Working Draft: Planck Time, Planck Length & Base-2 Exponential Notation

Planck Time to the Age of the Universe
Planck Length to the Observable Universe

More articles (working-drafts):
Tilings & Tessellations         
Just what’s happening here?

PLEASE NOTE: This page was started early in December 2014.  There are many simple errors within the chart below, so this page will be subject to frequent updates.

Are there any comparison between the progressions from the Planck Time and the Planck Length using base-2 exponential notation through the successive doublings out to their given limits, i.e. the Age of the Universe and the Observable Universe respectively?  At this point in time, I do not think there are, so we are making our first working draft attempt to do it here.

Perhaps it goes without saying… as you read this note, I appeal to you to ask questions and make comments and suggestions. Thank you.   Bruce Camber

The Planck Time, like the Planck Length, is an actual value. It can be multiplied by 2. Of course, if one were to multiply it by 2 over and over again, you can assume that you would reach those outer limits. That process looks a bit tedious. After all, the Age of the Universe is somewhere over 13.78 billion years and the Observable Universe is millions of light years from common sense. Yet, rather surprisingly, to complete that effort doesn’t require thousands of doublings. It is done in somewhere between 202 to 206 doublings. That is so surprising, the doublings for both are charted below.

These doublings do kind-of, sort-of end up somewhat in synch. Considering the duration and the length, and the nature of very large measurements, for all intents and purposes, they are synched! Though these charts will be tweaked substantially, the best confirmation is at the notations (or doublings) that define a day in Planck Time units correspond closely to distance light travels in a day in Planck Length units. And, the doublings within the Planck Time column for the definition of a week correspond closely with the distance light travels in a week within the Planck Length column. And, finally, the doublings in the Planck Time column that define a year correspond closely with the distance light travels within a year in the Planck Length column. These are the first baby steps of analysis. How many hundreds of steps are there to go to discern all the faces of its meaning? Who knows? From here, we will continue to look to see what meaning and relation evolves at a
particular notation where one column appears to impart value to the other. Just on the surface, this chart seems to suggest that there are other possible views of the nature of space and time where order (sequence), continuity, symmetries, and relations seem to play a more fundamental role.

Science and our common sense worldview assume the primordial nature of space and time. As a result of our work with the Planck Units, we hold that conclusion up for further inspection. How do things appear as one begins to approach the Planck Length and Planck Time in synch? As we add more Planck Units to this chart, what else might we see? What might we learn? So, we will add mass, electric charge, and temperature to these listings. And then, we’ll add the derived Planck Units (12) and then ask, "Is there anything more we can do to establish a range from the smallest to the largest? What might a comparative analysis at each doubling reveal to us?

At this point, we are attempting to learn enough to make a few somewhat intelligent guesses.

So, as a result of where we are today, I think it is okay to ask the question, "What would the universe look like if space and time were derivative of order-continuity and relation-symmetry, and of ratios where the subject-object are constantly in tension?"

By the way, on May 10, 2010, the very smallest unit of measured time was experimentally demonstrated;  the result was 1.2 × 10−17 seconds. That is a long way from 10−44 seconds!  For more background, see: http://phys.org/news192909576.html

This stream of  consciousness continues at the very bottom of this chart.

 

Planck Time Doublings: Primarily in Seconds

Planck Length Doublings: Primarily in Meters

204

The Age of the Universe: 13.78 to 13.8 billion years

8.310×1026 m or Future Universe

203

It appears that we are in the earliest part of 202 doubling:1019

4.155×1026 m or Near Future Universe

202

6.9309178×1018 seconds (21.9777+ billion years)18

2.077×1026 m or in the range of the Observable Universe

201

346,545,888,147,200,000 seconds (10.9888+ billion years)

1.03885326×1026 m approaching the Observable Universe

200 18

173,272,944,073,600,000 seconds (5.49444+ billion years)

5.19426632×1025 m

199

86,636,472,036,800,000 seconds (2.747+ billion years)

2.59713316×1025 m

198

43,318,236,018,400,000 seconds (1.3736+ billion years)

1.29856658×1025 m

197

21,659,118,009,200,000 seconds (686.806+ million years) 17

6.49283305×1024 m

196

10,829,559,004,600,000 seconds (342.4+ million years)

3.24641644×1024 m

195

5,414,779,502,320,000 seconds (171.2+ million years)

1.62320822×1024 m

194

2,707,389,751,160,000 seconds (85.6+ million years)

8.11604112×1023 m

193

1,353,694,875,580,000 seconds (42.8+ million years)

4.05802056×1023 m

192

676,847,437,792,000 seconds (21.4+ million years)

2.02901033×1023 m

191

338,423,718,896,000 seconds (10.724+ million years)

1.01450514×1023 m

19015

18914

18814

18714

18614

18513

18413

18313

18212

18112

169,211,859,448,000 seconds (5.3+ million years) 15

84,605,929,724,000 seconds (2.6+ million years) 14

42,302,964,862,000 seconds (1.3+ million years) 14

21,151,482,431,000 seconds (640+ thousand years) 14

10,575,741,215,500 seconds (320+ thousand years) 14

5,287,870,607,760 seconds (160+ thousand years) 13

2,643,935,303,880 seconds (83.7+ thousand years) 13

1,321,967,651,940 seconds (41.8+ thousand years) 13

660,983,825,972 seconds (20.9+ thousand years) 12

330,491,912,986 seconds (or about 10,472.9 years) 12

5.07252568×1022 m

2.53626284×1022 m

1.26813145 x1022 m

6.34065727×1021 m

3.17032864×1021 m or 3 Zettameters or 310,000 ly

1.58516432×1021 m or about 150,000 ly (1.5z)

7.92582136×1020 m

3.96291068×1020 m

1.981455338×1020 m

9.90727664×1019 meters

18012

17911

17811

17711

17611

17510

17410

17310

1729

171. 9

165,245,956,493 seconds 12

82,622,978,246.4 seconds 11

41,311,489,123.2 seconds 11

20,655,744,561.6 seconds 11

10,327,872,280.8 seconds 11

5,163,936,140.4 seconds 10

2,581,968,070.2 seconds 10

1,290,984,035.1 seconds 10

645,492,017.552 seconds 9

322,746,008.776 seconds 9

4.95363832×1019 m

2.47681916×1019 m

1.23840958×1019 m

6.19204792×1018 m

3.09602396×1018 m

1.54801198×1018 m

7.74005992×1017 m

3.87002996×1017 m

1.93501504 x1017 m

9.67507488×1016 m

1709

1698

1688

1678

1668

1657

1647

1637

1626

1616

161,373,004.388 seconds 9

80,686,502.194 seconds 8

40,343,251.097 sec 8(466 days)(Note: 31,536,000 s/year)

20,171,625.5485 seconds (233.468 days)8

10,085,812.7742 seconds (116.73 days)8

5,042,906.38712 seconds (58.36+)107

2,521,453.19356 s (29.1835 days)

1,260,726.59678 s (14.59+ days) 107

630,363.29839 s (7.29+ days) 106

315,181.649195 seconds (3.64794 days) 106

4.83753744×1016 m

2.41876872×1016 m

1.20938436×1016 m

6.0469218×1015 m [one light year (ly) is 9.4×1015 m]

3.0234609×1015 m

1.5117305×1015 m

7.55865224×1014 m

3.77932612×1014 m

1.88966306×1014 m (about 7-day light travel)

9.44831528×1013 m

1606

1595

1585

1575

1564

1554

1544

1534

1523

1513

157,590.824598 s (1.82 days)106

78,795.4122988 s (.911984 days) 105

39,397.7061494 seconds 105

19,698.8530747 seconds 105

9849.42653735 seconds 104

4924.71326867 seconds(3600 s in hour)104

2462.35663434 seconds 104

1231.17831717 seconds104

615.589158584 seconds (10.259+ minutes)103

307.794579292 seconds 103

4.72415764×1013 m

2.36207882×1013 m (or close to 24-hour light travel)

1.18103945×1013 m

5.90519726×1012 m

2.95259863×1012 m

1.47629931×1012 m

738,149,657 kilometers 1011

369,074,829 kilometers 1011

184,537,414 kilometers 1011

92,268,707.1 kilometers (range of earth-to-sun)1010m

1503

1492

1482

1472

1461

1451

1441

1431

142−1

141−1

153.897289646 seconds 103

76.948644823 s (16+ sec over 1 min) 102

38.4743224115 s (21.53 sec to 1 min) 102

19.2371612058 seconds

9.61858060288 seconds

4.80929030144 seconds 10?

2.40464515072 seconds 10?

1.20232257536 s (1s ≠ perfect tp multiple) 10?

6.0116128768×10−1 seconds

3.0058064384×10−1 seconds

46,134,353.6 kilometers 1010

23,067,176.8 kilometers 1010

11,533,588.4 kilometers 1010

5,766,794.2 kilometers 109

2,883,397.1 kilometers 109

1,441,698.55 kilometers 109 m

720,849.264 kilometers 108

360,424.632 kilometers108 m

180,212.316 kilometers (111,979+ miles)108 m

90,106.158 kilometers 107 m

140−1

139−2

138−2

137−2

136−2

135−3

134−3

133−3

132−4

131−4

1.5029032192×10−1 seconds

7.514516096×10−2 seconds

3.757258048 × 10−2 seconds

1.878629024 × 10−2 seconds

9.39314512 × 10−3 seconds

4.69657256 × 10−3 seconds

2.34828628 × 10−3 seconds

1.174143145978 × 10−3 seconds

5.8707157335 × 10−4 seconds

2.93535786675 × 10−4 seconds

45,053.079 kilometers 107

22,526.5398 kilometers 107

11,263.2699 kilometers or about 7000 miles

5631.63496 kilometers 106

2815.81748 kilometers 106

1407.90874 kilometers (about 874 miles )106m

703.954368 kilometers 105

351.977184 kilometers (218.7 miles 105

175.988592 kilometers (109.35 miles )105

87.994296 kilometers 104

130−4

129−5

128−5

127−5

126−5

125−6

124−6

123−6

122−7

121−7

1.46767893338 × 10−4 s

7.33839466688 × 10−5s

3.66919733344 × 10−5 s

1.83459866672× 10−5 s

9.1729933336 × 10−6 s

4.5864966668 × 10−6 s

2.2932483334 × 10−6 s

1.1466241667 × 10−6 s

5.73312083348 × 10−7 s

2.86656041674 × 10−7 s

43.997148 kilometers 104

21.998574 kilometers104

10.999287 kilometers or within 6.83464 miles104

5.49964348 kilometers 103

2.74982174 kilometers 103

1.37491087 kilometers 103

687.455439 meters 102

343.72772 meters or about 1128 feet 102

171.86386 meters or about 563 feet 102

85.9319296 meters 101

120−7

119−8

118−8

117−8

116−9

115−9

114−9

113−9

112−10

111−10

1.43328020837 × 10−7 s

7.16640104186 × 10−8 s

3.58320052093 × 10−8 s

1.79160026046 × 10−8 seconds

8.95800130232 × 10−9 seconds

4.47900065116 × 10−9 seconds

2.23950032558 × 10−9 seconds

1.11975016279 × 10−9 seconds

5.59875081396 × 10−10 seconds

2.79937540698 × 10−10 seconds

42.9659648 meters 101

21.4829824 meters 101

10.7414912 meters or 35.24 feet or 1.074×101 m100

5.3707456 meters 100

2.6853728 meters or 105.723 inches 100

1.3426864 meters or 52.86 inches 100

67.1343176 cm (19.68+ inches or 6.71×10-1

33.5671588 centimeters or 3.356×10-1 m

16.7835794 centimeters or 1.6783×10-1

8.39178968 cm (3.3+ inches or 8.39×10-2 m

110−10

109−11

108−11

107−11

106−12

105−12

104−12

103−12

102−13

101−13

1.39968770349 × 10−10 seconds

6.99843851744 × 10−11 seconds

3.49921925872 × 10−11 seconds

1.74960962936 × 10−11 seconds

8.7480481468 × 10−12 seconds

4.3740240734 × 10−12 seconds

2.1870120367 ×10−12 seconds

1.09350601835 ×10−12 seconds

5.46753009176 ×10−13 seconds

2.73376504588 × 10−13 seconds

4.19589484 centimeters 4.19589484×10-2 m

2.09794742 centimeters or 2.0979×10-2 m

1.04897 centimeters or 1.04897375×10-2 m

5.24486856 mm (about 1/4 inch) or 5.24×10-3 m

2.62243428 millimeters or 2.62243428×10-3 m

1.31121714 millimeters 1.31121714×10-3 m

.655608568 millimeters or 6.55608568×10-4 m

.327804284 millimeter or 3.27804284 x10-4 m

.163902142 millimeters or 1.63902142×10-4 m

81.9510712 microns or 81.9510712 x10-5 m

100−13

99−14

98−14

97−14

96−15

95−15

94−15

93−15

92−16

91−16

1.36688252294 × 10−13 seconds

6.83441261472 × 10−14 seconds

3.41720630736 × 10−14 seconds

1.70860315368 × 10−14 seconds

8.5430157684 × 10−15 seconds

4.2715078842 × 10−15 seconds

2.1357539421 × 10−15 seconds

1.06787697105 × 10−15 seconds

5.33938485524 × 10−16 seconds

2.66969242762 × 10−16 seconds

40.9755356 microns or 4.09755356 x10-5 m

20.4877678 microns or 2.04877678×10-5 m

10.2438839 microns or 1.02438839×10-5 m

5.12194196 microns (.0002+ inches or 5.12×10-6 m

2.56097098 microns or 2.56097098×10-6 m

1.28048549 microns or 1.2804854×10-6 m

640.242744 nanometers 6.40242744×10-7 m

320.121372 nanometers 3.20121372×10-7 m

160.060686 nanometers or 1.60×10-7 m

80.0303432 nanometers or 8.00×10-8 m

90−16

89−17

88−17

87−17

86−18

85−18

84−18

83−18

82−192

81−192

1.33484621381 × 10−16 seconds

6.67423106904 × 10−17 seconds

3.33711553452 × 10−17 seconds

1.66855776726 × 10−17 seconds  (smallest measurement – 2010)

8.34278883632 × 10−18 seconds

4.17139441816 × 10−18 seconds

2.08569720908 × 10−18 seconds

1.04284860454 × 10−18 seconds

5.21424302272 × 10−19 seconds

2.60712151136 × 10−19 seconds

40.0151716 nanometers or 4.00×10-8 m

20.0075858 nanometers or 2.00×10-8 m

1.00037929×10-8 meters or 10 nanometers

5.00189644×10-9 meters

2.50094822 nanometers or 2.50094822×10-9 m

1.25474112 nanometers or 1.25×10-9 m

.625237056 nanometers or 6.25237056×10-10 m

.312618528 nanometers or 3.12×10-10 m

.156309264 nanometers or 1.563×10-10 m

7.81546348×10-11 m

80−19

79−20

78−20

77−20

76−21

75−21

74−21

73−21

72−22

71−22

1.30356075568 × 10−19 seconds

6.5178037784 × 10−20 seconds

3.2589018892 × 10−20 seconds

1.6294509446 × 10−20 seconds

8.147254723 × 10−21 seconds

4.0736273615 × 10−21 seconds

2.03681368075 × 10−21 seconds

1.01840684038 × 10−21 seconds

5.09203420188 × 10−22 seconds

2.54601710094 × 10−22 seconds

3.90773174×10-11 m

1.95386587×10-11 m

9.76932936×10-12 m

4.88466468×10-12 m

2.44233234×10-12 m

1.22116617×10-12 m

6.10583084×10-13 m

3.05291542×10-13 m

1.52645771×10-13 m

7.63228856×10-14 m

70−22

69−23

68−23

67−23

66−24

65−24

64−24

63−25

62−25

61−25

1.27300855047 × 10−22 seconds

6.36504275236 × 10−23 seconds

3.18252137618 × 10−23 seconds

1.59126068809 × 10−23 seconds

7.95630344044 × 10−24 seconds

3.97815172022 × 10−24 seconds

1.98907586011 × 10−24 seconds

9.94537930056 × 10−25 seconds

4.97268965028 × 10−25 seconds

2.48634482514 × 10−25 seconds

3.81614428×10-14 m

1.90807214×10-14 m

9.54036072×10-15 m

4.77018036×10-15 m

2.38509018×10-15 m

1.19254509×10-15 m

5.96272544×10-16 m

2.98136272×10-16 m

1.49068136×10-16 m

7.45340678×10-17 m

60−25

59−26

58−26

57−26

56−27

55−27

54−27

53−28

52−28

51−28

1.24317241257 × 10−25 seconds

6.21586206284 × 10−26 seconds

3.10793103142 × 10−26 seconds

1.55396551571 × 10−26 seconds

7.76982757856 × 10−27 seconds

3.88491378928 × 10−27 seconds

1.94245689464 × 10−27 seconds

9.7122844732 × 10−28 seconds

4.8561422366 × 10−28 seconds

2.4280711183 × 10−28 seconds

3.72670339×10-17 m

1.86335169×10-17 m

9.31675848×10-18 m

4.65837924×10-18 m

2.32918962×10-18 m

1.16459481×10-18 m

5.82297404×10-19 m

2.91148702×10-19 m

1.45574351×10-19 m

7.27871756×10-20 m

50−28

49−29

48−29

47−29

46−30

45−30

44−30

43−31

42−31

41−31

1.21403555915 × 10−28 seconds

6.07017779576 × 10−29 seconds

3.03508889788 × 10−29 seconds

1.51754444894 × 10−29 seconds

7.58772224468 × 10−30 seconds

3.79386112234 × 10−30 seconds

1.89693056117 × 10−30 seconds

9.48465280584 × 10−31 seconds

4.74232640292 × 10−31 seconds

2.37116320146 × 10−31 seconds

3.63935878×10-20 m

1.81967939×10-20 m

9.09839696×10-21 m

4.54919848×10-21 m

2.27459924×10-21 m

1.13729962×10-21 m

5.68649812×10-22 m

2.84324906×10-22 m

1.42162453×10-22 m

7.10812264×10-23 m

40−31

39−32

38−32

37−32

36−33

35−33

34−33

33−34

32−34

31−34

1.18558160073 × 10−31 seconds

5.92790800364 × 10−32 seconds

2.96395400182 × 10−32 seconds

1.48197700091 × 10−32 seconds

7.40988500456 × 10−33 seconds

3.70494250228 × 10−33 seconds

1.85247125114 × 10−33 seconds

9.26235625568 × 10−34 seconds

4.63117812784× 10−34 seconds

1.15779453196× 10−34 seconds

3.55406132×10-23 m

1.77703066×10-23 m

8.88515328×10-24 m

4.44257664×10-24 m

2.22128832×10-24 m

1.11064416×10-24 m

5.5532208×10-25 m

2.7766104×10-25 m

1.3883052×10-25 m

6.94152599×10-26 m

3.47076299×10-26 m

30−35

29−35

28−35

27−36

26−36

25−36

24−37

23−37

22−37

21−37

5.78897265978 × 10−35 seconds

2.89448632989 × 10−35 seconds

1.44724316494 × 10−35 seconds

7.23621582472 × 10-36 seconds

3.61810791236 × 10−36 seconds

1.80905395618 × 10−36 seconds

9.045269781089 × 10−37 seconds

4.522263489044 × 10−37 seconds

2.26131744522 × 10−37 seconds

1.13065872261 × 10−37 seconds

1.735381494×10-26 m

8.67690749×10-27 m

4.3384537×10-27 m

2.16922687×10-27 m

1.0846134×10-27 m

5.42306718×10-28 m

2.711533591×10-28 m

1.35576679×10-28 m

6.77883397×10-29 m

3.38941698×10-29 m

20−38

19−38

18−38

17−38

16−39

15−39

14−40

13−40

12−40

11−40

5.65329361306 × 10−38 seconds

2.82646806528 ×10−38 seconds

1.41323403264 ×10−38 seconds

7.0661701632 × 10−39 seconds

3.530850816 × 10−39 seconds

1.7665425408 × 10−39 seconds

8.832712704 × 10−40 seconds

4.416356352 × 10−40 seconds

2.208178176 × 10−40 seconds

1.104089088 × 10−40 seconds

1.69470849×10-29 m

8.47354247×10-30 m

4.2367712×10-30 m

2.11838561×10-30 m

1.05919280×10-30 m

5.29596404×10-31 m

2.64798202×10-31 m

1.32399101×10-31 m

6.6199550×10-32 m

3.30997752×10-32 m

10−40

9−41

8−41

7−41

6−42

5−42

4−42

3−43

2−43

1−43

5.52044544 × 10−41 seconds

2.76022272 × 10−41 seconds

1.38011136 × 10−41 seconds

6.9005568 × 10−42 seconds

3.4502784 × 10−42 seconds

1.7251392 × 10−42 seconds

8.625696 × 10−43 seconds

4.312848 × 10−43 seconds

2.156424 × 10−43 s The second doubling

1.078212 × 10−43 s The first doubling

1.65498876×10-32 m

8.27494384×10-33 m

4.1374719232×10-33 m

2.0687359616×10-33 m

1.03436798×10-33 m

5.17183990×10-34 m

2.58591995×10-34 m

1.29295997×10-34 m

6.46479988×10-35 meters

3.23239994×10-35 m The first doubling, step, or layer.

5.39106(32)×10−44 seconds 1.616199(97)x10-35 meters

The Planck Time

The Planck Length

Endnotes:

1. We are in the process of refining this chart and will be throughout 2015 and 2016.

2. Our very first calculation with the Planck Length column (December 2011), resulted in 209 doublings! We found several errors. Then , with help of a NASA astrophysicist, Joe Kolecki (now retired), we updated our postings with his calculation of 202.34. Then, a French Observatory astrophysicist, Jean-Pierre Luminet, calculated 205.1 doublings. We are very open to all ideas and efforts! We are studying the foundations of foundations. One might call it a hypostatic science based on the simplest mathematics, simple geometries and observations about the way the universe coheres.

One might say, "The Finite is finite, the Infinite is the Infinite, and the constants and universals describe the boundary conditions and transformations between each. One manifests a panoply of perfections; the other has only momentary instants of perfection."

Open Questions:

What is a second?

What are Planck Units?

What is time?

What is a meter?

What is length?

What is space?

What happens just before the Planck time at 10-44 seconds? Theorists say that all of the four fundamental forces are presumed to have been unified into one force. All matter, energy, space and time "explode" from the original singularity.

3. Our online "Google" calculator often rounds up the last digit. It is usually beyond the eleventh postion to the right of the decimal point.

4. For more about this place and time, go to Hyperphysics (Georgia State): http://hyperphysics.phy-astr.gsu.edu/hbase/astro/planck.html

5. A copy of this chart has also been published in the following locations:

    a. http://walktheplanck.wordpress.com/2014/12/09/base/

    b. https://utable.wordpress.com/2014/12/12/planck/

    c. http://SmallBusinessSchool.org/page3053.html

    d. ResearchGate                           Documents: 3052, 3054, 3056

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