Pythagore and Gamma

[Jacques]

When I look at the gamma factor in relativity equations, I always see the Pythagore theorem

 

[math]\gamma=\sqrt{1-v^2/c^2}[/math]

If we take c for unit of speed we get

[math]\gamma=\sqrt{1-v^2/1^2}=\sqrt{1-v^2}[/math] and [math] 1=1^2 [/math]

so we can write

[math]\gamma=\sqrt{c^2-v^2}[/math]

[math]\gamma^2=c^2-v^2[/math]

[math]c^2=\gamma^2+v^2[/math]

 

When the gamma factor is applied to time, it make me thinks that time is more than one dimentionnal.

What do you think about that ?

[Johnny5]

When I look at the gamma factor in relativity equations' date=' I always see the Pythagore theorem

 

[math']\gamma=\sqrt{1-v^2/c^2}[/math]

If we take c for unit of speed we get

[math]\gamma=\sqrt{1-v^2/1^2}=\sqrt{1-v^2}[/math] and [math] 1=1^2 [/math]

so we can write

[math]\gamma=\sqrt{c^2-v^2}[/math]

[math]\gamma^2=c^2-v^2[/math]

[math]c^2=\gamma^2+v^2[/math]

 

When the gamma factor is applied to time, it make me thinks that time is more than one dimentionnal.

What do you think about that ?

 

Are you trying to imply that using a quadratic in the formulas, leads to something strange about time, i.e. it is two dimensional, when your intuition says it's one dimensional?

 

What are you trying to imply with the above argument?

[Jacques]

Exactly that time is more than 1 dimensional and my feeling is that it is 3 dimensional.

[Johnny5]

Exactly that time is more than 1 dimensional and my feeling is that it is 3 dimensional.

 

Well time isn't a dimension.

 

Regards

[Jacques]

Isn't it the 4th dimension in relativity ?

[Johnny5]

Isn't it the 4th dimension in relativity ?

 

There is a variable t, for time, used in relativity, and three spatial variables x,y,z. But what do you mean by the term 'dimension' ?

 

Regards

[□h=-16πT]

Yes the Pythagorean theorem is supposed to be in there. The gamma factor present in the time dilation and length contraction formulae come from the use of the minkowski interval. This interval is itself a slight variation on the Pythagorean theorem. Look it up. However, not to the extent of your last line, which is wrong.

[[Tycho?]]

There is a variable t' date=' for time, used in relativity, and three spatial variables x,y,z. But what do you mean by the term 'dimension' ?

 

Regards[/quote']

 

Dimension as in something required to define an event. You need x,y,z, and t. And yes, time is considered a dimension in relativity, hence the term "space-time".

[Jacques]

Johnny5

There are many way to define dimension. One definition is: dimension is the number of variables needed to describe a quatity. For example space need 3 variables to be defined (x,y,z). In relativity time is one dimensional (t) . Colors models use on computer and television are 3 dimensional (Red,Green,Blue)

 

□h=-16πT I will do some reading on that. I found that link on google http://www.voting.ukscientists.com/interva.html

 

Here is a link that consider time as a vector

http://members.triton.net/daveb/

What do you think of this site ?