[HN Gopher] Time is a dimension, but not like space
___________________________________________________________________
Time is a dimension, but not like space
Author : belter
Score : 135 points
Date : 2024-10-17 15:29 UTC (3 days ago)
(HTM) web link (bigthink.com)
(TXT) w3m dump (bigthink.com)
| nyc111 wrote:
| I would really appreciate if people writing these types of
| articles first give rigorous and unique definitions of space and
| time.
| blackbear_ wrote:
| Something like (from Wikipedia):
|
| > In the presence of gravity spacetime is described by a curved
| 4-dimensional manifold for which the tangent space to any point
| is a 4-dimensional Minkowski space.
|
| Perhaps? A good way to lose 99% of the readers before the end
| of the first sentence.
| mise_en_place wrote:
| Just represent it in a 4x4 multidimensional array that
| corresponds to the metric tensor.
| hn_throwaway_99 wrote:
| Yes, that will really pull in the laymen...
| nvader wrote:
| Reminds me of the mathematician who was asked how he
| mentally visualizes a 4 dimensional space.
|
| "I simply imagine an n-dimensional space, and then set n
| to 4"
| homebrewer wrote:
| >>> After Hilbert was told that a student in his class
| had dropped mathematics in order to become a poet, he is
| reported to have said "Good--he did not have enough
| imagination to become a mathematician"
|
| https://scienceworld.wolfram.com/biography/Hilbert.html
| golly_ned wrote:
| Reminds me of Geoffrey Hinton who, when asked how to
| imagine a 14-dimensional space, said: "imagine a
| 3-dimensional space, and say 'fourteen' very loudly"
| esperent wrote:
| This is great, can't believe I haven't heard it before.
| zbobet2012 wrote:
| I'm a huge fan of providing laymen explanations. And at some
| point if you _actually_ want to understand you have to stop
| using those and pickup and understand the math.
|
| http://therisingsea.org/post/mast30026/
|
| Has a good introduction to space, and the notion of a
| manifold, and what a Minkowski space is.
| verzali wrote:
| Ok, but almost nobody is going to read an article that
| requires you to work through 21 lectures, 9 tutorials, and
| 3 assignments first. It'd be great if they did, and it'd be
| nice to give the link for interested people, but otherwise
| it is just making the subject inaccessible to almost
| everyone.
| slashdave wrote:
| That's in the article on Minkowski space. It's actually a
| good summary, with a hyperlink to manifold.
|
| Here's the introduction to the "spacetime" page:
|
| > In physics, spacetime, also called the space-time
| continuum, is a mathematical model that fuses the three
| dimensions of space and the one dimension of time into a
| single four-dimensional continuum. Spacetime diagrams are
| useful in visualizing and understanding relativistic effects,
| such as how different observers perceive where and when
| events occur.
| whatshisface wrote:
| Time: a separation between individual events that can be
| crossed by cause and effect.
|
| Space: a separation between individual events that cannot be
| crossed by cause and effect.
|
| "Individual event" is meant in the familiar sense, like a
| "bang" from a gun, or your birthday party.
| HappMacDonald wrote:
| That's a solid burn, suggesting that nobody else came to
| their party
| ziofill wrote:
| My favourite explanation (which IIRC is in a book by Brian
| Greene) is that you can think that everything always moves at
| the speed of light _in a 4D spacetime_. That way, if you stand
| still, you 're moving only along time, and as you tilt your
| velocity vector more and more toward the space dimensions you
| have to travel more slowly along the time dimension. At the
| limit you are moving at the speed of light along some space
| axis and technically your time is "frozen".
| at_a_remove wrote:
| Or as I tell people, kidding on the square, we're trapped in
| a time machine hurtling us into the future at the rate of one
| minute every sixty seconds! It is important you say that last
| bit in a panicked, breathless voice.
|
| _My God, that means every three hundred sixty-five days or
| so, we 'll have gone forward a year!_
| colordrops wrote:
| But then it gets weird and the time axis changes scale
| relative to other elements in space.
| ndsipa_pomu wrote:
| For an observer, maybe
| colordrops wrote:
| There is no absolute frame.
| Ringz wrote:
| Thee is no ,,Stillstand", you can't stand still relative to
| anything in the universe.
| d1sxeyes wrote:
| Hm. That's a possibility. As I understand it though, an
| infinitely massive object would not move in space, and
| would experience time at the absolute rate of one second
| per second.
|
| Although that sounds theoretically impossible, I would
| remind you that somehow the opposite seems to be possible
| (a particle with zero mass that moves through time at a
| rate of zero seconds per second), despite that not making a
| lot of sense to a layperson.
|
| Footnote: Talking about time in seconds makes very little
| sense here because our notion of time is so heavily linked
| to how light moves through space, but hopefully my point is
| clear. Maybe someone has a better unit we could use to
| measure time independently of space?
| Ringz wrote:
| Your point is clear. As far as can wrap my head around
| those theoretical concepts: An infinitely heavy object
| can't move in space because there isn't any space left to
| move. I would say that this object would have
| concentrated all mass in one point, no space left to
| move. No observer left to measure. I would also say that
| there can't be two or more infinite masses at the same
| time, or they would _move_ (at the speed of c (?) But
| that would have additional implications on mass and time)
| to the point between them.
|
| But back to observable reality: let's say you fall into a
| dark place where the time stands still and that means you
| are not moving, from an outside observer you are still
| moving relative to the space outside your black hole.
| Let's say the observer fall on his way to your black hole
| into another black hole and experience the same
| phenomenon like you, from a third observers perspective
| everyone is moving.
| creata wrote:
| Some of the answers at
| https://physics.stackexchange.com/q/33840 explain why
| "everything always moves at the speed of light in a 4D
| spacetime" is a statement that, at best, has no content.
| DiscourseFan wrote:
| As per Kant:
|
| Time: inner sense, intuition of continuity, unity
|
| Space: outer sense, intuition of objects
|
| Its a bit more complex but that's a basic summary from the guy
| who came up with the "space and time" thing. Read the
| "Transcendental Aesthetic" in the _Critique of Pure Reason_ for
| more.
| User23 wrote:
| My understanding from Einstein's book Relativity is that the four
| dimensions of general relativistic spacetime do not correspond to
| any one of the time or space dimensions of special relativity or
| classical physics.
|
| It's a great read, and short too. He explains it much better than
| I could.
| ofrzeta wrote:
| Do you mean "Relativity: the special and general theory"?
| User23 wrote:
| Yes
| nyc111 wrote:
| "This is the underlying reason why, when you move at speeds that
| approach the speed of light, you start to experience phenomena
| such as time dilation and length contraction:"
|
| This is not even possible in pulp science fiction. In order to be
| able to move with the speed of light you need to transform
| yourself into a photon. Only a photon can move with the speed of
| light. Saying "close to the speed of light" changes nothing. You
| need to be light to move with the speed close to the speed of
| light. Macroscopic objects cannot move with speeds approaching
| light speed.
| klodolph wrote:
| "Close to the speed of light" means, like, 99% of the speed of
| light. You can even see the speeds listed on the graphs, which
| are given as a fraction of _c_.
| nyc111 wrote:
| "'Close to the speed of light' means, like, 99% of the speed
| of light"
|
| So, you are saying that it is possible to accelerate human
| body to 99% of speed of light without transforming the body
| into a massless particle?
| tsimionescu wrote:
| Yes.
|
| It will never be possible to get to 100%, but I principle
| anything below that is possible. Not just 99%, but
| 99.99999999% or however many you want.
|
| Of course, it's not actually feasible, you would need
| galaxies worth of energy to do so.
|
| But for something like 10% or even 50% of the speed of
| light, it's not even that implausible.
| etcd wrote:
| What is our current speed?
| ithkuil wrote:
| Our current speed is 99.999999% the speed of light,
| according to some frame of reference, 10% according to
| another frame of reference and 0% according to another.
|
| A lot of work is done by the words "get to" which is
| colloquial for "accelerate".
| DHRicoF wrote:
| > Not just 99%, but 99.99999999% or _however many you
| want_.
|
| Badly enough, even that's not true.
|
| We have a frame of reference given by the cosmic
| microwave background. When you move faster and faster at
| some limiting speed will create pions that will slow down
| the particle creating an effective slower max speed.
|
| https://bigthink.com/starts-with-a-bang/speed-limit-
| below-sp...
| icehawk wrote:
| Yes.
|
| Gven the average mass of a human body at 66kg:
| (((1/sqrt(1-((0.99 _c)^2 /c^2)))--1) _ 66kg * c^2) =
| 50,000PJ
|
| which is the amount of electrical energy the entire US
| produces in 0.287h???
| rbanffy wrote:
| I'd need about 40 minutes.
| antonvs wrote:
| You might want to look up the word "approach" in a dictionary.
|
| > Only a photon can move with the speed of light.
|
| Any massless particle must move at the speed of light. Gluons,
| the carrier of the strong force, are another example.
| nyc111 wrote:
| "Any massless particle must move at the speed of light"
|
| Does not change my argument. Human body is not a massless
| particle.
| dcow wrote:
| No, but it does betray your lack of formal exposure to the
| topic.
| icehawk wrote:
| And it can't move _at_ the speed of light. It can
| _approach_ the speed of light which isn 't the same thing
| as moving _at_ it.
| yarg wrote:
| Read the formula:
| https://en.wikipedia.org/wiki/Lorentz_factor
| rbanffy wrote:
| Which means you can approach the speed of light, but never
| travel at this speed in space.
| nyc111 wrote:
| I guess you guys found a way to accelerate human body to the
| speed of light without disintegrating. Why don't you prove your
| technique first with G-forces?
| mftrhu wrote:
| > accelerate human body to the speed of light
|
| Nothing with mass can have the same speed as light, but you
| can _trivially_ accelerate a human body - or something
| similar - to a speed which is arbitrarily close to it,
| without risking _anything_ from the G-forces involved.
|
| You just need to do it very slowly.
|
| That is, in any case, neither here nor there, since this is a
| thought experiment used in a discussion about the effects of
| moving at a speed close to _c_ - people in thought
| experiments are _stronk_.
| itishappy wrote:
| Why don't you? Here's a calculator:
|
| https://gregsspacecalculations.blogspot.com/p/blog-page.html
|
| 1G of acceleration (which I'd hope you agree is survivable by
| humans) over an extended time period can easily reach
| relativistic speeds. 1 day .0028c
| 1 week .02c 1 month .086c 1 year .77c
| 2 years .97c 3 years .996c 4 years .9995c
| 5 years .9999c
|
| The thing stopping us from doing this today is economics, not
| physics. Current rockets have about enough fuel for minutes
| of acceleration, and fuel requirements increase exponentially
| due to the tyranny of the rocket equation. If you skip the
| need for fuel (laser propulsion?) and find some way to
| decelerate (laser cooling propulsion???), then interstellar
| travel to pretty much anywhere becomes entirely reasonable
| within human lifespans.
|
| https://en.wikipedia.org/wiki/File:Roundtriptimes.png
| ndsipa_pomu wrote:
| > This is not even possible in pulp science fiction
|
| Incorrect - anything is possible in pulp scifi.
|
| > In order to be able to move with the speed of light you need
| to transform yourself into a photon. Only a photon can move
| with the speed of light.
|
| Incorrect - any massless particle will move at the same speed
| as light.
|
| > Saying "close to the speed of light" changes nothing. You
| need to be light to move with the speed close to the speed of
| light.
|
| Incorrect - it's perfectly feasible to accelerate particles to
| over 99% of the speed of light. e.g. the LHC can accelerate
| protons to 0.999999990 c. Also, it's not possible for massless
| particles including photons to move at anything other than the
| speed of light in a vacuum, so "close to the speed of light" is
| not possible unless the object has mass.
|
| > Macroscopic objects cannot move with speeds approaching light
| speed.
|
| Incorrect, though humans haven't been able to accelerate
| macroscopic (e.g. visible to human eye) objects to more than
| approx 0.064c (Parker Solar Probe), it's just a question of
| using enough power to accelerate the relevant object. There's
| no reason to think that a black hole accretion disk couldn't
| easily accelerate a lump of matter to more than 0.99c.
| at_a_remove wrote:
| I only got my undergrad in physics, but I think there is
| _something_ there to be mined between time as a dimension and the
| second law of thermodynamics. Why this one?
|
| First, I will render a quote which never failed to amuse me: "The
| law that entropy always increases holds, I think, the supreme
| position among the laws of Nature. If someone points out to you
| that your pet theory of the universe is in disagreement with
| Maxwell's equations -- then so much the worse for Maxwell's
| equations. If it is found to be contradicted by observation --
| well, these experimentalists do bungle things sometimes. But if
| your theory is found to be against the Second Law of
| Thermodynamics I can give you no hope; there is nothing for it to
| collapse in deepest humiliation." (Eddington)
|
| Why such _honor_? For one, in statistical physics, you can more
| or less derive the second law of thermodynamics, from scratch. No
| need for observation. It 's just _there_ the same way the
| quadratic equation is. Somewhere I have a cheap Dover reprint
| which contains a relatively easy to follow construction of the
| second law. _It 's the math._ You can measure things badly, you
| can find one phenomenon creating the appearance of another, but
| you cannot fool The Math.
|
| And so the statistical physics you can get from _just math_ gives
| you this arrow of time, flying only one way, just as we see from
| spacetime.
|
| To me, and again, I only got a few grad courses under my belt in
| it, this suggests not just a deep connection between entropy and
| spacetime, but the inevitability of it from the basic math
| (really, a talented high schooler could be coached through it)
| means that there is _something_ about large (for n = ?) numbers
| of particles losing the reversibility which is so often present
| in particle interactions where _n_ is smaller. What gives there?
| How do we go from this "trend" emerging to it being a property
| of spacetime even if no particles are sitting _in_ said
| spacetime.
|
| Not that I would have dared write the great Wheeler, but I have
| wondered if his "geon" concept would have fit in with this sort
| of thing. It seems so fundamental. One can imagine a universe
| with a different number of un-unified forces, or gravity dropping
| as the inverse-cube, or varying physical constants, but the math
| is still the same in these universes and it then suggests that
| there's no, uh, room for an _option_ wherein the time facet of
| spacetime is anything but an arrow flying forever on towards
| entropy in its many masks.
|
| A great task, or perhaps a very alluring windmill, for someone
| younger and brighter than I.
| mkleczek wrote:
| The older I am (and I am at my 50s) the more I have this
| intuition that entropy is a fundamental force driving not only
| physical phenomena but also social interactions, economy etc.
|
| Formalising this intuition is another story though...
| etcd wrote:
| We have the sun to provide us with low entropy energy and the
| atmosphere to dissipate high entropy energy, so stuff tbat
| happens on earth can be lowering in entropy possibly. Climate
| change excepted.
| majoe wrote:
| Tools from statistical physics have long been used in
| sociological and economical models.
|
| It's no wonder, because statistical physics was devised as a
| tool for the study of complex systems.
|
| For the same reason I don't deem entropy to be a fundamental
| property of physics, but one of complex systems. As far as I
| remember from university, the 2nd law of thermodynamics
| simply arises from the fact, that there are exponentially
| more unordered than ordered states.
|
| Though information itself may be a fundamental physical
| property. The recent interest in Quantum computers shines new
| light on the connection between information and Quantum
| Mechanics. It remains to be seen, how that point of view is
| compatible with relativity.
|
| I hope, that one day someone finds out, that the "time
| dimension" arises in the macroscopic limit from a graph of
| discrete causal events.
| mkleczek wrote:
| Not disputing anything you said but... The issue I see is
| that without notion of time it is difficult to talk about
| causality (I guess you could only talk about
| "entanglement"). It is actually difficult to talk about
| "events" at all - I guess you can only talk about "facts"?
| DeathArrow wrote:
| From the Wikipedia page on the second law of thermodynamics:
|
| >For example, the first law allows the process of a cup falling
| off a table and breaking on the floor, as well as allowing the
| reverse process of the cup fragments coming back together and
| 'jumping' back onto the table, while the second law allows the
| former and denies the latter. The second law may be formulated
| by the observation that the entropy of isolated systems left to
| spontaneous evolution cannot decrease, as they always tend
| toward a state of thermodynamic equilibrium where the entropy
| is highest at the given internal energy.[4] An increase in the
| combined entropy of system and surroundings accounts for the
| irreversibility of natural processes, often referred to in the
| concept of the arrow of time.[5][6]
| bawana wrote:
| Entropy is also defined as the number of different
| arrangements of particles in a system. We say that entropy is
| increasing in our universe. But we have also found that space
| is increasing. If space increases faster than particles move,
| entropy could even decrease
| itishappy wrote:
| I'm in a similar boat, but I've always felt the opposite! I've
| always felt the second law is kind of a shoe-in and maybe even
| shouldn't be a law at all.
|
| The first and third laws, "energy is never created or
| destroyed" and "for every action there's an equal and opposite
| reaction" are always true! To my knowledge, no process is ever
| allowed to break either law. (With exceptions for cosmological
| process like the expansion of the universe that we really don't
| purport to understand.)
|
| The second, "entropy can only increase" isn't! That's right, I
| said it. The processes it describes (a cup unshuttering, or
| coffee unmixing, or particles all finding their way into the
| same side of a box) are totally legal process, albeit
| statistically unlikely. If you restrict your system to few
| enough particles (say, n=3), random processes that decrease
| entropy are not only possible, but something that happens with
| regularity!
|
| Now, I make no claims to be right here. I suspect that
| Eddington fellow probably knows what he's talking about. But,
| this has been a longstanding thorn in my understanding of
| physics, so I'd be interested if anybody has any interesting
| insights!
| elashri wrote:
| > With exceptions for cosmological process like the expansion
| of the universe that we really don't purport to understand
|
| That's not accurate, expansion of the universe (that the
| standard model of cosmology describes) does not violate
| conservation of energy. It makes it a little different from
| the classical view.
|
| In classical mechanics, energy conservation is a well-defined
| concept in a static or non-expanding spacetime. However, in
| an expanding universe, especially one described by general
| relativity (like ours), the energy of the universe is not
| necessarily conserved in the traditional sense, because the
| global energy of the universe is difficult to define when
| spacetime itself is dynamic (expanding)
|
| So GR does not require global conversation of energy in the
| same way classical (here classical means strictly newtonian
| mechanics) mechanics does. This dynamic nature of the
| spacetime allows for energy to appear to "change" due to the
| expansion. It is more complicated when you add things like
| dark energy to the equation.
|
| One interesting aspect is the phenomenon of cosmological
| redshift. As the universe expands, light travelling through
| space is redshifted. This means that ita wavelength increases
| and its energy decreases. This "loss" of energy from light is
| not violating conservation of energy. It is rather
| consequence of the expansion itself.
|
| Now lets back to dark energy which is driving the accelerated
| expansion of the universe, the energy associated with the
| vacuum of space remains constant per unit volume, but as
| space itself expands, the total energy associated with dark
| energy increases. This again does not violate the laws of
| physics because energy conservation is more complex in
| general relativity than in Newtonian mechanics. And of course
| the local energy conservation works in a well-defined way if
| you take a localized region of the spacetime.
| alok-g wrote:
| Could you pls. point to the said book or some other resource
| for me to learn about this? As such, I follow what you have
| said, but would love to see the math too. Thanks.
| woopsn wrote:
| Ilya Prigogine wrote a lot about this, see eg Order Out of
| Chaos. He won the Nobel prize in chemistry for his work on
| nonequilibrium thermodynamics.
|
| The idea is more nuanced than one expects at first. Boltzmann
| had originally tried to prove that the second law is a
| mathematical statistical fact and several others tried as
| well. But Poincare showed that those systems which,
| regardless of their initial state, inevitably increase
| entropy later on inevitably reduce it (his recurrence
| theorem). There are also in fact reversible processes in
| nature, so it can't be that mechanics alone implies the
| procession of time. Something more involved is going on.
|
| Carlo Rovelli has also written a lot about the "thermal time"
| concept in his books.
|
| My takeaway from them is that you can't really get time out
| of mechanics by itself (statistical or otherwise). In the
| same way that you can't get baryon asymmetry. It is
| intrinsically a selection principle on initial conditions.
| heed wrote:
| Also consider the speed of light is also the speed of causality.
| If there was no such limit it means it would be possible for
| effects to precede causes which would lead to a very different
| kind of universe!
| wruza wrote:
| Wouldn't it just happen instantly and settle on some fixed
| point?
| Dylan16807 wrote:
| There's a lot of ways to implement that and most of them aren't
| a problem.
|
| For example: If there isn't a speed of light, how fast does
| light go? If it's variable but not instant, then depending on
| the details causality violations could still be very rare or
| impossible. If it's instant, then how do we define instant for
| different observers? I feel like relativity-style calculations
| don't really work. If "instant" is agreed upon by all observers
| then we won't have causality issues.
| dcow wrote:
| Could you even measure or experience variable speed
| causality? Or, it doesn't matter what made up constant you
| assign the speed of causality. You're just bits on a page and
| you only perceive _anything_ as the clock cycles.
| ben_w wrote:
| I've heard it claimed that we can only measure the round-
| trip speed of light, not the one-way speed of light,
| because the maths says that reality would look identical if
| it was 0.5c in the x+ direction and [?] in the x-
| direction.
|
| I find this hard to stomach, but I'm going to trust it also
| applies to e.g. magnetism being Lorenz transformed electric
| fields, because relativity violates "common sense" all over
| the place and reality doesn't care about my stomach.
|
| https://www.youtube.com/watch?app=desktop&v=pTn6Ewhb27k&the
| m...
| AnimalMuppet wrote:
| I also have heard that, multiple times. I don't buy it. I
| think there are at least two experiments that could show
| the difference.
|
| First, you could time the travel of light from one place
| to another. To do that, you need synchronized clocks. The
| easy way to do that is to start with clocks synchronized
| at a central point, then _very slowly_ move them from the
| central point to the endpoints. Why very slowly? Because
| you have to worry about time dilation with the clocks.
| For small v, the difference in the rate of time is
| approximately v^2 /2c^2 (to first order). The amount of
| time you have to maintain it is t = d/v. The
| corresponding difference in clock time still approaches
| zero as v approaches zero, so in principle, the clocks
| can be arbitrarily close to each other in time if you
| just move them slowly enough.
|
| But what if c has different values in opposite
| directions? Well, then time dilates different amounts for
| the clocks going in opposite directions, _but the amount
| of time dilation for each clock still approaches zero if
| the velocity is low enough_.
|
| Second: If you have a cyclotron or synchrotron, with
| charged particles moving in a circle in a magnetic field,
| and those charged particles are moving a significant
| fraction of the speed of light, if the speed of light is
| not uniform, their motion should deviate from a circle.
| Why? Because the force on them due to the magnetic field
| should be the same, but the acceleration should be
| different depending on what fraction of the speed of
| light they're moving. (Due to increased mass, if you
| think of it that way. If you don't, well, the equation
| doesn't change.)
|
| I think that _some_ experiments would fail to show a non-
| uniform speed of light, but I think experiments could be
| devised that _would_ show it.
| Dylan16807 wrote:
| _Unfortunately, if the one-way speed of light is
| anisotropic, the correct time dilation factor becomes 1
| /(g(1-kv/c)), with the anisotropy parameter k between -1
| and +1.[17] This introduces a new linear term, meaning
| time dilation can no longer be ignored at small
| velocities, and slow clock-transport will fail to detect
| this anisotropy. Thus it is equivalent to Einstein
| synchronization._
|
| https://en.wikipedia.org/wiki/One-way_speed_of_light
|
| A lot of scientists have thought about this. Step one is
| checking their work.
| AnimalMuppet wrote:
| Ah, I see.
|
| I see nothing there that would invalidate my synchrotron
| argument, though.
| setopt wrote:
| "Instant" (i.e. infinite speed of light) also permits
| causality. That's the historical Galilean model.
|
| That is in fact _the only other way_ to make a causal
| universe that satisfies a few common sense assumptions ("the
| laws of physics are the same in every location", "the laws of
| physics are the same in every direction", "the laws of
| physics are the same over time").
|
| "One more derivation of the Lorentz transformation" by Levy-
| Leblond is a very accessible derivation of this if you're
| interested in reading more. It was suggested that perhaps
| relativity should be taught this way in high school, instead
| of the historical approach of "c appears to be constant in
| experiments, so how do we work around that with math".
| Dylan16807 wrote:
| Couldn't you have the laws of physics change based on your
| speed but without changing based on location, direction, or
| over time?
|
| Also infinite speed of causality doesn't have to imply
| infinite speed of light, does it?
| setopt wrote:
| > Couldn't you have the laws of physics change based on
| your speed but without changing based on location,
| direction, or over time?
|
| No you can't, that's basically what e.g. the Levy-
| Leblonde reference proves :).
|
| I encourage giving a read if you're interested! The proof
| is just a few pages long, and doesn't require more
| advanced mathematics than the average intro to special
| relativity.
|
| If you're willing to give up either causality itself, or
| the invariances of physical laws we discussed above, then
| of course many other alternatives open up.
|
| > Also infinite speed of causality doesn't have to imply
| infinite speed of light, does it?
|
| That is correct!
|
| Without experimental data, we can just prove that there
| must be a "speed of causality" that is constant for every
| observer in a universe with the properties we discussed
| above.
|
| That there exist "photons" in this universe that manage
| to travel at this speed is an experimental result. The
| exact value of that upper "speed limit" is also an
| experimental result.
| Dylan16807 wrote:
| > The principle of reality is first stated in general
| terms, leading to the idea of _equivalent frames of
| reference_ connected through "inertial" transformations
| obeying a group law. [...] Only the Lorentz
| transformations and their degenerate Galilean limit obey
| these constraints.
|
| > I will take as a starting point the statement of the
| principle of relativity in a very general form: there
| exists an infinite continuous class of reference frames
| in space-time which are _physically equivalent_. [...]
| _no physical effects can distinguish between them_.
|
| Sounds like this entire paper is built on a foundation of
| assuming the laws of physics don't change based on speed.
| Am I misreading?
|
| In that case, the paper proves that the Lorenz transforms
| are the only way to have both relativity _and_ those
| rules, but they don 't show that those rules by
| themselves imply relativity.
| MattPalmer1086 wrote:
| How could an effect precede a cause if there were no speed
| limit to causality?
|
| No matter how fast an effect propogates, it is always after the
| cause (with an infinite speed, I guess effects happen
| instantaneously, but not before).
|
| Of course, this doesn't fit with a universe described by
| general relativity, where time can be different for different
| observers. But you wouldn't have a universe described by
| general relativity without that constraint in the first place.
| alde wrote:
| How would you compare two infinities? E.g. speed of light
| inside a moving train vs speed of light outside of it.
| MattPalmer1086 wrote:
| An infinite speed implies instantaneous effect. So it
| wouldn't matter how you were moving. If two people launched
| something that travelled with infinite speed, one on the
| train travelling at 100mph, and one on the ground beside
| it, it would take zero time for both of them to reach their
| destination.
|
| At least, that's what I surmise. I'm not a physicist.
| gavmor wrote:
| Here's a great video explaining how, due to relativity, FTL
| travel can cause grandfather paradoxes:
| https://youtu.be/an0M-wcHw5A?si=RYFGOmQOlaC2t0bM
|
| Edit: in short, not all reference frames can agree on the
| order of events, and FTL events propogate "backwards" between
| some reference frames.
| MattPalmer1086 wrote:
| Nice video, thanks for posting.
| david-gpu wrote:
| That doesn't mean that light (causality) couldn't be
| faster, right? You could increase the speed of light
| (causality) as much as you want and wouldn't run into any
| paradox.
| gavmor wrote:
| What does it mean to increase the speed of causality?
| This seems like asserting that we can add as many tick
| marks to the axis as we like, since the only universal
| unit of measurement is a velocity's percentage of C.
|
| If we imagine something going faster than the speed of
| causality, we're simply misconcieving the properties of
| space.
| MattPalmer1086 wrote:
| Right. The speed limit itself is arbitrary.
| coldtea wrote:
| Mainly in the sense that you can create an amp that goes
| to 11.
| andsoitis wrote:
| > How could an effect precede a cause if there were no speed
| limit to causality?
|
| > No matter how fast an effect propogates, it is always after
| the cause (with an infinite speed, I guess effects happen
| instantaneously, but not before).
|
| If everything happens instantaneously then there is no real
| cause and effect, and the universe would be over before it
| really got started.
| amelius wrote:
| No speed limit does not mean that everything goes
| infinitely fast.
| lazide wrote:
| If the speed limit is infinite, what else would you
| expect to happen?
| amelius wrote:
| Light traveling at infinite speeds, atoms and such not.
| andsoitis wrote:
| If effects were instantaneous then atoms would not exist.
| amelius wrote:
| There can be many types of effects in a hypothetical
| universe.
|
| Imagine a universe like Conway's way of life, where only
| neighboring cells can be affected in one timestep. Now
| add to it a rule that all blocks have a color, and the
| color of all blocks are changed when one block changes
| color. Now you have a universe with both immediate and
| non-immediate effects.
| jodrellblank wrote:
| But what is "One time step" in that universe? We have the
| idea of a light clock - light bouncing between two
| perfect mirrors in a vacuum - as an ultimate clock.
|
| The distance between the mirrors is a number of meters. A
| meter is based on how far light travels in a second. How
| long it takes light to go between them is based on the
| speed of light. Speed, distance and time are connected.
|
| If we untether the speed of light and it's unlimited,
| then in some sense there is no way to say how long it
| takes light to bounce between the mirrors - it doesn't
| take any time. And there is no way to say how far apart
| the mirrors are, if light passes between them instantly
| that implies there must be no gap to cross. If light
| crosses no distance in no time then it also bounces back
| covering no distance in no time, ahh does lots of bounces
| in no time. There goes the concept of a time step and any
| concept of "non immediate effects".
|
| If you try and add time as a separate thing, then you
| have some kind of Conway's game simulation - but that
| gives you a way to track where light is (which simulation
| cell it's in) and therefore a kind of distance (how far
| the mirrors are apart in simulation cells) and then you
| lock down how light moves in "simulation cells travelled
| per timestep" which brings you back to a fixed speed of
| light again.
| lazide wrote:
| A 'one level of cells in one timestep' _is_ a speed
| limit, and a very slow one actually.
| bryanrasmussen wrote:
| old grannies driving at 30mph on the freeway, me at
| infinity.
|
| on edit: not everything travels at the speed limit, if
| the speed limit right now is the speed of light - then
| why doesn't everything travel at the speed of light?
|
| People say if the speed limit was infinite that
| everything would happen instantaneously - but they still
| need to explain why everything should go at the speed
| limit in this other universe, when not everything goes at
| the speed limit in ours.
| lazide wrote:
| Almost everything (electrical fields, atomic radius, even
| speed of sound in materials) seems to derive in some way
| from the speed of light and related effects.
| bryanrasmussen wrote:
| perhaps this is an effect of having a speed limit in a
| universe, if a universe does not have any set speed limit
| (which is somewhat different than the phrasing speed
| limit is infinite) perhaps the discussed derivation of
| other speeds would not exist in the way it does in our
| universe.
| MattPalmer1086 wrote:
| Agreed, an infinite speed was just the most extreme edge
| case of having no limit.
| withinboredom wrote:
| I'm having trouble with this assertion. Light travels
| slower in water than in air, by your assertion that light
| is the limit of causality; then surely we can create a
| paradox with ftl right in a pool.
| coldtea wrote:
| > _Light travels slower in water than in air, by your
| assertion that light is the limit of causality_
|
| The limit of causality is the light speed limit in
| vacuum, not "whatever happens to be the max speed of
| light in some medium".
|
| Light (as in visible light) is also irrelevant to this,
| it's just an example of something moving at that speed.
| m3kw9 wrote:
| Speed of light may be dependent on other constants and it will
| have then unpredictable effects
| Etheryte wrote:
| The possibility of delays being zero does not imply that
| negative delays are possible.
| cjfd wrote:
| Actually, it does. Because of relativity events that occur at
| the same time in one frame of reference do not occur at the
| same time in another. A delay of zero between two different
| points implies that there is a reference frame where the
| delay is negative.
| soulofmischief wrote:
| Relativity was derived as a direct consequence of imposing
| an invariant speed of causality to the Lorentz
| transformations, therefore it cannot tautologically be used
| as justification for an invariant speed of causality.
| Etheryte wrote:
| I'm not sure that holds when you take the speed of light to
| be infinite. Depending on which end you look at it, you'll
| either be dividing by zero or having infinite energy, so I
| don't think relativity the way we understand it would still
| make sense in any way.
| choeger wrote:
| What even _is_ the speed of causality? Is there any way to
| determine that causality has made it halfway from cause to
| effect?
|
| Or is this just a metaphysical way of saying that no particle
| can move faster than the speed of light, assuming that
| causality is just an abstraction of moving particles around?
| hughesjj wrote:
| Network propagation delay ;-)
|
| Imagine the world without a speed of causality, where
| everything was updated instantaneously. No CAP theorm, no
| Byzantine generals.
|
| Being a programmer/information theorist would be so much
| easier lol
| crdrost wrote:
| It kind of is that (a metaphysical restatement), but it's
| more precisely understood as a kind of half-statement of the
| theory.
|
| That is, if you assume relativity, then for anything which
| moves faster than speed _c_ , there exists some reference
| frame where it appears to move backwards in time. (This needs
| to be slightly qualified because it's kind of like when
| you're looking in a mirror and you intuitively don't think it
| does what it actually does -- flip front to back -- but you
| mentally rotate and then think that it flips left-to-right.
| So to be clear, if someone on a hyperluminal rocket cracks an
| egg into a pan, there exists someone else whose best
| understanding of this situation is a rocket that is traveling
| "backwards" engine-first, onboard of which an egg is flying
| up from the pan into an eggshell. But you would mentally
| reorient to say that the rocket is traveling "forwards" and
| that "forwards" direction is backwards in time.)
|
| Now, this doesn't directly violate causality by itself, it
| depends on whether you can move faster than light according
| to an arbitrary observer. So if Carol goes faster than light
| according to Alice and then turns and goes faster than light
| according to Bob, and Bob is moving relative to Alice, _only
| then_ can Carol potentially meet up with her "past self"
| according to Alice & Bob. The idea is that the first time she
| moves, Alice says she's moving very fast, but forward in
| time, and Bob says she's moving backward in time. Then the
| second time she moves, Bob says she's moving very fast, but
| forward in time, and Alice says she's moving backward in
| time. You combine these two to find that both agree that she
| has objectively moved backward in time.
|
| The way this manifests in the mathematics is that in
| relativity, after something happens, light kind of
| "announces" that it happened to the rest of the world, via an
| expanding bubble of photons traveling away from the event at
| speed _c_. This expanding bubble is formally known as a
| "light cone". There is another light cone as well: before the
| event happens you can understand a contracting bubble of
| photons traveling towards the event. And basically these
| partition the world into five regions: The contracting bubble
| is the "objective past" of the event, that bubble itself is
| the "null past" of the event, the spacetime between the
| bubbles is the "general present" of the event, the expanding
| bubble is the "null future" of the event, and the points
| inside of the bubble are the "objective future" of the event.
| Moving faster than light, is moving from the objective future
| of an event, into its general present. This is "general"
| because different reference frames regard these points as
| either before or after the event in time. You need a second
| trajectory to then go from the general present of the event,
| to its objective past.
| pyinstallwoes wrote:
| The ontological dissonance in that title is spectacularly
| simulacrum level 4.
| stogot wrote:
| I see a variety of discussions of time with different views. Is
| there a good summary or journal review article?
| mellosouls wrote:
| This is the sort of question I think is useful to explore with
| ChatGPT et al, and of course you can ask for links.
|
| In the meantime, Stanford and IEP are always good for this sort
| of thing (including as a background for conversing with the
| former):
|
| https://plato.stanford.edu/entries/time/
|
| https://iep.utm.edu/time/
| tightbookkeeper wrote:
| You're just going to get philosophizing with scientific
| language.
|
| Beyond the mathematical model used for a particular physics
| question, there just isn't much consensus.
| roughly wrote:
| It won't necessarily convey all the different views, but The
| Order of Time by Carlo Roveli is an absolutely beautiful walk
| through the various interpretations of time down to the quantum
| level. The nature of time is not fully understood and Roveli
| understandably (and openly) has and endorses his own view here,
| but he covers the ground upon which there's consensus quite
| well.
| IgorPartola wrote:
| If I understand correctly, we experience time at nearly the speed
| of light. What I mean by that is that any particle's 4
| dimensional velocity vector has the magnitude of c which means
| that if it is mostly at rest in space then time has to be the
| major contributing factor but the magnitude of the vector. On the
| other hand something like a photon experiences to time at all as
| it moves through the 3 space dimensions at a total of c.
| crazydoggers wrote:
| I believe that's an accurate model, with the caveat that it's
| all relative. There's no universal reference frame. So for the
| photon and his pal photons, they experience time while you (in
| your reference frame sitting still) are the one moving at the
| speed of light and not moving through time.
|
| Edit: See below, the photon doesn't have its own reference
| frame so they still don't experience time.
| Filligree wrote:
| Photons absolutely do not experience time. The spacetime
| interval of any photon is always zero, and the spacetime
| interval tells you how much time any particle experiences.
| Note that it's invariant.
| crazydoggers wrote:
| Yes you're right.. the photon has no reference frame of its
| own then.
|
| So then that would just apply to massive objects with their
| own reference frames.
| aszantu wrote:
| I still don't get it, photon comes into existence and then
| slams into a thing for us to notice the existence. Between
| the being born and slamming into something time passes, no?
| Filligree wrote:
| If you use seconds and light-seconds as the units instead of
| meters, then the magnitude of the vector is just a constant 1.
|
| Another way of putting that: This isn't a vector at all, it's
| just a direction. Treating it as a vector gives rise to silly
| statements like "one second per second", which is yet another
| way to explain that it's magnitude 1... because it's a
| direction.
| IgorPartola wrote:
| Not really because a light second is meters.
|
| I mean like yes you can measure time and space with the same
| units in the way you suggest but then the concept of velocity
| changes as well.
| stouset wrote:
| I think that's GP's point. If you take at face value that
| your speed through spacetime is constant and that the only
| thing that can vary is the magnitude distributed through
| (x, y, z, t), then the only important component of your
| spacetime velocity is its angle in 4D space (e.g., your
| "direction").
|
| But also our own _personal_ velocity is stationary. We
| (AIAU, IANAP) always perceive our own velocity vector as
| (0, 0, 0, 1). When we undergo acceleration it only ever
| affects the directional components of every other part of
| the universe, not our own experiential frame.
| itishappy wrote:
| I've heard this described as "we all move at the speed of
| light." Also, since another way to describe alignment of two
| vectors is an angle, motion can be characterized by the angle
| it makes with the time axis.
|
| https://www.youtube.com/watch?v=au0QJYISe4c
| dbsmith83 wrote:
| A fidget spinner illustrates this for me--bear with me. When I
| spin it and it just stays at rest in my hand, it spins fast.
| But when I quickly move my hand carrying the spinner, you can
| see it slows down the spin rate, and then when I stop moving
| it, it speeds back up. While the mechanisms are entirely
| different (classical vs. relativistic) they both show motion
| can affect certain fundamental properties of a system, whether
| it be spin rate or the passage of time
| lacy_tinpot wrote:
| You can't "experience" time. Experience is memory and memory is
| the only thing you can "experience". Whether that memory has
| anything to do with time as such is debatable. Personally I'd
| say no.
| soulofmischief wrote:
| You're thinking of subjective experience, conscious
| perception of time. OP is referring more generally to the
| local speed of causality in a system at rest.
| crdrost wrote:
| You have understood it about as well as the article did!
|
| Now, there is a huge nuance here, which is that you _are_
| moving near the speed of light, to certain observers. This is
| like the whole "relativ-" prefix in "relativity", you are at
| rest in your rest frame, you are moving very fast in some other
| rest frames. The cosmic muon crashing into Earth, sees you as
| time-dilated! So with that nuance "we experience time at nearly
| the speed of light" just becomes kind of a tautology like "we
| experience time how we experience time."
|
| But a better way to think about this is, you are about two
| meters high, you are about a meter wide, about a half-meter
| dorsoventrally... and about 30 000 000 m in the other
| direction, if we're looking at the human reaction time/blink-
| of-an-eye range of 0.1s (think about how 10fps video is at the
| cusp of being continuous and how 20Hz is where clicks stop
| sounding differentiated and instead start sounding like a bass
| note).
|
| What this means is that if we look at you relativistically, you
| kind of look like a big "rope" with worldlines of other atoms
| coming in, braiding into your body, eventually leaving... but
| the strands of this rope are bundled into these cells that have
| worldlines over 99.9999% parallel. (Atoms within those cells
| move faster, but you're probably at least 99.999% parallel even
| if we make that statement?) And that astonishing parallelism is
| precisely why relativity is not very intuitively plausible to
| us.
| ByThyGrace wrote:
| > and about 30 000 000 m in the other direction, if we're
| looking at the human reaction time/blink-of-an-eye range of
| 0.1s
|
| So: distance over time, but is the time dimension only
| measurable in distance over time? Is there a purely time
| unit, or does that not make sense when speaking of spacetime?
| pelorat wrote:
| Correct, it's a mathematical dimension.
| quantadev wrote:
| One _Speculative_ Theory of Spacetime:
|
| Our universe is a 3D Manifold in a higher dimensional space.
|
| All event horizons have a "surface normal" (orthogonality)
| direction at any point. For example a conventional Black Hole (2D
| one) has an event horizon that is a 2D surface. That is, for a
| flatland creature living on that EH it takes two coordinates to
| define a location, but these flatlanders would experience "time"
| as the "growth" of the EH (like when more mass falls into it, and
| the EH grows), and the direction is "outward" (perpendicular to
| EH surface)
|
| Now here's the interesting part: Event Horizons come in all
| dimensions. Our "Universe" is a 3D EH, but of course at any point
| in space there's a unique "rate of time" and a common "direction"
| of time, which from a higher dimensional space perspective is
| simply the "orthogonal direction" to all our space directions.
| (Time orthogonal to Space [i.e. Minkowski]).
|
| As matter falls into our "Universe", that moves time forward for
| us. But our universe itself consists of all the "points" (Quantum
| Decoherence Points) which are co-located on a 3D manifold
| embedded in a higher dimensional space.
|
| This means the Big Bang has things exactly "inverted", and is
| wrong. Matter didn't "originate from inside". It's the opposite o
| that. Everything "fell in" from outside. The reason our universe
| is expanding and accelerating is because it's a black hole EH.
| Black Holes mainly just grow (excluding tunneling etc).
| threatripper wrote:
| Has this been investigated in detail by physicists? Does it
| hold up in theory?
| quantadev wrote:
| I think it's one of those things that borders on the
| unfalsifiable, similar to multiverse theory. I've had this
| concept for about a decade, but I did actually see a youtube
| video of a Cambridge (or some well known University for
| Physics) where a professor/researcher did present the idea,
| yes.
| nakedneuron wrote:
| I agree. The similarity between black holes and our universe is
| striking. The fact that matter inside it can not be observed
| from outside opens possibilities for all kind of quantum
| states, which is maybe, just the configuration of a universe
| (for example that one we are living in).
| quantadev wrote:
| There are many different "lines of reasoning" that lead to
| this conclusion as well. For example as an object approaches
| the speed of light, an observer will see it become smashed
| perfectly flat (length contraction) in the direction of it's
| travel, which is the logical equivalent of a "loss of one
| dimension".
|
| In other words as something tries to "escape" our 3D manifold
| the effect that has is to remove one a spatial dimension.
| Also as something goes to nearer to speed of light, we know
| it also loses "time" dimension. No flow of time (from
| perspective of observer).
|
| And all of these same "divide by zero" kind of
| impossibilities are precisely what's also happening on event
| horizons. In other words Special Relativity reinforces this
| theory. My claim is that even the Lorentz equations are
| showing us the way in which a dimension is lost. Lorentz is a
| "smooth" way of going from N dimensions to N minus 1
| dimensions.
|
| EDIT: So there must be a stronger relationship between
| Spinors and Lorentz than what's currently known! By having
| complex components, Spinors is the way to have "partial
| moves" in a direction, while still technically maintaining
| orthogonality to all other directions.
| defanor wrote:
| > Your motion through the x dimension in space, for example, is
| completely independent of your motion through the other two (y
| and z) spatial dimensions.
|
| If one considers motion at (or near) the speed of light, that
| speed would have to be shared among space dimensions, just as
| with the time dimension. So not that independent.
| 123pie123 wrote:
| i've never really 'properly' understood spacetime - can you
| expand on your comment?
|
| why would going v fast in the x direction affect y and z?
| ben_w wrote:
| If I am seen to go at [v_x, v_y, v_z] = [0.9, 0.9, 0.9]c,
| then I would be going at about 1.56c in the [1, 1, 1]
| direction, which is impossible.
| nkrisc wrote:
| Think of it as a maximum vector length. As one component of
| the vector nears the maximum length, the other components
| most reduce until the vector is aligned with only one axis
| and at the maximum length - the other components must all
| equal zero.
|
| That is - to my limited understanding - essentially why
| photons are "timeless".
| geon wrote:
| We constantly move at the speed of light through space-time.
|
| If we start to move through space, we slow down through time.
|
| If we go full speed through space, like a photon, we will not
| experience time at all. So from the perspective of a photon,
| everything happens at the same time, from the big bang to the
| heat death.
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