Newbie vs Einstein: Questions about Time Travel and Quantum Entanglement

[tnadys]

A couple questions.

Assume that you can travel arbitraily close to the speed of light and that you have figured out how to communicate via Quantum entanglement (Like Ender's Game).

I speed away from Earth at almost the speed of light. At the point when I stop accelerating, is it not valid to say that I am standing still and the Earth is moving away from me? If so why does time slow for me, instead of the earth? Why can this not be used to determine absolute speed instead of being limited to relative speed? What does this do to my quantum entangled communications? At what point does my mass cause me to become a black hole?

The second related question is, how do we know that time actually slows? If all of the atoms in my body slow (because their vibrations/motion would also have a speed limit) it would seem to me like time has slowed but it is in fact more like suspended animation. It seems to me that without knowing what time is there is no way to know. If it is in fact just suspended animation then it isn't time travel but just a speed limit. I don't think this is just semantics. My question really asks if time is slowed at all or just our perception of time. Am I missing something?

 

[paw]

At the point when I stop accelerating, is it not valid to say that I am standing still and the Earth is moving away from me?

Yes.

If so why does time slow for me, instead of the earth?

From your point of view clocks on Earth tick slower. From the point of view of an observer on Earth your clocks tick slower. It's a symetrical phenomenum.

Why can this not be used to determine absolute speed instead of being limited to relative speed?

Absolute with respect to what? That's the problem. Any inertial observer is free to consider themselves at rest.

At what point does my mass cause me to become a black hole?

At no point do you become a black hole. There's some good explanations in the FAQs.

The second related question is, how do we know that time actually slows?

Again, there are good explanations in the FAQs but the fact that muons created by cosmic rays in the upper atmospere reach the Earths surface, even though thay shouldn't last long enough, is pretty compelling proof.

My question really asks if time is slowed at all or just our perception of time. Am I missing something?

Time really does slow down when moving clocks are observed from the rest frame of an observer. It's not an issue of perception.

 

[tnadys]

I'm still not really getting it. I understand that point about it being from the perspective of the observer, but if I come back to Earth and stop, time has slowed for me not earth. I guess I don't get the relative part.

 

[atyy]

You are right, it is not relative, it is absolute. For you to come back to Earth you must change directions, ie. accelerate. In special relativity, motions with constant velocity are relative, but accelerations are absolute.

 

[tnadys]

But say you can accelerate almost instantly, so that virtually all the travel time is at a constant velocity. Then the acceleration is an insignificant part of the trip. Another approach is to return at a normal velocity so that time dilation is insignificant. The time effects from the first part still caused you to age less than earth. Is it, just that it appears relative while you are moving, but the absolute effects are apparent when you stop?

Another, way of asking the question is, if while I am traveling I should be able to tell time by the position of the planets/stars (I know that no light would catch me, but pretend). If it is relative there movement should slow down from my perspective (since they are moving away from me at relativistic speeds). But a stationary observer would see them move normal. If I stop moving where are the planets? If Time slows for me, they should have moved faster from my perspective, which is what the stationary observer would see.

Still confused. I am not questioning 100 years of relativity , but I cannot, make sense of these apparent contradictions. I accept that it is true, but I am having trouble wrapping my mind around it.

 

[russ_watters]

But say you can accelerate almost instantly, so that virtually all the travel time is at a constant velocity.

That's not the point. It doesn't matter how long the acceleration takes, it's the fact that you accelerated that breaks the symetry.

 

[tnadys]

It feels like we are going in circles here. If I leave the Earth at the speed of light then come back time has slowed for me not earth. I'm not sure what acceleration has to do with anything. While I am traveling time appears to slow for the Earth from my perspective and for me from their perspective. In reality I am the only one affected. In fact when I stop it will appear from my perspective to have sped up for them when it in fact hasn't. This is what I am trying to understand.

The reason I mentioned instant acceleration, is that the difference in time between me and Earth is determined by my velocity and how long I traveled not by how fast I got up to speed.

In my original question I mentioned using Quantum entanglement for communications. Which would allow you to communicate with the stationary observer. Would I not be able to tell that Time has slowed for me not him?

 

[cristo]

It seems to me that your question is a version of the twin paradox. You can search the S&GR forum for amny threads on this topic, which may help you understand.

In my original question I mentioned using Quantum entanglement for communications. Which would allow you to communicate with the stationary observer. Would I not be able to tell that Time has slowed for me not him?

I don't see this as a related question. It is more a question of Quantum Physics that relativity.

 

[George Jones]

The reason I mentioned instant acceleration, is that the difference in time between me and Earth is determined by my velocity and how long I traveled not by how fast I got up to speed.

There is still an asymmetry. You travel way form Earth in one inertial reference, and you travel back to Earth in another inertial reference frame, i.e., you switch inertial reference frames. The Earth stays in one (approximate) inertial reference frame.

 

[Al68]

I'm not sure what acceleration has to do with anything. While I am traveling time appears to slow for the Earth from my perspective and for me from their perspective.

In all of the resolutions I've read, from the ship's point of view, Earth's clock does run slow compared to the ship's clock, except during the acceleration (turnaround). If the turnaround is instantaneous, Earth's clock simply "jumps" ahead. Otherwise Earth's clock will run faster than the ship's clock during the acceleration, from the ship's point of view. There are many different opinions on this, but as far as I know, the consensus is that the Earth clock will "jump" or run faster than the ship's clock during the turnaround according to the ship observer.

Some say that this isn't due to acceleration, but due to the ship switching reference frames. Well, if we consider the ship to change velocity in arbitrarily small increments, and Earth's clock to "jump" ahead a little for each increment, that's equivalent to saying that the ship will consider Earth's clock to run faster during the acceleration.

According to Einstein's clock paradox resolution, the ship's clock run's slower than Earth's during the acceleration due to the equivalence principle (the ship observer can consider himself at rest in a gravity field with the Earth in freefall) causing the ship's clock to run slower than Earth's during the "turnaround".

Al

 

[Fredrik]

In all of the resolutions I've read, from the ship's point of view, Earth's clock does run slow compared to the ship's clock, except during the acceleration (turnaround). If the turnaround is instantaneous, Earth's clock simply "jumps" ahead. Otherwise Earth's clock will run faster than the ship's clock during the acceleration, from the ship's point of view. There are many different opinions on this, but as far as I know, the consensus is that the Earth clock will "jump" or run faster than the ship's clock during the turnaround according to the ship observer.

Some say that this isn't due to acceleration, but due to the ship switching reference frames. Well, if we consider the ship to change velocity in arbitrarily small increments, and Earth's clock to "jump" ahead a little for each increment, that's equivalent to saying that the ship will consider Earth's clock to run faster during the acceleration.

Not exactly. The problem is that there's no natural way to extend the accelerating coordinate system to points that aren't close on the rocket's world line so that it assigns a time coordinate to events on Earth as well. (There is a choice that can be considered natural when the acceleration is constant, but not when the acceleration is arbitrary).

You are of course right that the ship can't switch reference frames without accelerating, so it's not wrong to attribute the "jump" of the Earth clock to acceleration in this case. However, there is a version of the twin paradox where there's no acceleration. Instead of two twins, you consider three clocks with (straight) world lines that form a triangle in Minkowski space. (You can probably figure out the rest). In this case, we can't claim that acceleration resolved the paradox.

Also interesting in this context is the version of the twin paradox suggested by Kev in this thread. See DrGreg's spacetime diagram in #4. In this case, both twins have accelerated in exactly the same way, but SR still predicts that they won't be the same age when they meet. I like this version of the problem because it shows why it doesn't really make sense to think of acceleration as the cause of a second kind of time dilation.

According to Einstein's clock paradox resolution, the ship's clock run's slower than Earth's during the acceleration due to the equivalence principle (the ship observer can consider himself at rest in a gravity field with the Earth in freefall) causing the ship's clock to run slower than Earth's during the "turnaround".

This can only be considered a resolution if you already understand gravitational time dilation very well, and I don't see how anyone can understand that without first having a very thorough understanding of time dilation in SR. For example it's instructive to think about the relative ticking rates of two clocks at the front and back of an accelerating (Born) rigid spaceship, and then use the equivalence principle to carry the result over to GR, where the situation is supposed to be equivalent to two clocks attached to the ceiling and floor of a room in a gravitational field. What you want to do is pretty much the opposite.

I don't see why we would want to resort to a resolution that demands that you understand GR and trust the equivalence principle when there are much simpler resolutions.

 

[tnadys]

Thanks to all the people who responded. I think, I at least understand why I didn't understand. It does sort of seem like a consequence of math, rather than reality But given all the other strange things we have found out about the universe maybe not. I am a programmer, not a physicist. In my world a paradox is usually a mistake that ends badly :) This is something that my logical brain will probably never be able to accept as reality.

 

[sketchtrack]

I have a related question. We are accelerating around the sun by the forces of gravity. Does acceleration due to gravity also cause time dilation? I know that gravity itself causes time dilation. Is the time dilation that we call a factor of g actually a factor of acceleration due to G?

 

[JesseM]

But say you can accelerate almost instantly, so that virtually all the travel time is at a constant velocity. Then the acceleration is an insignificant part of the trip.

I always think it's easiest to think about the role of acceleration in terms of spacetime geometry. If both of us travel between two points on a 2D plane, and one of us goes in a path which has constant slope in a cartesian coordinate system on that plane (meaning the path is a straight line) while another goes on a path which has a changing slope in just one small region whereas the sections of the path both before and after have (different) constant slopes (so the path resembles a bent straw with two straight segments joined by a small curve), then this is enough to guarantee that the distance along the second path will be significantly larger than the distance along the first. It isn't as if all the extra distance suddenly accumulates along the short bent section of the second path, it's because of the geometry of the situation--in a 2D plane a straight line is always the shortest distance between two points, any other path between those points will be longer.

Something fairly similar is true for paths through 4D spacetime in relativity, except with the notion of "proper time" along a path through spacetime (the time as measured by a clock that has that path as its worldline) replacing the notion of distance along a path through 2D space. I elaborated on this in another post while I'll copy here:

If you draw two points on a 2D plane, and then draw two paths between these points, one of which has constant slope (in any cartesian coordinate system) and the other of which has a changing slope, then you always find that the one with constant slope has a shorter total length, because a straight line is the shortest distance between two points. For any given point on a path, you could create a cartesian coordinate system where the y-axis was parallel to the path at that point, and then look at the inverse-slope S = dx/dy of the second path at any given y-coordinate in this coordinate system, and write an equation for the rate at which the second path was accumulating length relative to a small increase in the y-coordinate dy at any given y-coordinate. Using the pythagorean theorem, the second path will have accumulated an additional length of [itex]\sqrt{dx^2 + dy^2}[/itex] for an increase in the y-coordinate dy, which is equal to [itex]dy \sqrt{{dx^2}/{dy^2} + 1}[/itex], and substituting in the term for the inverse-slope this becomes [itex]dy \sqrt{1 + S^2}[/itex]. Note that this looks a lot like the time dilation equation, which says that for any small increase in the coordinate time of a given inertial frame dt, a clock moving at speed v at that moment will accumulate a time [itex]dt \sqrt{1 - v^2}[/itex] (in units where c=1). And just as we could calculate the elapsed time on a path with varying speed v(t) using the integral I mentioned earlier, so it's true that if we have a function S(y) for the inverse-slope S as a function of y-coordinate for a given path, we can calculate the total length of the path between two coordinate y0 and y1 using the integral [itex]\int_{y_0}^{y_1} \sqrt{1 + S(y)^2} \, dy[/itex]. Since we know a straight line is the shortest distance between two points, we know that if we have two paths between a given pair of points on the plane, one of which has a constant S(y) and the other of which has a varying S(y), the math must work out so that the above integral is guaranteed to give a smaller answer for the one with constant S(y). It therefore shouldn't be too surprising that when you have two paths through between the same two points in spacetime, one of which has a constant v(t) and one of which has a varying v(t), then when you evaluate the integral [itex]\int_{t_0}^{t_1} \sqrt{1 - v(t)^2} \, dt[/itex], the one with constant v(t) is guaranteed to give a larger value (the only real difference here is the plus sign vs. the minus sign in the square root). Just as a straight line is always the shortest distance between points on a 2D plane, a non-accelerating path is always going to be the longest-time path between two points in spacetime.

I also talked a little more about this analogy to 2D geometry in post #9 from this thread.

 

[cosmik debris]

Thanks to all the people who responded. I think, I at least understand why I didn't understand. It does sort of seem like a consequence of math, rather than reality But given all the other strange things we have found out about the universe maybe not. I am a programmer, not a physicist. In my world a paradox is usually a mistake that ends badly :) This is something that my logical brain will probably never be able to accept as reality.

I think where you are confused is that really there are two distinct time dilation effects. One is the symmetrical "clock running slow" from each observers point of view, and the other is the time accumulated on a clock due to different paths through spacetime. The latter is much like the odometer on your car. We both go to the same place but on different paths and our odometers do not read the same. The clock in relativity plays the part of an odometer. In order for two people to meet again one has to change frames (whether by acceleration or something else) thus traveling a different distance through spacetime.

 

[Fredrik]

I have a related question. We are accelerating around the sun by the forces of gravity. Does acceleration due to gravity also cause time dilation? I know that gravity itself causes time dilation. Is the time dilation that we call a factor of g actually a factor of acceleration due to G?

Newton's theory describes gravity as a force, with a corresponding acceleration, but there's no time dilation in Newton's theory. In Einstein's theory, gravity isn't a force. Objects in free fall (such as a planet in orbit around the sun) are unaffected by forces.

Gravity does however cause a kind of time dilation. For example, if you put a clock on the floor and one in the ceiling of the room you're in, the one on the floor will be slower. This is because the motion of the clock in the ceiling deviates less from free fall than the motion of the clock on the floor. Any deviation will slow down the clock. This is exactly the same thing that happens if you put a clock on the floor and ceiling of an accelerating rocket that's far away from massive objects (and therefore unaffected by gravity).

 

[tnadys]

Is my problem that I am thinking in 3d plus time instead of treating it like 4 spatial dimensions? I really have no problem with the time dilation aspect. It has been demonstrated and isn't really in dispute. The basic problem is in the frame of reference aspect. If I speed away from earth, it may be valid to talk about frames of reference with respect to perception but, my motion doesn't actually affect the earth. I still think that there is a "normal" time (Earth's) and a "dilated" time (mine). There seems to me that their should be an explanation, that doesn't imply that I have an effect on the earth. Their really is only one person moving, with respect to the starting position.

 

[JesseM]

Is my problem that I am thinking in 3d plus time instead of treating it like 4 spatial dimensions? I really have no problem with the time dilation aspect. It has been demonstrated and isn't really in dispute. The basic problem is in the frame of reference aspect. If I speed away from earth, it may be valid to talk about frames of reference with respect to perception but, my motion doesn't actually affect the earth. I still think that there is a "normal" time (Earth's) and a "dilated" time (mine). There seems to me that their should be an explanation, that doesn't imply that I have an effect on the earth. Their really is only one person moving, with respect to the starting position.

Suppose instead of Earth, you depart from a space station, and move away inertially. Then instead of firing your rockets to turn around and return to the station, the station briefly fires its own rockets in your direction, and then coasts inertially until it catches up with you. In this case it'll be the station's clock that shows less elapsed time, not yours. Of course, you can analyze the whole thing from the point of view of an inertial observer who was originally at rest relative to the station before it fired its rockets, and continues to move inertially afterwards--in this frame your clock was ticking slower than the station's clock before the station accelerated, but then after the station accelerated it was moving even faster than you in this frame so its clock was ticking even slower, and it works out that the total time on the station's clock is predicted to be less in this frame. On the other hand, you could analyze the whole thing from the perspective of an inertial observer who saw your ship as being at rest after leaving the station, and in this frame the station starts out moving away from you, then fires its rockets to move back towards you (just like the traveling twin in the twin paradox), so its clock is ticking slower than yours during both phases in this frame. But if you do the math in this frame, you still find that the amount that the station's clock is predicted to be behind yours when you meet is exactly the same as the prediction made in the first frame (where your clock was ticking slower than the station's prior to the acceleration, and the station's clock was ticking slower than yours after the acceleration). So there isn't any "true" answer to whose clock is running slower at any given moment (like a moment before the station accelerates, where the two frames disagree about whose clock is ticking slower), but there is an answer all frames agree on about how much time has passed on each clock when they reunite, and the answer is always that the one who accelerated (the station in this example, you in the previous example) has elapsed less time.

 

[atyy]

Their really is only one person moving, with respect to the starting position.

Yes, there really is only one person moving, if by "moving" you don't mean moving with constant velocity, but you do mean accelerating/decelerating/changing direction.

Somewhat unrelated but perhaps helpful is the discussion in d'Inverno's Introducing Einstein's Relativity that it is not a trivial matter as to what an constitutes an ideal clock (ie. one that is unaffected by acceleration). He also says that it is not certain that time dilation applies to human aging, although it is likely, since we are made of things that constitute ideal clocks.

Another discussion I found helpful is in Woodhouse's book on special relativity - notes similar to his book may be found at his website (http://people.maths.ox.ac.uk/~nwoodh/sr/index.html ). Sections 2.3, 7.2, 8.0 were helpful to me. He states when discussing the proper time of an accelerated path, that only an ideal clock will measure the proper time, and gives the example of a pendulum as a non-ideal clock. He also says in his book, but not the notes, that it is important not to be dazzled by time dilation - proper time and coordinate time correspond to two different physical operations, and it is not surprising that different operations give different results.

 

[DrGreg]

The problem is that there's no natural way to extend the accelerating coordinate system to points that aren't close on the rocket's world line so that it assigns a time coordinate to events on Earth as well. (There is a choice that can be considered natural when the acceleration is constant, but not when the acceleration is arbitrary).

To avoid diverting this thread off-topic, I've responded to this in a new thread.

 

[DrGreg]

Is my problem that I am thinking in 3d plus time instead of treating it like 4 spatial dimensions?

Yes, I think so.

As four dimensions are hard to grasp, fortunately you don't have to. In this scenario we are interested only in one dimension of space and one dimension of time, so spacetime is effectively two-dimensional and we can draw it on a piece of paper. You might like to look at the diagrams attached to this post, and see if they make any sense at all.

I still think that there is a "normal" time (Earth's) and a "dilated" time (mine).

I suspect you already know this view is misleading, as you can also think of "normal" time (mine) and a "dilated" time (Earth's).

You have to realize when we compare one clock against another, we can't do a direct comparison if the clocks are a distance apart -- it takes time for information to move from one clock to the other. The comparison requires an agreed procedure; different observers use different procedures and so come to different conclusions. There is no objective truth about which clock is "really" ticking faster than the other.

 

[Al68]

For example it's instructive to think about the relative ticking rates of two clocks at the front and back of an accelerating (Born) rigid spaceship, and then use the equivalence principle to carry the result over to GR, where the situation is supposed to be equivalent to two clocks attached to the ceiling and floor of a room in a gravitational field. What you want to do is pretty much the opposite.

I think it's more like a ship observer (accelerating at 1G) launching a clock "upward" and letting it "fall" back, and comparing it to a clock attached to the ship right after it's "launched", and as it "returns". The ship observer can consider this as equivalent to the clock "accelerating" due to a gravitational field. And the clock changes direction relative to the ship for the same exact reason as the Earth changes direction relative to the ship in the twins paradox.

Al

 

[Al68]

I don't see why we would want to resort to a resolution that demands that you understand GR and trust the equivalence principle when there are much simpler resolutions.

Because it allows the ship's twin to consider himself "at rest" for the entire trip. Which I think was the point of the OP's question. And, like I'm sure you're sick of hearing , what I think was the core of Einstein's point when he first presented the clock paradox, and the reason he resolved it the way he did.

Al

 

[Al68]

Also interesting in this context is the version of the twin paradox suggested by Kev in this thread. See DrGreg's spacetime diagram in #4. In this case, both twins have accelerated in exactly the same way, but SR still predicts that they won't be the same age when they meet. I like this version of the problem because it shows why it doesn't really make sense to think of acceleration as the cause of a second kind of time dilation.

Not really, since time dilation due to acceleration (due to gravity or otherwise according to the equivalence principle) in GR also depends on the distance between the clocks, so the twins in Kev's example did not accelerate the same way in this respect.

Al

 

[Fredrik]

Not really, since time dilation due to acceleration (due to gravity or otherwise according to the equivalence principle) in GR also depends on the distance between the clocks, so the twins in Kev's example did not accelerate the same way in this respect.

The reason the distance is relevant in the case of gravitational time dilation is that the two clocks we would be comparing are deviating from geodesic motion by different amounts (caused by their different positions in the gravitational field). In kev's twin paradox, the two twins deviate from geodesic motion in exactly the same way.

 

[atyy]

The reason the distance is relevant in the case of gravitational time dilation is that the two clocks we would be comparing are deviating from geodesic motion by different amounts (caused by their different positions in the gravitational field). In kev's twin paradox, the two twins deviate from geodesic motion in exactly the same way.

The new twin paradox is a good one. The nice thing about paradoxes is not just to get the right answer, but to get the right answer in a way that seems intuitively correct (a matter of taste obviously, but which is the standard procedure in biology, where no equations are allowed).

Acceleration in and of itself does not cause time dilation in the sense that the proper time is calculated only using the instantaneous velocity, and indeed an ideal clock that is supposed to measure proper time has to be one that is not affected by acceleration. And anyway, the problem can be phrased so that the acceleration is of such a short duration that the additional ageing during that time is negligible.

However, acceleration is absolute in the sense that it can be detected by an accelerometer, and also in the sense that those little kinks, however short in duration, change the symmetry and the relativity of the whole situation. Since there is no more symmetry, there is no reason for the twins, triplets etc. to time dilate or to age the same way, and hence no psychological feeling of paradox - at least for me at 9 pm PST, August 13, 2008 - maybe I'll feel differently tomorrow.

 

[Al68]

The reason the distance is relevant in the case of gravitational time dilation is that the two clocks we would be comparing are deviating from geodesic motion by different amounts (caused by their different positions in the gravitational field). In kev's twin paradox, the two twins deviate from geodesic motion in exactly the same way.

Actually, that issue was one of the questions about Einstein's resolution I was going to ask in that other thread, but no one seemed familiar with it, so I didn't see any point. Einstein used the distance between the clocks in the twins paradox as equivalent to a difference in height between 2 clocks in a gravitational field.

 

[yuiop]

...

According to Einstein's clock paradox resolution, the ship's clock run's slower than Earth's during the acceleration due to the equivalence principle (the ship observer can consider himself at rest in a gravity field with the Earth in freefall) causing the ship's clock to run slower than Earth's during the "turnaround".

Al

Einstein's clock paradox resolution is completely contradicted by the consesus of opinion in the https://www.physicsforums.com/showthread.php?t=249722" thread.

In the case of tossing a clock upwards (and letting it fall back down), the inertial tossed clock ages MORE during freefall than the non inertial clock at rest with the gravity field.

At this point I am completely confused as to whether a geodesic defines a path of least distance or least proper time or what?

For example say we have a satellite orbiting just above the surface of some massive body with no atmosphere. Now say we have a rocket car on rails parallel to that orbit and its locked to the rails so that it does not take off when it exceeds orbital velocity. The rocket can get to the other side of the world in less time than the satellite according to any observer and its proper time will be even less than that of the satellite because of additional time dilation due to its additional relative velocity. What's going here?

Now let's take a look at a Feynman type idea. Imagine we have a photon that is traveling from point A in air to point B located in some glass medium the Euclidean straight line from A to B is not perpendicular to the the surface of the glass block. Now assume the photon has not been to school and does not know how to calculate the the exact angle it should bend at the air-glass interface in order to obey the laws of light refraction. Feynam instructs the photon to explore all possible paths and take the one that takes theleast external time. Additional restrictions are that when it gets to the interface, head directly to Band obey the speed limit posted at the air glass border and travel slower in the glass. It turns out that the path of least time according to an external observer exactly obeys the laws of refraction. In other words the photon by obeying Feynman's simple instructions does not need to know how to calculate the laws of refraction!

Can a similar analogy be made for gravity so that a free falling particle does not have to be able to understand the complex calculations of general relativity in order to obey the laws of gravity? Something like travel in any direction, only make infinitesimal deviations from a "straight" path and obey the local speed limits?

 

[Ich]

In the case of tossing a clock upwards (and letting it fall back down), the inertial tossed clock ages MORE during freefall than the non inertial clock at rest with the gravity field.

Where do you see a contradiction?

 

[Dale]

Einstein's clock paradox resolution is completely contradicted by the consesus of opinion in the https://www.physicsforums.com/showthread.php?t=249722" thread.

In the case of tossing a clock upwards (and letting it fall back down), the inertial tossed clock ages MORE during freefall than the non inertial clock at rest with the gravity field.

At this point I am completely confused as to whether a geodesic defines a path of least distance or least proper time or what?

Hi kev,

Look carefully, it is not a contradiction. A timelike geodesic is a path which (locally) maximizes proper time. The stay-at-home twin is on a geodesic and the traveling twin is not therefore the home twin ages more. Similarly in a gravitational field, the free-falling twin is on a geodesic and the stationary (proper acceleration) twin is not therefore the free-falling twin ages more.

 

[yuiop]

Hi Dalespam and Ich,

Where do you see a contradiction?

Hi kev,

Look carefully, it is not a contradiction. A timelike geodesic is a path which (locally) maximizes proper time. The stay-at-home twin is on a geodesic and the traveling twin is not therefore the home twin ages more. Similarly in a gravitational field, the free-falling twin is on a geodesic and the stationary (proper acceleration) twin is not therefore the free-falling twin ages more.

Ahh.. Ok, that makes more sense. I got the "wrong end of the stick" there somewhere

Thanks :)

I wasn't really confused, I just put a red herring in there to see if anyone actually reads my posts...

OK.. I'm lying.. I was confused

 

[Dale]

I wasn't really confused, I just put a red herring in there to see if anyone actually reads my posts...

Nice cover!

 

[Al68]

Hi Dalespam and Ich,






Ahh.. Ok, that makes more sense. I got the "wrong end of the stick" there somewhere

Thanks :)

I wasn't really confused, I just put a red herring in there to see if anyone actually reads my posts...

OK.. I'm lying.. I was confused

Hi kev

I read your post, too, but others responded before I could.

See, lots of people read your posts.

Al

 

[Charlie G]

What if the twin paradox begins with the twin heading to Earth at a constant speed close to that of light, this way no acceleration is necessary. Then he sees Earth's clock slower than his but Earth sees the opposite. So what happens, why aren't the twins younger than each other (I know that that isn't possible, but it seems to me that this is what would be the case) Can someone explain this to me? I ve been troubled by it ever since I came across the twin paradox.

 

[russ_watters]

Does the twin in the spaceship ever stop? How did they synchronize their clocks in the first place?