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Posts posted by ralfcis


Does relativity break the rules of physics? No, but the misconceptions about it do.
The Sun does not orbit the earth, the entire universe does not pass by a stationary spaceship nor does it revolve around a proton in the LHC and it's not just because of the force imbalance. Even acceleration can be approximated as an average constant velocity or its duration ignored over a long journey. In fact, acceleration has negligible effect at the start of a journey but has seemingly huge relativistic consequences on age difference the further it is removed from the start. Acceleration actually has no magical properties imbued it by relativity. The same for relative velocity. Even though things appear to move away from you in the rear view mirror, the Earth is not one giant treadmill activated by the wheels of your car. Relative velocity does not care if you've expended energy to move relative to something, establishing who's actually moving is unimportant. Perspective is illusion, not reality even though it was incorrectly elevated to reality by relativity.
Despite all this nonsense, there is a scenario that doesn't seem to make sense but is true. If you take a giant glass vacuum bottle and launch it into space, it's relative velocity to the vacuum it contains is exactly the same as its relative velocity to the vacuum it's travelling through. It's like the bottle doesn't exist. Matter has no relative velocity to vacuum or light (vacuum's electromagnetic field determines c). The Michelson Morley experiment was wrong to conclude there's no medium for light, it's the type of medium that's important.

There's little relative about relativity.
First, the principle of relativity asserts: The laws of physics are the same in all inertial frames of reference. So when I say all atomic clocks are universally accurate in their frames, which is in keeping with this first principle, I get nothing but condemnation from relativists and nonrelativists alike. Nonrelativists, who believe in absolute motion, believe velocity physically affects clock operation and that motion cannot possibly have an effect on time itself. Relativists, who worship the prophet, don't question Einstein's clock sync method even though most believe there's some possible difference between oneway and two way speed of light (there isn't). They will not stray from his teachings even though atoms hadn't yet been invented when he made up his method which depends on his assumptions about relativity to prove his assumptions about relativity. Circular arguments abound in relativity.
Like the debate about oneway/twoway light speed, the debate about relative velocity and absolute motion is moot. Relative velocity cannot be drawn on a spacetime diagram. The closest approximation is in the Loedel diagram where both participants have the same velocity but it's depicted as half (eg 1/3 c) of the true relative velocity (3/5 c). In any spacetime diagram there is always a third element which is the stationary backgound. Whether you want to argue that it's not absolutely stationary or just chosen stationary relative to the two participants, it doesn't matter to the math of the spacetime diagram which is impossible to draw without it. Relativists seem to have no problem with these contradictions deeming they're ok because they're counterintuitive which, by definition, makes them incontrovertible.
According to relativists, the only acceptable absolute motion is one that results in a force. They see no contradiction that both participants see the other as time dilating and length contracting while time ticks at the normal rate for both of them but seem to see a paradox that one can have time truly pass slower for the other if one of them feels a force. Actually this can happen without a force being involved.
If relativists had run the world, speed limit signs and speedometers (even odometers) would have been replaced by radar guns measuring relative velocity between every car. But practically, the world assumes absolute motion to a common reference frame to get practical results. There is no length contraction or need for reciprocal time dilation, no need for spacetime diagrams with coordinate rotations or imprecise depictions of relative velocity, and many other useless assumptions relativity foisted upon us for it to work. I have a much better explanation for relativistic phenomena and it's not newtonian or absolute.

The main equation of ralfativity:
The main equation (space and time velocity combination) is
c^{2} = v^{2} +v_{t}^{2 } also written as the gamma function Y = c / sqrt(c^{2}v^{2}) ( v_{t} = c/Y and v = c/Y_{t})
Here is the relativistic velocity combo equation:
w =(v+ u) / (1 + vu/c^{2})
So here is a more universal universal equation that includes relativistic velocity combination with space and time velocity combination:
c^{2} = ((v+u)^{2} + v_{t}^{2}u_{t}^{2} ) / ( 1 + vu/c^{2})^{2}
The main equation is also written as:
or (ct')^{2 }= (ct)^{2}  Yox^{2} (Minkowski hyperbolic (difference of squares) form where hyperbolas intersect the same proper time for all velocity lines)
or (ct)^{2 }= (ct')^{2} + Yox^{2} (Epstein pythagorean (sum of squares) form where circles intersect the same proper time for all velocity lines)
Since I include both perspectives in a Minkowski diagram without coordinate transforms, Yo is the perspective's gamma constant. Relativity does this in a far more complex manner using a far stricter and impractical treatment of relative velocity.
v = v_{h}(v_{t}/c +1) and v_{t} = v_{ht}(v/c +1)
v = 2c^{2}v_{h} / (c^{2} + v_{h}^{2}) and v_{t} = 2c^{2}v_{ht} / (c^{2} + v_{ht}^{2})
v_{h} = c(cv_{ht} ) / (c+v_{ht} ) and v_{ht }= c(cv_{h} ) / (c+v_{h} )
v/(cv) = 2cv_{h } / (c  v_{h})^{2}
Y = 2Y_{h}^{2 } 1 = (c^{2} + v_{h}^{2})/(c^{2}  v_{h}^{2}) = c/v_{t }= (1/(1v_{h}/v))_{ } 1 = 2c^{2}v_{h}v/(c^{2}  v_{h}^{2}) = 2Y_{h}^{2 }v_{h }/v
v_{h}=Yv/(Y+1)
(Yv)^{2 } = v^{2}/(1v^{2})^{ }
v= c(Y^{2}1)^{1/2}/Y
v_{t }= _{ }c/Y = DSR(c+v) = v_{ht} (1 +v/c)
t'=x(v_{h }+c)/c
v' = Yv
Yv =x/t'
Y_{u}/Y_{w}=DSR_{v}
The formula for Proper relativity of simultaneity is t'(1Y) (where t'=x/Yv) whereas the formula for "moving" perspective simultaneity was vx/c^{2}
the equation for proper age difference is t_{pad}=t′−x/Yv
t'=sqrt(t^{2}  x^{2})
t' =xDSRo/Yv
t_{ps}= xv_{ps} = xYv/(1+Y) which is the new formula for proper simultaneity
w_{t} = c / Y_{w} = c / (Y_{v}Y_{u}(1 + vu/c^{2})) and w =(v+ u) / (1 + vu/c^{2})
Y_{w}w = (v+u)_{ }Y_{u}Y_{v }
v_{ht} =cDSR (Doppler Shift Ratio)
cDSR = ((cv)/(c+v))^{1/2 }
DSR_{v} = Y_{u}/Y_{w} ^{ }where w is the combined velocity of u and v where u = c
Y(cv) = c/DSR
Y_{w}w = (v +u)(Y_{v}Y_{u}) where Y_{w} = Y_{v}Y_{u}(1 + vu/c^{2}) and w =(v+ u)/(1 + vu/c^{2})
DSR_{w} = DSR_{v} * DSR_{u} where DSR_{w}^{2} = (cw)/(c+w)
w = c(1DSR_{v}^{2 }DSR_{u}^{2 })/(1+DSR_{v}^{2 }DSR_{u}^{2 })
DSR = Y(1v/c)
The sign of the velocities is positive if the direction is positive where the distance increases in the direction of the vector. The velocity w is the relativistic combination of v + u.
A = (v+u)
B= (1+vu/c^{2})
sqrt(c^{2}B^{2}A^{2}) = c/YvYu =v_{t}u_{t}
v Y v_{h} v_{t} v_{ht} DSR t'
1 1 1 0 0 0
3280/3281 3281/81 40/41 81/3281 1/81 81
40/41 41/9 4/5 9/41 4/36 9
255/257 65/16 15/17 16/65 1/8 8
24/25 25/7 3/4 7/25 1/7 7
35/37 37/12 5/7 12/37 6/36 6
12/13 13/5 2/3 5/13 1/5 5
77/85 85/36 77/121 36/85 8/36 9/2
15/17 17/8 3/5 8/17 9/36 4
4/5 5/3 1/2 3/5 12/36 3
3/5 5/4 1/3 4/5 18/36 2
1/2 1.155 .268 .866 .577 1.73
8/17 17/15 1/4 15/17 3/5 5/3
5/13 13/12 1/5 12/13 24/36 3/2
1/3 1.06 .17 .943 .707 1.41
12/37 37/35 1/6 35/37 5/7 7/5
7/25 1/7 24/25 27/36 4/3
16/65 1/8 255/257 15/17 17/15
9/41 1/9 40/41 4/5
0 0 1 1
v c v_{h} c v_{t} c v_{ht} c DSR t'
21523360/21523361 21523360/21529922 6561/21523361 1/6561
t' = X(c+v_{h})/c (v_{h} is negative for v<0
So the formula for lost, evaporated, invisible age is t'(DSR  1)
t' = X(2v_{h})/(c+v_{h}) _{ }

Where's the advanced editor gone that allows subscripts and superscripts?

Luckily I had a major heart attack Jan 4 and can now go back on this physics forum which was the only one that allowed me to pursue my ideas without getting banned. I hope nothing's changed here as I plan to start over in this thread. My interactions with Popeye and Sluggo taught me that another's math is basically an impossible language to understand so I will restart at the most basic level. Relativity can be explained with basic algebra using only 2 formulae and without any of Einstein's circular arguments and constructs that proved relativity by assuming relativity was correct. Relativity is absolutely correct while none of Einstein's philosophical explanations are.
I spent years coming up with simple mathematical building blocks that can be put together without Einstein's cumbersome fine print rules for defining clock sync, spacetime paths, length contraction, and anything else he and Minkowski came up with. Of course all this has been claimed by countless people before me so just consider this as a purely mathematical exploration, beginning with two formulae (the one for gamma and the relativistic velocity combo formula) , that just coincidentally agrees with relativistic physical phenomena. There are no rotated frames here, only two types of lines v and vh (half speed velocity defined the relativistic velocity combo formula), their reciprocals and their behavior when multiplied by Y (gamma). The math also avoids square roots and squares in the equations to make them work using simple addition and subtraction. There is no clock sync, only light signals and the assumption atomic clocks all run at the normal clock rate within their frames.
In the next post I will print out forms of these equations that have proved most useful to me. Think of them as common phrases that are formed by the very few basic words in this language. The derivations are in my previous thread and I don't expect anyone to understand them but I'd like to keep them together in one spot so I can find, cut and paste them easily throughout this thread.

I just popped in to see what was happening so is this the new Hypography? Was it sold? I don't know how to navigate this site. I'm dying to come back and write. Will I still have the leeway I once enjoyed or are things stricter now?

Sorry I did not read all these posts because I've blocked most of these people and I'm trying to get some time to finish a post I started 2 weeks ago. Anyway, Popeye, Zeno's paradox is solved (infinity removed) when you consider distance and time joined as velocity. I use the same technique in my math. I don't need to explain relativity using distance and time separately, I always use Yv. What's doubly interesting is how the half speed Loedel perspective fits into all this to cancel the infinity of Y (gamma) (and all the wrong physics interpretations that go with that infinity) as v> c. If v>c then it's half speed v_{h} also approaches c. You do not end up with two gammas that approach infinity because v and v_{h} are always together in formulas and approach a finite number because the infinities cancel out.
Oops writing this blurb has deleted my previously saved work. Ok good I didn't have time to finish anyway. It looks like it will take me an infinite amount of time to get to rewriting that post. It was how to write the prime equation and make the invariant interval a time duration instead of a distance measurement. Simple at first as you divide both sides of the equation by c^{2} but then the fun starts.

So what's the escape velocity for this solar system and how big a sail would you require to achieve it. My guess is you haven't worked it, or any other required math, out yet.

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 halfspeed 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.

Hey Popeye, you're too busy to be engaged in this. I thought you were busy finding flaws in my "crank" ideas.

" If light speed is "absolute", then that speed c minus 300 million meters per second constitutes an ABSOLUTELY STATIONARY position. "
And you said you didn't believe in math. cc=0, brilliant! Except it's not.
PS To be precise there's a different answer if your talking about closing speed (ans= 0) as opposed to relative velocity (ans=c) which is subject to the relativistic velocity combo formula).

I have no idea what you're saying but it's wrong because he never started to do the math and has no intention of doing so.

"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 halfspeed 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.

Ok, show me your math explaining how muons make it to earth from the upper atmosphere. I agree, Einstein's math gives the correct answer but it is based on a foundation of illogical garbage. I have no math that uses time slowing or length contracting yet I can explain muons making it to earth mathematically using other less known relativistic concepts. You must be able to do the same because otherwise your opinions are not provable and are therefore just the ravings of a crank even if eventually proved true by someone else. Your beliefs don't make you a crank, your inability to back them up mathematically does.

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. 4^{2} + 3^{2} = 5^{2}. So the prime equation is written as (ct)^{2 }= (ct')^{2} + x^{2} (pythagorian) which is the same as (ct')^{2 }= (ct)^{2}  x^{2} (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.

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 coexistence, 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 cline 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.

Oops, the 2nd sentence. I've laid out how to measure the oneway 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 nonmoving 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.

Yes it's 75 pages of simple so far. But for your specific question, c may be constant for v=x/t but Yv is the amount of invariant space you travel in the time on your ship's clock. So if you travelled 4ly to proxima centauri in 3 yrs according to your clock, your Yv is 4/3c using invariant space in your time. If you think I'm breaking c by saying this then you haven't been paying attention.
As for the rest of what you said, you do have a theory, it's called relativity and in that theory c is kept constant for observed frames by time dilation being compensated for by length contraction. What problem were you addressing? You did not provide a possible solution, you told me to find it myself by adopting an alternate way of looking at the problem. We do not know from observation that time is not constant. In fact both participants clocks tick at the same rate in their own frames and each one sees the others clock exhibit 2 different rates of "slowing" of which neither is an actual slowing of time itself because that would contradict both seeing their own clocks tick at the same rate. You read some Wiki articles and you repeat them without applying critical thinking. You needn't take it personally, I give people a chance and if they offer me nothing thought provoking I turn them off by being rude and then I wait usually way too long to put them on ignore. This is the only forum that tolerates my bad behavior.

A lot of words but all you've said is for c to be constant, time and space must compensate. That's what Einy said, that's not what I say, hence the length of this thread. I'm not entertaining other theories, just here to answer any questions on my own theory. Do you see a problem with it or are you offering alternatives. I've listed the problems I see with Einativity and people continually ignore that list.

Popeye, the invariant "length" of the spacetime interval comes from the video I posted. This line is like a 4 dimensional straight line as it has both time and distance components. I haven't been able to gleen any significance from its existence (except that it's a reciprocal form of relativity's prime equation from which I derive all my equations) and have discounted its relevance to this discussion.

Popeye, here's how ralfativity handles the train in the station/pole in the barn scenario. It's very different from how Einativity does it. First Einativity since you're familiar with it:
https://photos.app.goo.gl/gswbA72uqG7Rjq9N9
The train is depicted as the red lines of simultaneity which are also the Minkowski rotated xaxis. Since they follow Einy's clock sync method, the train clocks are the same value at the endpoints. The train and station both have a proper length of 2 ly which is reciprocally contractible from a 2.5ly spacing between where the light signals hit the ends of the train simultaneously. The proper length of the train is distorted by the Minkowski rotation of the xaxis to make the x'axis which is also called the train's perspective line of simultaneity created by Einy's clock sync method. The train fits into the platform at t'=0 and a light signal will hit the ends of the train at t'=1.25 simultaneously from the train's perspective and at t=.625 (back) at t=2.5 (front) from the platform. So what's simultaneous for the train is not for the platform.
What Einativity does is join the two endpoints of the train with a line of length that is compressed by physical length contraction to fit into the station's rest length. Relativity of simultaneity is explained by this length contraction instead of vice versa.
In ralfativity,
https://photos.app.goo.gl/L63Hvd9iAxfSu11K9
the train's length is invariant at 2 ly. There is no Einy's clock sync method so the train's ends are not subject to being sync'd. The clock values are set by other rules I outlined in this thread. The light hits the back of the train at 1.25, the train moves on and the front is hit at 1.25 much later from a universal present perspective but simultaneous from the train's perspective because both times are labelled the same. There is absolutely no need to join these two points and say that's the length of the train when those points indicate a differing duration of time from different perspectives. Just because Einy's clock sync method or my rules make the clocks say the same time, it does not mean 0 time has passed between the light hitting the back and front of the train and the extended length of the train accommodates when its ends catch the light signals. I say the extended time the difference in the start of the the train and platform stopwatches is what gives the endpoints of the length invariant train to catch the light signals. Potato/tomato.
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.
https://photos.app.goo.gl/R3XFLfSqUjQVpLPK7
I spent a lot of time describing how this perspective works in this thread but what it does is allow the light signals themselves to reveal time and compensate for the diagram's corruption of the light signals' depicted lengths. In a Loedel depiction, the pink and yellow light signals have the same length and all spacetime diagrams must contain the same information independent of depiction. That's all unimportant to this specific question right now and so is the invariant spacetime interval which maybe one day I'll find some use for. The final answer I've found is I don't draw some fake line between time points and call it physically contractible length and declare that perspective has the power to contract it because we can measure that under the circumstances that create it and which disappears once those circumstances disappear. To me, that viewpoint is pure insanity no matter how symmetrical and spacetimey it makes Einativity's math. If you don't understand what I'm saying, read this over and over until you can ask specific questions. I wrote this fast so I may have been imprecise in some wording. This will be impossible to grasp or even see if you can only follow the prophet and his teachings. The scales have fallen from my eyes but everyone else is still walking around with them.

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. I thought I had blocked Sluggo. I'll fix that.

c^{2}t^{2 } x^{2} =c^{2}t'^{2 } x'^{2}
each side of the equation is the invariant length of the spacetime path.
So if Alice goes out 3 ly at .6c, her coordinates of (ct', x') are (4,0). Bob's coordinates of that same point are (ct,x) = (5,3)
So Bob's invariant length = sqrt (25  9) =4 which should equal Alice's invariant length of sqrt(160) =4.
So the spacetime path = 4ly from both perspectives. I don't know what the significance of this is.
This is from Greene's video on invariants. https://www.youtube.com/watch?v=AJs7rk3QGD4&list=PLj6DWzIvBi4PFDXCCV1bNhVUgDLTwVbFc&index=54&t=0s
I'm trying to work out what this all means for the pole in the barn scenario. In relativity, Alice's time dilates and the distance she travels contracts. So Bob says she travelled 3 ly in 5 yrs and Alice's clock says she travelled 4yrs so her distance must have been 3/Y = 12/5 = 2.4ly. But what this all has to do with the invariant length of 4ly and what's the length of the pole and the barn or train in the station I don't know yet. Is the invariant length somehow related to proper length? Does this somehow solve my dilemma of treating the pole as endpoint time coordinates (between which I have no real definition of spacetime length) instead of a contractible physical object. I'm trying to determine if relativity uses invariant length as what I'm looking for. This will take some time to sort out as i don't know what I'm trying to define.
In my train in the station example, my train is always the same proper length. I don't join the coordinate times when the back of the train sees the light to when the front of the train sees the light and call that the length of the train. This is exactly what you're doing when you say relativity of simultaneity of the endpoints does not preclude some sort of physical length variation. Einativity does join those points and calls them the new length of the train. I'm trying to see if these varying train lengths are somehow made invariant to get this craziness under control. Invariant spacetime paths must have been invented for a reason but I don't yet see it.

Wikipedia is the National Enquirer of world knowledge. The 1st sentence of that article was completely wrong so I didn't bother to read the rest. If you don't assume time passes at the same rate within each inertial frame then you can't assume you are motionless relative to the clock right beside you. I only deal in math and experimental evidence, I won't engage in philosophical arguments that deny them as also being philosophy.
Ralfativity
in Physics and Mathematics
Posted · Edited by ralfcis
Let us begin to construct the mathematical framework for ralfativity. There are 3 axes ( ct, ct' and x) plotted on a Cartesian coordinate system. There is no 2nd Minkowski coordinate system so equations like the Lorentz transforms do not exist. Because the two time axes ct and ct' look to be in distance units, relativists declare that time is a 4th spatial dimension. This is not true if you algebraically derive relativity's equations from the main equation which defines there is only one velocity in the universe (c) that has velocity through space (v) and velocity through time v_{t }components. The faster you are observed to go through space, the slower you are observed to go through time. The relativistic combo equation similarly limits the combination of any two relative velocities through space to c.
c^{2} = v^{2} +v_{t}^{2 } also written as the gamma function Y = c(c^{2}v^{2})^{1/2} ( v_{t} = c/Y ).
https://photos.app.goo.gl/c864tipaU1ZLRGNX6
Ratios of the various axes define different types of velocity and the reciprocals of those velocities represent different types of lines of simultaneity (not shown and not important for now).
What is important is the 1/slope of the .6c line represents the velocity (x/ct) the stationary observer sees with his clock while x/ct' = Yv =.75c is the velocity the moving observer sees using his own clock. The distance common to both is invariant and proper and does not require any assumption of length contraction or reference to the stationary clock.
Using this info about Yv, algebraically multiply both sides of Y = c(c^{2}v^{2})^{1/2 }by v
Yv = cv(c^{2}v^{2})^{1/2 } =x/ct'
and v=x/ct and you get the main equation as
(ct')^{2 }= (ct)^{2}  x^{2 }
which represents all 3 axes.
It could have just as easily been written as
t'^{2 }= t^{2}  x^{2 }/c^{2 }which would have led to the conclusion that all distance axes were really time axes according to relativist's logic. The time axis and length axes cannot be joined into the concept of spacetime because time does not behave like a distance axis and their lame logic does not make it so.
I will next show how the simple spacetime diagram I showed here can be combined with light signals to define the basic mathematical building block for relativity. Time slowing during constant relative velocity is an illusion. What causes that illusion is a mismatch in how start and end times are recorded differently from each perspective. Relativity of simultaneity causes the illusion of time dilation because perspective observations are illusion.