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# Relativity And Simple Algebra

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1-way speed of light isotropy, smallest variations:

Cialdea, Lett. Nuovo Cimento 4 (1972), pg 821.

Uses two multi-mode lasers mounted on a rotating table to look for variations in their interference pattern as the table is rotated. Places an upper limit on any one-way anisotropy of 0.9 m/s

Ragulsky, “Determination of light velocity dependence on direction of propagation”,

Phys. Lett. A, 235 (1997), pg 125. A “one-way” test that is bidirectional with the outgoing ray in glass and the return ray in air. The interferometer is by design particularly robust against mechanical perturbations, and temperature controlled. The limit on the anisotropy of c is 0.13 m/s.

[in SR, the measured speed of light is always c. This has been verified by years of experiment.]

Anssih, I came up with a one way speed of light determination on the physics stack exchange. All other tests are flawed. The measurement is done from two colocated clocks slowly separated at constant relative velocity. All other tests stop the motion of the clocks which induces a twin paradox permanent time diff which does not happen if you maintain constant velocity during the test of 1 light beam fired between clocks. The results are measured from the Loedel reference frame which allows one to peer into the universal instantaneous present as if the clocks were again colocated despite their separation. This is not philosophy or history but mathematically proven if there was anyone on the planet to look at the proof. There is no proving a negative like saying it can't be done is a universally accepted truth.

Well I'm a bit surprised there's this much confusion about this topic. The reason I said this is a well known fact was not an attempt to convince anyone "by authority" - I'd rather have everyone think this through themselves. And it's not very difficult to think through.

Basically Ralfcis' method is fine, I'm just saying that it is also a convention, not an actual measurable fact.

The real reason I use the word "fact" is that this topic has got nothing to do with any experiments - it is true by definition, if you just manage to handle your definitions properly. So just think this through carefully;

First of all the "aether detection" experiments 100 years ago all assumed that "objects" and "space" have independent existence from each other, and thus signals between macroscopic objects could be simply measured as if the measurement devices are not part of reality themselves. Really naive idea considering that there's (so called) "electromagnetic information" about everything around you all the time - all of "space" is always filled with information from everything around it (since you can "see it"), in that sense there's no such thing as "empty space", and certainly "space" everywhere has got a very real dependence on everything around it.

It would be very mind boggling mystery if objects and space actually had fully independent existence, don't you think?

Einstein doesn't explicitly mention one-way speeds because the impossibility of measuring them was well known at the time. This is why he starts off from defining a clock synchronization convention, and I suspect all physicists at the time would have understood him correctly. It's just the poor way relativity is taught as Minkowski space these days, that the important facts have become a bit hidden under the mud.

Once you have accepted that convention, you have effectively set one-way speed to C by convention. All the experiments that "measure it" simply use this convention to synchronize their clocks, and thus they have determined the end result before even starting. It is like saying "all experiments show that water always flows downhill", without realizing that your definition of "downhill" is determined by how water behaves on it.

Just imagine an experiment that has two spatially separated clocks, I'm sure you can easily convince yourself that you can't determine by light signals whether they are synchronized when you don't know about any possible bias in the speed of light.

Regarding the "moving the clocks slowly from one location", even if you move both clocks, again since you don't know the bias, you don't know which clock gets impacted more.

And btw the speed of the clocks is not relevant either - any motion will have an effect whose magnitude you can't measure because you don't know the bias.

It is certainly not valid to just assume there's no effect - if special relativity is valid, then there is an effect and we know exactly what type of effect. Furthermore we know the effect is such that natural observers can't measure it, for exactly the same reasons I've already discussed. (If we could measure this speed, we could very very easily establish universal simultaneity, and Minkowski spacetime would be completely viewed as a mental hack, nothing more, nothing less.) Also if Lorentz' aether theory is correct, the expectation is also the exact same effect on clocks (just plot oscillations with a bias and you see the same result).

Perhaps the easiest way you can convince yourself of this fact is to simply realize that if you plot this clock movement experiment on a spacetime diagram, you can plot how it would look like in terms of any arbitrary inertial frame, and you will get the same end result in terms of actually observable events (as long as you perform your frame transformations correctly). In each frame the speed of "C" against each clock is represented with different "bias", and the "world around" each clock is plotted in different state. The clocks cannot "measure" the bias on C no matter what inertial frame you plot the situation in, because they can only be in one spatial location at a time.

Just plot these experiments on spacetime diagrams yourselves if you feel the need. It's really not very difficult to see how your first assumptions are connected to how you end up seeing your "measurements".

I will also say that understanding this topic will allow you to understand special relativity in much deeper way that most people seem to grasp it. The whole idea works on the basis that one observer cannot receive information from anywhere "instantly", and thus it is mathematically trivial to represent reality with a convention of isotropic C.

It's just that if you take that mathematical fact too seriously, you also throw away the assumption of "dynamic universe". :shrug:

length contraction:

[in the 1905 paper, par.4, 'physical meaning', he describes a moving sphere 'viewed' as an ellipsoid, when measured from a system with synchronized clocks, per par.1. This is open to interpretation as an apparent or measurement effect.]

If you understand special relativity you should understand he is talking about how a different definition of simultaneity impacts a definition of space. It's not "apparent" (it's not even visually possible to "see" because we only "see" the finite speed signals from events), nor is it "measured" without first defining what type of simultaneity are we using.

Basically ralfcis is talking about a different convention for clock synchronizatoin / simultaneity. With different convention you also impact a definition of space and time. It's trivial to show that it is possible to create a fairly simple model with universal simultaneity, by using appropriate conventions.

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I guess what is throwing me off is your use of the term “length” when referring to a spacetime interval.

It may be that your way of thinking about this is more advanced than mine since I have never considered that a spacetime interval can be a length.

Probably the reason for that is that it contains quadratic terms, forcing me to think in terms of an area, not a length.

I do know, for example, that the area of a light-rectangle is frame invariant in SR.

Another way to think of it is as a displacement in spacetime, which would still be an area rather than a length as I understand it.

But I am working from memory. I will look for a source on exactly what a spacetime interval is, in a geometric sense.

I don't believe it can be a length or a vector as I am fairly sure a vector can not be frame invariant, in the direction of motion.

It is best understood as length. In fact the reason there's quadratic terms in there is that it's just a pythagorean equation (with a negative component).

You can just write it as

$s^2 = x^2 + y^2 + z^2 - (ct)^2$

https://en.wikipedia.org/wiki/Spacetime#Spacetime_interval

This trick is not useful for everything because it gives you somewhat ill-defined coordinates along the light cones. Basically the last term being negative means you get 0 length interval along light cones. Meaning, an event on earth gets the same exactl coordinate as some event on mars. That kind of sucks for some use cases :D

See;

http://foundationsofphysics.blogspot.com/2015/03/towards-quantum-gravity.html

-Anssi

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The true significance of what is happening can be seen from the Loedel half speed perspective which gives us a window into the instantaneous universal present.

The part I don't understand is, how does this method imply something about a universal present?

Or if you mean it just as a convention, also how to apply this convention in any situation involving more than 2 observers (or more than 2 inertial frames)?

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Posted (edited)

Oops, the 2nd sentence. I've laid out how to measure the one-way c according to the caveats of relativity.

I'm thinking you can experimentally measure the speed of time in observed moving frames, mathematically you can plot that you are motionless in your own non-moving frame. Physics is equivalent in all inertial frames so time passes at the same rate of c within all inertial frames. My theory extends this to within all frames because even if you are burning through time after a change in velocity, you do not experience time moving faster for you nor can you detect time moving differently than expected outside your frame. Only afterwards by comparing clocks in the Loedel perspective will you find time is permanently missing from your clock.

I've outlined the connection between Loedel perspective and a universal present in this thread. I hope you're mathematically inclined. Feel free to ask me specific questions as you start reading.

Edited by ralfcis
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It is best understood as length. In fact the reason there's quadratic terms in there is that it's just a pythagorean equation (with a negative component).

You can just write it as

$s^2 = x^2 + y^2 + z^2 - (ct)^2$

https://en.wikipedia.org/wiki/Spacetime#Spacetime_interval

This trick is not useful for everything because it gives you somewhat ill-defined coordinates along the light cones. Basically the last term being negative means you get 0 length interval along light cones. Meaning, an event on earth gets the same exactl coordinate as some event on mars. That kind of sucks for some use cases :D

See;

http://foundationsofphysics.blogspot.com/2015/03/towards-quantum-gravity.html

-Anssi

Arrrgh! Every time I see this nonsense: it's “just a pythagorean equation (with a negative component)” I have to wince.

Look here, the fact that the second term is negative means the function is hyperbolic!

It is NOT “just a pythagorean equation (with a negative component”. That is as silly as saying a duck is just a pigeon with webbed feet.

Is there anyone here who understands SR?

I am beginning to wonder.

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Posted (edited)

I don't want to get sidetracked in pointless minutiae but the hyperbolic nature of the equation stems from Minkowski's rotatation of the ct' axis wrt the ct axis (cartesian). The Epstein rotation of the ct axis wrt the ct' axis (cartesian) results in a circular pythagorian based spacetime diagram and prime equation (although I don't know what it is but it must be a sum of squares as opposed to a difference of squares). I'm not advocating Epstein as it's hard to wrap your mind around it when you're used to Minkowski but it does show that a lot of the assumptions of relativity are purely mathematical constructs and not set in stone as those who don't truly understand SR believe. The true meaning of relativity is distorted by the depictions and assumptions such as 4 vector spacetime, clock sync method, reciprocity, past/present/future co-existence, subjective reality, the depicted universal constancy of c,  etc. (If I remember correctly, in Epstein, c is not a 45 degree angle line common to all that is unchanged by perspective. Even in Minkowski, the c line is a composite of a bunch of overlapping differing length c lines. You won't find that in Wiki because relativity wants to keep that fact hidden as it undermines scriptural authority in the belief of one c-line for all.) I'm beginning to wonder if anyone's willing to risk their understanding of SR by reading this thread without subjectively redacting it.

Edited by ralfcis
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Posted (edited)

For anyone interested the green line is .6c drawn on an Epstein (or Brehme) diagram.

https://photos.app.goo.gl/Ka3sNAoLvSsKBv3j9

In minkowski, the coordinates (5,3), (4,0) are (4,3), (5,0) in Epstein. 42 + 32 = 52. So the prime equation is written as (ct)2 = (ct')2 + x2  (pythagorian) which is the same as (ct')= (ct)2 - x2 (hyperbolic).

Strangely there's almost no information for either Epstein or Brehme on google. Brehme is my spark for the equation v'=Yv instead of Einstein's clumsy interpretation of length contraction and time dilation but I can find no evidence of this on google.

Edited by ralfcis
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AnnsiH#1276;

First of all the "aether detection" experiments 100 years ago all assumed that "objects" and "space" have independent existence from each other, and thus signals between macroscopic objects could be simply measured as if the measurement devices are not part of reality themselves.

The revelation of SR was, 'motion altered measurement and perception'. Unthinkable in a world of absolute, ideal concepts, in a supposedly 'enlightened' world.

Measurement is the verification tool of science. It's accepted as proof, just as evidence is accepted in a court of law.

Clock synchronization is necessary to perform measurements. Since light speed is finite, there can be no universal time or universal synchronization.

The synch convention establishes a simulated and relative synchronization, which is the best that can be done so far. Einstein defined 1-way light speed as constant for a consistent theory to ensure the inertial frame observer's perception would be equivalent to that of a rest frame.

Nothing new or exotic here, since all things conceptualized are by definition. Human knowledge is in terms of ideal mental constructs, and a process of constant refinement.

Postulates like axioms are accepted as true, until violations are found, for the sake of theorizing. Postulate 2 for Special Relativity, constant propagation speed of light, could not apply in General Relativity, which included gravitation and absolute motion in the form of rotation.

Slow clock transport still causes unequal time dilations relative to the central slave clock.

The slower the motion the less the effects, but a balance has to be found between the time to move vs the minimum acceptable variation.

If you understand special relativity you should understand he is talking about how a different definition of simultaneity impacts a definition of space. It's not "apparent" (it's not even visually possible to "see" because we only "see" the finite speed signals from events), nor is it "measured" without first defining what type of simultaneity are we using.

"We have to take into account that all our judgments in which time plays a part are always judgments of simultaneous events.?"

1905 paper, par.1

He is defining simultaneity as a relative concept, vs an absolute concept.

The meaning of 'simultaneous' doesn't change.

Our sensory input is predominately visual, and light is the ideal tool for measurement, being universal, constant, and independent of its source.

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;

The invariant spacetime interval:

For Einstein it was the spatial distance between two events expressed as an equality.

It was invariant because events do not move, which is equivalent to the Lorentz ether, and why Einstein labeled the ether as 'superfluous'.

x2+y2+z2=c2t2

Minkowski, being a mathematician, generalized the expression to 4 variables, by using complex notation to transform t to it, making it an independent variable. In the process of mathematical manipulation and removing its identity, 'time' became just another line on paper.

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Arrrgh! Every time I see this nonsense: it's “just a pythagorean equation (with a negative component)” I have to wince.

Look here, the fact that the second term is negative means the function is hyperbolic!

It is NOT “just a pythagorean equation (with a negative component”. That is as silly as saying a duck is just a pigeon with webbed feet.

Is there anyone here who understands SR?

I am beginning to wonder.

Well, if you feel that it's not apt to bring up Pythagorean in this context, feel free to edit that same Wikipedia article as well :shrug:

I mean I understand how it could be misleading someone, but of course the reason the Wikipedia article also draw the same analogy is that the spatial dimensions are still simply euclidean, and really the only difference is the non-euclidean character of Minkowskis spacetime coming from the definition of t. So yes, those terms are quadratic because this thing basically has Pythagorean theorem in its derivation.

So the only thing I was pointing out was that it's unsual to view a spacetime interval as an area, it's more accurately length. Although I understand people don't want to use the word "length" because it overloads other usages of the word "length". Hence it's called "interval".

-Anssi

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Oops, the 2nd sentence. I've laid out how to measure the one-way c according to the caveats of relativity.

I'm thinking you can experimentally measure the speed of time in observed moving frames, mathematically you can plot that you are motionless in your own non-moving frame. Physics is equivalent in all inertial frames so time passes at the same rate of c within all inertial frames. My theory extends this to within all frames because even if you are burning through time after a change in velocity, you do not experience time moving faster for you nor can you detect time moving differently than expected outside your frame. Only afterwards by comparing clocks in the Loedel perspective will you find time is permanently missing from your clock.

I've outlined the connection between Loedel perspective and a universal present in this thread. I hope you're mathematically inclined. Feel free to ask me specific questions as you start reading.

I feel like my only question is, what is the significance of defining a Loedel frame, and how do you define it in a universe with more than 2 inertial observers?

Basically the question is, what is in your opinion the philosophical significance of being able to establish a Loedel frame?

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I don't want to get sidetracked in pointless minutiae but the hyperbolic nature of the equation stems from Minkowski's rotatation of the ct' axis wrt the ct axis (cartesian). The Epstein rotation of the ct axis wrt the ct' axis (cartesian) results in a circular pythagorian based spacetime diagram and prime equation (although I don't know what it is but it must be a sum of squares as opposed to a difference of squares). I'm not advocating Epstein as it's hard to wrap your mind around it when you're used to Minkowski but it does show that a lot of the assumptions of relativity are purely mathematical constructs and not set in stone as those who don't truly understand SR believe. The true meaning of relativity is distorted by the depictions and assumptions such as 4 vector spacetime, clock sync method, reciprocity, past/present/future co-existence, subjective reality, the depicted universal constancy of c,  etc. (If I remember correctly, in Epstein, c is not a 45 degree angle line common to all that is unchanged by perspective. Even in Minkowski, the c line is a composite of a bunch of overlapping differing length c lines. You won't find that in Wiki because relativity wants to keep that fact hidden as it undermines scriptural authority in the belief of one c-line for all.) I'm beginning to wonder if anyone's willing to risk their understanding of SR by reading this thread without subjectively redacting it.

Well yes, it is certainly possible to represent the same relationships in infinite number of ways, each potentially implying a different looking mental model of reality, yet reproducing the same exact observables.

And that is indeed the fact that is well lost on most people - they assume Minkowski spacetime is the only way to handle those relationships.

It is quite trivial to form a model where everything in the universe is moving at constant speed C, but one dimensions gets projected out (or flattened out) in terms of interactions. That model is mathematically identical to relativity too, and uses euclidean space through and through. Even general relativity can be reproduced with that type of model in fairly simple manner.

Perhaps the biggest significance of a model of that type is that it preserves a simple definition for coordinate systems (with fully orthogonal axes), and doesn't contain recursive concepts for space and time (conceptually, space can "bend" only if it does so in reference to another space).

If you click the link on my sig, there's an electronic book containing fully epistemological derivation (with exact mathematics) of that type of model ("epistemological" meaning a model that is focused on how information can be plotted in consistence ways - independent of how reality actually is).

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Clock synchronization is necessary to perform measurements. Since light speed is finite, there can be no universal time or universal synchronization.

The synch convention establishes a simulated and relative synchronization, which is the best that can be done so far.

Now this is the single most important topic when bringing in philosophy to the discussion about Relativity. The one bit I take issue with is when people say that impossibility of measuring something means that it also doesn't exists.

It is certainly impossible to measure any universal simultaneity as far as we know. It is quite a stretch to then say "it does not exists". Perhaps it does, perhaps it doesn't - it's not very clever to just assume one way or another.

I don't know if you were trying to say this or not - but I find the language you use can easily be taken as if you did, and this is incredibly common.

And yes, all theories include components that cannot be directly measured - they just act as the mental concepts with which ideas are communicated. Minkowski spacetime is also an obvious example of this.

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Posted (edited)

"I feel like my only question is, what is the significance of defining a Loedel frame, and how do you define it in a universe with more than 2 inertial observers?

Basically the question is, what is in your opinion the philosophical significance of being able to establish a Loedel frame?"

I keep answering this question. The Loedel perspective is the only one where both participants have the same proper time at any relative velocity at any distance apart. All other perspectives are a hysteresis of this. For every 2 observers, there is a different half-speed relative velocity for the Loedel perspective of them but what's universal for all is the rate of proper time. The philosophical significance is there is a universal present the cause of all perspective presents which is not the pre- or post Einsteinian definition of the present. Read, I won't answer this again. I'm not interested in the philosophy or history of science. Especially philosophy which is supposedly a search for the truth without any rules to do so and no wrong answers. It's useless. I won't get into discussions like this.

Edited by ralfcis
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"I feel like my only question is, what is the significance of defining a Loedel frame, and how do you define it in a universe with more than 2 inertial observers?

Basically the question is, what is in your opinion the philosophical significance of being able to establish a Loedel frame?"

I keep answering this question. The Loedel perspective is the only one where both participants have the same proper time at any relative velocity at any distance apart. All other perspectives are a hysteresis of this. For every 2 observers, there is a different half-speed relative velocity for the Loedel perspective of them but what's universal for all is the rate of proper time. The philosophical significance is there is a universal present the cause of all perspective presents which is not the pre- or post Einsteinian definition of the present. Read, I won't answer this again. I'm not interested in the philosophy or history of science. Especially philosophy which is supposedly a search for the truth without any rules to do so and no wrong answers. It's useless. I won't get into discussions like this.

Sorry, I still don't understand how you view this... With Loedel frame you only get shared notion of time between two observers, but what about the rest of the universe? Or just add a third observer; what is the convention you'd use in that case?

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Well, if you feel that it's not apt to bring up Pythagorean in this context, feel free to edit that same Wikipedia article as well :shrug:

I mean I understand how it could be misleading someone, but of course the reason the Wikipedia article also draw the same analogy is that the spatial dimensions are still simply euclidean, and really the only difference is the non-euclidean character of Minkowskis spacetime coming from the definition of t. So yes, those terms are quadratic because this thing basically has Pythagorean theorem in its derivation.

So the only thing I was pointing out was that it's unsual to view a spacetime interval as an area, it's more accurately length. Although I understand people don't want to use the word "length" because it overloads other usages of the word "length". Hence it's called "interval".

-Anssi

I suppose that making a comparison to trigonometric relationship and the Pythagorean triangle is a way of pedagogically introducing people to hyperbolic functions. Obviously, there is a similarity between the two.  However, the similarity can only be carried so far, as the geometry of Minkowski space is hyperbolic.  $(\Delta { s) }^{ 2 }=(c\Delta t{ ) }^{ 2 }-(\Delta x{ ) }^{ 2 }$ where $(\Delta { s) }^{ 2 }$ can be replaced by $I$, the invariant interval.

Now the hyperbolic functions $cosh\psi =\frac { c\Delta t }{ \Delta s }$ and $sinh\psi =\frac { \Delta x }{ \Delta s }$ when used in the hyperbolic identity ${ cosh }^{ 2 }\psi -{ sinh }^{ 2 }\psi =1$ will return the expression for the invariant spacetime interval $(\Delta { s) }^{ 2 }=(c\Delta t{ ) }^{ 2 }-(\Delta x{ ) }^{ 2 }$

My only point was just that Minkowski spacetime is based on hyperbolas, not trigonometric relationships such as the Pythagoras theorem.

Ok, back to figuring out what Ralfcis is trying to do here. I admit I have no idea.

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Posted (edited)

Don't try to absorb it all at once. Just baby steps. Ask about the 1st thing you trip over. I'm thinking of rewriting the whole thread and erasing all of my thought processes and only leave the conclusions. But I won't do this until December.

Ralfativity is based on proper relativity of simultaneity using a universal proper time present that can be glimpsed through the half-speed perspective (Loedel simultaneity). (.33c is half of .6c, .5c is half of .8c etc.) All the rest of relativity is rejected and I make experimental predictions Einativity can't make.

Edited by ralfcis

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