General Relativity and the Twin Paradox

[Cameramonkey]

I started to read it. Then I decided I was going to wait for the movie.

 

[Lpherr]

I didn't think inertia was tied to gravity. Doesn't an object of a certain mass resists a change in motion exactly the same amount regardless of how much gravity is present?

An object in motion, can't remain at a constant speed, or in a straight line, when gravity is pulling that object down, and ambient resistance slows it.
In space, those forces aren't equal to on our surface.

An example: a bullet will eventually be pulled to the ground by gravity, if, it isn't slowed enough by resistance, to simply fall.
In space, I would think until the bullet was to strike something (or be struck), it would continue?

I also am not a physicist.

 

[spencer rifle]

I am married to a twin and can assure you that she is a paradox. Many years of observation and direct experience have provided no meaningful answers.

I have decided to give up and just enjoy the mystery.

 

[JEBland]

For starters. The special relativity "paradoxes" are designed to trip you up.

There's a few trip-ups in all of this. Mostly that if we talk about a spaceship and moving at 0.99c and twins and aging, no one really has the ability to process that as a real-life event. Additionally relativistic physics is a bit different from non-relativistic physics. Many things generalize nicely, but some stuff doesn't.

A quick casual definition:
Relativistic physics is the quantitative description of mechanisms in a manner that is observer-independent.
-Special relativity was really invented to better understand Maxwell's equations describing electromagnetic waves (light), which don't obey the same set of transformations as we expect with say trains and throwing balls. This description turns out to be a pretty good description for comparisons between observers in two inertial (non-accelerating) reference frames, basically unified because in all sub-luminal inertial frames the speed of light is the same value. I don't think it's helpful to conjecture about what happens at the speed of light or past the speed of light since we can't know that, but it is something some folks like to debate.
- For accelerating frames of reference, we need general relativity (where the only limitation is that the observers/data collectors move in a way that we can do calculus on it).

IMO, the primary thing to focus on is the evidence for the basics.
We know that time dilation and length contraction work because of the experiments confirming the special relativistic effects in particle decays and such:

Experimental testing of time dilation - Wikipedia

en.wikipedia.org

Then you can look at GPS systems where there are both general (gravitational pull / mass density) and special relativistic corrections (satellites moving) going on. Those corrections are actually in opposition in terms of the net change in time. But then there are also atmospheric corrections, etc.

Then you ask, well, what do we do with acceleration.
Well, for everyday events (speed much less than c) these are basically symmetrical and no one cares. That is, the difference in aging is so small that other effects dominate differences.

So, how do we keep track of changes in time? Clocks. Those clocks do measure differences due to acceleration and that ought to be enough to satisfy us. Our goal is to quantitatively describe observations - if it's consistent with observations within error margins, then it's an acceptable interpretation. (We then ask, can we differentiate between these interpretation and design a new experiment, but this is a digression.)

Now you might ask "which twin is older" and the point is that if the two twins each have a flashlight so that they can see each other and a mirror so they can see themselves. Well, they just compare who looks older! This is no different than "how many times the clock goes around." If there's no light and no way to compare, then we can't answer. This is always the case. I don't know the air pressure of the room I'm in because I don't have a way to measure it. It's probably similar to the usual sea level pressure given that I'm on the East Coast within 50' of sea level at this moment, but that's just a guess using the observations I have available to me.

 

[AndreusMaximus]

An object in motion, can't remain at a constant speed, or in a straight line, when gravity is pulling that object down, and ambient resistance slows it.
In space, those forces aren't equal to on our surface.

An example: a bullet will eventually be pulled to the ground by gravity, if, it isn't slowed enough by resistance, to simply fall.
In space, I would think until the bullet was to strike something (or be struck), it would continue?

I also am not a physicist.

AFAIK this is all correct. I guess maybe I was just using terms wrong, but my understanding is that:

1) "Inertia" is a way of referring to how an object's mass will resist changes in the objects speed/direction. So once fired, a bullet will "naturally" continue forever, the only reason it doesn't do that on earth is because gravity and air resistance overcome its inertia, but in space, like you said, it will continue forever at the same speed until it hits something (or gets pulled in by something's gravity that it comes close enough to.)

2) "G-Forces" doesn't mean forces of gravity, but is a way of talking about the effects of inertia when a body is being rapidly accelerated. So if you're in a spaceship traveling at a constant speed (doesn't matter how fast it is, as long as the speed isn't changing) you won't feel any forces, you'll just be floating around freely. But if the spaceship fires it's rockets and begins to change its velocity, your body's inertia will resist that change, and it will feel like a force pulling you in the opposite direction of the acceleration. If the spaceship accelerates at just the right rate, in fact, it can feel just like being back on earth with earth's level of gravity. If the ship accelerates too fast, though, all the molecules of your body will be resisting that acceleration due to their inertia, and it will feel like they're all being pulled against the opposite side of the spaceship, which at around 4-5 times the acceleration of gravity on earth (that is, about 4-5 G's) you would pass out due to your heart no being able to overcome your blood's inertia enough to keep pushing it around your body, and at high enough accelerations would make you get flattened against the side of the spaceship as if you'd been steamrolled.

It's just like on earth, where a fighter pilot, if the plane accelerates fast enough, can experience G-forces that are several times as strong as earth's gravity, even though gravity is remaining the same for him, and even if he's accelerating parallel to the ground, or even towards the ground.

 

[AndreusMaximus]

For starters. The special relativity "paradoxes" are designed to trip you up.

There's a few trip-ups in all of this. Mostly that if we talk about a spaceship and moving at 0.99c and twins and aging, no one really has the ability to process that as a real-life event. Additionally relativistic physics is a bit different from non-relativistic physics. Many things generalize nicely, but some stuff doesn't.

A quick casual definition:
Relativistic physics is the quantitative description of mechanisms in a manner that is observer-independent.
-Special relativity was really invented to better understand Maxwell's equations describing electromagnetic waves (light), which don't obey the same set of transformations as we expect with say trains and throwing balls. This description turns out to be a pretty good description for comparisons between observers in two inertial (non-accelerating) reference frames, basically unified because in all sub-luminal inertial frames the speed of light is the same value. I don't think it's helpful to conjecture about what happens at the speed of light or past the speed of light since we can't know that, but it is something some folks like to debate.
- For accelerating frames of reference, we need general relativity (where the only limitation is that the observers/data collectors move in a way that we can do calculus on it).

IMO, the primary thing to focus on is the evidence for the basics.
We know that time dilation and length contraction work because of the experiments confirming the special relativistic effects in particle decays and such:

Experimental testing of time dilation - Wikipedia

en.wikipedia.org

Then you can look at GPS systems where there are both general (gravitational pull / mass density) and special relativistic corrections (satellites moving) going on. Those corrections are actually in opposition in terms of the net change in time. But then there are also atmospheric corrections, etc.

Then you ask, well, what do we do with acceleration.
Well, for everyday events (speed much less than c) these are basically symmetrical and no one cares. That is, the difference in aging is so small that other effects dominate differences.

So, how do we keep track of changes in time? Clocks. Those clocks do measure differences due to acceleration and that ought to be enough to satisfy us. Our goal is to quantitatively describe observations - if it's consistent with observations within error margins, then it's an acceptable interpretation. (We then ask, can we differentiate between these interpretation and design a new experiment, but this is a digression.)

Now you might ask "which twin is older" and the point is that if the two twins each have a flashlight so that they can see each other and a mirror so they can see themselves. Well, they just compare who looks older! This is no different than "how many times the clock goes around." If there's no light and no way to compare, then we can't answer. This is always the case. I don't know the air pressure of the room I'm in because I don't have a way to measure it. It's probably similar to the usual sea level pressure given that I'm on the East Coast within 50' of sea level at this moment, but that's just a guess using the observations I have available to me.

Sounds like you know a lot more about all this than I do, but I feel like there still has to be some logic applied to the observations in order to understand things. To me, the paradox isn't so much "How do we tell which twin is older?", which is easily answered by saying "look at them." It's more about, "If one twin is observed to have aged more than the other, but they both took the same path of motion relative to each other, how did that happen?"

And I think I was originally getting confused about the difference between acceleration relative to a given observer, vs proper acceleration.

So for instance if you had the two twins perform the twin paradox scenario, then you observed that one looked older than the other, someone trying to disprove relativity would go "Ah, see, it's all bogus! Since relativity says that the motion isn't objective but can only be measured relative to an observer, but each twin observed the other take the same path of motion relative to himself, then they ought to have aged the same. There's nothing that should have made them experience the journey differently except that one changed direction halfway through, while the other didn't. But if the change in direction was only relative and not objective, that shouldn't have made them experience the journey differently from each other."

It seems to me like this arises from a fundamental misunderstanding of relativity, since while relativity does allow us to describe motion (and thus acceleration) relative to any given observer, it does NOT eliminate to ability to measure changes in inertial frame, ie, proper acceleration, as an objective thing that is NOT relative to an observer, and thus we can still measure something objectively different about the traveling twin's journey vs. the home twin.

Does that sound right?

 

[Bugzilla]

I am married to a twin and can assure you that she is a paradox. Many years of observation and direct experience have provided no meaningful answers.

I have decided to give up and just enjoy the mystery.

You know a lot about the theory of relative ity?

 

[tsm]

Time slowing down for moving objects has been shown to occur via experiments. They’ve orbited an atomic clock that’s identical to another one on the ground and, although they started out synchronized, the one going around the Earth ran slower (and astronauts age slower by that same amount) by the calculated slowing down that traveling that percentage of the speed of light gives using Einstein’s equations. 17000 mph is slow compared to the speed of light, but it’s fast enough to measure time slowing down using the clock technology we can produce today. GPS satellites have to take relativity into account due to their orbital speeds or otherwise you’d find yourself in a farmer’s field when your car’s GPS was telling you it thinks you’re on the right road!

 

[Mij]

So for anyone on here who is interested in Einstein's theory of relativity (like me) or knows much about it (unlike me) here's a little something I've been working on for a while. I posted this to a physics forum that I just signed up for today (INGO, I cheated on you with another social media platform; please forgive me!!!) hoping to get some feedback, but thought I'd also post it here, too. I purposefully avoided any math to try and keep the basic principles in the forefront, so hopefully anyone who has a basic grasp of what the theory of relativity is should be able to read an understand it.


So I've been trying really hard to understand the theory of relativity at its most basic level lately, and recently I dove down the rabbit hole of the Twin Paradox. This has led me through a series of youtube videos, each one claiming to present a different solution, explain why the other videos presenting other solutions are wrong, and finally ended me up on a video that claimed to poke holes in the logic used by all the other videos, leaving me very confused.


At first I felt like I really wasn't understanding any of it, but I think I was finally able to formulate an answer that makes sense. To help me with this, I made my own, simplified, version of the Twin Paradox below. If anyone would be willing to take the time to read 1) My simplified/slightly modified Twin Paradox, 2) My paraphrasing of the video I saw that claims the paradox is still unresolved, and 3) An explanation, in my own words, of what I understand to be the real resolution of the Twin Paradox, and then let me know if what I have said makes sense or if I'm still missing the whole point, I would be extremely grateful!

(Note: I shorten "inertial frame of reference" to "inertial frame" throughout this whole thing; hopefully that's not too inaccurate or confusing!)

1) My "Simplified" Twin Paradox

Consider a universe that behaves exactly like our own: all the laws of physics are the same, the theory of relativity applies, etc.

This universe contains nothing whatsoever except two spaceships, each of which has one observer and one clock in it. The observers are named Bob and Rob. At the start of our thought experiment, the two spaceships are sitting next to each other, motionless relative to each other. (Gravity in this thought experiment is considered negligible, and thus ignored.)

An event occurs in which the two spaceships move apart from each other, then come back together.

From observer Bob's perspective, it appears that Rob's spaceship accelerates rapidly away from him, quickly reaching a speed very close to the speed of light, then, when Rob's spaceship is several light years away, it suddenly appears to accelerate rapidly in the other direction, and begin to travel back towards Bob, again quickly approaching the speed of light, then finally when it is close to Bob, Rob's spaceship appears to decelerate extremely rapidly, and comes to rest next to Bob's spaceship, leaving the two spaceships motionless relative to each other, in the exact same position as they were at the start of our thought experiment (again all of this from Bob's perspective.)

What does Rob see from his perspective? Well, just copy and paste the above, switch Bob and Rob's names, and the event will look exactly the same to Rob, only mirrored.

Finally, ask the question; for whom was time experienced more quickly relative to the other? Did Bob experience a longer time and Rob a shorter one, or vice versa?

2) The Claim That the Paradox is Unresolved

Now, the consensus of all the videos I've seen on the Twin Paradox seems to be that the Twin who remains still will age more quickly than the one who moves.

HOWEVER, the whole point of the relativity of motion, is just that; motion is relative. In the above example, Rob observes Bob move away from him, then back to him, himself remaining still. But observer Bob sees himself as remaining still, while Rob moves away, then back to him. According to relativity, neither Bob nor Rob is more correct or incorrect in their perception; both are correct given themself as the observer.

So how do you know which one experienced time more quickly? Taking planets and other things that we perceive as stationary out of the equation, Bob and Rob have no way of knowing which one of them actually moved, and which one didn't, therefor, there cannot be any logical way of claiming that one would have experienced time any differently than the other.

3) My Paraphrasing of the Real Explanation (or what I hope is...)

It seems to me that much of the confusion surrounding what is the correct solution to the paradox stems from conflating acceleration with changing one's inertial frame. It appears to me that acceleration simply meaning changing one's speed relative to an observer. If this is the correct definition of acceleration, than a person in free fall will be accelerating relative to an observer on the ground. However, they will NOT be changing their inertial frame; to an observer on the ground they will be in motion, but in their own space-time a person in free fall is not moving or accelerating at all; they are simply remaining in the same space as that space curves towards the mass that is bending space (I'm sure there's some inaccuracies in how I described that, but that's the best I can put it.)

Thus we can see that acceleration and changing one's inertial frame are not the same thing. You can accelerate without changing your inertial frame, like the person who is in free fall does. You can also change your inertial frame without accelerating relative to a given observer, like two people who are in cars that go from 0-60 in the same direction at the same time: relative to each other they haven't accelerated or even moved, but they've both definitely changed their inertial frame. Acceleration is something relative to an observer; it can change based on which observer you're looking from. Changing one's inertial frame is something objective, and is not at all connected to acceleration, other than the fact that in the physical world we often see objects that are experiencing a force that changes their inertial frame also accelerate relative to us at the same time, so we tend to confuse the two.

In the final video I watched, I think the guy was basically stuck on the question: "In a universe devoid of all other objects (ie, empty space,) how do you objectively tell if an observer is changing their inertial frame or not?" Since he conflated changing one's inertial frame with changing one's acceleration, he then argued that since acceleration is relative, and both twins can claim that they experienced no acceleration (from their own perspective as an observer) that it followed they can both claim to have not changed their inertial frame. But this is where he's wrong; acceleration, that is, changing one's speed, is relative to an observer. But changing one's inertial frame is an objective thing, and not relative to any observer. Anything that is changing its own inertial frame will appear to be changing its inertial frame to ALL observers.

So if changing one's inertial frame doesn't mean accelerating, what does it mean? My layperson's explanation of changing one's inertial frame would go like this: "Any time an observer is experiencing a force that their body's mass resists, they are changing their inertial frame." That's probably not a very precise way of putting it, but what I'm basically trying to say is that if there is a force that cause an observer to change the way it would travel through space-time if that force hadn't existed, than the inertial frame of that observer has changed.

(Side note: In a way, I think it would be accurate to say that those who say the Twin Paradox is resolved because one twin experienced acceleration and one did not are partially right (or at least they have the spirit of the correct answer, and are just putting it wrong.) What they really ought to say is that since the "travelling twin" experienced a force that changed his inertial frame (which is the very thing that made him accelerate/decelerate from the perspective of the "earth twin") THAT is what makes the travelling twin experience time differently than the earth twin, and what makes their situation asymmetrical.)

So the final answer to my above modified "Twin Paradox" thought experiment is this: In order for Bob and Rob to have moved relative to each other, one (or both) of them had to change their inertial frame. If Bob changed his inertial frame, resulting in the relative motion, while Rob remained in the same inertial frame, then Bob will experience a shorter time during the relative motion, while Rob will experience a longer time. But if Rob changed his inertial frame while Bob did not, then when they come back together it will be Rob who experienced less time passing. During the motion, the one who is experiencing the change in inertial frame will experience evidence of this because the mass of his body will resist the change, meaning that he experience something that feels like gravity (even though, of course, it has nothing to do with gravity) pulling him towards the side of his spaceship opposite of the direction he is moving in. The one who is not changing his frame of reference will not experience this. Of course, a third possibility exists in all this, which is that the relative motion that Bob and Rob perceived was caused by both of them changing their inertial frame. For instance, they could have both had a change in their inertial frame that was equal but opposite, and thus, to an observer who started out at the same location as them but didn't change their inertial frame, Bob and Rob would have appeared to move in opposite directions at the same speed, and for the same time and distance, and then started moving back towards each other and come back to rest at the same starting point as this third observer. If this is what happened, then Bob and Rob would both have experienced the same length of time at the end of the motion. In short, you can't answer the question "which of them, if any, experienced more time than the other?" without first knowing who changed their inertial frame in order to cause the relative motion in the first place.

(Other side note: There's also a really funny aspect to this thought experiment, which is this: Pretend that Bob and Rob are creatures who cannot feel the effects of the forces that change their inertial frame, and they and their clocks are both strapped down so they won't slide around as the inertial frame changes. Also pretend that the windows to their spaceships are one-way mirrors, so they can both look out and see the other spaceship moving off into the distance (they have really good eyesight and can see lightyears away.) But they can't see inside the other person's spaceship, and thus have no clue how the other person is experiencing time relative to themselves. If this is the case, then during the time that they are moving apart then back together, they will have no way of knowing which one is changing their inertial frame, and which one isn't, thus, at whatever point in time the two spaceships come back together, one of them will have just experienced a longer span of time than the other one, but neither one will know if they are the one who experienced the shorter or longer time, unless they are able to dock their ships together so they can go in and look at each other's clocks.)

So, if you read through the whole thing, thank you so very much! Please try to poke any holes in it that you can; I'm really trying to understand the basic concepts at play hear, and I'd love to be educated in how I can improve my understanding.


Some of the videos I watched, in case anyone is wondering:

This guy’s been talking to my wife.

Light don’t bend

The cats dead

Max Planck was an alien

The fly on the plane was going faster than the plane (plane train) duh!!!

 

[Lpherr]

Time slowing down for moving objects has been shown to occur via experiments. They’ve orbited an atomic clock that’s identical to another one on the ground and, although they started out synchronized, the one going around the Earth ran slower (and astronauts age slower by that same amount) by the calculated slowing down that traveling that percentage of the speed of light gives using Einstein’s equations. 17000 mph is slow compared to the speed of light, but it’s fast enough to measure time slowing down using the clock technology we can produce today. GPS satellites have to take relativity into account due to their orbital speeds or otherwise you’d find yourself in a farmer’s field when your car’s GPS was telling you it thinks you’re on the right road!

This happens quite frequently.

 

[jamil]

Hey, I'm just trying to get quality posts. @jamil told me that the longer a post is the more likely it is to be considered quality.

Huh? Wut?

 

[jamil]

In this alternate universe, is there a BigRed that loves Abraham Lincoln?

No. But there is one where BigRed didn’t get banned.

 

[Lpherr]

In this alternate universe, is there a BigRed that loves Abraham Lincoln?

In that universe, would it be Abe that loves BigRed?

Big Red would say that he *****n believes so.

 

[amboy49]

This thread makes my head hurt !

 

[nonobaddog]

The "twin paradox" is not really a paradox at all since there is no logical discrepancy

Twin paradox - Wikipedia

en.wikipedia.org

 

[JEBland]

Sounds like you know a lot more about all this than I do, but I feel like there still has to be some logic applied to the observations in order to understand things.

I mean, I guess I ought to since I have a BS in it and have nearly completed my PhD in Physics. Truth be told, I don't work with relativity very often and even when physicists do, we don't try to confuse ourselves with these paradoxes, we're trying to make sense of experiments or simulate what happens when say a supernova explodes (which I also don't do).

To me, the paradox isn't so much "How do we tell which twin is older?", which is easily answered by saying "look at them." It's more about, "If one twin is observed to have aged more than the other, but they both took the same path of motion relative to each other, how did that happen?"

And I think I was originally getting confused about the difference between acceleration relative to a given observer, vs proper acceleration.

So for instance if you had the two twins perform the twin paradox scenario, then you observed that one looked older than the other, someone trying to disprove relativity would go "Ah, see, it's all bogus! Since relativity says that the motion isn't objective but can only be measured relative to an observer, but each twin observed the other take the same path of motion relative to himself, then they ought to have aged the same. There's nothing that should have made them experience the journey differently except that one changed direction halfway through, while the other didn't. But if the change in direction was only relative and not objective, that shouldn't have made them experience the journey differently from each other."

It seems to me like this arises from a fundamental misunderstanding of relativity, since while relativity does allow us to describe motion (and thus acceleration) relative to any given observer, it does NOT eliminate to ability to measure changes in inertial frame, ie, proper acceleration, as an objective thing that is NOT relative to an observer, and thus we can still measure something objectively different about the traveling twin's journey vs. the home twin.

Does that sound right?

That's mostly correct. I'd argue that the problem is conflating various meanings of the word relative/relativity. There's always a problem of jargon/semantics, and sometimes even within a field. We talk about the relative motion of two cars when they collide because it's very important to the crash. But here, we've got relative frames and objects moving inside them, and it get somewhat messy. After typing and then re-reading what you've written, I think you've got the basic idea right as well as where the "see, it's all bunk" claim falls short.

A small digression because I think it's interesting/mildly relevant and, most importantly, I typed it before I reread your reply.
Suppose:
Alice and Bob are playing catch in the yard and throwing the ball at about 15 mph. Carl is riding a train going by at 5mph is going to measure that one is throwing it at 10 and the other at 20 mph. This all works when we take into the relative motion of the frames of reference. But the relationship is not really true, just approximately... and it's a *really* good approximation. That is, until ~1900. The vast majority of things we (humanity) observed work that way. It's still true in the low-speed (with respect to light) approximation. We teach it in school because it works really well.

What Einstein noticed was that this type of transformation accounting for the speeds in Alice and Bob's frame and the relative motion of Carl's frame doesn't apply to the equations that govern how light behaves. He then repurposed some math that was designed for how the aether would affect light (which was supposedly the medium that light traveled from the Sun to reach Earth). Of course, there is no aether. But the aether-derived transformations work with the description of objects (like a ball being tossed) when there are large speeds involved. Large speed for practical purposes on the ground (say the mass spectrometer in the basement of Purdue's physics building) is about 1% of the speed of light. Get the special relativity part wrong, and what you measure as one isotope is actually another, not a very good mass spec!

Over this time scale for Alice Bob and Carl (ABC, get it?), the Earth's spin isn't a huge factor, nor is the orbit around the sun, or the solar systems motion inside the Milky Way, or the galaxy's motion inside the cluster...
Meaning that the Train-Ball (called Galilean) transformations work really well to describe observations on Earth with the usual everyday behavior since the objects are all more-or-less subject to the same environment on a small scale.



Back to the question:
So, does (special/general) relativity say that the only thing is the relative motion? No. Actually, that's far closer to the Galilean (train and baseball) framework than it is special/general relativity since in the Galilean framework we just add/subtract velocities symmetrically to make it work out. This is that fundamental misunderstanding as to what we mean by relative/relativity in physics that you mentioned. If I recall my undergraduate textbook, the authors introduced a third rocket ship who just happens to be going by and witnessing all of this and what does he see? And of course, the twin who leaves Earth and returns is the younger one.

To reiterate my earlier definition:
When talking about special/general relativity the core question is "how do we describe the laws of physics in an observer-independent manner?" That's the whole game. By laws we mean the equations that describe the behavior of the system. Special relativity is basically the theory of fast stuff that's basically non-accelerating and isolated from the stuff around it, which is why it's always "assume person X has an inertial frame..." General relativity allows for any two frames including accelerating observers in curved space (other stuff is around).
^ I'm being a bit hand-wavy in the last two sentences.

In the context of Rob and Bob.
They're twins. So at some point the were together and in the same inertial frame (okay, two inertial frames moving parallel to each other, but babies are tiny). They then separate and come back.
They (at least one) had to accelerate in order for that to happen. Maybe they did so in a way that their relativistic effects are the same, maybe they didn't. "Well, I didn't take notes on /observe anything that allows us to distinguish them initially and therefore there is no effect even if the twins aged differently" is not a valid statement.
Not measured =/= unchanged. This does not contradict something along the lines of "if I can't detect a difference, then I can't say if there is a difference." If you can observe the difference, then something is different, even if you don't know what happened in more detail.

The article @nonobaddog posted is nice; a little dense, but pretty good for an interested reader with enough math background.

 

[Lpherr]

I mean, I guess I ought to since I have a BS in it and have nearly completed my PhD in Physics. Truth be told, I don't work with relativity very often and even when physicists do, we don't try to confuse ourselves with these paradoxes, we're trying to make sense of experiments or simulate what happens when say a supernova explodes (which I also don't do).

Our own Sheldon.

 

[DoggyDaddy]

Our own Sheldon.

Bazinga!

 

[jamil]

This guy’s been talking to my wife.

Is she TL;DR too?

 

[COOPADUP]

This may be too deep to fathom.