Time in Special Relativity

Dude, I have communicated in this forum and I am not interested in being measured by you.

I have produced a geometric object in the stationary frame that successfully maps each point to the moving light sphere. Each point is timed r/cγ and each point is a distance r/γ when mapped with LT just as Einstein claimed his proof did but failed.

\(\frac{(x-vr/c)^2}{(r)^2}+\frac{y^2}{(r/\gamma)^2}+\frac{z^2}{(r/\gamma)^2}=1\)

\(t = \sqrt{ x^2+y^2+z^2}/c\)

Now, take your little ole LT and show me you can map the entire stationary light sphere to the moving light sphere such that the moving light sphere is a distance k from the origin.

You cannot do it and yet mine does.

Therefore, your language and communication on this is incorrect and wrong.

Let me teach you.

The light sphere in the context of the moving frame must be a distance r in all directions just like the stationary light sphere.

When you have convinced yourself you cannot do it with the stationary light sphere, use my equation to get the correct answer.

Remember, for every point on the stationary light sphere of radius r, the corresponding mapped point must be a constant distance from the origin of the moving frame compared to all other mapped points.

 

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All you are doing is slicing the 4-D object of a light cone in the \((x,y,z,t)\) against a constant value of \(\tilde t\) which makes no sense to the observer in \((x,y,z,t)\) who sees the slices of constant \(t\) as spherically symettric.

Your objection is unreasoned and unphysical, since an observer in the \((x,y,z,t)\) frame only cares about slices of constant \(t\) and an observer in the \((\tilde x,\tilde y,\tilde z,\tilde t)\) frame only cares about slices of constant \(\tilde t\) when determining if something is spherical or not.

Better written as \(\begin{eqnarray} \left( \gamma(x-vr/c) \right)^2+y^2+z^2 & = & r^2 \\ c^2 t^2 - x^2 - y^2 - z^2 & = & 0 \end{eqnarray}\)
or for ultimate geometrical clarity \(\begin{eqnarray} \tilde x^2+\tilde y^2+\tilde z^2 & = & r^2 = c^2 \tilde t^2 \\ c^2 \tilde t^2 - \tilde x^2 - \tilde y^2 - \tilde z^2 & = & 0 \end{eqnarray}\)
to see that you are just talking about time slices where \(\tilde t = \frac{r}{c}\).

 

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Your problem is the following.

The objective is to prove for all points of some object in the stationary frame you can find the moving light sphere.

We already know Einstein's proof failed. It did not produce the moving light sphere such that each point of the mapping was a constant distance r from the origin in the moving frame.

You are simple quoting failed math that cannot achieve this objective.

Try to stay on task of the objective.

 

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If you are interested, I can do computer simulations.

If you want to test a model, I will make a picture of it and post the results.

All my theorems have been verified by simulations to .00000001.

I am sure you test your thinking this way.

Anyway give me a case and I will run it through my simulators.

I wil post the picture of the events.

 

I did not see this post.

Each point on the ellipsoid, using LT, maps to a constant distance from the light emission point in the moving frame.

I am not seeing your problem.

Neither you, AN, nor Einstein were able to do this.

However, before I make judgments, what do you mean by these slices since my proof fits the bill and Einstein's proof does not?

 

OK I see your objection now.

You are claming this ellipsoid is static.

I saw that also. Very good point.

You can prove the following,

Assume the stationary light sphere has acquired a radius r. Given ε > 0 , if the stationary light sphere expands (r+ε) and elapses (r+ε)/c since light emission, then the moving light sphere expands (r+ε)/γ and elapses (r+ε)/(cγ).

This eliminates your time slice problem.

If you want me to prove this I will.

 

Oh, this looks simple, the below equation is a stinking nasty rotten proof.

I just wrote it down but needs to be proved.

\(c^2 t^2 - x^2 - y^2 - z^2=0\)

This must be shown to be true for points on the ellipsoid. You can't just say it.

In fact, I proved it is true.

I also proved, in the moving frame t' = t/γ for all points on the ellipsoid.

 

You originally wrote:

and I applied only the most trivial mathematical operations to rearrange this in the form with the most digestible pedagogical content.

That this equation is implied by your equation is trivial to demonstrate.
Start with \(t = \sqrt{ x^2+y^2+z^2}/c\) -- Since it is legal to multiply both sides by equals, this implies \(c t = c \sqrt{ x^2+y^2+z^2}/c\) and since \(c \ne 0\) and multiplication is associative and commutative, it implies \(c t = \sqrt{ x^2+y^2+z^2}\) and since multiplying both size by equals is legal, \(c^2 t^2 = x^2+y^2+z^2\), finally we may add \(-x^2-y^2-z^2\) to both sides which results in \(c^2 t^2- x^2-y^2-z^2 = 0\) which is pedagogically important since the left size is preserved by the Lorentz transform and the right side is a constant which is independent of any choice of x or t.

 

Something wrong here that I didn't notice before. I have got to stop doing algebra at 4 in the morning.

 

There's a lot you don't see.

Jack, here's a verbal warning, if you continue to simply lie and demand people tell you things you've previously been told (and then ignored) or you claim no one has provided you with information when infact people have done so, multiple times, I'm going to start reporting your posts. You've been given the proof that light spheres map to light spheres about a dozen times now. All you're doing is just repeating the same thing again and again and then ignoring any time someone does provide the proof you demand. If you're unable to engage in an informed discussion then I'm going to start reporting your posts.

And your denouncement of everyone else and your claims to have killed SR aren't judgements? Your claim I'm too 'primitive' to keep up with you isn't a judgement?

So you don't even know what a time slice is?! I must have used the phrase dozens of times in my posts when I explained how the light sphere maps to a light sphere and only now you're admitting you don't know what they are? Clear evidence (further evidence) you simply ignore people's posts, despite demanding they reply to you, or lie about understanding them when you don't. And the fact you keep misusing the word 'proof' shows you haven't done all the 'decidable logic' you want people to think you have. When someone claiming to be educated in logic can't use the word 'proof' properly they are simply making a fool of themselves. But then I guess that's the least of your worries.

 

No, it is fine.

 

Sorry, I did not mean to imply that proof was hard.

This is the one that is hard.

\(t = \sqrt{ x^2+y^2+z^2}/c=r/c+v\sqrt{ r^2-(y\gamma)^2-(z\gamma)^2}/c^2\)

This relationship sets up the entire moving light sphere in the stationary frame.

r is the radius of the light sphere in the stationary frame and x,y,z are not on that radius except for two points but are on the ellipsoid.

 

I have no idea what you are talking about.

I have produced equations for a moving ellipsoid in the stationary frame that is the image of the light sphere in the moving frame.

It is different from the stationary light sphere.

You have the equations.

If they do not map with LT the the light sphere in the moving frame, then let me know.

 

No, I did not but I figured it out.

It is the differential of the times for the stationary light sphere at r/c and t' for a given point on the stationary light sphere.

Looks like we forgot the moving light sphere.

In reality, it turns out LT maps the time the stationary light sphere hits a point to the time the moving light sphere hits a point.

If that time in the moving frame is < r/(γc), then the moving light sphere already hit it before the stationary light sphere did. You can figure out the rest.

Do not forget, the conjunction of the light postulate and the relativity postulate must be simultaneously true in both frames.

You are used to switching light emission points in the frame to another by sheer will.

You then apply the conjunction of the light postulate and the relativity postulate.

Your problem is you have not figured out that science does not work by will and you need a mathematical mechanism to perform this switch. In other words, the switch must include the fact the light postulate and the relativity postulate and simultaneously true in both frames or the switch is not allowed.

I am providing that crossover to allow the switch between light emission points which diverge as the origins of the frames move.

However, in so doing, I can prove the moving light sphere has a faster speed in the direction of travel from the view of the stationary frame.

Do not forget, we are here because we looked at Einstein's consistency proof of relativity and found he did not map the stationary light sphere to the moving light sphere. He only mapped one point and if another point was selected from the stationary light sphere, his proof failed.

On the other hand, if Einstein's consistency proof had been correct, you could simply refute me and make me look silly, which of course you cannot do because his proof did not produce the moving light sphere.

 

The puzzle with time is that time we can not observe. We can observe only material change i.e. motion. Already Einstein and Gödel discuss the there is no time in the universe. Their idea is fully developed here. Clocks run in space only and not in time. Space itself is timeless. According to the formalism X4 = i x c x t fourth coordinate is spatial too. Time is not 4-th of space. Space-time is not 3D + T, space-time is 4D. Time “t” is a tick of clock and is only a component of X4. This is missing comprehension of SR. In SR space-time is timeless. Physical time is run of clock in space. There is no physical time behind run of clocks. Time dilatation means that clocks run slower; not because time shrinks, there is no time in the universe, universe is timeless.

With clocks we measure numerical order of material change i.e. motion. Fundamental unit of numerical order is Planck time. Planck time tp is derived from velocity of light that is as fundamental constancy of the universe: tp = pd /c, where pd is Planck distance. The smallest distance photon can move between two points A and B of space is Planck distance. Distance between A and B is a sum of Planck distances: d AB = sum dp1+ dp2 + dp3…….+ dpn. Numerical order of photon motion is tp1, tp2, tp3….tpn.

In the space “before” and “after” exist only in a sense of numerical order to, t1, t2, t3…tn of material change that we measure with clocks. In the same way as t2 is after t1, number 2 is after number 1. t0 presents beginning of the measurement, tn end of the measurement.

There is no travel into past as one can travel in space only. Some physical phenomena are immediate as EPR. For them tn is zero. Zeno problem of motion and time is resolved. Archile and turtle move in space only and not in time.

Velocity is derived from numerical order: v = d /tn.
Frequency is derived from numerical order: frequency = 1/tn.

View of physical time as a run of clocks in timeless space was published recently: - Amrit S. Sorli, Davide Fiscaletti, Dusan Klinar, Time is a measuring System derived from Light Speed, Physics Essays, Vol 23. Num 2. (2010)


We experience material change i.e. motion in the universe through the psychological time “past-present-future” that has its basis in neuronal activity of the brain. Recent research confirms that: - Catalin V. Buhusi, Warren H. Meck, What makes us thick?, Functional and neural mechanisms of interval timing, Nature reviews, Volume 6, October 2005

Universe is without time as predicted by Einstein and Gödel: -Yourgrau P, World without time: The forgotten legacy of Gödel and Einstein, Amazon (2006)

Understanding of timeless nature of the universe requires awareness of inner psychological time through which one experiences material change i.e. motion. Observer has ability to watch, to witness how scientific mind creates scientific theories. By developing this ability of watchfulness one discovers that inner psychological time is his/her basic frame of experience. He/she becomes aware of timeless nature of the universe.

 

This thread looks to have fallen apart.

Jack is banned three days for trolling---you are not welcomed to post your drivel here.