx}{dt}\), ie the instantaneous velocity is defined by infinitesimals dx and dt. You don't just get to integrate up \(\frac{dx}{dt} \to \frac{x}{t}\), that's a classic high school error. As such the whole way you're going about things is flawed.

The Lorentz transforms, as I mentioned, are defined on vectors, not coordinates so really we should be talking about \((dt,dx) \to (dt',dx') = \big( \gamma(dt - \frac{v}{c^{2}}} dx) , \gamma(dx - v dt) \big)\). Then when you put this into the line element expression you find it doesn't change, \(-(c\,dt)^{2} + dx^{2} = -(c\,dt')^{2} + (dx')^{2}\). So how does this tell us anything about the light speed in each frame? Well light moves on null paths so \(ds^{2} = 0\) so \(-(c\,dt)^{2} + dx^{2} = 0\) so \(|\frac{dx}{dt}| = c\). But then the same applies in the other frame, \(|\frac{dx'}{dt'}| = c\).

Notice how I haven't had to put in any gamma factor by hand or just assume the final result, it drops out of the Lorentz transformation naturally. Notice too that the Lorentz transform is much more elaborate than \((t,x) \to (t',x') = \gamma (t,x)\). In fact that transformation isn't a Lorentz transform, as it doesn't preserve \(ds^{2}\). The shifts \(-\frac{v}{c^{2}}dx\) and \(-v dt\) are essential to make the Lorentz transform work. This is why, as I mentioned before, is it standard to make statements about coordinate origins when talking about frame transformations, that is needed to get the shifts right. Notice also that under the general Lorentz transform \(\frac{dx'}{dt'} \neq \frac{dx}{dt}\), \(\frac{dx'}{dt'} = \frac{dx - v dt}{dt - v dx}\) and certainly this cannot be converted into \(\frac{x'}{t'} = \frac{x-vt}{t-vx}\). This is a particularly unhelpful way of describing the system as it doesn't include the constraint on the space-time interval (ie ds=0 for null vectors).

If you are unable to initiate 'a useful and constructive' discussion without, as Syne says, wandering into troll territory then don't post. If you don't know something about special relativity then ask a direct question to get a direct response. Pretending you do know so someone can come along and steam roll your knowingly mistaken claims is not terribly constructive and only serves to engender exasperation from people, especially when you've only just registered and thus no one knows whether you're 'goading' or 'trolling'.

But the way in which it was done was not. Ends justifying the means and all that,

And here in lies the problem and it is one of the reasons I have so little patience for people like Reiku. Most people don't understand mathematics or physics, it might as well all be written in Welsh for all the sense it makes to most people. As such said people cannot tell the difference between someone spouting BS they made up but scatter buzzwords throughout compared to someone who actually knows what they are talking about. Reiku sets out to exploit this deliberately, to con people into thinking he grasps various high level physics models. To do this he lies and spreads misinformation, infecting other people with his ignorance. Hence why I think it is important to slap down his BS when he tries it. Likewise with people like Farsight, who also presents himself as knowledgeable when the opposite is true. Maxilla's posts have been doing the same thing, getting relativity wrong, posting flawed attempts at mathematical reasoning and deride other people's knowledge as if to try to appear knowledgeable himself. And you fell for it. No fault on your part, you don't know any relativity so you cannot be expected to tell BS from SR. But if you come away from a thread like this thinking SR works as Maxilla has been claiming then you'd be mistaken, you'd be infected by his ignorance. In instances where someone knowingly posts nonsense to fool people it is trolling. Maxilla has done you a disservice, it should be him you're complaining about, not Syne.

 

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:bugeye: :bugeye: :bugeye:

Troll, indeed.

 

I always appreciate your posts AN, and I see you really do spend time caring for the forum. It was the continual moaning by Syne that made me comment. I find that people do that just to get someone else into trouble.
I have not read the thread intensely so it hasn't taught me anything as yet, other than showing up my lack of math again.
I'll stay out of the argument from now on.

 

AN, your posts are certainly substantive, but I feel that in this case you're making criticisms that are not pertinent to the OP's main point.

It should be obvious that if one observer alters their distance perception and the other observer alters their time perception by the appropriate factor then the ratio of d/t will remain unchanged. It's as simple as that.

 

How long did it take you to put that troll together? You're the consummate intellectual dishonest troll. Look at your troll in post #17. In another post you called Farsight brilliant. That confirms Syne comment about two hacks working together to blow smoke up their own posteriors. How about the post where you hang on to 'stupidity' by saying the measurement of the stick, using a string, includes the speed of light in the measuring device because the stick is a piece of wood with electrons giggling around in it. That was as intellectually dishonest as it gets. Almost as stupid as Farsight telling Id that there's two different speeds of light in the same frame of reference. LOL when you told me you have a good understanding or GR. Every intellectually dishonest crank I've ever come across says that and immediately goes on to proof that's a lie. You and Farsight will never get tired of being wrong because 'being right' is way more important than 'you guys' actually learning something about the science. The threads you've started are a troll.

 

If you meant c appeared to be an invariant ratio of x/t, as opposed to a specific physical value, that was a large part of what I was getting at.

Right now I am considering things in AN’s post, I have limited time and when I calculate the Lorentz transformations he wrote, for the example I put up, the values are not coming out exact and I’m not sure why? I won’t be saying much until I have time to go over it more and figure out why my calculations are off.

Maxila

 

Hey bruce, did you ever apologize to wlminex? You said you would if you were proven wrong; you even said you wife could attest to your integrity when it came to admitting that you're wrong about something. Do you need me to dig out the links of what I'm referring to?

 

Did you ever apologize to me for trying to 'set me up' in a wager? I'm not apologizing to wlminex because he has a PHD in 'I can't remember what it was' while posting intellectually dishonest nonsense, in the physics and math threads, and got himself banned for doing so 'way to often'. You'd think a PHD would have enough knowledge of the scientific method to keep from being tossed in a public science forum. Quit trolling this forum with your intellectually dishonest nonsense. What you wrote to me after the remedial explanation I gave you was pathetic. You only care about 'being right'. The height of intellectual dishonesty. Trying to stick up for your intellectually dishonest brethren. Dig all you want. I should have told you to kiss my posterior the first time I apologized to you.

 

Yes, of course I care about being right, but when I'm clearly wrong I admit it. You, on the other hand, have been proven to be of low character. You mock and deride people, projecting "trollish behavior" on anyone that you can, letting others do the actual work in the debate while you and Syne look over AlphaNumeric's shoulder and say "yeah...what HE said!" You add nothing of substance to the conversation. Consider yourself on the ignore list.

 

How would you know if I add something to the discourse? You're petty much a scientific illiterate. You're comment about my abilities is intellectually dishonest. I mock and deride you for being a scientifically illiterate, intellectually dishonest crank. I don't have any qualms with that.

 

As we can all see, Maxila, RJBeery, and to a lessor extent and seemingly contrite about it, Robittybob have by far contributed the most trolling, whining, and off-topic posts to this thread. Maxila has admitted to intentionally goading and overstating his knowledge while criticizing that of others. RJBeery has hypocritically contributed nothing but commiserating support for Farsight and Maxila's faulty understanding, while making accusations of just that, posted off-topic, cross-posted, and generally detoured the thread by throwing a fit and instigating. Since he seems contrite, I think I can understand Robbittybob mistaking valid criticism, as he does not seem to recognize the difference between science and pseudoscience.

While I do not expect RJBeery capable of it, I know so little about Maxila that I will give him the benefit of the doubt that he is capable of apologizing for his behavior. Since AlphaNumeric was gracious enough to fill in the details of the exact criticisms I made, it should be clear that I am familiar with SR, and all the thinly veiled ad hominems were unwarranted and contributed to the response he got.

 

This paragraph from AN's post is very revealing. The paragraph beginning: "Clearly your reasoning is wrong since if the speed of light worked like that then a variety of phenomena involving high speed charged particles would behave differently.". The speed of light doesn't appear to be invariant. It is invariant for all measurements conducted in local coordinate and local proper frames. AN's paragraph declares that nature disagrees with your position. So you might want to start there.

 

I did address that, hence that bit about factorising the same expression in two different ways, one gives less distance, the other longer time. But Maxilla went further than that, talking about just inserting a factor of gamma and saying the muons experience light speed at a rate differing by a factor of gamma. Maxilla wasn't actually applying any Lorentz transforms. On one hand he was comparing a non-relativistic view point with a relativistic one and then compared two different frames of the same system, though in that case he didn't apply Lorentz transforms so much as shuffle around an expression he'd just written down ex nihilo.

Take it over to the government forum, not here. There's a thread for everyone to wail on wlminex and Farsight over there. Don't make me split the thread.....

Do you actually know how to apply Lorentz transforms? I proved that the transform I use is a Lorentz transform, so if you cannot get it to work then it is your problem.

Why don't you show everyone your workings and we can go through it?

 

The thing you never recognize, even though I’ve stated it many times, is I never disagreed that c is invariant in every frame, and I never tried to show otherwise. If I thought it was disagreeing with empirical evidence in any way, I would never have posted anything I saw to contradict that evidence and I still believe nothing I've said contradict's empirical evidence or the invariant dynamic of c in every frame.

What I was pointing out in the comparison of frames was a difference in relative physical values as they related to a constant ratio value of c; which I am putting off until AN helps me with the transformations I posted, and I contemplate his post in more depth. Rest assured nothing I discussed, I saw as disagreeing with the fact c is an invariant value in every frame. In fact it seems apparent it's exactly why any transform of time must use c, because it is the one constant value relative to how each frame observes t to x, y, z, as its inherent value is a constant ratio of x/t, it yields a constant transformation of t realtive a frames x,y,z.

Maxila

 

I’d really appreciate that because I cannot figure what I have done wrong? I did notice for the t to t’ transform you accidentally left out an x and wrote, y(dt-v/c^2) in lieu of y(dt-vx/c^2) , I’ll start with that.

Where x units are km and time us microseconds (µs), c = .3km per µs, v = .294km per µs, the ground frame x to the muon is 10km, the relative velocity is .98c. Muon travel time to the ground is 34µs, gamma is 5 (I calculated gamma in an earlier post).

t’= y(t-vx/c^2) (*note I assume delta and left out d)

t’=5(34-.294*10/.3^2)

t’=5(34-2.94/.09)

t’=5(34-32.666)

t’=5(1.334)

t’=6.67

That value of t’ was calculated by the Georgia State University physics department (linked in OP) to be 6.8, so I assume I’ve done something wrong?

For x’ it’s worse:

x’=y(x-vt)

x’=5(10-.294*34)

x’=5(10-9.996)

x’=5(.004)

x’=.02km

That should be 2km not .02km, I thought I set my units correctly (x=km, c=km/µs, t=µs)?

Thanks for helping.
Maxila

 

You think I don't recognize what you're doing? You're doing stuff folks do when they haven't learned the theory. You don't seem to be able to understand what measurements mean in relativistic theory. You still haven't figured out the the speed of light isn't invariant in every frame. Or why I always denote in which frames measurements are invariant or frame dependent. When you say stuff like the 'muon sees 1/5 c ......' You probably think the stuff I say about where the measurements are made is quirky. Like when I said 'If the muon could measure the speed of light over segments of it's path to the earth' the measurement would always be invariant. Those measurements would be conducted in the muons local proper frame where the spacetime event 'muon measures the local speed of light while falling to the earth' occurs. All measurements made in the local proper frame are invariant. I've explained this many times in ways that should be real easy to understand. The theory of relativity makes correct predictions that describe natural phenomena in it's domain of applicability. It's not about juggling algebra, and vague unscientific terms like 'appears' and 'sees'. You've continued with this nonsense from the time you made your first post. I can only conclude that you're not really interested in learning the theory. I hope that I'm wrong. AN's explanations require more knowledge of physics. I've been trying to explain some key stuff at what I consider a remedial level. There's two basic sides of the theory. Theoretical predictions and empirical measurements. So you need to learn the theoretical side to derive the predictions and the experimental side to test the predictions. They're some recent informative posts such as Id's posts on how NIST derives standard measurements in the Lab frame. Good luck.

 

Just on that note because there is so much negativity in that sentence and double negatives can cause ambiguity, are you saying "the speed of light is variant (is a variable) in every frame"?.

 

NO. It's invariant when measured in local coordinate and local proper frames. It's frame dependent when measured from remote coordinate frames.

(dr/dt)_local=1 invariant

(dr/dt)_remote=1-2M/r frame dependent