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I was under the impression that you mentioned particle decay here in the context of the topic. In that way, I was considering you meant the decay of a fast or accelerated particle from which you would measure decay. Could you please explain what you mean to point out, specifically the relation to observable/ detectable time dilation in decaying particles?

If time dilation were a direct effect of velocity, and velocity is space traversed in unit time, then time dilation must be related to space because to say it that time is related to time would be a circular definition.

Now, just to let you know, I have great respect for you and your education, and were I a fresh graduate I could see your points from a more current standpoint, but I do have issues here and I do appreciate your every word. So no disrespect when I question.

Ok, so we can accurately measure neutron decay rates via the boson/ e-and-antineutrino product percentage. When we accelerate our heap of neutrons to near lightspeed, we notice slower decay rates. In my previous proposed model, I posit that as an object or system of particles is accelerated, at least the axial spatial dimension contracts commensurately, per the lab's perception not the perception of the accelerated system. From the standpoint of the neutrino, the lab contracts. It takes the neutron a shorter time to pass the same distance in the lab, and thus less time passes for the neutron system than if it had remained in the non-accelerated state. Because the neutron system is the party being accelerated, it experiences the change relative to the lab which remains at constant time flow. Under this model, and by the above details, the length-time relationship is easily explained, in my opinion. Where do you find error?

You are not considering the neutron standpoint view of the lab in the first part of your statement. The neutron sees a shortened length which it traverses. If you are running along and measure the distance you go by two poles, then if you are going fast enough for the two poles to appear closer together (length contraction at near c), then it appears to you that you have traversed the poles in less time than it would normally take were the poles the same distance apart. Yes I am accounting for the different velocities. Let us inspect further. Suppose there were no time dilation. Then the neutron in its reference frame would not observe any length contraction, and per the time on a watch on its tiny little wrist, it would not notice any difference at a given speed. Remember, each observer in their own reference frame thinks it's all peaches and cream normality and everything else is smokin' along. So if the length contraction did not occur, then the neutron moving at a fixed speed after acceleration would expect a specific time to pass in the distance it traverses. It would be normal and after deceleration and comparison, he would agree with lab observation.

The only way for us to keep our heads out of the mystical realm of mysterious missing time is to think logically about the viewpoint of each observer. In the neutron's view, the only realistic way for it to observe less time passing from point A to B is to actually see a shorter distance between A and B. The neutron, seeing a shorter distance between A and B, has not decayed as much by the time it gets to B simply because it was closer and therefore took less time, again from the neutron's standpoint, to arrive. Thus, in the neutron's view, it still has a little more time to say goodbye to its family before departing to boson heaven.

We can see now that time dilation is a length related phenomena. However, you have one last major valid point, and that if all references are valid, why is time dilation biased to one observer? Would they not both see the same dilation and thus cancel? Let us dive into your 'Suppose' scenario to help clarify.

Your point about this possible paradox raised an eyebrow for me when I was first learning relativity as well, but I solved it quickly using the following consideration. The body undergoing accelerations and the body remaining at rest are two separate physical situations. During acceleration, what physical differences does the accelerated body feel versus the body/system at rest? It feels a physical compression against the field (or rocket propellant or whatever arcane technology is being used) against which it accelerates. Go from 0 to 150 miles per hour in a gas blown hydro boat and you'll lose control of your bladder. Inertia and acceleration effects are felt by matter. It's not just a photon observation. The lab's unaccelerated reference frame does not feel any physical effects to modify any resultant phenomena on its matter. The neutron feels physical effects which are different than the lab feels. So why are you so confident that in the lab, 'our interpretation should be equally valid?' It is possible, I admit, that the critical point of dilation occurs only during the accelerations. Perhaps in circular colliders, the fact that centripetal accelerations are constantly felt by the particles contributes to a smooth dilation dataset. Perhaps were we to able to build a straight collider underground traversing thousands of miles, so we could observe a coasting period.

Hmmm, let's go further. Still, I do not feel that there is anything strange going on. Though we cannot be sure of any model, we CAN say with certainty based on observations that the body which experiences acceleration effects experiences time dilation. Now, since we observe what appears to be spatial modification, in for example detecting light around from behind a star or other massive object, we know that gravity causes what appears to be spatial modification. Gravity being an acceleration, we can conclude that acceleration causes spatial modification effects to appear, as seen by an outside observer. Hmm. I see your point too. If we discard all theory and just go on observation and pure logic based on experiment, we can conclude that physically, the difference between lab and neutron is acceleration. We can further say that this acceleration causes slower time in the neutron.

ok 5:30am and I am a zombie. So far i seem to have managed to half-contradict myself. But I do not agree that time dilation is some odd mysterious effect. There is an explainable cause.

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I'm confused as to why length contraction is so much more believable than time dilation.
Also, if both the neutron and the lab are moving at constant velocities, then neither is accelerating, and so both have equally valid viewpoints. There are linear collision laboratories; they don't work as well as the circular ones, but they exist and they exhibit time dilation. Thus acceleration alone cannot account for the time dilation.
I'm just trying to argue that there are situations in which the time dilation can be observed independently of length contraction.
Besides which, if the neutron is accelerated, then if anything its viewpoint should be less valid, not more, than the lab's.

c = 1. Locally, that is.

Thank you both for discussing further. Yes, Layra, I agree that if you take a purely abstract mathematical view, then there is no difference. And Iguana, yes I feel that time dilation is Lorentz contraction related. Both space and time have particular definitions and physical realities which we must remember if we are positing about manifested 'reality.' Space defines position in a 3 coordinate system, as far as we can directly observe. Time has at least one observable dimension. But what is this thing called time? Everything must have a physical reality to it, even if we have not yet completely discerned its details. With scientific inquiry, we will one day. Until then, we can only describe it. In doing so, we must be careful not to extrapolate too far without humbly remembering our position.

Speaking of position, in the literal context, I see another way to help explain my thinking. Time can be metaphorically considered as our 3D space sweeping through a fourth spatial dimension, much as a 2D plane sweeping through a third would see displacement not attributable to the senses or concept of space from a 2D reference point. Once passed, a place on a 2D plane sweeping through 3D cannot go back in its time consideration without somehow accessing that third spatial dimension, perhaps by hyperjumping off its own plane and re-entering another plane sweeping near-through the previous point of occupation. Normally coasting along in the plane would feel no resistance. However, nudging it off its normal path by acceleration, it feels resistance. This acceleration could be seen as our hyperjump- taking the object off the normal plane vector and into another. When released, our object will coast, but along a path which is different post-acceleration, i.e. on another similar but not exact on the same plane were it to have been left to coast.

Every 'action' we take in our 3D world requires that we accelerate some matter to change its position versus what it would have experienced if not for our interference. Thus, we are accelerators. Continuing our metaphor, we are changing the normal 3D path of something. When this occurs, we are, in a way, moving it from one 3D space-path to another. The object undergoing shift from one coast-path to another is changing planes in 2D, and volumetric spaces in 3D.

Now let us examine this from the viewer's standpoint. A 2D viewer perpendicular to the acceleration vector observes the object contract because of the nose of the object moving relatively away and the tail moving relatively toward, and we consider a 2D photon-equivalent as having a maximum speed and therefore the faster the object travels, the more compressed it appears to be. This is merely an observed effect. So Layra, your consideration is valid in that both parties should have equal observations under this view. It is due to acceleration, however, that something new happens physically.

Under acceleration, the physical object is being moved from its normal coasting vector space reference frame to another, similar to the 2D object being accelerated from its coast vector to another. In our 2D metaphor, we considered that it could be seen as jumping from one plane to another 'near-by' one. We can consider the 3D metaphor to be similar, in that acceleration plucks us off one space and into another when the acceleration relinquishes. There is a real physically-felt inertial difference between a coasting object and an accelerating object. The accelerated object moves from one 3D space-reference frame to another, it is unsurprising that we observe changes in that versus both cancelling out. The object is changing reference frames, not us. The time-as-a-higher-spatial-dimension works to a point, but still does not explain trajectories or change directly. But that depth of exploration into the phenomenon of time is unnecessary for our understanding of its apparent modification.

Unless you get into physical changes, describing time dilation using pure mathematics of course can lead to items of note which may not translate into physical reality. As Einstein noted, "In so far as mathematics refers to reality, it is not certain, and in so far as it is certain, it does not refer to reality." We must remember that mathematics is a tool by which natural philosophers may describe physical processes.

Let me give you an example of mathematics diverging from reality. Before the Copernican revolution, Ptolemaic geocentric models bred highly complex mathematical descriptions of the movements of the various heavenly bodies. The at-first-blasphemous heliocentric model vastly simplified and beautified the mathematics, Tycho Brahe and Kepler respected for their role as well. Prior, the mathematical descriptions were close, and in some cases precise, but due to an incorrect model, extrapolations from that prior math were not accurate. The extent to which we can assume physical realities based on its fitting with our equations works only to the extent that our model is accurate. And accurate is a relative term, as we can become even more exact as we uncover more scientific detail.

Physical 'reality' is the world in which we find ourselves. We have learned that we are made of complex particular organizations of these things called atoms, and on down to our latest made-up virtual 'particles.' What occurs during inertial effects is acceleration of these atoms through a sea of electromagnetic disturbances and various kinds of 'particles' flitting about. We know by experiment that something occurs which causes the accelerated particle system to proceed, with whatever internal processes occur, at a measurably slower rate than if they were undisturbed. As Layra points out, experiment also shows more time dilation effect on a particle in a circular collider (constant centripetal acceleration) than one which is linear. This suggests that indeed acceleration may be more of a factor than the speed difference itself. Dilations with both reference frames coasting may simply be apparent space effects, and acceleration could be the factor directly affecting 'time.' Current mathematical predictions and explanations can only go a few steps removed from experiment before they become guesses at best. That time dilation occurs is clear. That spatial effects cause it is logical but not proven, yet we must remain consistently logical for us to even form a competent testable hypothesis. As has been proven in every major scientific advancement, mysteries are subject to explanation given sufficient analysis. We can at least be confident that time dilation is a physical effect felt by an accelerated body.

It is logical that the accelerated body has its constituent parts stressed away from normal as well. Something in this stress retards its internal processes. The logically derived candidate model I will not explain here due to the misconceptions of contemporary science having taught most of you to scorn anything not in your textbooks. Suffice to say that there is a completely comprehensible physical mechanism for this time dilation at the quantum level. Length contraction happens physically only if the accelerating force is not uniformly applied (a pilot is squished somewhat against his chair due to G forces felt in a turn, for example). For a particle to NOT be length-contracted during acceleration, some ubiquitous field would have to accelerate every internal particle equally and simultaneously. Aside from our assumptions about gravity, which is another topic entirely, no experimentally verifiable physical mechanism for such a completely uniform and ubiquitous interaction on an object yet exists, and therefore all models and mathematical assumptions which rely upon such speculations are not supportable and thus are not reliable when we try to build it back up into a general physical interpretation or explanation for observable physical phenomena.

Therefore, all we can say physically is that there is a change in a body under acceleration, and this change causes its internal processes to slow. We also can see that spatial contraction APPEARS to occur. It may indeed be that the time dilation ends up being a purly spatial effect. But we must remember that heated objects give off much more radiation than cooled objects. The Brownian motion of molecules consists of rapid short accelerations. Accelerations cause time dilation effects. More accelerations cause us to detect more radiation. Increased radiation, therefore, may be linked, at least with this example, to time dilation. So there are all manner of speculations which can be pointed to as causative and resultant effects of any model one creates, such as 'while feeling acceleration, some of a body's matter is translated to energy from the rest frame's viewpoint,' but ultimately we must continue to probe by experiment to uncover more truth. Until one has sufficient data, all this is speculation.

But we can be consistent in our logic and thereby make sure our lens remains focused. Time requires space, and the movement of physical systems from one place to another in that space, to measure it, and therefore time is a function of space, not some disconnected scalar. We may say 1 second, but really we are saying that at STP, a cesium atom has vibrated approximately 9,192,631,770 oscillations. 'Second,' then, is merely a metaphorical construct for the underlying spatial phenomena. Therefore, when we say meters per second, we are comparing a specific measurable spatial distance traversed to some other spatial phenomenon, be it vibrations of cesium atoms or comparing it to how far a laser beam of light traveled in the 'time' it took our measured object to traverse that meter. Mechanical, digital, and atomic clocks, and even our own brains, measure the amount, distance, or some other physical quantity of change. Objects under acceleration experience a real spatial effect, and we measure that less of its internal physical processes occur versus if it remained in our inertial reference frame. Since all of these processes are derived from spatial phenomena, we can say that it is likely for the time dilation effect to be at minimum indirectly related to spatial effects, if not directly.

After a few hours sleep, it seems I can at least remain logically consistent. =D

Comments?

Please (a) realize that my statements are within the context of their surrounding topic, and (b) read the balance of my posts before you draw assumptions.
i have not separated time and space. Read again and see that I attempt to bridge them. And yes I am familiar with Minkowski's 4D manifold. This thread attempts to help explain, not add more complexity. Dropping names as metaphors to replace having to explain your conceptualizations of the relevant sections is not our goal here. Rather, we seek actual understanding versus abstractions. In that spirit I have taken time to explore the topic from a wider perspective. About the spacetime manifold concept, see my above consideration that it may be possible to view time as our 3D space sweeping through a 4th dimension, much as a 2D being may consider time as its plane sweeping through a 3rd dimension. Sad that I have to repeat this to one who seems so adept in physics. Yes I accept that geometric spacetime interpretations are in accord with relativistic mathematics. The precise and testable predictions based on that are not necessarily a physical interpretation or explanation of the underlying physical causes, however. The point of my entering this discussion was to try and help explain relativistic effects to the original thread originator. This I have attempted to do by exploring possible physical reasons for the dilation effects. And for that I do not apologize. Attempting to stuff more math down the threadstarter's throat and try to explain by saying, 'we've tested our model and so we know it is reality,' borders on a circular self-supporting argument. You still are not explaining what occurs on a physical level. Instead, you are substituting mathematical models for real-world explanation. They are not the same. While I respect your acumen, I remind you of the extrapolative boundaries of intangible descriptions.