Very simple relativity questions

[Pagey]

I've only just started reading on this topic at a very basic level, i just have a few questions which I am uncertain about.

If one is to travel at 99.99% the speed of light in a rocket car on earth, a day for the person traveling at this speed would seem to be a week for everybody else on earth. Will the person in the car feel time pass quickly or it will everything seem normal. Secondly, if the time passes quicker inside the car, will the person age at the same rate as everyone else outside but just die at a younger age or when the car stops the person will be much younger than everybody else?

 

[Xezlec]

If one is to travel at 99.99% the speed of light in a rocket car on earth, a day for the person traveling at this speed would seem to be a week for everybody else on earth. Will the person in the car feel time pass quickly or it will everything seem normal.

The whole point of relativity is that the same exact laws of physics apply to anyone in any frame of reference. So the person in the rocket car, as long as he doesn't have any windows to see the outside world, has no idea that he is even moving. All the usual laws of physics apply from his point of view, so nothing seems unusual or indicates to him that he is moving, let alone that his time is different from everyone else's time.

Secondly, if the time passes quicker inside the car, will the person age at the same rate as everyone else outside but just die at a younger age or when the car stops the person will be much younger than everybody else?

Of course when he gets out of the car he will be younger than the rest of us. Relativity isn't just some effect on human biology, it's a real physical principle.

 

[birulami]

The whole point of relativity is that the same exact laws of physics apply to anyone in any frame of reference.
[snip]
Of course when he gets out of the car he will be younger than the rest of us. Relativity isn't just some effect on human biology, it's a real physical principle.

I guess this is what usually goes by the name of the 'twin paradox'. Given that from the point of view of the guy in the rocket car the rest of the world is speeding by, the question arises why, after he stops, ehem, the world stops speeding by, he is indeed younger than all the rest. If they were speeding, they should be yonger.

The usual killing answer in any forum then is that due to the acceleration and deceleration involved, this is not covered anymore by Special Relativity. Instead General Relativity is needed and consequently I have to learn what a tensor is before I can understand why it is as it is.

Nevertheless I venture to ask if there is a way to understand the twin paradox without learning tensors first.

Harald.​

 

[Xezlec]

I guess this is what usually goes by the name of the 'twin paradox'. Given that from the point of view of the guy in the rocket car the rest of the world is speeding by, the question arises why, after he stops, ehem, the world stops speeding by, he is indeed younger than all the rest. If they were speeding, they should be yonger.

The usual killing answer in any forum then is that due to the acceleration and deceleration involved, this is not covered anymore by Special Relativity. Instead General Relativity is needed and consequently I have to learn what a tensor is before I can understand why it is as it is.

Yes, this is the twin paradox, and no, I don't think you need to know what a tensor is to have at least some understanding of it. I don't know what a tensor is (well, OK, I do, but I'm not enough of a math-head to actually be able to approach GR), but I think I have some understanding.

Since one of them is accelerating and decelerating, it actually doesn't look from his point of view like the whole world is moving and he is standing still. He can't say that. He feels acceleration and deceleration, so he knows that he is moving. He doesn't just "see the world slow down and stop", he actually feels himself slow down and stop, like you would if you were in a speeding car that slammed on the brakes. The rest of the world feels no such acceleration and deceleration, so they actually can claim they aren't moving.

The golden rule of SR is that all reference frames are valid, except reference frames that are accelerating, decelerating, or feeling gravity. So Earth is a valid reference frame in the twin paradox (if we assume Earth's gravity is so weak it can be considered "about 0" in cosmic terms), but the spaceship moving the other guy around the planet is not a valid reference frame. SR can't really say anything about "his point of view" during the time he is accelerating and decelerating. However, Earth's point of view on the whole situation, can be described, rock solid, using SR.

This is no big deal, it just means if you want to understand what's happening, you have to analyze the whole thing from Earth's point of view to get the right answer. Looking at it from Earth's POV, he is younger. So that's what happens. And whatever happens from the traveller's point of view, we know it must be some kind of situation that ends up in "everyone else being older" when he stops and steps off the spaceship, because we know (by using a valid reference frame to do the physics) that that is what needs to happen.

 

[Chris Hillman]

If one is to travel at 99.99% the speed of light in a rocket car on earth, a day for the person traveling at this speed would seem to be a week for everybody else on earth. Will the person in the car feel time pass quickly or it will everything seem normal. Secondly, if the time passes quicker inside the car, will the person age at the same rate as everyone else outside but just die at a younger age or when the car stops the person will be much younger than everybody else?

http://www.math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html

 

[Jamneutron]

I guess this is what usually goes by the name of the 'twin paradox'. Given that from the point of view of the guy in the rocket car the rest of the world is speeding by, the question arises why, after he stops, ehem, the world stops speeding by, he is indeed younger than all the rest. If they were speeding, they should be yonger.

Harald.​

If a traveller from the Earth's frame of reference takes an atomic clock with him, the atomic clock will show less time has passed upon the travellers return compared to an identical clock left on earth. Hence the vibrations of the atoms constituting the travellers clock have slowed down during the journey in this instance from an Earth Frame. Therefore relative motion slows atomic activity. Is this correct? Also at the approach to light speed does atomic activity not also approach zero.

 

[HarryDaniels]

If a person is traveling at any speed there time is going slower. The only reason you say at the speed of light is that the difference would be noticable. For instance, if observer A was stationary- if Earth was the inertial frame- and another person, or B, was moving faster than that person over the earth, even if it was only slightly, there time would be going slower.

Also, time goes slower if the person is further away from the gravitational force. For instance, the earth. If someone was on the 100th floor and someone else was on the ground, the person on tthe grounds time would be going slower, assuming that they were both stationary.

Hope this helps.

 

[Jamneutron]

If a person is traveling at any speed there time is going slower.

Hope this helps.

Yes thanks - as I thought.

Any idea on the mechanism for how the changed velocity causes the slowing in atomic activity for the traveller WRT the Earth frame.

 

[GRDixon]

If a traveller from the Earth's frame of reference takes an atomic clock with him, the atomic clock will show less time has passed upon the travellers return compared to an identical clock left on earth. Hence the vibrations of the atoms constituting the travellers clock have slowed down during the journey in this instance from an Earth Frame. Therefore relative motion slows atomic activity. Is this correct? Also at the approach to light speed does atomic activity not also approach zero.

From the perspective of the Earth's rest frame everything at rest in the rocket's rest frame is happening more slowly ... even the rate of an onboard Cesium clock. But from the perspective of the ship's rest frame, everything at rest in the Earth's rest frame is happening more slowly. These effects can be measured, using the clocks and measuring rods in one's rest frame. But note that when the rocket changes rest frames, and comes to rest in the Earth's rest frame, then an onboard astronaut must reassess his position. Believing now that the measuring rods and clocks at rest in his new (earth) rest frame give correct measurements, he realizes that it was himself who was actually aging more slowly while he was moving relative to Earth's rest frame. When he comes to rest in Earth's rest frame, his onboard clock will read less than the Earth rest frame clock at that location. And, since all the clocks at rest in Earth's rest frame are presumably synchronized, he concludes that he's aged less than his counterpart who remained "back home" permanently at rest in Earth's rest frame. (He can verify that this is the case by returning to his starting point.)

 

[Jamneutron]

I can accept that the travellers has aged more slowly.
But why is this, or how did this happen. How does relative motion or increased gravity cause a slowing of clocks?. Or is this a naieve question to ask.

 

[GRDixon]

I can accept that the travellers has aged more slowly.
But why is this, or how did this happen. How does relative motion or increased gravity cause a slowing of clocks?. Or is this a naieve question to ask.

Regarding time dilation and relative speed, you might find it useful to go to www.maxwellsociety.net and then click on the "Learning To Love The Lorentz Transformation" link (about 6 lines down on the home page).

 

[Loonwolf]

This question has puzzled me for years. Can anyone give an answer that makes sense?

Two spacecraft , A and B are next to each other in space. They synchronise their clocks.
They both start moving away from each other at immense speed.
From the point of view of spacecraft A, it is standing still, while from their point of view spacecraft B is moving at close to the speed of light, and the clock on spacecraft B is moving slower.
From the point of view of spacecraft B, it is standing still, while from their point of view spacecraft A is moving at close to the speed of light, and the clock on spacecraft A is moving slower.

They then both stop and start moving towards each other in the same way.
From the point of view of spacecraft A, it is standing still, while from their point of view spacecraft B is moving at close to the speed of light, and the clock on spacecraft B is moving slower.
From the point of view of spacecraft B, it is standing still, while from their point of view spacecraft A is moving at close to the speed of light, and the clock on spacecraft A is moving slower.

So it made no difference whether one stood still and the other moved, or both moved. The time dilation occurred because of relativity.

When they meet they compare their clocks.
Spacecraft A sees their clock is showing a later time than slower clock B.
Spacecraft B sees their clock is showing a later time than slower clock A.

Are they forever arguing about what time both clocks are displaying? Do they perceive a different value is displayed on both clocks depending which spacecraft they were in?

What if an observer stayed in between them, and watched them traveling at the same speed, do they see a third value on both clocks that says the same time?
And the same for their own clock, do they see one value while those who went in both spacecraft see a different value on their clock, but at least can agree between them that they see the same value?

And if all this craziness is true, what if the clocks are a part of a time bomb? Do the clocks explode for some people, and not explode for others?

 

[JesseM]

This question has puzzled me for years. Can anyone give an answer that makes sense?

Two spacecraft , A and B are next to each other in space. They synchronise their clocks.
They both start moving away from each other at immense speed.
From the point of view of spacecraft A, it is standing still, while from their point of view spacecraft B is moving at close to the speed of light, and the clock on spacecraft B is moving slower.
From the point of view of spacecraft B, it is standing still, while from their point of view spacecraft A is moving at close to the speed of light, and the clock on spacecraft A is moving slower.

They then both stop and start moving towards each other in the same way.
From the point of view of spacecraft A, it is standing still, while from their point of view spacecraft B is moving at close to the speed of light, and the clock on spacecraft B is moving slower.
From the point of view of spacecraft B, it is standing still, while from their point of view spacecraft A is moving at close to the speed of light, and the clock on spacecraft A is moving slower.

What do you mean by "point of view"? Normally in relativity if you talk about an observer's point of view you're talking about the inertial frame where they're at rest, but if spacecraft A turns around, there is no single inertial frame where it was at rest both before and after the turnaround (likewise with B), because an inertial frame is defined as one moving at constant velocity for all time (constant speed and constant direction). The idea that moving clocks run slow only applies in inertial frames, it wouldn't apply in a non-inertial coordinate system. And if you want to switch what inertial frame you use in the middle of the journey--switching from the frame where A was at rest during the outbound trip to the frame where A was at rest during the inbound trip, for example--then you have to take into account the relativity of simultaneity, which says that different frames have different opinions about which pairs of spatially-separated events happened at the "same time". So in this case, the first frame's opinion about what clock-reading on B was simultaneous with the event of A turning around will be different than the second frame's opinion on that question. In this section of the twin paradox FAQ there's a diagram showing lines of simultaneity for an observer ('Stella') that turns around at the midpoint of her journey, the downward-sloping blue lines being lines of simultaneity in the frame where she was at rest during the outbound leg, and the upward-sloping blue lines being lines of simultaneity in the frame where she was at rest during the inbound leg--you can see there's a large gap between the event on the worldline of the other observer ('Terence') that was simultaneous with the turnaround in the first frame, and the event on his worldline that was simultaneous with the turnaround in the second frame.

Anyway, in your scenario if the move apart and come together in a perfectly symmetrical way (from the perspective of the frame that sees them moving apart and coming back together at equal speeds in opposite directions), they will both be the same age when they reunite, and all inertial frames will agree on this prediction.

 

[Loonwolf]

By "point of view" I mean "in the experience".

Forget about the turning around and coming back then. But that should make no difference anyway, only the relative speeds and the fact time time slows down for moving objects relative to stationary ones.

People claim if a spaecraft travels away from Earth, then turns around and comes back it is the same as if it had just traveled twice the distance in a straight line. Time has slowed down for it during the time it is travelling, no matter what the direction.

From the point of view of A: A is stationary, B is moving. Time moves slower for B.
From the point of view of B: B is stationary, A is moving. Time moves slower for A.

Does time move slower for A or B when the clocks are compared?

(And for C, that sees both A and B moving and itself standing still?)


Is this true, a spacecraft leaves Earth very fast, returns, it seems to have traveled into the future. The occupant is younger than his twin brother who stayed on Earth?

If so then the reverse should also be true: The one in the spacecraft stayed in the same place and the Earth leaves very fast, returns, it seems to have traveled into the future. The occupant of Earth is younger than his twin brother in the spacecraft .

 

[JesseM]

By "point of view" I mean "in the experience".

What does "experience" mean? Are you talking about what they see visually with their eyes? Because that's not what time dilation in relativity is about (for example, if a clock is moving towards you you'll actually see it ticking faster rather than slower, it's only when you adjust for the different time the light from each tick had to take to reach your eyes that you conclude it was 'really' ticking slower in your frame)

Forget about the turning around and coming back then. But that should make no difference anyway, only the relative speeds and the fact time time slows down for moving objects relative to stationary ones.

"Relative to stationary ones" is too vague, you can only judge whether a clock slows down by picking a particular spacetime coordinate system (reference frame) and looking at how much coordinate time passes between ticks of a clock. In a non-inertial coordinate system, the usual time dilation formula doesn't apply, clocks which are moving in the rest frame of a non-inertial observer might even speed up rather than slowing down. Only if you're talking about a purely inertial observer does it make sense to say that clocks moving relative to that observer are guaranteed to slow down (and 'relative to that observer' is just shorthand for 'in that observer's inertial rest frame').

People claim if a spaecraft travels away from Earth, then turns around and comes back it is the same as if it had just traveled twice the distance in a straight line.

Who claims that, exactly? It's true that if you're calculating the time dilation of the spacecraft in the Earth's rest frame, then the speed is all that matters, it doesn't matter whether the ship turns around or not. But if you're interested in calculating the time elapsed on the Earth's clock from the point of view of a frame where the ship has an unchanging position coordinate, it certainly does matter whether the ship moves inertially or whether it accelerates at some point in its journey, because the normal time dilation equation only works in inertial frames.

From the point of view of A: A is stationary, B is moving. Time moves slower for B.
From the point of view of B: B is stationary, A is moving. Time moves slower for A.

Not if "from the point of view of" = "in the non-inertial rest frame of", in that case it's no longer guaranteed that the clock of a moving observer ticks slower than the clock of a stationary observer. This would be true if A and B were moving apart in a purely inertial manner, though.

Does time move slower for A or B when the clocks are compared?

You can only "compare" the clocks at a single location if one or both of them moves non-inertially, you have to specify whether this happens.

 

[Loonwolf]

You seem to be avoiding the questions I am asking!

Xezlec claimed "Of course when he gets out of the car he will be younger than the rest of us." Speaking of a very fast car instead of a spacecraft , but the same applies. Is this true?

But from the point of view/experience/frame of reference of the one in the car/ spacecraft , they stayed still, while the Earth was moving very fast. It was in fact the Earth that was accelerating instead of the car/ spacecraft . Is this true?

There doesn't even have to be ANY acceleration, just two bodies moving relative to each other.

And in the case of the two spacecraft moving away from each other, which one sees time slowed down when looking at the other moving relative to it?

The clocks do not have to be at a single location if you do not want them to be!

 

[JesseM]

You seem to be avoiding the questions I am asking!

No, I'm pointing out the ambiguity in your wording, and asking for clarification. If you don't answer my questions I can't help you--for example, can you address my first question about whether "experience" means what an observer sees visually or what is true in their rest frame or something else?

Xezlec claimed "Of course when he gets out of the car he will be younger than the rest of us." Speaking of a very fast car instead of a spacecraft , but the same applies. Is this true?

Xezlec implied the car was moving inertially the whole time with the statement "So the person in the rocket car, as long as he doesn't have any windows to see the outside world, has no idea that he is even moving" (if the car was moving non-inertially, the person in the car would feel G-forces and therefore know he was accelerating). If "we" are also assumed to be inertial observers, then it is true in our frame that the guy in the car has aged less at the end of the journey, but in the inertial frame where the car was at rest throughout the journey, the opposite will be true, it will be we who have aged less than the guy in the car. Since the end of the car's journey happens far away from us, this is just an illustration of how different frames disagree about simultaneity for events which happen far apart. If both we and the guy in the car are aged 20 when the car departs us, and the car moves away at 0.6c, then if the end of the journey is defined as the point where the guy in the car turns 28, in our inertial rest frame this event is simultaneous with the event of us turning 30 but in the car's inertial rest frame this event is simultaneous with the event of us turning 26.4, so the two frames disagree about who has aged less.

The clocks do not have to be at a single location if you do not want them to be!

If they are not at a single location, then there is no single frame-independent answer to which clock has elapsed more time, because different frames disagree about the simultaneity of distant events.

 

[jtbell]

There doesn't even have to be ANY acceleration, just two bodies moving relative to each other.

If one of the bodies doesn't accelerate, they can't re-unite in order to compare their clocks directly. There's no physical contradiction caused by each body's clock "running slow" in the other body's rest frame, after you take relativity of simultaneity into account.

(This is in the flat spacetime of special relativity; if the bodies are in free-fall along different paths under the influence of gravity, such that they can re-unite without having to fire rocket engines or whatever, then you have to analyze the results using general relativity.)

 

[Loonwolf]

The clocks do not have to be next to each other, just their values compared, wherever they are. There is no gravity, no firing of rocket engines, etc.

It seems people are trying to create confusion where there is none. I will start again and simplify the question...

There are two twins in spacecraft flying through empty space. Relative to each other each one is standing still from their own point of view, while the other is moving close to the speed of light.

Spacecraft A observes time passing normally, but since spacecraft B is moving very fast then time is moving slower for them, their clock shows an earlier time and the twin is younger.
Spacecraft B observes time passing normally, but since spacecraft A is moving very fast then time is moving slower for them, their clock shows an earlier time and the twin is younger.

Which twin is younger, which clock shows the earlier time?

 

[starthaus]

Spacecraft A observes time passing normally, but since spacecraft B is moving very fast then time is moving slower for them, their clock shows an earlier time and the twin is younger.
Spacecraft B observes time passing normally, but since spacecraft A is moving very fast then time is moving slower for them, their clock shows an earlier time and the twin is younger.

Which twin is younger, which clock shows the earlier time?

In the above scenario they are both the same age. Their clocks show the same exact elapsed time.

 

[Dale]

The clocks do not have to be next to each other, just their values compared, wherever they are. There is no gravity, no firing of rocket engines, etc.

It seems people are trying to create confusion where there is none. I will start again and simplify the question...

There are two twins in spacecraft flying through empty space. Relative to each other each one is standing still from their own point of view, while the other is moving close to the speed of light.

Spacecraft A observes time passing normally, but since spacecraft B is moving very fast then time is moving slower for them, their clock shows an earlier time and the twin is younger.
Spacecraft B observes time passing normally, but since spacecraft A is moving very fast then time is moving slower for them, their clock shows an earlier time and the twin is younger.

Which twin is younger, which clock shows the earlier time?

People are not trying to create confusion, they are trying to point out that your scenario as expressed is ill-posed. If you want to compare the value of two clocks that are not located right next to each other then you must specify which reference frame is being used to determine simultaneity. Due to the relativity of simultaneity different reference frames will disagree about simultaneity, and this disagreement will determine the outcome of your experiment.

So, once you specify which reference frame is used for the comparison then we can answer the question as to which clock shows the earlier time.

PS starthaus is assuming that you are referring to the reference frame where the clocks are moving apart at the same speed. If that is the reference frame that you want to use then starthaus' answer is correct, otherwise you will get a different answer.

 

[starthaus]

PS starthaus is assuming that you are referring to the reference frame where the clocks are moving apart at the same speed. If that is the reference frame that you want to use then starthaus' answer is correct, otherwise you will get a different answer.

If that's what he's asking, that's the appropiate answer he's going to receive. I have a hunch that next we'll hear something along the lines of the Dingle "paradox". :-)

 

[jtbell]

The clocks do not have to be next to each other, just their values compared, wherever they are.

If the clocks are not right next to each other, there is no way to compare their readings, that gives the same results in all inertial reference frames.

 

[starthaus]

If the clocks are not right next to each other, there is no way to compare their readings, that gives the same results in all inertial reference frames.

There is a way of comparing them, even if they aren't next to each other. This is a bastardization of the way the GPS works, one clock "transmits" its current digital reading to the other as a radio wave . The "receiving" clock" adjusts the received number for distance and relative speed .

So, in Loonwolf scenarion, if both clocks have been synchronized prior to launch and if their carrying spaceships have been moving inertially, the result of the above algorithm is that they will forever conclude that the "other" clock is "slow" by the same amount. This would be a nice experiment to run to verify Dingle's "paradox".

 

[Dale]

The "receiving" clock" adjusts the received number for distance and relative speed

That requires specifying the reference frame. jtbell is correct, unless they are next to each other there is no method to compare which gives the same result in all reference frames.

 

[Loonwolf]

For example, the spacecraft are moving towards each other (or else one is moving while the other is still, it makes no difference), then the two clocks can be next to each other for a moment if you REALLY need them to be.

It just seems to me people are making excuses why they can't answer the question simply. I don't want to hear the excuse, "Well, how would they be synchronised in the first place?" or anything like that, just looking for the simple answer to the question. They show the same time in the beginning.

If time moves more slowly for the moving object relative to the stationary one, but BOTH are moving and BOTH are stationary at the same time, depending on who is looking then there must be an answer that will satisfy, or else it's all nonsense.

And if you are saying they will show the same time then that's the same as saying that there is NO SUCH THING as this time dilation for fast moving objects, it's all a myth.

 

[Dale]

It just seems to me people are making excuses why they can't answer the question simply.

It is not our fault that you are giving an incomplete question and it is not our mistake that you refuse to specify important details when you are told that they are important. You need to specify the reference frame whenever you make any kind of comparison or measurement or setting of two distant clocks. Otherwise your question is simply incomplete.

What you are doing here is the equivalent of saying "what is 2 +" and then we respond by saying "2 + what" and then you claim that people are "making excuses" when they point out that your question is bad and needs more information.

Here is an example of a completely specified question: "Inertial clocks A and B are moving towards each from some distance apart and are initially synchronized in A's reference frame. Which clock reads less when they meet?" And the answer to that question is "B". Specifying the reference frame is not very difficult, I don't understand why you are so reluctant to do so.

 

[starthaus]

That requires specifying the reference frame. jtbell is correct, unless they are next to each other there is no method to compare which gives the same result in all reference frames.

The method works in either clock frame. In the case of GPS, the choice as which clocks "receives" the timestamp is the ground-based clocks since they need to be fabricated the cheapest possible way.

 

[starthaus]

And if you are saying they will show the same time then that's the same as saying that there is NO SUCH THING as this time dilation for fast moving objects, it's all a myth.

This is certainly wrong. From the perspective of an observer that sees the two clocks moving at the same speed v away from (or towards) him the two clocks show the same elapsed time in the case of your scenario. Compared to the observer's clock , both of the two moving clocks show less time than his clock. To fix the ideas:

Observer in the middle, sees T time elapsed on his clock and T*sqrt(1-(v/c)^2) time elapsed on the two clocks moving away (or towards) him with speed v.

 

[Dale]

The method works in either clock frame. In the case of GPS, the choice as which clocks "receives" the timestamp is the ground-based clocks since they need to be fabricated the cheapest possible way.

The GPS clocks are only synchronized in the earth-centered inertial frame (ECIF). Any time you are using GPS you are implicitly using the ECIF.

 

[starthaus]

The GPS clocks are only synchronized in the earth-centered inertial frame (ECIF). Any time you are using GPS you are implicitly using the ECIF.

Sure. I am not talking about synchronization, I am talking about the transmission of timestamps from the satellite clocks to the ground clocks. What I have said (repeatedly) is that this process can be used in comparing the clock readouts in lieu of reuniting the clocks.

 

[Dale]

Sure. I am not talking about synchronization, I am talking about the transmission of timestamps from the satellite clocks to the ground clocks. What I have said (repeatedly) is that this process can be used in comparing the clock readouts in lieu of reuniting the clocks.

Understood. What I have said (repeatedly) is that this procedure requires the specification of some reference frame as jtbell mentioned.

The point is that Loonwolf does not recognize that his question is incomplete, that he needs to specify the reference frame whenever he compares distant clocks. Your method of comparison will not relieve him of the need to specify the reference frame.

 

[JesseM]

For example, the spacecraft are moving towards each other (or else one is moving while the other is still, it makes no difference), then the two clocks can be next to each other for a moment if you REALLY need them to be.

But in this case different frames disagree about which clock was ahead of the other one in the past before they crossed paths, so different frames can still disagree about which clock has been ticking slower (and has elapsed more time since some previous moment) despite the fact that they both agree about what times the two clocks read when they meet. For example, suppose the two clocks are moving towards each other at 0.6c, and when they meet, clock A reads 30 years while clock B reads 28 years. Then in the rest frame of clock A, 10 years earlier clock A read 20 years while clock B also read 20 years, so in this frame clock B elapsed less time in the 10 years before they met. But in the rest frame of clock B, 10 years earlier clock A read 22 years while clock B read 18 years, so in this frame clock A elapsed less time in the 10 years before they met. Again it's just a matter of the relativity of simultaneity, the two frames cannot agree on how the readings of the two clocks compared when they were far apart.

It just seems to me people are making excuses why they can't answer the question simply. I don't want to hear the excuse, "Well, how would they be synchronised in the first place?" or anything like that, just looking for the simple answer to the question. They show the same time in the beginning.

It's not an "excuse", it's a basic feature of relativity that clocks far apart cannot be "synchronized" in any frame-independent way. If in one frame two clocks far apart "show the same time in the beginning", then in other frames the two clocks do not show the same time in the beginning, there's no getting around this in relativity. You seem to want a "simple answer" that is "simple" in the sense of rejecting the relativity of simultaneity, and thus in rejecting relativity itself!

 

[Loonwolf]

OK, I give up then, I'm never going to get my answer. It's a simple question. The two clocks showed the same time in the beginning. Whether they could or couldn't be synchronised in any "frame-independant way" when they are far away is irrelevant - I was specifically asking for the answer in the case when they WERE showing the same time in the beginning. They don't need to be physically synchronised, they just happen to be showing the same time in the beginning. - by coincidence if necessary. From BOTH reference frames they showed the same time in the beginning. There, specified.

When they are next to each other which clock is showing the earlier time? Why can I not get the answer to this simple question?

 

[JesseM]

OK, I give up then, I'm never going to get my answer. It's a simple question. The two clocks showed the same time in the beginning. Whether they could or couldn't be synchronised in any "frame-independant way" when they are far away is irrelevant - I was specifically asking for the answer in the case when they WERE showing the same time in the beginning.

It's still not clear whether you are understanding the relativity of simultaneity. There is no case where it is objectively true that they "were showing the same time in the beginning", if they were far apart. The very words "showing the same time in the beginning" only have meaning relative to a particular choice of coordinate system (a way of labeling events with position and time coordinates). No matter what physical procedure you use to synchronize the clocks at the beginning, there will be one inertial coordinate system where the events of both clocks showing some reading (12 noon, say) happen at the same t-coordinate in that system, and other inertial coordinate systems where the those same events happen at different t-coordinates so the clocks are out-of-sync. Saying the clocks were "showing the same time at the beginning" is like saying the clocks "had the same x-coordinate at the beginning"--this can only be true relative to a particular choice of how you orient your x-axis (one where the x-axis is perpendicular to the line between the two clocks), it would always be possible to describe the exact same physical situation using a different coordinate system with an x-axis oriented at a different angle so the same clocks don't have the same x-coordinate at the beginning.

If you understand that all claims about simultaneity are coordinate-dependent, and you're just asking about a case where we choose to use a coordinate system where the clocks are synchronized at the beginning, then just say so and no one will object to your question. But as long as you continue to use language like "the clocks show the same time at the beginning" without making clear you understand that this can only be true in one choice of coordinate system, people are going to continue to try emphasize this point about how simultaneity can only be defined in a coordinate-dependent way.

 

[Dale]

Whether they could or couldn't be synchronised in any "frame-independant way" when they are far away is irrelevant - I was specifically asking for the answer in the case when they WERE showing the same time in the beginning.

It is not irrelevant, it is critically important. Your statement that "they WERE showing the same time in the beginning" is meaningless because you aren't saying which reference frame it refers to. When you say that two distant clocks are showing the same time you have to specify the reference frame. It is as simple as that. Your failure to obtain an answer is because your question is incomplete, as you have been told over, and over, and over, ...

 

[thack45]

When they are next to each other which clock is showing the earlier time? Why can I not get the answer to this simple question?

Are you just wanting to understand why two initally syncronyzed clocks read different times after one of them has traveled at higher speeds for some time?

 

[Loonwolf]

So now people are saying that it is IMPOSSIBLE that one clock can be showing the same time as another clock which is in a different place? And that ten thousand billion trillion clocks all over the universe would each show a time that wasn't even approximately the same as any other?

There is NO physical procedure whereby the clocks are synchronised in the beginning. They just happen to be showing the same time, BY CHANCE.

I HAVE said which reference frame it refers to, BOTH.

OK, it's a case where we choose to use a coordinate system where the clocks are synchronized at the beginning. So nobody will now object to the question and will answer it?

I'm just wanting the simple answer to the question I have asked, when the two clocks are next to each other, which shows the earlier time?

 

[Dale]

So now people are saying that it is IMPOSSIBLE that one clock can be showing the same time as another clock which is in a different place?

Nobody said that, we simply said (repeatedly) that you have to specify the reference frame.

I HAVE said which reference frame it refers to, BOTH.

That is not possible. It is against the relativity of simultaneity. You have to pick one or the other or some third reference frame. It is not possible that it is simultaneous in more than one reference frame.

OK, it's a case where we choose to use a coordinate system where the clocks are synchronized at the beginning. So nobody will now object to the question and will answer it?

I'm just wanting the simple answer to the question I have asked, when the two clocks are next to each other, which shows the earlier time?

The one that was traveling faster in that "coordinate system where the clocks are synchronized at the beginning" will show the earlier time.

 

[JesseM]

So now people are saying that it is IMPOSSIBLE that one clock can be showing the same time as another clock which is in a different place? And that ten thousand billion trillion clocks all over the universe would each show a time that wasn't even approximately the same as any other?

There is NO physical procedure whereby the clocks are synchronised in the beginning. They just happen to be showing the same time, BY CHANCE.

You are either still misunderstanding or are willfully misrepresenting my point. You are talking as though there is some definite objective truth about whether two clocks are synchronized, and that I'm just saying that it's very hard to make it so they are synchronized at the beginning, that it can only happen by coincidence or something. But that's not it at all! What I'm saying is that the word "synchronized" itself has no objective frame-independent meaning, therefore it is impossible to have a situation where the clocks will be objectively synchronized at the beginning, not even by coincidence. If you just want the clocks to be synchronized in a non-objective way, relative to the coordinates of one particular frame, then it's very easy to come up with a procedure to ensure that!

If you are arguing in good faith and not willfully misrepresenting me, can you please address my analogy of the clocks "having the same x-coordinate at the beginning"? Specifically, please address these questions:

1. Do you agree that for any given pair of clocks at rest with respect to one another, we can find some coordinate system in which both clocks are at rest where the x-axis is oriented in such a way that both clocks have the same x-coordinate, and another coordinate system where both clocks are also at rest but with the x-axis at a different angle, such that the same two clocks have a different x-coordinate? Yes/No

2. If you agree with #1, then do you agree that means that it's impossible for two clocks to objectively have the same x-coordinate at the beginning, in a sense that doesn't depend on what coordinate system you use? That the very notion of "having the same x-coordinate at the beginning" can only make sense relative to a particular choice of coordinate system? Yes/No

I HAVE said which reference frame it refers to, BOTH.

Impossible. If the two clocks are moving inertially towards one another, and the clocks are synchronized at the beginning in one clock's rest frame, that automatically means they were not synchronized at the beginning in the other clock's rest frame.

OK, it's a case where we choose to use a coordinate system where the clocks are synchronized at the beginning. So nobody will now object to the question and will answer it?

Yes, in this case the question is perfectly sensible. If the two clocks are moving inertially towards each other, and they are initially synchronized relative to a particular choice of inertial coordinate system, then whichever clock has a higher velocity relative to that coordinate system will show a smaller time when the two clocks meet.

 

[Saw]

JesseM, what do you mean by "objective" and "objectively"? It seems to me you use the term as a pure synonim of "non-frame-dependent". If so, please confirm, I think it might help Loonwolf to understand the point.

 

[JesseM]

JesseM, what do you mean by "objective" and "objectively"? It seems to me you use the term as a pure synonim of "non-frame-dependent". If so, please confirm, I think it might help Loonwolf to understand the point.

Yes, that's basically all I mean, but if I just said "frame-independent" Loonwolf might get the idea that there was a real truth about the matter and that some frames were "wrong" while others were "right". I wanted to get across the idea that not only is simultaneity completely dependent on your choice of frame, but that there is also no physical basis for judging one frame's judgments about simultaneity to be more correct than any other's, since the laws of physics don't pick out a preferred frame.

 

[Saw]

Yes, that's basically all I mean, but if I just said "frame-independent" Loonwolf might get the idea that there was a real truth about the matter and that some frames were "wrong" while others were "right". I wanted to get across the idea that not only is simultaneity completely dependent on your choice of frame, but that there is also no physical basis for judging one frame's judgments about simultaneity to be more correct than any other's, since the laws of physics don't pick out a preferred frame.

Yes, you are saying that the two judgments about simultaneity are not only different (frame-dependent) but on equal footing = none is more correct. Agreed. I am not sure, though, that you should then say that none of them is objective, i.e. that what they share (equal footing) is their lack of objectivity. After all, each judgment is obtained through an objective measurement method: the Einstein convention for clock synchronization. In fact, some authors like to state the opposite, i.e. that the two judgments share (equal footing) their objectivity = they are not the result of a distorted perception due to the features of the observing subject.

In any case, whether you call them objective or not, what is important to highlight, in my opinion, is that simultaneity judgments are not final but "instrumental": they solve problems and they solve them in the same manner in all frames. So the mere fact that two observers disagree on simultaneity is not dramatic (it's not paradoxical); it would be problematic if that led to a disagreement on what happens and what does not, but such is not the case.