# Min/max Time dilation

by salvestrom
Tags: dilation, min or max, time
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Quote by salvestrom
 Quote by ghwellsjr 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).
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.
 Quote by salvestrom 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.
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.
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 Quote by ghwellsjr 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. 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?
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 Quote by salvestrom 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?
No, this is inaccurate, repeating the same errors pointed out many times in this thread. Errors:

1) "Cleopatra is travelling at 99.9999% the speed of c". In relativity, this is an inherently meaningless statement. I assume you mean Cleopatra is traveling 99.9999% c relative to Anthony. This also means Anthony is traveling 99.9999% c relative to Cleopatra.

2) Cleopatra perceives Anthony's clock running very slow. Anthony perceive Cleopatra's clock running very slow. This is the reciprocal time dilation pointed out at the very beginning of this thread, that you seem unwilling to accept, even though it is the most elementary concept of SR.

Why not read part 1 of Einstein's 1905 paper that Gwellsjr gave you a link for. Read it carefully, with an open mind.
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 Quote by salvestrom In my first post I only ever refer to "rate of time", time dilation is never mentioned in the post.
But you did:
 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.
 Quote by salvestrom 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?
No, if anything, the rate of time is the reciprocal of the 'length' of a second (or other unit of time). The Time Dilation Factor is the ratio of the 'length' of a second (or other unit of time) on a moving clock to the 'length' of the same unit of time on a stationary coordinate clock and is given the name "gamma". This, of course means that you have to establish a coordinate system, otherwise known as a Frame of Reference and you have to know the speed of the clock/observer in that FoR. Then you can easily calculate gamma with the simple formula:

γ = 1/√(1-β2)
where β is v/c.

More often, gamma is applied to the tick rates of clocks because we are more familiar with how they keep time rather than how long a second is. Then we can say that the Proper Time on a moving clock is the reciprocal of gamma times the Coordinate Time of a real or virtual stationary clock.
 Quote by salvestrom 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?
Yes, Einstein did in his 1905 paper in section 4 with this equation:

τ = t√(1-β2)
where τ (tau) is the Proper Time on the moving clock (or observer) and t is the Coordinate Time on the stationary clock (or observer).
 Quote by salvestrom 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??).
Relativity is not concerned with this kind of detail.
 Quote by salvestrom 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?
No, it's all mixed up.

First off, just say that you have a Frame of Reference in which Anthoney is at rest and Cleopatra is traveling at 99.9999% the speed of c. The CMB is not a factor. Since Cleo is the one that is traveling, her clock is the one that is time dilated meaning it is ticking more slowly than Anthoney's according to our selected Frame of Reference. You can apply the formula above for the Proper Time rate of both clocks.

I have no idea what you mean by:
 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
Time dilation is not an issue between two clocks. It is an issue between each clock's Proper Time and the Coordinate Time of a Frame of Reference. Although it is true that "it is impossible for anyone to be experiencing less time dilation than Anthoney is", since he is at rest in our chosen FoR, the first half of your sentence doesn't make any sense.

However, in a different FoR, say where Cleopatra is at rest and Anthoney is traveling at 99.9999% of c, Anthoney's clock will be time dilated and Cleo's will have no time dilation. We could also pick a FoR kind of "half way" between the two of them so each of them is traveling at about 99.9% of c in the opposite direction and they will both be experiencing the same time dilation.

But again, this doesn't take into account how each one observes the other clock for which, as I said, you need to use Relativistic Doppler. Relativistic Doppler is the same in all Frames of Reference, in fact it is not related to any theory but an analysis of what can be measured.
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 Quote by PAllen No, this is inaccurate, repeating the same errors pointed out many times in this thread. Errors: 1) "Cleopatra is travelling at 99.9999% the speed of c". In relativity, this is an inherently meaningless statement. I assume you mean Cleopatra is traveling 99.9999% c relative to Anthony. This also means Anthony is traveling 99.9999% c relative to Cleopatra. 2) Cleopatra perceives Anthony's clock running very slow. Anthony perceive Cleopatra's clock running very slow. This is the reciprocal time dilation pointed out at the very beginning of this thread, that you seem unwilling to accept, even though it is the most elementary concept of SR. Why not read part 1 of Einstein's 1905 paper that Gwellsjr gave you a link for. Read it carefully, with an open mind.
You need to read my posts more carefully, because in one of them I made it perfectly clear I have no problem with Anthoney and Cleo mutually percieving the other as slower. And the paragraph you quoted makes no statement to the contrary. I simply make no direct mention of what Cleo observers of Anthoney's clock. In fact, the final sentence indirectly acknowledge is it.

Your number 1) statement is slightly less settled from my point of view.
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 Quote by ghwellsjr But you did
I reread that post and missed that :/. I sit corrected.

It's late, so on that blunder, I shall retire for now.
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 Quote by salvestrom Your number 1) statement is slightly less settled from my point of view.
Is this because you believe there is an absolute speed/rest?
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 Quote by salvestrom You need to read my posts more carefully, because in one of them I made it perfectly clear I have no problem with Anthoney and Cleo mutually percieving the other as slower. And the paragraph you quoted makes no statement to the contrary. I simply make no direct mention of what Cleo observers of Anthoney's clock. In fact, the final sentence indirectly acknowledge is it. Your number 1) statement is slightly less settled from my point of view.
Statement (1) is the defining principle of relativity. You have a completely different theory without it.

I see there is a different way to read a key sentence I responded to, and I mis-interpreted what you meant. Unfortunately, the alternative interpretation is equally false. You say:

"
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"

So, you are emphasizing that Anthony perceives Cleopatra's clock very slow (and don't care about what Cleopatra perceives). However, the statement is false anyway. Introduce Bob, moving at .9c relative to Anthony in the opposite direction as Cleopatra. Then Bob sees Cleopatra's clock going slower than Anthony sees it. Specifically, here is the order of time rates each perceives:

Anthony: Anthony, normal; Bob slow; Cleopatra very slow.
Bob: Bob normal; Anthony slow; Cleopatra very very slow (slower than Anthony sees Cleopatra).
Cleopatra: Cleopatra normal; Anthony very slow; Bob very very slow.
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 Quote by salvestrom Given the spacetime connection, then, yes, length contraction will go hand in hand. 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?
There is no "scale" for time dilation of zero to infinity. You already agreed (superficially I guess)that time dilation and length contraction go "hand in hand".

From the perspective of your "time dilation scale" you cannot ignore length contraction. There is a "scale" of sorts, length on one end time on the other, not zero and infinity.

To say it differently time is a "unit", a I'm sure you would agree a "unit" is not actually representing any numerical value i.e. no zero through to infinity on this "scale". But, length measurements can "blend" into time measurements (&vice versa of course) and viola, time dilation/length contraction.

This "blending" could be seen as a "scale" of sorts, with an interval being purely timelike on one end and purely spacelike on the other.

Im not sure if your graphing calculator illustrates this, but consider that c is the fastest speed, any movement in a spacial dimension starts to "pull" the time dimension across that spacial dimension, that is the "blending" of the time & length measurements.

Now after all this talk of time & length measurements, consider that speed (length*time) is relative. So it follows that time & length are relative, If you agree that motion is relative (i.e. no absolute rest), it is the exact same as agreeing there is no absolute measurement for time / length.

I think I reitterated the inseperable relationship between time and length enough to get the point across that you cannot "zero in" on a time dilation "scale".

Why is the "relationship inseperable"? It's motion that inherantly "blends" these units together. Specifically it is comparative motion where these units blend. "transform" might be the term used to describe this.

There is a part of relativity that I find doesn't fit well with my intuition, and is simular to this thread.

Time dilation /length contraction is not linear from "at rest" through to near c. That is, with the help of superman, we (me & superman ) accelerate our solar system to near c, using the stars to coordinate the starting position. A few years later, superman and I forgot we already did this, so we do it again, and again and again ect. all subsequent times we did this we re-coordinated the start position again and accelerated from there obsvering our speed going from 0 through to near c again, following the same non-linear whatever. These observations would be made each time the excersise was done. Relative to the original start position we are travelling nearer to c, despite having observations of accelerating from zero to near c numerous times. ( i get comparing the two observations is apples to oranges).

Anyways, it's this "layering" of relative motion that starts to make me confussed why we can't find something/anything that we could coordinate speed to. Not that I question the validity of classical physics, just my ability to reason it , in this way. hint hint

I think because momentum is a function of speed it would be relative, so there is no absolute "zero" momentum. Simular with gravity, free fall is zero gravity.
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 Quote by russ_watters Is this because you believe there is an absolute speed/rest?
This is a good question. My original post certainly came at it from the prespective that there seemed to be. I'm not yet wholly convinced there isn't. Alot now hinges on any progress made regarding PAallen's last two posts. And so without further ado:

 Quote by PAllen Statement (1) is the defining principle of relativity. You have a completely different theory without it.
Defining principal or not, it is by far the most bizarre aspect of the entire theory and not something that just clicks into place.

 I see there is a different way to read a key sentence I responded to, and I mis-interpreted what you meant.
I failed quite miserably at rereading one of my own posts.

 Introduce Bob, moving at .9c relative to Anthony in the opposite direction as Cleopatra. Then Bob sees Cleopatra's clock going slower than Anthony sees it. Specifically, here is the order of time rates each perceives: Anthony: Anthony, normal; Bob slow; Cleopatra very slow. Bob: Bob normal; Anthony slow; Cleopatra very very slow (slower than Anthony sees Cleopatra). Cleopatra: Cleopatra normal; Anthony very slow; Bob very very slow.
Bob is good. But first, your prior post stated Anthoney is travelling at 99.9999% c from Cleopatra's frame of reference. While I understand the idea of treating any observer as being stationary and the universe as the thing that is moving, are there not certain realities that show Cleo is the one moving?

I.e. Cleopatra will have gained mass, Anthoney will not. Cleopatra has the potential to blindly fly into a planet, Anthoney doesn't. If travelling at 99.9% c Cleo will have a Lorentz factor of just over 22. Am I interpreting this correctly as saying that over a distance of 22 lightseconds Cleo will only experience a second of time?

As for Bob. If he and Cleopatra match speed in opposite directions, you are effectively saying that Anthoney will see them both tick at the same rate, and that their dilation will continue to infinity as they continue to accelerate. And that Bob and Cleo will see each other as slower and not that their clocks are moving the same?

@George. In the section you asked me to look at the only thing I could see that seemed relevant was that he said we could ignore fourth and higher magnitudes. Is this what you were referring to?
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 Quote by salvestrom This is a good question. My original post certainly came at it from the prespective that there seemed to be. I'm not yet wholly convinced there isn't. Alot now hinges on any progress made regarding PAallen's last two posts. And so without further ado: Defining principal or not, it is by far the most bizarre aspect of the entire theory and not something that just clicks into place.
Actually, it was universally accepted from Galileo's time, except for a short, confusing period in the 1800s, before Einstein re-established Galileo's principle: you cannot distinguish a state of rest; all inertial frames are equivalent. However, this principle plus Maxwell's equations required some conceptual changes to space and time.
 Quote by salvestrom Bob is good. But first, your prior post stated Anthoney is travelling at 99.9999% c from Cleopatra's frame of reference. While I understand the idea of treating any observer as being stationary and the universe as the thing that is moving, are there not certain realities that show Cleo is the one moving?
No, no, no.
 Quote by salvestrom I.e. Cleopatra will have gained mass, Anthoney will not. Cleopatra has the potential to blindly fly into a planet, Anthoney doesn't. If travelling at 99.9% c Cleo will have a Lorentz factor of just over 22. Am I interpreting this correctly as saying that over a distance of 22 lightseconds Cleo will only experience a second of time?
Many mistakes here. Energy (and relativistic mass) are frame dependent. From Anthony's point of view, Cleopatra has more energy (which you may equate to mass). From Cleopatra's point of view, Anthony has more energy (which you may equate to mass). Suppose there were a planet at rest relative to Cleo. Anthony can't smash into it?

Traveling 22 light seconds of Anthony's distance, Cleo will experience 1 second. Traveling 22 light second of Cleo's distance, Anthony will experience 1 second.
 Quote by salvestrom As for Bob. If he and Cleopatra match speed in opposite directions, you are effectively saying that Anthoney will see them both tick at the same rate, and that their dilation will continue to infinity as they continue to accelerate. And that Bob and Cleo will see each other as slower and not that their clocks are moving the same?
Yes. In this adjusted scenario, Anthony will see Bob and Cleo equally slow; Bob will see Anthony slow and Cleo slower; Cleo will see Anthony slow and Bob slower.
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 Quote by salvestrom @George. In the section you asked me to look at the only thing I could see that seemed relevant was that he said we could ignore fourth and higher magnitudes. Is this what you were referring to?
I think you have me mixed up with someone else. What post # is this in?
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 Quote by ghwellsjr I think you have me mixed up with someone else. What post # is this in?
In post 22 you said that Einstien removed the infinities in section 4.
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 Quote by PAllen Actually, it was universally accepted from Galileo's time, except for a short, confusing period in the 1800s, before Einstein re-established Galileo's principle: you cannot distinguish a state of rest; all inertial frames are equivalent. However, this principle plus Maxwell's equations required some conceptual changes to space and time.
I was referring to the notion of two observers relative to each other both observing the other as being slower.
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 Quote by salvestrom I was referring to the notion of two observers relative to each other both observing the other as being slower.
Ah, but that's the only way to preserve the principle of relativity. If some inertial observer sees 'fast clocks run slow', and another inertial observer sees 'fast clocks run fast', we have different laws for different inertial observers. As soon as you admit time dilation at all, 'fast clocks slow' for both is the only way to make it work while preserving equivalence of inertial frames.
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 Quote by PAllen Traveling 22 light seconds of Anthony's distance, Cleo will experience 1 second. Traveling 22 light second of Cleo's distance, Anthony will experience 1 second.
Can you ellaborate please on "Anthoney's distance" and "Cleo's distance".