https://www.quora.com/Why-did-the-universe-become-so-big-so-fast-after-the-big-bang
the
moment of the Big Bang is a mathematical artifact, a degenerate, or
singular, state, in which the distance between any point and any other
point was exactly zero.
But
that initial, singular state is not actually part of the universe. The
earliest moment of the universe is an arbitrarily small time after the
initial singularity, and at that time, the universe was infinite in size
just as it is infinite in size today.
This is one of the many peculiarities when we deal with infinities....
The classic example is the demonstration that there as many integers as
there are even numbers, since we can make a one-to-one correspondence
between elements of the two sets. The same applies when we compare the
very early universe and the present universe: both are infinite, and we
can make a one-to-one correspondence between the points in them, even
though the distance between any two points is greater today than it was
in the past.
I mapped every integer on the number line to the corresponding even
integer, i.e., twice that number. The mapping is one-on-one; every
integer has a corresponding even integer, and conversely, every even
integer can be divided by two. This is, in fact, one way of showing an
oddity concerning infinities: There are just as many even numbers as
there are integers!
https://www.quora.com/If-mass-and-energy-are-the-same-why-do-dark-matter-and-dark-energy-behave-differently
The
real meaning is as follows: dark matter and dark energy are “dark”
because they are completely invisible, not interacting with light or
ordinary matter at all. (They’re really transparent, not dark in the
conventional sense.) Dark matter is just invisible stuff with no
pressure. Dark energy is just invisible stuff with huge negative
pressure.
And
of course perhaps neither exist. They are both conjectured constituents
of the cosmos, with no direct detection. Assuming they exist helps
build equations that offer a decent match for observed reality, but that
is not enough. Without direct detection, we can never be sure if our
conjectures are on the right track. But again, to stress, do not read
meaning into the words, “matter” and “energy” into dark matter vs. dark
energy. The distinguishing characteristic between the two is pressure.
https://www.quora.com/If-light-can-be-attracted-by-gravity-then-how-can-it-remain-the-same-velocity-when-traveling-away-from-a-gravitational-source
In
the case of material particles, their kinetic energy is related to
their velocity. So when a particle gains energy by falling in a
gravitational field, it speeds up. When it loses energy while escaping
from a gravitational field, it slows down.
Not
so light. When light gains kinetic energy, it does not speed up: its
frequency increases. And when it loses energy, it does not slow down;
its frequency decreases.
This
was, in fact, one of the original predictions of Einstein when he
constructed the general theory of relativity: that light escaping from a
gravitational well will lose kinetic energy, hence its frequency will
decrease, shift towards the red end of the spectrum.
https://www.quora.com/Universe-is-expanding-which-means-gravitational-potential-energy-is-increasing-Dark-energy-is-causing-that-expansion-If-energy-is-conserved-then-is-the-amount-of-dark-energy-decreasing-and-being-converted-into
The gravitational potential energy between them (which is negative) is
increasing (it would increase to zero when everything is infinitely far
away from everything else). This increase in energy, however, is
accompanied by a corresponding decrease in kinetic energy. The net
result is that the energy density remains constant, on average.
Now
throw in dark energy. Dark energy has tremendous negative pressure.
What does that mean? Well, when pressure is positive, gravity does work
when it pulls things together. E.g., when a cloud of gas collapses into a
star, gravity is doing work, and that work is then stored in terms of
the repulsive potential energy that is responsible for the positive
pressure.
When
pressure is negative, the exact opposite happens. Gravity does work by
making things expand, instead of pulling things together. This is why
dark energy responds to gravity as though it was repulsive. And when
dark energy dominates, it means that the expansion rate of the universe
is increasing, not decreasing, over time.
But
what happens to the work that gravity does? In case of normal stuff
with positive pressure, it produces, well, more pressure, heat,
whatever. In case of dark energy? The work done by gravity produces more
dark energy. And thus, the energy density of dark energy remains
constant even though the universe expands. This is why, after a certain
point, dark energy becomes dominant; everything else gets diluted, but
dark energy doesn’t.
If
the model is correct, our universe reached this point about 4–5 billion
years ago, which is when its accelerating expansion began.
So
yes, gravitational potential energy is increasing. It is accompanied by
a decrease in kinetic energy. When it comes to dark energy, however,
gravitational potential energy is decreasing, and it is accompanied by
an increase in dark energy, keeping the dark energy density constant.
https://www.quora.com/Why-does-time-move-forward-and-not-backwards-Is-there-a-reason-that-the-direction-of-time-is-the-way-it-is?no_redirect=1
If, indeed, time had been seen to reverse in regions where entropy
decreases (and the entropy of your house decreases at night when it
cools), then the theory would have been "verified". But the entropy
arrow theory has always been careful NOT to make any predictions. It
isn't a theory, at least, not a scientific theory....it's observation which introduces apparent randomness,... Entropy increases as you go backwards in time too!
https://www.quora.com/Viktor-T-Toth-affirms-that-univrse-expansion-is-no-more-than-galaxies-moving-apart-from-each-other-while-other-professional-physicists-say-here-that-space-itself-is-increasing-so-distances-increase-even-without-any
Gravity
is re-added in GR (after having been unceremoniously omitted in SR) not
as a force applying via the relativistic equivalent of Newton’s Second
Law, but as a modified First Law: the “natural” motion of a particle
with no net force on it (gravity not counting in the sum) is not a
straight line at constant speed, but a “geodesic” path through the 4D of possibly distorted spacetime. Gravity as we traditionally thought of it is then — no joke — a pseudo-gravitational force akin to centrifugal force, which we add to the accounting to salvage the traditional wrong
form of the First Law when we obstinately use a lab standing on the
surface of a planet (rather than a “falling elevator” lab yielding to
its natural plummeting motion). Behind the scenes we’re grappling with
what amounts to a failure of the 4D version of Euclid’s Fifth Postulate
and the traditional wrong version (inertial trajectories that start
parallel should stay parallel) remains an important part of our
intuition about what space should mean. If we’re going to use the word
“space” at all, it’s unavoidably going to bring allusions to both the
stress-free chain intuition and the parallel inertial trajectories
intuition.
So the “comoving coordinates”
picture, in which galaxies have constant coordinates and all the
increase of distance is allowed for via a time-dependent scale factor
that changes the interpretation
of the coordinates, naturally incorporates the fact that the galaxies
have no true (non-gravitational) forces on them and are moving
inertially with no proper acceleration.
The
above is the politic answer that accentuates the agreements and
minimizes the disagreements. However, at the risk of straw-manning, I do
get the sense that Victor a-priori rejects the very idea of a metric
theory of gravity based on geodesics, and is holding out for a
quantum-field-theory of gravity with nothing but true forces between
particles in flat spacetime, which merely simulates a metric theory of gravity (because, ex hypothesis, the force exchange particles, to be called gravitons, couple to all other particles by virtue of their mass, thus manifesting as a universal pseudo-pseudo-gravitational
force). That smacks a bit of Geocentrism or Lorentz Ether Theory for my
taste, but make of it what you will.
Viktor Toth Quora quotes:
The
actual universe (not just the part that we see) is, in our current best
cosmological model, is a spatially flat, spatially infinite spacetime.
Depending
on how we define distance (a distance that can no longer be measured,
mind you) we may conclude that their distance from us is increasing
faster than the famous vacuum speed of light. So what? That distance is a
mathematical abstraction not an observable quantity. What is important
is that none of these distant galaxies are exceeding the vacuum speed of
light at their location. Nothing accelerated to the speed of light. Our
causal relationship changed.
https://www.quora.com/If-distant-galaxies-flying-away-faster-than-light-are-causally-disconnected-how-did-they-become-causally-disconnect-if-nothing-can-accelerate-to-the-speed-of-light
First
of all, it’s not space. It’s (mostly) time. Here on the surface of the
Earth, the time component of the curvature tensor dominates Newtonian
gravity. The spatial components contribute at the parts-in-a-billion
level.
But let us take a step back. What is “space” and “time”? Not metaphysical, operational definitions.
We
do not measure space or time directly. We observe events that involve
matter. In particular, we observe lumps of matter that produce regular
events in a reliable fashion; in fact, lumps of the same kind will
produce events at the same frequency even if they had different
histories. Let’s call these things (say, cesium atoms) “reliable
clocks”....
We
can count the events (the ticks) that these clocks produce. What the
theory tells us is that this is a measure of “proper time”, a property
of the path that the clock takes. Using proper times and light rays for
synchronization, we can establish relationships between events. Those
relationships are readily mapped using a four-dimensional coordinate
system. Thus we conclude that the ensemble of all possible events forms a
set that can be mapped by four-dimensional coordinates: i.e., a
four-dimensional manifold.
Some
of the things lumps of matter do are interactions between distinct
lumps. These interactions are mediated by other forms of matter, such as
the electromagnetic field. These interactions can be described using
the language of geometry, but usually, the “geometry” depends on the
material properties of the interacting matter. (E.g., the ratio between
its electric charge and its mass.)
Gravity
is one of these interactions but it has a unique property: the geometry
it induces does NOT depend on the material properties of the
interacting matter. The geometry is, in fact, universal.
This
permits us to take the gravitational field tensor and drop it in top of
our four-dimensional spacetime manifold, endowing it with a “metric”.
The presence of a metric induces geometry: we now have a means to
calculate things like lengths or angles.
https://www.quora.com/Einstein-It-is-wrong-to-think-that-the-geometrization-has-significant-meaning-It-is-only-a-kind-of-a-clue-helping-us-find-numerical-laws-Whether-you-connect-a-geometric-view-to-a-theory-is-a-private-matter-Is-then
Redshift is always about a relationship between emitter and detector. It can be due to two reasons:
- The emitter and detector are moving relative to each other,
- The emitter and detector are situated at different gravitational potentials.
For relatively nearby cosmic objects, the first reason (Doppler redshift) dominates.
For
objects much farther away, we see light that was emitted cosmological
timescales ago, when the universe was much more dense and thus the
average gravitational potential much stronger. This results in
gravitational time dilation (i.e., clocks were ticking more slowly back
than than today) and this contributes to the observed redshift; in fact,
for really distant objects, this is the dominant source of redshift.
https://www.quora.com/During-the-Big-Bang-did-space-expand-faster-than-the-speed-of-light
what relativity theory tells us about the vacuum speed of light is that
its value is not observer-dependent. A ray of light that moves at the
vacuum speed of light for one observer moves at the vacuum speed of
light for all observers. A consequence is that a thing that’s
slower-than-light in one reference frame is slower-than-light in all
reference frames, so accelerating to beyond the vacuum speed of light is
not possible.
https://www.quora.com/How-can-one-say-that-space-is-expanding-while-contending-that-it-is-infinite-If-space-is-expanding-are-all-the-quantum-fields-and-vacuum-energy-decreasing-in-field-strength-and-density-Are-the-contents-of-space
The
expansion of spacetime is the observation that the material fields of
this universe are less dense now than they were in the past, and also,
insofar as physical objects are concerned that are not bound to each
other by gravity or other forces (e.g., distant clusters of galaxies),
the distance between them is increasing.
This has nothing to do with whether or not the universe is finite or infinite.
https://www.quora.com/In-the-Feynman-Lectures-on-Physics-there-is-a-statement-that-says-If-an-object-moves-with-the-speed-less-than-one-hundred-miles-a-second-the-mass-is-constant-within-one-part-in-a-million-What-does-this-mean
rest
mass is an intrinsic property of an object, kinetic energy is not; it
depends on the observer. So while the rest mass of an object never
changes, two observers who move relative to each other will disagree on
an object’s “relativistic mass”.
Nonetheless,
since mass and energy are equivalent, it is not incorrect to say that a
moving object has this and that much relativistic mass-energy, one just
needs to be aware of what it actually means.
https://www.quora.com/How-does-cosmic-expansion-affect-our-understanding-of-distances-in-the-universe-Why-is-measuring-distance-so-tricky
recognizing
what type of a star we are looking at, and knowing how bright it
appears to be vs. how bright it should be at a given distance. From
this, we infer its distance. This works up to great distances with very
luminous stars, and even greater distances when it comes to transient
very bright events, notably Type Ia supernovae.
But
now we run into the first question again, trying to use some means
(obviously not meter sticks this time) trying to measure the distance of
something that is moving relative to us (in this case, moving because
of cosmic expansion.) We see the light of that distant supernova not as
it appears today, but as it appeared, possibly billions of years ago,
when the event happened. So any distance we infer is some kind of an
artificial number, an estimate of how far the supernova was when the
event occurred, not how far it is today.
In
fact, today, that supernova remnant may be so far away, it’s no longer
within our observable universe. So any “distance” becomes a piece of
mathematical fiction: Not something that can be measured by any means,
since we cannot observe that remnant, now or ever, as it is today.
And
there is yet another complication. Never mind expanding cosmos: the
average gravitational field of the cosmos also changes as the density of
matter changes. This affects light in a variety of ways. Depending on
how we account for (or not) for these effects, we can get wildly
different results, both the geometry of light rays and their intensity.
The
result is a mess. Take a hypothetical object that is observed at the
time the cosmic microwave background was emitted. The intuitive concept
of “distance” has no meaning here. That object today would be about 45
billion light years from here, way beyond our cosmological horizon. This
is its comoving distance. Light from that object took roughly 13.8
billion years to get here. Call it light travel distance: 13.8 billion
light years. That object will appear faint due to cosmological redshift.
Judging by its brightness, we obtain a “luminosity distance” of
something like 50 trillion (!) light years. Yet the object will appear
much bigger than it has any business being. Its “angular diameter
distance” is barely over 40 million light years.
All
these are valid “distances”, derived from observable quantities under
different definitions and assumptions. None correspond to the intuitive
concept of a “distance” because there is one thing that cannot possibly
be done, not even in principle, when it comes to an object beyond our
cosmological horizon: send a signal or lay down a series of measuring
sticks to actually measure what we might call “distance” in daily usage.
....................................................
At
its most rigorous level, time is the ordering relation between events.
In physics, it is the parameter by which change is measured and
causality is preserved. Modern science abandoned the idea of a universal
clock long ago; relativity shows that time is inseparable from space
and varies with motion and gravity. What a clock measures is not “time
itself,” but the rate at which physical states evolve.
Time
also has direction. The past differs from the future not because of
metaphysics, but because of entropy. The arrow of time emerges from
irreversible processes, from the statistical tendency of systems to move
toward disorder. This is why memory points backward and expectation
forward.
Time progresses continuously and all experiments require observing
events as time progresses, Before living things ever existed, the earth
existed but no scientist was there to observe it and coercion
experiments. So? Does that mean time did not exist then?
Motion
is of course the combination of time and distance. Try and measure time
without motion, it’s impossible. Every watch has moving parts, as do
sundials, hourglasses and timekeeping candles....
Now, take a photon—it is one of two particles in the universe with zero
mass! That is, all its energy must be in motion all the time, which is
exactly what we observe—photons never stop and move at a constant
velocity! The other consequence is that photons don’t technically see
time. By moving at the speed of light, time as we know it ceases to
exist for them, but unfortunately we can’t reach their velocity to see
what it is they perceive.
https://www.quora.com/What-is-the-ACTUAL-definition-of-time-1
It means someone standing still at a low point of a gravitational field
will measure a bluer frequency than someone standing still at the top
of a gravitational field.
I
say this because light has no inherent frequency. It is only a resting
(also moving, because it’s still at rest relative to itself) observer
that can measure a frequency.
You
can look at this two ways: the photon increases energy as it falls in,
increasing frequency. Or the person at the bottom measures time slower
than the one at the top.
https://www.quora.com/When-a-photon-enters-a-gravitational-field-its-frequency-decreases-consequently-redshifting-Does-that-photon-recover-its-frequency-when-it-leaves-the-gravitational-field
in
a gravitational field, the speed of light is the same constant for all
observers… so long as they are local with respect to the measurement
being made. However, when you look at an experiment from a distance, the
speed of light may no longer appear constant from that distant
location, because, as a result of gravitational time dilation, your
clock may be ticking at a different rate.
This
effect is real, measurable, and important. This gravitational slowing
down of light is actually known as the Shapiro effect, or Shapiro delay,
first described by Irwin Shapiro in 1964, offered as a “fourth
classical test” of general relativity (the first three were proposed by
Einstein: the gravitational bending of light, the anomalous perihelion
advance of Mercury, and gravitational redshift.)
The
full time delay between source and receptor arises as a combination of
two contributions: the fact that light follows a bent (hence, longer)
trajectory, and the fact that near the source, it appears to slow down
with respect to the clock of a distant receiver.
https://www.quora.com/If-light-trajectory-is-curved-when-passing-by-a-massive-object-is-the-speed-of-light-still-constant-in-the-curve-And-if-being-constant-or-not-depends-on-the-observer-wouldnt-this-break-the-principle-of-general-or
An observer cannot simultaneously travel at the speed of light and then measure its speed as the same as a stationary observer.
The implication is that there are no observers that can travel at the speed of light.
https://www.quora.com/If-photons-experience-no-time-do-they-see-the-entire-universe-as-one-moment
All
subatomic particles (and energy fields) which have no mass, don’t
experience time at all. Remember that the spacetime fabric is generated
by subatomic particles which have mass (like a sort of vessel to contain
itself). Space & Time are extensions of matter itself and don’t
exist without it.
https://www.quora.com/In-relativity-one-is-told-about-space-like-dimensions-and-time-like-dimensions-What-is-the-basis-for-distinguishing-them
What
is important to observe is that the Lorentz transformation leaves the
light cone unchanged (invariant). Not only that, but whatever is inside
the light cone stays inside the light cone; whatever is outside stays
outside. (This is just another way of saying, by the way, that no
Lorentz transformation can change slower-than-light motion to
faster-than-light motion or vice versa.)
This is the basis for distinguishing timelike vs. spacelike dimensions. Timelike dimensions (well, the
timelike dimension) stay inside the light cone; spacelike dimensions
stay outside the light cone. The topologies of these two regions of
spacetime are quite different.
Spacetime (that is to say, the four-dimensional manifold of every possible event) has no shape.
The
shape comes not from spacetime but from the gravitational field. Which,
on account of gravity being universal, defines the one and only, unique
geometry that matter can sense.
Unlike
spacetime, the gravitational field, aka. the metrical field, is a
physical field. It carries energy and momentum. It facilitates the
interaction between distant masses. It can be detected by a
gravitational wave detector. And yes, it does determine measurements of
length and time as well (made using meter sticks and clocks that are
made of matter that always interacts with the gravitational field), so
we can perhaps be forgiven when we lump the manifold and the metric
together and just say that “spacetime is bent”.
https://www.quora.com/How-can-spacetime-be-reshaped-and-bent-if-it-is-purely-a-mathematical-construct
we’re
disagreeing about the direction of increasing time. In our own
reference frame we have no speed, we’re only moving in the time
direction and the other guy who has lots of speed doesn’t share our time
direction.
https://www.quora.com/If-time-stops-at-the-speed-of-light-then-how-can-anything-move-at-that-point
Also, we don’t ever see moving (relative to us) clocks run faster - they always appear to be running slower. A
good answer really can’t be given without working through the math - if
you start with the assumption that all observer agree on the speed of a
light beam and simply follow the math, you are led inexorably to the
fact that moving (relative to us) clocks will always be seen to run more
slowly than stationary (relative to us) clocks.
https://www.quora.com/Is-time-the-same-as-gravity-according-to-Einstein
Newtonian
gravity is about how fast clocks are ticking. Simply put, the stronger
the Newtonian gravitation potential, the slower clocks tick there.
Other
parts of spacetime curvature also contribute, of course, but only very
little, or else the speeds involved must be very high. For instance,
when light (which can be thought of as a stream of “ultrarelativistic”
particles, moving at or near the vacuum speed of light) is deflected by
gravity, it is deflected in equal parts by time and space curvature;
hence, the deflection angle is twice what you would get using Newtonian
physics alone.
But
apart from extreme cases, “time curvature” and (Newtonian) gravity are
pretty close to being the same thing under normal, everyday
circumstances.
https://www.quora.com/How-did-Einstein-imagining-riding-a-beam-of-light-lead-him-to-the-theory-of-relativity-Is-there-a-secret-to-imagining-riding-at-the-speed-of-light-What-happens-if-I-keep-imagining-riding-at-the-speed-of-light
So,
imagining that you could travel along beside a light beam, matching its
speed, leads to an impossible situation. Therefore, it must be
impossible to travel at that speed.
The
problem is that that stationary sinusoidal field configuration contains
magnetic field with non-zero curl, and Maxwell’s equations explicitly
forbid that.
That’s all there is to it - a proof by contradiction.
https://www.quora.com/The-universe-is-expanding-faster-than-light-so-time-is-going-backward-Is-it-possible-that-the-future-of-the-universe-is-its-past
The
fact that distant parts of the universe recede from us faster than the
speed of light is a completely different animal. These regions of the
universe are said to be "causally disconnected" from ours, hidden behind
an "apparent horizon" precisely because relative to us, they're
receding faster than light... but in their own local vicinity, nothing
moves faster than light either. So causality is protected, and there are
no journeys into the past either.
So no, no matter how poetically appealing it sounds, the future of the universe is NOT its past.
https://www.quora.com/Is-the-speed-of-light-the-fastest-possible-speed-for-any-type-of-object-or-is-it-possible-for-something-to-travel-faster
Yes
I think we agree that clocks can slow down relative to other clocks.
And of course if we measure a second somewhere, whatever we measure as a
second will be a local second. All the answer says is that a local
second in one frame can last longer than a local second in another,
which is correct.
https://www.quora.com/How-do-we-know-that-we-are-not-hurtling-through-space-at-near-light-speed we are traveling at exactly light speed. (if you think in terms of 4 dimensional space-time, instead of just 3 dimensional space).
Nothing
with rest mass can move at the speed of light through space, but in 4
dimensional spacetime you are always moving because time stands still
for no one.
Even if you are standing still, you are moving at the speed of light in 4 dimensional space time!
It’s
that you and the other guy are just disagreeing about what counts as
stationary. Each of you has a clock and that clock measures time in that
rest frame. A rest frame is one that’s moving only in the future time
direction.
https://www.quora.com/If-time-slows-down-at-high-speeds-high-speeds-relative-to-what
And the straightest path, i.e. shortest distance, is the path of
greatest proper time. So you have to keep in mind two kinds of time. One
is coordinate time, which is just a label we can put on events, the
same way we put a longitude and latitude on them. The other is physical
time which is duration along a path, the way we talk about the distance
between points depending on the roads we take.
https://www.quora.com/Whats-so-challenging-about-accepting-that-time-can-move-at-different-speeds-and-how-can-we-explain-it-without-all-the-complex-math
it [relativity] just uses a tool for managing passing time in which we treat time as a dimension of space....We
account for entropy through statistics … this produces an asymmetry in
the time axis that does not usually exist in the space ones....psychological arrow of time points in the direction of increasing entropy. That doesn’t conflict with general relativity at all.
https://www.quora.com/According-to-general-relativity-theres-no-such-a-thing-as-time-On-the-other-hand-entropy-seems-to-be-a-timeline-so-how-do-both-concepts-get-unified
A
photon does have infinite speed from a certain point of view. That
would be its own view. Since ZERO time elapses no matter the distance it
covers you could say that is infinite speed. However since the distance
it travels in the direction it is headed is only two dimensional it has
covered no distance at all.... So speed is just the wrong scale to consider here - you need to consider energy or momentum.
This
isn’t a trick - it’s always the case that you can turn infinite scales
into finite scales and vice versa. The math behind it is called
“conformal transformation.” The physicist Roger Penrose has a way of
drawing a picture of the entire infinite universe on a finite piece of
paper. It’s called a Penrose diagram,...So
you can think of “speed” as a conformal transformation of an
energy/momentum scale. Speed is like the “on diagram” distance in a
Penrose diagram - it “runs out” within the finite page. And speed “runs
out” at c.
- There's proper velocity, which is a measure of how far the light moves for every second that passes for it.
- There's time dilation, which is a measure of how much the light advances into the future for every second that passes for it.
- There's rapidity, which is analogous to an angle; but it's an angle between space and time.
The only measure that's finite is classic velocity, the ratio of proper velocity to time dilation.
dτ is the time-like separation between two events (points
in spacetime identified by when and where they are). In the same way
that the collection of all points in space with the same dr forms a circle, the collection of all events in spacetime with the same dτ
forms a hyperbola.
This notion of proper time is an important one in Relativity, because it's an invariant quantity: no
matter what frame of reference you use (in effect, the choice of valid
coordinate systems), the separation between two events dτ
will always be the same. This is similar to how the distance between
two points is always the same no matter how much you spin around...The equation for proper time is dτ2=dt2‐(dr/c)2.
That use of a minus instead of a plus is what makes all the difference,
as that changes it from an equation of a circle to the equation of a
hyperbola. (The c in the equation is a spacetime conversion factor, saying in effect that there are 299,792,458 meters in a second.)...Any finite amount of “rotation” will fall short of a true diagonal, because the change in dr/c will always be slightly less than the change in dt; and infinite “rotation” will exactly reach that diagonal, where dr/c=dt....the ratio between them approaches a finite limit. That ratio is what we traditionally call speed: a change in distance (dr/c) over a change in time (dt).https://sciencefringeareas.quora.com/If-light-has-no-mass-then-the-speed-of-light-should-be-infinite-Why-does-light-have-finite-speed
Photons (and anything traveling at “c”) do not have a reference frame
*at all*. This is a consequence of the definition of the invariant speed
and of a rest reference frame. It is fairly simple.
- Anything that travels at the invariant speed “c” travels at that speed in ALL reference frames.
- A rest reference frame is one in which the object is at rest (traveling with 0 velocity) relative to itself.
- If
an object travels at the invariant speed “c” then in must travel at
that speed in ALL reference frames, including its own rest reference
frame.
the concept of time for an object traveling at light speed becomes
meaningless. This is because, according to relativity, as an object's
velocity approaches the speed of light, time dilation increases without
bound. At light speed, the equations that describe time dilation lead to
undefined results, indicating that the passage of time cannot be
defined for such an object.
Light
has mass in the sense that it contains a quantity of energy, but it is
not referred to as mass when it travels freely at c. If that energy is
absorbed by matter, it then shows up as additional mass. Whenever energy
is bound up in things that collectively travel at less than c, all of
that energy becomes classed as mass, but if you break the object up and
turn it entirely into electromagnetic radiation that shoots off in
multiple directions at c, none of that energy is called mass.
https://www.quora.com/Why-do-scientists-state-that-once-the-speed-of-light-is-reached-the-time-stops-Is-it-a-true-fact-or-just-a-theory
You’
never see ‘your’ time slow down. ‘You’ always see things as if ‘you’
are at rest. Other things are always moving relative to (stationary)
‘you’....I
meant from the POV of an observer, who was overseeing both events
simultaneously. They'd see light in both frames (of reference) travel at
c, and the events in each frame would be observed to pass more slowly
than if observing a,stationary frame.
https://www.quora.com/If-you-are-travelling-at-nearly-the-speed-of-light-how-fast-is-light-travelling-away-from-you
yes this is very much how “you” is defined as an “external observation.” Louis de Broglie’s Law of Phase Harmony was a critique of relativity from the perspective of quantum physics. de Broglie called the Law of Phase Harmony his “greatest discovery” and he has a Nobel Prize yet his “Law of Phase Harmony” is not taught in physics classes! Why? Well Bell’s Inequality that got the Nobel Prize and disproved Einstein is still misunderstood by other Nobel Prize physicists as Professor Jean Bricmont has detailed so well. Quantum physics professor Basil J. Hiley who had collaborated with David Bohm, who confirmed the Law of Phase Harmony, tried to explain to Nobel physicist Roger Penrose that indeed it is noncommutativity as nonlocality that is the secret of the foundation of reality in quantum biology. I have a paper on this secret - it’s based on listening as logical inference - NOT an external visual observation as the definition of the I or Self. see the academic journal “Cosmos and History” - peer-reviewed, open access Dec. 2024 issue for “noncommutativity music as biophysics” article. You can also read Nobel physicist Gerard ’t Hooft’s article “Light is Heavy” for a good start.
If
two objects in inertial frames are moving in relation to one another
and yet both measure light as traveling at the same speed, that means
that the relative movement of one MUST be causing distortions in space
and time (the components of speed) in the frame of the other. At the
speed of light, those distortions are so great that space is contracted
to 0 and time dilated to infinity. Something moving at the speed of
light carries the most possible distortion it can create in the
observer's frame while still having a meaningful existence.
https://www.quora.com/Whats-the-fundamental-reason-why-the-speed-of-light-cannot-be-broken-Why-does-the-universe-want-to-preserve-the-upper-barrier-on-speed-of-light-so-much-so-that-it-readily-slows-down-time-rather-than-see-the-speed-barrier-broken
light
is just one example of something that moves at this speed, and the
reason it does is because it has no mass. Gravity also moves at the same
speed. Anything with no mass must move at the special speed in the eyes of any observer.
https://www.quora.com/What-makes-the-speed-of-light-unique-in-terms-of-measurement-in-space-and-time-Are-there-other-methods-of-measuring-these-concepts
AI:
Noncommutativity can violate invariance
because it introduces a dependence on the order of operations,
which breaks symmetries like Lorentz invariance in physical theories.
In many standard theories, the order of operations does not matter,
meaning the result is the same regardless of the sequence (this is the
commutative property). However, in a noncommutative theory, this is not
true, leading to consequences like the violation of fundamental
symmetries, such as the conservation of energy-momentum, which is linked
to translational invariance
.....................
you (and your reference frame and clock) are always moving at the speed
of light through spacetime, and what you think of as stationary is
really moving in the time only direction....so
that now, *relative* to the former stationary state, you are moving
thru space too. But you’re moving less thru time, your clock runs slower
*relative* to a clock left in the frame we called stationary,
Galileo
illustrated the relativity of motion by noting that the motion of a
boat drifting down a placid river was undetectable below decks in the
boat.
https://www.quora.com/Can-you-explain-simply-why-time-slows-as-you-move-faster
proper
time may imply a different amount of time measured along some
space-time path — which is one of the deepest answers to the so-called
twin paradox — but it says nothing about the rate of passage, as it is
called.
https://sciencephysicsmath.quora.com/In-simple-terms-why-does-time-slow-down-as-you-travel-closer-to-the-speed-of-light
More importantly, Pythagoras’s theorem is different in space-time. In normal space, we can say C2=A2+B2
and it then follows that the shortest distance between two points is a
straight line. In space-time, the equivalent equation (using only one
spatial dimension for simplicity) is s2=x2−(ct)2
and the minus sign has serious counter-intuitive consequences, such as a
straight path between two points actually maximising the proper time
(i.e. the time as would be experienced, or measured, on such a path).
What
this means is that any irregular (non-straight) path for one twin —
whether it is a simple turnaround or a series of random accelerations
and decelerations — will mean that the proper time for that path will be
less than the one for something travelling at a steady constant
velocity (i.e. a straight world-line in space-time). The other
explanations are simply special cases of this. ...
The age discrepancy arises from the different space-time paths that
they take. When they meet at some given space-time location then they
will see the difference.
If
two people simply walked different paths to get to a common meeting
point, they could compare their routes and one might notice that they
had used more shoe leather. This is similar only insomuch as they become
aware when they meet, and not before. Neither has experienced time at a
faster or slower rate — merely a different amount of it........
The
complication is because the rotating twin’s constantly changing
inertial frame can be said to have a speed relative to the other twin. I
suspect that the ageing difference would be visible to them — good
question!...........
if
you count ticks of clocks, one at rest and the other three moving fast
in three perpendicular directions (as seen by the stationary clock),
together with one for each pair as above, and square those counts, you
obtain uniquely a quadratic form. It’s then an experimental fact that
this quadratic form counts the squares of clock ticks on all clocks. In
particular it makes no difference which clocks to use to measure it.
And
it’s nondegenerate. So the orthogonal complement of the clock is three
dimensional. It’s also an experimental fact that on the orthogonal
complement this quadratic form is negative definite, so it’s minus a
Pythagorean metric, and that this Euclidean space is in fact “space”, as
experienced by that clock.
That’s the essential physical content.
If you understand this much, the rest is working out the mathematical consequences of the model.
https://www.quora.com/Why-is-Einsteins-theory-of-relativity-considered-difficult-to-understand-even-for-physicists-Can-you-explain-why-it-may-not-make-sense-to-some-people
In
spacetime, two observers in different reference frames can no longer
agree on “now.” Neither can they agree on “when.” “Now” for one observer
might be the past for the other. Clocks do not tick at the same rate in
spacetime. The distance from one place to another and the time it takes
to get there is malleable. Straight lines are no longer straight and
gravity is a pseudo-force caused by curvature in the presence of matter.
There may be places in the universe where the passage of time no longer
has any meaning and the known laws of physics break down.
But
don’t get too comfortable with spacetime. Like all models, it has
limits. Some of the math used in Einstein’s theory break down under
extreme conditions like black holes or at the big bang. Solving that
conundrum and unifying Relativity with Quantum Mechanics is the next
holy grail of physics.
https://www.quora.com/What-is-spacetime-8
Relativity
says that there is a universal “now”, but it is impossible for me to
verify the conditions of now at another place without getting a signal
from there or to travel there. But both of them takes time and by the
time I get that information, time will pass and things change by the
time I verify them. I see the sun the way it was 8 minutes ago not the
way it is now.
Physical
processes happen all over the universe at a certain rate. There is such
a thing as psychological experience of time and it is the result of
remembering how things used to be and seeing the difference between that
and how they are now. “My room was organized and now it’s messy” gives
me the sensation of time passing.
But
to have a quantitative sensation of time we need time measuring devices
with an accurate rate. That can be moon cycles, seasons, sun dials,
hour glasses and clocks.
Spacetime
is a concept of imagining a tiny clock at every single point in space
that measures the local time at that particular point. But this is just a
model because obviously there is no clock at every single point in
space.
Special
relativity’s idealized spacetime model says that without mass all these
clock are and remain synchronized all the time. This is not true
because there is gravity everywhere and the clocks do get out of synch.
But general relativity deals with that.
https://www.quora.com/Why-is-spacetime-curved
“Time
curvature” affects the rate of clocks. As a general rule, in a
gravitational field, clocks tick slower than elsewhere. This effect is
primarily responsible for gravity. All other effects, including space
curvature, contribute only a tiny, tiny correction except in the
presence of extremely strong gravitational fields (surface of a neutron
star, immediate vicinity of a black hole.)
https://www.quora.com/What-is-space-curvature-as-opposed-to-time-curvature-really
- :
for something moving at the vacuum speed of light, spatial curvature
and time curvature contribute equally, doubling the effect of gravity on
their trajectories.
To wit: Time curvature affects clocks; space curvature changes geometry.
