Understanding Time Dilation: How Fast Do You Have to Go?

[robphy]

JesseM, there is no problem for me to accept that "the math works out so it's always the one that accelerated that shows less total time." My point here was how do we determine who accelerated.

Sam, to determine who accelerated, take a look at the other thread
https://www.physicsforums.com/showthread.php?t=96775

 

[nemosum]

K, like I said in another thread of mine, I don't know all the mathematics for this kind of stuff, so go a little easy on me. Let's say that two men, Bob and Jon, are out in the middle of no-where, thousands of light-years away from anybody of mass. Bob is stationary, and Jon is traveling at a constant speed, fast enough that one year to him is 50 years to Bob. Jon is also flying straight toward Bob.

Jon--------> Bob

According to Jon, Bob is aging 50 times faster he is. And according to Bob, Jon is aging 50 times faster than he is. Right?
So, one Jon-year passes before Jon reaches Bob, then Jon stops abruptly. Bob would have aged 50 years while Jon only aged one, right? But if Jon doesn't stop, and merely passes Bob, than they would each see the other being 50 years older than themselves.
This is how I understand it, but it seems to me impossible, so I must not me getting something. Could someone enlighten me?

 

[jackle]

...My point here was how do we determine who accelerated...

We have already answered your question in this thread once. Here.

...you will experience G-forces when you accelerate in space, just like how when you're in a car that's accelerating you feel yourself pushed back into the seat. From the point of view of an inertial frame, this isn't a true "force" like gravity (it's sometimes called a http://www.hcc.hawaii.edu/~rickb/SciColumns/FictForce.04Feb96.html for this reason), it's just that the car seat is accelerating and it has to overcome the inertia of your body to accelerate it to the same speed. But from the point of view of your own non-inertial frame, it feels just like a force is pulling you backwards...

It is clear that the universe "knows" who is accelerating. When you swing a bucket round with water in, you can get it so it doesn't tip out but you can't do the trick by running fast around the bucket. This has been known about long before relativity. Please give it a go if you need to.

According such understanding of mine, from Bob's viewpoint Alice moves away and returns to him; from Alice's viewpoint Bob moves away and returns to her. According to this understanding of mine, either observer will find the other has accumulated more time (10 minuses), a symmetrical result.

Relative motion has to be constant before that type of symmetry exists.

 

[jackle]

...Bob would have aged 50 years while Jon only aged one, right?...

Jon and Bob start off separated by a lot of space-time. There is no moment in time that they can agree on to start counting how long they have aged (because of the space-time seperation, and relative motion). As nothing travels faster than light, Bob could send a light signal to tell Jon to start counting. Jon could then start counting but because Bob is traveling so quickly towards Jon, Jon receives the signal and Bob rushes past nearly as soon as the light gets there. The whole experiment is ruined! (Although we can get the result using maths...)

So, we can make Jon and Bob twins, and start them off in the same hospital ward. Then, we know from relativity that the traveling twin will age less, as explained previously.

 

[Sam Woole]

We have already answered your question in this thread once. Here.
It is clear that the universe "knows" who is accelerating. When you swing a bucket round with water in, you can get it so it doesn't tip out but you can't do the trick by running fast around the bucket. This has been known about long before relativity. Please give it a go if you need to.
Relative motion has to be constant before that type of symmetry exists.

As we could see from post #142, I was not alone in understanding the twin paradox in the way I did, that is, either twin can be considered as moving. Even Einstein said so: the railway station moves to the train or the train moves toward the station.

I have brought up my doubts about the shifting of ideas, from math to clocks. There was further shift, from clocks to humans. When Bob's clock accumulated 10 more minutes than Alice's clock, relativists believed Bob was 10 minutes older than Alice. Such belief means, something moving toward the Earth will cause differential aging. If this is good science, then what can we deduce from the fact that photons are moving toward the earth? Of course there is a huge host of other things moving toward our Earth such as muons, meteors, solar wind, etc. Are they causing differential aging?

 

[russ_watters]

As we could see from post #142, I was not alone in understanding the twin paradox in the way I did, that is, either twin can be considered as moving. Even Einstein said so: the railway station moves to the train or the train moves toward the station. [emphasis added]

Again, moving and accelerating are not the same thing. You keep missing that and post #142 does not mention it. Please acknowledge that: you seem, to be ignoring it.

...then what can we deduce from the fact that photons are moving toward the earth?

Nothing relevant here: photons always move at C and have no rest frame.

Are they causing differential aging?

No. Where are you getting that idea?

It seems you are still looking for things that are slowing down physical processes and ignoring the simple and obvious possibility that physical processes do not vary in rate, but rather that time itself is observer dependant.

 

[mfox]

afbla

Time dilation occurs at any speed. It's only a matter of how large the effect is. In fact, with electric currents traveling in wires, the effect that we call electromagnetism is due entirely to Lorentz contraction (which has a magnitude equal to the time dilation). That easily measurable effect occurs with speeds of a cm per second and lower.
Mike

 

[Phantom]

As we could see from post #142, I was not alone in understanding the twin paradox in the way I did, that is, either twin can be considered as moving. Even Einstein said so: the railway station moves to the train or the train moves toward the station.
I have brought up my doubts about the shifting of ideas, from math to clocks. There was further shift, from clocks to humans. When Bob's clock accumulated 10 more minutes than Alice's clock, relativists believed Bob was 10 minutes older than Alice. Such belief means, something moving toward the Earth will cause differential aging.

Theres the error, the mistaken conclusion, that is giving you all these problems with understanding this particular relativistic effect..

In fact it does not matter at all, in which direction (vector) the acceleration is. It is the differential in accelerations (inertial shift), that is responsible for the observed effect of "time dilation".

Although I have not thoroughly read all 10 pages of this thread, I scanned most of them and did not see that anyone had mentioned that the effect has been empirically observed. With experimental confirmation of the relativistic prediction, in accordance with the theory, what other explanation can you provide to account for the finding?

If this is good science, then what can we deduce from the fact that photons are moving toward the earth? Of course there is a huge host of other things moving toward our Earth such as muons, meteors, solar wind, etc. Are they causing differential aging?

As I have pointed out, this conjecture is based on a false premise. The movement of objects towards Earth does not cause differential aging ; unless you are talking about an object that was once in Earth's inertial frame, was removed and accelerated to relativistic speeds and is now returning. A clock of that object would demonstrate the predicted "differential aging" in accordance with the theory.

Special relativity is a non-intuitive theory with many apparent "paradoxes"...thats precisely the part that people struggle with. Particularly, as you do, with the concept of simultaneity. It feels "wrong". But, it is not. Keep plugging away, you'll get it eventually.

 

[Sam Woole]

Again, moving and accelerating are not the same thing. You keep missing that and post #142 does not mention it. Please acknowledge that: you seem, to be ignoring it.

I agree that moving and accelerating are not the same thing. But according to my understanding of Einstein's theory, it is the relative uniform motion that is causing time dilation. From the viewpoint of the observers on the railway station, time dilation will happen on the train; from the viewpoint of observers on the train, time dilation will happen on the railway station. Post #142 explicitly said so; either person (Bob or Jon) is considering the other aging 50 times faster. Many other people understood Einstein's time dilation in the same way as I did. This implies that Einstein's theory gives self-contradictory results such as a>b and a<b; Bob older than Jon and also younger than Jon.

 

[Doc Al]

I agree that moving and accelerating are not the same thing. But according to my understanding of Einstein's theory, it is the relative uniform motion that is causing time dilation.

OK.

From the viewpoint of the observers on the railway station, time dilation will happen on the train; from the viewpoint of observers on the train, time dilation will happen on the railway station.

Time dilation is not something that happens "over there"; it is a relationship of time and space between moving frames. Let's rephrase these statements more accurately:

As measured by observers on the railway platform, clocks on the train will run slowly; As measured by observers on the train, clocks on the railway platform will run slowly.

Post #142 explicitly said so; either person (Bob or Jon) is considering the other aging 50 times faster. Many other people understood Einstein's time dilation in the same way as I did. This implies that Einstein's theory gives self-contradictory results such as a>b and a<b; Bob older than Jon and also younger than Jon.

You still seem to think that a moving reference frame that observes time dilation somehow physically affects the moving clock. That if the train observes the platform clocks, these platform clocks are somehow slowed with respect to everyone. Not true.

I strongly suggest that you pick up a book, if you are really interested in learning relativity, and study it systematically.

 

[russ_watters]

I agree that moving and accelerating are not the same thing. But according to my understanding of Einstein's theory, it is the relative uniform motion that is causing time dilation. From the viewpoint of the observers on the railway station, time dilation will happen on the train; from the viewpoint of observers on the train, time dilation will happen on the railway station. Post #142 explicitly said so; either person (Bob or Jon) is considering the other aging 50 times faster. [snip] This implies that Einstein's theory gives self-contradictory results such as a>b and a<b; Bob older than Jon and also younger than Jon.

In addition to what Doc said, the simplest way to resolve the apparent contradiction is to bring the two clocks together to compare them. And doing that requires an acceleration of one or both clocks. When you do that, you have unbalanced what used to be a perfectly symmetrical situation.

Before one observer accelerates, either can be considered stationary. Afterwards, only one can, because you can feel the acceleration.

[snop]Many other people understood Einstein's time dilation in the same way as I did.

Just because a lot of people misunderstand it in the same way, doesn't make their misunderstandings correct.

Be pragmatic about it: If relativity "worked" the way you think it does, you are correct that it wouldn't work. But scientists and engineers think relativity works in a different way, and in that way, it does work. So even if Einstein meant what you think he did, you'd still be wrong because Einstein doesn't own relativity. It has grown beyond his contribution and if this was an error, it has now been corrected.

 

[Sam Woole]

In addition to what Doc said, the simplest way to resolve the apparent contradiction is to bring the two clocks together to compare them. And doing that requires an acceleration of one or both clocks. When you do that, you have unbalanced what used to be a perfectly symmetrical situation.
Before one observer accelerates, either can be considered stationary. Afterwards, only one can, because you can feel the acceleration. .

Your words made us to think that Einstein's theory was like a child's play. Unless we sit clocks together, we would not know their difference. But DrGreg's demonstration showed quite the opposite. It showed that we became aware of the difference between the two clocks even if the clocks, Bob and Alice, were many light minutes apart, which is a huge distance.

Your argument on acceleration also contradicted DrGreg's demonstration, which stated that the motion was constant. In a constant motion, how can any observer "feel" the motion?

Just because a lot of people misunderstand it in the same way, doesn't make their misunderstandings correct.

To me, it is you who were misunderstanding, not me. Let me show you why.

In DrGreg's demonstration, there was a constant distance between Bob and Alice, say d; a constant v, and a constant c. Light needs 20 minutes to travel the d, while Alice needs 120 minutes. The time interval 120 minutes is Newtonian time, absolute time, obtainable by means of Newton's equation t = d/v. It is also the normal time we all earthlings stationary on Earth will get. Don't you agree?

My understanding of time dilation is, the moving clock will suffer time dilation, accumulating less time. Less than what? I believe it is less than the normal, absolute time that clocks stationary on Earth would get. That is, Alice's clock should accumulate less than 120 minutes. The traveling twin will become younger while the earthbound twin will age normally.

But DrGreg's demonstration did not show such a time dilation. Instead it showed that the moving observer Alice accumulated exactly normally, 120 minutes, aging normally, while her motion had caused the stationary clock to accumulate more than 120 minutes, aging faster. Don't you think that you were misunderstanding?

This is as if to say, scientists such as Hafele and Keating claimed that they could make the clocks stationary on Earth to work faster by transporting other clocks in the air. I think this was worse than misunderstanding.

As I have pointed out earlier, such a demonstration of DrGreg's led to the deduction that, any thing moving toward Earth will cause life forms there to age faster. If this deduction is false (It must be), I think time dilation is false likewise, impossible to be understood properly.

 

[DrGreg]

Your argument on acceleration also contradicted DrGreg's demonstration, which stated that the motion was constant. In a constant motion, how can any observer "feel" the motion?

Half way through my demonstration Alice did a U-turn. That part wasn't constant. She would have felt a huge G-force as she decelerated and then sped off in the opposite direction. Bob would have felt no G-force at all.

To me, it is you who were misunderstanding, not me. Let me show you why.
In DrGreg's demonstration, there was a constant distance between Bob and Alice, say d;

It wasn't constant, it was changing all the time.

a constant v, and a constant c. Light needs 20 minutes to travel the d, while Alice needs 120 minutes. The time interval 120 minutes is Newtonian time, absolute time, obtainable by means of Newton's equation t = d/v. It is also the normal time we all earthlings stationary on Earth will get. Don't you agree?

There is no such thing as “absolute time”. Everyone has their own time.

My understanding of time dilation is, the moving clock will suffer time dilation, accumulating less time. Less than what?

A very good question. All dilation is one clock relative to another clock.

I believe it is less than the normal, absolute time that clocks stationary on Earth would get. That is, Alice's clock should accumulate less than 120 minutes. The traveling twin will become younger while the earthbound twin will age normally.

But DrGreg's demonstration did not show such a time dilation. Instead it showed that the moving observer Alice accumulated exactly normally, 120 minutes, aging normally, while her motion had caused the stationary clock to accumulate more than 120 minutes, aging faster. Don't you think that you were misunderstanding?

But Alice is now 10 minutes younger than Bob. Isn't this what you said in the previous paragraph?



What makes you think the Earth is “stationary” anyway? It’s moving round the sun, the sun is moving round the galaxy, the galaxy is receding from other galaxies…

Everything moves relative to something else!

 

[jackle]

Your words made us to think that Einstein's theory was like a child's play. Unless we sit clocks together, we would not know their difference

If two objects are experiencing each other's clocks/time-system to be going slowly compared to their own, their clocks can not agree on two events being simultaneous. (Although, Post 65 uses Synchronization by being in the same place, instead of by going at the same speed, which can be valid). You can use relativity to work out what each person sees, but you can not choose a time that their clocks will both agree on to analyse, when they are separated and also in relative motion. If you want the clocks to go at the same speed and be instantly comparable at a glance, you must bring them together. Alternatively, loose yourself in the maths and definitions.

 

[jackle]

But DrGreg's demonstration showed quite the opposite. It showed that we became aware of the difference between the two clocks even if the clocks, Bob and Alice, were many light minutes apart, which is a huge distance.

DrGreg's demonstation from post 68 was done using relativity and maths. The acceleration in the scenario also meant that there is a "right" answer not a symmetrical situation.

Your argument on acceleration also contradicted DrGreg's demonstration, which stated that the motion was constant. In a constant motion, how can any observer "feel" the motion?

DrGreg in post 68 demonstrates the twin paradox, based on acceleration.

In DrGreg's demonstration, there was a constant distance between Bob and Alice, say d; a constant v, and a constant c.

Which post number?

My understanding of time dilation is, the moving clock will suffer time dilation, accumulating less time. Less than what? I believe it is less than the normal, absolute time that clocks stationary on Earth would get.

There is no absolute time in relativity. Discard this notion if you wish to understand the theory.

But DrGreg's demonstration did not show such a time dilation. Instead it showed that the moving observer Alice accumulated exactly normally, 120 minutes, aging normally, while her motion had caused the stationary clock to accumulate more than 120 minutes, aging faster.

Motion doesn't cause stationary clocks to age faster in relativity. Instead, a different path through space-time leads to a different amount of aging.

As I have pointed out earlier, such a demonstration of DrGreg's led to the deduction that, any thing moving toward Earth will cause life forms there to age faster. If this deduction is false (It must be), I think time dilation is false likewise, impossible to be understood properly.

You can only understand it if you do not dismiss the ideas like you have been. You also need to correct the recurring mistakes in your understanding of the theory to get a clear picture of it.

 

[Sam Woole]

Half way through my demonstration Alice did a U-turn. That part wasn't constant. She would have felt a huge G-force as she decelerated and then sped off in the opposite direction. Bob would have felt no G-force at all.

Sorry, your responses were making the dilation idea less and less credible. Here you said "she decelerated". What does it mean? When did she begin her deceleration? And "she sped off", what does it mean? Did she also speed off when she started her journey from Bob? All your words meant (to me) Alice was traveling at variable speeds, not one constant speed. If so, then Alice could not cover equal distances in equal time intervals. But your demonstration showed equal distances in all equal time intervals. Your acceleration argument violated your own design.

"She sped off" means, she begins with 0 miles per second and accelerates to 1, 2, 3,...n miles per second. Due to the very low speeds in the beginning, and the low speeds in her final stage reaching Ted, she might need to accelerate so much as to surpass the c in her mid motions, otherwise how can she finish the distance (between Bob and Ted) in one hour? I believe you were making things worse and worse for the time dilation idea.

Even if I accept that Alice experienced accelerations and decelerations, the G-force, such a situation would still work against you. This situation meant, pursuant to your demonstration, that the moving observer Alice's experience with G-force will not dilate her own time. Instead, a stationary observer Bob's time, many light minutes away from the moving observer, will be expanded. An instantaneous action took place as a result of Alice's acceleration and deceleration.

I believe you were making things worse and worse.

It wasn't constant, it was changing all the time.

This sentence of yours was given in response to my statement that there was a constant distance between Bob and Alice. I am sorry, I typed in the wrong name. I meant a constant distance between Bob and Ted. It should be understandably so because I gave 120 minutes for Alice to cover such a distance. I wish jackle would take note of my clarification.

What makes you think the Earth is “stationary” anyway? It’s moving round the sun, the sun is moving round the galaxy, the galaxy is receding from other galaxies…
Everything moves relative to something else!

This one I think was not my mistake. My words were "clocks stationary on earth".

The motion of the Earth was used by SR dissidents to attack the twin paradox. In response SR supporters came up with acceleration and G-force and so forth. But as I have pointed out above, the acceleration argument will not convince dissidents like me either.

 

[JesseM]

Even if I accept that Alice experienced accelerations and decelerations, the G-force, such a situation would still work against you. This situation meant, pursuant to your demonstration, that the moving observer Alice's experience with G-force will not dilate her own time. Instead, a stationary observer Bob's time, many light minutes away from the moving observer, will be expanded. An instantaneous action took place as a result of Alice's acceleration and deceleration.

Your use of the phrase "instantaneous action" doesn't really make sense to me here. Alice's clock rate changes relative to Bob's coordinate system, but Bob doesn't actually experience any instantaneous effects where he's sitting at the moment Alice changes velocities. It might help to consider coordinate systems created physically in the way Einstein did in his paper--imagine each inertial observer has a giant grid of rulers filling space, and each observer's grid is at rest relative to himself. At each marking on an observer's grid, there is a clock attached to the ruler, and all the clocks have been "synchronized" using light-signals (for an illustration, take a look at fig. 16 at the bottom of http://www.physicspost.com/articles.php?articleId=88&page=5 ). So to identify the space and time coordinates of an event, a given observer just has to look at the markings on the rulers in his system that were right next to the event as it happened, and look at the time on the clock in his system that was right next to the event as it happened. So, for example, if the event of Alice's clock reading "80 seconds" happened as she passed the clock in Bob's system that read "100 seconds", and the event of Alice's clock reading "96 seconds" happened as she passed another clock in Bob's system that read "120 seconds", then in Bob's system her clock had only ticked 96-80 = 16 seconds when 120-100 = 20 seconds had passed in his own coordinate system, so her clock was only ticking at 0.8 the normal rate in his system. But suppose that immediately after Alice's clock read 96 seconds, she changed velocities, and then later when her clock read "102 seconds", she was passing a third clock in Bob's system that read "130 seconds". Now her clock has only ticked 102-96 = 6 seconds while 130-120 = 10 seconds have passed in Bob's coordinate system, so her clock is only ticking at 0.6 the normal rate in his system. But there's nothing "instantaneous" going on here, because we're talking about local readings on different clocks that are all located at different spots in Bob's giant ruler/clock grid, Bob won't actually know about the change until the light from these local readings has had time to reach him at the center of the grid.

 

[Janus]

Sorry, your responses were making the dilation idea less and less credible. Here you said "she decelerated". What does it mean? When did she begin her deceleration? And "she sped off", what does it mean? Did she also speed off when she started her journey from Bob? All your words meant (to me) Alice was traveling at variable speeds, not one constant speed. If so, then Alice could not cover equal distances in equal time intervals. But your demonstration showed equal distances in all equal time intervals. Your acceleration argument violated your own design.

In such thought experiments you can make the acceleration phases of the trip as short as you want (By increasing the rate of acceleration), to the point where they are neglible when compared to the total trip time.

"She sped off" means, she begins with 0 miles per second and accelerates to 1, 2, 3,...n miles per second. Due to the very low speeds in the beginning, and the low speeds in her final stage reaching Ted, she might need to accelerate so much as to surpass the c in her mid motions, otherwise how can she finish the distance (between Bob and Ted) in one hour? I believe you were making things worse and worse for the time dilation idea.

Again, we can make this acceleration phase as short as we want. Also, as she accelerates, see will see the distance between Bob and Ted contract. It is this contracted distance that she traverses, and why her clock only records 1 hr to make the trip according to her.

Even if I accept that Alice experienced accelerations and decelerations, the G-force, such a situation would still work against you. This situation meant, pursuant to your demonstration, that the moving observer Alice's experience with G-force will not dilate her own time. Instead, a stationary observer Bob's time, many light minutes away from the moving observer, will be expanded. An instantaneous action took place as a result of Alice's acceleration and deceleration.
I believe you were making things worse and worse.

What happens is that the aceleration experienced by Alice affects her determination of how fast time is progressing for Bob during that period.

The motion of the Earth was used by SR dissidents to attack the twin paradox. In response SR supporters came up with acceleration and G-force and so forth. But as I have pointed out above, the acceleration argument will not convince dissidents like me either.

What actually happened is that the "SR dissidents", after dipping their toes into SR, came up with what they thought was an argument against it. Then others pointed out that the argument didn't take everything into account. They did not "come up" with it, it was always a part of SR. The dissidents just never delved deeply enough into the theory to learn that, and now that they've 'staked out their claim', they refuse to budge.

 

[Sam Woole]

Your use of the phrase "instantaneous action" doesn't really make sense to me here. Alice's clock rate changes relative to Bob's coordinate system, but Bob doesn't actually experience any instantaneous effects where he's sitting at the moment Alice changes velocities.

My instantaneity charge referred to DrGreg's demonstration only. For example, in post #68, Alice started her return trip and applied the 3/2 rate. When Alice's clock accumulated 10 minutes (showing 13:10), the application of the 3/2 rate made Bob's clock to accumulate 15 minutes (showing 12:55). This accumulation must take place instantaneously, otherwise Bob's clock could not have produced the end result of 14:10. Namely as soon as Alice started to return, Bob's clock instantaneously started to work faster; Bob did experience an instantaneous effect pursuant to DrGreg's demonstration.

 

[Sam Woole]

What happens is that the aceleration experienced by Alice affects her determination of how fast time is progressing for Bob during that period.

I took your words above to mean, Alice's determination had been executed by Bob's clock. For example, at her time 13:10 (post #68), Alice determined that Bob's clock should read 12:15. As soon as she made such a determination, Bob's clock obeyed and executed 12:15. Since her determination was made when she was many light minutes away from Bob, wasn't the execution an instantaneous action? It must be, otherwise Bob's clock could not have produced the 14:10 at the end.

DrGreg's demonstration means to me, you people were using faster-than-light speeds to justify Einstein's theory.

 

[jtbell]

What happens is that the aceleration experienced by Alice affects her determination of how fast time is progressing for Bob during that period.

I took your words above to mean, Alice's determination had been executed by Bob's clock.

I took Janus's "determination" to mean "perception", or alternatively, "calculation" or "prediction", without any implication of causation. Bob's clock of course has no way of "knowing" how Alice is moving, nor whether she is changing her state of motion or not.

Similarly, my desk has no idea of what direction I am observing it from. Nevertheless, the angle from which I view it determines the shape that I perceive, and as I walk around the desk, its apparent shape (more precisely a two-dimensional projection of its three-dimensional shape) changes.

 

[JesseM]

My instantaneity charge referred to DrGreg's demonstration only. For example, in post #68, Alice started her return trip and applied the 3/2 rate. When Alice's clock accumulated 10 minutes (showing 13:10), the application of the 3/2 rate made Bob's clock to accumulate 15 minutes (showing 12:55). This accumulation must take place instantaneously, otherwise Bob's clock could not have produced the end result of 14:10. Namely as soon as Alice started to return, Bob's clock instantaneously started to work faster; Bob did experience an instantaneous effect pursuant to DrGreg's demonstration.

If you keep track of the difference between when things happen in Bob's coordinate system (which as I said in my last post, can be understood in terms of local readings on a large grid of rulers and synchronized clocks at rest relative to Bob) and when he sees them happen using light-signals, you'll see that there is no instantaneity here. In post #110 I explained when certain events would happen in Bob's coordinate system--for example, in Bob's coordinate system Alice would turn around at 13:05 (in that post I actually said 13:04.998, but that was a roundoff error), but he does not actually see her turn around until his clock reads 13:30. Since she departed at 12:00 and was moving at v=0.3846154c in his coordinate system, at t=13:05 she would have been traveling for 65 minutes at v=0.3846154c, so her distance would be 65*0.3846154=25 light-minutes. So if she turns around at 13:05 in his coordinate system, the light from this event will take 25 minutes to reach Bob, so he won't see it until 13:05 + 25 = 13:30. And not until 13:30 does he see the rate of her clock ticks change.

Another way of thinking about this is in terms of Bob's grid of rulers and synchronized clocks--when his own local clock reads 13:30, if Bob looks through his telescope at Alice, he will see her fire her rockets to turn around right when she is next to a marking on his ruler that reads "25 light-minutes", and he will see through the telescope that the clock attached to that position on the ruler reads "13:05 minutes". So he will conclude that although he's only seeing it now, the event of her turning around "really" happened 25 minutes ago in his frame (just like if you look at a supernova thousands of light-years away, you know that event really happened thousands of years ago).

 

[Sam Woole]

I took Janus's "determination" to mean "perception", or alternatively, "calculation" or "prediction", without any implication of causation. Bob's clock of course has no way of "knowing" how Alice is moving, nor whether she is changing her state of motion or not.
Similarly, my desk has no idea of what direction I am observing it from. Nevertheless, the angle from which I view it determines the shape that I perceive, and as I walk around the desk, its apparent shape (more precisely a two-dimensional projection of its three-dimensional shape) changes.

I felt your "desk" simile was supportive to my dissenting voice. If we apply this simile to DrGreg's demonstration, we saw its flaw clearly. That is, regardless how Alice perceived (or determined, or calculated), her perception cannot change the properties of Bob's clock; our perception of our desk cannot change its properties. It follows that the twin paradox, time dilation, differential aging are all false.

 

[russ_watters]

I felt your "desk" simile was supportive to my dissenting voice. If we apply this simile to DrGreg's demonstration, we saw its flaw clearly. That is, regardless how Alice perceived (or determined, or calculated), her perception cannot change the properties of Bob's clock; our perception of our desk cannot change its properties. It follows that the twin paradox, time dilation, differential aging are all false.

Oy! After 11 pages, that is where your understanding is?

Maybe it's time to throw some reality back into this: you do understand that the GPS system test's SR and GR's time dilation predictions, in addition to successfully dealing with the relativity of simultenaity, on a constant basis, right?

It almost seems like what you aren't able to get your arms around (or simply refuse to accept) is that when looking at someone else's clock through a telescope, it takes time for the signal to reach you, so what you see through the telescope isn't what the clock shows now. And you can run yourself in circles until smoke comes out of your ears trying to figure out when "now" is, or you can simply accept that the concept of "now" is observer dependant. Saying that I see a certain time on a clock, while calculating that the person standing next to it sees a different time does not imply that the clock is showing two different times at the same time!

IfI'mlookingthroughatelescopeataclockthenwhatIseenowisn'tnowontheclockbutwhatisnowontheclockisdifferentfromwhat
Iseesohowcantheclockhavetwodifferentreadingsonitatthesametime?

 

[DrGreg]

For example, at her time 13:10 (post #68), Alice determined that Bob's clock should read 12:15.

I have just gone back and looked at post #68. I can't find anything in that post that would support this assertion.

I would prefer to use the tables I used in https://www.physicsforums.com/showpost.php?p=791307&postcount=103" (instead of #68) as they are less likely to misinterpretation. Can you please reformulate your assertion in terms of these tables and then explain it?

 

[Sam Woole]

I have just gone back and looked at post #68. I can't find anything in that post that would support this assertion.
I would prefer to use the tables I used in https://www.physicsforums.com/showpost.php?p=791307&postcount=103" (instead of #68) as they are less likely to misinterpretation. Can you please reformulate your assertion in terms of these tables and then explain it?

It was the same message regardless which table we follow. In tables in post #103, you used numbers different from post #68. These numbers were more likely to be misinterpreted by me, not less. If you don't mind, I suggest simpler numbers such as 0 minutes to begin with. At 60 minutes, Alice would have reached Ted like this:
Bob's clock-----image in Alice telescope---Alice's clock
60 minutes ------------40------------------60 minutes.

According to the supernova example pointed out by JesseM, as well as to the delay pointed by you, though Alice saw 40 in her telescope, yet she knew the true number on Bob's clock was 60, the same like her own.

Now Alice would start to return. Your table in post #103 showed that Bob's clock eventually accumulated 10 more minutes than Alice's. In order to accumulate these additional minutes, of course there must be a beginning, from 1,2,3... 10. I charged that this "beginning" was an instantaneous action resulted from Alice's return.

Let me repeat, when Alice reached Ted, both clocks had equal time, 60 minutes. Only after this point, Bob's clock started to have more minutes than Alice's as a result of the 3/2 rate.

If you refer to my post #163, I do not believe that the application of the Doppler effect or the 3/2 rate can cause Bob's clock to work faster. You may have any kind of calculations, but you cannot change the properties of Bob's clock by means of calculations.

 

[JesseM]

It was the same message regardless which table we follow. In tables in post #103, you used numbers different from post #68. These numbers were more likely to be misinterpreted by me, not less. If you don't mind, I suggest simpler numbers such as 0 minutes to begin with. At 60 minutes, Alice would have reached Ted like this:

Bob's clock-------image in Alice telescope---------Alice's clock
60 minutes ---------------40-----------------------60 minutes.

According to the supernova example pointed out by JesseM, as well as to the delay pointed by you, though Alice saw 40 in her telescope, yet she knew the true number on Bob's clock was 60, the same like her own.

NO! As I've said to you many times, the slowdown of Alice's clock as seen by Bob is not just due the delays in light-signals, it's also due to genuine time dilation, so even after he takes into account the delay, he will still conclude that Alice's clock is running slower than hers. Likewise, Alice will also conclude that Bob's clock is running slower than hers, even after she takes into account the signal delay.

As I said in my previous post, Bob will see Alice turn around at 13:30 according to his own clock, and when he takes into account the light-signal delay (based on the fact that her distance when she turned around was 25 light-minutes from him), he will conclude that this event really happened at 13:05 in his frame. Since his clock read 12:00 at the moment they departed from each other, in his frame Alice way flying away for 1 hour and 5 minutes before she turned around. But at the moment Alice turns around, Bob can see that her clock read 16:00 at that moment, and since her clock read 15:00 at the moment she departed, Alice was only flying away for 1 hour and 0 minutes according to her own clock! So you can see that even after taking into account light signal delay, Bob concludes that Alice's clock was running slow, due to time dilation.

Now look at things from Alice's point of view. From her perspective, when she turned around, if she looked through a telescope she would see Bob's clock reading 12:40 at that moment. If she has her own grid of rulers at rest relative to herself, she will see that at that moment, he was about 16.666... light-minutes away in her frame. Since her own clock read 16:00 at the moment she saw this, she would conclude that the event of his clock ticking 12:40 really happened at 16:00 - 16.666... = 15:43.333... minutes in her frame. So after taking into account signal delays, she concludes that her clock had elapsed 43.333... minutes at the moment that his clock had elapsed 40 minutes, meaning his clock was genuinely running slower than hers in her own frame.

If you refer to my post #163, I do not believe that the application of the Doppler effect or the 3/2 rate can cause Bob's clock to work faster. You may have any kind of calculations, but you cannot change the properties of Bob's clock by means of calculations.

Do you understand that the formula for the doppler effect in relativity is different from the formula for the doppler effect in classical mechanics (say, the doppler effect with sound waves), and that this difference is because the relativistic formula was derived using the assumption that time dilation is real?

 

[DrGreg]

It was the same message regardless which table we follow. In tables in post #103, you used numbers different from post #68. These numbers were more likely to be misinterpreted by me, not less. If you don't mind, I suggest simpler numbers such as 0 minutes to begin with. At 60 minutes, Alice would have reached Ted like this:

Bob's clock-------image in Alice telescope---------Alice's clock
60 minutes ---------------40-----------------------60 minutes.

In the above line you are making an assumption that Alice’s clock shows 60 minutes “at the same time as” Bob’s clock shows 60 minutes (whatever that means). In other words you are assuming that Bob and Alice’s clocks remain synchronized. That is the very thing my argument is trying to disprove. If you simply assume that whatever I am trying to demonstrate is wrong, how can I demonstrate anything? You have to let go of your assumptions and ask what if clocks didn’t remain synchronized? Would it make sense? That’s what Einstein did and came to the conclusion “yes”.

According to the supernova example pointed out by JesseM, as well as to the delay pointed by you, though Alice saw 40 in her telescope, yet she knew the true number on Bob's clock was 60, the same like her own.

Alice does not know what the true number is, unless she performs a relativistic calculation (in which case she will calculate approximately 55 minutes 23 seconds (¹²/₁₃ hours).

This is the reason I prefer to use the numbers in post #103, so that you are less likely to misinterpret 13:00 on Bob’s clock as being “the same time as” 16:00 on Alice’s clock. Alice and Bob have different definitions of simultaneity and do not agree on this. Bob’s assessment is that Alice’s 16:00 occurs at his 13:05 (see JesseM’s post). Alice’s assessment, whilst traveling away from Bob, is that Bob’s 13:00 would occur at her 16:05 (if she were to keep on traveling away instead of turning round).

To give an analogy: when you measure the length of a rod you wouldn’t measure the two ends using two different rulers. So, to measure an interval of time you can’t measure the start and the end using two different clocks. You can’t measure the time it takes for light to travel from Bob to Alice by measuring the start with Bob’s clock and the end with Alice’s clock.

 

[Sam Woole]

NO! As I've said to you many times, the slowdown of Alice's clock as seen by Bob is not just due the delays in light-signals, it's also due to genuine time dilation, so even after he takes into account the delay, he will still conclude that Alice's clock is running slower than hers. Likewise, Alice will also conclude that Bob's clock is running slower than hers, even after she takes into account the signal delay.
As I said in my previous post, Bob will see Alice turn around at 13:30 according to his own clock, and when he takes into account the light-signal delay (based on the fact that her distance when she turned around was 25 light-minutes from him), he will conclude that this event really happened at 13:05 in his frame. Since his clock read 12:00 at the moment they departed from each other, in his frame Alice way flying away for 1 hour and 5 minutes before she turned around. But at the moment Alice turns around, Bob can see that her clock read 16:00 at that moment, and since her clock read 15:00 at the moment she departed, Alice was only flying away for 1 hour and 0 minutes according to her own clock! So you can see that even after taking into account light signal delay, Bob concludes that Alice's clock was running slow, due to time dilation.

I did read your recent posts but I am sorry I could not understand them. Currently DrGreg was trying to prove that time dilation is genuine, while I was trying to show his proof was flawed. Flawed or not, I believe we cannot use time dilation to justify an experiment designed to prove time dilation. It was tantamount to using a flaw to justify a flaw.

Because of your use of the time dilation, you gave more and more numbers that never appeared in DrGreg's demonstration. These numberbs complicated matters more and more, leading to more difficulties and arguments. For instance you said the distance between Bob and Alice (at Ted) was 25 light-minutes.

based on the fact that her distance when she turned around was 25 light-minutes from him

. How could I understand this 25 light-minutes? Very difficult.

I wish you would not give any more numbers. Whether DrGreg's demonstration is flawed or not, I believe we must justify it according to only those numbers he has given. No more new numbers.

Not only no more new numbers, we should simplifiy them. For instance, when the two clocks came together to compare, Bob's clock read 14:10 and Alice's read 17:00. The result of the comparison is: Alice's clock had worked a lot faster than Bob's, the traveled twin had become a lot older.

 

[JesseM]

I did read your recent posts but I am sorry I could not understand them.

What about them didn't you understand? Do you understand, for example, that if I see an event through a telescope that's 25 light-minutes away, then if I assume light travels at c in my frame, that must mean the event actually happened 25 minutes before I saw it? That's just the same principle as the idea that if we spot a supernova today happening 10,000 light-years away, it must have actually happened 10,000 years ago. And that's really all you need to understand my recent posts, all I was ever doing was showing the time that Alice or Bob saw a reading on the other one's clock, then subtracting the light-signal delay to figure out when the other one's clock was "really" showing that reading. I know all the numbers may look a little intimidating, but I think you can follow them if you read carefully.

Currently DrGreg was trying to prove that time dilation is genuine, while I was trying to show his proof was flawed.

I don't think he's really trying to prove it's genuine--he's just telling you what Sam and Alice would see if you assume the relativistic doppler shift equation is correct, but the relativistic doppler shift equation already assumes that time dilation is real. It doesn't make any sense to accept the numbers in DrGreg's example and yet reject time dilation, because he only got those numbers using a formula that assumes time dilation is real. If you used the non-relativistic doppler shift equation, then the numbers would be different.

Do you understand how regular, non-relativistic doppler shifts work? It's pretty simple--suppose I'm traveling away from you at 20 meters per second, and every second I shoot my bb gun at a wall next to you. Also suppose each bb pellet travels at a constant speed relative to you, 100 meters per second. Despite the fact that I am shooting a new pellet every second, you will not see the pellets hit the wall every second--the reason is that after each second I am 20 meters further away, so each new bb pellet has 20 meters further to travel than the last one. Since the pellets travel at 100 meters per second, it will take them 0.2 seconds to travel 20 meters, so each new pellet takes 0.2 seconds longer than the last one to travel from my gun to the wall. So you will see the pellets hit the wall every 1.2 seconds rather than every 1 second. That's all the non-relativistic doppler shift is--it's just a consequence of the fact that the distance between two observers is changing, so each successive signal has a different distance to travel than the previous one.

But in relativity, this is only part of the doppler shift. The other part is that we assume in relativity that if I am traveling at high speed relative to you, my clock will genuinely slow down in your frame--that's time dilation. So if I'm sending a signal once every second according to my own clock, then not only is there a larger gap between signals than one second because I'm moving away from you, but the gap between signals is increased even more because one second on my clock lasts longer than a second according to your clocks. So the relativistic doppler effect takes into account both these factors, the changing distance and the time dilation. If you don't accept time dilation, then you shouldn't accept the relativistic doppler formula, and thus you shouldn't accept DrGreg's numbers in the first place! But it's silly to accept his numbers, which he got using the relativistic doppler equation, but then reject time dilation--it just doesn't make sense.

Flawed or not, I believe we cannot use time dilation to justify an experiment designed to prove time dilation.

Then why are you arguing as though you accept that the numbers DrGreg gave would be what Alice and Bob would see, but you just reject time dilation? Again, if you reject time dilation, it doesn't make sense to accept those numbers in the first place.

And if you think time dilation is "flawed", do you think it's logically flawed in the sense of leading to some internal contradiction, despite the fact that no mathematicians seem to agree, or do you just think that the theory isn't the correct one for describing the real world? If the first, I promise that you're wrong and that it can be proved mathematically that no contradictions arise. If the second, then we should be discussing the experimental evidence in favor of time dilation (there's a whole lot of it), not a hypothetical example which assumes time dilation is real.

Because of your use of the time dilation, you gave more and more numbers that never appeared in DrGreg's demonstration. These numberbs complicated matters more and more, leading to more difficulties and arguments. For instance you said the distance between Bob and Alice (at Ted) was 25 light-minutes.

based on the fact that her distance when she turned around was 25 light-minutes from him

. How could I understand this 25 light-minutes? Very difficult.

Why is it hard to understand? 25 light-minutes is just the distance light travels in 25 minutes, just like a "light year" is the distance light travels in a year. I could translate this into a distance in kilometers if you'd prefer, but that'd make the calculations uglier. If the problem was that you didn't know what a "light minute" was, then you could have just asked--in general, please ask me when you don't understand a specific thing in one of my posts, otherwise this discussion isn't going to get anywhere!

I wish you would not give any more numbers. Whether DrGreg's demonstration is flawed or not, I believe we must justify it according to only those numbers he has given. No more new numbers.

But you keep bringing up issues which demand additional numbers, like the issue of whether there is anything "instantaneous" going on. To show that no instantaneous effects happen, I had to explain the difference between the time that Bob sees certain things happen and the time he calculates they 'really' happened in his frame, just like we distinguish between the date we see the light from a distant supernova and the date it actually happened.

Not only no more new numbers, we should simplifiy them. For instance, when the two clocks came together to compare, Bob's clock read 14:10 and Alice's read 17:00. The result of the comparison is: Alice's clock had worked a lot faster than Bob's, the traveled twin had become a lot older.

No, DrGreg specifically set up the problem so that the clocks were out-of-sync initially, so that you wouldn't make the mistake of thinking that if an event happened at 16:00 on Alice's clock, it must have happened "at the same time" that Bob's clock also read 16:00. Just look at the numbers, you can see that the two clocks were set to different times at the start--when Alice and Bob started out traveling away from each other, Bob's clock read 12:00 and Alice's read 15:00. If you like you could imagine that this difference was because Alice and Bob lived in different time zones, and when they came to meet at Alice's launch pad they forgot to reset their clocks to the time zone of the launch pad. So if Bob's clock read 14:10 when they reunited, that means it must have advanced 2 hours and 10 minutes between the time Alice left (12:00 according to his clock) and the time she returned; if Alice's clock read 17:00 when they reunited, that means it must have advanced only 2 hours between the time she left (15:00 according to her clock) and the time she returned. So if they were the same age when she departed, she must have been 10 minutes younger when they reunited.

 

[DrGreg]

For instance you said the distance between Bob and Alice (at Ted) was 25 light-minutes.

based on the fact that her distance when she turned around was 25 light-minutes from him

. How could I understand this 25 light-minutes? Very difficult.

The 25 light-minutes can be deduced from my tables in https://www.physicsforums.com/showpost.php?p=791307&postcount=103".

The following rows appear within those tables:

Bob...abcdefghijklm.Alice
12:40 a>>>>>>>>>>>>m 16:00 (first table)
13:30 a<<<<<<<<<<<<m 16:00 (second table)

From Bob’s point of view, light leaves him (a) at 12:40, is reflected from Alice at (m), and is received by him (a) at 13:30. So this reflected light takes a total of 50 minutes to make the round trip there and back, a total distance of 50 light-minutes. The distance from (a) to (m), according to Bob, is therefore half of this, 25 light-minutes.

Also, from Bob’s point of view, he will conclude that the light reached Alice halfway between 12:40 and 13:30, that is, at 13:05. This also agrees with JesseM’s figures.

All of the above assumes that the speed of light relative to Bob is the same in both directions, Bob to Alice and Alice to Bob.

 

[Sam Woole]

Time dilation question

I don't think he's really trying to prove it's genuine--he's just telling you what Sam and Alice would see if you assume the relativistic doppler shift equation is correct, but the relativistic doppler shift equation already assumes that time dilation is real. It doesn't make any sense to accept the numbers in DrGreg's example and yet reject time dilation, because he only got those numbers using a formula that assumes time dilation is real. If you used the non-relativistic doppler shift equation, then the numbers would be different.

Now I came to the realization that some thing was fundamentally wrong, with me, or with you, depending on what perspective we look at the issue. As soon as I saw DrGreg's tables, I assumed he was trying to convince me that time dilation is genuine. Now it turned out that my assumption was wrong. Instead, DrGreg was using the genuine time dilation to show me how it works. If time dilation is genuine, of course his demonstration (those tables) is genuine likewise.

But my wrong assumption was not entirely my fault becasue, all along I have repeatedly declared my disbelief in time dilation, as can be found from my posts before DrGreg's post #68.

Hence maybe we should start all over again: Show me why time dilation is genuine. We shall leave all the other disagreements behind. All the foregoing discussion was a waste of time but I was not the only one to blame.

And if you think time dilation is "flawed", do you think it's logically flawed in the sense of leading to some internal contradiction, despite the fact that no mathematicians seem to agree, or do you just think that the theory isn't the correct one for describing the real world? If the first, I promise that you're wrong and that it can be proved mathematically that no contradictions arise. If the second, then we should be discussing the experimental evidence in favor of time dilation (there's a whole lot of it), not a hypothetical example which assumes time dilation is real.

As I have declared, I do think time dilation is flawed. I like to find that it is not. I am not able to talk about the entire SR. It is too big to me.

Why is it hard to understand? 25 light-minutes is just the distance light travels in 25 minutes, just like a "light year" is the distance light travels in a year.

DrGreg knew why I had difficulty in understanding the 25 light-minutes. The distance between Bob and Ted was designed to be a constant 20 light-minutes. A non-believer in time dilation like me would have difficulty to understand that a constant distance would suddenly lose its constancy. DrGreg explained that it became into 25 minutes because of time dilation.

 

[DrGreg]

DrGreg knew why I had difficulty in understanding the 25 light-minutes. The distance between Bob and Ted was designed to be a constant 20 light-minutes. A non-believer in time dilation like me would have difficulty to understand that a constant distance would suddenly lose its constancy. DrGreg explained that it became into 25 minutes because of time dilation.

It didn't "become" 25 light-minutes because of time dilation. It always was a constant 25 light-minutes (according to Bob, and Ted, but not Alice).

The figure of 20 light-minutes that you calculated was incorrect because you obtained it by subtracting a time on Bob's clock from a time on Alice's clock. As I explained in the final paragraph of post #168, that is not a valid thing to do. All time intervals must be calculated using the same clock at the start and finish.

You say you are a "non-believer in time dilation". Why do you continue to take part in this forum? If you genuinely want to understand relativity, you will eventually have to be persuaded to become a believer. You will never understand it if you persist in your non-belief as a matter of faith.

 

[JesseM]

Now I came to the realization that some thing was fundamentally wrong, with me, or with you, depending on what perspective we look at the issue. As soon as I saw DrGreg's tables, I assumed he was trying to convince me that time dilation is genuine. Now it turned out that my assumption was wrong. Instead, DrGreg was using the genuine time dilation to show me how it works. If time dilation is genuine, of course his demonstration (those tables) is genuine likewise.

But my wrong assumption was not entirely my fault becasue, all along I have repeatedly declared my disbelief in time dilation, as can be found from my posts before DrGreg's post #68.

Hence maybe we should start all over again: Show me why time dilation is genuine. We shall leave all the other disagreements behind. All the foregoing discussion was a waste of time but I was not the only one to blame.

In that case, maybe we should just discuss the experimental evidence in favor of time dilation? There's plenty of it--GPS navigation systems all assume time dilation in their calculations, the decay time of particles accelerated to relativistic speeds is slowed down by just the amount predicted by the time dilation experiment, and there have even been experiments where very precise atomic clocks were placed on board the space shuttle and found to have lost a few microseconds when they returned. If you're interested in learning more about any of this, I or others here could go into more detail about it.

DrGreg knew why I had difficulty in understanding the 25 light-minutes. The distance between Bob and Ted was designed to be a constant 20 light-minutes. A non-believer in time dilation like me would have difficulty to understand that a constant distance would suddenly lose its constancy. DrGreg explained that it became into 25 minutes because of time dilation.

I was just talking about the distance between Bob and Alice, not Ted (I haven't been reading all the posts on this thread since the beginning, so I didn't even remember that a third observer was introduced). The distance between Bob and Alice was constantly changing, because they started at 0 distance from each other, then Alice flew away at constant velocity for a while (distance increasing), then she turned around and flew back towards Bob at constant velocity (distance decreasing) until they reunited (distance 0 again).

 

[russ_watters]

Hence maybe we should start all over again: Show me why time dilation is genuine. We shall leave all the other disagreements behind. All the foregoing discussion was a waste of time but I was not the only one to blame.

Now we're getting somewhere. Editorially, it shouldn't have required 11 pages of discussion for you to just come out and say you assume time dilation doesn't exist. All that math and case studies are utterly useless if you just simply don't accept their validity. And I do consider that to be all you - you shouldn't have been arguing the case studies if you didn't accept the basis of them them in the first place! Your arguments made it seem like you were confused about how the cases worked, not that you simply didn't accept what they were saying. And in addition, many people have posted physical evidence and you have ignored it (such as in my previous post).

So...

Show me why time dilation is genuine.

Well, you seem to have ignored all evidence posted so far... Could you comment on some of the evidence already posted? For example, my previous post, where I mentioned the GPS system? I just asked if you are aware of how the GPS system works - we can explain it to you if you need us to.