Frosci midterm (Brain and Behavior + Astrophysics)
neuron cells
– nerve cells
– carry electrical pulses that transfer from 1 neuron to another
– over 100 billion in brain
– 3 parts:
1. cell body (grey matter)
2. dendrites (grey matter)
3. axons (white coated in myelin)
signals picked up by dendrites –> cell body –> action potentials (electrical charge) –> axon –> terminal ending
– within a neuron – info transfer is mostly electrical – fast = 1-100 m/s
– between neurons = chemical = slow (.5 m/s)
– perturb neurons by introducing of inhibitory neurotransmitters –> disruption at synapse
– also if myelin coating is missing or damaged –> inhibit ability of electric currents to be transmitted between neurons
– carry electrical pulses that transfer from 1 neuron to another
– over 100 billion in brain
– 3 parts:
1. cell body (grey matter)
2. dendrites (grey matter)
3. axons (white coated in myelin)
signals picked up by dendrites –> cell body –> action potentials (electrical charge) –> axon –> terminal ending
– within a neuron – info transfer is mostly electrical – fast = 1-100 m/s
– between neurons = chemical = slow (.5 m/s)
– perturb neurons by introducing of inhibitory neurotransmitters –> disruption at synapse
– also if myelin coating is missing or damaged –> inhibit ability of electric currents to be transmitted between neurons
glial cells
-support cells
– not electrical
– transfer substances during brain function
– “glue” material between neurons
– not electrical
– transfer substances during brain function
– “glue” material between neurons
dendrites
– the ears of the neuron
– receive inputs from other neurons
– receive inputs from other neurons
axons
– the mouth
– transmitter of info to other neurons
– transmitter of info to other neurons
synapse
– place where neurons transmit and receive info from one another
– place of meeting between dendrites of one cell and axons of another
– gap between neurons – no touching
– here neurotransmitters are released – can be excitatory or inhibitory (prevents signal from moving)
– place of meeting between dendrites of one cell and axons of another
– gap between neurons – no touching
– here neurotransmitters are released – can be excitatory or inhibitory (prevents signal from moving)
2 types of communication between brain cells
1. electrical
2. chemical
2. chemical
electrical communication
– action potentials
– neurons not very good at conducting these types of signals -myelin coats neurons and makes electrical signals more efficiently transmitted
– neurons not very good at conducting these types of signals -myelin coats neurons and makes electrical signals more efficiently transmitted
myelin
– coats neurons to make them better at conducting electrical signals
– white and wrapped around axons
– when myelin breaks down –> multiple sclerosis
– white and wrapped around axons
– when myelin breaks down –> multiple sclerosis
corpus callosum
– highway of communication
– highway of myelinated axons that carry info from right to left side of brain and vise versa
– damage to corpus callosum – not much happens cuz we process stuff w/ both sides of brain
– highway of myelinated axons that carry info from right to left side of brain and vise versa
– damage to corpus callosum – not much happens cuz we process stuff w/ both sides of brain
the cortex
– outer layer of brain
– 2mm thick
– 1 cubic mm of cortex = 100,000 neurons
most of cortex looks the same
– made of grey matter (uncoated cell bodies) – beneath = white matter = axons
– 2mm thick
– 1 cubic mm of cortex = 100,000 neurons
most of cortex looks the same
– made of grey matter (uncoated cell bodies) – beneath = white matter = axons
broca’s aphasia
– 1861
– loss of speech
– someone who could understand speech but after stoke couldn’t speak it
– loss of speech
– someone who could understand speech but after stoke couldn’t speak it
frontal lobe
– motor
parietal lobe
– decision
– somatosensory (receives sensory input from body)
– somatosensory (receives sensory input from body)
temporal lobe
– memory
– fear
– fear
occipital lobe
– vision
prefrontal cortex
– executive control
How do we study mind-brain
– cognitive psychology – what is language/thought/memory w/o thinking about brain
-neuroscience
-computer science
– philosophy
-neuroscience
-computer science
– philosophy
how do we study mind
– break things down:
– sensation and perception
– attention
– language
– memory search
– decision when to stop
– output
break down behavior into parts we can define and measure
– perturb brain –> measure behavior
– measure brain during behavior
-The key is convergence. When different methods lead to the same answer.
– sensation and perception
– attention
– language
– memory search
– decision when to stop
– output
break down behavior into parts we can define and measure
– perturb brain –> measure behavior
– measure brain during behavior
-The key is convergence. When different methods lead to the same answer.
visual neglect
– after stroke, people neglect 1 side of space
lesions
– wounds in brain
– due to trauma, disease, stroke, surgery
– compare healthy vs lesioned, look for spared functions vs. impaired functions
– due to trauma, disease, stroke, surgery
– compare healthy vs lesioned, look for spared functions vs. impaired functions
optogenetics
– light can turn specific types of neurons on or off
– very precise, order of milliseconds
– only animals for now
– very precise, order of milliseconds
– only animals for now
fMRI (and limitations)
– functional magnetic resonance imaging
– fMRI measures radio signals emitted by hydrogen atoms in your brain under a magnetic field.
– We would really like to measure the level of brain activity (i.e., activity of neurons). That is, the
intensity of the radio signals is a proxy for the activity of the neurons.
– The assumptions needed to get from (i) to (ii) include: increased local neural activity leads to
increased local blood flow; increased local blood flow leads to a change in the ratio of
oxygenated to de-oxygenated hemoglobin, which leads to a difference in the emitted radio
signals.
– non-invasive
– different than mri
– measures blood flow, not tissue itself – an indirect measure of neural activity; a proxy
– how it woks:
1. magnetic resonance differentiates between oxygenated blood and deoxygenated blood
2. active areas get a fresh blood flow –> more O2
3. Measures the relative change in oxygen –> change in h signals (a proxy for neural activity)
– how to interpret results:
-run statistics on output
– graph it in images
– Localize to the brain.
Isdor Isaac Rabi – physicist – discovered that magnetic field and radio wave pulses can cause spin of certain nuclei
– h atoms in brain emit signal (radio frequency) – signal varies based on what surrounds the H atoms
similar to catscan – your brain, or other tissue, absorbs x-rays
– resting vs active state of neuron:
-active = more blood flow = more action potential
– increase in local neural activity = increase in local blood flow
Limitations of fMRI include:
a. Poor spatial resolution – thousands of neurons per voxel.
b. Poor temporal resolution – signal takes seconds, whereas action potentials take
milliseconds.
c. The study subject has to lie still inside the fMRI machine, which limits the type of
experiments that can be conducted. For example, one cannot get an fMRI image of the
brain of a subject while playing basketball.
– fMRI measures radio signals emitted by hydrogen atoms in your brain under a magnetic field.
– We would really like to measure the level of brain activity (i.e., activity of neurons). That is, the
intensity of the radio signals is a proxy for the activity of the neurons.
– The assumptions needed to get from (i) to (ii) include: increased local neural activity leads to
increased local blood flow; increased local blood flow leads to a change in the ratio of
oxygenated to de-oxygenated hemoglobin, which leads to a difference in the emitted radio
signals.
– non-invasive
– different than mri
– measures blood flow, not tissue itself – an indirect measure of neural activity; a proxy
– how it woks:
1. magnetic resonance differentiates between oxygenated blood and deoxygenated blood
2. active areas get a fresh blood flow –> more O2
3. Measures the relative change in oxygen –> change in h signals (a proxy for neural activity)
– how to interpret results:
-run statistics on output
– graph it in images
– Localize to the brain.
Isdor Isaac Rabi – physicist – discovered that magnetic field and radio wave pulses can cause spin of certain nuclei
– h atoms in brain emit signal (radio frequency) – signal varies based on what surrounds the H atoms
similar to catscan – your brain, or other tissue, absorbs x-rays
– resting vs active state of neuron:
-active = more blood flow = more action potential
– increase in local neural activity = increase in local blood flow
Limitations of fMRI include:
a. Poor spatial resolution – thousands of neurons per voxel.
b. Poor temporal resolution – signal takes seconds, whereas action potentials take
milliseconds.
c. The study subject has to lie still inside the fMRI machine, which limits the type of
experiments that can be conducted. For example, one cannot get an fMRI image of the
brain of a subject while playing basketball.
Why are neurotransmitters important?
What does it mean that brain is plastic?
What does it mean that brain is plastic?
– neurons literally physically change when learning happens
facial recognition fmri experiment
– show face to person in fmri and see brain activity
– control = showing someone a jumbled face
– compare which neurons are active when showing face vs. smooshed face
– voxel = 3d pixel
– limitations:
– 1 voxel could be thousands of neurons (spatial)
– time for blood to flow to brain (temporal)
– control = showing someone a jumbled face
– compare which neurons are active when showing face vs. smooshed face
– voxel = 3d pixel
– limitations:
– 1 voxel could be thousands of neurons (spatial)
– time for blood to flow to brain (temporal)
left/right vs top/bottom brain
– left + right important b/c corpus callosm
– top and bottom important b/c mouse experiment shows that when top brain is shut off, function still happens –> bottom brain worked independently but intertwined w/ top + similar w/ left and right
– modularity (localization) vs. holism (no localization)
– top and bottom important b/c mouse experiment shows that when top brain is shut off, function still happens –> bottom brain worked independently but intertwined w/ top + similar w/ left and right
– modularity (localization) vs. holism (no localization)
memory
– selective
– robust but also vulnerable; accurate but often biased
– to create memories –> long term changes in brain –> long term changes in neurons
– activating a synapse can make it stronger- minutes, hours, and even days later
– dendrites grow nubs after long term potentiation (a persistent increase in synaptic strength following high frequency stimulation of a chemical synapse) –> these spines allow neurons to form more connections with each other
– robust but also vulnerable; accurate but often biased
– to create memories –> long term changes in brain –> long term changes in neurons
– activating a synapse can make it stronger- minutes, hours, and even days later
– dendrites grow nubs after long term potentiation (a persistent increase in synaptic strength following high frequency stimulation of a chemical synapse) –> these spines allow neurons to form more connections with each other
is memory distributed or localized
– karl lashley
– brenda milner and sue corkin
– its both
– brenda milner and sue corkin
– its both
Karl Lashley
– tried to localize the engram (trace of memory) – the single location of a memory
– he took rats and made them learn series of mazes and remember them –> put lesions in brain but it didn’t matter where the lesions were, it mattered how big they were
– failed to pinpoint location of memory
– concluded that memory is distributed across brain
– he took rats and made them learn series of mazes and remember them –> put lesions in brain but it didn’t matter where the lesions were, it mattered how big they were
– failed to pinpoint location of memory
– concluded that memory is distributed across brain
sue corkin and brenda milner
– studied patient hm
– early evidence for localized memory
– early evidence for localized memory
patient hm
– surgery to treat intractable epilepsy at age 27
– the seizures were localized to medial temporal lobe, centered on hippocampus
– outcome of surgery – treated seizures, healthy recovery in general, but no new memories
– no memories of new people, places, moments
– other kinds of learning were fine – henry improved at the task of drawing a star in the mirror each time he did it, even though he had no memory of ever doing it before
– selective memory impairment – some memory was unimpaired
– anterograde amnesia – episodic (declarative) memory – inability to create new memories, not remember old ones
– 2 fundamental insights:
1. Different parts of brain support different kinds of memory
2. a specific and critical role for hippocampus and medial temporal lobe in episodic memory
– the seizures were localized to medial temporal lobe, centered on hippocampus
– outcome of surgery – treated seizures, healthy recovery in general, but no new memories
– no memories of new people, places, moments
– other kinds of learning were fine – henry improved at the task of drawing a star in the mirror each time he did it, even though he had no memory of ever doing it before
– selective memory impairment – some memory was unimpaired
– anterograde amnesia – episodic (declarative) memory – inability to create new memories, not remember old ones
– 2 fundamental insights:
1. Different parts of brain support different kinds of memory
2. a specific and critical role for hippocampus and medial temporal lobe in episodic memory
anterograde vs. retrograde
– anterograde = new memories
– retrograde = old memories
– retrograde = old memories
Measuring different forms of learning experiment
– choose between orange or blue butterfly –> 200 times in a row –> change which is correct choice –> start developing sense of which is right choice each time –> when correct, show random image
– test how well people learn which choice is correct (learning from feedback)
– test how well people remember random images (memory for feedback)
– people w/ damage to hippocampus = good at learning from feedback but bad at memory for feedback
– people with damage to basal ganglia = bad at learning from feedback but good at memory for feedback
– double dissociation – 2 groups w/ damage to different parts of brain = 2 groups w/ opposite pattern
– test how well people learn which choice is correct (learning from feedback)
– test how well people remember random images (memory for feedback)
– people w/ damage to hippocampus = good at learning from feedback but bad at memory for feedback
– people with damage to basal ganglia = bad at learning from feedback but good at memory for feedback
– double dissociation – 2 groups w/ damage to different parts of brain = 2 groups w/ opposite pattern
hippocampus
– in healthy people, the hippocampus is more active for experiences that are later remembered
– necessary for long term episodic memories but not for other kinds of memories (habits, working memory)
– important for spacial awareness
– imagination and thinking about future – patients w/ amnesia have trouble imagining future events (imagine your are lying on a tropical beach…)
– necessary for long term episodic memories but not for other kinds of memories (habits, working memory)
– important for spacial awareness
– imagination and thinking about future – patients w/ amnesia have trouble imagining future events (imagine your are lying on a tropical beach…)
hippocampus mouse experiment
– put electrodes in mouse hippocampus and have mouse move through maze
– different groups of neurons respond when mouse is at different parts of maze
– these neurons = place cells
—> neurons in hippocampus represent spatial map
– london cap driver experiment – mrs london cab drivers –> bigger hippocampus?
– different groups of neurons respond when mouse is at different parts of maze
– these neurons = place cells
—> neurons in hippocampus represent spatial map
– london cap driver experiment – mrs london cab drivers –> bigger hippocampus?
action potential
– either fires or not
– once fired, size of electrical impulse does not change
– within a single neuron, the size of ap depends on many factors
– once fired, size of electrical impulse does not change
– within a single neuron, the size of ap depends on many factors
random error
Random errors occur due to variability in measurements. In a careful measurement of nearly any quantity,
the obtained result will be either greater than or less than the “true” value, by a small, random amount.
Sometimes the result will be too high, sometimes too low, and as a result, repeated measurements of the
same quantity will give a set of results scattered around the true value. Sources of random error may
include fluctuation in the measurement apparatus itself (e.g., electrical noise in a digital multimeter),
variability in the interaction of the measurement with the environment (e.g., air currents in a room
changing the reading on a scale), or deviation in a human experimenter’s interpretation and recording of
results. A measurement with only a small amount of random error is said to high have precision.
Statistical tools can help describe and minimize the impacts of random error in a measurement. Since the
results are scattered fairly evenly around the true value, the mean value of the measurements is not
affected much by random errors, as long as enough measurements have been taken. Random errors do,
however, increase the variability of the measurements and therefore increase both the standard deviation (SD) and the standard error of the mean (SE). Increasing the total number of measurements reduces the
contribution of random errors to the SE.†
the obtained result will be either greater than or less than the “true” value, by a small, random amount.
Sometimes the result will be too high, sometimes too low, and as a result, repeated measurements of the
same quantity will give a set of results scattered around the true value. Sources of random error may
include fluctuation in the measurement apparatus itself (e.g., electrical noise in a digital multimeter),
variability in the interaction of the measurement with the environment (e.g., air currents in a room
changing the reading on a scale), or deviation in a human experimenter’s interpretation and recording of
results. A measurement with only a small amount of random error is said to high have precision.
Statistical tools can help describe and minimize the impacts of random error in a measurement. Since the
results are scattered fairly evenly around the true value, the mean value of the measurements is not
affected much by random errors, as long as enough measurements have been taken. Random errors do,
however, increase the variability of the measurements and therefore increase both the standard deviation (SD) and the standard error of the mean (SE). Increasing the total number of measurements reduces the
contribution of random errors to the SE.†
systematic error
Systematic errors represent a bias in the measurement, resulting in measured values that consistently fall either above or below the true value. Systematic errors can occur in many different ways. The bias may be
inherent in the design or setup of the experiment. Asking a group of (stereotypical) fishermen to report the size of the fish they caught may result in a systematic over reporting of fish size. Likewise, measuring the
fish of only those who volunteer to have their catches measured may result in a sampling bias, resulting in a systematically inflated measurement of a typical catch. Alternatively, the bias may be inherent in the measurement apparatus itself. Asking fishermen to measure their catches with the same faulty ruler may result in a systematic underreporting of size. A systematic error can also occur in the analysis of accurately measured data. Converting the fish length from inches to centimeters with the wrong unit
conversion factor would result in a consistently incorrect value.
Systematic errors, particularly those with their roots in the design of the experiment itself, are the most difficult errors to identify and minimize. Since systematic errors bias all measurements in the same
direction, they change the mean value of the measurements, by an amount that cannot be quantified using the standard error of the mean or other statistical techniques. A measurement with large systematic errors is said to have poor accuracy.
inherent in the design or setup of the experiment. Asking a group of (stereotypical) fishermen to report the size of the fish they caught may result in a systematic over reporting of fish size. Likewise, measuring the
fish of only those who volunteer to have their catches measured may result in a sampling bias, resulting in a systematically inflated measurement of a typical catch. Alternatively, the bias may be inherent in the measurement apparatus itself. Asking fishermen to measure their catches with the same faulty ruler may result in a systematic underreporting of size. A systematic error can also occur in the analysis of accurately measured data. Converting the fish length from inches to centimeters with the wrong unit
conversion factor would result in a consistently incorrect value.
Systematic errors, particularly those with their roots in the design of the experiment itself, are the most difficult errors to identify and minimize. Since systematic errors bias all measurements in the same
direction, they change the mean value of the measurements, by an amount that cannot be quantified using the standard error of the mean or other statistical techniques. A measurement with large systematic errors is said to have poor accuracy.
Lonnie Sue
– encephalitis –> destroyed hippocampus –> no new memories
– show her pics in an fmri and repeat some and see which ones she could remember –> see whether or not hippocampus is responsible for retaining copies of recent visual stimuli and relaying them to visual cortex –> regular people = control –>Lonnie sue does remember images —> repetition suppression is a type of short term memory that doesn’t require hippocampus
– show her pics in an fmri and repeat some and see which ones she could remember –> see whether or not hippocampus is responsible for retaining copies of recent visual stimuli and relaying them to visual cortex –> regular people = control –>Lonnie sue does remember images —> repetition suppression is a type of short term memory that doesn’t require hippocampus
Dopamine
– prefrontal cortex
– neurotransmitter
– striatum
– 2 main pathways:
1. motor control
2. reward and value
– most rewards increase dopamine in brain (natural: food, sex; and drugs)
– plays a key role in learning habits based on rewards via signaling of prediction errors
– these learning signals shape actions and decisions in the striatum, a target of dopamine input
– neurotransmitter
– striatum
– 2 main pathways:
1. motor control
2. reward and value
– most rewards increase dopamine in brain (natural: food, sex; and drugs)
– plays a key role in learning habits based on rewards via signaling of prediction errors
– these learning signals shape actions and decisions in the striatum, a target of dopamine input
dopamine monkey juice experiment
put electrodes in monkey brains –> to record dopamine neurons in brain + thought overtime something good happens –> see something in dopamine neurons
– scientists give juice as reward
– every time bell rings –> scientist bring juice so monkeys start to associate bell w/ juice so dopamine increases when bell sounds, not when juice comes
– bell sounds but juice is withheld –> decrease in dopamine neuron activity
– shows that dopamine has something to do w/ predicting when something good will happen
– dopamine = surprise, not reward itself
– scientists give juice as reward
– every time bell rings –> scientist bring juice so monkeys start to associate bell w/ juice so dopamine increases when bell sounds, not when juice comes
– bell sounds but juice is withheld –> decrease in dopamine neuron activity
– shows that dopamine has something to do w/ predicting when something good will happen
– dopamine = surprise, not reward itself
reward prediction error
– predict reward that doesn’t come
– when cue happens dopamine increases, but if no reward after cue = prediction error and dopamine decreases
-Reward prediction error describes differences between expected and actual rewards and/ or consequences
– when cue happens dopamine increases, but if no reward after cue = prediction error and dopamine decreases
-Reward prediction error describes differences between expected and actual rewards and/ or consequences
shape choosing decision experiment
choose between triangle and circle and behind one is money and behind other is nothing –> create reward prediction errors (b/c people expect reward to be behind certain shape but it isn’t) –> see if there are places in the brain that connect w/ reward prediction
Parkinson’s dopamine experiment
– parkinson’s disease = low dopamine
– fmri activity in striatum = a proxy for dopamine input
– parkinson’s patient’s were worse at learning from prediction errors than regular people
– parkinson’s patients that were given treatment that increases dopamine were also better at learning from prediction errors
– fmri activity in striatum = a proxy for dopamine input
– parkinson’s patient’s were worse at learning from prediction errors than regular people
– parkinson’s patients that were given treatment that increases dopamine were also better at learning from prediction errors
accumulation of evidence experiment
– teach rats to tell us decisions using their eyes –> how do neurons respond when we give them evidence
– different elements predict outcome w/ different probability – this decision requires accumulation of evidence
– more evidence = more neural response
– different elements predict outcome w/ different probability – this decision requires accumulation of evidence
– more evidence = more neural response
parietal cortex
– an area that connects visual input to eye movements
– neurons here have spatially selective response fields
– LIP – important for controlling eye movements
– neurons here show persistent activity that is not directly related to info from the senses, reflecting a decision about a future action – this activity is not static: neurons ramp up their firing as evidence is accumulated towards a decision
– reflect accumulation of evidence to make decision
– neurons here have spatially selective response fields
– LIP – important for controlling eye movements
– neurons here show persistent activity that is not directly related to info from the senses, reflecting a decision about a future action – this activity is not static: neurons ramp up their firing as evidence is accumulated towards a decision
– reflect accumulation of evidence to make decision
decisions about food
– ask patients to choose which food they prefer and how much they prefer it
– anorexia vs. healthy controls
– decisions in patients w/ anorexia are related to more activity in the striatum
– brain activity in the experiment is related to actual food consumption
– anorexia vs. healthy controls
– decisions in patients w/ anorexia are related to more activity in the striatum
– brain activity in the experiment is related to actual food consumption
decision making summary
– different brain regions contribute to different aspects of decision making
– the striatum and dopamine support habitual decisions, actions
– neurons in parietal cortex reflect accumulation of evidence towards a decision
– understanding how brain makes decisions has important implications for disease
– the striatum and dopamine support habitual decisions, actions
– neurons in parietal cortex reflect accumulation of evidence towards a decision
– understanding how brain makes decisions has important implications for disease
Null hypothesis
there is no difference between the results
alternative hypothesis
there is a difference between results
striatum
– habitual decisions/actions – dopamine
special relativity
– no one is preferred
– only applies to uniform motion
– motion is relative
– the laws of physics should look the same to all observers in uniform motion
– you should be able to do anything in uniform motion that you can do in your living room
– newtons 1st law – a body in motion stays in motion
– in the absence of forces, particles travel in straight lines
– 2 observers in uniform relative motion agree that projectiles travel in straight lines (agree on laws of physics)
– relativity is constructed to adhere to rule that speed of light is fixed speed = not relative
– speed is relative – 2 people in different states of motion will disagree on how fast something is traveling
– only applies to uniform motion
– motion is relative
– the laws of physics should look the same to all observers in uniform motion
– you should be able to do anything in uniform motion that you can do in your living room
– newtons 1st law – a body in motion stays in motion
– in the absence of forces, particles travel in straight lines
– 2 observers in uniform relative motion agree that projectiles travel in straight lines (agree on laws of physics)
– relativity is constructed to adhere to rule that speed of light is fixed speed = not relative
– speed is relative – 2 people in different states of motion will disagree on how fast something is traveling
speed of light
– fixed
– 300 million m/s (300 thousand km/s)
– strength of electric force + strength of magnetic force
– 300 million m/s (300 thousand km/s)
– strength of electric force + strength of magnetic force
time dilation
– light clock: moving clock seems to tick slower than stationary one (for alice)
– time elapsed for moving object = time elapsed for stationary object/y
– time = distance/speed
– gamma factor
– don’t notice time dilation unless traveling near the speed of light
– time elapsed for moving object = time elapsed for stationary object/y
– time = distance/speed
– gamma factor
– don’t notice time dilation unless traveling near the speed of light
gamma factor
– amount by which time dilates and length contracts
– v=0, y=1
– v –> c, y –> infinity
– y always greater than 1
– 1 divided by the square root of 1 minus (v divided by c) squared
– v=0, y=1
– v –> c, y –> infinity
– y always greater than 1
– 1 divided by the square root of 1 minus (v divided by c) squared
Length contraction
– gamma factor
– only notice when traveling near speed of light
– contact only in direction of motion
– only notice when traveling near speed of light
– contact only in direction of motion
rest energy
– motion through time
– discovered by einstein
– discovered by einstein
e = mc^2
– the mass of a body in relative motion increases
– it becomes energetically very expensive to push a massive object near the speed of light
– e = ymc^2 -special relativity always needs to be considered but when speeds are low -> y= 1 so you don’t notice so e=mc^2
– we can never build a rocket powerful enough to boost an astronaut to the speed of light
– would require infinite amount of energy
– it becomes energetically very expensive to push a massive object near the speed of light
– e = ymc^2 -special relativity always needs to be considered but when speeds are low -> y= 1 so you don’t notice so e=mc^2
– we can never build a rocket powerful enough to boost an astronaut to the speed of light
– would require infinite amount of energy
faraday and maxwell
– late 1800s
– did experiments w/ speed of light
– found that speed is 3.0 * 10^8 –> relative to ether
– einstein disproves either
– did experiments w/ speed of light
– found that speed is 3.0 * 10^8 –> relative to ether
– einstein disproves either
neutrinos
– neutral electrical charge
– very small
– scientist did experiment which showed that they moved faster than speed of light but this was disproved
– very small
– scientist did experiment which showed that they moved faster than speed of light but this was disproved
gravity
– one of few fundamental forces
– can’t be put into equation w/ other fundamental forces
– just a number, like the speed of light
– newtonian gravity – f=GMm/r^2 – implies that the force of gravity is communicated instantaneously
– there is no time dependence in Newton’s Law. This further implies that the gravitational force
is communicated faster than the speed of light. Einstein set out to resolve this conundrum by
figuring out what gravity actually is, and how it is communicated.
– gravity is feeling of weightlessness when you remove other objects that could interrupt your falling
– newton gravity = need for forces, no equivalence principle, instantaneous effects, effective, static spacetime,
– einstein gravity – no forces, awful calculations, equivalence principle, effective, dynamic spacetime
– consequences of einstein gravity = gravitational waves, black holes, formation of universe
– can’t be put into equation w/ other fundamental forces
– just a number, like the speed of light
– newtonian gravity – f=GMm/r^2 – implies that the force of gravity is communicated instantaneously
– there is no time dependence in Newton’s Law. This further implies that the gravitational force
is communicated faster than the speed of light. Einstein set out to resolve this conundrum by
figuring out what gravity actually is, and how it is communicated.
– gravity is feeling of weightlessness when you remove other objects that could interrupt your falling
– newton gravity = need for forces, no equivalence principle, instantaneous effects, effective, static spacetime,
– einstein gravity – no forces, awful calculations, equivalence principle, effective, dynamic spacetime
– consequences of einstein gravity = gravitational waves, black holes, formation of universe
the equivalence principle
– to experience gravity is to be weightless (free fall)
– at international space station – falling around earth which is why astronauts float – not cuz they aren’t feeling Earth’s gravity
– you can’t tell difference between standing on floor w/ gravity or accelerating – can’t distinguish between accelerating and feeling gravitational field
– at international space station – falling around earth which is why astronauts float – not cuz they aren’t feeling Earth’s gravity
– you can’t tell difference between standing on floor w/ gravity or accelerating – can’t distinguish between accelerating and feeling gravitational field
General Relativity
– empty space is flat – in empty space, things fall freely in straight line –> trace flat grid
– in presence of heavy mass – paths along which we fall is curved
– spacetime is curved
– mass and energy curve spacetime and fall along curve
– light follows curved paths – this is confirmed when when a scientist goes to Madagascar and views a total solar eclipse and can see light from another star bending around sun
– the more mass you concentrate in the planet, moon, or star, the more we notice curves
– there is a preferred perspective – person nearest to black hole thinks that time is slowing down for him and person far from black hole also thinks that time is slowing down for other person
– in presence of heavy mass – paths along which we fall is curved
– spacetime is curved
– mass and energy curve spacetime and fall along curve
– light follows curved paths – this is confirmed when when a scientist goes to Madagascar and views a total solar eclipse and can see light from another star bending around sun
– the more mass you concentrate in the planet, moon, or star, the more we notice curves
– there is a preferred perspective – person nearest to black hole thinks that time is slowing down for him and person far from black hole also thinks that time is slowing down for other person
gravitational waves
– in the shape of spacetime, travel at the speed of light
– if sun disappeared, gravitational waves would be created –> planets would travel out in straight line –> signal of disappearance of sun sent out to planets @ speed of light
– if sun disappeared, gravitational waves would be created –> planets would travel out in straight line –> signal of disappearance of sun sent out to planets @ speed of light
escape velocity
v = square root of 2GM/r
– depends only on mass of body it is trying to escape, not mass of object itself
– if size of body is r = 2gm/c^2 – then to escape you need to launch c (black hole)
– depends only on mass of body it is trying to escape, not mass of object itself
– if size of body is r = 2gm/c^2 – then to escape you need to launch c (black hole)
event horizon
r=2gm/c^2 – swarzchild radius
– the region beyond which not even light can escape – not privy to events on other side
– time stops
– the region beyond which not even light can escape – not privy to events on other side
– time stops
black holes
– dark
– nothing – if you approach event horizon, literally is nothing is there
– time dilation – person on black hole = square root of (1 – 2gm/rc^2) person not on black hole
– einstein believed that black hole could not for in nature
– star bigger than sun –> runs out of fuel –> begins to collapse and heats and explodes in supernova –> core is left w/o anything else and begins to collapse under its own weight –> black hole
– make sound
– light on inside
– nothing – if you approach event horizon, literally is nothing is there
– time dilation – person on black hole = square root of (1 – 2gm/rc^2) person not on black hole
– einstein believed that black hole could not for in nature
– star bigger than sun –> runs out of fuel –> begins to collapse and heats and explodes in supernova –> core is left w/o anything else and begins to collapse under its own weight –> black hole
– make sound
– light on inside
LIGO
– ray weiss – made musical instrument to record sounds of spacetime – shines laser that bounces of mirrors
– 1st detection of 2 black holes that collided over a billion years ago
– 1st detection of 2 black holes that collided over a billion years ago
the universe
– everything: the space and time, the galaxies, the black holes etc
– started 13.8 billion years ago
– universe is expanding (einstein thought universe was forever and static )
– started 13.8 billion years ago
– universe is expanding (einstein thought universe was forever and static )
light year
– a unit of distance
– distance light can travel in one year
– 30 million s
– 9 trillion km
– distance but also looking back in time
– a star that is one light year away – we are seeing an image of the star as it was 1 year ago
– no info travels faster than speed of light
– we can only see far away objects as they were in the far past, we can’t see them as they are now
– milky way = 100,000 light years across
– b/c of speed of light we can probe universe in terms of time
– distance light can travel in one year
– 30 million s
– 9 trillion km
– distance but also looking back in time
– a star that is one light year away – we are seeing an image of the star as it was 1 year ago
– no info travels faster than speed of light
– we can only see far away objects as they were in the far past, we can’t see them as they are now
– milky way = 100,000 light years across
– b/c of speed of light we can probe universe in terms of time
the copernican principle
– we are not in privileged locations and we don’t have privileged perspective
– the universe should look roughly similar from the point of view of any other galaxy
– the universe on the largest scales should look the same from all locations (homogenous) and should look the same in all directions (isotropic)
– the assumption that the universe is homogenous and isotropic
– the universe should look roughly similar from the point of view of any other galaxy
– the universe on the largest scales should look the same from all locations (homogenous) and should look the same in all directions (isotropic)
– the assumption that the universe is homogenous and isotropic
expansion of universe
– scientist imagined universe as cosmic ocean instead of round –> led them to argue that relativity predicts that if we fill volume of universe w/ all galaxies –> universe would expand b/c of pressure –> Einstein doesn’t believe this and adds constant to relativity equation that makes it so that mathematically the universe isn’t expanding (proven wrong by Hubble)
– the space between the galaxies is stretching
– the galaxies are pushed apart
– from any galaxy there would be the illusion of being at the center
– Hubble observed that all galaxies are moving away and that further away galaxies are moving faster
– the space between the galaxies is stretching
– the galaxies are pushed apart
– from any galaxy there would be the illusion of being at the center
– Hubble observed that all galaxies are moving away and that further away galaxies are moving faster
hubble’s law / recessional velocity
– the distance between the galaxies grows
– from our perspective, the galaxies have a velocity away from us, but they aren’t moving relative to the expansion (just space between)
– the recessional velocity obey’s hubble’s law
v = h*d
v = velocity at which you see a galaxy recede
h = hubble’s constant – related to the rate at which the universe expands (only constant in speed but not in time –> so in future this number will be bigger)
d = the physical distance between you and the galaxy
– the more distant the galaxy, the faster it appears to recede
– the galaxy isn’t really moving – it’s the space that’s stretching between the galaxies
– h today is 23 km/s/million lyrics
– from our perspective, the galaxies have a velocity away from us, but they aren’t moving relative to the expansion (just space between)
– the recessional velocity obey’s hubble’s law
v = h*d
v = velocity at which you see a galaxy recede
h = hubble’s constant – related to the rate at which the universe expands (only constant in speed but not in time –> so in future this number will be bigger)
d = the physical distance between you and the galaxy
– the more distant the galaxy, the faster it appears to recede
– the galaxy isn’t really moving – it’s the space that’s stretching between the galaxies
– h today is 23 km/s/million lyrics
look back time
– the time between reception and emission
– if one galaxy emits a burst of light and one billion years later the other galaxy receives it, at that the moment the light is received, the galaxies must be more than 1 billion light years away from each other b/c the space is stretching
– if one galaxy emits a burst of light and one billion years later the other galaxy receives it, at that the moment the light is received, the galaxies must be more than 1 billion light years away from each other b/c the space is stretching
the big bang
– a trillionth of a trillionth of a trillionth of a second after the big bang, the universe is full of hot primordial light
– everywhere
– primordial light
– everything was hot and dense and is cooling and expanding as time goes on
– look back time to primordial light- the age of the universe is 13.8 billion years
– everywhere
– primordial light
– everything was hot and dense and is cooling and expanding as time goes on
– look back time to primordial light- the age of the universe is 13.8 billion years
cosmological mysteries
– everything we know comes to less than 5% of the energy density
– over 25% of the energy density is in the form of dark matter (acts like matter gravitationally)
– can’t see dark matter, but galaxies are heavier than the mass traced by luminous matter
– nearly 70% of energy density is in the form of dark energy (universe is accelerating –> hubble’s constant is increasing b/c of dark energy)
– can’t see dark energy, but the expansion is getting faster
– over 25% of the energy density is in the form of dark matter (acts like matter gravitationally)
– can’t see dark matter, but galaxies are heavier than the mass traced by luminous matter
– nearly 70% of energy density is in the form of dark energy (universe is accelerating –> hubble’s constant is increasing b/c of dark energy)
– can’t see dark energy, but the expansion is getting faster
charles pickering
director of harvard observatory
– pickering’s haram – group of female computers
– henrietta – characterized variable stars –> allow her to know if she was looking at something faint and close or far and bright –> Hubble uses this to determine distance of stars/space objects
– pickering’s haram – group of female computers
– henrietta – characterized variable stars –> allow her to know if she was looking at something faint and close or far and bright –> Hubble uses this to determine distance of stars/space objects
balloon analogy
– take a balloon and stain it with ink dots –> blow balloon up –> looks as tho nearby dots are moving away slower than farther ones –> dots not moving but space between them is –> same thing w/ universe
– flaws:
– makes it seem as tho we are outside of space looking down on it (we can’t get outside of universe)
– makes it look like balloon is expanding into 3d –> universe isn’t expanding into another dimension
– flaws:
– makes it seem as tho we are outside of space looking down on it (we can’t get outside of universe)
– makes it look like balloon is expanding into 3d –> universe isn’t expanding into another dimension
cosmic microwave background (primordial light)
– background light left over from big bang
– we see the light that has traveled to us for 13.8 billion years in all directions
– distance between us and cmb = 45 billion light years or either side b/c of expansion of universe
– we see the light that has traveled to us for 13.8 billion years in all directions
– distance between us and cmb = 45 billion light years or either side b/c of expansion of universe