special relativity paradox "froyd's dog"

[dr froyd]

name inspired by schrödinger's cat by unrelated to quantum mechanics. This paradox uses only special relativity, in particular time dilation under relativistic speeds. I think it's related to the twin paradox, but to me this one is a simpler scenario. Yet the solution to this paradox is unclear to me.

let's say there's a planet exactly 1 light year away from earth. Assume we have a space ship that can travel at near light-speed. It would work with any relativistic speed but let's say it travels at 0.99999x the speed of light to avoid math.

this spaceship travels from earth to this other planet, with the dog onboard. To avoid complications related to acceleration, let's assume that instead of taking off from earth and landing on the other planet, the experiment starts when the spaceship passes earth, traveling in a straight line towards the planet, and it is "at the other planet" when the ship is right next to it.

when the spaceship passes earth, the dog happens to be old and has exactly 0.5 years left to live. Since the planet is 1 light year away it has no chance of reaching it alive.

but due to time dilation, from earth's (inertial) reference frame, time on the space ship almost stands still due to its speed.

let's say that when the space ship passes the other planet, someone on the ship sends a selfie that includes the dog (and we see the planet in the background).

now the paradox: on the picture that is received by earth, is the dog dead or alive? From the ship's reference frame, it has spent about 1 year on this voyage, so the dog must be dead. But from earth's reference frame, the dog has almost not aged at all so it must be alive.

 

[sushi]

my iq is too low for this, let me think about it

it depends on earth clock and ship's clock

 

[Cognisant]

I don't understand what the problem is, that local time is different to non-local time is the entire point of special relativity.

Suppose we have a way of transmitting data instantly over any distance via quantum entanglement or some-such woo nonsense. With this people on Earth have a live video feed of what's happening on the ship and from their perspective events on the ship are happening in slow motion because time there is progressing slower.

From Earth's perspective the trip takes a year, from the perspective of the people on the ship it might only take a few weeks and the closer the ship is traveling to the speed of light the less time they experience. If the ship were traveling at the speed of light time aboard the ship will have effectively come to a stop, and if the ship is traveling faster than the speed of light then time aboard the ship starts progressing in reverse.

If you have a magical ship that can instantly accelerate to the speed of light and come to an immediate inertia-less stop at your destination then for you the trip would feel like teleportation, you press that go button and you instantly (from your perspective) arrive at your destination. From an outside perspective it will also look a lot like teleportation but if they had a magical super duper high speed camera then they'd be able to see your ship traveling and if they could peer through a window into the ship everything inside would be motionless. (also pitch black because light isn't moving)

If you travel five light years at the speed of light then five years will pass (from Earth's perspective) and about the same would pass at your destination, but for you the trip would be instantaneous. So you have a holiday at this destination for two weeks, then you get back on your ship and fly back to Earth, for you only two weeks have passed but when you arrive back at Earth everyone you know is now ten years and two weeks older than when you left.

Now for the really crazy shit, what happens if you travel five light years at twice the speed of light? From the point you press the go button and the ship reaches the speed of light time stops, and an instant later, as you reach twice the speed of light, time aboard the ship is now progressing in reverse, at the same rate time on Earth is progressing forwards (more or less). But this is a five light year trip, from Earth's perspective it's going to take you 2.5 years (because twice the speed of your holiday trip) but you haven't been on that ship for 2.5 years so what happens?

If by some magical bullshit we could watch from Earth with a live video feed we would see you stand up from your pilot's chair, walk backwards out of the cockpit and continue walking backwards until you open the door (the way you closed it playing in reverse) and walk out of the ship, and outside that door we see Earth. So everybody freaks out and runs to the landing pad but there's nothing there because that's not where you are, that's where you were, you're currently back on Earth, in the past.

Of course you don't notice this, causality plays out EXACTLY as it did before and we have absolutely no ability to experience time progressing backwards, we only experience time going forwards. But now for the really crazy shit, the ship arrives at its destination, or rather doesn't, because you're still back in time, back on Earth in the past, and so is everything aboard the ship, and the ship itself.

The conventional belief is that this means you arrive at your destination 2.5 years before you left Earth and that's kinda sorta technically correct but also totally wrong.

You do arrive 2.5 years before you left but you can't be there until you actually get there and you don't actually get there until after you press the go button. Because that would mean you could go there and return 5 years before you left and now there's two of you and you're interacting with yourself so that you doesn't go on the trip creating a grandfather paradox and it's all just very stupid.

The way my clockwork brain works this out is that you arrive spatially before you arrive temporally and in the interim you sorta don't exist, in the present, you still exist in the past and the past still plays out exactly the same. So from your perspective you press the go button and you arrive at your destination instantly, exactly the same as if you traveled at the speed of light, and that you experienced your past twice is completely unknown to you.

From Earth's perspective the trip takes 5 years, which is kinda bullshit because you traveled twice as fast so you should arrive in half the time, but in this case the universe says fuck you. You did arrive spatially in 2.5 years but you're also now temporally displaced 2.5 years and that time needs to play out before you can actually arrive so the trip takes 5 years from Earth's perspective. The speed of light isn't a speed limit, it's a time limit, you can go as fast as you fucking want but you're never getting there before you arrive.

The people on Earth watching a live feed from a magic camera strapped to your head get to see your timeline play out 2.5 years in reverse and then 2.5 years forwards, which meant they had to strap that camera to your head 2.5 years before you left and you've been wearing it the entire time. Don't think about this part too hard because it's a magic camera which means we're getting information that technically shouldn't be obtainable, at least not in the way its being obtained.

Once you arrive back at the temporal point when you press the go button, your ship instantly arrives at its destination, or rather you've already been there 2.5 years, just in your own little bubble of the past outside of normal time/space.

 

[dr froyd]

From Earth's perspective the trip takes a year, from the perspective of the people on the ship it might only take a few weeks and the closer the ship is traveling to the speed of light the less time they experience.

is this purely a length-contraction effect?

 

[dr froyd]

by the way, this is a very good video on the twin paradox and how even physicists often don't understand it:

 

[EndogenousRebel]

Pretty sure quantum physics is what makes this makes sense lol, cuz don't understand quantum physics and I don't understand this.

So, time, wraps around matter and space.

Going really fast makes you go through less time. Lots of gravitational force also pulls time away from space and matter towards the gravitational center.

It's not necessarily about mass or speed, it's about where time is depending on these factors?

Having time closer to you means that you experience more of it. So someone at sea level experiences more time, than someone in the mountains. So a pull of time towards us, counterintuitively slows things down, relative to spaces where there is less time.

This is why people who are on Earth say that a clock in space ticks "faster" in space. The watch is still mechanically the same, and would be fine if brought to Earth. To the people on the space station, the Earth is slower, a massive gravitational force, when to most people on Earth, the people on the space station are going faster.

We know that astronaut's reaction times increase (slower) when they are in space. About 40-ms. Not that much, but still, noticeable. They simply have less time to react. Haha.

Spaceflight alters reaction time and duration judgment of astronauts

We report a study on astronauts aimed at characterizing duration judgment before, during, and after long-duration stays on board the International Space Station. Ten astronauts and a control group of 15 healthy (non-astronaut) participants performed a ...

www.ncbi.nlm.nih.gov

I can't help but pose a question in response to this thread then. If two watches were made in the same factory, one was taken to space and brought back, and of course was now ahead, are both the watches not the same age? Will the battery not die at the same.. time?

It's a weird thing to speculate if causation such as chemical reactions even requires time to be present, but obviously movement is still possible so long as you have no mass.

ANYWAYS. The dog experiences non-light speed objects as slowing down temporally, it's own experience of time will increase drastically, not even sure how that would look and feel to be honest. What about the processes in the body?

Over my head, honestly. Fuck a definitive answer

I want to say that the dog lives longer than half a light year, because the amount of time it's gone through is less. Did it "stop" time for itself. No. It definitely was going through some on the ride there. How would that work. No clue.

 

[Cognisant]

Having time closer to you means that you experience more of it. So someone at sea level experiences more time, than someone in the mountains. So a pull of time towards us, counterintuitively slows things down, relative to spaces where there is less time.

No that's because the planet spins at a constant rate.

Imagine the minute hand of a clock, that armature rotates around the center at one revolution per minute regardless of how long the armature is, but the longer the armature the further distance the tip has to travel to return to its original point. Velocity = Distance / Time

A satellite in geosynchronous orbit, that is to say it stays over the same point above the ground, is covering a much greater distance in a 24h planetary rotation than someone standing on the ground, because it is much further from the center of rotation.

Distance has nothing to do with it, I could probably make a digital watch run slower if I spun it fast enough in a very expensive centrifuge, granted not slower by much.

We know that astronaut's reaction times increase (slower) when they are in space. About 40-ms. Not that much, but still, noticeable. They simply have less time to react. Haha.

They're probably just tired, going to space is stressful and being in space is uncomfortable.

I can't help but pose a question in response to this thread then. If two watches were made in the same factory, one was taken to space and brought back, and of course was now ahead, are both the watches not the same age? Will the battery not die at the same.. time?

Practically speaking it wouldn't matter, but technically speaking one watch would be "younger" than the other.

ANYWAYS. The dog experiences non-light speed objects as slowing down temporally, it's own experience of time will increase drastically, not even sure how that would look and feel to be honest. What about the processes in the body?

You cannot experience time, you are process that occurs at the rate of time.

 

[dr froyd]

ok i tried to use the Lorentz transform on this scenario, looks like there's no paradox after all. If I did this correctly, that is (im a complete noob in physics, first time I'm touching this stuff)

so letting speed be fraction of speed of light [imath]\beta = v/c[/imath] and putting [imath]x = 1[/imath] and [imath]t = 1[/imath] as the location and time of arrival at the other planet in earth's inertial frame, for the ship we get
[math]t' = \frac{c - \beta}{c \sqrt{1 - \beta^2}}[/math]and letting speed approach speed of light [imath]\beta \rightarrow 1[/imath] then [imath]t'[/imath] goes to zero. And same with its position [imath]x'[/imath]

i.e. in the ship's reference frame it spends about zero time and travels about zero distance.

so then it's all consistent; in both frames the dog hasn't aged at all when it reaches the planet

 

[dr froyd]

but doesn't this contain the same paradox as the twin paradox, still?

from the dog's frame, time on earth hasn't elapsed at all when it reaches the other planet, i.e. everyone is as old as when it left earth.

but from earth's frame, the dog spent 1 year to reach the planet but without aging, so people on earth are 1 year older relative to the dog.

so it's not symmetric despite the fact that both frames can act as the inertial one?

this to me this is a 1-way trip version of the twin paradox (although im probably missing something again)

 

[EndogenousRebel]

Having time closer to you means that you experience more of it. So someone at sea level experiences more time, than someone in the mountains. So a pull of time towards us, counterintuitively slows things down, relative to spaces where there is less time.

No that's because the planet spins at a constant rate.

Imagine the minute hand of a clock, that armature rotates around the center at one revolution per minute regardless of how long the armature is, but the longer the armature the further distance the tip has to travel to return to its original point. Velocity = Distance / Time

A satellite in geosynchronous orbit, that is to say it stays over the same point above the ground, is covering a much greater distance in a 24h planetary rotation than someone standing on the ground, because it is much further from the center of rotation.

The satellite is also going around the Sun as the Earth does, on top of rotating to compensate the tips around it.

The further the satellite, the faster the time is, because it's going further from the Earth's pull. So there is more time in this space.

Distance has nothing to do with it, I could probably make a digital watch run slower if I spun it fast enough in a very expensive centrifuge, granted not slower by much.

This is correct due to speed.

We know that astronaut's reaction times increase (slower) when they are in space. About 40-ms. Not that much, but still, noticeable. They simply have less time to react. Haha.

They're probably just tired, going to space is stressful and being in space is uncomfortable.

Plausible. Though I'm pretty sure that being in an area that literally has a different dynamic with time is an contributing factor.

I can't help but pose a question in response to this thread then. If two watches were made in the same factory, one was taken to space and brought back, and of course was now ahead, are both the watches not the same age? Will the battery not die at the same.. time?

Practically speaking it wouldn't matter, but technically speaking one watch would be "younger" than the other.

The watch was created at x point in time. Then it essentially time traveled to the future in orbit and was brought back to Earth. No?

ANYWAYS. The dog experiences non-light speed objects as slowing down temporally, it's own experience of time will increase drastically, not even sure how that would look and feel to be honest. What about the processes in the body?

You cannot experience time, you are process that occurs at the rate of time.

lol an expression of time? Time is passing and if it's not then I am not. Sure it's happening whether I experience it or not, but you're definitely experiencing it as it's all around us.

 

[PeopleDoSuck]

I don't think it's really a paradox. It's a question or problem of determining which one undergoes a force. If you know, it's a trivial question. But if you don't know, how do you determine which one is in motion?

Inertia. Things resist motion, unless you expand energy to move them. You could think about it like this - the Earth, the other planet, and ship exist as part of a greater 3-dimensional space, we'll call a galaxy. The galaxy is their greater inertial space. If the Earth and the other planet were in motion together, both would see the entire galaxy shift around them. And the ship similarly. If everything around you suddenly shifts in unison, then you know you are in motion, not them, due to inertia.

 

[ZenRaiden]

We aren't talking about physics here are we though?
Not in Newtonian sense.
The dog is not moving in relation to other things.
The dog cannot age.

 

[dr froyd]

I don't think it's really a paradox. It's a question or problem of determining which one undergoes a force. If you know, it's a trivial question. But if you don't know, how do you determine which one is in motion?

i would maintain it is paradoxical in light of special relativity because special relativity doesn't say anything about the effect of force on time dilation; the point of constructing the scenario the way ive tried in this thread is to explicitly remove force and acceleration from the picture

If everything around you suddenly shifts in unison, then you know you are in motion, not them, due to inertia.

talking about who is moving and who is stationary is nonsensical in relativity, you can only measure motion relative to other objects.

 

[PeopleDoSuck]

I don't know if this was explained:

now the paradox: on the picture that is received by earth, is the dog dead or alive? From the ship's reference frame, it has spent about 1 year on this voyage, so the dog must be dead. But from earth's reference frame, the dog has almost not aged at all so it must be alive.

The ship's time slows down relative to the planets when traveling fast. So it travels that lightyear distance in less than a lightyear of time.

What this means, if taken to the extreme, given infinite energy, if the ship reaches the speed of light, it can travel anywhere in the universe instantly, but its time also stops, and the universe goes through infinite amount of time as well. Extremes help me understand concepts better.

I don't think it's really a paradox. It's a question or problem of determining which one undergoes a force. If you know, it's a trivial question. But if you don't know, how do you determine which one is in motion?

i would maintain it is paradoxical in light of special relativity because special relativity doesn't say anything about the effect of force on time dilation; the point of constructing the scenario the way ive tried in this thread is to explicitly remove force and acceleration from the picture

I know. But it doesn't have to because it's just talking about the inertial frame. Things stop being inert when a force is applied.

But if you reduce it down to that, then there is no answer because there's no way to know. That's why the inertial frame of reference is so important to relativity.

 

[PeopleDoSuck]

I replied, but awaiting moderator approval. I don't know if it's because I edited it or it was awaiting approval before. If you can read this, but not the message before, then it's because I edited and am awaiting approval.

 

[PeopleDoSuck]

Okay, well, uhh hmm, that answers that. Here's the "awaiting approval" post. Maybe relativity is kind of dumb, but this is my response.

I don't know if this was explained:

now the paradox: on the picture that is received by earth, is the dog dead or alive? From the ship's reference frame, it has spent about 1 year on this voyage, so the dog must be dead. But from earth's reference frame, the dog has almost not aged at all so it must be alive.

The ship's time slows down relative to the planets when traveling fast. So it travels that lightyear distance in less than a lightyear of time.

What this means, if taken to the extreme, given infinite energy, if the ship reaches the speed of light, it can travel anywhere in the universe instantly, but its time also stops, and the universe goes through infinite amount of time as well. Extremes help me understand concepts better.

I don't think it's really a paradox. It's a question or problem of determining which one undergoes a force. If you know, it's a trivial question. But if you don't know, how do you determine which one is in motion?

i would maintain it is paradoxical in light of special relativity because special relativity doesn't say anything about the effect of force on time dilation; the point of constructing the scenario the way ive tried in this thread is to explicitly remove force and acceleration from the picture

I know. But it doesn't have to because it's just talking about the inertial frame. Things stop being inert when a force is applied.

But if you reduce it down to that, then there is no answer because there's no way to know. That's why the inertial frame of reference is so important to relativity.

 

[PeopleDoSuck]

I think the paradox is more to illustrate a segway into Simultaneity of Relativity and the importance of the inertial frame. But that's my opinion on the matter.

 

[ZenRaiden]

Every object with mass has energy.
All matter is in state of decay.

Objects moving have a different frame of reference.

This could be viewed as if all space is a sea of water.

A photon moving at a speed of light, is like a very slim needle gliding through water.

It simply is not touched by the energy of water, as it has zero drag.

SO photons travel real fast, and don't get slowed down by water and they reach max speed.

Water can be seen as time as well.

SO for simplicity sake one could say if water touches you age faster, and you weight more.

Not only it is helpful to view all space as water, but rather water that flows constantly, down wards.

So all time + space is endless waterfall of water we cannot see.

I prefer imaging that all universe is in free fall constantly dropping down wards as if on a plate going dropping down.

SO Earth is motionless in theory, but in relation to Sun its in motion. In relation to all objects its in motion to galaxy and galaxies and all other energies.

So why drop the universe this way?

Well then it explains why things moving are being dragged.

The faster they go the less affected by the dropping universe.

That is why photons are closest to symmetry and hence least affected by universe.

Falling universe also simplifies gravity.

Because it explains why more gravity means less symmetry and hence curves space.

So if say the dog weights 0 mass he could be moving at speed of light or be motionless and still have same amount of energy.