Trigonometry and Relativity

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Offline jeffreyH

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Trigonometry and Relativity
« on: 04/09/2016 14:40:29 »
Inspired by David Cooper I have put together the following. The range 0 to 1 relates directly to the sine and cosine functions within the range 0 to π/2 radians. This range can be used to represent the ration v/c that shows up as the ratio of squares in the gamma function.

So that if

θ = arcsin v/c

and

α = cos θ
β = sec θ

then length contraction l  and time dilation t can be expressed as

l = Lα
t = Tβ

where L = proper length and T = proper time. If we set c = 1 then we can relate this to the unit circle. This applies to quadrant I where all values are positive. Investigation of the angles involved and what they might imply is ongoing.
Fixation on the Einstein papers is a good definition of OCD.

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Offline GoC

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Re: Trigonometry and Relativity
« Reply #1 on: 04/09/2016 19:23:31 »
If you believe in Relativity and follow light being independent of the source it becomes obvious that all views are from the past. At relativistic speeds you move away from the image created faster and now view the image of the past at an angle different from perpendicular. The image contracts by the vector angle of the observer receiving the image. What could be simpler. Contraction is visual and not physical!

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Offline jeffreyH

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Re: Trigonometry and Relativity
« Reply #2 on: 04/09/2016 21:06:07 »
The only way that light is related to the above is via the speed of light (c) used in the ratio v/c. Nowhere do I mention photons?
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Offline GoC

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Re: Trigonometry and Relativity
« Reply #3 on: 04/09/2016 22:08:08 »
If your not relating those angles to SR relativity than you are just doing an exercise in trig. If there was no photons we would have no proper length to discuss. I felt it was implied. Forgive me if I was incorrect.

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Offline jeffreyH

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Re: Trigonometry and Relativity
« Reply #4 on: 04/09/2016 22:16:31 »
It would be better to have maxima along the positive x axis and minima perpendicular at 90 degrees.

So that

θ = arccos v/c

and

α = sin θ
β = csc θ

In which case we can attempt to map this positions in the gravitational field at varying potentials right up to the photon sphere and the event horizon of a Schwarzschild black hole.
Fixation on the Einstein papers is a good definition of OCD.

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Offline jeffreyH

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Re: Trigonometry and Relativity
« Reply #5 on: 04/09/2016 22:19:30 »
There, now I've mentioned photons.
Fixation on the Einstein papers is a good definition of OCD.

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Offline jeffreyH

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Re: Trigonometry and Relativity
« Reply #6 on: 05/09/2016 08:26:52 »
For related equations please see

https://www.av8n.com/physics/spacetime-trig.htm
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Offline Thebox

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Re: Trigonometry and Relativity
« Reply #7 on: 05/09/2016 10:15:20 »
Inspired by David Cooper I have put together the following. The range 0 to 1 relates directly to the sine and cosine functions within the range 0 to π/2 radians. This range can be used to represent the ration v/c that shows up as the ratio of squares in the gamma function.

So that if

θ = arcsin v/c

and

α = cos θ
β = sec θ

then length contraction l  and time dilation t can be expressed as

l = Lα
t = Tβ

where L = proper length and T = proper time. If we set c = 1 then we can relate this to the unit circle. This applies to quadrant I where all values are positive. Investigation of the angles involved and what they might imply is ongoing.


It is interesting how ''alien'' something looks when a person  like myself does not understand it.

Can you first explain cos and sin in simple terms?

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Offline jeffreyH

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Re: Trigonometry and Relativity
« Reply #8 on: 05/09/2016 12:04:34 »
Inspired by David Cooper I have put together the following. The range 0 to 1 relates directly to the sine and cosine functions within the range 0 to π/2 radians. This range can be used to represent the ration v/c that shows up as the ratio of squares in the gamma function.

So that if

θ = arcsin v/c

and

α = cos θ
β = sec θ

then length contraction l  and time dilation t can be expressed as

l = Lα
t = Tβ

where L = proper length and T = proper time. If we set c = 1 then we can relate this to the unit circle. This applies to quadrant I where all values are positive. Investigation of the angles involved and what they might imply is ongoing.


It is interesting how ''alien'' something looks when a person  like myself does not understand it.

Can you first explain cos and sin in simple terms?

https://en.m.wikipedia.org/wiki/Trigonometric_functions
Fixation on the Einstein papers is a good definition of OCD.

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Offline Thebox

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Re: Trigonometry and Relativity
« Reply #9 on: 07/09/2016 06:58:11 »
Inspired by David Cooper I have put together the following. The range 0 to 1 relates directly to the sine and cosine functions within the range 0 to π/2 radians. This range can be used to represent the ration v/c that shows up as the ratio of squares in the gamma function.

So that if

θ = arcsin v/c

and

α = cos θ
β = sec θ

then length contraction l  and time dilation t can be expressed as

l = Lα
t = Tβ

where L = proper length and T = proper time. If we set c = 1 then we can relate this to the unit circle. This applies to quadrant I where all values are positive. Investigation of the angles involved and what they might imply is ongoing.


It is interesting how ''alien'' something looks when a person  like myself does not understand it.

Can you first explain cos and sin in simple terms?

https://en.m.wikipedia.org/wiki/Trigonometric_functions

so x=cos  ?

y=sin?

tan= angle?


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Offline jeffreyH

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Re: Trigonometry and Relativity
« Reply #10 on: 07/09/2016 08:41:07 »
Careful now people might actually get the impression that you know this stuff. That can't possibly be true.
Fixation on the Einstein papers is a good definition of OCD.

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Offline Thebox

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Re: Trigonometry and Relativity
« Reply #11 on: 07/09/2016 08:49:42 »
Careful now people might actually get the impression that you know this stuff. That can't possibly be true.


I don't know this although I have glanced cos and sin before.   

I have no  idea why we call it cos and sin when x and y would seem to do, why do we rename X and Y ?


added- why can't we just overlay a protractor?






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Offline Colin2B

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Re: Trigonometry and Relativity
« Reply #12 on: 07/09/2016 09:30:03 »
I don't know this although I have glanced cos and sin before.   

I have no  idea why we call it cos and sin when x and y would seem to do, why do we rename X and Y ?
You are not just renaming them. You are using them in a formula, so you can show how x or y varies with the value of different angles, the protractor won't do that.

Have a real look at the link Jeff gave, not just a glance. This is one of the fundamentals of maths and it's worth understanding.
Note I say understanding, not just learning by rote.

PS you can find some good maths textbooks in German if that helps [;)]
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Offline Thebox

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Re: Trigonometry and Relativity
« Reply #13 on: 07/09/2016 16:57:44 »
I don't know this although I have glanced cos and sin before.   

I have no  idea why we call it cos and sin when x and y would seem to do, why do we rename X and Y ?
You are not just renaming them. You are using them in a formula, so you can show how x or y varies with the value of different angles, the protractor won't do that.

Have a real look at the link Jeff gave, not just a glance. This is one of the fundamentals of maths and it's worth understanding.
Note I say understanding, not just learning by rote.

PS you can find some good maths textbooks in German if that helps [;)]

I am reading it and have read it, do not yet understand  it .


Is tan=x,y?


edit - sorry ignore the tan =x,y , is X,Y equal to 90 degrees?  and then tan is worked within this?

added - I drew this so far?


Hope I am not spoiling your thread Jeff, I am trying to understand what you are discussing.

« Last Edit: 07/09/2016 17:17:01 by Thebox »

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Offline jeffreyH

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Re: Trigonometry and Relativity
« Reply #14 on: 07/09/2016 18:47:12 »
Think of a triangle with all 3 sides the same length. Two of the sides will form a right angle of 90 degrees (pi/2 radians). Sine, cosine and tangent can be described by the 'word' sohcahtoa. This stands for sine is opposite side divided by adjacent side, cosine is adjacent side divided by the hypotenuse and tangent is the opposite side divided by the adjacent side. Let me know when you have worked out why this is true. And no nonsense.
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Offline alancalverd

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Re: Trigonometry and Relativity
« Reply #15 on: 07/09/2016 23:31:50 »
Quote
Think of a triangle with all 3 sides the same length. Two of the sides will form a right angle of 90 degrees (pi/2 radians).

Oh no they won't!
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Offline jeffreyH

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Re: Trigonometry and Relativity
« Reply #16 on: 08/09/2016 00:56:46 »
Quote
Think of a triangle with all 3 sides the same length. Two of the sides will form a right angle of 90 degrees (pi/2 radians).

Oh no they won't!

Yes like what Alan said. No right angle. All the angles are ?? degrees. Hint they add up to 180. Tough crowd!
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Offline jeffreyH

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Re: Trigonometry and Relativity
« Reply #17 on: 08/09/2016 00:58:24 »
P.S. There are 3 angles.
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Offline Thebox

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Re: Trigonometry and Relativity
« Reply #18 on: 08/09/2016 08:14:02 »
P.S. There are 3 angles.

Now I am confused you seem to be arguing with each other about a triangle.


A triangle has 3 ''sides'' 


If cos=sin we have one 90 degree and two acute angles, if a triangle is an equilateral triangle, there is no 90 degree and 3 acutes?

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Offline jeffreyH

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Re: Trigonometry and Relativity
« Reply #19 on: 08/09/2016 08:22:38 »
P.S. There are 3 angles.

Now I am confused you seem to be arguing with each other about a triangle.


A triangle has 3 ''sides'' 


If cos=sin we have one 90 degree and two acute angles, if a triangle is an equilateral triangle, there is no 90 degree and 3 acutes?

Sorry for confusing you. Yes there are 3 acute angles in an equilateral. Keep on going. It's worth the effort.
Fixation on the Einstein papers is a good definition of OCD.

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Offline Thebox

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Re: Trigonometry and Relativity
« Reply #20 on: 08/09/2016 08:31:21 »
P.S. There are 3 angles.

Now I am confused you seem to be arguing with each other about a triangle.


A triangle has 3 ''sides'' 


If cos=sin we have one 90 degree and two acute angles, if a triangle is an equilateral triangle, there is no 90 degree and 3 acutes?

Sorry for confusing you. Yes there are 3 acute angles in an equilateral. Keep on going. It's worth the effort.

The easy way would  be to ''draw'' a square around the triangle and calculate within the square, however I do know that is not your way, so how do we work out the acute angles, I don't understand the formula as yet.

And how do we determine which way up the triangle is to apply cos and sin?

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Offline alancalverd

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Re: Trigonometry and Relativity
« Reply #21 on: 08/09/2016 10:13:19 »
The only time cos x  = sin x is when x = pi/4 or 5pi/4.

Wake up, guys, this stuff is pre-'O' level - in fact only just post-11-plus!
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Offline Thebox

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Re: Trigonometry and Relativity
« Reply #22 on: 08/09/2016 10:15:57 »
The only time cos x  = sin x is when x = pi/4 or 5pi/4.

Wake up, guys, this stuff is pre-'O' level - in fact only just post-11-plus!


Its only easy if you know the answer Alan, I have no idea about this subject, I am has fresh as a junior when it comes to this.


pi/4  I dont follow that?


If cos is ten miles long and sin is ten miles long, then surely cos=sin?  or am I confusing this with calculus?



« Last Edit: 08/09/2016 10:29:33 by Thebox »

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Offline alancalverd

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Re: Trigonometry and Relativity
« Reply #23 on: 08/09/2016 13:10:00 »
I strongly advise you to learn some elementary maths before paddling in the waters of science. Maths is the language of physics just as German is the language of Germany. 
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Offline Thebox

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Re: Trigonometry and Relativity
« Reply #24 on: 08/09/2016 13:15:02 »
I strongly advise you to learn some elementary maths before paddling in the waters of science. Maths is the language of physics just as German is the language of Germany.

I thought trig was maths?  that I have ventured into,  I know what  pi is and the divide by 4, but I dont get how that relates, but yes perhaps I should start with some maths less complex looking.

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Offline GoC

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Re: Trigonometry and Relativity
« Reply #25 on: 08/09/2016 16:25:51 »
Thebox

      Trig is just short hand geometry. First have a complete understanding of Pythagoras. I will give you an example using Relativity and Lorentz contraction. Relativity says light is independent of the source. Say we have two space ships going 1/2 the speed of light in parallel physically. A signal is sent from one ship to the other. It leaves as a reflected sphere of the ship. At half the speed of light the signal is sent from position x0y0 and you are physically at x0y4 when the signal is sent. You receive the signal sent from x0y0 when you reach x2y4. It is an arc angle in the sphere from the position of the past but it is a straight line vector to your position. Considering you were parallel (180 degrees) when the signal was sent the vector changes it to 30,60,90 degrees. A right triangle is created from the physical position from the past to your current physical position when receiving the signal. Because of the extra length light had to travel through space you get a contracted view. You can use a trig function to get that contracted view. Cos 30 = 0.866025 for half the speed of light. You might recognize that value in the Lorentz contraction. Sq. Rt. 1-1^2/2^2 = Sq. Rt. 1-0.25 = Sq. Rt. 0.75 = 0.866025.

What is the most interesting is you will have a different angle than parallel. There would be a rotation of the image because it was from the past position. You could actually view the front of the parallel ship from the past position when the signal was sent.

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Offline Colin2B

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Re: Trigonometry and Relativity
« Reply #26 on: 08/09/2016 23:37:12 »
If cos is ten miles long and sin is ten miles long, then surely cos=sin?  or am I confusing this with calculus?
Cos, sin and tan are not distances but ratios. Start with basics https://www.mathsisfun.com/algebra/trigonometry.html or you will always be confused.
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Offline Thebox

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Re: Trigonometry and Relativity
« Reply #27 on: 09/09/2016 21:32:45 »
If cos is ten miles long and sin is ten miles long, then surely cos=sin?  or am I confusing this with calculus?
Cos, sin and tan are not distances but ratios. Start with basics https://www.mathsisfun.com/algebra/trigonometry.html or you will always be confused.


Thank you Colin, that link looks a bit easier to understand.  I have the link open has I write.

Sine Function:
sin(θ) = Opposite / Hypotenuse
Cosine Function:
cos(θ) = Adjacent / Hypotenuse
Tangent Function:
tan(θ) = Opposite / Adjacent


cos is always the adjacent?

sin is always the opposite?

and tangent is always an ''hippopotamus''?  lol.

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Offline Colin2B

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Re: Trigonometry and Relativity
« Reply #28 on: 09/09/2016 22:49:45 »
.
and tangent is always an ''hippopotamus''?  lol.
Except you have forgotten the squaw on the other 2 hides lol lol

Glad you find that link easier. Perhaps we can let Jeff have his thread back!
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Offline jeffreyH

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Re: Trigonometry and Relativity
« Reply #29 on: 10/09/2016 11:54:06 »
If cos is ten miles long and sin is ten miles long, then surely cos=sin?  or am I confusing this with calculus?
Cos, sin and tan are not distances but ratios. Start with basics https://www.mathsisfun.com/algebra/trigonometry.html or you will always be confused.


Thank you Colin, that link looks a bit easier to understand.  I have the link open has I write.

Sine Function:
sin(θ) = Opposite / Hypotenuse
Cosine Function:
cos(θ) = Adjacent / Hypotenuse
Tangent Function:
tan(θ) = Opposite / Adjacent


cos is always the adjacent?

sin is always the opposite?

and tangent is always an ''hippopotamus''?  lol.

Since this is about triggernometry I think I'll call you Dave. Well Dave you see ratios is a funny thing ain't they. If you have 3/4 and you scale it up to 6/8 or 30/40 the answer is always the same. Just as if you scale up a particular triangle the sine, cosine and tangent will be the same. Hence you can find tables of values for these functions. So yer hippopotamus will always belong to the same squaw. All right my son?
Fixation on the Einstein papers is a good definition of OCD.

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Offline jeffreyH

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Re: Trigonometry and Relativity
« Reply #30 on: 10/09/2016 14:07:26 »
Ok, back to the point. The past and future light cones are related to Minkowski spacetime as can be seen on the following page.

https://en.m.wikipedia.org/wiki/Light_cone

I will be relating trigonometry to both Minkowski spacetime and the light cones in a slightly different way.
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Offline Thebox

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Re: Trigonometry and Relativity
« Reply #31 on: 10/09/2016 16:14:22 »
Ok, back to the point. The past and future light cones are related to Minkowski spacetime as can be seen on the following page.

https://en.m.wikipedia.org/wiki/Light_cone

I will be relating trigonometry to both Minkowski spacetime and the light cones in a slightly different way.



Sorry Jeff for interrupting again, would you like me to start a new thread?


, because the light cone at first glance is observer effect, directional light from such as a flashlight, when the obviously physicality of light is to permeate spherically. also the interpretation of the past and future is incorrect.


added - actually you are in new theories, therefore I can contest your thread?







« Last Edit: 10/09/2016 16:24:23 by Thebox »

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Offline jeffreyH

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Re: Trigonometry and Relativity
« Reply #32 on: 10/09/2016 20:30:10 »
I don't mind as long as you stay on topic. And don't ask about equilateral triangle's. Lol.
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Offline Thebox

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Re: Trigonometry and Relativity
« Reply #33 on: 10/09/2016 22:22:40 »
I don't mind as long as you stay on topic. And don't ask about equilateral triangle's. Lol.

OK, thank you Jeff, I intend to stay on topic to what you are mentioning. I clicked the link to find the light cone, I have seen this before but never discoursed it.

You say ....
''I will be relating trigonometry to both Minkowski spacetime and the light cones in a slightly different way.''


Interesting , but if you are basing something on the light cone model which is rather prehistoric and dated and rather lacks in logic, (i.e garbage), then surely your intentions can only show something from the light cone model that is equally false because the light cone model is false to begin with?

Also if you are relating trig to Minkowski space time, then surely as  space has no direction, lines or angles, your relating can be only expressed in virtual terms?


Although I have got to admit I still have no idea what you are talking about, but I do know the light cone is poor logic.



added - I extended the diagram for you Jeff. this may save you ''time''



« Last Edit: 11/09/2016 10:17:46 by Thebox »

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Offline David Cooper

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Re: Trigonometry and Relativity
« Reply #34 on: 11/09/2016 23:14:46 »
Hi Box,

What's the problem with light cones? They're simply a way of showing a sphere expanding over time by eliminating one (or two) space dimension(s) from the diagram and using one of the freed-up dimensions (the one running up and down the page) to show time. The cones that you're rejecting are pictures of a sphere expanding, so you just have to learn to read them the right way to recognise that.

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Offline Thebox

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Re: Trigonometry and Relativity
« Reply #35 on: 11/09/2016 23:17:41 »
Hi Box,

What's the problem with light cones? They're simply a way of showing a sphere expanding over time by eliminating one (or two) space dimension(s) from the diagram and using one of the freed-up dimensions (the one running up and down the page) to show time. The cones that you're rejecting are pictures of a sphere expanding, so you just have to learn to read them the right way to recognise that.


The interpretation of future and past  is incorrect and  a cone is not a sphere, the diagram looks like an over exaggerated Pulsar.

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Offline jeffreyH

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Re: Trigonometry and Relativity
« Reply #36 on: 12/09/2016 14:10:49 »
The light cone is a valid mathematical construct.
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Offline Thebox

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Re: Trigonometry and Relativity
« Reply #37 on: 12/09/2016 14:58:35 »
The light cone is a valid mathematical construct.


It may be, but  I miss the point of value or valid when the actual model is completely a false model and nothing like reality, so in which Universe is this any  use when it is made up and incorrect?

Please see past and future thread, I will leave this thread now Jeff because I can't be doing with contradiction and make  believe models with maths made to fit the model, a model that is not reality to begin with.


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Offline David Cooper

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Re: Trigonometry and Relativity
« Reply #38 on: 12/09/2016 18:18:06 »
The interpretation of future and past  is incorrect and  a cone is not a sphere, the diagram looks like an over exaggerated Pulsar.

I've drawn a couple of diagrams for you, both in the attached image. The top diagram is of two photons moving apart. To start with, they are both in position 1, then they move apart to the positions labelled as 2, then they move further apart to 3, then to 4, then to 5. You can only work out the timings of when the photons are in each of these places by reading the numbers.

In the lower diagram, the exact same events are shown, but this time we are showing time vertically, and that means we don't need the numbers any more to show us when the photons were in different places - we can tell where they were at different times simply by looking at how high up the diagrams they are. What we actually have is a series of one-dimensional pictures of the two photons, each of these pictures shown higher up the screen than the one before, but it is still a representation of two photons moving apart in opposite directions. The result is a more complex 2D picture taking up the shape of a "cone".
« Last Edit: 12/09/2016 18:20:43 by David Cooper »

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Offline David Cooper

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Re: Trigonometry and Relativity
« Reply #39 on: 12/09/2016 18:37:38 »
And now here's a similar set of diagrams which attempts to do the same thing with another space dimension included, so it's an expanding circle shown at higher levels in the cone each time. The top left diagram shows four photons moving outwards from the centre, but it's a confusing mess, made worse this time by the lack of numbers to help you work out which photons are the same photon at different times as they move apart. The diagram under it shows the same thing, but looking in at an angle such that the photons moving up and down the screen appear to be moving more slowly, but you should be able to imagine that they are on a surface like a table set out in front of you and that all four photons are still moving apart at the same speed as each other. The diagram on the right shows the same action again, but this time it uses height up the screen to indicate time, but with a complication in that after the photons have moved away from the start, the nearest photon to you is then shown lower on the screen than the one furthest from you for the same moment in time - this is the result of the limitations of trying to show three dimensions (two of space and one of time) on a 2D screen. I won't even attempt to show all three space dimensions plus one time dimension on a 2D screen - you are expected to use your imagination to make that leap for yourself, but the idea of using cones to describe expanding spheres is fully valid.
« Last Edit: 12/09/2016 18:41:45 by David Cooper »

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Offline Thebox

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Re: Trigonometry and Relativity
« Reply #40 on: 12/09/2016 19:48:40 »
And now here's a similar set of diagrams which attempts to do the same thing with another space dimension included, so it's an expanding circle shown at higher levels in the cone each time. The top left diagram shows four photons moving outwards from the centre, but it's a confusing mess, made worse this time by the lack of numbers to help you work out which photons are the same photon at different times as they move apart. The diagram under it shows the same thing, but looking in at an angle such that the photons moving up and down the screen appear to be moving more slowly, but you should be able to imagine that they are on a surface like a table set out in front of you and that all four photons are still moving apart at the same speed as each other. The diagram on the right shows the same action again, but this time it uses height up the screen to indicate time, but with a complication in that after the photons have moved away from the start, the nearest photon to you is then shown lower on the screen than the one furthest from you for the same moment in time - this is the result of the limitations of trying to show three dimensions (two of space and one of time) on a 2D screen. I won't even attempt to show all three space dimensions plus one time dimension on a 2D screen - you are expected to use your imagination to make that leap for yourself, but the idea of using cones to describe expanding spheres is fully valid.



Scratches head trying to relate any relativity to your diagrams.


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Offline David Cooper

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Re: Trigonometry and Relativity
« Reply #41 on: 12/09/2016 21:03:01 »
Scratches head trying to relate any relativity to your diagrams.

Well, given that the second of my attached diagrams has been viewed precisely zero times at a size big enough to deternine what it shows, I don't think I'll go to such trouble again. These cones represent expanding spheres whether you understand that or not, so rejecting them on the basis that they don't is an error, and that error is holding you back from understanding things. Perhaps you need to find an expert where you live to discuss this kind of stuff with so that they can do it more effectively than is possible through texts and static diagrams. It will likely take a lot of demonstrations in the air with lots of hand waving to get the ideas through.

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Offline jeffreyH

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Re: Trigonometry and Relativity
« Reply #42 on: 12/09/2016 21:07:13 »
fromage frais! fabrique belgique, di stefano. Such brilliance Trigger. I think the horse is fossilised no need to flog it
Fixation on the Einstein papers is a good definition of OCD.

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Offline Thebox

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Re: Trigonometry and Relativity
« Reply #43 on: 12/09/2016 22:47:23 »
Scratches head trying to relate any relativity to your diagrams.
Perhaps you need to find an expert where you live to discuss this kind of stuff with so that they can do it more effectively than is possible through texts and static diagrams. It will likely take a lot of demonstrations in the air with lots of hand waving to get the ideas through.


My pc is on my big tele, I also have my pages zoomed at about 130%, it is a big diagram relative to me.

And yes , perhaps I do need find a local expert, I can show things on a chalk board and with a few various accessories far easier.


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Offline jeffreyH

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Re: Trigonometry and Relativity
« Reply #44 on: 17/09/2016 20:06:31 »
Think of a triangle with all 3 sides the same length. Two of the sides will form a right angle of 90 degrees (pi/2 radians). Sine, cosine and tangent can be described by the 'word' sohcahtoa. This stands for sine is opposite side divided by adjacent side, cosine is adjacent side divided by the hypotenuse and tangent is the opposite side divided by the adjacent side. Let me know when you have worked out why this is true. And no nonsense.

To correct an error a triangle with its two legs the same length, called a right and isoceles triangle, is what was intended above. Apologies for the confusion.
Fixation on the Einstein papers is a good definition of OCD.