universe + special relativity Flashcards
distances and measurements used in universe + special relativity?
distances and measurements used in universe + special relativity are:
• lightyear: the distance light travels in one year (1 ly = 9.5x10^15m)
• astronomical unit: the average distance between the earth and sun (1 AU = 1.5x10^11m)
• arcsecond: 1/3600 th of a degree
• arcminute: 1/60 th of a degree
• parsec: the distance away an object must be to have a parallax of one arcsecond when observed from Earth (1 pc = 3.1x10^6m or 1 pc = 3.3ly)
explaining RADAR
• RADAR stands for Radio Detection and Ranging
• RADAR makes use of radio waves to determine the distance to an object, hence speed and acceleration can be determined by calculation
• RADAR only works for short distances because the time delay (Δt) becomes greater and the signal becomes weaker for larger distances
how to calculate the distance to and velocity of an asteroid?
1) send out a pulse, pulse then returns, record the time taken for pulse to return (Δt1)
2) wait a certain amount of time (eg 100 seconds)
3) send a second pulse, pulse then returns, record time for pulse to return (Δt2)
4) find the distance the asteroid is at before ‘100s’ by multiplying each each recorded time (from 1 and 3) by the speed of light (the speed of radiowaves)
5) find Δs (the distance travelled in the certain time)
6) relative velocity = Δs / (certain time)
use relative velocity =
Δs / (t2 - t1)
what are the assumptions when determining asteroid speed?
some of the assumptions when determining asteroid speed are:
1) speed of the signal is the same both ways (constant speed of light)
2) moment of reflection is halfway through each time delay (Δt)
what is the doppler shift? and what can it be used for?
• the doppler shift is a change in the observed wavelength due to the relative motion of the source and observer
• spectral lines are caused by atoms absorbing / emitting light at a particular wavelength…
•… receding stars show red shift, approaching stars show blue shift
what is the doppler effect? what happens when source moves towards observer + what happens when source moves away?
• the doppler effect is the apparent change in the observed frequency (and wavelength) of a wave when the source is moving relative to the observer
• if the source is moving towards the observer, the frequency appears to increase and the wavelength appears to shorten
• if the source is moving away from the observer, the frequency appears to decrease and the wavelength appears to lengthen
what is a parallax?
⋅ a parallax is the apparent change in position of an object (eg close stars) relative to a fixed background when viewed from a changing angle
what is the parallax angle?
⋅ the parallax angle (θ) is half the angle that the object (eg close star) appears to move through (in 6 months)
what happens when θ is really small? (parallax)
⋅ when θ is really small (concerning parallax), tanθ (in degrees) = θ (in radians)
what is the equation for parallax?
⋅ the equation for parallax is:
(in degrees:) tanθ = 1 AU / d
(in radian:) θ = 1 AU / d
where:
⋅ AU is astronomical unit
⋅ θ is parallax angle
⋅ d is distance from earth to object (eg close star)
what happens if d decreases? (parallax equation)
⋅ when d decreases (in the parallax equation), the more parallax it shows as the earth orbits the sun
• bc parallax angle ∝ 1/d
what is a standard candle?
⋅ a standard candle is a star of known luminosity that is used as a comparative measure for other stars
what is the doppler shift?
⋅ the doppler shift is a change in the observed wavelength of a wave due to the relative motion of the source and the observer
what can the doppler shift be used for? (not cosredshift)
⋅ the doppler shift can be used to tell if stars are receding or approaching us:
1) spectral lines of a star are caused by atoms absorbing / emitting light at a particular wavelength
2) receding stars show red shift and approaching stars show blue shift
what is the equation used for doppler shift?
⋅ the equation used for doppler shift is:
z = Δλ / λ = v / c
where:
⋅ z = fractional increase in λ (wavelength)
⋅ λ = emitted wavelength
⋅ Δλ = change in wavelength
⋅ v = recessional velocity (of star)
⋅ c = speed of light (can also just be speed of wave)
NOTE:
⋅ equation is correct for vs much smaller than speed of light- for vs near speed of light, special relativity modifies this
what is cosmological redshift?
⋅ cosmological redshift is the stretching of the wavelength of light to longer wavelengths as the space it is travelling through expands
what is hubble’s law?
⋅ hubble’s law states that “distant galaxies are moving away at a speed proportional to their distance”
what is the equation for recession velocity? (cosmological redshift)
⋅ the equation for recession velocity ( in cosmological redshift) is:
v = (H0)r
where:
⋅ v = recession velocity
⋅ H0 = the Hubble constant
⋅ r = distance
what is Hubble time?
⋅ Hubble time is the time since galaxies were close together (as a singularity) i.e. the time scale / age of the universe
⋅ it is calculate using:
1 / H0 = r / v
⋅ the bigger H0 means the younger the universe is, so the faster the universe must have expanded to reach its present size
what is the big bang?
⋅ the big bang is the probable origin of the universe - a very hot, dense state from which it has expanded and cooled
what is cosmic microwave background radiation?
⋅ cosmic microwave background radiation (CMBR) is microwave radiation that permeates the universe
⋅ CMBR is red shifted radiation from an early hot state of the universe
⋅ CMBR has the largest known redshift, having been produced with a wavelength of the order 1μm to now the order 1mm (1000x larger)
what has happened to the temperature of CMBR as the universe has redshifted until now?
⋅ the temperature of CMBR has fallen by a factor of 1000 (from 3000K to 3K) (inverse of wavelength of CMBR, which has increased by a factor of 1000) as the universe has redshifted until now
is there variation in the temperature of CMBR across the universe? and what is believed to have formed from these variations?
⋅ yes there are variations in the temperature of CMBR across the universe
⋅ it is believed that stars and galaxies formed from these non-uniformities
⋅ the cosmological expansion has stayed the same however
what is special relativity?
⋅ special relativity explains the motion of bodies with very high speeds, speeds close to the speed of light
⋅ (low speeds produce the results as predicted by Newton’s Laws)
what was Einstein’s First Postulate?
⋅ Einstein’s First Postulate was that: “the laws of physics are the same for all observers in all inertial frames of reference”.
⋅ so physical behaviour cannot depend on any absolute velocity
what was Einstein’s Second Postulate?
⋅ Einstein’s Second Postulate was that: “the speed of light is the same for inertial frames of reference”.
⋅ the speed of light does not depend on the motion of the light source or observer (in other words, the speed of light in free space is invariant)
what is the Lorentz Factor?
⋅ the Lorentz Factor (relativistic factor) (γ) is the factor by which time changes for an object, while that object is in motion as measured by an observer
⋅ it can be calculated using the equation below:
where:
⋅ γ = lorentz factor
⋅ v = speed of object
⋅ c = speed of light
NOTE:
⋅ if v tends to 0, γ tends to 1, so t = t0, same as predicted by Newton’s Laws
⋅ if v = c, we get γ = 1/0 which is undefined, so this supports the idea that nothing can go faster than the speed of light (superluminal travel is impossible)
what are inertial frames of reference?
⋅ inertial frames of reference are frames with a constant or zero velocity (i.e. where Newton’s Laws apply, as there is no net external force acting on the frame)
⋅(nothing is truly ‘at rest’ or truly ‘moving’, only relative to another object)
what are space-time diagrams?
⋅ in space-time diagrams, the line that traces out on a space-time diagram is called a worldline
⋅ for an object moving at non-zero relative velocity, its worldline moves up the time axis (y-axis) to or away from the observer (x=0)
⋅ for an object with zero relative velocity, it traces a vertical worldline on the space-time diagram
⋅ a light pulse travels at 1 light second per second so has a worldline at 45 degrees
⋅ due to the second postulate, this is true for every space-time diagram
⋅ a steeper gradient means the object is moving slower (moving less distance during a longer time)
⋅ a worldline cannot have an angle less than 45 degrees as objects cannot travel faster than the speed of light
what are some of the assumptions for space-time diagrams?
in space-time diagrams, we assume:
⋅ that the speed of light is constant, so the reflection occurs halfway through the ‘flight time’ of the pulse to and from the object
⋅ that the speed of light is not affected by the motion of the distant object
what does time dilation mean?
⋅ time dilation means that the amount of time between two events differs depending on whether you are at rest relative to them
⋅ eg) clocks moving relative to an observer run slowly as seen by the observer
describe the Time Dilation and Light Clock Thought Experiment?
in the light clock thought experiment:
1) a pair of mirrors between which light bounces
2) one tick is when the light travels to the other mirror and back
3) consider a stationary light clock on a train where the light pulse bounces vertically, ie as viewed by a person on the train
4) the distance to the other mirror is d = (c x t0), so the time to return to the same mirror is 2t0; t0 is the time as measured by a stopwatch on the train
5) the train moves with a speed (v) so an observer outside the train sees the train measured by a stopwatch in the frame of the observer
6) according to the observer, the light pulse moves at an angle a distance (c x t) there and a distance (c x t) back to the first mirror
7) t > t0 so ct is greater than ct0, hence the observer sees the clock ‘tick’ slower when the clock is moving
8) using a diagram, this mathematical derivation can be seen to only need Pythagoras’ Theorem:
what is the equation for ‘dilated time’?
the equation for dilated time is:
t = γ x t0
where:
⋅ γ is the lorentz factor
