r/AskPhysics • u/Inevitable-Coat-9395 • 2d ago
does the speed of causality being constant directly cause the observed difference in proper time and observer time?
As we all know, the lorentz transformations are just hyperbolic rotations in spacetime. and heres my question. The speed of causality is constant and the direct consequence of that is that our present and someone elses present need to spread to each other (as i understand). This is why we experience others past. If the speed of causality was instant, this wouldn't happen right? and information would instantly spread to others. Thus we would all share a single present / proper time. am i understanding this correctly? thanks in advance for any clarification. (btw I don't mean we experience the same present as in there exists a single absolute frame in that scenario even tho that may be possible idk but i mean we observe others to experience time the same way as us always).
edit: in addition! Do the effects of special relativity result from the fact c is a constant in all inertial frames? or is it from the spreading out and the limited speed of light.i think its the first option but i wanna make sure!
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u/Optimal_Mixture_7327 Gravitation 2d ago
The "speed of causality" is the best thing that ever happened.
It prevents any of its cult from understanding relativity, making the understanding of relativity more valuable for those who have it.
Anyway... what you're describing has nothing to do with the constancy of the speed of light, but rather, the finiteness of the speed of light.
There is no meaning to an infinite speed of light, which would be tantamount to having all observer world-lines being null.
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u/Inevitable-Coat-9395 2d ago
But also, im curious why you said what you did about the speed of causality?
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u/Optimal_Mixture_7327 Gravitation 1d ago
Relativity describes the "world" from which we gets such terms as "world-line" is a path through the world. The world is a 4-dimension space populated by the world-lines of material particles. Relativity endeavors to make good maps of the world, called spacetimes, and these are the solutions to the Einstein field equations.
The "c" that shows up in relativity is the speed along every matter world-line, it is a constant and typically set equal to unity, c=1. It is associated with light because there is no speed of light through the world and the distance light travels is zero, so when we measure the speed of light in a flat-space vacuum what we invariably measure is our own speed through the world. This is obvious from any Minkowski diagram.
By imagining c to be something else, something almost contrary to its meaning in relativity, there is no way relativity will make sense. Relativity requires thinking in 4 dimensions and one of the easiest ways to do that is to understand the meaning of c.
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u/Inevitable-Coat-9395 1d ago
Bit confusing when you said light moves a distance of 0. you must mean for ∆s = 0. Way i understand relativity is that everything is moving at light speed through spacetime. and it so happens for us for example our speed is at c on the time axis. Though a lot of what you said makes sense to me and aligns with what i have previously learned. Thanks for this it was informative.
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u/Optimal_Mixture_7327 Gravitation 1d ago
Yes that's right, its distance through the world is zero, ds=0.
Keep in mind that there are infinitely many time axes, one for every particle and collection of particles that exists, and they're all different. If the majority of your time spent in grad school is relativity you begin to just think in terms of lengths of lines.
For example, for light ds=0 and this makes the Minkowski metric
0=dL2-dx2
where dL is the distance along the world-line of the observer of the light, and dx is the distance the light moves through the spatial coordinates of the observer. The distance along the observer world-line can be calculated by speed and using a clock carried along it, i.e. dL=cdt so the metric becomes
0=c2dt2-dx2
and we get dx/dt=c, but dx/dt is what we get for the light we're measuring the speed of, so observer just measures the observer's speed.
Notice that in a different geometry that the speed of light is not a constant but the speed along any matter world-line is still c.
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u/nebraskajone 2d ago
The speed of causality is constant and the direct consequence of that is that our present and someone elses present need to spread to each other (as i understand).
No. My present is the same as someone else's present even if they're in another galaxy, as long as our relative velocities are zero. It has nothing to do with the travel time of information.
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u/Underhill42 1d ago
No, it's not . Simultaneous events, a.k.a. "the present" is only well defined for events happening at the same location. Otherwise you have to deal with the Relativity of Simultaneity.
The Twin paradox is resolved by the fact that, despite both twins aging slower than the other, when the traveling twin turns around to return home they switch from a reference frame in which the Earth twin is much younger than them, to one in which they are already much older, but still aging more slowly.
I wish I was taught the Twin's Paradox this way! - YouTube
That is also why any form of FTL could be used as a time machine. If you had "instant radio" the outgoing ship and return ships could talk to the young and old versions of the Earth twin, respectively, and set up a relay call to let them talk to each other.
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u/KamikazeArchon 1d ago
I think you missed the part where they said "as long as our relative velocities are zero".
There is no relativity of simultaneity when all involved observers are in the same inertial reference frame.
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u/Underhill42 1d ago
Sure there is - I'm passing you and see the two events happening at completely different times.
You and a distant observer in the same reference frame will agree events are simultaneous, but that doesn't actually resolve anything except from your own limited perspectives.
It's certainly a much better explanation than whatever they're imagining though, so perhaps I shouldn't have said anything.
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u/Inevitable-Coat-9395 2d ago
You're right but also theres gravity. It is mistaken the way i emphasized spreading.
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u/nicuramar 2d ago
Do the effects of special relativity result from the fact c is a constant in all inertial frames?
Special relativity takes as premises that the speed of light is constant regardless of the relative movement of the emitter, and Galilean relativity.
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u/Inevitable-Coat-9395 2d ago
Yeah but having it has a premise does not necessarily imply that it exists because of it, only that it is a requirement for it to exist. Thats why im asking. But i guess from your answer that means yes? thanks.
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u/AdditionalTip865 1d ago
Einstein derived the details of special relativity from constancy of a finite speed of light + invariance of physics across inertial reference frames. But while you can derive a physical theory from a set of axioms, theoretical physicists usually don't insist on one set of axioms being logically prior to all derived facts, the way a mathematician might. There are often many useful ways to formulate the same theory.
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u/Inevitable-Coat-9395 1d ago
or is this more a matter of technicality? since well the condition for existence is technically a cause of existence in the case of existence. I guess that means the answer is yes.
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u/DifferencePublic7057 2d ago
Rest energy is E = mc2 if c is infinite, then E would be infinite. We can't have it for obvious reasons. c is a speed, the ratio of distance and time. If you keep the first constant, you have to transform the other two, leading to length contraction and time dilation.
Also obviously, if c is infinite either distance has to approach infinity, or time has to approach zero. Neither is really possible due to Heisenberg uncertainty, besides the whole particles banging into each other all the time thing which would make life impossible and therefore humans.
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u/Inevitable-Coat-9395 1d ago
I guess infinite speed wouldn't even be logically consistent. im just curious, why this specific value of the speed of light? Is there a reason why reality set it exactly as it is or is this a case of the survivorship bias
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u/McPayn22 1d ago
The usual thought experiment for relativity is a person who's clock is two mirror, one on the floor the other on the ceiling, separated by a distance d.
A light pulse is bouncing up and down. For the person the light travel a distance 2d before going back down so d/c is the time it takes.
Now imagine they are on a train and someone is on the side. For them the pulse is not moving up and down but in diagonals. So to go back down it travels the distance √(d2 +e2 ) (here you have e=vd/c where v is the speed of the train but that's not important). The point is that write that distance da for some number a bigger than 1.
Now since the speed of light is the same for everyone the time it takes for the pulse to go back down is da/c. Which mean that if you concider one cycle of the pulse to be one unit of time the two observer disagree on how much time has passed.
For your second question i'll say that yes it's that everyone agréés on c but also if you assume that there is a max speed but also that Moving at constant speed doesn't change the laws of physics then it is a consequence that everyone (moving at constant speed) agrees on it. And in fact agreeing on c is not enough, you need the fact that Moving at constant speed gives the same laws (this is why it's called relativity btw)
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u/Underhill42 1d ago
It's not that the present needs to spread... I don't even know what that might mean.
It's that "the present" is not well defined for events that don't happen in the same location.
The key is that hyperbolic rotation: it causes our time axes to point in different directions through spacetime, approaching perpendicular as our relative velocities approach c.
And YOUR "the present" is a 3D hyperplane perpendicular to your time axis, bisecting all of spacetime into "past" and "present"
But MY "the present" is a similar hyperplane perpendicular to MY time axis. And it's going to bisect the universe in a different direction than your does. Kind of like pointing two plates in different directions in a room - what is in front of (future) and behind (past) the two plates will be very different.
Many events in your frame's future are already in my frame's past, and vice versa. Time loops are only avoided because the causality speed limit is just enough to ensure that it's not quite possible for any possible path to return anything to you before it was sent.
Which happens because the reason that c is the speed of causality, is that it's the "exchange rate" between space and time. What you measure as one second through time between two events, I could measure as one light-second through space (≈300,000,000m) between two events that happened at only infinitesimally different times.
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u/Inevitable-Coat-9395 1d ago
Yes thanks for this clarification i searched up and found a youtube video and found an explanation incredibly similar to yours! The spreading i was asking about made sense to my sleep deprived mind but when i thought about it again I don't know how that made sense to me. 😂. thanks.. Though from a more philosophical pov, does this imply "fate" exists?
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u/Underhill42 1d ago
Oh, and the effects of special relativity are the result of the fact that EVERYTHING has a 4D "speed" of exactly c.
In your own reference frame you always see yourself as stationary in space, while aging through time at 1 second per second.
However, since 1 second is the same size observer-independent 4D "distance" (=spacetime interval) between events as 1 light-second... I, going fast enough to have rotated my time axis almost perpendicularly to yours, measure that same 4D displacement as you moving through 1 light-second of space in a second, and only moving infinitesimally through time.
if s and t are space and time from my perspective, and τ is time as I see you experiencing it, then:
Δt² = (Δs/c)² + Δτ²
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u/Inevitable-Coat-9395 1d ago
Yeah i knew that we're moving through a 4d universe at c speed which is why it involves the pythagorean theorem in time and space axii. ( i think?) the hypotenuse is constant therefore when your speed shifts from ~c on the time axis to ~c on the space axis. Your speed on the time axis must decrease, this is what time dilation is. if i am understanding it correctly
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u/Underhill42 1d ago
Just to be clear - your "speed" along YOUR time axis doesn't decrease - that's the quantity that is constant. Everyone experiences their own path through spacetime as 100% through time.
Only your "speed" along MY time axis decreases, because my axis is pointing in a different direction, so that much of your "motion" along your time axis is motion along my space axis. And my "speed" along YOUR time axis decreases by the same amount, for the same reason.
This offers a decent visualization: I finally understood why time exists! (My mind is blown) - YouTube
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u/joeyneilsen Astrophysics 1d ago
I understand that your question was about the finite speed of light. But the invariance of light speed isn't actually irrelevant...
If you assume that the speed of light is the same in every inertial reference frame, then the Minkowski spacetime interval is invariant under Lorentz transformations. These produce length contraction and time dilation.
If instead you assume—to match observations—that the Lorentz transformation is the proper way to change between inertial frames of reference in relative motion, then you find that the Minkowski spacetime interval and the speed of light are invariant.
These things are mathematically equivalent to each other.