This document summarizes key concepts from Einstein's theory of relativity, including:
1) Moving clocks run slower than stationary clocks, as time depends on the observer's frame of reference (time dilation).
2) Moving objects appear shorter in the direction of motion, an effect called length contraction.
3) The mass of a moving object increases relative to an observer, known as relativistic mass increase.
4) The twin paradox explains that in a scenario where one twin travels in a rocket close to light speed while the other stays on Earth, the traveling twin ages less upon returning due to the effects of time dilation.
What does mean 2 rates of time?
1 Day On The Sun = 1 Year On Earth
In this equation there are 2 rates of time
How to create them? By relativistic effects –in the solar group
I have claimed that there's a physical point moves by a velocity =0.9999 C – where c= light known velocity =0.3 mkm/sec
Based on this light velocity length contraction with rate 71 can be created but if the moon orbital inclination 5.1 degrees effect on the result will be 71 x 5.1 = 365.25 days (also Length contraction effect may contract 71 mkm to be seen as 1 mkm)
But if
Time And Distance Equivalence (Proves) (my previous paper)
That means
1 Day On The Sun = 1 Year On Earth
Example
10921 km (Moon Circumference) x 86400 seconds (Solar Day Period) = 940 mkm (Earth orbital circumference)
(Moon = Earth Moon)
What does this equation tell us?
The equation tells that
If Earth revolves around the sun one complete revolution in one solar day only – so the moon circumference will equal a distance passed by Earth Motion during 1 second period.
So this equation refers to the possibility of existence more than one rate of time in the solar system – where T1= 1day and T2 = 365.265 days
What does mean 2 rates of time?
1 Day On The Sun = 1 Year On Earth
In this equation there are 2 rates of time
How to create them? By relativistic effects –in the solar group
I have claimed that there's a physical point moves by a velocity =0.9999 C – where c= light known velocity =0.3 mkm/sec
Based on this light velocity length contraction with rate 71 can be created but if the moon orbital inclination 5.1 degrees effect on the result will be 71 x 5.1 = 365.25 days (also Length contraction effect may contract 71 mkm to be seen as 1 mkm)
But if
Time And Distance Equivalence (Proves) (my previous paper)
That means
1 Day On The Sun = 1 Year On Earth
Example
10921 km (Moon Circumference) x 86400 seconds (Solar Day Period) = 940 mkm (Earth orbital circumference)
(Moon = Earth Moon)
What does this equation tell us?
The equation tells that
If Earth revolves around the sun one complete revolution in one solar day only – so the moon circumference will equal a distance passed by Earth Motion during 1 second period.
So this equation refers to the possibility of existence more than one rate of time in the solar system – where T1= 1day and T2 = 365.265 days
CM [010] Galileo's Acceleration & Newton's LawsStephen Kwong
Second part of Newton's first law and the second law is in concern with acceleration and force. This was precursored by Galileo Galilee just a generation before Newton.
Why anything rather than nothing? The answer of quantum mechanicsVasil Penchev
The state of “nothing” is not stable
❖ The physical nothing is not a general vacuum
The being is less than nothing
❖ The creation is taking away from the nothing
Time is the destruction of symmetry
❖ The creation need not any (external) cause
The state of nothing passes spontaneously (by itself) into the state of being
❖ This represents the “creation”
The transition of nothing into being is mathematically necessary
❖ The choice (which can be interpreted philosophically as “free will”) appears necessary in mathematical reasons
❖ The choice generates asymmetry, which is the beginning of time and thus, of the physical word
❖ Information is the quantity of choices and linked to time intimately
Brief review of velocity and acceleration along with mathematically explained feature . speed of lava bomb is also explained in these slides and the example of cap is qouted
theory of relativity by albert einstein hfhfdhdffsdadgkgfkjhajgdjkhajkgkgfajhjwvfgjkhakgjgkdhfaksvjkgvdgkahfvgkgjkghjgdskagkjgjkgkhfkkgakjgfkadhjkfhkgakhkfddakgvfjkagfgsakjgfvajfjbjavfjvdfdjadsgkfjgasdkhfgasgfjagsgfgkjgagjggsfjgfkgkagkjgajkfvgjkgjsvmbmdasfjgfjgajkgajkfgjkgsfakjgfjskjgkajfgkgsaksjkgksjgfakjg hjfhjfjhfjhfhjfhjfjhhjfdhgchgfjhcghfhchghchccdksbfjkagAKJGHASKHJKSFKJHAFSJGHAKJHFDSKJHJSVJKDHFKGHFDJBSFMBMN SDJGJKBSDJKB DSBFMVBAMNF DFGAJGJFG FNSDVBFSDMBBMNFDSMNF DFSADMBAFMNVDMNFVMNABMFMDVMNFDMNFDDSGFJGGGFGFAKJGFKGKFGKADKAKGDGFDAVAMN FDAVFJKGKAGFD FDJv jhdvsgfjhgsdjhf fjdjkgkfgkakgkgskfg dfjgkjadgkga fdjjhgdfg fajgkdjgkgsdf dfjgjkjagakf jfaakgkgf fdkjgfkga
CM [010] Galileo's Acceleration & Newton's LawsStephen Kwong
Second part of Newton's first law and the second law is in concern with acceleration and force. This was precursored by Galileo Galilee just a generation before Newton.
Why anything rather than nothing? The answer of quantum mechanicsVasil Penchev
The state of “nothing” is not stable
❖ The physical nothing is not a general vacuum
The being is less than nothing
❖ The creation is taking away from the nothing
Time is the destruction of symmetry
❖ The creation need not any (external) cause
The state of nothing passes spontaneously (by itself) into the state of being
❖ This represents the “creation”
The transition of nothing into being is mathematically necessary
❖ The choice (which can be interpreted philosophically as “free will”) appears necessary in mathematical reasons
❖ The choice generates asymmetry, which is the beginning of time and thus, of the physical word
❖ Information is the quantity of choices and linked to time intimately
Brief review of velocity and acceleration along with mathematically explained feature . speed of lava bomb is also explained in these slides and the example of cap is qouted
theory of relativity by albert einstein hfhfdhdffsdadgkgfkjhajgdjkhajkgkgfajhjwvfgjkhakgjgkdhfaksvjkgvdgkahfvgkgjkghjgdskagkjgjkgkhfkkgakjgfkadhjkfhkgakhkfddakgvfjkagfgsakjgfvajfjbjavfjvdfdjadsgkfjgasdkhfgasgfjagsgfgkjgagjggsfjgfkgkagkjgajkfvgjkgjsvmbmdasfjgfjgajkgajkfgjkgsfakjgfjskjgkajfgkgsaksjkgksjgfakjg hjfhjfjhfjhfhjfhjfjhhjfdhgchgfjhcghfhchghchccdksbfjkagAKJGHASKHJKSFKJHAFSJGHAKJHFDSKJHJSVJKDHFKGHFDJBSFMBMN SDJGJKBSDJKB DSBFMVBAMNF DFGAJGJFG FNSDVBFSDMBBMNFDSMNF DFSADMBAFMNVDMNFVMNABMFMDVMNFDMNFDDSGFJGGGFGFAKJGFKGKFGKADKAKGDGFDAVAMN FDAVFJKGKAGFD FDJv jhdvsgfjhgsdjhf fjdjkgkfgkakgkgskfg dfjgkjadgkga fdjjhgdfg fajgkdjgkgsdf dfjgjkjagakf jfaakgkgf fdkjgfkga
Nature is quirky. Whenever things don't quite match up, She changes them so they will. The results often seem to be bizarre and nonsensical, but the more you study it you realize how profoundly wise Nature is. It all started with a thought experiment that Einstein said he came up with at around the age of 16. The young Einstein wondered what would happen if he chased a light beam and caught up with it. This essay describes two of the most important discoveries in science: The Special Theory of Relativity and the General Theory of Relativity. Both of these discoveries were made by a single man, Albert Einstein, over a period of one decade (1905 – 1915). This essay is directed at an audience of amateur scientists like myself. I will approach these two theories on the basis of their underlying principles, deriving as much as possible using basic geometry and a bit of elementary calculus. I will not go into the depth needed to become a “relativist.” Mastery of general relativity would require a good working knowledge of tensors, which is beyond the scope of this essay. Nevertheless, I think amateur scientists like myself will get something useful out of it.
It should be helpful, special thanks to our teacher (whose name is in the power point and the one who made it) from whom I asked his permission to post it here.
Astronomers are gravity experts. All of the heavenly motions described in the preceding chapters are dominated by gravitation. Isaac Newton gets the credit for discovering gravity, but even Newton couldn’t explain what gravity was. Einstein proposed that gravity is a curvature of space, but that only pushes the mystery further away. “What is curvature?” we might ask.
This chapter shows how scientists build theories to explain and unify observations. Theories can give us entirely new ways to understand nature, but no theory is an end in itself. Astronomers continue to study Einstein’s theory, and they wonder if there is an even better way to understand the motions of the heavens.
The principles we discuss in this chapter will be companions through the remaining chapters. Gravity is universal.
Saeed Jafari
hematic appreciation test is a psychological assessment tool used to measure an individual's appreciation and understanding of specific themes or topics. This test helps to evaluate an individual's ability to connect different ideas and concepts within a given theme, as well as their overall comprehension and interpretation skills. The results of the test can provide valuable insights into an individual's cognitive abilities, creativity, and critical thinking skills
Travis Hills' Endeavors in Minnesota: Fostering Environmental and Economic Pr...Travis Hills MN
Travis Hills of Minnesota developed a method to convert waste into high-value dry fertilizer, significantly enriching soil quality. By providing farmers with a valuable resource derived from waste, Travis Hills helps enhance farm profitability while promoting environmental stewardship. Travis Hills' sustainable practices lead to cost savings and increased revenue for farmers by improving resource efficiency and reducing waste.
DERIVATION OF MODIFIED BERNOULLI EQUATION WITH VISCOUS EFFECTS AND TERMINAL V...Wasswaderrick3
In this book, we use conservation of energy techniques on a fluid element to derive the Modified Bernoulli equation of flow with viscous or friction effects. We derive the general equation of flow/ velocity and then from this we derive the Pouiselle flow equation, the transition flow equation and the turbulent flow equation. In the situations where there are no viscous effects , the equation reduces to the Bernoulli equation. From experimental results, we are able to include other terms in the Bernoulli equation. We also look at cases where pressure gradients exist. We use the Modified Bernoulli equation to derive equations of flow rate for pipes of different cross sectional areas connected together. We also extend our techniques of energy conservation to a sphere falling in a viscous medium under the effect of gravity. We demonstrate Stokes equation of terminal velocity and turbulent flow equation. We look at a way of calculating the time taken for a body to fall in a viscous medium. We also look at the general equation of terminal velocity.
The use of Nauplii and metanauplii artemia in aquaculture (brine shrimp).pptxMAGOTI ERNEST
Although Artemia has been known to man for centuries, its use as a food for the culture of larval organisms apparently began only in the 1930s, when several investigators found that it made an excellent food for newly hatched fish larvae (Litvinenko et al., 2023). As aquaculture developed in the 1960s and ‘70s, the use of Artemia also became more widespread, due both to its convenience and to its nutritional value for larval organisms (Arenas-Pardo et al., 2024). The fact that Artemia dormant cysts can be stored for long periods in cans, and then used as an off-the-shelf food requiring only 24 h of incubation makes them the most convenient, least labor-intensive, live food available for aquaculture (Sorgeloos & Roubach, 2021). The nutritional value of Artemia, especially for marine organisms, is not constant, but varies both geographically and temporally. During the last decade, however, both the causes of Artemia nutritional variability and methods to improve poorquality Artemia have been identified (Loufi et al., 2024).
Brine shrimp (Artemia spp.) are used in marine aquaculture worldwide. Annually, more than 2,000 metric tons of dry cysts are used for cultivation of fish, crustacean, and shellfish larva. Brine shrimp are important to aquaculture because newly hatched brine shrimp nauplii (larvae) provide a food source for many fish fry (Mozanzadeh et al., 2021). Culture and harvesting of brine shrimp eggs represents another aspect of the aquaculture industry. Nauplii and metanauplii of Artemia, commonly known as brine shrimp, play a crucial role in aquaculture due to their nutritional value and suitability as live feed for many aquatic species, particularly in larval stages (Sorgeloos & Roubach, 2021).
This presentation explores a brief idea about the structural and functional attributes of nucleotides, the structure and function of genetic materials along with the impact of UV rays and pH upon them.
Phenomics assisted breeding in crop improvementIshaGoswami9
As the population is increasing and will reach about 9 billion upto 2050. Also due to climate change, it is difficult to meet the food requirement of such a large population. Facing the challenges presented by resource shortages, climate
change, and increasing global population, crop yield and quality need to be improved in a sustainable way over the coming decades. Genetic improvement by breeding is the best way to increase crop productivity. With the rapid progression of functional
genomics, an increasing number of crop genomes have been sequenced and dozens of genes influencing key agronomic traits have been identified. However, current genome sequence information has not been adequately exploited for understanding
the complex characteristics of multiple gene, owing to a lack of crop phenotypic data. Efficient, automatic, and accurate technologies and platforms that can capture phenotypic data that can
be linked to genomics information for crop improvement at all growth stages have become as important as genotyping. Thus,
high-throughput phenotyping has become the major bottleneck restricting crop breeding. Plant phenomics has been defined as the high-throughput, accurate acquisition and analysis of multi-dimensional phenotypes
during crop growing stages at the organism level, including the cell, tissue, organ, individual plant, plot, and field levels. With the rapid development of novel sensors, imaging technology,
and analysis methods, numerous infrastructure platforms have been developed for phenotyping.
Richard's aventures in two entangled wonderlandsRichard Gill
Since the loophole-free Bell experiments of 2020 and the Nobel prizes in physics of 2022, critics of Bell's work have retreated to the fortress of super-determinism. Now, super-determinism is a derogatory word - it just means "determinism". Palmer, Hance and Hossenfelder argue that quantum mechanics and determinism are not incompatible, using a sophisticated mathematical construction based on a subtle thinning of allowed states and measurements in quantum mechanics, such that what is left appears to make Bell's argument fail, without altering the empirical predictions of quantum mechanics. I think however that it is a smoke screen, and the slogan "lost in math" comes to my mind. I will discuss some other recent disproofs of Bell's theorem using the language of causality based on causal graphs. Causal thinking is also central to law and justice. I will mention surprising connections to my work on serial killer nurse cases, in particular the Dutch case of Lucia de Berk and the current UK case of Lucy Letby.
Deep Behavioral Phenotyping in Systems Neuroscience for Functional Atlasing a...Ana Luísa Pinho
Functional Magnetic Resonance Imaging (fMRI) provides means to characterize brain activations in response to behavior. However, cognitive neuroscience has been limited to group-level effects referring to the performance of specific tasks. To obtain the functional profile of elementary cognitive mechanisms, the combination of brain responses to many tasks is required. Yet, to date, both structural atlases and parcellation-based activations do not fully account for cognitive function and still present several limitations. Further, they do not adapt overall to individual characteristics. In this talk, I will give an account of deep-behavioral phenotyping strategies, namely data-driven methods in large task-fMRI datasets, to optimize functional brain-data collection and improve inference of effects-of-interest related to mental processes. Key to this approach is the employment of fast multi-functional paradigms rich on features that can be well parametrized and, consequently, facilitate the creation of psycho-physiological constructs to be modelled with imaging data. Particular emphasis will be given to music stimuli when studying high-order cognitive mechanisms, due to their ecological nature and quality to enable complex behavior compounded by discrete entities. I will also discuss how deep-behavioral phenotyping and individualized models applied to neuroimaging data can better account for the subject-specific organization of domain-general cognitive systems in the human brain. Finally, the accumulation of functional brain signatures brings the possibility to clarify relationships among tasks and create a univocal link between brain systems and mental functions through: (1) the development of ontologies proposing an organization of cognitive processes; and (2) brain-network taxonomies describing functional specialization. To this end, tools to improve commensurability in cognitive science are necessary, such as public repositories, ontology-based platforms and automated meta-analysis tools. I will thus discuss some brain-atlasing resources currently under development, and their applicability in cognitive as well as clinical neuroscience.
Comparing Evolved Extractive Text Summary Scores of Bidirectional Encoder Rep...University of Maribor
Slides from:
11th International Conference on Electrical, Electronics and Computer Engineering (IcETRAN), Niš, 3-6 June 2024
Track: Artificial Intelligence
https://www.etran.rs/2024/en/home-english/
Earliest Galaxies in the JADES Origins Field: Luminosity Function and Cosmic ...Sérgio Sacani
We characterize the earliest galaxy population in the JADES Origins Field (JOF), the deepest
imaging field observed with JWST. We make use of the ancillary Hubble optical images (5 filters
spanning 0.4−0.9µm) and novel JWST images with 14 filters spanning 0.8−5µm, including 7 mediumband filters, and reaching total exposure times of up to 46 hours per filter. We combine all our data
at > 2.3µm to construct an ultradeep image, reaching as deep as ≈ 31.4 AB mag in the stack and
30.3-31.0 AB mag (5σ, r = 0.1” circular aperture) in individual filters. We measure photometric
redshifts and use robust selection criteria to identify a sample of eight galaxy candidates at redshifts
z = 11.5 − 15. These objects show compact half-light radii of R1/2 ∼ 50 − 200pc, stellar masses of
M⋆ ∼ 107−108M⊙, and star-formation rates of SFR ∼ 0.1−1 M⊙ yr−1
. Our search finds no candidates
at 15 < z < 20, placing upper limits at these redshifts. We develop a forward modeling approach to
infer the properties of the evolving luminosity function without binning in redshift or luminosity that
marginalizes over the photometric redshift uncertainty of our candidate galaxies and incorporates the
impact of non-detections. We find a z = 12 luminosity function in good agreement with prior results,
and that the luminosity function normalization and UV luminosity density decline by a factor of ∼ 2.5
from z = 12 to z = 14. We discuss the possible implications of our results in the context of theoretical
models for evolution of the dark matter halo mass function.
ESR spectroscopy in liquid food and beverages.pptxPRIYANKA PATEL
With increasing population, people need to rely on packaged food stuffs. Packaging of food materials requires the preservation of food. There are various methods for the treatment of food to preserve them and irradiation treatment of food is one of them. It is the most common and the most harmless method for the food preservation as it does not alter the necessary micronutrients of food materials. Although irradiated food doesn’t cause any harm to the human health but still the quality assessment of food is required to provide consumers with necessary information about the food. ESR spectroscopy is the most sophisticated way to investigate the quality of the food and the free radicals induced during the processing of the food. ESR spin trapping technique is useful for the detection of highly unstable radicals in the food. The antioxidant capability of liquid food and beverages in mainly performed by spin trapping technique.
Nutraceutical market, scope and growth: Herbal drug technologyLokesh Patil
As consumer awareness of health and wellness rises, the nutraceutical market—which includes goods like functional meals, drinks, and dietary supplements that provide health advantages beyond basic nutrition—is growing significantly. As healthcare expenses rise, the population ages, and people want natural and preventative health solutions more and more, this industry is increasing quickly. Further driving market expansion are product formulation innovations and the use of cutting-edge technology for customized nutrition. With its worldwide reach, the nutraceutical industry is expected to keep growing and provide significant chances for research and investment in a number of categories, including vitamins, minerals, probiotics, and herbal supplements.
8. Einstein’s hypotheses:
1. The laws of nature are equally valid
in every inertial reference frame.
Including
Maxwell’s eqns
2. The speed of light in empty space is
same for all inertial observers, regard-
less of their velocity or the velocity of
the source of light.
9. All observers see light flashes go b
y them with the same speed
c
v
Both guys see the light flash
travel with velocity = c
No matter how fast t
he guy on the rocket
is moving!!
10. Even when the light flash is travelin
g in an opposite direction
c
v
Both guys see the light flash
travel past with velocity = c
11. Gunfight viewed by observer at rest
Bang
! Bang
!
He sees both shots
fired simultaneously
15. Viewed by a moving observer
Bang
!Bang
!
He sees cowgirl shoot
1st & cowboy shoot later
16. Time depends of state of motion
of the observer!!
Events that occur simultaneously
according to one observer can occur a
t different times for other observ
ers
20. Same events, different observers
x
y
x
t
(x1,t1)
x
(x2,t2)
x1 x2
x’
y’
x1’
(x1’,t1’)
y’
x’
x1’ x2’
(x2’,t2’)
t’ t’
Prior to Einstein, everyone agreed
the distance between events depends
upon the observer, but not the time.
dist’
dist
21. Time is the 4th dimension
Einstein discovered that there is no
“absolute” time, it too depends upon
the state of motion of the observer
Newton
Space
&
Time
Einstein
Space-Time
completely
different
concepts
2 different aspects
of the same thing
22. How are the times seen
by 2 different observe
rs related?
We can figure this out with
simple HS-level math
( + a little effort)
23. Catch ball on a rocket ship
w=4m
t=1s
v= =4m/s
w
t
Event 1: boy throws the ball
Event 2: girl catches the ball
24. Seen from earth
w=4m
v0t=3m
v= = 5m/s
d
tt=1s
V0=3m/s
V0=3m/s
Location of the 2
events is different
Elapsed time is
the same
The ball appears
to travel faster
25. Flash a light on a rocket ship
w
t0
c=
w
t0
Event 1: boy flashes the light
Event 2: light flash reaches the girl
26. Seen from earth
w
vt
c= =d
tt=?
V
V
Speed has to
Be the same
Dist is longer
Time must be
longer
(vt)2+w2
t
27. How is t related to t0?
c = (vt)2+w2
t
t= time on Earth clock
c =
w
t0
t0 = time on moving clock
ct = (vt)2+w2
(ct)2 = (vt)2+w2
ct0 = w
(ct)2 = (vt)2+(ct0)2 (ct)2-(vt)2= (ct0)2 (c2-v2)t2= c2t0
2
t2 = t0
2c2
c2 – v2
t2 = t0
21
1 – v2/c2
t = t0
1
1 – v2/c2
this is called g
t = g t0
28. Properties of g = 1
1 – v2/c2
1
1 – (0.01c)2/c2g =
Suppose v = 0.01c (i.e. 1% of c)
1
1 – (0.01)2c2/c2
=
1
1 – (0.01)2g =
1
1 – 0.0001
= 1
0.9999
=
g = 1.00005
29. Properties of g = (cont’d)1
1 – v2/c2
1
1 – (0.1c)2/c2g =
Suppose v = 0.1c (i.e. 10% of c)
1
1 – (0.1)2c2/c2
=
1
1 – (0.1)2g =
1
1 – 0.01
= 1
0.99
=
g = 1.005
30. Let’s make a chart
v g =1/(1-v2/c2)
0.01 c 1.00005
0.1 c 1.005
31. Other values of g = 1
1 – v2/c2
1
1 – (0.5c)2/c2g =
Suppose v = 0.5c (i.e. 50% of c)
1
1 – (0.5)2c2/c2
=
1
1 – (0.5)2g =
1
1 – (0.25)
= 1
0.75
=
g = 1.15
33. Other values of g = 1
1 – v2/c2
1
1 – (0.6c)2/c2g =
Suppose v = 0.6c (i.e. 60% of c)
1
1 – (0.6)2c2/c2
=
1
1 – (0.6)2g =
1
1 – (0.36)
= 1
0.64
=
g = 1.25
34. Back to the chart
v g =1/(1-v2/c2)
0.01 c 1.00005
0.1 c 1.005
0.5c 1.15
0.6c 1.25
35. Other values of g = 1
1 – v2/c2
1
1 – (0.8c)2/c2g =
Suppose v = 0.8c (i.e. 80% of c)
1
1 – (0.8)2c2/c2
=
1
1 – (0.8)2g =
1
1 – (0.64)
= 1
0.36
=
g = 1.67
36. Enter into the chart
v g =1/(1-v2/c2)
0.01 c 1.00005
0.1 c 1.005
0.5c 1.15
0.6c 1.25
0.8c 1.67
37. Other values of g = 1
1 – v2/c2
1
1 – (0.9c)2/c2g =
Suppose v = 0.9c (i.e.90% of c)
1
1 – (0.9)2c2/c2
=
1
1 – (0.9)2g =
1
1 – 0.81
= 1
0.19
=
g = 2.29
38. update chart
v g =1/(1-v2/c2)
0.01 c 1.00005
0.1 c 1.005
0.5c 1.15
0.6c 1.25
0.8c 1.67
0.9c 2.29
39. Other values of g = 1
1 – v2/c2
1
1 – (0.99c)2/c2g =
Suppose v = 0.99c (i.e.99% of c)
1
1 – (0.99)2c2/c2
=
1
1 – (0.99)2g =
1
1 – 0.98
= 1
0.02
=
g = 7.07
40. Enter into chart
v g =1/(1-v2/c2)
0.01 c 1.00005
0.1 c 1.005
0.5c 1.15
0.6c 1.25
0.8c 1.67
0.9c 2.29
0.99c 7.07
41. Other values of g = 1
1 – v2/c2
1
1 – (c)2/c2g =
Suppose v = c
1
1 – c2/c2
=
1
1 – 12g =
1
0
= 1
0
=
g = Infinity!!!
42. update chart
v g =1/(1-v2/c2)
0.01 c 1.00005
0.1 c 1.005
0.5c 1.15
0.6c 1.25
0.8c 1.67
0.9c 2.29
0.99c 7.07
1.00c
43. Other values of g = 1
1 – v2/c2
1
1 – (1.1c)2/c2g =
Suppose v = 1.1c
1
1 – (1.1)2c2/c2
=
1
1 – (1.1)2g =
1
1-1.21
= 1
-0.21
=
g = ??? Imaginary number!!!
44. Complete the chart
v g =1/(1-v2/c2)
0.01 c 1.00005
0.1 c 1.005
0.5c 1.15
0.6c 1.25
0.8c 1.67
0.9c 2.29
0.99c 7.07
1.00c
Larger than c Imaginary number
51. Relativistic mass increase
m0 = mass of an object when it
is at rest “rest mass”
m = g m0
mass of a moving
object increases
by the g factor
as vc, m
as an object moves
faster, it gets
harder & harder
to accelerate
g
v=c
52. summary
• Moving clocks run slow
• Moving objects appear shorter
• Moving object’s mass increases
54. Twin paradox
Twin brother
& sister
She will travel to
a-centauri (a near-
by star on a special
rocket ship v = 0.9cHe will stay home
& study Phys 100
a-centauri
55. Light year
distance light travels in 1 year
dist = v x time
1cyr = 3x108m/s x 3.2x107 s
= 9.6 x 1015 m
We will just use cyr units
& not worry about meters
= c yr
56. Time on the boy’s clock
tout =
d0
v
4.3 cyr
0.9c
= = 4.8 yrs
According to the boy
& his clock on Earth:
tback =
d0
v
4.3 cyr
0.9c
= = 4.8 yrs
ttotal = tout+tback = 9.6yrs
57. What does the boy see on her cloc
k?
tout =
tout
g
4.8 yrs
2.3
= = 2.1 yrs
According to the boy
her clock runs slower
tback =
tback
g
4.8 yr
2.3
= = 2.1 yrs
ttotal = tout+tback = 4.2yrs
58. So, according to the boy:
his clock her clock
out: 4.8yrs 2.1yrs
back: 4.8yrs 2.1yrs
total: 9.6yrs 4.2yrs
59. But, according to the gi
rl, the boy’s clock is mov
ing &, so, it must be run
ning slower
tout =
tout
g
2.1 yrs
2.3
= = 0.9 yrs
According to her, the
boy’s clock on Earth says:
tback =
tback
g
2.1 yrs
2.3
= = 0.9 yrs
ttotal = tout+tback = 1.8yrs
60. Her clock advances 4.2 yrs
& she sees his clock advance
only 1.8 yrs,
She should think he has aged l
ess than her!!
61. As seen by him
Events in the boy’s life:
As seen by her
She leaves
She arrives
& starts turn
Finishes turn
& heads home
She returns
4.8 yrs
4.8 yrs
short time
9.6+ yrs
0.9 yrs
????
0.9 yrs
1.8 + ??? yrs
62. turning around as seen by her
He sees her
start to turn
He sees her
finish turning
According to her, these
2 events occur very,very
far apart from each other
Time interval between 2 events depends
on the state of motion of the observer
63. Gunfight viewed by observer at rest
Bang
! Bang
!
He sees both shots
fired simultaneously
65. Viewed by a moving observer
Bang
! Bang
!
He sees cowboy shoot
1st & cowgirl shoot later
66. as seen by him
In fact, ???? = 7.8+ years
as seen by her
She leaves
She arrives
& starts turn
Finishes turn
& heads home
She returns
4.8 yrs
4.8 yrs
short time
9.6+ yrs
0.9 yrs
???
0.9 yrs
1.8 + ???yrs
7.8+ yrs
9.6+ yrs
67. No paradox: both twins agree
The twin that
“turned around”
is younger
68. Ladder & Barn Door paradox
1m
2m
???
ladder
Stan & Ollie puzzle over how
to get a 2m long ladder thru
a 1m wide barn door
69. Ollie remembers Phys 100 & the
theory of relativity
1m
2m
ladder
Stan, pick up
the ladder &
run very fast
tree
70. View from Ollie’s ref. frame
1m
2m/g
Push, St
an!
V=0.9c
(g=2.3)Ollie Stan
71. View from Stan’s ref. frame
2m
1m/g
V=0.9c
(g=2.3)
Ollie Stan
But it does
n’t fit, Olli
e!!
72. If Stan pushes both ends of the
ladder simultaneously, Ollie sees the
two ends move at different times:
1mToo soo
n Stan!
V=0.9c
(g=2.3)Ollie StanStan
Too late
Stan!
75. status
Einstein’s theory of “special relativity” has be
en carefully tested in many very precise ex
periments and found to be valid.
Time is truly the 4th dimension of space & ti
me.