Even More Paradoxical: The Twin Paradox in Curved Spacetime
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- čas přidán 17. 06. 2021
- The Twin Paradox gets a stranger, even more mind-bending upgrade in General Relativity's world of curved spacetime. We explore the surprising and relatively unknown results to these new scenarios, while getting our toes wet in some of GR's conceptual frameworks. And finally, after several twists and turns, we are able to narrow down the only relevant criteria for resolving the Twin Paradox.
Links to relevant papers discussed in the video:
arxiv.org/pdf/0905.2428.pdf
arxiv.org/pdf/0909.5364.pdf
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The conventional solutions never sat well with me and it's very gratifying to see that this actually does go deeper. Can't wait for the follow up video of determining spacetime paths.
I’m loving your view of this paradox and the fact you acknowledge how difficult this paradox is to understand! I’ve spent years not understand this thing lol
Love the evolution of this channel; great job!
The near universal neglect of mentioning the spacetime interval in twin paradox explanations has always struck me as fucking strange.
Subbed.
Best physics videos on CZcams
Thx
Agreed
Yes it is, there are 3 others i believe , all equal top notch. Then the next 5 are getting really good too.
Ps I've been watching Richard Fienman's lectures, they are posted, and they are absolutely fantastic. So God damned good Dialect himself will tell you I'd bet
Try David Butler
@@KINGFAROOQ1216 Which other ones?
This. I've been looking for this kind of explanation for years. My new favorite CZcams physics creator.
What's amazing is how all the established wisdom of "consensus science" got such a basic question of a theory that's been around for over 100 years wrong. This is a great lesson in not just accepting conventional wisdom, even by experts, if it doesn't make sense to you. There's room for discoveries in even some of the most trodden ground.
@@chrimony Can you elaborate? What did "consensus science" get wrong?
@@rsm3t I think it was the idea that acceleration is the reason for the difference in aging/time of two bodies in space-time.
im finally starting to understand, was kinda skeptical about this a couple videos in at first, but this is making more sense the further along I go!
yeah, becouse he is backpedaling and trying really hard to hide it. The acceleration really solves the original twin paradox becouse in the flat space-time this causes the space-time path to be longer. He just generated buzz by basically calling everyone else stupid and made some outrageous claims. Then started to describe more general problem and described more generalized solution to the problem and called the original solution wrong. There is a reason why every explanation of twin paradox involves acceleration. People who are just starting to learn about special theory of relativity need simpler explanation that does now involve general theory of relativity.
Wow. After watching all the so called twin paradox explanation videos and reading many things about this issue, I finally begin to understand. Thank you!
You said two contradictory things at the end. At 17:43 you said:
In flat spacetime acceleration is what causes shortest spacetime path and on the next clip, you crossed it off along with feeling force and changing frame.
Love where this series is going. In the same way that aerodymic designs on a rocket are a subtle mislead (or maybe just a joke), static coordinate lines are misleading. In fact, the Alice rocket, firing its engines to "stay in one place" is just someone standing on the surface of the earth. Someone standing on the surface of the earth is actually being accelerated against geodesic free fall (toward the center of the earth), so there is the same force involved, experienced as weight. I think this is maybe where the series leads. Animating the coordinate lines (since the video occurs in time) would show this.
there is also no mention that a rocket would only accelerate until reaching escape/terminal velocity, and then accelerate when turning back. the rest of the journey would be at constant velocity.
@@carlosgaspar8447 that is discussed in previous parts
Very thought-provoking! Thank you for putting great work and consideration into these videos. I've enjoyed seeing the progression in the discovery of what really solves the twin paradox.
Reframing the discussion in curved spacetime is something I've never thought through before, but it turns out that just as relativity originally challenged the intuition of Newtonian physicists and afforded them a fuller understanding of the universe, so general relativity has challenged our intuition and afforded us a fuller understanding of the twin paradox.
I'm almost jumping up&down in excitement 😊. I just happen to be muddling around in curved reference-frames , because I was studying polytopes & aperiotopes in both Euclidean and Non-Euclidean geometry. And the notion of 'The Shortest Path' also called 'geodesic ' is central in all those geometries.
Wow, this is so well done both at a pedagogical and production level. Amazing!
Strangely, all is this made sense to me when I was 13 years old because it was explained to me by a physicist on irc. But all these years later, you're the only person I've ever seen who has explained it in the same way as the people on irc.
Irc really is a world leading community.
Thank you for your video. I love it. Amazing.
I only wish you'd put the math into the video. Because the math isn't very hard to add. Hope you'll consider a video on the math, sir.
Here's my take on the paradox in the simple original version. Bob and Alice are in one point in space and not moving relative to each other. Now they define a point to which Alice will travel to and back at relativistic speeds. Let's use 0.6C for this example. You have just decided on that location in this current inertial frame. Therefore the second Alice starts moving in the direction of that far point, the distance between their origin and the goal will experience length contraction. That means from her new inertial frame after she is done accelerating (or we can ignore acceleration for simplicity), she will now have to travel a lesser distance than what Bob is seeing her travel, but she still sees that end point moving towards her at 0.6C. Less distance at the same speed, therefore she will age less. You can solve the problem from both frames of reference, or any other frame of reference, but the parameters of the problem are different for different frames.
Den överlägset bästa jag sett om detta! Underbart.
Absolutely incredible. So if either twin experiences an energy change by either changing mass or momentum, wouldn't that be the only thing needed to break symmetry? A change in energy will affect the curvature of spacetime, which in turn directly affects time perceived. Please discuss this in the next one, thanks.
Curvature of spacetime won't be affected
No. You can have twins paradox where both twins are in inertial frames of reference. One twin can be in a high circular orbit, the second twin can be in a low eccentric orbit that tangentially intersects the high circular orbit.
The twin in the high orbit will be younger. Neither twin is noticing a change in momentum, nor any acceleration, nor any force at all. They are both in free fall.
@@TheLazyVideo but the in the lower, excentric orbit, has to go faster to stay in orbit, so the extra speed compensates for the extra proximity to the gravitational field.
Just watched the entire series. I sincerely hope you're right. This all makes much more sense to me than the other eplanations but still ... god damnit physics! :D
Thanks for your videos and efforts guys!
@@nadirceliloglu397 I guess I just go with my gut then next time. ;)
But seriouesly, I am sticking with this one now because it makes sense to me. If you got a good article or something with a better explanatioon, please let me know.
Thanks a lot for that detailed analysis of the twin paradox.
interesting. was not aware of these recent papers. looking forward to next video
The most general solution is to calculate the proper time for each twin. You can do that in curved space or flat space. However, that doesn't invalidate the other answers to the twin paradox. In particular, in flat spacetime, the twin who feels a force will be the younger twin. The reason is that they have changed inertial frames and as such need to resynchronize their clocks. So these explanations are not wrong. They are simply not generalised. However, they give valuable insight into resolving the paradox, which is to look for an asymmetry in the experiences of the twins.
As I learned recently it is important to take into consideration the topology of the space you are in. Considering the locally flat 2D Euklidian space for simplicity, there are 5 different topologies: plane, cylinder, Möbius band, torus, Klein bottle. Now there are paths for the twins that have different homotopy types. For the torus you can circle it in two ways, one of which goes through the whole. Twins that follow such paths (no acceleration) are always younger than a twin that rests or takes a path without circling, even when accelerated. In 3D there are 18 such topologies. In General Relativity, you have to take the metric into account as well. You basically have to be a mathematician to understand all this.
See, for example, Time, Topology and the Twin Paradox
Jean-Pierre Luminet
Laboratoire Univers et Théories, CNRS-UMR 8102, Observatoire de Paris, F-92195 Meudon cedex, France
There's also one more type of twin paradox you can consider. In GR you can have a finitely sized universe that "wraps around". You can have one twin go around the entire universe and meet the other twin again without accelerating at all.
Two years since the last video. What happened? Did Dialect just give up? These are some of the best videos on the paradox and I'm hungry for more.
Not at all! Our quest to resolve the twin paradox took us into studying General Relativity; eventually that threw us back towards Special Relativity. We essentially address the paradox problem again under the lens of Dynamical Relativity in "What Time Dilation Actually Is", and will probably devote a video towards it in the near future.
Thanks for this great series about the twins paradox. It really made me think. The conclusion of this video sounds perfect: who ages more is the one with the longer (in space-time metric) world line. But this recreates the paradox, because the world lines can be drawn differently depending of who considers him/herself at rest. In other words, there are always two spacetime diagrams, one for each twin's perspective. We can state which is the real one only because we have an absolute point of view. At the moment, only Einstein's observation about an apparent temporary universe-wide gravitational field (shown in the previous video of the series) seems to me that is able to break the simmetry. Maybe I'll find the answer in next video...
It will be very interesting to hear if there are fatal problems with the spacetime path-solution as well, as you indicate. Since 1985 I have thought this was the correct solution to the paradox, but I look forward to be corrected 🙃
We pick 4 random points in space and time and we make a 4D grid. That's our spacetime. If we allow the grid to be infinite in all dimensions, then that grid encapsulates the entire Universe.
Someone else is going to pick 4 other points at random and from his perspective his grid wont look like our grid, and our grid won't look like his.
Why can't we unify both grids, in a way that all the possible grids are all the same grid - just seen from diffrent points of view?
Imagine a single 4D hyperbolic grid, projecting a 4D Euclidean grid to every observer in the Universe.
They will see their own grid as we see Sun's reflection of itself when it hits the sea. But, that bright line that the Sun creates at the sea - is unique to every observer, because depending on where they are, that's where they will see it. Its caused by the Earth's curvature. Italo Calvino the Italian poet and author, called it "the sword of the sun" www.ampersand-ampersand.com/images/screening/theswordofthesun.pdf in his book "Palomar", and its unique for everyone of us.
That doesn't mean though that there are infinite versions of our Sun. Our Sun is a single entity and so is our spacetime.
So in that sense we should be able to define absolute motion in respect to that spacetime grid - since things DEFINITELY age more or less than others. Or in other words - since 2 twins can separate and come back and one is younger than the other - there is DEFINITELY something absolute relative to which they moved at aparently different ways.
@@-_Nuke_- It's an interesting point of view. But that should mean that the principle of relativity applies only to an euclidean geometry spacetime, while in this particular hyperbolic one that you postulate, which generates all possible euclidean points of view, everything becomes absolute. But the Minkowski metric is in itself an hyperbolic geometry, and the twins paradox takes place in it as well. So, the Minkowski metric is not the absolute metric you are talking about and there should be other one that encompasses the whole spacetime and generates by projections all other possible hyperbolic and euclidean geometries. I'm at the boundary of my knowledge, here. Maybe, just maybe, there is another type of geometry at play here that we have not been able to identify. Anyway, the whole idea of an absolute geometry which generates the relative ones is nevetheless interesting.
But spacetime intervals are invariant. You might disagree on time or space, but everyone agrees on spacetime intervals.
@EliteTeamKiller S.I. are invariant in a Lorentz transformation, but space and time vary and the issue is precisely to know who ages more (or less). So, to derive time. Suppose two spaceships meet. Each one sees the other zipping by and each can claim to be at rest. Who ages more? We could say: "Who cares? They'll never meet again, so the question has no meaning, as they'll never share an event again". But, now let's suppose the universe is an hypersphere. After a long time, the one that is moving (either A or B) zips by again. Who has aged more, from each other's point of view?
Could the solution possibly be that SR and GR are not correct and there isn't curved space-time, but instead what we actually perceive as space and time?
This channel is gold. I wish you could help me understand why longer paths are actually shorter, the physical intuition escapes me right now. Looking forward to every new release on this channel!
@@nadirceliloglu397 Nobody cares buddy.
@@nadirceliloglu397 I’m sure you have it all figured out, just like everyone else on the internet. Post a video explaining it instead of wasting time with these worthless posts. You think I’m going to believe you just because you said so? That’s not how any of this works.
@@nadirceliloglu397 lol get a grip
I also love your other video on "the real explanation of gravity" since your objections to the explanations by these popular channels I was also having--esp with the gradient thing which suggested some kind of torque that went from one time to another---total insanity.
These are the best Twin Paradox videos on the internet. So please, where are the continuations??
We want to find out the real solution.
PS: Since the explanations are wrong, how can we assure the math results (of who ages more) are right? Just through empirical experiments?
The solution has to do with mass. Gravity influences time and creates time dilation.
An object reaching the speed of light is becoming more massive. (Following e = mc²)
The twin paradox is pure theory.
The only thing we have tested so far:
2 atomic clocks in a building near the equator! One in the cellar one on the top floor.
Time dilation is noted. The top floor clock is faster than the one in the cellar.
2 airplanes started with two atomic clocks flying in the opposite direction over the equator. The one flying in direction of the earth rotation the clock is slower than the one in the plane flying in the opposite direction.
So rotation is essential and the center of mass is essential.
@@BartvandenDonk But many disagree with that and claim that only Special Relativity (no gravity) is necessary to solve the paradox.
I really appreciate your work!
Great thought experiments and explanation and presentation. I've always wondered at rest and inertial relative to what? Accelerating relative to what? I also wondered about some global inertial frame and also frame changing...good to know I wasn't totally off. It's such a hard concept for me.
Do you actually have the answer explaining the twin paradox? This exploration and farther exploration in next and next of your video takes already 2 years
SOMEONE GIVE ME NEXT VIDEO FAST. I NEVER GOT CONVINCED WITH OLDER EXPLAINATIONS.
Newton's Laws of Motion. F=ma, Force equals Acceleration. Acceleration equals Force.
In a gravitational environment, force is applied to an object. That object becomes accelerated. In time or in space? If we look at nasa's flight data, we see that, during lift-off, heart rates are accelerated. Accelerated heart rates equal shorter lifespan as evidenced by hummingbirds. If we properly analyze the Hafele-Keating and other flying clock experiments, we can see that both clocks used the same amount of force and thus experienced the same amount of time. The lower acceleration reading went into the extra distance traveled. Time doesn't slow down, it just gets spread out over a greater distance.
Does an accelerated heart rate cause you to age faster (physical appearance) or just die sooner (shorter lifespan). There is some indication that zero gravity (less force) will extend a person's lifespan (nasa's twins experiment).
You cannot go by the clock on the wall as it is in a different frame of reference than the observer. It's Force is metered out at a constant rate.
This is a really fantastic topic! I'm interested in theoretical physics, and plan to do a PhD of physics after I graduate years later. Perhaps I could take this as one of my options.
I dont advise.. you do a phd in relativity may be to work on a better correcter to gps system only to end up not using relativity. Just dont
The Twin paradox is also a paradox in the flat spacetime, since both observers see time move more slowly for the other observer as they move apart without any acceleration. So which one is aging more than the other? Since they can't both be right and there is no preferred frame, then this must just be an optical illusion! Time and space appear to alter for other inertial moving frames when observed using farfield propagating light, but the effects are an illusion.
This has be proven using the electromagnetic fields propagating between 2 radio wave antennas. In this experiment, the time delay was measured as 2 antennas were moved from the nearfield to the farfield, and the results show conclusively that in the nearfield, light propagates instantaneously, and only after a wavelength does it reduce to the speed of light c. Analysis of the experiment showed that this occures not for the phase and group speed, but also the information speed. This complete contradicts Special Relativity, which assumes that the speed of light is only speed c. A re-derivation of Relativity shows that using instantaneous nearfield light yields Galilean transformations. Since time and space are real and can not depend on the frequency of light used, then Relativity must be an optical illusion. Time and space for inertial moving objects can appear to change, but the effects are not real, and can be proved by using instantaneous nearfield light. Time and space are absolute as indicated by Galilean Relativity, and only present time exists. So there is no twin paradox. Yes, observers using farfield light in moving inertial frames will see time slow down in each other's inertial frame, but the effects are not real. For more information see the following CZcams presentation. William D. Walker and Dag Stranneby, New Interpretation of Relativity, 2023. czcams.com/video/sePdJ7vSQvQ/video.html
Oh well. After seeing this video, i find you way more informative. Thank you.
I'm trying to find the study that involved 2 accelerating twins in spaceships, anyone have a link?
I can only find the study about circular orbit.
I'm struggling to figure out what exactly the twins see in each of their perspectives.
It is people like you who helped me understand general relativity.
General relativity is pseudo-science. It wants you to believe that mass curves space when in fact, motion curves space. A rotating body creates a circular path of increasing rates of acceleration as the radius increases.
You have a curious aversion to accepting acceleration as the factor determining the traveling (accelerating) twin as returning younger in the "twin paradox." You offer a scenario where both twins accelerate from earth in different directions, but you have them accelerate at different rates, and (surprisingly??) the one who accelerates more returns younger.
Then you introduce gravitation as-if its introduction to consideration belies the situation that excludes it. But when one twin is orbiting the earth there is no INERTIAL acceleration -- the factor deemed determinative in the original thought experiment. The other twin, although remaining in place relative to the earth, IS accelerating against gravity in order to do so. The APPARENTLY accelerating twin is floating freely inside her spacecraft while the APPARENTLY stationary twin is pressed agains a bulkhead inside her craft. Naturally, UNSURPRISINGLY therefore, it is the twin accelerating against gravity, not the one orbiting freely, that ages less. Inertial acceleration remains the factor which produces less aging in the inertially accelerating twin.
you didn't watch the entire video did you
The more you dig in twin paradox the more you find that it is ill formulated and you discover you still need absolute frame to determine who is moving really..we notice that in light gyroscope
This video is much better, as it implies that the true solution of the paradox is that the twins trace different paths through spacetime, and hence with different arc lengths and different proper times elapsed, and curve spacetime changes the arc lengths of paths compared to flat spacetime. But you still have a problem with thinking that acceleration is always relative, when that's only the components of the spacetime acceleration, but the spacetime acceleration vector itself is invariant under coordinate transformations.
The 4-acceleration vector or proper acceleration is a measurement of 3-acceleration with respect to an inertial frame. The context for defining inertial or non-inertial frames however does not exist within the framework of either special or general relativity (or worse, such frames are defined circularly, via absence of a 3-acceleration) leaving 4-acceleration to be as much of a relative concept as 3-acceleration.
@@dialectphilosophy Again, this is wrong, the proper acceleration is a Lorentz scalar.
@@dialectphilosophy 4-acceleration is defined as the covariant derivative (or the connection) of the 4-velocity in the direction of itself. The connection is defined to be coordinate independent, and 4-velocity is defined as the vector field whose vectors are tangent to a path in spacetime, and this path is also coordinate independent since it's defined as an assignment of a set of points on the spacetime manifold. Therefore 4-acceleration as a vector field cannot be relative. 3-acceleration is relative because it's merely the spatial components of the 4-acceleration, which depend on the coordinate frame you choose to decompose the 4-acceleration.
@@Etc2496 Your confusion here is pretty simple. In the context of the theory of General Relativity, 4-acceleration is, as you write, defined and treated as 'absolute'.
However, a model is not reality, and merely regurgitating textbook definitions of what 4-acceleration is or isn't doesn't alter the fact that General Relativity offers no definition for what characterizes absolute acceleration (other than that which is determined by an accelerometer, but an accelerometer can easily be demonstrated to be an instrument only capable of making relative measurements.)
So when we say "acceleration is relative" in our videos, we are NOT saying that General Relativity treats acceleration as relative (a mistake many people actually do make, and which we address in our Einstein video) since the framework of GR considers acceleration to be absolute. Rather, we are asserting that this assumption is fundamentally and logically inconsistent and does not meet the proper criteria of an empirical science, so in fact GR cannot be an entirely complete theory. Just as the assumptions of absolute space and time were realized to be fallacious by philosophers centuries before the advent of the theories of relativity, so too is the concept of absolute motion obviously flawed and bound to fall sooner or later.
@@dialectphilosophy I mean, yes, a model is not reality. However, you and me are both talking about GR, which is first and foremost a mathematical model, and therefore it makes sense that we talk about its mathematical framework as well as how it explains physical phenomena according to such framework, since we don't yet have access to a better model for reality.
In GR, an accelerometer simply lets you distinguish between if you are following a geodesic path or not. If you are not, then you are in a state of acceleration and the accelerometer will confirm this. In real life, this is indeed what we observe, since there is a difference between being in free fall (in a geodesic) vs standing on Earth's surface, for example. The mere fact of whether or not you are following a geodesic path IS NOT RELATIVE, since it depends on the inherent geometry of spacetime, and not in frames of reference. Therefore, being in a state of acceleration cannot be relative, since otherwise it would mean that spacetime geometry depends on how you observe it, which is not what we see.
The problem with your last paragraph is that, while yes, what you are saying may be true, you are as of now only speculating about how the universe works, since as I said before, GR is one of the most successful theories we have come up with. You are free to make such hypotheses, I also do this, but keep in mind that GR still hasn't been superseded and there are a milliard of other possible models that could equally as of now replace GR. You are correct that GR implies that some stuff is absolute, but this is just a requirement of the principle of relativity, although I don't know what you mean by absolute motion.
I do take some issue with classifying Science Asylum's video in the Feeling Force category; in my opinion, it's clear that the video is in the changing frames category. But admittedly it does make the graph look nice, doesn't it?
Hey i am in love with your channel and you are motivating me to go on my own journey into relearning SR & GR. Since you mentioned a lot of conventional channels and books dont do this topic justice, do you have a textbook recommendation that sheds light into SR and GR with the same skepticism you are teaching it with?
Thanks and any reading material or books would be appreciated.
Yes we highly recommend Hans Reichenbach's, "The Philosophy of Space and Time". It advocates for the truth of relativity, but doesn't take the "math-is-reality" viewpoint that modern physics does and in consequence sheds a lot of light on why we use the math the way we do.
@dialectphilosophy thank you,
Just another follow up question
What do you think about the variable speed of light theory?
@noname-sg6qx light is an electromagnetic wave. It's propagation through space is determined by the permittivity (electrical energy) and permeability (other energy sources) of space.
Fiber optics has a higher transmission rate than copper or aluminum. Electromagnetic fields drain energy from photons causing an increase in wavelength.
The early universe was denser and hotter and had more electrical energy per cubic meter allowing for a faster wave propagation. Sound travels faster through warm water than cold. If you look at the CMB, there are hot and cold spots. Just not enough energy difference to make a significant difference in the speed of light.
Light doesn't have a speed but a propagation rate and, given the current uniformity of space, it's going to be same everywhere. Given what we currently know about the universe, that uniformity came about around 14 billion years ago at first light.
Who are you? How can I contact you to discuss ideas more deeply?
I enjoyed watching your video! In the first part you describe flat spacetime- special relativity only?
A twin paradox is described where the twins both travel away from each other with opposite speeds, then turn around and meet each other.
According to the paper you mentioned in the video, the solution to this twin paradox is the twin that have the longest path in the spacetime diagram is the younges on retun.
But in a previous video on the resolving of the twin paradox, it is stated that one should always draw 2 spacetime diagrams in the twin paradox?
In this example there is actually 3 spacetime diagrams to draw:
1. Viewpoint of stay at home twin
2. Viewpoint of twin 1 travelling away at constant speed
3. Viewpoint of twin 2 travelling away in opposite direction at constant speed
It seems that when you refer to the longest path in the spacetime diagram, it is from the viewpoint of the stay at home twin (actually triplet)?
If we assume that twin 2 returns to the stay at home twin earlier than twin 1 (in the limit instantaneously, giving the standard twin paradox), then twin 2 is the early twin and twin 1 the late twin.
But, from the viewpoint of the late twin 2, the clocks of early twin 1 and the stay at home twin are running slower!
And from the viewpoint of the early twin 1, the clocks of late twin 2 and the stay at home twin are running slower!
So it is not clear to me how the paper can claim to have resolved this twin paradox?
The late twin 2 will see the clock of the early twin 1 running slower, and vice versa?
Another paradox that you might be interested in is the TTP paradox:
Question on @Quora: Quora question A twin departs slowly to Alpha Centauri. Later a second twin leaves at a faster speed and joins the slow twin near AC, when they exchange photos.As it is symmetrical, can the TTP paradox be resolved using special relativ…
www.quora.com/Quora-question-A-twin-departs-slowly-to-Alpha-Centauri-Later-a-second-twin-leaves-at-a-faster-speed-and-joins-the-slow-twin-near-AC-when-they-exchange-photos-As-it-is-symmetrical-can-the-TTP-paradox-be-resolved?ch=99&oid=100093761&share=82da7350&srid=PrYZx&target_type=question
In the TTP (Travelling twins paradox) paradox both twins travel to a destination at different speeds, but there is no return journey. Acceleration and turnaround can therefore be eliminated as breaking the symmetry. Perhaps you can consider doing a video sometime?
@@renedekker9806 “you should always draw the spacetime diagram in an inertial frame”,
But this is just the point: all the twins are in inertial frames! So you can choose the travelling twin as being stationary on the spacetime diagram!
@@renedekker9806 “the twin that leaves first is in an inertial frame the whole duration of the trip. So we can draw the spacetime diagram in her frame. “,
No, both twins are in inertial frames, the one twin just leaves later on! So you can draw the spacetime diagrams from both viewpoints and hence obtain contradictions!
@@renedekker9806 “In her frame the second twin first moves away and then comes back, and therefore the second twin will age less.”,
But what about the viewpoint of the second twin, why ignore it? They are both in inertial frames, so why is there a preferred frame?
@@renedekker9806 “the second twin is not in the same inertial frame the whole time.”,
But neither is the first twin! The first twin also have to launch from earth and land on the star. So the twins are symmetrical- both have to accelerate and decelerate to reach the star!
@@renedekker9806 Thanks for your reply. Some relativists will argue that the turnaround (when you have deceleration and acceleration) have a profound effect. For example, RoS (relativity of simultaneity) is ioften nvoked to explain why the travelling twin sees the earth twin’s clock running faster (not slower).
If the changing of frames of the travelling twin at the turnaround have no influence, then both twins will predict the other’s clock to be running slower- a physical paradox!
So at the turnaround it is postulated that changing frames (deceleration then acceleration) have a profound influence on the travelling twin’s prediction of the earth clock! But what physical reason is behind this (other than fixing a wrong prediction of SR)?
One can also argue that the travelling twin is really the earth twin and the stationary twin is the travelling twin! If you apply the same procedure as above (that the travelling twin predicts the clock of the stationary twin to run faster at the turnaround) then the prediction of SR is that the earth twin measures the travelling twin’s clock to be running faster! Hence a contradiction is again obtained.
This cleared things up.
In think, if one wants to wake someone (like me) up about the twin paradox, the variations described in this video would be easier to grasp than subtle arguments about acceleration and force (people are often not used to go into such "philosophical" detail).
Please try to be patient with us "less astute thinkers". Thank you.
Question: can we then conclude that the twins cannot know which of them is older and younger untill them reunite (assuming they dont know each others paths in spacetime beforehand)?
This is quite interesting indeed... very much contrary to the impression given in the usual treatment of the dilemma.
@@imaginingPhysics Or maybe each of them live in their version of multiverse...This paradox is confusing.
Maybe time is just an illusion. And particle with force/energy applied to them will undergoes change in state of matters slower, thus appears experience time slower?
Because we can only measure time by using the change in state of matters, biologically, chemically, or mechanically.
@@imaginingPhysics if they're not accelerating relative to each other, they will always agree on who is older. There is no paradox unless there is acceleration.
I have watched this series in order through this one. Time for some questions:
1) regarding the classic TP, you did not mention that the twin that rocketed away had to initially accelerate to high speed, DEcelerate to a stop, REaccelertate back to high speed, and finally DEcelerate again to a stop. How do those maneuvers translate into effects on time (both local and as witnessed by Emmy)?
2) How would the above situation change if the rocketing twin turned around at speed (both with and without using additional power to overcome velocity change due to the turn)?
3) How would the current video play out if the orbiting twin were at different radii (and thus established said orbit at different speeds)? Posit 0.5C & 0.9C.
4) For the current situation (as well as for the follow-on paper of the twin rocketing away and then free falling), suppose that the stationary twin is simply resting on an immovable (wrt the center of the massive object) platform, instead of firing rockets. What of these scenarios?? It would seem to be the same as a GPS satellite orbiting the earth, which is proven to elapse time differently than on the surface of the earth.
I don't have answers to all your questions @kevinboles3885, but with regard to (4), your example involving a twin on a stable platform would be substantially different from twin in a satellite in orbit.
In your example, the platform is accelerating the twin away from the earth (and off her geodesic). This is precisely what the rockets are doing in the original example (and what the ground/floor/chair are doing to you and me right now).
An orbiting satellite, by contrast, is in free fall, i.e. it is following a geodesic and is not accelerating. As a result, a twin on a platform (or in a spaceship firing her rockets to maintain a constant distance from earth) will be travelling a longer spacetime path than a twin in orbit, and her clock will, accordingly, tick faster (i.e. she will age more quickly).
Does explain the entangled photon EPR paradox too. So finding out the spin of one photon is similar to working out which twin is the older or younger twin. Because the photon never travel the same path through space-time after splitting then one will always older or younger (spin up or spin down) so it only seems they communicating faster than light but all we are probably doing is stopping to see which is the older or younger photon. Thanks.
I think this video may be misleading. The reason the "stationary" twin ages less is likely because it is accelerating more. Whether you are standing "still" in a gravity well or accelerating to stay in the "same place" the important thing is you are accelerating. Speed is relative. Acceleration is less relative. You feel acceleration directly. Time feels the acceleration and slows.
Curved spacetime aside, I still have a question regarding flat spacetime.
If acceleration is not absolute, what is the absolute quantity that allows you to detect that you're accelerating?
The planes can tell that they are accelerating by studying the motion of bodies inside the plane. If A sees nothing peculiar but B sees a notepad accelerate until it gets pressed against the plane, then we know it's asymmetrical and B was the one that was accelerating.
You aren't comfortable with allowing the term acceleration to mean anything more than the rate of change of relative velocity. So what would you call this absolute property that identifies this asymmetry, and why can't it be used to identify inertial frames? Why can't it allow you to identify which of the mirrored spacetime diagrams is correct to use?
That's an excellent and apt question, which goes to the heart of the issue, consequently it deserves a full and sufficient answer.
So first off: if as described in your example, B sees a notepad accelerate, the only empirical deduction he can make is that the notepad has accelerated with respect to him. Acceleration, as you say, only fundamentally measures rate of change of a relative velocity.
Now, to reach the absolute quantity that you describe, the invariant "absolute acceleration" so-to-speak, the observer has to make a further deduction: he has to assume that his accelerometer has been already calibrated in an inertial frame. In this case of your notepad, this calibration stems from the observers familiarity with the workings of notepads on earth; i.e. the observers knows confidently that a notepad isn't going to be magnetically attracted to objects outside the plane, or exhibit any other internal forces of motion that would suddenly propel it towards the wall.
But this knowledge about the notepad isn't contained within the system itself; it stems from familiarity with the workings of the notepad in larger contexts.
An analogy would be stepping onto a scale to determine whether you're overweight or not. If the scale hasn't been properly calibrated, the reading it gives you won't yield any useful information about whether you are overweight or not. Only if you are certain the scale has been priorly calibrated via the use of a known weight, can you be certain that the measure of your weight will be accurately reflected. Thus the reading on the scale is a relative measure: it only tells you the difference of weight between you and the measuring instrument. But you need a second piece of knowledge -- knowledge that the scale has already been calibrated with a prior-known weight, before you can come to the conclusion that the reading on the scale is your actual or "absolute" weight. This is essentially the argument of our video "Do Inertial Frames Resolve the Twin Paradox?"
So what is the absolute property that identifies the asymmetry of the paradox? Your guess is still as good as ours. Our current theories of relativity certainly do not account for it.
Acceleration, is misleading. In truth, you are constantly in motion with a fixed magnitude of motion, all while present within the 4D space-time environment. So, picture yourself being within a black room that is present within a spaceship. You are sitting in a chair that is pointing toward the left side of the spaceship. However, you have assumed that the seat points toward the front of the space ship, due to you being completely unaware that the black room had been slowly rotated to its current orientation. When the spaceship suddenly turns to the left, you feel yourself being compressed into the chair, and thus you assume that the spaceship is accelerating, even though it has simply changed its direction of travel. If it then turns to the right, your body is forced forward, and you now think that the spaceship is slowing down. So you have to understand that if you are in your car and you hit the accelerator peddle, in truth you have hit the change in direction of travel peddle. The same applies to the brake peddle. Your car is still in motion with space-time just as much as previously. All you have done when pressing these peddles is change its direction of the cars travel.
There are practical demonstrations of time dilation, the flight of atomic clocks, or the extended life of muon particles moving at relativistic speeds. Both demonstrate time moving more slowly, so they must offer some insight into the twins paradox, particularly the example of the muon decay, as it could be considered as a twin with the earth bound laboratory where it's arrival is detected.
So any solution for the asymmetry in the twins paradox must apply to both muon extended decay life, and the experiments where atomic clocks have been flown around the world and their time compared with similar stationary clocks.
This series of videos have certainly been thought provoking, but seem surprising, given that the operation of the GPS navigation system is dependent on an understanding of relativistic time dilation and general relativity. So while I followed the logic through this series that pointed out the limitations of the explanations for the twins paradox, it comes as a surprise that the true reason is still a subject for debate. In other words, while personally not happy with the CZcams and text book explanations, i assumed that some academics must know the true answer, given so much technology is depend upon it. I trust you will provide the answer in the next video in the series.
There is no answer. Acceleration is just not relative, anyone who understands GR enough knows this.
The equivalence principle states that accelerating away from a gravitational force is the same as accelerating in a zero g environment. One results in motion while the other does not.
But then, if you stay still in a strong gravitational field, next to a black hole for example, your time is or isn't slower with respect to someone staying still respect to you but far from the black hole?
which software do you use to make this animations?
At 15:10, BOTH twins accelerate. One twin accelerates only enough to resist the space-time curvature and the other accelerates much greater to overcome the same curvature and to move outward... but only for the first stage of his journey. NEITHER "is in inertial freefall for the entire trip."
What stops it from being explained as acceleration cancelling gravity for one twin and therefore no time dilation for them while the orbiting twin is constantly experiencing gravity, and their proper time being slowed down?
They both experience gravity, it doesn't cancel out, if anything accelerating increases gravity.
Finally someone that draws BOTH spacetime diagrams!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Sir🙏, please give us a clarification about Grand father paradox
If Bob started in orbit and ended in orbit, then he didn't ever share the same inertial frame as Alice, and if he did share her inertial frame at the start and end of the experiment, he would have experienced acceleration. And for Bob to have been "launched" from Alice's inertial frame away from the planet, to then fall back and join her again, he would also have to experience acceleration.
The twin who is maintaining a constant distance from the Earth (by applying a continuous thrust away from the Earth) is in fact accelerating against the curvature of space time (which is bent by the Earth's mass). Her stationary position (with respect to the Earth) is comparable to the stationary position of the Earth's surface, which is likewise accelerating upwards (which is why we Earth-dwellers feel upwards pressure from the ground, i.e. "gravity").
The twin inside her spacecraft likewise feels the pressure of her seat back accelerating against the curvature of space time. By contrast, the other twin, who is maintaining a stable orbit around the Earth, is in freefall, has zero acceleration relative to the curvature of space time, and feels weightless.
putting the info in this video together with some of the others, how is acceleration in space with rockets different than acceleration on the surface of the planet?
what would happen if the spacetime was curved as the earth is, meaning every direction you travel through the universe will take you back to the same place. In this case, the twin that got away from earth would eventually travel the whole universe and come back to the same place without any acceleration whatsoever but only one of them would have aged
Another brilliant video! Had never seen clear explanations of the discarded solutions, let alone this new one, but in this video a got it so clearly, at least conceptually, for all of them. Fantastic graphics, awesome coherent explanation!
After 10 years of casually watching dozens of of videos on the topic and always coming away finding something sketchy about all of them, and even more sketchiness in comment sections by people who not only proclaim they have finally come to an understanding, but proclaim the channel owner as some kind of pedagogical second-coming in an explanatory power rivaling the talents of Richard Feynman, I finally stumbled upon this obscure outpost and watch almost all his videos in a single hour and a half sitting.
This man is seriously underrated and under-represented in youtube's right sidebar. It's the physics equivalent of Google News sidebar of Fact Check, Polygraph, and the like.
12:40 Well, it's not wrong in the sense that the presence or absence of the acceleration in the flat (Minkowski) spacetime case is in fact the _only_ difference between the twins. So in this sense it's correct, and the "only" mistake that people make when they say this is the "cause" of the difference is merely mixing up _correlation_ with _causation_ which is BTW a standard mistake in science. In the Minkowski case the acceleration comes in 100% correlation with the difference in elapsed proper times of the twins but it's not the cause. In all cases the cause is simply the metric tensor experienced at all points (events) along each trajectory. As such, in every case, be it Minkowskian or curved, there will be _something_ that will pop up as a difference between the twins. In each case this will be something _correlated_ but not _the cause._ What it is exactly in each scenario depends on the details of the trajectories and the geometry they are embedded in. If one takes the spacetime curvature seriously, then the whole thing is no more surprising that various correlations of this type one can draw between different trajectories connecting a pair of points in a hilly terrain.
Great, thanks
What if the person accelerating is going in the opposite direction of the travelling Earth?
Wouldn't that change things dramatically?
The situation proposed in the 2009 A-B paper was fairly well understood long before 2009; it is basically the situation of the famous flight of atomic clocks around the world (1970s or before), and also of the Global Positioning System, in both cases with Alice firing her rockets to remain stationary wrt the gravitating body being replaced with Alice fixed on the surface of Earth (the motion of Alice there, wrt the Earth's center, with the Earth's rotation is small enough to be neglected.) The time-rate of the flying atomic clock, and of the clocks in the GPS satellites, in both cases measured in Alice's coordinate system, is governed by two factors, their speed wrt her and their gravitational potential wrt her. These two have opposite effects. The movement wrt the center of the Earth slows the flying or orbiting clocks wrt it and her, while the difference in gravitational potential wrt her (positive potential for the flying & GPS clocks wrt her, because of their greater altitude) speeds them up. The net result for the flying clocks was, if I remember correctly, a speeding up wrt Earth for the westward-flying clock, & I don't remember certainly about the eastward-flying clock, whose speed wrt the center of the Earth was greater than that of the westward-flying clock, so the speed-caused time-rate reduction was greater. The effect for the GPS, also if I remember correctly, is that the GPS clocks, at about 12,000 miles above Earth, run faster than Alice's clock, as measured by Alice. A clock orbiting Earth at zero altitude (if it could) would experience no gravitational potential difference-caused time-rate difference wrt Alice, but would experience a speed-caused slowing, so would run slower. A clock orbiting at great altitude would experience almost maximum (for orbiting clocks) gravitational potential difference-caused speeding up, but almost no relative speed-caused slowing, so would run faster.
As for the original twin paradox, it is true that the acceleration of the far-traveling twin in order to return to the non-traveling twin is the factor that breaks the symmetry between the two and causes the traveling and accelerating one to be the younger upon his return to the other (when the two clocks can be directly compared). Generalizing this to imply that in all situations the one who accelerates would be younger, which isn't the case, so the acceleration can't be the cause of the difference in ages in the original twin paradox, is a silly fallacy. The final resolution of the various such twin paradoxes, that the relationship of the relativistic lengths (metric) along the space-time paths traveled by the two determines which twin is older upon their meeting again, is correct, since the absolute value of the relativistic (Lorentzian) length of the path traveled by something is proportional to the proper time experienced by it while traveling along that path, so the one who travels the greater length is older (assuming they start without any difference). This agrees with what is said in the first paragraph.
They really do need to figure out the flaw in how they make them GPS clock, I hear it's because in Thier math equations they don't add the the speed of the satellites to C because " nothing can travel faster than light...
@@dexter8705in BB
I dunno why the video author doesn't understand the stuff in the last paragraph especially. They've repeatedly said in multiple videos that acceleration in not the answer to the asymmetry in the standard Twin paradox example, because the same reasoning can't be applied to an example in curved spacetime. Duh! Nobody said it is.
Technically, even in curved spacetime, acceleration (proper) is still the reason for the asymmetry in time dilation. Just not in the very common sense of the word, including the common misunderstanding that there is a force acting on falling bodies in gravity. In curved spacetime, it is the twin who is positioned still w.r.t the Earth, and not the twin who is free-falling in an orbit around the Earth, who is accelerating. So, following the same logic as the standard example, the orbiting twin will be the older one.
In one of the other videos, the video author also says that accelerometers don't solve the issue, when in fact, they absolutely do. In all these cases, if both the twins carried a pair of accelerometers and they were put in whatever spacetime and with whatever forces acting on them, and we use their readings to calculate when and by how much the time dilation asymmetries occurred we can always tell who is going to be older. There won't be any paradox.
Ur best video !
7:02 What is that? That has to be the most section in all of this series. How is the left one the greater spacetime graph distance.
@13:11 it says right there “absolute movement” makes no sense. Why do you think he is referring to acceleration?
I'm not sure you can cross off changing frames, as that seems to be what's involved in making one worldline longer than another in spacetime.
That is, they seem to be the same explanation. Rather, the difference in length of worldlines (in the units space-time) appears to explain why jumping* from one reference frame to another (together with time spent in each one) makes one twin younger than the other.
* In one go as in the TechEd video, many infinitesimal jumps, or more than one discrete jumps by either party.
There's certainly a correlation between jumping frames and shorter spacetime paths in flat-spacetime, but in curved spacetime we see that correlation vanish, which of course tells us that jumping frames cannot be the fundamental agent of asymmetry.
Bravo! This solution (the length of the spacetime path) is the solution of the paradox I think is the correct one too. I think I read about it in the wonderful book Relativity Visualized by Lewis Carroll Epstein when it came out in 1985.
Well, it's not a solution. It's paraphrase of the original question: "which twin gets older?"
Why? Because the length of the spacetime path IS the amount of time one "gets older by". We DEFINE "getting older" using the "true time" that passed for the observer in question (time that observer measures for himself). The true time is parametrization of the worldline (spacetime path) and its amount is the length of that worldline.
Saying "the twin whose spacetime path is longer aged more" is THE SAME as saying "the twin who aged more aged more". Not the solution, just paraphrase.
@@pawemarsza9515 Very good point! So I rephrase the solution then. The solution to the twin paradox is not to try to find something outside of the spacetime paths that "breaks the symmetry" between the twins, like acceleration and so on. Suggesting something that seemingly "breaks the symmetry" in one setup will be false in another setup. As you point out all that matters is which twin has the longer spacetime path in each case. Period.
But you still see a problem with this? You still think we need to find something outside of spacetime paths that "breaks the symmetry"? Why?
@@nickergodos1554 both bob and alice can get the same spacetime distance in the original paradox relative to eachother, why does the twins who accelerates perspective get chosen?
@@nickergodos1554 I don't see any problem. The only true solution to twin paradox is "there is no paradox".
If we are given external information (curvature of spacetime) we can easily calculate proper time for each twin. If we don't have that information, we can only measure their clocks after they ended their journey. That's it, nothing paradoxical.
The conclusion of this example at 5:35 must be incorrect. If both twins travel the same distance, with same acceleration and speed they should be aging at the same rate. What am I missing here?
How is the degree of the curve determined?
"What breaks the symmetry? What truly resolves the paradox?".
Well in flat spacetime, it's the fact that one twin is accelerating with respect to an inertial reference frame. And THIS means that this twin will have the shorter spacetime path. So that's pretty simple.
Now in the CURVED spacetime scenario, there is no symmetry to break. The twins take different paths through curved spacetime, so there's no apparent symmetry in the first place. The question about symmetry breaking only applies in the flat spacetime scenario. And the answer there is as I've said above.
There is a serious flaw in that rebuttal of the original paper. The original paper was very clever in that it compared time dilation of motion, while maintaining keeping the same level of gravitational time dilation. The rebuttal had differing velocities AND differing gravitational time dilation... and if you modify both of these variables you can produce any number of results that can actually lean in either direction. You need to exclude gravitational time dilation if you want to determine what causes time dilation from motion..
So, the rebuttal doesn't actually address the real issue of what is happening in regards to time dilation in flat space. IMO, the original definitely casts doubt on either the rationale of general relativity or special relativity. Either space isn't "curved" in the abstract sense Einstein thought (and instead there is actually an acceleration), or there is some absolute reference frame that is deciding who is more at rest... or possibly both of these..
So while its technically true that the object orbiting takes a longer path through space time, that really isn't saying much. At its core, we are simply acknowledging that it flew around in a circle while the other did not. It still doesn't bypass all the ideas that acceleration or changes of frame, which did not happen according GR, were not the cause. As far as GR/SR is concerned, we were basically able to compare something flying away from us in a straight line. On one hand, this isn't totally unexpected. We have an object undergoing typical time dilation, while sharing the same gravitational time dilation. What I essentially think this shows is that there must be one twin in flat SR that logically needs to be experiencing more time dilation. It may not be provable, but I think this shows that its a logical necessity.
Added up we all be traveling the speed of light 🤔 Just most of that is in time+ a little in space..Less time = more distance.. The one who's world line travels longer on the space axis travels less time, so younger..
For us and anyone, it's all time. It's the amount of coordinate time and space of others moving relative to us that changes.
Time ticks more slowly in a gravity well. Time also ticks more slowly with faster acceleration. The younger one is the one who experienced more acceleration whether due to gravity or rockets.
If anybody who hasn't read one of them pdf files in the description, you are missing out.
You'r awesome
This is not that hard to resolve once you understand you have 2 opposing forces which cause acceleration. The first force is the force of gravity and the second one is the acceleration of Alice's space ship. For Alice it would be like standing on the surface of the Earth, the acceleration of the ship would play the role of the electromagnetic force holding the surface layer of Earth's mantle together and opposing the force your weight is putting on it through Earth's gravitational attraction.
In a way both gravity and the ship's acceleration cancel out so Alice herself can't undergo acceleration to change her frame of reference. While Bob's plane undergoes acceleration in order to reach the orbit state, so his clock ticks slower. Also he's closer to Earth, so spacetieme is more stretched and time flows slower for him, in addition to him undergoing acceleration to reach the orbit state.
A good analogy here would be flying in a helicopter. Even though the helicopter hovers above Earth and stays at the same distance from Earth, this doesn't mean the pilot or anyone else is weightless or experiencing time dilation compared to observers on Earth's surface. The pilot experienced time dilation only during the time he spent accelerating to reach the hover position, then when he decelerated to stay in the hover position, his clock ticks at the same rate, as the observers on the ground.
Is the key to the solution to the twins paradox in Special Relativity (flat space) disclosed at 3:00 with the time contracting effects? And isn't this the same relativistic effect that causes someone near an event horizon of a black hole to age less than an observer watching far away, which age difference would be preserved if the observer near the event horizon reunited with the far away observer? I am a not math person but attempt to understand time and relativity intuitively and your videos are a big help. Thanks.
Thanks for watching! Yes, at the horizon of a black hole, it is the acceleration of the observer located there (meaning their rotating planes of simultaneity) which is primarily responsible for the time dilation effects of seeing distant observer's clocks running fast.
In regards to the twin paradox, acceleration can only be used as a solution when we can easily establish who is or isn't "absolutely accelerating", a problem which gets thorny when we attempt to dive into the philosophically problematic meaning of "absolute". Moreover, here in curved spacetime, we can still have the twin paradox with neither twin accelerating (in the case for instance in which they travel different orbital paths around a planet), so the question becomes somewhat trickier, as now instead of absolute acceleration, it appears spacetime curvature can also induce rotating planes of simultaneity.
@@dialectphilosophy At 15:39 you said that there is only one creterea, that of the lenths of their spacetime paths.
But in your first videos, you claimed that acceleration can be relative, therefore we have 2 diagrams for the 2 points of view and we can place both the Earth and the Spaceship at inertial frames. Therefore the lenths of the spacetime paths... Are going to come out equal if we consider both diagrams as valid...
So we still don't have an answer to why the Earth twin ages differently than the traveling twin right?
@@-_Nuke_- No sir, at least not a convincing one. More on the twin paradox from us should be coming out in the next few months.
@@dialectphilosophy Awesome to hear that!
Time dilation is responsible for the Twin Paradox. In Special Relativity this dilation is supposed to occur thanks to the inertial frame of reference. As Einstein explains in his SR work, the motion is considered to be a linear translation that is not accelerated. The velocity is fixed. It's just like the classic Galilean frame in this respect. Curvature and acceleration are ignored in SR. And this is meant to model Earth's orbit around the Sun.
Einstein's subsequent gravitational ether theory (as he put it), "General Relativity" explains what Einstein thinks happens when a body is in an accelerated state. He posits a complete equivalence between acceleration and gravity. The earlier theory does not explain gravity. Here Einstein essentially states that gravity is no longer considered a force in the classical sense of the term. Instead, the impact of mass on the fabric of existence itself is the reason why we experience gravitation. This is why Einstein concluded that the ether was indeed necessary and not superfluous. You can look up Einstein's "Ether and Relativity" speech for yourself. I believe it is from the year 1920. Here the light path can be used to measure motion, whereas in Special Relativity the Lorentz Transformation prevents this.
According to the satellite experts, both versions of Relativity are used for communication satellites. Special Relativity is used to describe a satellite's orbital velocity and General Relativity is used to describe a satellite's distance from Earth, if memory serves.
Truly fascinating! Would you know any books or sources to study special and/or general relativity and which better address these topics you discuss in your videos? I am quite afraid to study using some sources that are generally considered reliable but which actually get some subtleties wrong.
I can recommend the wonderful book Relativity Visualized by Lewis Carroll Epstein
No acceleration is necessary, please check out the Brian Green lecture he's pretty smart with this stuff. He might even have a doctorate in psychics. That right there tells you something, huh, huh? Yeah! But seriously it's an amazing lecture with very little mathematics and yet everything is explained beautifully.
There are so many questions things like this foster. Like how we define time. We count vibrations in atoms to determine time. We send those atoms out in satallites and because they are moving so fast, we determine they move in different time than us. Or is it just that the atoms vibrate at different frequencies?
So, if we put a telescope that watches a very regular pulsar and track it's flashes and a satellite does the same, eventually it will count more flashes than we do? How can a satellite moving through time faster than us cause a pulsar a billion light years away to send out more pulses to it than to us? Or, do the pulses slow down for it, so it keeps in sync with us?
If a satellite is being sent to another solar system and we magically invent an engine that can get it up to half the speed of light. We would expect the star, when it's looking at it, to get brighter, from its perspective. It would be flying very quickly headlong into the photos the system's sun emitted, so it should collect them faster, this it would appear brighter. Still, we would have to take into account too that with the speed, it would be travelling faster in time too. So, would the sun not brighten then? Because their time is moving faster than the star's, the star's output would appear to drop dramatically compared to their timeframe.
Plus a lot of this comes back to a question I have about the speed of light with respects to claims that there are no fixed on relative points in space where objects can be claimed to be at an absolute stop without any speed at all.
How can that be if the speed of light is a constant? Being a constant means no speed can be added to light by anything. Not the rotation or orbit of Earth, not the sun's rotation in the galaxy, not the galaxy's movement in relation to other galaxies. So, this by its nature implies that the moment a photon is emitted, it is decoupled from any speeds at which it's emitting atom was traveling. This means that the photon is emitted from a hard fixed point in space devoid of any relativistic speed, a point that is completely and universally fixed and does not change relative to anything. A point where if an object existed there, would actually be completely devoid of any movement in the universe and when emitting light, that light would actually emit in all directions at the exact same relative speed from.
Also, keeping this in mind, couldn't it be at least theoretically possible to detect a Doppler shift in light emitted on Earth depending on the direction you emit light that could tell us the absolute velocity and direction is traveling in the universe compared to light's fixed origins? If light is a constant, shouldn't the light be compressed some when emitted in the direction the Earth is traveling and decompressed when shon in the opposite direction?
I come from a programming background, and on 3D games, every object in the game's universe, every object you see, every light source and direction of the light emitted, is all defined from one arbitrary point in space in the game. Everything in a game comes to existence at the same point in space and is mathematically translated, rotated, and transformed to where it ends up. Yes, objects can be calculated relative to each other, but guess what. Under all of the math, they are all being calculated ultimately relative to that fixed arbitrary point in space where everything is defined from.
I've never been able to understand why physics has pushed so hard to avoid the same reality in the universe. They insist on complicating everything by insisting on observers and relativism. Everything should be definable from a fix point in space devoid of relativism.
Maybe we don't have precise enough instruments yet to detect the Doppler effect of Earth's relative motion compared to the fixed point light is emitted from. Still, I would have to think we could at least include it in the theory and admit that light itself being constant means there can be a constant point in space devoid of any speed at all
Also, yes, I know that if would likely be impossible for matter to stay still at one of these fixed points because spacetime warps and gravity, even super far from galaxies, would still have some affect to even minutely affect its position.
Anyways, just some stuff that bangs around my head at times. I don't claim to be right, especially as I don't know all the math and most of the time we get presented with basic interpretations of things more than full realities of tests and such
Okay, I talked to someone else in another comment and determined that the Doppler effect induced into the light being emitted would be impossible to detect using a detector on Earth because the detector would be traveling at the same speed.
So, in a way, it would be like two trains traveling at the same speed some distance apart on the same track. If either sounded their horns, they would sound normal to the other train. So, while the movement of one the rear train compressed the sound waves moving forward from it, the fact that the ears of the people on the front train are moving at the same speed decompresses the sound wave, as it is moving towards their ears more slowly.
I instead devised a different way that to detect the fixed position of the constant.
If both trains agree to blast their horns at the exact same time, the rear train will hear the other's horn more quickly than the front train. This would be because the the distance the sound from the front train towards the rear train would be shorter than the sound going in the opposite direction.
So, in the same way, light could reveal a fixed point in space. Put a set up satallites up in space with coordinated timers. Each will have a laser emitter and a laser detector and will fire their lasers at the other at precisely the same moment. Each will also be in fixed positions in relation to the other. They will then count how long it takes the light for the other one to reach them. If the satellites are moving along the axis they sit on, then one satellite should get the opposing satellites signal in a shorter time than the other. Note, this absolutely does not work if a single laser is reflected. Also, there will be no phase variance detectable or Doppler effect noticable. The only detectable trait would be the initial travel time and possibly the end time. From the lights perspective, they would be traveling from equidistant points and so there would be no difference to them in travel time to the points where the other was emitted from. It's the detectors that change position over time, one racing towards a laser and another racing away from the other laser. It may be fractional, but the one racing towards will narrow the distance while the one racing away will widen the distance. If light truly is a constant speed, then the travel times would have to be different. If both have exactly the same travel times, that to me would be definitive proof that the emitters added their respective speeds to the speed of their photons and thus light couldn't have a constant speed
If the times were different though, the time gap could then be used to calculate the fixed point in space where the lasers emitted the light from and how fast the salellites moved away from those points, thus giving us a definite fixed speed relative to only a fixed point in space.
Basically, I can't see how anything can be called a constant without fixed no relative positions in space existing. Otherwise they can't be constants. I have another person insisting a that the laser would always travel both ways in the same time and light still would have a constant speed. But then, that would mean that if we then shone that light to another galaxy, because that galaxy is moving at a different speed and direction compared to us, that our light wouldn't be traveling at the speed of light from that galaxy's perspective. It just doesn't add up. We know we're moving at a pretty good speed in space, because our solar system is orbiting our galaxy quite quickly, with respects to our personal measure of what quick is. We know our movement can't be added or subtracted from lights constant speed. So any detectors we have would be moving as well, and just like with the trains, they should offset making contact with light because of their movement in relation to its constant speed.
This is probably worded poorly, but you should get the point.
@@haddow777 " _Put a set up satallites up in space with coordinated timers. Each will have a laser emitter and a laser detector and will fire their lasers at the other at precisely the same moment. Each will also be in fixed positions in relation to the other. They will then count how long it takes the light for the other one to reach them. If the satellites are moving along the axis they sit on, then one satellite should get the opposing satellites signal in a shorter time than the other_ "
in the frame in which they are moving this will be the case. but in the frame in which they are stationary ,both satellites would get the opposing one's signal simultaneously
" _Basically, I can't see how anything can be called a constant without fixed no relative positions in space existing. Otherwise they can't be constants._ "
Speed of light is called a constant, because in every frame, its speed is c. You dont need any fixed positions in space.
@@riverchess-so7pr I get why you say that, but unfortunately, I don't think you can claim it as reality. Yes, the books all claim it is true, based on the Michelson-Morley experiment.
The reality is that the Aether experiment (less typing) was seriously flawed and was designed to prove only one way that light could be affected by motion, but not all ways. So, while the experiment failed to prove what they personally thought was how light travelled, that failure does not prove that light is a constant from all frames of reference.
Their idea of how light travelled was through a substance called Aether, and in their minds, a photon was like a boat on water. Now, if this was the case and the Earth was moving through this water, they felt that the relative motion would be like the Aether was flowing through the Earth. So, any photons fired into this flow would have to fight the current to make progress. Any photons fired perpendicular would similarly have to fight the current to maintain their direction.
The machine was specifically designed to find these struggles the light would have had to go through, most specifically, the perpendicular path. They understood that the photons heading straight against the Aether, fighting against the current, would eventually turn back and catch a ride with the current. So any losses in time they made going one way would be made up with gains on the way back.
The perpendicular route though, would in a way, be traveling through the Aether in an angular fashion to maintain their path. So, from an outside observer's perspective, its journey from the spitter mirror to the mirror and back would take a triangular path through the Aether rather than just a back and forth straight path. This would mean those photons traveled longer distances than the ones in the beam that went straight. So, they would be out of phase.
So yes, their machine proved that line of understanding was incorrect. Here is another way to look at it through, that their machine never took into account, and therefore could never give any valuable data on.
When a train is sitting still and sounds its horn, let's say an observer on the ground is standing far enough away to hear the sound in 5 seconds. Now, if the train passes that spot doing any speed, if they sound their horn at exactly the same spot, the observer will still hear it precisely 5 seconds later. It doesn't even matter which direction the train is travelling.
This is because once the sound is created, it becomes completely detached from the train and any speed its moving. Chances are, if the train is moving fast enough, it won't even be near the location when the observer hears the sound. This is because the sound is travelling from the fixed point in space it was created at.
This could be applied to light as well.
Let's repeat the Aether experiment with this in mind. First, let's make the assumption that the whole beam is emitted from the left and the detector is closer to us. Also, let's assume that Earth's motion is in line with the initial beam and in the same direction as well. So, in the old experiment, they would have claimed the Aether was flowing towards the light source.
So, right off the bat, the whole beam is heading towards the splitter mirror from the fixed point in space the photons making it up were created. Now, it isn't being slowed by any flow of Aether, what is actually happening is the experiment is moving away from the photons. So, while they are heading towards the splitter mirror at the speed of light, the mirror is moving away from them, creating more distance for them to travel to get to it. When they do, they are split as expected.
Now, the beam going forward is also chasing a mirror moving away from it, so it will be traveling a longer distance to get to it too. Once reflected back though, now it is heading towards a splitter mirror that is heading towards it, shortening the distance between them. Since the mirror is traveling at the same speed as the other mirror, it erases any losses the beam had before. So, in effect, the return trip of this beam could be calculated like this, Xnew=((x+d)+(x-d))/2, or Xnew=x. Since all you get with a round trip like this is the average of both trips and both trips are different by the exact same amount, an average will only ever result in the same distance traveled.
In any event, that isn't the important part right now. The perpendicular beam will head at a 90 degree angle to the beam that went straight. Now, unlike what they thought at the time, there is nothing moving the beam sideways, so it moves in a completely straight line. What really happens is the mirror it is traveling towards is moving sideways. Since this in no way alters the distance the beam travels, it has zero effect on the beams travel time.
The same happens when it travels back. The detector is moving sideways too, but again, no change in distance, so when the beams combine, the phase is in line. In fact, under these conditions, they frequencies will always be in line no matter how the Earth's motion alter's the photon's travel paths. It literally cannot do anything else, so from this perspective, the experiment is highly flawed and could never provide useful results unless light actually flowed through a substance like the Aether they thought existed.
So, in reality, your claims my experiment with the satellites wouldn't work as I described is completely unfounded.
Also, yes, I know that the way I described the experiment working would create a drift between the beams. If we were looking at the experiment from the back side of the detector, the perpendicular beam would be slightly to the left and the straight beam would be slightly to the right. This still would not have any effect on the frequencies lining up, because the travel distances would be the same no matter what. Plus, the misalignment would be off by nanometers to possibly one or two micrometers, depending on the length the light had to travel after being split and also depending on the absolute velocity of the Earth relative to the fixed position in space the photons fired from. I don't think at the time they could have even measured a horizontal misalignment by that amount. If the Earth was moving some significant portion of the speed of light or the mirrors were a few thousand kilometers away, all that would happen is eventually the light would miss the mirror or the detector by being off to the side of it. It still wouldn't affect the phase of the frequencies, because even at those speeds the light would be traveling the same distances, not that they would be able to measure them against each other anymore.
Simple physics. Newton's Law of Motion.
F=ma. Less acceleration equals either more mass or less force. This is going to come as a shock but its nor reported anywhere. And I mean anywhere.
CLOCKS IN MOTION USE THE SAME AMOUNT OF ENERGY(FORCE) AS STATIONARY CLOCKS.
Why the difference in clock cycles? That energy went into the extra distance traveled.
CLOCKS MEASURE MOTION IN SPACE. NOT MOTION IN TIME.
Tree ring growth patterns? Are they caused by changes in gravity, Earth's rotational speed, or sunlight (energy) from the sun?
An astronaut's heart rate is in an accelerated heart rate during lift-off while the onboard clock is registering fewer click cycles. Why? Doesn't Relativity dictate that biological processes slow down with mechanical processes?
Why do atomic clocks slow down? Simply from redshifting of the electromagnetic wave that accelerates the atom to the 9B oscillation rate.
FORCE DECREASES WITH DISTANCE.
in order to maintain the same amount of Force at the target with an increase in distance, the Force emanating from the source must also be increased. GPS clocks run at a different frequency (force) to account for the difference in distance traveled.
Build a clock that can identify a change in force and automatically increase it, and you have a device that is in sync with your ground station.
The illustration at 15:56 is confusing because longer path (two sides of triangle) is marked as shorter path than actually shorter path (one side of the triangle)
I understand that this is only some analogy but instead explaining the matter introduces confusion.
Yeah, it could be clearer. They are talking about a SPACETIME path, but the drawing is very easily interpreted as simply a path through space, ignoring time.
First, imagine only space. Take two different points in space, like your home and your workplace. You can travel from your home to your workplace, and the amount of space traveled depends on the path you take. A straigth path means the shortest path through space.
Now add time. Let's name two events at spacetime, 08:00 at home and 09:00 at workplace. You could travel from home to work in one hour, taking the shortest path through space (when you arrive at work, your dashboard clock reads 09:00). Or you could travel a lot longer path through space and still reach your workplace before your boss gets angry (you could hop into a space ship, travel to Mars and back, and be at workplace exactly when your bosses clock reads 09:00). Because you would have to move very fast to get to Mars and back, general relativity says that some amount of time dilation takes place and your shipboard clock might only show 40 minutes elapsed, but your bosses clock at work reads 09:00.
Your path through space was longer in a spaceship, but you experienced less time passing. This is what they mean on the video when they say "your spacetime path was shorter".
Lengths are determined with respect to the metric, and the metric for flat spacetime (the Minkowski metric) has a minus sign on the time component. So when you have a right triangle, and one side is timelike, the Pythagorean theorem becomes a^2 - b^2 = c^2, where a is the spatial leg, b is the temporal leg, and c is the hypotenuse. If a < b, then c^2 is negative, which is interpreted as c being timelike.
I like to think about it this way: one twin is moving through more space, while the other moves through more time. If you take the magnitude of their spacetime traversed, they must be equal (assuming they start and arrive at the same moment in spacetime in the same inertial frame). Therefor the twin that moves through more space, must move through less time. This works very simply in flat spacetime. But with gravity becomes more complex. The visual works well here though, when one twin is orbiting, you can see the spacetime lines going through him the same as the stationary twin, so he obviously moves through more space. When he flows WITH the spacetime, though, he has to age more to catch up to the stationary twin who let spacetime flow through them.
Someones been watching Brian green
Okay, to make it easier to understand, both spaceships are always in motion within the 4D space-time environment, and both are in motion with an equal magnitude of motion. Even earth itself is in motion within space-time just as much as are the two spaceships in motion. The only thing that can be changed, is the direction of which your motion is pointing within the 4D space-time environment. So, if you leave things just as they are, and thus the two spaceships are at rest with respect to each other, both will be moving across the dimension of time, equally. However, if one spaceship adds motion across space, and then back, this subtracts from the percentage of its motion that was originally movement across the dimension of time. But still, after this is completed, both spaceships have still moved an equal distance across the 4D space-time environment. The only difference is that one spaceship moved less across the time dimension than did the other, and this is due to dedicating more of its ongoing motion to now being spatial motion.
It is incorrect to assert that the spaceships travel equal distances on the spacetime manifold. When the twins are reunited at a coincident place in time and space, one of them will have traveled a greater spacetime path than the other. This twin will be the older one.
@@dialectphilosophy Every object that exists within space-time, is in motion exactly as much as are photons of light in motion. That is the path taken by all photons. If one of two spaceships was truly at rest in space, then all of its motion would now be across the dimension of time. That would be its path of motion. First let's say that it remained on this path for 2 seconds. Meanwhile, the other spaceship at the beginning of those 2 seconds, decided to take a different path. Instead, it went off to the left at a certain velocity, and then returned around to head on back to the first spaceship, and all of this was completed in the very same 2 seconds. Due to both being in motion to the exact same degree, and doing so within a 4D space-time environment, both would have covered the very same distance within that 4D environment. The only difference is that one chose to dedicate all of its motion to being motion across the dimension of time, while the other did not. The other moved less across time due to setting its path to include a measure of motion across space.
@@new-knowledge8040 You are conflating spacetime “distance” with spacetime “motion.” You are correct in asserting that, in the theory of relativity, everything travels at the speed of light, i.e., that the tangent four-vector to the path traveled by an object on the spacetime manifold (ds/dτ) has magnitude c. However, you have asserted that if two spaceships move apart and then come back together again, they have traveled equal distances on the spacetime manifold. This is not correct. (The twin paradox in fact relies on the twins having traveled unequal distances on the spacetime manifold, as we explain in our video.) Distance on the spacetime manifold is defined as ∫ds, or ∫ (ds/dτ)dτ, or ∫cdτ, so in fact distance on the spacetime manifold is essentially the product of the four-velocity c and the proper time elapsed as measured by a clock moving in that frame. Since the spaceships do not inhabit the same frame, their clocks will show different amounts of proper time, meaning they traveled different spacetime distances. (If distance = rate * time, you have to remember that although the rate of the two spaceships moving along on the 4-d manifold is the same, the time registered on their clocks is NOT.)
General Relativity can be very subtle and complex sometimes, we understand the source of your confusion.
@@dialectphilosophy And I understand the source of your confusion.
In Einsteinian relativity, speed through spacetime is equal for everyone. This means that the distance covered and time elapsed can be adjusted accordingly!
You keep saying that the idea of absolute acceleration doesn't make much sense and I can see the point but it also seems to be impossible to get rid of it in theoretical models.
If you look up Brian Greene's lecture on relativity special relativity that is on his world science Channel web site he has an entire class which explains this. If you're willing to spend a few hours learning how to do basic relativistic equations you will see that there is no need for acceleration and yet you will still see a change in the rate of Aging or the passage of time.
I'd be inclined to listen to you if you can tell me how much space you are travelling through while you are standing stationary in one spot?
At 14:32 you state "The second twin however is launched radially outward in a high velocity". Launching from inertia to high velocity must by definition be acceleration, right?
At 14:50 you state "The twin who is travelling is in inertial free fall for the entire trip". How can the second twin both be "launched" ie. accellerated AND be in free fall for the entire trip? A contradiction it seems. What does that do to your entire reasoning?
Hi, thanks for watching, and great question! Technically, the radially-traveling twin doesn't have to be "launched" -- he can start out already traveling at a high velocity. This might be difficult to imagine with twins, so instead replace them with clocks. When the two clocks start out in a coincident position, we can have one clock that is already traveling at a high velocity and one that is not, and we can also have them both read the same time (the same age). Then, when the clocks are reunited/recombined, the free-falling clock will show more elapsed time. No acceleration whatsoever needed.
Additionally, its not clear that the initial acceleration when the twins share a coincident position would make much of a difference anyhow; in the traditional twin paradox in flat spacetime, when Bob blasts off of earth, no difference in aging results between him and his sister, since they both occupy the same "height" in the pseudo-gravitational field that results. Hope that clears up your confusion.
Clocks is a better example because we can image the many gps and related satellites that are currently orbiting earth.
@@dialectphilosophy The problem with assuming that one twin (or clock) is already traveling at a certain velocity is that the twins (or clocks) no longer share a frame of reference at the initial state. There's no paradox when starting with two different frames of reference, one of which is accelerating to stay in place and the other is is in a freefall, but with enough velocity to travel away from the planet, then fall back.
@@Mythago314 You can have both twins start in the same reference frame by having them in free-fall together, then you can have one twin accelerate to stay-in-place. The respective aging of the twins would then still be the same in this case as presented in the video.
@@Mythago314 armchair physicist doesn't understand even the basics and comes to lecture lol.
Does time "ticks" faster or slower on Mercury than on Neptune ?
- 1 slower : Mercury has lower gravitational potential than a clock on its surface will be slower than on Neptune's. (gravitational field). Clocks that are far from massive bodies (or at higher gravitational potentials) run more quickly, and clocks close to massive bodies (or at lower gravitational potentials) run more slowly (wikipedia).
- 2 : faster : Mercury has smaller orbit speed than Neptune (inertial frame). Special relativity indicates that, for an observer in an inertial frame of reference, a clock that is moving relative to them will be measured to tick slower than a clock that is at rest in their frame of reference. (wikipedia). But can we say that Neptune moves faster relative to Mercury ?
- 3 : The effect is the difference of both 1 and 2
The links for the papers are not working
The case where one person is orbiting the Earth should be calculated by considering the speed which give a slowing down of the time and the distance from the Earth which speed up the time (say relative to the earth surface) because the spacetime at the orbit is running faster ( note that time is a property of the space). E, g. Take a GPS satelite, it is orbiting at 3.874 kilometers per second and loosing about 7 micro sec a day relative to earth caused by the speed. The weaker gravity at its hight make the time speed up about 45 micro sec per day. ( in practice the excentricity of the orbit needs also to be considered)
I would like to know why the speed of light is considered a constant, instead of a horizon in space time.
If you travel at the speed of light, you are able to look at your watch and observe it ticking. Am I wrong?
Anything that orbits a black hole, as we do, is on a curved space time that travels down to the singularity. The curve does not magically stop at the speed of light.
what a editing. cudos!
At 15:30, if it is just the "shortest SPACETIME path travelled" idea, then Einstein's Special Relativity would not apply, correct? It would mean that one of the frames would always be considered non-inertial. For Einstein's Special Relativity, there is no way out, because it is a basic, logical contradiction caused by applying the Principle Of Relativity to the Lorentz/Voigt math transforms. The first postulate of the Principle Of Relativity IS THE SYMMETRY that needs to be "thrown out" in order to "resolve" the paradox, i.e. throwing out Einstein's Special Relativity and going back to Lorentz Theory "resolves" the paradox.
czcams.com/video/p8ph6sqppps/video.html
watch my solution to the twins paradox., It is much different
man you are also here lol.
*"At **15:30**, if it is just the "shortest SPACETIME path travelled" idea, then Einstein's Special Relativity would not apply, correct? It would mean that one of the frames would always be considered non-inertial. For Einstein's Special Relativity, there is no way out, because it is a basic, logical contradiction caused by applying the Principle Of Relativity to the Lorentz/Voigt math transforms. The first postulate of the Principle Of Relativity IS THE SYMMETRY that needs to be "thrown out" in order to "resolve" the paradox, i.e. throwing out Einstein's Special Relativity and going back to Lorentz Theory "resolves" the paradox."* Except admitting in non-inertial frames wouldn't be any more throwing out Einstein's theory than throwing out Classical physics because you can't apply the Galilean relativity principle every time you step on the gas peddle.
Einstein's first postulate being: *"The principle of relativity - the laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems in uniform translatory motion relative to each other."*
Note that he is only telling us, by definition, that inertial reference frames are the only ones in which the laws of physics will take on a similar form among a variety of distinctly different but still inertial behaving frames. So then, by definition, if a frame wasn't inertial then all this would mean is the laws under guiding this physical systems changes would then take on a different form to when you were in any other arbitrary inertial frame.
In Classical physics this happens all the time in supposed non-inertial frames when it was the case in other roughly inertial frames for conservation of momentum to apply (the relativity principle is respected) now you would observe a non-conservation of momentum. That this occurs neither negates Classical physics in being applicable in this frame or negate the relativity principle when regarding inertial frames.
*Finding a situation where by definition the principle can't be applied doesn't negate the principles' application when the definition is respected.*
The T38 Jets are appropriate, Lovely plane
But how does the shortest spacetime path explain the original twin paradox? Can't it be argued that either of the twins could have the shortest path depending on which twin is considered stationary in a spacetime diagram?
The idea, if I understand correctly, is that you make two diagrams: one with one twin being stationary and another one with the other twin being stationary. Then you you can compare the two paths for each of them when they are the moving ones.
On a flat spacetime, they will be symmetrical, but on a curved spacetime they won't. That's what I understand they mean: that the curvature of spacetime is what makes their paths asymmetrical.
Since the curvature of spacetime is gravity, it would be as Einstein suggested: gravity makes the difference (though probably Einstein gave a different explanation about how gravity makes the difference).
@@Alberto-mq7gw Maybe you're right. The only problem I see is that this makes special relativity fundamentally wrong (and maybe it is), since both twins could be put in a flat region of spacetime for the whole thought experiment, leaving the paradox unsolved. I guess the only way to solve the paradox then would to consider the effect of the twins in the curvature of spacetime, maybe?
That's a very valid question! It definitely can be argued that either twin could have the shortest path if they are considered stationary on a spacetime diagram. In fact, we argue that exact thing in "Solutions to the Twin Paradox are Still Wrong."
The solutions in General Relativity demonstrate that the fundamental criteria for the twin paradox is the length of the four-dimensional path traveled by an observer/object -- meaning ideas of motion such as velocity/acceleration are not even relevant to the paradox at all. However, this shifts the focus of the issue to what constitutes/determines the length of a spacetime path? In GR, it's clear this answer has a lot to do with the mass/energy content that occupies a spacetime region. However, this doesn't help us much in flat spacetime, where the influence of mass/energy contents is taken to be negligible.
So the short answer to your question is: the paradox certainly still remains in flat spacetime, because currently our only idea for producing consistent path lengths is to invoke absolute acceleration -- an idea of course which makes ultimately little sense. But what the solutions of GR seem to be hinting at is that our idea of motion is a crutch; and that something else is likely going on to produce the objectivity of spacetime lengths, whether in flat or curved spacetime.
@@dialectphilosophy Watch my video of the twins paradox. It is much of a different explanation.
@@dialectphilosophy The length of a path in Minkowski-space-time (or a curved pseudo-Riemannian manifold) is independent of the reference system you use. Like the length of a path in Euclidean space (or curved Riemannian manifold) is independent of the coordinate system you use.
From the principle of constant speed of light follows that the space-time
intervall ds^2 = dr^2-c^2dt^2 (or switched signs, it doesn't matter) is invariant under coordinate transformations (which means switching to other frames). The space-time intervall is the same as proper time (up to signs) for dr = 0. The length of a path in space-time is the integral over the space-time intervall, e.g. proper time which means that the length of a path is independent of the choice of a reference frame.
The shorter the path in space time (which in every space-time diagram is the one looking longer) the less proper time is experienced, hence the traveling twin always has to be younger in the classical thought experiment.
For those who are interested: I suggest the Lecture Notes on General Relativity by Matthias Blau, it's really comprehensive and available online.
what if what drives time is in fact the expansion of the structure of the universe and forced motions against this expansion eg through acceleration create changes in time? In that case, a freely falling object is perfectly in track with the expansion and remains unaffected by any time displacement except for an accelerating object violently trying to escape the structure of space. 🇸🇪🇸🇪🇸🇪