Does time dilation prove the existence of an absolute zero velocity?

[Robert Rapplean]

You may think you've seen this before, since I've seen similar discussions in the archives of this, but I think I've distilled the thoughts down to a couple of facts that contradict the common beliefs regarding relativity.

Let me preface this with a basic observation: Lorenz invariance does not apply between things that change their inertial frame of reference. The transforms state that all frames are equivalent, not that there is no difference between them, or that experiments that cross between frames will always produce the same results.

The contradicting statements are as follows. If either of these is mistaken, please let me know where I can find a reference.
1. Velocity is always relative, not absolute.
2. When an object decelerates, time dilation decreases.

For the second statement to be true, there must be a difference between acceleration that increases time dilation and acceleration that decreases time dilation (a.k.a. deceleration). When thinking about this, please remember that we aren't talking about two objects and their relative movement, but also talking about the typical speed of the rest of the universe in relation to those two objects.

For General Relativity, we know that moving things out of a gravitational field will decrease time dilation. It's pretty obvious that, just by measuring microscopic differences in time dilation, we could identify the direction of the gravitational gradient (even if we couldn't feel it) and follow that arrow to a point of minimal gravitational dilation. An absolute zero might not be possible simply because there is nowhere in the universe that doesn't feel the effects of other gravitational bodies, but you could still follow the gradient.

Similarly, it should be possible to follow such a gradient towards an absolute zero velocity. Again, no more achievable than absolute zero temperature, but if you can measure a gradient, you can follow it. If you can follow it, then it must lead somewhere.

My conclusion is that there must be an absolute zero velocity, even if such a thing is meaningless for the purpose of Lorenz invariance.

Thoughts?

 

[andrewkirk]

2. When an object decelerates, time dilation decreases.

For the second statement to be true, there must be a difference between acceleration that increases time dilation and acceleration that decreases time dilation (a.k.a. deceleration). When thinking about this, please remember that we aren't talking about two objects and their relative movement,

On the contrary, that is what is being referred to in statement 2. Velocity-based time dilation is only a meaningful concept in relation to two identified inertial frames of reference. It is a concept from special relativity that only deals with inertial reference frames.

There is no such thing as 'deceleration relative to the rest of the universe'. There is such a thing as reduction in magnitude of peculiar velocity, but that is a concept from general relativity, and is not what 2 is referring to.

 

[Dale]

The contradicting statements are as follows. If either of these is mistaken, please let me know where I can find a reference.
1. Velocity is always relative, not absolute.
2. When an object decelerates, time dilation decreases.

Both statements are correct. They do not contradict each other.

For the second statement to be true, there must be a difference between acceleration that increases time dilation and acceleration that decreases time dilation (a.k.a. deceleration).

Yes, there is a difference, but there is no absolute truth to that difference. It is a difference that depends on the reference frame. The same object at the same moment will be accelerating in one reference frame and decelerating in another. In a frame where it is accelerating its time dilation is increasing and in a frame where it is decelerating it’s time dilation is decreasing.

Similarly, it should be possible to follow such a gradient towards an absolute zero velocity. Again, no more achievable than absolute zero temperature, but if you can measure a gradient, you can follow it. If you can follow it, then it must lead somewhere.

You can do that but there is nothing absolute about it. Each frame would say that the minimum time dilation is at rest in that frame.

 

[Robert Rapplean]

Yes, there is a difference, but there is no absolute truth to that difference. It is a difference that depends on the reference frame. The same object at the same moment will be accelerating in one reference frame and decelerating in another. In a frame where it is accelerating its time dilation is increasing and in a frame where it is decelerating it’s time dilation is decreasing.

This, at least, is a new suggestion. Thank you. Can you throw magic words my way so I can dig through that research?

My understanding is that time isn't relative to anything. Its passage is the one absolute in the universe, although everything experiences it at its own rate. I'm failing to see how something can be simultaneously increasing and decreasing the rate at which it experiences time.

You can do that but there is nothing absolute about it. Each frame would say that the minimum time dilation is at rest in that frame.

This statement suggests that it's impossible for anything to perceive an object with less time dilation than itself, yes?

 

[A.T.]

This statement suggests that it's impossible for anything to perceive an object with less time dilation than itself, yes?

Depends on what you mean by "perceive" and if you are in flat or curved space-time (near gravity sources).

 

[Orodruin]

My understanding is that time isn't relative to anything. Its passage is the one absolute in the universe, although everything experiences it at its own rate.

Then your understanding of tine dilation is wrong. What you are missing is that time is relative, in particular simultaneity is.

Also, your statement 1 is true also in classical physics and statement 2 is a result of special relativity that logically follows from its postulates. Obviously you are not going to disprove relativity using statements that are derived from the relativity postulates.

 

[Mister T]

YThe transforms state that all frames are equivalent, not that there is no difference between them, or that experiments that cross between frames will always produce the same results.

The results of measurements are invariant. Reference frames are mathematical constructs, they can't effect the results of measurements.

And by the way the assertion that all inertial frames are equivalent is called the Principle of Relativity. It's not a consequence of Lorentz transformation. In fact, it's an underlying assumption of the transformation equations,

 

[Ibix]

I'm failing to see how something can be simultaneously increasing and decreasing the rate at which it experiences time.

That would be contradictory, yes. But relativity says you will always see your own wristwatch tick at one second per second. Other observers may say your watch is speeding up or slowing down depending on whether they see you as accelerating or decelerating.

You seem to have some fairly fundamental misunderstandings about relativity. By way of a reference, therefore, I'd suggest Taylor and Wheeler's Spacetime Physics. The first chapter is available online if you want to have a look before buying.

 

[Nugatory]

This, at least, is a new suggestion. Thank you. Can you throw magic words my way so I can dig through that research?

Simple example:
A and B are moving towards one another. A clock between them is initially at rest relative to A (so moving relative to B) and accelerates towards A until it is moving at the same speed as B. Its speed relative to A will increase (acceleration); its speed relative to B will decrease (deceleration) until eventually it is at rest relative to B.

A will find that the clock is initially ticking at the same rate as his own clock, but runs slower as it accelerates. B will find that the clock is initially running slower than his own clock but runs faster as it decelerates until it is ticking at the same rate as his own.

The apparent contradiction here is the same as the apparent contradiction in the standard textbook examples - because A and B are moving relative to one another, A will find that B's clock is running slower than his own, but also B will find that A's clock is the one that is running slow - and the resolution is the same: Relativity of simultaneity.

 

[Orodruin]

and the resolution is the same: Relativity of simultaneity.

My signature remains as relevant as always ...

 

[Dale]

Can you throw magic words my way so I can dig through that research?

It will be easier and clearer to use math. Are you familiar with the Lorentz transform and algebra, how about calculus, or four-vectors?

My understanding is that time isn't relative to anything. ... I'm failing to see how something can be simultaneously increasing and decreasing the rate at which it experiences time.

That is a misconception. Time is also relative. Specifically, coordinate time is relative to the reference frame.

There is a separate concept of time called proper time, which is the time on a clock that travels with an object. It is invariant, but it also cannot be extended beyond the worldline of the object.

This statement suggests that it's impossible for anything to perceive an object with less time dilation than itself, yes?

Yes, with a couple of important caveats. First, it is only true in flat spacetime. And second, “perceive” in this case means “calculate with respect to its momentarily comoving inertial frame”.

 

[Mister T]

This statement suggests that it's impossible for anything to perceive an object with less time dilation than itself, yes?

Time dilation depends on relative velocity, the greater the velocity the greater the amount of time dilation. When the velocity is zero there is no time dilation.

Saying that you can't have less of something is a strange way to say that a magnitude is zero.

 

[russ_watters]

Similarly, it should be possible to follow such a gradient towards an absolute zero velocity. Again, no more achievable than absolute zero temperature, but if you can measure a gradient, you can follow it. If you can follow it, then it must lead somewhere.

I don't think you have thought through how you would to this and what it would look like.

For example, if you had two spaceships flying toward each other, neither accelerating and they were continuously broadcasting time signals, each would measure the other's clock running faster than their own, and by the same amount. This has to be true, otherwise the Lorentz transformation wouldn't work!

My conclusion is that there must be an absolute zero velocity...

That isn't a conclusion, it's just a belief you have. Nothing in your post - even if correct - implied there must be one, just that we could find it if there was one. People have been experimenting on that assumption for 150 years and failing to find it.

 

[Ibix]

For example, if you had two spaceships flying toward each other, neither accelerating and they were continuously broadcasting time signals, each would measure the other's clock running faster than their own, and by the same amount.

To note, here Russ is referring to the direct measurement of tick rate, with no adjustment for the Doppler effect due to changing distance. If you do adjust for that, you recover the "moving clocks run slow" result of time dilation.

 

[russ_watters]

To note, here Russ is referring to the direct measurement of tick rate, with no adjustment for the Doppler effect due to changing distance. If you do correct for that, you recover the "moving clocks run slow" result of time dilation.

I think the statement works both ways.

 

[Ibix]

I think the statement works both ways.

I'm not disagreeing with what you wrote (and I've removed a sentence from my quote of your post to make it more clear what I was referring to). I was just making explicit the distinction between the direct invariant measurements and their interpretation in a reference frame. Failing to realize that this distinction even exists seems to be a fairly common source of confusion when learning relativity, from experience here.

 

[Robert Rapplean]

It will be easier and clearer to use math. Are you familiar with the Lorentz transform and algebra, how about calculus, or four-vectors?

Thanks, Dale. Yes, I've worked with all of those. I had to build an understanding of quaternions for a rendering project about eight years ago. I'm still trying to wrap my head around Minkowsky space-time.

That is a misconception. Time is also relative. Specifically, coordinate time is relative to the reference frame.

I think that this statement is imprecise. Unless you know of a phenomena where time runs backwards or not at all (black holes don't count), then it's just the perception of the passage of time that is relative, not time itself.

 

[russ_watters]

...it's just the perception of the passage of time that is relative, not time itself.

How do you define and measure the difference between "perception of time" and "time itself"? Hint: "time" has one definition, not two.

Unless you know of a phenomena where time runs backwards or not at all...

That doesn't really have any connection to what followed it.

[mod hat]
Several moderators are participating in this thread and have been surprisingly deferential so far. Please note: PF is a place for learning and discussing known science. It isn't a place for speculation or assertion that hundred year old, solidly proven theories are wrong. This thread needs to take on a more learning and less challenging tone or it will need to be locked.

My apologies. I didn't realize that this site harbored those who have naught to defend themselves but affront and insults.

You weren't affronted or insulted. But you do need to review our rules again:
https://www.physicsforums.com/threads/physics-forums-global-guidelines.414380/

 

[Robert Rapplean]

I don't think you have thought through how you would to this and what it would look like.

For example, if you had two spaceships flying toward each other, neither accelerating and they were continuously broadcasting time signals, each would measure the other's clock running faster than their own, and by the same amount. This has to be true, otherwise the Lorentz transformation wouldn't work!

Thanks for the suggestion. I'll try that.

 

[Robert Rapplean]

How do you define and measure the difference between "perception of time" and "time itself"? Hint: "time" has one definition, not two.

If you mark off any event, everything in the universe will thereafter consider that event to be in the past, although It's just the amount in the past that is in question.

 

[Nugatory]

Unless you know of a phenomena where time runs backwards or not at all (black holes don't count, then it's just the perception of the passage of time that is relative, not time itself.

You may be conflating two different things, both of which are quite precisely defined (although often misrepresented in the popular literature): proper time and coordinate time.

Proper time is what your wristwatch or other clock colocated with you measures; the clock ticks five times while you experience the passage of five seconds. It is not frame-dependent - you counted five ticks and aged five seconds as the watch ticked five times and everyone agrees about that. Other observers moving relative to you may talk about time dilation but that has no bearing on your experience (right now you are moving at several tens of kilometers per second relative to a Martian astronomer watching you through a telescope from Mars, and at a substantial fraction of the speed of light relative to an alien in some distant galaxy. None of this affects what you experience as you watch your clock tick off five seconds).

Proper time is necessarily the time interval between readings of the same clock (that's what @Dale was saying above when he said that it cannot be extended beyond the worldline of a single observer). Suppose we ask how much time you experienced between when your wristwatch read 12:00:00 and some distant clock read 12:00:05? Now we can't just count ticks; instead we need to know what your wristwatch reads at the same time that the remote clock reads 12:00:05 so that we can calculate the difference between that reading and 12:00:00 to get our answer. Note that this is never something that you experience directly; if the other clock is a light-year away that "other clock reads 12:00:05" will pass completely unnoticed by you. Note also that the answer depends on the way that you define "at the same time"; you need some convention for assigning time values to events that are not colocated with you and your wristwatch. These assigned values are time coordinates, and differences between them are coordinate time, as opposed to proper time. Normally we assign coordinate times using the most natural rule: if light from an even reaches me when my wristwatch reads $T$ and the event happened at a distance $D$ from me, then the event happened at the same time that my wristwatch read $T-D/c$ (because it took time ##D/c for the light to get to me).

Coordinate time is frame dependent. Observers moving relative to one another, even if they have initially synchronized their clocks, will assign different times to different events. This is the key to the paradoxical-seeming symmetry of time dilation: if A and B are moving relative to one another, both will find that the other clock is slower than their own. A assigns the same time coordinate to "A's clock reads 12:00:25" and "B's clock reads 12:00:15" to conclude that B's clock is running slow. B however assigns the same time coordinate to the events "A's clock reads "12:00:09" and "B's clock reads 12:00:15" to conclude that is A that is slow, by the same factor of 3/5 (which corresponds to a relative speed of .8c).

 

[Nugatory]

This thread had drifted into an unfortunate and ugly argument unrelated to the original question. A radical postectomy ("postectomy": surgical procedure for excising off-topic posts) has been performed. The "last edited" notes will indicate which posts have been affected by the postectomy.

The original question from post #1 can be paraphrased as "Time dilation decreases with deceleration; does that not allow us to identify an absolute zero velocity by decelerating something until the time dilation disappears?" That's the topic of the thread.

All posters are reminded that:
- Physics Forums is here to explain what relativity does say and how it answers that question.
- Arguments that relativity is somehow wrong or incomplete are not allowed under the forum rules.
- Please please please do no post into this thread again until you have read it over once from the beginning.

 

[FactChecker]

Similarly, it should be possible to follow such a gradient towards an absolute zero velocity. Again, no more achievable than absolute zero temperature, but if you can measure a gradient, you can follow it. If you can follow it, then it must lead somewhere.

My conclusion is that there must be an absolute zero velocity,

The gradient is in the coordinate system of a "stationary" observer, not the coordinate system of the moving, accelerating/decelerating object. It is the "stationary" observer who detects the velocities and time dilation of the moving object. So yes, the gradients can lead to a zero -- when the velocity matches zero with respect to the "stationary" observer. That is not absolute. It is relative to the "stationary" observer's frame, whoever that is assumed to be in any scenario.

 

[Dale]

Thanks, Dale. Yes, I've worked with all of those. I had to build an understanding of quaternions for a rendering project about eight years ago. I'm still trying to wrap my head around Minkowsky space-time.

Ok, so time dilation is given by $$\gamma=\frac{1}{\sqrt{1-v^2}}$$ so to find how fast it is increasing we just take the derivative $$\frac{d}{dt}\gamma=\frac{va}{(1-v^2)^{3/2}}$$
This is positive whenever $v$ and $a$ are in the same direction and negative whenever they are in the opposite direction. So if an object is accelerating in the positive x direction, $a>0$, and moving in the positive x direction, $v>0$, then the time dilation increasing. At that same event, in a frame moving in the positive x direction at $u>v$ we have $v’$ is negative and so time dilation is decreasing.

I think that this statement is imprecise. Unless you know of a phenomena where time runs backwards or not at all (black holes don't count), then it's just the perception of the passage of time that is relative, not time itself.

Let’s not anthropomorphize by using words like perception or experience.

Time is what a clock measures. There are four known fundamental forces: electromagnetism, strong, weak, and gravity. Time dilation has been measured for clocks based on all four forces. Furthermore the amount of time dilation is the same for all.

So clocks based on all mechanisms measure the same dilation. We could attribute this to a measurement error, but then we would have to explain why the measurement error for EM is what it is, and why the error for the strong force is what it is, and why they are equal, and why the error for the weak force is what it is and why it is equal to the strong force and ... It quickly becomes far more reasonable to just say that time dilates.