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# Relativity And Simple Algebra

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In my travels from forum to forum, I've met few people who even know what algebra is let alone how to use it. In high school, algebra was my worst subject but now I've learned to love math.. Before I start I must warn people:

Warning: This thread contains simple math and may cause serious cranial distress.

There that should frighten away almost everyone.

So I'm going to construct a theory of relativity from first principles using only simple algebra. I'm not going to start with any of Einstein's assumptions or terminology but my one assumption will generate  most of the same results as Einstein's theory of relativity and then some. ("then some" meaning it can make predictions relativity can't make)

The color of the math will be different. Relativity and Minkowski favor hyperbolic equations that  are the difference of squares whereas I prefer the Epstein/Pythagorean circular equations that are the sum of squares. Don't worry, Epstein and Minkowski spacetime diagrams are convertible into each other but it's an extremely painful process so I will stick with the more familiar Minkowski while using sum of squares equations. Think of it as being a mathlete employing parallel bar techniques on a pommel horse.

Hi this is future me revising posts I made in the past. The following paragraph is true but I no longer use this concept of rotated coordinate systems. I now only use 1 cartesian coordinate system with 3 axes: ct, ct' and x.

It all starts with two blank sheets of Cartesian graph paper that will be placed on top of each other and rotated. Each will have a vertical axis labelled ct  and a horizontal  axis labelled x . The rotated sheet will have the labels ct' and x' to differentiate the sheets. At no time will either square Cartesian coordinates be crushed sideways into any Minkowski rhombic coordinates. However as one sheet is rotated joined at the origin to the other, it's Cartesian squares will get larger and larger until they get infinitely large once a 45 degree rotation (signifying light speed) is achieved. Don't worry if you can't visualize what I'm talking about, it will be illustrated in the next post.

Edited by ralfcis
Trolling buffonery. Don't be a dick

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So your not using any of Einstein's assumptions or terminology, or postulates, but are going to develop practically the same results as SR and or GR?

Any chance that you can explain your theory in plain English before you delve into some maths?  I don't agree that Mathematics is the language of the universe, or that it can prove anything.

It may be able to support an hypothesis, but it can also be made to support a competing and contradictory hypothesis at the same time.

So please explain your hypothesis in simple English, as even Einstein said, "If you cant explain your theory to a barmaid, then you don't understand it yourself".

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I'm not allowed to present a personal theory on the physics forum. A math presentation is not a personal theory. This is just a demonstration of an alternate method to derive relativity from nothing but algebra. It will provide another perspective on how relativity derives its formulae. For example, labelling the "time" axis as ct seems innocuous but it is an assumption that leads to the correct answers which then means the assumption was correct. It's called proof by inductive inference which is just another name for circular argument. Your hypothesis is unproven but if it proves a result that supports your hypothesis, your hypothesis must have been correct all along.  Relativists will not accept that this is how relativistic math works and will knee-jerk deflect the argument to the fact relativity is supported by extensive empirical evidence which it is. One other subtle assumption will also be used. I will appear to derive gamma from thin air but it too depends on the "time" axis being ct which is actually a "distance", not time. Your job is to follow the thread and disagree somewhere before the conclusion because once it's reached, it will be too late.

PS. In later posts I changed the word "distance" to duration when describing the ct or ct' axes. The distance unit is in light years which is how much time it takes for light to travel that distance. The distinction becomes more important once we start discussing the rate of time (ct'/t) within a moving frame from an outside perspective. The rate of time within a frame is always ct/t = c no matter what the outside perspective is. As I will show later, during an imbalance of relative velocity when the observed participant makes a velocity change and the reality of that change takes time to propagate outwards, the party who made the change will be unaware that his rate of time is much faster than c which results in permanent age difference between the two parties. Relativity uses a much different explanation on how age difference occurs. Much more on this later.

Everything in the universe experiences itself running at the normal rate of time which is c even though to an outside observer, time may be passing at unlimited multiples of the normal passage of time within an observed frame. This would manifest itself as the televised video broadcast from the frame as slow motion or fast forward instead of normal "play" speed. This is not a manifestation of the rate of perspective time due to reciprocal time dilation but is a manifestation of the rate of proper time due to the reciprocal Doppler Shift Ratio DSR. At .6c relative velocity, the velocity through perspective time is c/Y = .8c and for prper time is .5c separating or 2c coming together. Perspective time is our own subjective present which is a light speed delayed form of prper time which is outside the timelike interior of the light cone. These concepts are new and will be further defined as we progress.

Edited by ralfcis
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I'm not allowed to present a personal theory on the physics forum. A math presentation is not a personal theory. This is just a demonstration of an alternate method to derive relativity from nothing but 2 sheets of paper and algebra. It will provide another perspective on how relativity derives its formulae. For example, labelling the "time" axis as ct seems innocuous but it is an assumption that leads to the correct answers which then means the assumption was correct. it's called proof by inductive inference which is just another name for circular argument. Your hypothesis is unproven but it proves a result that supports your hypothesis. That's how relativistic math works. You tell that to a relativist and he'll slap your face and ban you for life. One other subtle assumption will also be used. I will appear to derive gamma from thin air but it too depends on the "time" axis being ct which is actually a distance, not time. Your job is to follow the thread and disagree somewhere before the conclusion because once it's reached, it will be too late

Well, I'm probably not the right guy to follow your math, as I am just interested in Physics. There, that will get a bunch of guys shouting out that Physics IS MATH. But I don' buy that claim.

You don't need any math to know that if you go around a corner too fast in your car, it will spin out, or to follow the reasons why that will occur. You only need to employ mathematics if you want to calculate the difference between the point of spinout if you use 30 psi in the tires instead of the current 25psi.

And I doubt that you will be banned from this forum for explaining the details of your "personal theory", regardless of how unusual it may be, as long as you don't beat people over the head for not believing you. They can choose to continue reading your posts or not.

From my point of view, the first way, Einsteins way of deriving relativity's equations  is nothing but one error heaped on the first, so it is incapable of proving anything useful.

As your method arrives at the same end, I cant get excited.

That's why I was just interested in hearing about your concepts that allowed you to derive relativity without using Einstein's logic, or lack of.

I was expecting to see some leaps of faith or unsubstantiated claims in your hypothesis similar to those that exist in Einstein's Hypothesis.

Relativists can now shout again... "WHAT leaps of faith or unsubstantiated claims are in Einstein's hypothesis? and "its not a hypothesis now, its all proven!"

I don't listen to Relativists these days.

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But, Ralfcis, algebra was simple from day one.  In one day you could have explained relativity with algebra.  I was looking forward to that.  But you've spoiled day one and now where will you go?  Or, better yet,  where will I go?

Away!

Marcospolo, you should listen to those "Relativists" (note quotes).  Listen carefully.  You will find that at least half of what they say was never said by Einstein.   They seem not to know the meaning of the base word of 'relativity' (relative to ---).

While we are at it, could we please change Alice's and Bob's names?  If not just get rid of Alice and Bob, period.

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Would you  prefer Hazel and Mr. B. or George and Gracie maybe?

Edited by ralfcis
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Would you  prefer Hazel and Mr. B. or George and Gracie maybe?

George and Gracie? How old are you anyway, Ralf?

When are we going to see some math magic?

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I'm 61. I have this little friend Cassandra who hates me on physics, says it's a waste of time, keeps hitting me with sanctions if I continue and if I ever leave my computer open, would delete everything I've ever written. So I can only engage in very quiet moments. It's comin though.

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Every Christmas I go to Indigo with my little friend to buy way overpriced chocolates at half price and a book for toilet reading. This year's selection was Mathematics an illustrated history of numbers. It has pictures, so how can you lose, and I'm on my 5th re-read. Just today I came upon the part that described what a 4th dimensional being would look like to us. The book said it would look like a being that would be changing it's size over time (as it was standing in one spot I assume). I assume that because beings moving toward or away from us appear to change size over time without being 4 dimensional.

I think the book lacks imagination on this point but it does agree with relativity's view of time. A time being standing next to us would have his 3 space dimensions run at a different time rate than us. His movements would be either unnaturally slow or fast compared to those caused by our natural rate of time. Slower I could buy because he would be in our past and his movements would have to speed up in order to catch up with the present. But once caught up, he couldn't move faster than us because that would mean the future already exists and we're the ones moving too slow into it. Causality would be violated. Despite all the evidence to the contrary, relativity insists causality can be violated; quantum physics has also joined this bandwagon. The max speed of information c, which is the normal rate through time within any frame, prevents anyone from going into the future before anyone else. Einstein unfortunately said the past present and future are just persistent illusions which means they all exist concurrently. Do relativists seriously believe this? Then I think they're on the wrong delusional path.

Unfortunately it's going to take several days to show the math. But in the meantime I'd like you to ponder the difference between the distance the ct axis represents and the distance the x axis represents in a spacetime diagram. A light year is a distance unit (x) but ct is a time unit that can also be read as light time so why are they different? Ponder the difference between a coordinate, a duration and a rate. London and Paris are coordinates or places in space. The distance between them is a duration in space. The rate of space is the velocity it would take to cross that distance. Time also has coordinates as readings on a clock; 6pm or 3:30am for example. It also has duration as in there are 24 hrs in a day. But no one seems to recognize time also has a rate. Just as the rate for distance is x/t, the rate for time is ct/t. One is the velocity through space and the other is the velocity through time which reduces to c (the max velocity through time) within a stationary frame but is ct'/t for an observed moving frame. From here, relativity's equations practically write themselves.

Edited by ralfcis
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My post above was not meant to imply a 4th dimensional being could time travel. He certainly couldn't travel into the future before anyone else because he would still be limited by the max speed of light through time. Also his slower motion would not imply he is in our past but it would look to be so just like it looks due to reciprocal doppler shift and the delay of light over distance.

I have changed my views on the following paragraph. Now, time dilation is not a measure of time slowing but is a result of the  proper simultaneity of when clocks start timing from the two perspectives. If you base relativity on the behavior of proper time, there is no time dilation, length contraction or relativity of simultaneity (therefore no Lorentz transforms) which are all due to perspective time.

Popeye asked on another thread if there is any empirical evidence for time dilation. An experiment could be done between two rolling carts in an office. Each would have a TV, a TV camera with transmitter and recorder, and an atomic clock. Two scientists could push the carts apart and record the results each cart would see. In the Captain Kangaroo/ Mr. Green Jeans example where MGJ separates from CK at .6c, both recorders will capture the clocks slow to half the normal rate (due to the doppler shift) but time dilation can't be seen, only calculated (see post 562).  Of course the office example will see much tinier effects.Fortunately the atomic clocks are time microscopes and can see time in extremely fine resolution.

The above test was refined in post #651.

Edited by ralfcis
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Let's take the spacetime diagram and divide the three axes by t making the axes velocities rather than distances (or durations).

ct'             ct'/t

ct   |  /       ct/t |  /

|/__           |/__

x               x/t

The vertical axis is now the velocity through time at the normal rate of c. People can't grasp this as the velocity through space c is very fast so how can the velocity through time c be so slow especially on Monday afternoons. That's like asking how a billion stars can take up so much room and a billion microbes can't be seen with the naked eye. It's not the number that matters, it's what it's applied to.

To make writing the rest of the math easier, let's assume vt =ct'/t and v= x/t where vis the velocity through time and vis the velocity through space. Using pythagoras in the 2nd graph we see that c= vt2 + vx (In English this means all frames combined velocities through space and through time are always c). So vt2 = c2 -vx2. and v=sqrt((c- v). We recognize this as part of the formula for gamma so v=c/Y.

From the graph we see v= ct'/t = c/Y so  t=Yt' which is the formula for time dilation.

Plugging this result into the formula for c2, we see that (ct)2 =(ct')2 + x. This relativistic  formula reflects the fact that the time that disappears off the traveller's clock with respect to the observer's clock is converted and stored as the distance between them. The  missing time duration is converted into a distance duration. This fact allows for the conversion between perspective time and proper time. The equivalent time of the distance between them is the difference in perspective time from proper time on their watches. More on this later.

Edited by ralfcis
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I no longer require this post as I no longer need to explain relativity using coordinate rotation.

Here's what it looks like to rotate 1 graph paper over another at the origin:

http://www.sciencech...=6117&mode=view

Here's the rotation at .6c. Notice .6c is not part of the stationary frame but is the ct' axis of the moving frame rotated.  Notice how the x'-axis folds up over the x-axis to have a positive slope for relativity. I'm sure there is a reason for this like avoiding bringing negative time into the slope of the x'-axis. Either way the x'-axis (which represents length contraction which I'll show later has no mathematical relevance) has no relevance to the velocities shown in this graph. x/ct is 1/slope of the .6c velocity line. x/ct' is 1/slope of the gamma velocity line which has a lot of significance which I'll explain later. ct'/ct is the velocity through time slope of the line which is .8c for a .6c velocity line.

The next graph shows the rotation continuing to .8c. You will notice the squares of the rotated cartesian coordinates start to swell. Also ct'/ct, the velocity of time through time = .6c for a .8c velocity through space. If I have time I'll plot a graph of Vvs vx for all vx from 0 to c. I'm not sure what it will look like.

If you're not following, you're not using pythagoras c2=a2+b2 to derive the answers I'm giving. Any questions? Maybe I should dump the algebra and use plain old arithmetical numeric examples. Most people can never get over the terror of using letters instead of numbers. I don't think you'll ever see a simpler mathematical derivation of relativity than this. I can go on and derive the formula of relativity of simultaneity and derive a conversion formula to time dilation (but I won't bother).

Edited by ralfcis
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I just read an article explaining why relativity's formula is

c2τ2=c2Δt2–Δx2

(mine is (ct)2 =(ct')2 + x2   which is exactly the same formula because t' is τ)

As stated in the article, the purpose is to artificially make c the same from all perspectives. c is the same from all perspectives anyway but this  math trick allows c from each perspective to be overlapped onto the same graphical 45o line. The lines may have the same slope but they do not share the same units. c in a .6c frames is actually two x units/ two t units whereas in the stationary frame it's one x unit/ one t unit. No one actually tells you of this charade as it has terrible implications if you try to use light signals between the two parties. The light signals may have the same slope but they do not have the same meaning and change length depending on who's stationary and who's moving. A Loedel STD will have equally long light lines but a Minkowski won't. Just more smoke and mirrors thrown at you that no one will admit to.

Edited by ralfcis
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The advantage of deriving relativity from plain old algebra is that it can catch instances where relativity slips in its own self-fulfilling assumptions. The math was fudged  to flip the x'-axis in what should have been a simple coordinate rotation so that all frames could share the same c line. This then affected the true length of the light signal lines between the participants and will influence how light signals report ages between the parties.The question we will explore in this section is if clocks all tick at the same universal rate within each frame and the speed of light is constant from all perspectives, can we use light signals to establish clock differences from the perspective of that universal clock rate? Can the universal accuracy of atomic clocks,  the universal clock rate of all frames,  and the resultant  hyperbolically connected clock readings be deemed a new universal present that will supercede Einstein's disjointed subjective presents of perspective?

We've already seen that relativity has made the light signals unreliable for this measurement but we can compensate for this using Loedel STD's. We also need to question whether Einstein's clock sync method somehow taints the results. In this day and age we do not need to consider his method because of the universal accuracy of atomic clocks. But since relativity likes to slip hidden assumptions into the math so that its prophesies are self-fullfilling, we need to use the algebraic method to identify if the clock sync method has deeply embedded itself to influence the theory or not.

One concept that has deeply embedded itself into relativity is length contraction. We've seen at .6c, the doppler shift ratio shows the rate of causal time for each of Bob and Alice's televised broadcast is mutually seen to be as half speed slow motion. The reciprocal time dilation is calculated to  show mutual clock readings as being 80% slower. The reciprocal of time dilation is a rate of perspective time equal to the velocity of time through time( v= c/Y). The doppler shift ratio is a rate of proper  time equal to the relativistic half speed of v. (Remember for vx  =.6c, v=.8c and vht =  c dsr= .5c)  More on this later.

The point being that why doesn't the doppler shift ratio show length contraction happening in the televised broadcast? Time dilation is showing up as slow motion so why wouldn't the video show Bob and Alice flatter in the direction of motion? As they moved around the cabin in slow motion, there should always be flattening on one side. Surely, that would be indisputable proof that length contraction is real and not some made up math construct of whether you stick Y with t or x in an equation. Einstein stuck Y with m instead of v in his derivation of E=mc2 and we got some ridiculous notion that matter starts bulging and multiplying the closer it approaches c. Matter is unaffected by this and it's some weird fluke that this analog formula became applicable to digital (quantum) nuclear reactions. How do they explain that? They don't, they keep that fact hidden.

Edited by ralfcis
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As I said, the basis of relativity is simple frame rotation between two inertial frames. But relativity took it a step further and rotated the x' axis in the opposite direction as it rotated the ct' axis in order that the two c lines artificially overlap. This is what length dilation (a new term that works like time dilation) and length contraction look like from relativity and from a simple rotation. They look the same either way.

The formulas for time dilation and length contraction are t=Yt' and x'=Yx, not quite the same but similar. The difference is clear in the STD. Time dilation is from Bob's perspective and length contraction is from Alice's perspective. It's like in the muon example where the travelling muon sees the distance it must travel to earth contract or the earth sees the muon has more time than the earth gives it to travel that distance. However, both effects are not happening concurrently. The muon doesn't get the double advantage of seeing the distance to earth shrink and that it gets more time from the earth`s perspective to do so. It's either or.

Most people have been brainwashed to think the muon example can only be solved using length contraction thereby length contraction is real. They ignore the fact the problem can be solved by time dilation from the earth's perspective and they are kept in the dark that the muon can see time contraction from it's perspective. Yes, that's right, time contraction. It's a line just like length contraction except it's a slanted line from t'=2 to t=1.6.

This simply means that all muons within their own frame have 2.5 time units to live (the muons are their own clocks) but they see the earth time contract to 1.6 time units for the distance they must cover which the earth and the muon agree upon before the muon starts moving. They then have plenty of time to cover that distance before their time runs out. No need to introduce length contraction as time dilation from either perspective solves the problem just fine.

PS. As a side note that will probably confuse you: Contraction can be thought of as double dilation. Bob can see through Alice's eyes what Bob's dilation looks like from her perspective. He sees her dilate, she sees him dilate so he can see from his perspective through Alice's perspective what his time contraction looks like.

PPS. My posts should be making relativists squeamish and they'll soon get out their tar and feathers and pitchforks and claim I am saying all this not from the simple math I'm showing but from a hidden agenda of a personal theory. My personal theory is way wilder than anything I`m presenting here. I`m just using math to help relativity at least get on the right path and then I`ll kill it anyway when I present my theory later.

If the cranks weren`t terrified of math and if they could read with comprehension, they`d be all over this thread but I`d prefer if those with math skills would challenge me here or declare that what I`m saying is correct.

Edited by ralfcis
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As promised it's time to make a graph of vt vs vx.

For vx =0, .1c, .2c, .3846c (5/13), .6c, .8c. .8824c (15/17), .9756c (40/41), c

v= c, .995c, .98c, .923c, .8c, .6c, .47c, .22c, 0

Y= 1, 1, 1.02, 1.083, 1.25, 1.67, 2.125, 4.55, infinity

We'll also plot the doppler shift ratio which is half relativistic speed of v

So dsr = c, .9c, .83c, .67c, .5c, .33c, .25c, .12c, 0

DSR vs vis surprisingly linear from 0 to .8824c.

Let me add the half relativistic speeds of vx

half speed 0f v= 0, .05c  ,.1c, .2c, .33c, .5c,  .6c, .8c, c

So the graph of vvs vis a circle with radius c. It's a result of the pythagorean relationship between the two. The numbers listed above will be referred to often.

It's not important if you don't see why I did this, it's more for me to graphically visualize what I was talking about earlier.

Edited by ralfcis
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I'm not fluent in word salad but I actually understand what you're saying. One guy admitted to me they spread the BS  until you're allowed to see the real theory way up in the academic level. Then it's no longer in algebra-land.

Delusional conspiracy theory stuff. Science does not work like that at all. Just read the book I recommended to you, or one like it. It is nobody's fault but your own if you won't do the hard work to master the theory, before you try to criticise it.

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