Why does time slow down the faster you go?

[ghwellsjr]

Simple. As I read the document, it was meant as theoretically testable prediction - a specific way the twin paradox could be carried out, for example. The clause you cite is irrelevant because Einstein knew gravity existed, and knew the Earth was oblate. What he didn't know yet was about gravitational time dilation. I am dealing with it the same way as I do all other scientists. It is you who insists Einstein must be treated differently from everyone else.

So you're saying that Einstein's prediction was wrong:

If one of two synchronous clocks at A is moved in a closed curve with constant velocity until it returns to A, the journey lasting t seconds, then by the clock which has remained at rest the traveled clock on its arrival at A will be ½tv²/c² second slow. Thence we conclude that a balance-clock at the equator must go more slowly, by a very small amount, than a precisely similar clock situated at one of the poles under otherwise identical conditions.

 

[PAllen]

As I said at the end of my post, the same argument applies to any chemical reaction that produces electromagnetic radiation.

Eg)
Path 1: transport hydrogen and oxygen from point A to point B, combine them and observe the frequency of the light produced
Path 2: combine hydrogen and oxygen at point A, transport the water to point B, and also transmit the radiation produced.
Conservation of energy implies the radiation transmitted is not shifted in frequency, hence the time dilation is the same.

I believe Einstein's own PhD research is rather relevant to the implication in that last sentence.

You completely missed my point. He also wouldn't have expected any of those to be affected if B was uphill. No one would have, in 1906. Everyone would assume the increase in potential energy was encapsulated in the matter, and the light emitted at higher elevation and detected at lower elevation would not be affected. That is, in 1906, everyone would expect the result to exactly the same whether A and B were both at sea level or A was in Death Valley, B was the top of Mount Everest.

 

[PAllen]

So you're saying that Einstein's prediction was wrong:

Yes, because Einstein would have believed that gravity and oblateness were not among the conditions to be accounted for in 1906, therefore would have believed this experiment to be a valid test. That is why he bothered proposing it.

This is the last I will say. Clearly, nothing I say will make a difference. After several rounds of identical statements, this is pointless. Feel free to add a pointless 'last word'.

 

[ghwellsjr]

So from now on, every time someone mentions the Twin Paradox with a traveling twin and an earthbound twin, you're going to point out that you cannot ignore the effects of gravity.

 

[Elroch]

You do not appear to be disagreeing with what I wrote, PAllen, but with something entirely different. Let me summarise:

(1) I understand that Einstein believed that a point at sea level on the equator would experience time dilation compared with a point at sea level at the pole. He said "Thence we conclude that a balance-clock at the equator must go more slowly, by a very small amount, than a precisely similar clock situated at one of the poles under otherwise identical conditions"
(2) I gave an argument why this was not so, which in no way relied on the effect of height on time dilation or general relativity.

I invite you to review my previous posts (#27 and #30) and see if my argument is flawed or say why Einstein could not have come to the same conclusion as I did from this argument.

The thing that makes my argument deceptively simple is that sea level neatly compensates for both the difference in gravity and velocity at the equator by creating a surface which (ideally) can be navigated without using energy. Of course this is a slight idealisation which assumes the oceans move perfectly in step with the Earth's rotation, but a pretty good approximation. To be even more picky, it assumes that the gravitational influence of the sun and moon is ignored, or else that lunar and solar gravitation produce tides without lag (there is actually approximately 2 hours delay) which are incorporated into a time-varying sea level. Either approximation seems perfectly reasonable for this discussion.

 

[PAllen]

You do not appear to be disagreeing with what I wrote, PAllen, but with something entirely different. Let me summarise:

(1) I understood that Einstein believed that a point at sea level on the equator would experience time dilation compared with a point at sea level at the pole. He said "Thence we conclude that a balance-clock at the equator must go more slowly, by a very small amount, than a precisely similar clock situated at one of the poles under otherwise identical conditions"
(2) I gave an argument why this was not so, which in no way relied on the effect of height on time dilation or general relativity.

I invite you to review my previous posts (#27 and #30) and see if my argument is flawed or say why Einstein could not have come to the same conclusion as I did from this argument.

I believe your argument would be considered irrelevant in 1906 by Einstein and everyone else. I say this because they would believe the same consequences were true irrespective of sea level.

 

[Elroch]

If Einstein would accept my argument, he would not expect a difference in clocks between points at sea level at the equator and the pole. So if you wish to not accept my point your choices are:

(1) my argument is wrong
(2) there was some reason why Einstein would not believe it

Which is it?

Please be specific in either case, as to which part of the argument.

 

[PAllen]

If Einstein would accept my argument, he would not expect a difference in clocks between points at sea level at the equator and the pole. So you still need to say either my argument is wrong, or there was some reason why Einstein would not believe it. You need to do one or the other or accept my point.

No I don't. You argument is not wrong, but I do not accept your point. I claim your argument is irrelevant to the 1906 understanding. I believe Einstein would, despite your argument, believe there would be adifference at the equator and pole - precisely because he would view the issue of sea level and conservation of energy as irrelevant.

[As with the other circular argument on this thread, have the last word on this if desired - I have no more to say. For some reason, our back and forth is not facilitating mutual understanding. Maybe someone else can help.]

 

[Elroch]

PAllen, the idea that Einstein would consider conservation of energy as "irrelevant" seems rather outrageous. The role of sea level is rather subtle, as it automatically incorporates two factors.

I would have thought Einstein would instantly see the point that transporting masses at sea level requires no energy. The more demanding point (to me) is that a difference in time dilation between two points would result in a change in the energy in electromagnetic radiation transmitted between the two points (by shifting the frequency). Would this be a conclusion he could reach from his understanding of the photon?

 

[Elroch]

I will explain why PAllen's curt dismissal of the issue I brought up is unjustifed (and why this is so revealing about the way understanding of the new physics developed).

If Einstein had come up with a thought experiment that showed that something he believed to be true broke the law of conservation of energy, far from considering conservation of energy to be "irrelevant" he would surely have considered this very significant. He would have had to conclude that if the thought experiment was valid either his belief was incorrect or the law of conservation of energy was genuinely broken, which could be as radical a discovery as special relativity.

In March of Einstein's "miracle year" of 1905 Einstein had published a paper showing that light was composed of particles, despite exhibiting wave properties. Obviously, since quantum mechanics was still undiscovered, this was something only partially understood. My question is, was his improved (but still partial) understanding of the nature of light enough in June of the same year (when he published his first paper on special relativity) to have given him the chance to conclude that the energy in a light signal transmitted between two points at different time dilations would change according to the time dilation?

My considered view is he probably could have if he had combined his two pieces of work. He knew that the packets of light had energy equal to h nu. With this frequency clearly being measured relative to a clock, the energy shift is clear, as long as one rejects the unacceptable idea that the number of photons changes depending on which frame one counts them in.

Pretty straightforward with a century of hindsight, but not at all in the year when special relativity and the quantisation of light were born. Given that, two years later in 1907, Einstein was the first person to realize that gravitational time dilation occurred, perhaps he can be forgiven for having not inferred this with a simple thought experiment in 1905!

 

[PAllen]

I will explain why PAllen's curt dismissal of the issue I brought up is unjustifed (and why this is so revealing about the way understanding of the new physics developed).

If Einstein had come up with a thought experiment that showed that something he believed to be true broke the law of conservation of energy, far from considering conservation of energy to be "irrelevant" he would surely have considered this very significant. He would have had to conclude that if the thought experiment was valid either his belief was incorrect or the law of conservation of energy was genuinely broken, which could be as radical a discovery as special relativity.

In March of Einstein's "miracle year" of 1905 Einstein had published a paper showing that light was composed of particles, despite exhibiting wave properties. Obviously, since quantum mechanics was still undiscovered, this was something only partially understood. My question is, was his improved (but still partial) understanding of the nature of light enough in June of the same year (when he published his first paper on special relativity) to have given him the chance to conclude that the energy in a light signal transmitted between two points at different time dilations would change according to the time dilation?

My considered view is he probably could have if he had combined his two pieces of work. He knew that the packets of light had energy equal to h nu. With this frequency clearly being measured relative to a clock, the energy shift is clear, as long as one rejects the unacceptable idea that the number of photons changes depending on which frame one counts them in.

Pretty straightforward with a century of hindsight, but not at all in the year when special relativity and the quantisation of light were born. Given that, two years later in 1907, Einstein was the first person to realize that gravitational time dilation occurred, perhaps he can be forgiven for having not inferred this with a simple thought experiment in 1905!

Does doppler violate conservation of energy? Does time dilation between inertial frames? It 'appears to', and there is much nonsense written about this.

Einstein would see that, if his prediction was true, energy was conserved in the polar frame for the process of emission; or in the equator frame for the process of emission. Then the rest is just relativistic doppler, which he already understood (and certainly did not consider to violate conservation).

 

[ghwellsjr]

Einstein would see that, if his prediction was true, energy was conserved in the polar frame for the process of emission; or in the equator frame for the process of emission. Then the rest is just relativistic doppler, which he already understood (and certainly did not consider to violate conservation).

Einstein considered only one frame in his original prediction of the Twin Paradox at the end of section 4 of his famous 1905 paper introducing Special Relativity. The observer/object/clock on the equator is not inertial. The observer/object/clock at one of the poles is inertial. The frame under consideration is one in which the observer/object/clock at one of the poles is at rest. Since the observer/object/clock on the equator is in constant motion in the frame under consideration and the observer/object/clock at one of the poles remains at rest in the same frame, the time dilation applies only for the observer/object/clock on the equator and the effect of time dilation is not symmetrical or reciprocal. Einstein did not attempt to explain the Twin Paradox from a frame in which the observer/object/clock on the equator was at rest in his 1905 paper. Neither did he employ Relativistic Doppler in his explanation.

 

[PAllen]

Einstein considered only one frame in his original prediction of the Twin Paradox at the end of section 4 of his famous 1905 paper introducing Special Relativity. The observer/object/clock on the equator is not inertial. The observer/object/clock at one of the poles is inertial. The frame under consideration is one in which the observer/object/clock at one of the poles is at rest. Since the observer/object/clock on the equator is in constant motion in the frame under consideration and the observer/object/clock at one of the poles remains at rest in the same frame, the time dilation applies only for the observer/object/clock on the equator and the effect of time dilation is not symmetrical or reciprocal. Einstein did not attempt to explain the Twin Paradox from a frame in which the observer/object/clock on the equator was at rest in his 1905 paper. Neither did he employ Relativistic Doppler in his explanation.

Right, but Elroch has modified Einstein's original proposal to one involving redshift. I am then left to guess how Einstein would respond to this in 1905. My guess is that he would think as I outlined, and deny there is any issue with conservation of energy. He would see it as simply an instance of transverse doppler, and shrug, what's the problem? Energy is conserved in the emitter frame, the rest is doppler.

 

[Elroch]

PAllen, with all due respect, you appear to be missing a crucial point. The comparison of energies takes place at the same place at the same velocity, so is nothing to do with the Doppler effect (which is about comparing something in two different frames, whether they be Galilean or Lorentzian). You can't make energy in the same frame fail to add up using the Doppler effect.

In the thought experiment, you have two paths some stuff can take from A to B, with no external transfer of energy, and if you believe there is a difference in clocks, you have an energy imbalance. It is trivial to modify the thought experiment to create a perpetual motion machine. This is why the conclusion could not have been brushed off as something irrelevant.

The only way to make the energy add up is if whether you annhilate the particles at A and send to radiation to B or send the particles to B and then annihilate them, you get exactly the same radiation at B. If the only effect was transverse Doppler, the radiation would be a different color. The energy argument indicates that at sea level something compensates exactly for this transverse Doppler effect. This something is gravitational time dilation, of course.

[As for the frames, the exact nature of them doesn't really affect the argument. In a nutshell, all that matters is that if a mass can move between them doing zero work, radiation can move between them without being shifted in frequency]

[If there is any doubt about the link between frequency and the clocks, consider measuring the length of a day by counting the cycles of the radiation]

 

[PAllen]

PAllen, with all due respect, you appear to be missing a crucial point. The comparison of energies takes place at the same place at the same velocity, so is nothing to do with the Doppler effect (which is about comparing something in two different frames, whether they be Galilean or Lorentzian). You can't make energy in the same frame fail to add up using the Doppler effect.

In the thought experiment, you have two paths some stuff can take from A to B, with no external transfer of energy, and if you believe there is a difference in time dilation, you have an energy imbalance. It is trivial to modify the thought experiment to create a perpetual motion machine. This is why the conclusion could not have been brushed off as something irrelevant.

In your description in #27 and #30, I see doppler. You compare doing a light emittting reaction at the pole, measuring frequency; with doing the same reaction at the equator and transmitting the radiation to the pole. That transmission entails transverse doppler due to the equator's motion. It is a change of reference frame. Maybe you mean something different, but that is how I read your posts.

 

[ghwellsjr]

Right, but Elroch has modified Einstein's original proposal to one involving redshift. I am then left to guess how Einstein would respond to this in 1905. My guess is that he would think as I outlined, and deny there is any issue with conservation of energy. He would see it as simply an instance of transverse doppler, and shrug, what's the problem? Energy is conserved in the emitter frame, the rest is doppler.

If the Earth were transparent them maybe Relativistic Doppler might have been a consideration, unless somebody ran a long fiber optic cable from the pole to the equator.

 

[PAllen]

If the Earth were transparent them maybe Relativistic Doppler might have been a consideration, unless somebody ran a long fiber optic cable from the pole to the equator.

That's Elroch's problem not mine. He just said 'imagine transmitting the light'. So I tried to imagine it.

 

[Elroch]

Glad to hear you're using your imagination, PAllen. :)

Transverse Doppler is relevant to the physics, but entirely irrelevant to the logic of the argument. Similarly the precise nature of the frames is irrelevant to the argument. If you do not realize this yet, please think a bit.

The top level logic is as follows:

If the clocks at the equator and at the pole run at different speeds, you can make a perpetual motion machine, therefore they don't.

To put in a bit of detail:

If the clocks run at different speeds, radiation transmitted between the two points must be shifted in frequency (because the cycles can be used as a clock), which changes the amount of energy in it. Since mass can be transferred between the points without a change in energy, conservation of energy is broken.

Note 1: This implicitly uses the fact that the distance between the two points is constant (you could use the fact that the two points repeatedly return to the same relative position instead)
Note 2: The part about mass being transferred between the two frames without input of energy relies on the special property of (idealised) sea level, of course.

I suspect anyone following this will agree with me that all the components of this argument were established in 1905, but no-one happened to put them together. Does anyone disagree? If so, please specify which exact part of what I wrote above was not available at that time.

 

[PAllen]

If the clocks run at different speeds, radiation transmitted between the two points must be shifted in frequency (because the cycles can be used as a clock), which changes the amount of energy in it. Since mass can be transferred between the points without a change in energy, conservation of energy is broken.

.
This is transverse doppler. Transverse doppler is due precisely to time dilation different between inertially moving frames (these are not quite, but Einstein was ignoring this, and so shall we ...).

Note 1: This implicitly uses the fact that the distance between the two points is constant (you could use the fact that the two points repeatedly return to the same relative position instead)
Note 2: The part about mass being transferred between the two frames without input of energy relies on the special property of (idealised) sea level, of course.

If a body goes from the pole to the equator, a polar observer sees it gaining speed - accelerating. It changes frame, and time dilates. It is being acted upon - if the surface were frictionless, it would be clear that force would need to be applied on the way from the pole to the equator and back, to achieve the change in frames.

I suspect anyone following this will agree with me that all the components of this argument were established in 1905, but no-one happened to put them together. Does anyone disagree? If so, please specify which exact part of what I wrote above was not available at that time.

I continue to see that Einstein would view this as an unsurprising application of transverse doppler.

 

[ThomasT]

That is absurd. Basic thought experiments make it plainly obvious why time slows for a moving body.

I agree that there's a perfectly acceptable and formally correct explanation in terms of different spacetime paths via the standard geometric interpretation of SR.

As Naty1 pointed out, and with which I agree, " PAllen's post # 9 gives as precise an explanation as is currently known".

I was just expressing my personal opinion that the spacetime path explanation is not as deep an explanation as might satisfy one, based on (also just my personal opinion) the notion that a deeper explanation (either a testable formalism or at least a somewhat well developed conceptualization) in terms of wave mechanics or particle interactions might be possible.

I don't think that that's an absurd opinion to have, but it might be considered as such by those who think that the spacetime path explanation is as deep an explanation and understanding of relativistic differential aging as can or will ever be developed.

 

[PAllen]

In SR, if you start with clocks together, separate them, and bring them together, they will generally differ (the path with greater deviation form an inertial path will accumulate less time). The exact same thing is true in GR.

In SR, mutual observation of inertial clocks is symmetric - each sees the other slower. In GR, this is still true for 'nearby clocks' with different inertial motion. Quite generally, SR global behavior becomes GR local behavior.

Finally, for comparing inertial and non-inertial clocks (or two non-inertial clocks) without bringing them together, you have asymmetric effects in both SR and GR. For example, in SR, clocks will run slower at the front of a long uniformly accelerating rocket[edit: compared to the rear of the rocket], and this effect is not symmetric.

Since this has been referenced a few times as a description of what 'is' (how deep is not of particular interest to me), I need to correct a typo. In a long, uniformly accelerating rocket in empty space, the clocks at the rear runs slower than the clocks in front. I was thinking 'faster' and wrote 'slower'.

 

[PAllen]

Elroch,

Let me try to explain why I don't see the whole issue of idealized sea level as relevant.

Consider two cases: (A) without gravity; (B) with gravity.

A) We remove the Earth altogether. We have a long axle with an orthogonal bar protruding. The bar is spinning about the axle. Assume this framework is of negligible mass. You have a clock at the top of the axle and at the tip of the bar. Einstein predicts, completely correctly, that a clock on the bar would run slow compared to one on the axle, and light from it would be red shifted as observed from the axle top observer. All of this is correct and and involves no violations of energy conservation. Einstein believed, in 1905, the the Earth would be equivalent to this (there was, as yet, no basis for him or anyone else to believe otherwise). Since this is a completely correct prediction, why would your arguments about sea level and gravitational equipotential lead to a change in analysis?

B). Same set up, but where the bar joins the axle, we have superdense mass concentration. Now, it happens that, along the bar, there will be clocks running slower than the 'pole clock', then (a bit closer to the axle) the same speed, then (a bit closer yet) faster than the polar (axle top) clock. Now in this set up, describe precisely, your conservation of energy argument, without any confusion now about friciton and gaining energy from the angular momentum of the Earth (which your original setup entailed).

 

[Elroch]

[EDIT: this was a response to PAllen's penultimate post]

PAllen, I believe that you are intelligent enough to be able to understand the logic of my post rather than ignore what I say and repeat points that are irrelevant to the logic. Why don't you?

As well as that, you make an error in believing that it takes energy to move a mass from sea level at the pole to sea level at the equator (ignoring irreversible losses due to friction). If it did, the sea could find a lower energy state by adding some water at one point and subtracting it at the other (indirectly, of course). The fact that the sea is moving with the Earth does not affect this principle (though of course it has a big influence on the sea level at different latitudes in order to make the principle true. Think of it this way: there is no place in the (idealised) oceans where you can waterski without a boat (I am assuming an idealised smooth sea which rotates perfectly in step with the Earth, or this becomes very messy and moves from physics to some other applied subject). This local fact implies moving masses about on the sea takes no energy (in principle).

 

[PAllen]

PAllen, I believe that you are intelligent enough to be able to understand the logic of my post rather than ignore what I say and repeat points that are irrelevant to the logic. Why don't you?

As well as that, you make an error in believing that it takes energy to move a mass from sea level at the pole to sea level at the equator (ignoring irreversible losses). If it did, the sea could find a lower energy state by adding some water at one point and subtracting it at the other (indirectly, of course). The fact that the sea is moving with the Earth does not affect this principle (though of course it has a big influence on the sea level at different latitudes in order to make the principle true. Think of it this way: there is no place in the (idealised) oceans where you can waterski without a boat (I am assuming an idealised smooth sea which rotates perfectly in step with the Earth, or this becomes very messy and moves from physics to some other applied subject).

I genuinely don't understand your point or its relevance, and don't find you being at all helpful in clarifying it, if it is correct.

I also don't see you engaging my arguments at all with logic, only with ad hominem comments.

For example, your comments here about the ocean seem completely irrelevant to my arguments. I'm saying (and did, in an earlier post) suppose at the surface of the ocean, making it smooth, we placed a frictionless surface. Then launch (slowly) a clock from the pole (still subject to gravity). It would reach the equator in a state of motion a thousand mph different than a clock floating on the ocean. Without taking gravitiational time dilation into account, why wouldn't Einstein (sitting at the pole) think the clock at the equator, that looked stationary, skimming on the frictionless surface, runs the same as his. While the clock carried by the ocean at 1000 mph runs slower.

 

[Elroch]

[EDIT: Another cross post! Sorry if I haven't appeared helpful. I got the wrong impression you understood but chose to not address the points directly.]

One preparatory note. When I talk about a point at sea level, I mean a point moving at the rotational speed. This is crucial to the energy arguments.

Elroch,

Let me try to explain why I don't see the whole issue of idealized sea level as relevant.

With all due respect, the reason you don't see it as relevant is because you don't yet understand it. The crucial point is that you can move a mass from one point at the surface of an ocean in equilibrium to another without using energy. The reason this is so is that you can't reduce the energy state by moving a little bit of the surface water from one point to another. You see?

Consider two cases: (A) without gravity; (B) with gravity.

A) We remove the Earth altogether. We have a long axle with an orthogonal bar protruding. The bar is spinning about the axle. Assume this framework is of negligible mass. You have a clock at the top of the axle and at the tip of the bar.

In your system it takes energy to move a mass from one point to the other and you can extract energy by moving it back. So crucially different.

Einstein predicts, completely correctly, that a clock on the bar would run slow compared to one on the axle, and light from it would be red shifted as observed from the axle top observer. All of this is correct and and involves no violations of energy conservation.

Yes, if the point at the end of the bar is at a lower potential, clocks will go slower.

Einstein believed, in 1905, the the Earth would be equivalent to this (there was, as yet, no basis for him or anyone else to believe otherwise).

Einstein could have seen the relevance of being at sea level, which roughly means being at equal potential. Admitedly, it would appear that he probably didn't consider this factor and merely thought of the equator moving when he wrote his paper on special relativity. But he did have enough information to do so.

I hope that makes the crucial difference clear.

 

[PAllen]

With all due respect, the reason you don't see it as relevant is because you don't yet understand it. The crucial point is that you can move a mass from one point at the surface of an ocean in equilibrium to another without using energy. The reason this is so is that you can't reduce the energy state by moving a little bit of the surface water from one place to another. You see?

Let's focus on this. Again, I agree with this but don't see the relevance. I hope you also see, that despite this, the ocean is doing work on a boat moving from the pole to the equator (in any inertial frame). Consider introducing a huge number of giant boats at the pole (one at a time) and moving each to the equator with minimal energy. The angular momentum of the Earth (minus the boats) is now lower, with the boats having picked up kinetic energy and angular momentum in an inertial frame at rest with respect to the poles.

Thus, despite your equipotential argument (and again, assuming we can make no recourse to gravitational time dilation), I see a simple case of boats being accelerated relative to inertial motion; at the equator, they are (moment to moment) nearly inertial observers at 1000 mph relative to inertial polar observer.

Perhaps it would help if you did something which I haven't see yet: describe precisely a sequence of steps in which a violation of conservation of energy is seen in a single inertial (non-rotating) frame of reference. I have understood all of your conservation arguments to involve mixing of frames, which is not valid.

 

[Elroch]

There is no contradiction because the Corioli's force interfering with the motion of the boats is always perpendicular to their motion. Hence no energy.

As for the single frame violation of conservation of energy, simply do one of the paths backwards to make a loop. Not practical but makes the point.

Eg start at an inertial frame at the North pole, annihilate an electron and a positron, send the gamma rays to the equator. If time dilation there will be some energy left over if you recreate an electron and positron, send the spare energy and the two particles back to the pole. perpetuum mobile

 

[PAllen]

There is no contradiction because the force interfering with the motion of the boats is always perpendicular to their motion. Hence no energy.

Now who is ignoring who? I literally have nothing to respond to unless you describe a violation of conservation of energy in a single inertial frame. [Note, the boats have KE and angular momentum in any inertial frame].

Note, that if you try treat a non-inertial frame as if it is inertial, you trivially have violation of conservation of energy.

 

[Elroch]

:-) See cross-edited post above.

With regard to your belief that it takes energy to go one way, are you claiming that you could extract energy by going the other way? We are ignoring friction.

Thank you for discussing this in a way that will be productive. This is refreshing.

 

[PAllen]

:-) See cross-edited post above.

With regard to your belief that it takes energy to go one way, are you claiming that you could extract energy by going the other way? We are ignoring friction.

You can't ignore friction, else you can't get from the pole to the equator moving along with the water.