Einstein's time dilation is determined with t’=t(1-v^2/c^2)^1/2. It is thought that the time dilation is confirmed with that the life of the flying mesons is longer than that at rest.
However, this is not true.
First, there does not be the stationary meson. Any particle is always moving. There are only the faster and slower moving mesons.
Second, no experiment for explaining the time dilation determined that what speed was used to distinguish the slower mesons from the faster ones. Or, in another word, are there the slower mesons? And, how much is the difference of the speeds between the slower and faster mesons?
Third, if there were the slower and faster mesons, the mesons are decaying according to a certain law. Thus, the life of some of the slower mesons is longer than that of parts of the slower ones. And, for the same reasons, the life of some of the faster mesons is longer than that of parts of the faster ones. Therefore, no life of both the slower and faster mesons is accordant with t’=t(1-v^2/c^2)^1/2.
There's something called the Quantum Zeno effect, first observed on mesons by Misra and Sudarshan , which has nothing to do with time dilation, although at first sight it would seem that it does : it has to do with coherence (brought about by measurement) and the way coherence can shield particles from decoherence effects, thus preventing particle decay for longer than ought to be the case.
I think you refer to a particular type of mesons: cosmic muons. In the interpretation of the modern and post-modern physics, the existence of cosmic muons on the earth's surface would be the most important experimental proof of the time dilation demonstrated in Special Relativity. The contemporary physics that is based on the Theory of Reference Frames gives instead another explanation of the experimental existence of those mesons.
Hi guys,
Alrik is right. First, the notion of speed depends on the frame of reference.
Moreover, the presence of muons in cosmic radiation on earth is far from being the only proof. In accelerator experiments like ATLAS, CMS, LHCB and previous ones one produces many particles and some of them live long enough to allow a measurement of the length they do before decying. Since they move in magnetic field their momentum can be measured. Kowing the mass, momentum and decay distance allows one to test special relativity in details and the results are in perfect agreement with the calculations. So, the answe to Yin Zhu is simple: time dilation has been proved in numerous occasions using unstable particles like tau-lepton, K_short, Lambda, B-hadrons etc.
(as all scientific proofs these measurements have a given accuracy and one cannot exclude a deviation at a level smaller than the accuracy of the measurement)
Ehud
Two brief considerations:
1. It is true that the speed depends on the reference frame but in modern and post-modern physics it is true for all speeds unless for the speed of light. It generates a heavy asymmetry with respect to the concept of relativistic speed that is justified in modern phisics only by the Lorentz Transformation and that in contemporary physics has been subjected to strong criticism in the order of the Theory of Reference Frames.
2. With regard to time dilation of particles inside accelerators it is manifest that measures of momentum and decay length are insufficient to prove the time dilation because of the indetermination on the third variable. In the measure process that you have considered the third variable is the result of a calculation for which an effective experimental proof would be the direct measure of the third variable.
I'm not sure I want to discuss this theory of reference frames.
Yet, since you ask: take for example a muon. You know its mass and from the curvature of its trajectory in a magnetic field you know its momentom. Knowing the mass and momentum allows you to compute the velocity.
I agree, computing the velocity and measuring the decay length it is possible to compute the decay time, that nevertheless isn' t the result of a direct measure. The consequence is that like this no theory can be verified.
With regard to the theory of reference frames it is surely a heretical theory with respect to current theories and therefore myself am not sure I want to discuss it.
Note that there are several muon experiments. One involves cosmic muons. There the velocity is determined by seeing which muons cross a large absorber and are then absorbed in a thinner absorber. This selcts muons in a narrow velocity trange. These muons were measured both at the altitude of Mt. Washington (roughly 6000 feet) and at sea level. The fluxes were then compared. So there are a few assumptions, but they are quite reasonable and easy to check. The fact that the muons move at something like 0.995 c is not measured directly.
On the other hand, there is an experiment in which muons are observed in an accelerator and their decay monitored. This is a high precision experiment, the velocity can be directly measured and the results coincide to a high level of precision with the predictio of relativity. Other experiments for time dilation exist: thus the emission lines of atoms in fast moving beams are affected by time dilation. In these cases, the velocities of the atoms are known because they were accelerated by a known electric field.
As to your statements that there are no muons at rest: you can certainly take a muon at velocities so low with respect to your laboratory that you observe the muon's decay without any relativistic effect. This has been done. Of course, we should always intepret correctly what is meant: it is not so that muons are ``made to decay more slowly'' by going fast. In their own reference frames, muons always decay at the same rate. But someone who observes the muons in rapid mtion will also observe them to decay more slowly.
Perhaps you should read carefully whatWikipedia and the sources it cites haas to say about time dilation. The relevant experiments are Frisch and Smith AJP (cosmic muuons) Bailey Nature (muons in accelerator) Ives Stillwell J. opt soc of america (moving atoms).
Leyvraz,
In all of the experiments, the key problem is that: what is the speed of the slow ones?
The time dilation for the fast mesons is calculated with t’=t/[1-(0.995c/c)^2]^(1/2). Here, the speed 0.995c has nothing to do with the speed of the slow ones.
In this explanation, the speed of the slow mesons is assumed to be equal to zero. But, in fact, no particle is at rest. Thus, if the speed of the slow mesons is 0.1c, the observation of the dilation of the flying mesons is not accordant with the Lorentz transformation.
It is clear, in all of the experiments, the speed of the slow mesons has not been considered.
Valentin, I agree with your reasoning. Only I would specify:
"What is happening is not correctly explained by Special Relativity and by Lorentz's Transformations".
Yin Zhu: If you read the paper, slow mesons are mesons which have been stopped. This means very low velocities, maybe thermal (300 m/sec). It is a far lesser source of error than all other issues. The time dilation for such velocities can safely be neglected. Experiments do not work with infinite precision, and effects which are below the detection abilities of an experiment are rightly disregarded. Thus if the velocity is thermal, gamma - 1 is about 10^(-12), which cannnot at all be measured.
In fact, even if slow muons were at 0.1 c, as you surmise, the effect woud only be 0.5%, since gamma=1.005 for v=0.1 c. Even that effect would not affect the experiment's conclusions, since they observe a difference in time of a factor of 9.
Valentin:
A muon decaying always is found to decay in its own rest frame at a rate of 2.2 microseconds, whether it is produced in a cosmic ray shower or at rest in a lab. This is a consequence of the principle of relativity. A muon moving very fast with given to the laboratory frame is seen to decay far more slowly than these 2.2 microseconds. Of course, a muon at rest in the laboratory frame is also seen by an observer moving along with the cosmic ray to decay more slowly. That is
1) all muons decay with a half-life tau0 in their own rest frames
2) all muons, as seen from a frame moving with velocity v with respect to the muon's frame, decay with a half-life tau0/sqrt(1-v^/c^2).
In this experiment, cosmic ray muons are seen to decay more slowly from a vantage point at Earth. It does not mean that the symmetric situation would not behave as predicted. It just has not been observed in this specific experiment.
No contradiction.
I observe in preceding comments five different reference frames are considered: own rest reference frame of muon, the reference frame of slow muon, the reference frame of fast muon, the reference frame of laboratory, the moving reference frame with speed v. It would seem for all five reference frames the Principle of Relativity is valid. The Principle of Relativity nevertheless has no relation to time changes, but those changes would be generated only by Lorentz's transformations. Besides there is no direct experimental test of measurement of those changes but only indirect measures of the speed for which the same theory, and not the experiment, proves its own validity. With regard to elementary particles we are able to measure directly only decay lengths and indirectly speeds as per results of preferred theories. It is insufficient to be defined an experimental confirmation. Besides in order to avoid easy confusions I would advice to make use of only two reference frames each time.
Leyvraz
There are three problem in the usual explanation for the time dilation with the lifetime of the faster mesons.
First, as you knew, the slow mesons are that that have been stopped. Thus, whether the lifetime of these mesons are affected by this “stopped”? And, the speed of the “stopped” mesons is not the normal speed.
Second, if the normal speed is, for instance, 0.2c, then the time dilation cannot be obtained from the slow mesons.
However, the lifetime of the mesons with the speed of 0.2c is very close to that of the mesons "at rest".
Third, the lifetime of the mesons "at rest" must be determined with large number particles, not with one or several particles.
In addition, the problems presented by Danci and Sasso also need be considered.
Valentin> That is a mathematical contradiction. What is happening there is not correctly explained by the theory of relativity.
But Valentin, that looks like a contradiction only because you did the analysis wrong. In the frame of the earthbound observer the stationary muon decays before the moving one, at the same position (let us say). This means that the decay events have a timeline separation. So that must be the case in all inertial frames, since Lorentz transformations preserve causality.
So your first reaction should not be "not correctly explained by the theory of relativity" and make a fool of yourself by making your analysis and the reaction public. Your first reaction should be "Hmm... this looks very strange; it can't be like that; I must have made a mistake; let me give it another try". It very simple to resolve your "paradox" if you apply the Lorentz transformation as taught in introductory courses. I leave it to your enjoyment to resolve it yourself. After that you should consider deleting or editing your post, since it is an embarrassment to you. I (and others) can respect you for having an alternative to SR, but that respect evaporates when you make such blatant mistakes public. We all make blatant mistakes, but fortunately most of them eventually ends up the shredder (sometimes due to good help from referees and others).
It may be that you prefer to use some other transformation rules and obtain an inconsistent result, but that is not a problem with special relativity.
Hint: Write down the coordinates of two creation events and the two decay events in the stationary frame of the earth. What are the their coordinates in the Lorentz transformed frame?
I have of course done both problems --- they represent two different physical situations --- and everything in between. Lorentz transformations provide consistent and educating results. I will use this example as a nice exercise as soon as I get an opportunity. Thank you for contributing to the special theory of relativity!
"In the frame of the earthbound observer the stationary muon decays before the moving one, at the same position (let us say). This means that the decay events have a timeline separation. So that must be the case in all inertial frames, since Lorentz transformations preserve causality."
This statement presents two usual errors that have to be corrected:
1. The moving muon, considered with respect to the resting reference frame (for instance laboratory) decays after the same muon considered with respect to the moving reference frame (t>t'). The first error concerns therefore reference frames and Lorentz's transformations..
2. The second error regards Lorentz' transformations. In fact they aren't relations of causality but simply kinematic relations.
The contradiction pointed out by Valentin concerns the first error, in fact exchanging the two reference frames (absolute resting reference frames don't exist) we have the exact contrary: the resting muon considered with respect to the moving reference frame decays before the same muon considered with respect to the resting reference frame (t'>t).
If these errors will not be corrected, future generations of young researchers will continue to be ruined by bad masters.
The best verification of time dilation is perhaps the 2010 measurements of Chou et. al., linked to below. They don't consider moving muons decaying at random, but an atomic clock undergoing periodic motion compared with a similar clock at rest in the laboratory frame. They are able to detect the time dilation for relative speeds less that 10 m/s! In full agreement with the special relativity predictions, of course.
Since this was 5 years ago, there may very well exist even more accurate results today (I didn't take the time to check).
http://web.phys.ntnu.no/~kolausen/FY3452/.Science-2010-Chou-1630-3.pdf
H Chris Ransford> the Quantum Zeno effect, first observed on mesons by Misra and Sudarshan
It was not an experimental observation, it was a theoretical suggestion --- a quantum mechanical version of the well known fact that a watched kettle never boils! It is related to the fact that the theoretical decay curve for an unstable state does not always follow an exponential law; it starts out flat for very short times. Then, when you do measurements very often you essentially always detects a living system, and each time the decay process is restarted with the flat curve.
More detailed calculations show that the initial time region must be extremely short, on the order of the Planck time. Hence, it is not an observable effect in particle physics. Maybe in condensed matter systems...
Brief comment on the proposed paper:
The equation (1) at page 1632 is the figment of imagination. The subsequent approximation is the fruit of calculation errors. Besides time dilation is calculated as frequency shift (well-known also in classic physics) and this frequency shift also according to Einstein's approximation (v
Daniele> I would prefer a reply by one of paper authors
Which you would certainly get --- if you were a reviewer or editor for Nature or Physical Review Letters. But don't expect them to answer dubious postings on Q&A. David Wineland was one of the 2012 Nobel prize winners in physics, and this group is very likely number one in the world in its field.
I understand of course that they, compared to you and Valentin, must be a bunch of dilettantes and ignorants with absolutely no knowledge or concern or control over the intricacies and experimental limitations of their project.
They probably have not even discovered any self-contradictions in the special theory of relativity!
Kare, you continue to be ironical but your last claim is right:
They probably have not even discovered any self-contradictions in the special theory of relativity!
Besides you didn't understand the world of science and of communication is changing and if you despise RG I don't understand why you continue to make use of. I don't want to do other comments and I will not reply other claims.
My best regards.
Yes, I was very happy with my last sentence, expecting it to have a shameless appeal to everyone.
I don't dislike RG at all! I have even invited new members here (admittedly by accident --- just like I was invited). But I certainly will not invite top-notch physicists to answer questions from a thread like this.
I am concerned about the Q&A institute of RG, to a large degree it does not seem to work as intended.
@Daniele: ``The equation (1) at page 1632 is the figment of imagination. The subsequent approximation is the fruit of calculation errors.''
Could you be specific? To me it looks like a perfectly reasonable relativistic treatment. It does have approximations, such as assuming that at each phase of the atomic oscillation we can define a frequency, but this is entirely reasonable for an optical frequency (10^(15) Hz) modulated by an atomic motion of MHz. The frequency is thus Doppler shifted and affected by time dilation. The Doppler shift disappears in the average and only the time dilation remains.
Of course, this is relativistic. You may wish to reanalyse the data in classical terms. I look forward to seeing this.
In any case, unless you wish to take back your above remarks, it would only be decent to let the readers of RG know where tyou have found an error.
Best wishes, Francois
Dear Kare,
A work like Zhou and coworkers’ were done by another team. But, their result was argued.
Please see:
Hohensee M A, Chu S, Peters A, et al. Comment on:‘Does an atom interferometer test the gravitational redshift at the Compton frequency?’，Classical and Quantum Gravity, 2012, 29(4): 048001.
Best wishes
Yin
Yin Zhu> their result was argued.
The debate you are referring to seems rather unrelated to the 2011 Science article I linked to; moreover this debate appears to be on the theoretical level. The discussion seems to be related to another approach (with potentially much higher accuracy?).
I checked ISI Web of science for citations of the Chou et. al article. There was already 133 entries. I am not going to read them all, but from the titles I could not spot any better experiments (nor disputes about the results).
Valentin> "Argument from authority"
I don't trust them because they are authorities, but because they have for long demonstrated their abilities to do this type of experiments. Their works are closely scrutinized by the best experimental and theoretical groups in the world. When it comes to experimental results, all outsiders must necessarily invest a certain amount of trust when accepting results, and more the further you are from the labs. Results for good labs can be trusted more, both because they have earned their reputation for good experiments and analysis, and because their results are better checked by independent competent groups.
There was a lot of commotion about cold fusion a couple of decades ago. And almost every lab could detect cold fusion. Except the best ones. There are no authorities in science, but there are obvious differences in qualities. Like knowing what the relevant orders of magnitude of atomic forces are.
By the way, I have just discovered a fundamental flaw with arithmetic. Consider the equations
(1) a - b = 4, which implies that a > b
(2) b - a = 4, which implies that a < b.
But that is a mathematical contradiction! What is happening here is not correctly explained by arithmetic, the world of which must be filled with miracles!
@F.Laywraz,
I am answering because you asked my viewpoint. The equation (1) at page 1632 is the basis of the author's reasoning. For this equation they call the reference (17) where there is:"See supporting material in Science Online", i.e. a "Chinese box" in which there is nothing. I think the main equation of the paper had to be demonstrated into the paper: it is only a formal question, but if I was the journal editor I would have asked this authors.
Let us see now the substance. You claim:
"The frequency is thus Doppler shifted and affected by time dilation. The Doppler shift disappears in the average and only the time dilation remains".
From your comment it seems that time dilation and Doppler shift are two non-connected physical phenomena. I remind that here we are considering dynamic events in the absence of gravitational field. In Einstein's Special Relativity instead Doppler shift and time dilation are strictly related and just time dilation generates Doppler shift when there is an oscillation as in this case. In the considered case time dilation and Doppler effect disappear together or both are present..
With regard to the fact " I reanalyse the data in classical terms" I would want to specify that I reanalyse the data according to the Theory of Reference Frames.
.
http://gsjournal.net/Science-Journals/Research%20Papers-Miscellaneous/Download/2116
I don’t think the result in
Optical clocks and relativity, Chou C W, Hume D B, Rosenband T, et al. Science, 2010, 329(5999): 1630-1633
Is valid. Because the Hafele-keating experiment is incredible. Please see:
Is the Hafele-keating experiment credible?
https://www.researchgate.net/post/Is_the_Hafele-keating_experiment_credible
Dear Yin
Any false theory shows its fallacy in reference to the real world, which we sometimes expose by experiment but only when we approach it critically. For example, consider M&M experiment. Fitzgerald and Lorentz did not bother to correctly examine the experiment and consequently Lorentz transformation equations were created which is the basis of relativistic physics including STR. I have shown that if we consider the movement of the half-silvered-mirror in the experiment then the fallacy of relativistic physics is exposed, meaning it was based on a non-existent foundation right from the outset.
When you then start thinking about the consequences of special relativity it shows its true colour. Let us consider another experiment to help us understand the issue better. The experiment carried out by David H. Frisch and James H. Smith in 1963. They tried to prove time dilation and consequently length contraction based on comparing the counts of muons at sea level and at 1920 m height. A very brief overview of this experiment and its consequences is given in TwinsParadox_ZS.pdf page 15-19 which I uploaded to RG a while ago. I did not criticize the assumptions in the experiment and the way it was conducted as I had a much greater concerns.
If we accept the result of this experiment, i.e. STR, then we must completely change our assessment of some very fundamental phenomena in nature. For example, we know that light takes about 8 minutes to reach us from the Sun. If we accept the reality of length contraction, according to the experiment, then in the reference frame of photons the distance between the sun and the earth is shortened to almost zero, considering the space between those two bodies is not entirely vacuous. Thus, light should reach us in microseconds rather than minutes. In fact, any photon traveling in vacuum from any source, near or billions of light years away, should reach us instantaneously as any distance is reduced to zero for photons. This is one of the contradictions with our everyday experiences.
If the movement of the half-silvered-mirror exposes the fallacy of Lorantz transformation, the fallacy of this experiment is blatantly exposed by simply apply the theory to the movement of light.
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