Embed Size (px)
Citation preview
8/14/2019 Mathematics for the Univocity of Space-Time by Parker Emmerson 2010
http://slidepdf.com/reader/full/mathematics-for-the-univocity-of-space-time-by-parker-emmerson-2010 1/28
8/14/2019 Mathematics for the Univocity of Space-Time by Parker Emmerson 2010
http://slidepdf.com/reader/full/mathematics-for-the-univocity-of-space-time-by-parker-emmerson-2010 2/28
In[8]:= PolarPlotB2 p 4 p - 2 p + p 2 - p 2 Sin@bD2 2 p + p 2 - p 2 Sin@bD2
4 p - 2 p + p 2 - p 2 Sin@bD2 2 p + p 2 - p 2 Sin@bD2, 8b, - p ê 2, p ê 2<F
Out[8]=5 10 15 20 25
-1.0
-0.5
0.5
1.0
In[45]:= SphericalPlot3DB2 p 4 p - 2 p + p 2 - p 2 Sin@bD2 q
H4 p - qL q, 8q, - 2 p , 2 p <, 8b, - p ê 2, p ê 2<F
Out[45]=
2 Mathematics for the Univocity of Space-Time by Parker Emmerson 2010.nb
Printed by Mathematica for Students
8/14/2019 Mathematics for the Univocity of Space-Time by Parker Emmerson 2010
http://slidepdf.com/reader/full/mathematics-for-the-univocity-of-space-time-by-parker-emmerson-2010 3/28
In[46]:= SphericalPlot3DB2 p H4 p - qL 2 p + p 2 - p 2 Sin@bD2
H4 p - qL q, 8q, - 2 p , 2 p <, 8b, - p ê 2, p ê 2<F
Out[46]=
Mathematics for the Univocity of Space-Time by Parker Emmerson 2010.nb 3
Printed by Mathematica for Students
8/14/2019 Mathematics for the Univocity of Space-Time by Parker Emmerson 2010
http://slidepdf.com/reader/full/mathematics-for-the-univocity-of-space-time-by-parker-emmerson-2010 4/28
In[47]:= SphericalPlot3DB2 p H4 p - qL q
4 p - 2 p + p 2 - p 2 Sin@bD2 q
, 8q, - 2 p , 2 p <, 8b, - p ê 2, p ê 2<F
Out[47]=
4 Mathematics for the Univocity of Space-Time by Parker Emmerson 2010.nb
Printed by Mathematica for Students
8/14/2019 Mathematics for the Univocity of Space-Time by Parker Emmerson 2010
http://slidepdf.com/reader/full/mathematics-for-the-univocity-of-space-time-by-parker-emmerson-2010 5/28
In[1]:= SphericalPlot3DB2 p H4 p - qL q
H4 p - qL 2 p + p 2 - p 2 Sin@bD2, 8q, - 2 p , 2 p <, 8b, - p ê 2, p ê 2<F
Out[1]=
In[3]:=
2 p 4 p - 2 p + p 2 - p 2 Sin@bD2 2 p + p 2 - p 2 Sin@bD2
H4 p - qL q=
2 p 4 p - 2 p + p 2 - p 2 Sin@bD2 q
4 p - 2 p + p 2 - p 2 Sin@bD2 q
=
2 p 4 p - 2 p + p 2 - p 2 Sin@bD2 q
H4 p - qL 2 p + p 2 - p 2 Sin@bD2
Mathematics for the Univocity of Space-Time by Parker Emmerson 2010.nb 5
Printed by Mathematica for Students
8/14/2019 Mathematics for the Univocity of Space-Time by Parker Emmerson 2010
http://slidepdf.com/reader/full/mathematics-for-the-univocity-of-space-time-by-parker-emmerson-2010 6/28
In[19]:= SphericalPlot3DB2 p 4 p - 2 p + p 2 - p 2 Sin@bD2 2 p + p 2 - p 2 Sin@bD2
H4 p - qL q,
8q, - 2 p , 2 p <, 8b, - p ê 2, p ê 2<F
Out[19]=
6 Mathematics for the Univocity of Space-Time by Parker Emmerson 2010.nb
Printed by Mathematica for Students
8/14/2019 Mathematics for the Univocity of Space-Time by Parker Emmerson 2010
http://slidepdf.com/reader/full/mathematics-for-the-univocity-of-space-time-by-parker-emmerson-2010 7/28
8/14/2019 Mathematics for the Univocity of Space-Time by Parker Emmerson 2010
http://slidepdf.com/reader/full/mathematics-for-the-univocity-of-space-time-by-parker-emmerson-2010 8/28
8 Mathematics for the Univocity of Space-Time by Parker Emmerson 2010.nb
Printed by Mathematica for Students
8/14/2019 Mathematics for the Univocity of Space-Time by Parker Emmerson 2010
http://slidepdf.com/reader/full/mathematics-for-the-univocity-of-space-time-by-parker-emmerson-2010 9/28
In[16]:= SphericalPlot3DB2 p 4 p - 2 p + p 2 - p 2 Sin@bD2 q
H4 p - qL 2 p + p 2 - p 2 Sin@bD2, 8q, - 4 p , 4 p <, 8b, - p , p <F
Out[16]=
2 p H4 p - qL 2 p + p 2 - p 2 Sin@bD2
H4 p - qL q=
2 p H4 p - qL 2 p + p 2 - p 2 Sin@bD2
4 p - 2 p + p
2
- p
2
Sin@bD2
q
=
2 p H4 p - qL 2 p + p 2 - p 2 Sin@bD2
H4 p - qL 2 p + p
2
- p
2
Sin@bD2
Mathematics for the Univocity of Space-Time by Parker Emmerson 2010.nb 9
Printed by Mathematica for Students
8/14/2019 Mathematics for the Univocity of Space-Time by Parker Emmerson 2010
http://slidepdf.com/reader/full/mathematics-for-the-univocity-of-space-time-by-parker-emmerson-2010 10/28
In[13]:= SphericalPlot3DB2 p H4 p - qL 2 p + p 2 - p 2 Sin@bD2
4 p - 2 p + p 2 - p 2 Sin@bD2 q
, 8q, - 4 p , 4 p <, 8b, - p , p <F
Out[13]=
10 Mathematics for the Univocity of Space-Time by Parker Emmerson 2010.nb
Printed by Mathematica for Students
8/14/2019 Mathematics for the Univocity of Space-Time by Parker Emmerson 2010
http://slidepdf.com/reader/full/mathematics-for-the-univocity-of-space-time-by-parker-emmerson-2010 11/28
In[15]:= SphericalPlot3DB2 p H4 p - qL 2 p + p 2 - p 2 Sin@bD2
H4 p - qL 2 p + p 2 - p 2 Sin@bD2, 8q, - 2 p , 2 p <, 8b, - p ê 2, p ê 2<F
Out[15]=
2 p H4 p - qL q
4 p - 2 p + p 2 - p 2 Sin@bD2 q
=2 p H4 p - qL q
4 p - 2 p + p 2 - p 2 Sin@bD2 2 p + p 2 - p 2 Sin@bD2=
2 p 4 p - 2 p + p 2 - p 2 Sin@bD2 2 p + p 2 - p 2 Sin@bD2
4 p - 2 p + p 2 - p 2 Sin@bD2 q
Mathematics for the Univocity of Space-Time by Parker Emmerson 2010.nb 11
Printed by Mathematica for Students
8/14/2019 Mathematics for the Univocity of Space-Time by Parker Emmerson 2010
http://slidepdf.com/reader/full/mathematics-for-the-univocity-of-space-time-by-parker-emmerson-2010 12/28
SphericalPlot3DB2 p H4 p - qL q
4 p - 2 p + p 2 - p 2 Sin@bD2 2 p + p 2 - p 2 Sin@bD2,
8q, - 2 p , 2 p <, 8b, - p ê 2, p ê 2<F
Out[21]=
12 Mathematics for the Univocity of Space-Time by Parker Emmerson 2010.nb
Printed by Mathematica for Students
8/14/2019 Mathematics for the Univocity of Space-Time by Parker Emmerson 2010
http://slidepdf.com/reader/full/mathematics-for-the-univocity-of-space-time-by-parker-emmerson-2010 13/28
In[23]:= SphericalPlot3DB
2 p 4 p - 2 p + p 2 - p 2 Sin@bD2 2 p + p 2 - p 2 Sin@bD2
4 p - 2 p + p 2 - p 2 Sin@bD2 q
, 8q, - 4 p , 4 p <, 8b, - p , p <F
Out[23]=
Mathematics for the Univocity of Space-Time by Parker Emmerson 2010.nb 13
Printed by Mathematica for Students
8/14/2019 Mathematics for the Univocity of Space-Time by Parker Emmerson 2010
http://slidepdf.com/reader/full/mathematics-for-the-univocity-of-space-time-by-parker-emmerson-2010 14/28
In[25]:= SphericalPlot3DB
2 p 4 p - 2 p + p 2 - p 2 Sin@bD2 q
4 p - 2 p + p 2 - p 2 Sin@bD2 2 p + p 2 - p 2 Sin@bD2, 8q, - 4 p , 4 p <, 8b, - p , p <F
14 Mathematics for the Univocity of Space-Time by Parker Emmerson 2010.nb
Printed by Mathematica for Students
8/14/2019 Mathematics for the Univocity of Space-Time by Parker Emmerson 2010
http://slidepdf.com/reader/full/mathematics-for-the-univocity-of-space-time-by-parker-emmerson-2010 15/28
Conclusion
r Ø2 p H4 p - qL q
H4 p - qL q
t = q ê k = q ê 2 p
q = 2 p t
r Ø2 p H4 p - qL q
H4 p - qL q
In[27]:= q := 2 p t
Mathematics for the Univocity of Space-Time by Parker Emmerson 2010.nb 15
Printed by Mathematica for Students
8/14/2019 Mathematics for the Univocity of Space-Time by Parker Emmerson 2010
http://slidepdf.com/reader/full/mathematics-for-the-univocity-of-space-time-by-parker-emmerson-2010 16/28
In[28]:= SphericalPlot3DB2 p 4 p - 2 p + p 2 - p 2 Sin@bD2 q
H4 p - qL q, 8t, - 1, 1<, 8b, - p ê 2, p ê 2<F
Out[28]=
16 Mathematics for the Univocity of Space-Time by Parker Emmerson 2010.nb
Printed by Mathematica for Students
8/14/2019 Mathematics for the Univocity of Space-Time by Parker Emmerson 2010
http://slidepdf.com/reader/full/mathematics-for-the-univocity-of-space-time-by-parker-emmerson-2010 17/28
In[29]:= SphericalPlot3DB2 p H4 p - qL 2 p + p 2 - p 2 Sin@bD2
H4 p - qL q, 8t, - 1, 1<, 8b, - p ê 2, p ê 2<F
Out[29]=
Mathematics for the Univocity of Space-Time by Parker Emmerson 2010.nb 17
Printed by Mathematica for Students
8/14/2019 Mathematics for the Univocity of Space-Time by Parker Emmerson 2010
http://slidepdf.com/reader/full/mathematics-for-the-univocity-of-space-time-by-parker-emmerson-2010 18/28
In[30]:= SphericalPlot3DB2 p H4 p - qL q
4 p - 2 p + p 2 - p 2 Sin@bD2 q
, 8t, - 1, 1<, 8b, - p ê 2, p ê 2<F
Out[30]=
18 Mathematics for the Univocity of Space-Time by Parker Emmerson 2010.nb
Printed by Mathematica for Students
8/14/2019 Mathematics for the Univocity of Space-Time by Parker Emmerson 2010
http://slidepdf.com/reader/full/mathematics-for-the-univocity-of-space-time-by-parker-emmerson-2010 19/28
In[31]:= SphericalPlot3DB2 p H4 p - qL q
H4 p - qL 2 p + p 2 - p 2 Sin@bD2, 8t, - 1, 1<, 8b, - p ê 2, p ê 2<F
Out[31]=
In[3]:=
2 p 4 p - 2 p + p 2 - p 2 Sin@bD2 2 p + p 2 - p 2 Sin@bD2
H4 p - qL q=
2 p 4 p - 2 p + p 2 - p 2 Sin@bD2 q
4 p - 2 p + p 2 - p 2 Sin@bD2 q
=
2 p 4 p - 2 p + p 2 - p 2 Sin@bD2 q
H4 p - qL 2 p + p 2 - p 2 Sin@bD2
Mathematics for the Univocity of Space-Time by Parker Emmerson 2010.nb 19
Printed by Mathematica for Students
8/14/2019 Mathematics for the Univocity of Space-Time by Parker Emmerson 2010
http://slidepdf.com/reader/full/mathematics-for-the-univocity-of-space-time-by-parker-emmerson-2010 20/28
In[32]:= SphericalPlot3DB2 p 4 p - 2 p + p 2 - p 2 Sin@bD2 2 p + p 2 - p 2 Sin@bD2
H4 p - qL q,
8t, - 1, 1<, 8b, - p ê 2, p ê 2<F
Out[32]=
20 Mathematics for the Univocity of Space-Time by Parker Emmerson 2010.nb
Printed by Mathematica for Students
8/14/2019 Mathematics for the Univocity of Space-Time by Parker Emmerson 2010
http://slidepdf.com/reader/full/mathematics-for-the-univocity-of-space-time-by-parker-emmerson-2010 21/28
In[33]:= SphericalPlot3DB2 p 4 p - 2 p + p 2 - p 2 Sin@bD2 q
4 p - 2 p + p 2 - p 2 Sin@bD2 q
, 8t, - 2, 2<, 8b, - p , p <F
Out[33]=
Mathematics for the Univocity of Space-Time by Parker Emmerson 2010.nb 21
Printed by Mathematica for Students
8/14/2019 Mathematics for the Univocity of Space-Time by Parker Emmerson 2010
http://slidepdf.com/reader/full/mathematics-for-the-univocity-of-space-time-by-parker-emmerson-2010 22/28
In[35]:= SphericalPlot3DB2 p 4 p - 2 p + p 2 - p 2 Sin@bD2 q
H4 p - qL 2 p + p 2 - p 2 Sin@bD2, 8t, - 2, 2<, 8b, - p , p <F
Out[35]=
2 p H4 p - qL 2 p + p 2 - p 2 Sin@bD2
H4 p - qL q=
2 p H4 p - qL 2 p + p 2 - p 2 Sin@bD2
4 p - 2 p + p 2 - p 2 Sin@bD2 q=
2 p H4 p - qL 2 p + p 2 - p 2 Sin@bD2
H4 p - qL 2 p + p 2 - p 2 Sin@bD2
22 Mathematics for the Univocity of Space-Time by Parker Emmerson 2010.nb
Printed by Mathematica for Students
8/14/2019 Mathematics for the Univocity of Space-Time by Parker Emmerson 2010
http://slidepdf.com/reader/full/mathematics-for-the-univocity-of-space-time-by-parker-emmerson-2010 23/28
In[36]:= SphericalPlot3DB2 p H4 p - qL 2 p + p 2 - p 2 Sin@bD2
4 p - 2 p + p 2 - p 2 Sin@bD2 q
, 8t, - 2, 2<, 8b, - p , p <F
Out[36]=
Mathematics for the Univocity of Space-Time by Parker Emmerson 2010.nb 23
Printed by Mathematica for Students
8/14/2019 Mathematics for the Univocity of Space-Time by Parker Emmerson 2010
http://slidepdf.com/reader/full/mathematics-for-the-univocity-of-space-time-by-parker-emmerson-2010 24/28
In[37]:= SphericalPlot3DB2 p H4 p - qL 2 p + p 2 - p 2 Sin@bD2
H4 p - qL 2 p + p 2 - p 2 Sin@bD2, 8t, - 2, 2<, 8b, - p ê 2, p ê 2<F
Out[37]=
2 p H4 p - qL q
4 p - 2 p + p 2 - p 2 Sin@bD2 q
=2 p H4 p - qL q
4 p - 2 p + p 2 - p 2 Sin@bD2 2 p + p 2 - p 2 Sin@bD2=
2 p 4 p - 2 p + p 2 - p 2 Sin@bD2 2 p + p 2 - p 2 Sin@bD2
4 p - 2 p + p 2 - p 2 Sin@bD2 q
24 Mathematics for the Univocity of Space-Time by Parker Emmerson 2010.nb
Printed by Mathematica for Students
8/14/2019 Mathematics for the Univocity of Space-Time by Parker Emmerson 2010
http://slidepdf.com/reader/full/mathematics-for-the-univocity-of-space-time-by-parker-emmerson-2010 25/28
In[38]:= SphericalPlot3DB2 p H4 p - qL q
4 p - 2 p + p 2 - p 2 Sin@bD2 2 p + p 2 - p 2 Sin@bD2,
8t, - 2, 2<, 8b, - p ê 2, p ê 2<F
Out[38]=
In[39]:= SphericalPlot3DB
2 p 4 p - 2 p + p 2 - p 2 Sin@bD2 2 p + p 2 - p 2 Sin@bD2
4 p - 2 p + p 2 - p 2 Sin@bD2 q
, 8t, - 2, 2<, 8b, - p , p <F
Mathematics for the Univocity of Space-Time by Parker Emmerson 2010.nb 25
Printed by Mathematica for Students
8/14/2019 Mathematics for the Univocity of Space-Time by Parker Emmerson 2010
http://slidepdf.com/reader/full/mathematics-for-the-univocity-of-space-time-by-parker-emmerson-2010 26/28
In[40]:= SphericalPlot3DB2 p 4 p - 2 p + p 2 - p 2 Sin@bD2 q
4 p - 2 p + p 2 - p 2 Sin@bD2 2 p + p 2 - p 2 Sin@bD2, 8t, - 2, 2<, 8b, - p , p <F
26 Mathematics for the Univocity of Space-Time by Parker Emmerson 2010.nb
Printed by Mathematica for Students
8/14/2019 Mathematics for the Univocity of Space-Time by Parker Emmerson 2010
http://slidepdf.com/reader/full/mathematics-for-the-univocity-of-space-time-by-parker-emmerson-2010 27/28
Mathematics for the Univocity of Space-Time by Parker Emmerson 2010.nb 27
Printed by Mathematica for Students
8/14/2019 Mathematics for the Univocity of Space-Time by Parker Emmerson 2010
http://slidepdf.com/reader/full/mathematics-for-the-univocity-of-space-time-by-parker-emmerson-2010 28/28
28 Mathematics for the Univocity of Space-Time by Parker Emmerson 2010.nb
