Relative Time Dilation Paradox

[Qfwfq]

Yup- Al's right.

Nope, not quite right, especially when he says things like "Acceleration is irrelevant" and "ds^2 is a constant".

 

ds^2, the square of proper time, is an invariant and UA should know the difference before pontificating so much. The clock that passes through the most space accumulates the least proper time for the same total interval, this can happen for the same initial and final points only if there was acceleration. I also disagree with the statement "The universe is not Euclidean, Galilean, or Newtonian", a space-like submanifold is locally Euclidean, Galileo and Newton weren't actually wrong.

 

UA, it is a paradox, nobody said it's an unresolvable one, see the etymology of 'paradox'. You should also avoid phrases such as "Get over your prejudices" when someone is only seeking help.

[geistkiesel]

In your example, both ships broadcast their accumulated proper time. The proper time of each ship is, in fact, an invariant. As such, your statement is true. All observers should note the proper time elapsed in the two symmetrical ships is identical. This doesn't make time dilation any less physical, and doesn't pose a problem with time dilation.

-Will

You are correct, there is no problem with time dilation posed in my post. However, we must recognize that if the observers on A and B are each looking at the other's clock as slower than their own, this cannot be proved by measurment. Each ship's proper time will be the same, the tick rates will be the same and dilation will not be measurable wrt to the A and B observers. The earth observer might have a different measurement of both clocks readings though.

 

I was just emphasizing that when each observer "sees" the other ship's clock as running slower (he has no way of knowing the ships are symmetrical) this "seeing" is not a

physical observation, or measurement

it is merely a theoretical "justifrication" that has no reality based physical analog attached.

 

Geistkiesel

[Erasmus00]

. I was just emphasizing that when each observer "sees" the other ship's clock as running slower (he has no way of knowing the ships are symmetrical) this "seeing" is not a physical observation, or measurement it is merely a theoretical "justifrication" that has no reality based physical analog attached.

 

But the classic case of the twin paradox, where you have an asymmetry, i.e. ,the twin turns around, shows that this time dilation must be physical,not merely apparent. By the time the twin returns, much less proper time has elapsed on his clock.

-Will

[geistkiesel]

What you fail to understand is that time is a relative quantity, not an absolute quantity. You say it has no physical reality, but I disagree. Just because its not absolute doesn't mean it isn't physical.

-Will

Will, Ok, but we must avoid any semantic errors here. The two ships we are discussing (both launched simultaneously from earth with the same measured velocity wrt earth) pass each other and each radiates their time at that instant; assume both had been radiating pulses continuously at 1 second intervals as measured by each sending frame. Let us assume the clocks are synchronized when the ships acclerated from earth. When they pass each other the pulse sequence, time between pulses, and elapsed times on the two clocks will be the same. Whatever we mean by "physical reality" I claim that in the above conditions the

result of the measurments

that each frame makes of the other's elapsed time and pulse rate will be identical. A and B measures each other's pulse rate is the same as their own. Each clock will indicate the same elapsed time. An earth observer wil see that each ship radiates the same pulse rate and total elapsed time.

 

I am not trying to impose any"absolutenss" in the discussion to here. I do not expect the observers on each ship to make the same assumptions regarding their individual state of motion and the consequences of their assumptions. I do insist that if both observer's assume the other's clock is moving slower than their own, there is no experiment that can everdemonstrate this. Both clocks cannot be ticking slower than the other, regardless of any considerations the observers make. One can be ticking slower than the other, both can be ticking at equal rates (as measured by each other), but both cannot be faster ticking nor both slower ticking wrt the other as measured by each other. In other words when the A observer receives B's tick rate as analyzed by the A instruments, He will not ever say, "I see that the B tick rate is slower than mine, and my tick rate is slower than the B rate."

 

This is all I am stating.

Geistkiesel

[Qfwfq]

I was just emphasizing that when each observer "sees" the other ship's clock as running slower (he has no way of knowing the ships are symmetrical) this "seeing" is not a physical observation, or measurement it is merely a theoretical "justifrication" that has no reality based physical analog attached.

No, Geistkiesel, it is the physical observation, or measurement, and it matches up with the predictions of SR.

 

What you need to understand is that you are talking about a transformation of coordinates, no more, no less. The thing that we aren't aware of from normal perception is that this tranformation can "mix" spatial and time coordinates. The coordinates of each observer aren't "right" or "wrong" for the whole universe but they are more appropriate for each observer and for anything at rest for them.

[geistkiesel]

No, Geistkiesel, it is the physical observation, or measurement, and it matches up with the predictions of SR.

 

What you need to understand is that you are talking about a transformation of coordinates, no more, no less. The thing that we aren't aware of from normal perception is that this tranformation can "mix" spatial and time coordinates. The coordinates of each observer aren't "right" or "wrong" for the whole universe but they are more appropriate for each observer and for anything at rest for them.

Qfwfq, I am not making any value judgements here. I am merely remarking that when the two observers pass each other nose to nose that there is no way that both assuming the other's clock runs slower than their own can be verified. I understand completely your statements regarding "normal perceptions" and the "mix" of spatial and time coordinates. The simple measurement I described cannot show, nor verify, both mental states i.e. "both running slower than the other" when they are considering the other's clock speed as running slower than his own.

 

So what physical measuremnt or observation matches up with what I described regarding the mutual "seeing" the other's clock is running slower? I suspect your statement here is directed at some other experimental arrangement.

Geistkiesel :esheriff:

[Qfwfq]

Sorry, Geist, you're right, in a sense, I would talk about impossibility of "objectivating" the difference. If there is never acceleration of either clock, there's no point in saying which one is "right" and which one is "wrong". This is part of the argument resolving the paradox.

 

What I meant is that it has been amply verified but, in the simplest manner, this implies accelerations. A more subtle verification is that of the muon average decay time. This is a statistical comparison between this time for muons held in the lab, at low velocity, and that for muons in cosmic rays.

[geistkiesel]

Sorry, Geist, you're right, in a sense, I would talk about impossibility of "objectivating" the difference. If there is never acceleration of either clock, there's no point in saying which one is "right" and which one is "wrong". This is part of the argument resolving the paradox.

 

What I meant is that it has been amply verified but, in the simplest manner, this implies accelerations. A more subtle verification is that of the muon average decay time. This is a statistical comparison between this time for muons held in the lab, at low velocity, and that for muons in cosmic rays.

Qfwfq, Thanks Q. Again I mean nothing more than it is impossible for the two clocks to simultaneously (as wehn passing noso to nose) both measure lower than the other, especially in the sense where I attempted to make the copnditions exactly symmetrical.

 

The muon decay times is another problem and for a while i was stuck in a rut. Then there came a litttle bird whispering in my ear.

 

The muons are not generated in open space. Rather they are generated in the atmosphere and have a 1/2 life of 1.56 micro seconds (or 2 micro seconds by some accounts). If an observer at 2000 meters , for instance, is counting muons at a rate of say 600/hr then 1/2 of these were generated at between 2000 and 2600 meters and 1/4 generated at between the next 600 meters or 3200 meters and so on.

 

The fault of those insisting that muon decay is definite proof of time dilation ( I haven't disagreed with "dilation" yet, just the "both clocks can't be lower than the other at the same instant" condition) is the failure to realize that the muons are bening generated at a spectrum of levels in the atmosphere. To satte that 500 muons survived a 4000 meter to say 1000 meter altitude trek through the atmosphere (made up numbers) is failing to recognize that the muons are being generated at much within that 4000 to 2000 meter travel. At lower levels during the time the muons are being counted at various altitudes muons are being generated.

 

The little bird that whispered on my shoulder, HJ Zweig:

RELATIVITY UNRAVELED – 2005”

 

Here is an excerpt of Zweig's regarding muon decay and time dilation.

 

3. Muon Half Life (modified 1 – 12 – 05) .

The experiment involving muons that is supposed to confirm that time dilates does no such thing. The explanation does not take into account the interaction of creation and decay of muons in predicting how many are found at any given altitude. Here is how the experiment should have been analyzed.

In an experiment conducted on a mountain, muons were detected at 6000 ft and measured to have a flux of 550 per hour. Simultaneously, they were measured at 2000 ft and found to have a flux of about 420 per hour. The distance is about 1200 meters and if muons have a half life of about 2 microseconds (in the experiment the assumption is 1.56 microseconds, in some texts it is 2 microseconds), they would, at the speed of light travel about 600 meters before half are gone. After 1200 meters only about 1/4, or less, would be left, so no more than about 120 should survive – but we get almost four times that many. Consequently, their half-life must have increased due to their speed.

Here is what is wrong with that argument. Muons are created in the upper atmosphere, not in outer space. Assuming a half life of two microseconds, then, of the 550 muons detected at 6000 feet (or 2000 meters), about half would have originated at a height of 2600 meters, or less; about 1/4 would have originated at a height between 2600 and 3200 meters, about 1/8 would have originated at a height between 3200 and 3800 meters, etc. The same argument applies at 2000 feet (about 650 meters). Of the 420 that are detected, about 1/2 originated between 660 and 1260 meters, 1/4 originated between 1260 and 1860 meters and 1/8 originated between 1860 and 2460 meters. So perhaps 1/8 of the 550 muons, about 85, can be expected to survive the journey. The rest of the 420 come from muons created during the hour that the measurements were taking place, in the region of space between 2000 and 6000 feet altitude. Adding 210, 105, and 85 gives us 400. Considering the crudeness of the estimates that is not far from the 420 that were observed at the lower elevation. A simplistic application of the exponential decay law leads to an erroneous inference about time dilation. It is not simply a matter of survival, but the interaction of birth and decay that is at work here.

An experiment by Frisch and Smith, done in 1963, tried to filter out Muons that did not have a high enough energy. Only those corresponding to an assumed speed of between .9950c and .9954c were to be counted. They had the lower station at about sea level, and observed about 560 per hour at 6000 feet and about 410 per hour at sea level. They believed that by filtering out slower muons with less energy at 6000 feet, they will encounter only those with high energy (and about the same speed) which survive at the lower altitude. They assumed, of course, that such high energy muons are not formed below 6000 feet. In that case they would not need to consider the interaction between creation and decay for altitudes below 6000 feet. They rely on other experiments for this assumption – but give no specifics.

I can't judge the truth of this claim, but it seems highly doubtful. Even though the cosmic rays, which give rise to the muons, have traveled through 80% of the matter in the atmosphere, by the time they reach 6000 feet, this does not mean that 100%, or even 80%, have been eliminated. Fewer get through to the lower altitudes, but that would not preclude high-energy muons forming below 6000 feet. In that case, their inferences are not valid. A solution is to count primary cosmic ray protons at 1000-foot increments from sea level to 8000 feet. The ratio between the flux at 2000 feet and that at 4000 feet to the flux at 8000 feet would allow a more accurate assessment of the interaction between creation and decay of the resulting muons at lower altitudes.

Also, note that these experiments are insensitive to the actual mean life of muons. If for example the mean life were 10 microseconds instead of 2, it would mean that about half the muons detected at 6000 feet, that is 2000 meters, originated between 2000 and 5000 meters, one quarter between 5000 and 8000 meters, etc. At 2000 feet, or 660 meters, one half originated between 660 and 3660 meters, etc. The ratio of 410 to 550 should then mirror the ratio between muons created near 3660 meters to those created near 5000 meters. With a two-microsecond half-life, the ratio 410 to 550 should correspond to the ratio of cosmic ray fluxes at about 1260 meters and 2600 meters. Unless the two ratios are dramatically different, the experiment will have a difficult time differentiation between a half-life of 2 and a half-life of 10 microseconds.

Moreover, once it is clear that the Lorentz Transformation is wrong, and that synchronization of clocks on bodies in relative motion is possible, SRT is invalidated. Then the shoe is on the other foot. The issue of time dilation must be defended and not assumed. It is up to ‚believers’ and reluctant scientists to show why an explanation of these experiments, that does not require time dilation, is invalid. In any case, the experimental evidence, still to be obtained, can probably resolve the matter.

 

 

Geistkiesel

[Bobby]

I joined this forum because I have always had a problem understanding why a space traveller returning to earth will be younger than his twin brother. I get ( I hope) the reasoning behind time dilation generally but didn't know why it wasn't equally valid for the earthbound twin to be younger than the traveller since his speed relative to his brother is the same as his brother's to him. Thanks to a link supplied by Buffy on an earlier thread I now at least see that the traveller's experience is different from the "stationary" twin due to the accelerations undergone and that he passes through more than one inertial frame of reference so the scenario is not symmetrical. However, I still can't really grasp what is happening in physical terms; if any of you bright sparks can explain it simply for me or have an appropriate analogy it might stop my brain aching.

Also, am I correct in saying that if two clocks at the same point, A, in space flew in opposite directions, travelled the same distance and arrived back at A at the same time they would still be in synch' (both behind a third clock that remained at A) but if one travelled further or arrived back earlier it would be behind the other?

 

 

Special relativity points out how time and distance change due to velocity. Notice that it doesn't say anything about acelleration. If Betty gets into her spaceship and acellerates away at one g (32 ft/sec^2) then according to the equivalence principle, she can just as well be considered as never having left the Earth's gravitational field. Thus If Betty undergoes any relativistic effects due to acelleration, Ann (her stay at home twin) should undergo the same effects due to her (Ann) being in a gravitational field.

 

How can this problem be overcome? Simple. The relativistic effects are not caused by acelleration, they are caused by the difference in velocity.

 

There appears to be a deep connection between time and gravity. T1 = T2 (1 + gh/c^2) is an equation from General Relativity where g is the force of gravity, h is the distance from the gravity source and C is the speed of light. As Betty's spaceship speeds away, light from her ship will become red shifted (stretched over space). If you think about it, this indicates that Betty's spaceship is also stretched over space. If the wavelength of light becomes longer, fewer of these waves will pass a particular point. In other words, as wavelength increases frequency goes down. But frequency is associated with time. If Betty's spaceship follows the same rules as does light, then the frequency of Betty's heart become slower, thus she ages less.

[xersan]

I joined this forum because I have always had a problem understanding why a space traveller returning to earth will be younger than his twin brother. I get ( I hope) the reasoning behind time dilation generally but didn't know why it wasn't equally valid for the earthbound twin to be younger than the traveller since his speed relative to his brother is the same as his brother's to him. Thanks to a link supplied by Buffy on an earlier thread I now at least see that the traveller's experience is different from the "stationary" twin due to the accelerations undergone and that he passes through more than one inertial frame of reference so the scenario is not symmetrical. However, I still can't really grasp what is happening in physical terms; if any of you bright sparks can explain it simply for me or have an appropriate analogy it might stop my brain aching.

Also, am I correct in saying that if two clocks at the same point, A, in space flew in opposite directions, travelled the same distance and arrived back at A at the same time they would still be in synch' (both behind a third clock that remained at A) but if one travelled further or arrived back earlier it would be behind the other?

 

You are right, welcome to independent brains. The special theory (SRT) is a test that <When will the human solve the inappropriateness of SRT>. I want to give you a clue : The time contraction is also possible in SRT. Please analyse motion of the light that travels to against direction of its source by the same way of SRT. You will find the light's velocity " c " again, but tempo of time must become faster.

[Bobby]

You are right, welcome to independent brains. The special theory (SRT) is a test that <When will the human solve the inappropriateness of SRT>. I want to give you a clue : The time contraction is also possible in SRT. Please analyse motion of the light that travels to against direction of its source by the same way of SRT. You will find the light's velocity " c " again, but tempo of time must become faster.

 

 

 

 

If Ann is approaching Betty and Carol is approaching Betty from the opposite direction but at a slower velocity than Ann, here is what I understand would be seen.

 

Any combination in which the velocities are toward each other will be blue shifted.

Any combination in which the velocities are away from each other will be red shifted.

 

A light shift will change both the light's wavelength and it's frequency, thus a red shift has a longer wave length and a lower frequency than a blue shift.

 

 

The change in frequency does not mean that the light is going slower. Wavelength and frequancy go hand - in - hand. As wavelength grows, frequency becomes longer. The reason for this can be seen in the following example.

 

Suppose you connect a wire between a switch and a DC battery. Close the switch for five seconds (allowing a current to flow) then open the switch for five seconds and repeat several times.

 

When you close the switch and a current begins to flow, the electric and magnetic fields from the current begins to spread outward at the speed of light. These fields continue to move outward until the switch is opened five seconds later, thus interrupting the current flow. These actions will create an electromagnetic wave with a frequency of 5 seconds and a wavelength of 5 seconds times the speed of light.

[xersan]

I am sure that your ideas are useful and they have potential meaning. I shall work to analzye your circuit example (in motion)

 

I may say: If Einstein was alive, he will take back his theory (SRT) because of the results of analyzing with opposite directional light.

[Erasmus00]

 

I may say: If Einstein was alive, he will take back his theory (SRT) because of the results of analyzing with opposite directional light.

 

I am unaware of these results. I've never seen any disproof or experiment whose results go against SR. Please link, or give a reference.

-Will

[Bobby]

I am sure that your ideas are useful and they have potential meaning. I shall work to analzye your circuit example (in motion)

 

I may say: If Einstein was alive, he will take back his theory (SRT) because of the results of analyzing with opposite directional light.

 

 

The speed of light does not depend on the direction of motion. The wavelength and frequency does, but not the speed.

 

SRT was a theory about unacellerated motion. GRT, which came later, was an extension og SRT. As such, SRT must be modified by GRT. I suspect Einstein would agree with the following statement. "All motion is relative to the gravitational fields through which it moves."

[Erasmus00]

SRT was a theory about unacellerated motion. GRT, which came later, was an extension og SRT. As such, SRT must be modified by GRT. I suspect Einstein would agree with the following statement. "All motion is relative to the gravitational fields through which it moves."

 

It is a common misconception that relativity cannot handle accelerations. The simple time dilation formulas only hold true in inertial frames, but a framework can be developed to handle accelerations within SR.

-Will

[Bobby]

It is a common misconception that relativity cannot handle accelerations. The simple time dilation formulas only hold true in inertial frames, but a framework can be developed to handle accelerations within SR.

-Will

 

 

I think I have heard something like this before. Can you point me to some references?

 

Regards BP

[Erasmus00]

I think I have heard something like this before. Can you point me to some references?

 

Regards BP

 

Anything that develops a nice treatment of 4-vectors (Minkowski space). The notion of 4 vectors, including 4 acceleration is developed, as well as the SR equivalent of F=ma.

-Will