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# Minkowski SpaceTime diagrams re assigned

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9 minutes ago, TheProdigalProdigy said:

1.He is not using the diagram to prove anything, although it's a tool that can be used in a proof of such things.

2.) That's called reductive arithmetic. Like condensing a convoluted paragraph.

Well, due to the number of contestable choices he makes in the development of his diagram, its not really a very useful tool is it? It can hardly be used as support for any theory.

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Ok, consider these two equations that relate to the derivation of the Lorentz transformation.

They are done by Sal, from one Lecture, and the first is the initial equation, the second is after he starts to stuff it up beyond all usefulness. (replacing t with ct is the very problem.) ##### Share on other sites

Just now, marcospolo said:

Equation two:

Now what I want you to do, is (without any simplification at all) just assign actual numerical values for all the variables. then do the math.

Repeat with same variables on the second equation.

You will learn that the two equations that are supposed to be the one magic equation of Lorentz, end up giving two totally different results.

This can only mean that a mistake was made when going from equation one, to equation two.

let c=300, v=200, t = 1 make up some hard values then figure it out. Irrespective of the numbers used, the two equations should come up with the same result. But they dont. ##### Share on other sites

1 minute ago, TheProdigalProdigy said:

I don't see how this has anything to do with demonstrating how relativistic change is measured via plot segmentation despite the fact that, per segment, there is no such change.

Well, as Einstein relied on Minkowski for his spacetime diagram, which is intertwined with both Special and General Relativity, I thought i was a good time to look at the same issue of the validity of Time Dilation and Length contraction from the Lorentz point of view, also used by Einstein in his theory.

If Lorentz math is nonsense then so too is spacetime and special reactivity.

So humor me, do the simple math as per the one equation, at two different stages of its development.

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3 minutes ago, TheProdigalProdigy said:

Okay now I see how it relates.

Giving two results is the point of having a stationary and non-stationary observer. It seems like Sal succeeded.

No.  No no.  The inclusion of the gamma factor which you can supply from published calculations for a given velocity, so you can plug that into the equations to match the velocity you have chosen... well, the equation will totally balance BECAUSE of the gamma correction factor. Its not supposed to balance without gamma.

But to kick off, the left side of the equation at picture one, does not even equal the left side of the same equation at picture two!

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3 minutes ago, marcospolo said:

No.  No no.  The inclusion of the gamma factor which you can supply from published calculations for a given velocity, so you can plug that into the equations to match the velocity you have chosen... well, the equation will totally balance BECAUSE of the gamma correction factor. Its not supposed to balance without gamma.

But to kick off, the left side of the equation at picture one, does not even equal the left side of the same equation at picture two!

ALSO,  if you delete the "Gamma squared" from equation one, you get a perfectly balanced equation. Add gamma, and it becomes unbalanced.

But in the second version of the same equation, you end up with gibberish no matter it has gamma or not.

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2 minutes ago, TheProdigalProdigy said:

That's because the ct observer operates under the laws of special relativity. How that differs from observer (left side of the equation) is an example of General Covariance.

Its an equation that supposed to have both sides always equal on value.

But the same equation as its developed, becomes unequal, AND also gives a totally different value for the left side when all they did was swap variables that were identical in value. x=ct   so they swapped x for ct.

anyway, equation vs1 version has a different end result than the same equation at version 2.

So there must be a mistake in there. No excuses.

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1 minute ago, TheProdigalProdigy said:

ct and t y values are not supposed to be the same.

we assigned constant numerical values for all variables, so the equation which balances WITHOUT gamma in Picture 1, MUST also balance out for the same equation in Picture 2.

But it does not. Please explain. (it does not even balance out when you use gamma.)

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1 minute ago, TheProdigalProdigy said:

Are you talking about what Wigner labeled as Minkowski's "geometric symmetry" in his 4D mod for SR?

Well they would be if both observers were stationary (t) or SR (ct). That's why it's General Covariance and not Special Invariance.

I supplied you with two pictures.

In pic one, there was an equation for lorentz transform.

In pic two, the very same equation was "simplified" or in the process of simplification.

The original equation was based on Galilean transform where both sides would balance exactly. x=x'-vt

If we use real values for all variables and constants, the first version of the equation balances out correctly without using gamma.

But using the same values, we get a totally different result in version two. And gamma makes it worse.

This means an error has been introduced.

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2 minutes ago, TheProdigalProdigy said:

ct=/=t

I don't see any final numerical result of the equations here.

what does ct=/=t mean in English? And I don't see that in the equations either.

Why not say that because I can flip pancakes at 100 times a second, we can therefore substitute pancakes where we have seconds, in an equation that's expecting seconds. because pancakes flipping =/= second.

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8 minutes ago, TheProdigalProdigy said:

The variables can be constant in each but unequal from one another, for two graphs

the equations are  the same equation, in the process of simplification and substitution.

But a discrepancy has appeared in the second incarnation.

(a discrepancy means a error)

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1 minute ago, TheProdigalProdigy said:

But one variable in pic 1 was different than in pic 2

which variable change and why?

anyway, you are still left with the same issue.

You recall that Sal was working through the development of the gamma factor according to Lorentz.

The end result would be an equation that provided the solution for Gamma for a specific velocity.

But the two equations, given the same velocity, both end up with different results.

Mathematics, algebra say that these two versions of the same equation must provide the same result. They do not.

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8 minutes ago, TheProdigalProdigy said:

I know you know exactly what I'm referring to because you used the word picture and now you're using the word equation exclusively. Picture 1 was deleted from a post I made so I know you saw that it was t not ct

The picture you used was from the Khan video called, "Visualizing multiple Newtonian path–time diagrams"

where the "y axis is labeled "t", for time.

I am not using information from this video.

My two pictures are of the same equation, in different stages of development.

My video and equations are from Sal's lesson entitled, "Lorentz transformation derivation part 1 "

The y axis is now labeled ct. but it is exactly equal numerically to the numerical value of the x axis units. namely the distance light goes in one second. 3,000,000 meters in one unit on x axis, and 3,000,000 meters is one unit on the scale of Y axis. But before, x scale units were equal to 3,000,000, BUT y scale units were equal to ONE.  This is a ratio of 1:3 million. but now in the revised equation, the scale is 1:1 yet nothing has changed visually.

This is possible in a diagram to organize it like this, but it will give errors if you just equate one unit of x axis is the same numeral as the y axis, when the actual unit types are incompatible.

For instance, what is the answer when you subtract 2 from 4?  Answer is 2

How about subtract 2 cows from 4 gallons? This is impossible because you have mixed incompatible types.

Same where you have in the lorentz equation, subtraction of a velocity from a distance in meters. Its impossible.

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4 minutes ago, TheProdigalProdigy said:

That's ridiculous man, come on.

I know it ridiculous, that why I don't like it when you do it in the lorentz equation.

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6 minutes ago, TheProdigalProdigy said:

Okay, misunderstanding but it seems like you're straw-grasping for a non-contradiction in the use of the diagram or trying disprove lorentz contraction or the use of a plain t y axis as an example of a stationary observer, because of ratio inequalities in two equations that may or may not be related?

the "two" equations are the very same equation, yet they compute to a different result given the same input data. 