Classical to Quantum
Classical to Quantum | ChatGPT, fundamental physics and SR using sound, not light | Wild Egg Maths
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39 views Oct 1, 2023
Let's start a conversation about fundamentals of physics with ChatGPT, aiming to understand aspects of Special Relativity (SR) from a novel point of view, where the current esteemed and distinguished role of light is abandoned. Instead we want to look at the consequences of investigating the world around us using sound, like a bat, with echolocation. This has some surprising implications, not least since sound does not fool us as much as light does, on account of the much more understandable speed of sound, and the obvious corollary that we have to pay more attention to what "simultaneous" actually means. This is of course a crucial issue in SR.
Although ChatGPT is not so sophisticated mathematically, its wide knowledge and seeming willingness to consider novel points of view is quite refreshing!
0:01
hello everyone I'm Nan wildberger thanks
0:03
for joining me on this adventure today
0:05
we have something really interesting
0:07
because I'm chatting with my friend chat
0:09
gbt
0:11
4 we are having a very interesting
0:14
discussion uh led by my leading
0:17
questions in a direction that I'm
0:19
interested in going on the foundations
0:22
of physics taking a very very sort of
0:26
basic orientation to how we might go
0:28
about setting up an initial
0:30
investigation into the nature of the
0:32
world and to simplify things I want to
0:35
first of all stick with a
0:37
one-dimensional situation all right and
0:40
I want to cut to the Chase and just
0:43
restrict ourselves to the very
0:46
minimum that we need in terms of
0:49
technology to explore to observe this
0:53
one dimensional world so that's what I'm
0:56
going to try to get gp4 talking about is
1:00
is potential setup for doing this and
1:03
then some of the
1:05
mathematical U consequences and what I'm
1:09
trying to do is touch base with a video
1:12
that I made about 10 years ago called
1:15
bats echolocation and a Newtonian view
1:18
of special relativity which we're going
1:20
to have to talk a lot more about so
1:21
there's a lot of interesting um Concepts
1:24
in there that are very relevant for our
1:27
understanding Einstein's special
1:29
relativity and some of the issues um
1:31
that really need to be discussed there
1:33
so
1:36
me suppose that you wanted to
1:38
investigate physics from a very
1:39
Elementary point of view and that you
1:41
didn't have any current physical
1:42
knowledge as you do but you just wanted
1:45
to investigate fundamental properties of
1:47
the world around us of the various five
1:49
senses suppose I was only going to give
1:51
you one to use in observing the world
1:54
which one would it be chat GPT for
1:57
replies if we were to investigate the
1:59
fundamental properties of the world
2:01
around us from a very Elementary point
2:02
of view using only one sense the sense
2:04
of sight would be the most beneficial
2:06
Choice Vision provides a broad range of
2:08
information about the environment from
2:10
motion and spatial relationships to
2:11
color and light many fundamental
2:13
concepts in physics such as motion
2:15
reflection refraction and wave
2:17
interference can be directly observed or
2:19
inferred through site throughout history
2:21
many discoveries in physics were made
2:23
through Visual observations making it a
2:25
powerful tool for understanding the
2:26
world around us absolutely can't agree
2:29
more
2:30
now me suppose however that I gave you
2:33
sound instead with the ability like a
2:36
bat to send out sound signals and
2:39
receive them to determine positions of
2:42
objects around you how would you proceed
2:45
in investigating the world around us
2:47
from a physics point of
2:51
view chat GPT if given the sense of
2:56
sound especially with echolocation
2:58
ability similar to a that the
3:00
investigation of physics would take a
3:02
different yet still insightful path
3:05
here's how we might proceed one distance
3:08
and motion by sending out sound signals
3:11
and receiving them we could deduce the
3:13
relative distance of objects based on
3:15
the time it takes for the sound to
3:17
return faster returns mean closer
3:19
objects this could lead to a basic
3:21
understanding of motion and relative
3:22
position two density and medium
3:25
different materials will reflect sound
3:27
waves differently a soft material absorb
3:30
more sound while a hard material might
3:31
reflect it more sharply through
3:33
echolocation we might deduce the
3:35
presence of different materials
3:37
additionally sound travels at different
3:39
speeds in different media air water
3:41
solid materials leading to insights
3:43
about the properties of those
3:45
media three frequency and pitch
3:49
different objects might reflect sound at
3:51
different frequencies depending on their
3:53
size shape and material observing these
3:55
differences would provide insights into
3:57
the nature of sound waves leading to
3:59
Concepts like frequency wavelength and
4:01
possibly
4:03
resonance Doppler effect if an object is
4:06
moving relative to us the frequency of
4:08
the reflective sound will change this
4:11
shift in frequency could lead to an
4:13
understanding of the Doppler effect a
4:14
fundamental Concept in wave
4:16
mechanics wave interference by emitting
4:19
sound waves at different frequencies or
4:21
from different positions we might notice
4:23
areas where the sound is Amplified
4:25
constructive interference or reduced
4:27
destructive interference this would give
4:29
insight into wave
4:31
Behavior Sound Speed by comparing the
4:33
time it takes for sounds to reflect off
4:36
of known distances the speed of sound in
4:38
different media could be estimated and
4:41
temperature effects Sound Speed in air
4:43
can change with temperature with Keen
4:45
sensitivity we might notice sound
4:47
returning more quickly or slowly
4:49
depending on the ambient temperature
4:51
leading to investigations into thermal
4:54
physics while the sense of sight
4:56
provides a wide scope of observable
4:58
phenomena sound especially with
5:00
echolocation capabilities would offer a
5:03
unique and in-depth perspective into the
5:05
properties of materials wave mechanics
5:07
and motion over time with careful
5:10
observation and experimentation many
5:13
foundational Concepts in physics could
5:14
still be deduced using just this
5:18
sense this is an incredibly good answer
5:21
it's incredibly good it's so he's or she
5:24
or it is right on the money here I
5:28
think let me also point out um another
5:32
aspect of the comparison between sound
5:34
and Light which actually was a a
5:36
motivating point for me uh is that sound
5:39
obviously goes much slower and so the uh
5:44
the scale of sound and Its Behavior is
5:47
more you know in tune with our scale in
5:51
the world in other words it's easier for
5:53
us to appreciate sound as a moving thing
5:57
rather than light which appears to all
6:00
intents and purposes as being
6:01
effectively instantaneous so light fools
6:05
us in a way that sound does
6:09
not okay back to me that's a most
6:13
excellent answer thank you so now
6:15
suppose we get specific and we're
6:16
investigating one-dimensional mechanics
6:19
just particles moving around on a
6:21
one-dimensional line perhaps having
6:23
elastic or inelastic collisions suppose
6:26
that you are at the origin of this
6:28
one-dimensional space with echolocation
6:31
capabilities how would you go about
6:33
investigating the resulting Dynamics and
6:39
mechanics chat gbt given a
6:42
one-dimensional space and echolocation
6:45
capabilities investigating the Dynamics
6:47
and mechanics would be a fascinating
6:49
Endeavor here's a structured
6:52
approach position and motion by sending
6:55
out sound signals and measuring the time
6:56
it takes for the sound to bounce back we
6:58
can determine the relative position of a
7:00
particle tracking these times
7:01
continuously would allow us to
7:03
understand the motion of the particle
7:05
velocity by noting the change in
7:07
position over time we could derive the
7:09
concept of velocity if the reflected
7:11
sound is returning more quickly over
7:13
consecutive time intervals the particle
7:14
is approaching conversely if it's
7:16
returning more slowly the particle is
7:19
receding collisions when two particles
7:21
Collide their subsequent positions and
7:23
velocities would change by observing
7:26
these changes a elastic collisions if
7:29
the total relative velocity before the
7:31
Collision is the same as after but
7:34
possibly in opposite directions for the
7:35
two particles we can infer the Collision
7:37
is perfectly elastic in elastic
7:39
collisions if there's a decrease in the
7:41
total relative velocity post Collision
7:44
some energy has been converted to other
7:45
forms like sound or heat indicating an
7:48
inelastic
7:49
collision conservation of
7:52
momentum and this is a very important
7:55
Point here even without the concept of
7:57
mass mass in quotes okay as it's hard to
8:01
discern just with
8:03
sound and as in as side as it's also
8:07
very hard to discern just with
8:10
light mass is much more problematic than
8:14
people uh usually assume but anyway
8:17
let's carry on we could deduce that
8:19
something remains unchanged before and
8:21
after Collision when observing multiple
8:24
particles this would be an observation
8:26
of the conservation of
8:28
momentum
8:31
and a theme that will become important
8:34
for us later is that there's a potential
8:36
here for using this kind of observation
8:39
to actually get at what mass
8:42
is okay so we don't have to think about
8:45
mass in terms of gravitational uh you
8:48
know forces um or even in terms of
8:51
inertial masses although this is an
8:54
aspect of that but just observing what
8:56
happens in collisions which is something
8:58
that we can do with with sound or with
9:00
light that gives us at least a
9:03
springboard for tackling
9:06
mass for force and acceleration if a
9:09
particle suddenly changes its velocity
9:11
without any Collision we might infer an
9:13
unseen Force acted upon it over time by
9:16
comparing the magnitude of velocity
9:17
changes in various scenarios we can
9:20
develop the idea of acceleration and
9:21
perhaps deduce a relationship between
9:23
force and
9:25
acceleration Doppler effect if the
9:27
particles are moving rapidly the fre
9:29
quency of the reflected sound would
9:30
change based on their velocity by
9:32
observing this effect we could fine-tune
9:34
our understanding of velocities and
9:35
possibly discern constant velocities
9:37
from accelerating decelerating
9:40
motions sound intensity and mass this is
9:43
speculatively if particles have
9:45
different sizes or masses they might
9:47
reflect sound with different intensities
9:50
this would be a rough way to
9:51
differentiate between light and heavy
9:53
particles leading us to consider the
9:55
Mass's effect on motion and collisions
9:58
again trying to get at Mass
10:01
somehow and finally external influences
10:03
if a particle changes its motion without
10:05
any apparent Collision we might infer
10:08
external influences or forces at play
10:11
this could lead to Concepts like
10:12
friction or even a basic understanding
10:14
of fields if such influences are
10:16
consistent and
10:17
detectable so using echolocation in a
10:20
one-dimensional space would be a unique
10:21
challenge still with consistent
10:23
observation experimentation and Analysis
10:27
many foundational concepts of mechanics
10:29
could be deduced or inferred over
10:34
time another great
10:37
answer me okay let's be specific suppose
10:41
that we give you an internal clock so
10:44
there's Time Zero Time 1 time 2 Etc and
10:46
that's all you have okay so what
10:48
mechanism would you use in order to
10:50
define the position and time of various
10:53
events that you could register with your
10:56
echolocation capabilities
11:02
chat GPT given an internal clock that
11:04
marks discrete time intervals and the
11:06
ability to use echolocation we can set
11:09
up a systematic mechanism to measure
11:11
position and time of various events
11:13
here's how when you emit a sound wave
11:16
and it reflects back from an object the
11:18
time taken for the sound to return can
11:20
be used to determine the object's
11:22
distance this is based on the equation d
11:24
= c * T / 2 where D is the distance to
11:27
the object C is the speed of sound in
11:29
the medium which remains constant in our
11:32
scenario and T is the total time taken
11:34
for the sound to travel to the object
11:36
and back the division by two accounts
11:38
for the round trip of the sound
11:40
wave two time intervals with the
11:43
internal clock ticking at discrete
11:45
intervals we' operate as follows emit a
11:47
sound wave exactly when the clock ticks
11:49
for example at Time Zero listen for the
11:52
reflected sound if it's received exactly
11:54
at the next tick time one then the
11:57
object is at a distance correspond
11:58
responding to half the sound's travel
12:01
distance in one time
12:03
interval if the reflection is received
12:05
at a later tick we simply adjust our
12:07
distance calculation based on the known
12:09
speed of sound and the total time
12:10
intervals that have
12:12
passed position time data points for
12:15
every object or event detected record
12:18
the time interval from the internal
12:20
clock and the calculated distance
12:22
position at that time this results in a
12:25
set of time position data
12:27
points
12:29
SpaceTime or maybe better yet time
12:33
space mapping motion by comparing
12:36
successive time position data points for
12:38
an object its motion can be understood
12:41
if the position remains constant over
12:43
multiple ticks the object is stationary
12:45
if the position changes consistently
12:47
increasing or decreasing by a fixed
12:48
amount every tick the object is moving
12:50
with a constant velocity if the position
12:52
change varies over time the object may
12:54
be accelerating or
12:56
decelerating and collisions and events
12:58
if two objects approach each other and
13:00
suddenly change their relative
13:01
velocities or directions at a specific
13:03
time tick a collision or interaction can
13:06
be inferred the precise time and
13:08
position of the event would be the tick
13:10
and the respective positions when this
13:12
change is detected using this systematic
13:15
approach the Echolocation capabilities
13:17
combined with the internal clock can
13:19
provide a rudimentary but effective
13:21
position time graph of sorts for objects
13:24
and events in the one-dimensional
13:27
space
13:30
okay I agree with everything it's saying
13:32
so
13:33
far me excellent so just to put your
13:36
observation into mathematical context
13:38
suppose that an event occurs somewhere
13:40
at time T at position X on this
13:42
onedimensional space and that you detect
13:45
it by a sound wave omitted at a time T1
13:50
emitted by a Time T1 and received at
13:53
time T2 what then are the deduced time T
13:57
and position x coordinates of that event
13:59
in terms of T1 and
14:03
T2 we're doing a bit of math here
14:06
now let's see if we can do this to
14:09
deduce the time T and position X of the
14:11
event we need to consider the speed of
14:12
sound C and the time taken for the sound
14:15
wave to travel here's the
14:18
breakdown time taken for the sound wave
14:20
to travel to the event and back delta T
14:23
equals T2 minus T1 since this time
14:26
accounts for the round trip to the event
14:28
and back the time taken for the sound to
14:30
travel just to the event is delta T over
14:34
2 let me just asterisk this point okay
14:37
um this is um maybe a reasonable
14:40
assumption but it's not entirely um
14:44
Justified okay it it may be that the
14:46
situation is such that this assumption
14:49
doesn't necessarily hold in any case
14:53
distance to the event using the formula
14:55
D equals c * t for distance traveled by
14:57
the sound position X or distance to the
15:00
event is X = C * delta T / 2 so C * T2 -
15:06
T1 over 2 and to find the time T when
15:10
the event occurred we consider that it
15:13
happened halfway between when the sound
15:14
was emitted and when the sound was
15:16
reflected back since sound travels at a
15:18
constant speed and it takes equal time
15:20
to go and come back for a point source
15:22
in 1D
15:23
space okay again there's that assumption
15:26
which we probably need to asterisk
15:29
okay but in any case let's carry on
15:31
hence little t equal T1 + delta T / 2
15:34
and that turns out to be T1 + T2 over 2
15:37
just the average of the initial and
15:40
final um times so in summary the X the
15:44
position is C * T2 - T1 / 2 and the time
15:48
is T = T1 + T2 /
15:53
2 okay and now I ask how about if we
15:57
don't assume a prior ruling or
16:00
positional indexing of the
16:01
one-dimensional space doesn't it make
16:04
sense to use sound and our clock to
16:06
Define
16:08
displacements oppositions on this line
16:10
what that mean here to define
16:12
displacements or positions I guess or
16:15
positions on this
16:19
line chat GPT certainly without a
16:22
predefined referencing or indexing of
16:24
the one-dimensional space we can still
16:26
use sound and our clock to Define
16:28
relative positions and displacements
16:30
along the line here's how setting An
16:33
Origin so without an external reference
16:35
the most logical choices do Define the
16:37
observ position your position as the
16:39
origin this means that all positions and
16:40
displacements we calculate will be
16:42
relative to this point measuring
16:44
displacements when an event occurs and
16:46
is detected via echolocation the time
16:49
taken for the sound to return gives a
16:50
measure of the displacement from the
16:51
origin using the formula d = c * delta T
16:54
/ 2 or delta T = T2 minus T1 we can
16:56
determine the displacement D of the
16:58
event from our origin and directionality
17:00
since the space is onedimensional there
17:02
are only two directions left and right
17:05
or forward and backward without inherent
17:08
directional information from
17:09
echolocation you would need another
17:11
mechanism to determine direction or
17:13
you'd have to arbitrarily choose a
17:15
direction as positive and the other as
17:17
negative once this is set you can
17:19
consistently measure displacements in
17:21
that chosen direction as positive and
17:22
the opposite direction as
17:24
negative relative motion and position by
17:27
emitting sound waves at regular
17:29
intervals and tracking changes in the
17:30
measured displacement of objects events
17:32
you can deduce relative motion if the
17:34
displacement of an object decreases with
17:36
successive measurements it's moving
17:37
towards the origin if it increases it's
17:39
moving away an event timing as before
17:42
the time T of an event relative the
17:44
observer's clock would be tal T1 + T2 /
17:47
2 this gives the time of occurrence of
17:50
the event relative to the internal
17:52
clocks readings by using these methods
17:54
even without a predefined spatial
17:57
reference you can create a framework of
18:00
relative positions displacements and
18:02
event timings using sound and the
18:05
internal clock this would be
18:07
foundational in developing a Mechanics
18:10
for the onedimensional
18:14
space so to summarize I ask what would
18:17
be the time T and position X of an event
18:20
corresponding to sound emission and
18:21
receiving at T1 and T2 respectively and
18:24
conversely given an event with
18:25
coordinates T and x what are the
18:27
corresponding values of t T1 and T2
18:29
required to detect that event and then
18:31
it summarizes these things um the time
18:34
of the event is the average between T1
18:37
and T2 and the position is C * T2 - T1
18:41
over 2 where C is the speed of
18:43
sound and uh using the earlier equation
18:46
for T rearranged to get T1 is T minus X
18:49
over C and t2al t plus X over
18:53
C and then I again reiterating what I
18:56
was trying to say before this analysis
18:58
presupposes an an existing set of units
19:00
not just for time but also position but
19:03
in our naive setup we only have a clock
19:04
and sound we don't in fact have prior
19:07
position coordinates so wouldn't it be
19:09
more logical to frame the position in
19:11
terms of time and sound rather than the
19:13
other way
19:15
around then chat GPT says absolutely
19:18
you're right given the constraints
19:21
you've laid out our position units
19:23
should be based on time and sound which
19:25
becomes our sole medium for
19:27
understanding spatial relationships this
19:30
is particularly relevant when working
19:31
from first principles without
19:33
pre-established units or reference
19:35
frames for example if you're looking at
19:38
the universe right um you know there's
19:40
not a lot of pre-established coordinates
19:43
out there it's all just what we can
19:45
figure out from our observations here on
19:48
planet Earth in any case given the setup
19:51
the unit of time this is naturally
19:52
defined by the ticking of the internal
19:54
clock unit of position one logical
19:56
choice would be to use the time taken
19:58
from for a sound to travel as a unit of
19:59
position for instance if the sound takes
20:02
one tick to return after being emitted
20:04
uh the object is said to be one tick
20:06
unit away this translates spatial
20:08
distance into time which is a Natural
20:10
Choice given the setup and then um in
20:15
terms of uh in terms of that the time of
20:17
the event T is then the average of T1
20:20
and T2 and then the position X is T2
20:23
minus T1 / 2 so basically we're um
20:27
setting C uh the speed of sound equal to
20:30
one here and using position units in
20:33
terms of that so here x is expressed in
20:36
terms of clock ticks or time units not a
20:38
traditional spatial unit and conversely
20:40
given an event event at position X in
20:42
time units and time T the U the time of
20:45
the sound emission T1 is T minus X the
20:48
time of sound receipt is t + x this red
20:52
definition makes the units of position
20:54
inherently tied to the properties of
20:56
sound and the internal clock and it
20:58
aligns perfectly with the constraints
21:00
and tools available in the given
21:02
scenario finally thanks very much Chad
21:05
gbt I am highly impressed by your clear
21:07
reasoning and Analysis chat gbt thank
21:11
you for the kind words I'm glad I could
21:13
assist you if you have any more
21:15
questions or topics to discuss I'm here
21:16
to help enjoy exploring this fascinating
21:19
realm the fascinating Realms of physics
21:22
and
21:26
Beyond