Some questions about the title. I know that at the speed of light the passage of time is effectively zero. Something I've never come across before is the amount of mass required to generate a gravitational field strong enough such that gravitational time dilation is also reduced to 0. Is there a knowwn value? These two situations represent the minimum rate of time in their respective areas, one of which is definitely 0. It seems apparent, then, that at the opposite end there are two, at least theoretical, upper limits on the rate of time. An object at rest (v=0) and a gravitational field of strength=0. The closest that can be found for these situations is out in the middle of an inter-supercluster supervoid. G would at least be negligable, if not 0. This would seem to give us a scale from where a coordinate clock at infinity, unsurisingly, records 1 second per second, while a clock whizzing by at the speed of light will not move at all. Where do we sit on this scale (beyond "near the 1"). What is our relative time relative to these two extremes? :)
Perhaps. Perhaps it is the physical functioning of the universe that is affected. Who knows for certain. Time is an unresolved question. But even using the correct relativistic terminology we still end up with a min/max scale.
why min/max scale for just time; is it not more specifically a time/length scale? i.e. speed How can you get the concept of time on its own? Do you not think length required for a concept of time, and less intuitively vise versa.
I see three problems with your conception: 1) A clock cannot move at c, period. 2) Time dilation can only be defined in relation to clock comparisons, not as some absolute across the universe. 3) Some clock comparisons are reciprocal, some are not. By this, I mean that for two clocks moving rapidly past each other, each considers the other clock as slow (I call this a reciprocal clock relation). In contrast, for two clocks hovering at different distances from a star, the closer one considers the further one to be fast, and further one considers closer one to be slow (this is a non-reciprocal relation). Even independent of gravity, there similar non-reciprocal clock relations for clocks moving non-inertially. So, if we try to form your uniform scale, you immediately have the following issue: for any clock (clock1), anywhere (even just before reaching a singularity), moving in any way, there exists a possible clock (clock2) such that clock1 considers clock2 arbitrarily slow compared to theirs, and clock2 considers clock1 arbitrarily slow. (This reciprocal relation may be brief, but it is always possible to achieve for some nearby clock2).
Your whole premise is flawed: that "a clock whizzing by at the speed of light will not move [tick] at all". No matter how fast a clock is moving, that is, no matter how much it has accelerated, the speed of light is just as far removed from it as when it first started. The speed of light is not an attainable limit for a clock. You are also mixed up on the meaning of time dilation. It is a number always greater than 1. There is no upper limit. This is why Einstein said in his 1905 paper in the middle of article 4: You should change your thinking from "I know that at the speed of light the passage of time is effectively zero" to "I know that at the speed of light the passage of time has no meaning".
Given the spacetime connection, then, yes, length contraction will go hand in hand. 1) I had absolutely no intent to suggest a physical object of any mass could be accelerated to c. The equation that demonstrates this is one of the earliest recollections I have of being introduced to Relativity and I played with it extensively on my graphics calculator. 2) I've read of cases where time dilation is defined relative to a coordinate clock at infinity, in 0 gravity and at 0 momentum. Isn't the Lorentz factor for time dilation representative of a scale? Thank you for the link to the paper. Isn't the point of time dilation that it avoids the issue of a beam of light trickling out of the headlights of a car, which is already travelling at some fraction of the speed of light? It does this by slowing time so that the time component of the measured speed is dilated and any observer in the same reference frame will, if asked to measure c, observer nothing unusual. In conjunction with another poster's comments: If a clock is in a negligable gravitational field and at rest there is no possible circumstance that can have less effect on the clock's recording of time. What you are saying is a clock that goes flying past at 90% the speed of c will be observed to be ticking slower by the observer in the coordinate clocks frame of reference?
You can compare any clocks. Comparing clocks to a particular clock at infinity is possible, but that doesn't mean this clock provides any absolute or limiting time scale. There will be other possible clocks that see this clock going arbitrarily slow. This clock will see other clocks going arbitrarily slow. Time is relative, and you cannot produce a ordering of time rate on all possible clocks in the universe. Put another way: pick any clock at infinity. There will always be another clock at infintiy that sees that clock arbitrarily slow. And this is true for all clocks at infinity.
Let's start with the statement that any observer (without regard to any reference frame) will, if asked to measure the speed of light, get c. This is an observed fact of nature and is true independently of any theory or concept of a frame. It is also true no matter how much the observer has accelerated in the past. Now according to Special Relativity, you can assign an observer to any Frame of Reference. If your choice of FoR is one in which he is at rest, then he will not be experiencing any time dilation. If your choice of FoR is one in which he is traveling at any speed, he will be experiencing time dilation, athough he will not be able to detect it. The faster he is traveling, the greater the time dilation. If he then accelerates in that FoR, his time dilation will increase but there is no limit to how high his time dilation can go and it can never reach infinity. In Special Relativity, every clock always ticks at the same rate. It doesn't matter how high the gravity field is are how fast the clock is traveling. As Einstein said, "Time is what a clock measures". If it ticks once per second, it always ticks at once per second. If by observered, you mean, after the effect of light propagation time is removed, then yes, the observer will determine that a clock flying past him at 90% the speed of c will be measured to be ticking slower than his own but the flying clock will also measure the stationary observer's clock to be ticking slower than itself.
Wouldn't all clocks at 0 motion in negligable gravity actually be ticking at the same relative rate? They are, after all, under the precise same influences...? The point of putting the clock at infinity is to have it at rest and unaffected by any real gravity, not for it to be infintely distant. We could exchange infinity for a supervoid.
zero motion? The possibility of defining such contradicts SR. Pick a clock you believe is at zero motion (e.g. with respect to CMB radiation). That has no bearing on my statement: a clock in relative motion to this clock will see it going slow compared to theirs. So how do you declare it to be the fastest clock in the universe?
Sorry, but some of what you have put seems to ... contradict isn't the word, but we seem to be suffering a language barrier. Let me see if I can translate myself a bit better... I'm not, and haven't suggested, time dilation can increase to infinity or that anyone experiencing time dilation can tell they are. Only that the time dilation will increase to the point the passage of time to an outside observer... Okay. Let's start again. Let's use Anthoney and Cleopatra. Anthoney is travelling at near light speed. Cleo is observing this from her milk bath, at rest. Eventually, as Anthoney increases his speed closer to c, he will appear to cease moving altogether, from Cleo's viewpoint. You and others are also stating that Cleo, from Anthoney's viewpoint has also ceased moving - I have no problem with this and don't suggest it isn't true. And let's forget clocks, let's just put clocks aside entirely for now. Infact, let me stop here and you can tell me if the above paragraph is consistent with relativity, if not the history of Rome.
Firstly, my original post accepted it was more likely theoretical rather than actual. I also pointed out that the closest you might get to such a situation is a supervoid. The behaviour of a clock relative to one in a supervoid or even at infinity is not what I asked in the piece you are quoting. I don't declare anything. If I was all so fired up sure of myself, I wouldn't have come here to discuss it. It seems a natural extension of the mechanics of time dilation.
I'll try again. "All clocks at zero motion in" in negligible gravity or otherwise is counter to the core concept of relativity - that there is no possibility of detecting or preferring some state of zero motion. "The point of putting the clock at infinity is to have it at rest" There is no such thing as 'at rest' in relativity. Only at rest relative to something else; and it won't be at rest relative to a different thing. The core concept of relativity is no absolute rest, period.
No, it is actually counter to the concept of the reciprocal (not absolute) nature of time dilation due to relative motion.
When you say that Anthoney is traveling at near light speed and Cleo is at rest, you are merely choosing an arbitrary Frame of Reference and in that Frame of Reference, nothing, except light, can travel at the speed of light and so nothing will cease moving (by that I think you mean waving his arms around, for example). Anthoney can be moving very, very, very slowly but never ceasing. No matter how slowly he is moving his arms, he can always travel faster so that he moves his arms half as slowly, again and again, without limit. But you can never pick a Frame of Reference in which he is actually traveling at the speed of light and so will cease all motion. His time dilation can always be doubled any number of times and never reach infinity.
This is a version of Zeno's paradox. But, Cleopatra will find it extremely difficult to tell Anthoney is still moving, without watching him a very, very long time. We seem to only be establishing that the upper and lower limit of time dilation, at least, are theoretical (nothing of mass can reach c and no object can be entirely still). Perhaps I can continue the analogy so you can see why I think as I do and perhaps find some way to bridge the gap. My thinking goes like this: Anthoney is experiencing a lot of time dilation. Cleopatra, although experiencing some time dilation, from being in a gravitational field, has far less motion. In fact, perhaps we can agree to put her in a hypothetical space station, and minimise gravitational affects for simplicities sake. Your question to me is why do I agree that they both see each other slow, yet have this notion of a scale, which puts cleo "above" Anthoney. It comes about from a long held notion that time doesn't exist so apparent time dilation requires an explanation. Although more recently I have begun considering time as an actual thing, I'm pretty happy to switch about while pondering the many wonders of the universe (not using both in one universe you understand). Anyway, my perception was that Cleo sees Anthoney slow down because of Anthoney's increasing velocity. Anthoney, however, sees Cleo slow down because his ability to process information is as affected as his ability to move his arms - even if he can't tell. Well, I guess technically, if he knows he got onboard a spaceship that was planning to accelerate to some fraction of lightspeed he might be able to make an educated guess about what's going on, but this is beside the point. I hope this has shed light on where I am coming from and might allow us to take a non-Zeno-like step forward. One thing I should note is that I'm totally open to the notion that this is all just a symmantical interpretation. @PAllen I'm pretty sure I've read several times of clocks with v=0. Is this not the same as "at rest". EDiT: I realise that technically, Anthoney's information processing 'dilation' is also due to his velocity.
No. There is no 'at rest'. The whole point of relativity is that speed can only be defined in a relative way. It is valid to say 'Fred moves at velocity v wrt Sam' but not to say 'Fred moves at velocity v '. The second statement is as meaningless as saying 'Fred is at rest.' You should have paid attention to this
Yes, it will take a very, very long time, but in these thought experiments, time, distance, energy, acceleration, etc, are no problem. Now in your first post, you said that time dilation can vary between 0 (clock stopped), as a lower limit, to near 1, as an upper limit. But you were really talking about tick rate which is the reciprocal of time dilation. "Dilation" means "getting bigger" not smaller. I attempted to point out that the time dilation factor can vary between exactly 1 and has no upper limit. You were attempting to point out that one of the limits could be reached by a clock traveling at a speed of c and wondering where the corresponding limit was for gravitational time dilation. I wanted you to see that if you properly view time dilation as a number greater than or equal to one, then both types of time dilation (one due to speed and one due to gravity) have no upper limit. You also need to be aware that every clock keeps time with no time dilation, in other words, its time dilation is 1. This is what we call Proper Time. This is one of the tenets of relativity, that time is relative for every clock. It isn't until we assign a clock to a Frame of Reference in which it has a speed relative to that FoR that we then can talk about its time dilation factor as defined by that FoR. It sounds to me like you are talking about Relativistic Doppler which is how a pair of inertial observers sees the other ones clock running slower than their own by the same amount. It doesn't matter which FoR you assign them to, one of them may get all the time dilation but they still each see the other ones clock running slow compared to their own by exactly the same amount. It gets a little more complicated when one (or both) of them is accelerating but essentially the same principle applies. But I'm not sure if I have addressed your Zeno issue. I really don't know what your concern is.
In my first post I only ever refer to "rate of time", time dilation is never mentioned in the post. I totally understand what you are saying about time dilation, that when calculated it has a value of 1 and upward (I believe wikipedia has a chart that says the lorentz factor is just over 22 at 99% c, but don't quote me!). Rate of time = the 'length' of a second. Is this the more accurate way to describe time dilation? I also do understand that observer's travelling at some portion of c will have no innate awareness of time dilation. A hapless stranger waking in an enclosed, windowless room would have no way to distinguish between being on board a spaceship travelling at 90% c and being a mile underground on Earth. Infinities are usualy sought to be removed from theory, as I understand it. Has anyone attempted to address the ever decreasing movement of an observer at speeds approaching c? Noone has ever tried to argue that there is a point where such a fractional movement is impossible? Wouldn't Planck's constant become involved, where the energy of such a small motion is below the constant (or does the increasing energy required to accelerate the object overcome this??). The line I put in bold: My first mention of Zeno was just an observation. This is the first time I've ever seen it come in a realistic situation. My second comment about a "non-Zeno-like step" was a pun; a hope that we would do more than move by half the remaining distance between our respective positions. ;) The non-bold paragraph. Hmm. Let's say Anthoney is in the middle of a supervoid, at rest with respect to the CMB. Cleopatra is travelling at 99.9999% the speed of c. They both have time pieces. It seems to me to be true that there is no other clock in the universe that could record Cleopatra's clock as running slower than Anthony does, because it is impossible for anyone to be experiencing any less time dilation than Anthoney is (assuming that we have placed him at a point that is as distant from any source of gravity as can be found). The only way for either to observe a slower rate of time is if Cleo continues the infitessimal crawl ever closer to c (I also recognise that each tiny increase is exponentially bigger than the previous one). Again, is the above paragraph accurate?