Is Time's Speed Just Wild Speculation?

[m.starkov]

Ok, got it. But what can you say about the second point?

 

[Dale]

Ok, got it. But what can you say about the second point?

I assume that by "second point" you mean:

So the question is how can I find this "observed velocity"?

Use the Lorentz transform. Follow my example in post 99.

 

[m.starkov]

No! )
I mean my post from Jul10-09, 03:12 PM.
I can't understand how amount of time elapsed can depend on "k"?!

 

[Dale]

How can it possible: the amount of time elapsed depends on "k"!

The time must depend on k since the speed is, at all times, proportional to k and therefore the time dilation is at all times a function of k.

The "k" is relative coefficient!

k is not relative, it is proportional to the acceleration, which is absolute.

Go ahead and do the derivation using the general formula above. You will get the right dependence on k if you do it carefully. Be aware, not all values of k will be possible, so don't be surprised if you get strange (eg imaginary) results for large k.

 

[m.starkov]

Ok, but what about values?
I have put my values (50000 and -100000) as you see on the picture, but I getting values different from yours ones. Is that ok?

And there are some more points there about this.
You say acceleration is absolute. Ok.
If I have acceleration caused by gravity then can I use this formula too?

So if I have a rotating alpha particle then if it will get into some electric field then the rotation will get slower due to time dilation effect, correct?

 

[Dale]

Ok, but what about values?
I have put my values (50000 and -100000) as you see on the picture, but I getting values different from yours ones. Is that ok?

What are you referring to? The only two values I showed agreed with your values.

If I have acceleration caused by gravity then can I use this formula too?

I would rather not get into general relativity while you are still shaky on special relativity. But in essence, yes, a generalization of this equation is called the metric and is of critical importance for gravity and GR.

 

[m.starkov]

Ok,
So if I will sit every day on a carousel I will be yonger than others?
Acceleration will be always with me, so my time should go slower, yes?

 

[vin300]

,
So if I will sit every day on a carousel I will be yonger than others?

If you stay on the fifth floor you be 3 minutes older in 1000 years than groundfloor

 

[Dale]

So if I will sit every day on a carousel I will be yonger than others?

Yes, I think it would be a worthwhile exercise for you to calculate this. It is a useful problem for its own sake since rotation is so common, and it will help build your confidence and proficiency.

Use the spacetime interval (as shown above) to determine the difference between two clocks, one that is on the carousel and the other that is on the ground that is right next to the carousel. The only real difference from what I showed above is that you will need to use two spatial dimensions to describe the worldline.

 

[m.starkov]

Yes I can try. But first I would like to clarify some points.
Here we have no changes in velocity, only movement direction changes.
Does it cause the time dilation effect?
To make conditions simple: we are in open space and not on an orbit of any planet.

 

[A.T.]

Yes I can try. But first I would like to clarify some points.
Here we have no changes in velocity, only movement direction changes.

That's still a change in velocity (vector) just no change in speed (scalar). But it still means proper acceleration.

Does it cause the time dilation effect?

In flat space time the proper accelerated will experiences less proper time between meetings that the inertial one.

It would be interesting to compute this also in the non-inertial frame of the carousel guy. There are metrics that describe space-time for a uniformly accelerated observer. Can they be used here?

 

[m.starkov]

So I really can't understand now why these guys who performed time dilation approvement experiment use Aircrafts?
It's enough to use carousel in a garden or just to take a rope and spin the clocks by hands!
Can I reproduce that experiment by myself?
I mean can I take two electronic watches, ensure its sync during a month and then put one of them on a carousel and see what will happen in the following month?
I believe we can compensate china's watch precision with a long time of experiment. We will know watches precisions.
Am I right in my conclusions?

 

[DaveC426913]

So I really can't understand now why these guys who performed time dilation approvement experiment use Aircrafts?
It's enough to use carousel in a garden or just to take a rope and spin the clocks by hands!
Can I reproduce that experiment by myself?
I mean can I take two electronic watches, ensure its sync during a month and then put one of them on a carousel and see what will happen in the following month?
I believe we can compensate china's watch precision with a long time of experiment. We will know watches precisions.
Am I right in my conclusions?

Because the discrepancy is tiny tiny tiny. Too small for watches on carousels.

 

[m.starkov]

Wait a minute. For aircraft way for several thousands of kilometers the discrepancy was NOT so tiny tiny tiny.
And here I'm putting my clocks on the end of a rope and the other end of a rope I bind to ventilator making clocks to rotate at high speed.
So the acceleration is high here and it suffer acceleration for ALL the time (for aircraft case acceleration is only at the take off and landing).
Thus I expect here not so tini discrepancy.
If you are strong in formulas then I would like you to give approx. value for the following conditions.
Radius = 0.5 meter
Ventilator Speed = 2000 rpm
EarthTime = 1 month

 

[Gigan]

The linear speed of a clock on that rig would be .5m x 2000rpm = 1000 m/min = ~ 17m/sec (I know I'm rounding up)

The equation for time dilation is:
$$\triangle t \prime = \frac{\triangle t}{ \sqrt{1-v^2/C^2}}$$

Put in your data (assuming your month has 31 days of exactly 24 hours) and you get a difference of $$5.3 \times 10^{-9}$$ seconds.
The clock that has been spinning will be 5.3 nanoseconds behind one that is stationary.(I'm fairly certain that math is right even if this is my first post :) )

 

[matheinste]

Wait a minute. For aircraft way for several thousands of kilometers the discrepancy was NOT so tiny tiny tiny.
And here I'm putting my clocks on the end of a rope and the other end of a rope I bind to ventilator making clocks to rotate at high speed.
So the acceleration is high here and it suffer acceleration for ALL the time (for aircraft case acceleration is only at the take off and landing).
Thus I expect here not so tini discrepancy.
If you are strong in formulas then I would like you to give approx. value for the following conditions.
Radius = 0.5 meter
Ventilator Speed = 2000 rpm
EarthTime = 1 month

Aircraft circling the Earth are continually accelerating.


Matheinste.

 

[m.starkov]

The linear speed of a clock on that rig would be .5m x 2000rpm = 1000 m/min = ~ 17m/sec (I know I'm rounding up)

The equation for time dilation is:
$$\triangle t \prime = \frac{\triangle t}{ \sqrt{1-v^2/C^2}}$$

Put in your data ...
5.3 nanoseconds behind one that is stationary.

The Keyword is "linear".
I'm not so sure we can use this formula in this experiment.
Because the movement is not linear.
The major sense of this experiment is that clocks is always under acceleration.
Your formula doesn't "feel" that acceleration.
Dalespam recommends to use always Lorentz transformation formula.
But I'm not strong enough in Math to handle it.
May be someone else can do it.
It will be very good if we can reproduce time dilation effect just at home using ventilator and china's watches.
Yes, temperature will be different and also may be some electrostatic charge can affect results.
But we can reduce these conditions as we can and... since this is not for public this is just for ourselves. If calculated value will be just aprox. as actual - it will be very nice!

 

[m.starkov]

Aircraft circling the Earth are continually accelerating.
Matheinste.

During the flight it suffers only centripetal acceleration which is not so high.

 

[matheinste]

Just FYI.
Aircraft accelerates only at takoff and landing.
During the flight it suffers only centripetal acceleration which is not so high.

Circular motion, with or without gravity is accelerated motion. An object following a curved path is accelerating towards the instantaneous center of curvature of that path. In the case of circular motion the acceleration is at all times towards the center of the circle. The acceleration is real.
What would be the point of the aircraft circling the Earth if the only effective accelerations were at landing and take off?

Matheinste.

 

[Ich]

I'm not so sure we can use this formula in this experiment.

Of course you can. It is completely general (in flat spacetime). Have a look at http://www.fourmilab.ch/etexts/einstein/specrel/www/" .

 

[Dale]

Dalespam recommends to use always Lorentz transformation formula.
But I'm not strong enough in Math to handle it.

I think you can handle it. You did very well previously, especially considering that I gave some bad advice. Plus, you have access to some math software (Maple?). Just follow the steps:

1) Pick some inertial frame.

2) Write down the parametric form of the path ( t(r), x(r), y(r), z(r) ) in terms of some arbitrary parameter r.

3) Optionally, (not necessary, will not affect the results, but you seem interested in doing it) use the Lorentz transform to find the path, or worldline, in any other inertial frame. The parameter, r, is unchanged.

4) Find the derivatives: dt/dr, dx/dr, dy/dr, dz/dr.

5) Evaluate the integral form of the metric:
$$\tau = \int \sqrt{\left(\frac{dt}{dr}\right)^2-\left(\frac{dx}{c \, dr}\right)^ 2-\left(\frac{dy}{c \, dr}\right)^ 2-\left(\frac{dz}{c \, dr}\right)^ 2} \, dr$$

 

[ibcnunabit]

what is the speed of time?

I understand the sense of the question, but within a given frame of reference, the question is meaningless. If time "sped up" or "slowed down", it would do so for everything in that frame, and would be indetectible. Also, speed is a concept that's derived from time, so to try to build it into time somehow would be faulty reasoning.

AND YET:

Physicists talk all the time about time speeding up or slowing down in one frame relative to another. You need the 2nd frame of reference to describe the other frame--but even then, that's only comparing to your own frame--it's not an absolute measure. It can be described as a proportion between the two, but that proportion would be unitless. It would be a constant like 1.2 or 0.7. The same would be true if a strong gravitational field were applied. Time would be "slower," but that change in the time stream would be indetectible to the entity upon which it was applied. Others, however, could conceivably detect it and measure relative to their own frame.

Cheers,
Mike from Shreveport

 

[m.starkov]

Basically, all of the usual relativity formulas (time dilation, length contraction, relativistic velocity addition, etc.) are special cases of the Lorentz transform. Because they are special cases if they are accidentally misused you can get contradictions, which is what happened here. It is always safer to use the Lorentz transform rather than the special-case formulas whenever possible, which I will do in the write-up.

Well, finally I have managed to bring my brains together.

The major question for me for the moment: how Lorentz transformation formulas can help here?
AFAIK Lorentz transformation formulas can be used only for calculating Position and Time in another INERTIAL frame.
But my clocks frames are NOT inertial!

So I really can't understand how we can find TIME elapsed in not-inertial frame using only inertial-to-inertial transformations?

It is not in Math, I just can't get the principle...

Can somebody help me?

Dalespam?

 

[Dale]

The major question for me for the moment: how Lorentz transformation formulas can help here?
AFAIK Lorentz transformation formulas can be used only for calculating Position and Time in another INERTIAL frame.
But my clocks frames are NOT inertial!

So I really can't understand how we can find TIME elapsed in not-inertial frame using only inertial-to-inertial transformations?

It is not in Math, I just can't get the principle...

Can somebody help me?

Don't worry, this is a very common misconception (see Baez's http://math.ucr.edu/home/baez/physics/Relativity/SR/acceleration.html" ). Special relativity can easily handle accelerating objects, as long as you do the analysis in an inertial reference frame.

In other words, don't forget that reference frames are nothing more than coordinate systems. There is never any requirement that you attach a coordinate system to every object, nor is there even a requirment that every coordinate system be attached to some object. In fact, the most generally useful reference frame, the center of mass frame, usually does not correspond to the rest frame of any single particle. The whole point of SR is that you can use any inertial reference frame to do your analysis, not that you need to attach a coordinate system to each object and re-do your analysis multiple times.

 

[RLS.Jr]

The speed of time is dependant on our speed of travel. Tell me how fast we are going and I will tell you the speed of our time.

 

[DaveC426913]

The speed of time is dependant on our speed of travel. Tell me how fast we are going and I will tell you the speed of our time.

OK, I'll bite.

We're traveling at 93,141 mi/s relative to Milky Way galactic centre. What is the speed of our time?

 

[GoodPR]

rls.jr your going to have to caculate the effect gravity has on this speed of time your speaking of also

 

[Austin0]

what is the speed of time?

I propose that the speed of Time is c.

 

[Count Iblis]

What is the speed of the x-coordinate?

 

[RLS.Jr]

OK, I'll bite.

We're traveling at 93,141 mi/s relative to Milky Way galactic centre. What is the speed of our time?

Our speed is determined by adding all the vectors of travel in respect to the center of the Universe. Picking one vector (93,141 mi/s relative to Milky Way galactic centre) is as incomplete as determining Lance Armstrong's average speed of a 8 hour race by measuring distance in a random 60 second interval.

However, if you wanted the speed of our time based on 'Milky Way Galaxy Time', and added all vectors of travel (earth's rotation: ~900 mph; Earth's orbit: ~66,600 mph; our solar system's motion within the galaxy: ~41,666 mph) and came up with an instant vector (much less than 93,141 mi/s) then it could be done. Let's hypothetically say that at this second it is 84,000 mph relative to Milky Way galactic centre. Now, based on our relative speed compared to C, what is the speed of our time (in Milky Way terms)?

 

[PaulRacer]

OK, I'll bite.

We're traveling at 93,141 mi/s relative to Milky Way galactic centre. What is the speed of our time?

Half the speed of light? Now were talkin'. How do we know this? From my understanding time spans from infinity to zero. But 1 second will always be 1 second to the person experiencing it firsthand. Love this site.

 

[DaveC426913]

Our speed is determined by adding all the vectors of travel in respect to the center of the Universe. Picking one vector (93,141 mi/s relative to Milky Way galactic centre) is as incomplete as determining Lance Armstrong's average speed of a 8 hour race by measuring distance in a random 60 second interval.

However, if you wanted the speed of our time based on 'Milky Way Galaxy Time', and added all vectors of travel (earth's rotation: ~900 mph; Earth's orbit: ~66,600 mph; our solar system's motion within the galaxy: ~41,666 mph) and came up with an instant vector (much less than 93,141 mi/s) then it could be done. Let's hypothetically say that at this second it is 84,000 mph relative to Milky Way galactic centre. Now, based on our relative speed compared to C, what is the speed of our time (in Milky Way terms)?

Well, it was your question; presumably you had an answer.

I was just interested if your were going to propose an answer that was anything other than 'one second per second' - to which I would have cried foul.

 

[RLS.Jr]

Well, it was your question; presumably you had an answer.

I was just interested if your were going to propose an answer that was anything other than 'one second per second' - to which I would have cried foul.

Fine, here is your answer:

Assuming we are traveling at 84,000 mph or 23.333333333 mps relative to the center of the Milky Way Galaxy...the speed of our time is 1.000000007844765 MGT (Milky Way Galaxy Time)

Of course, this is just a hypothetical 'instant'. If we put a vector model together tracking our constantly changing speed relative to the center of the Galaxy we would accurately know the speed of our time (relative to MGT). As it is, we can assume a relative time flux of 1-1.000000013249398 MGT.

This is derived by adding all known speed vectors between the Earth and the center of the Milky Way Galaxy, ~30.323888 mps, which illustrates the highest potential speed if all vectors aligned. With 0 mps being the lowest potential speed relative to the center of the Galaxy, the most accurate assessment of the speed of our time is:
1 - 1.000000013249398 MGT

 

[DaveC426913]

Fine, here is your answer:

Assuming we are traveling at 84,000 mph or 23.333333333 mps relative to the center of the Milky Way Galaxy...the speed of our time is 1.000000007844765 MGT (Milky Way Galaxy Time)

All that calculating for nothing...

I picked 93,141 mi/s deliberately because it is half of c.

Of course, this is just a hypothetical 'instant'. If we put a vector model together tracking our constantly changing speed relative to the center of the Galaxy we would accurately know the speed of our time (relative to MGT). As it is, we can assume a relative time flux of 1-1.000000013249398 MGT.

This is derived by adding all known speed vectors between the Earth and the center of the Milky Way Galaxy, ~30.323888 mps, which illustrates the highest potential speed if all vectors aligned. With 0 mps being the lowest potential speed relative to the center of the Galaxy, the most accurate assessment of the speed of our time is:
1 - 1.000000013249398 MGT

OK, I kind of thought that's what you were going to say.

I don't know why you think our time would change because I've specified our speed relative to some arbitrary object. Note that I can give you my speed relative to multiple objects simultaneously. How are you going to calculate our speed of time if I give you speeds relative to six different galaxies?

Our time is 1s per s.

 

[RLS.Jr]

All that calculating for nothing...

I picked 93,141 mi/s deliberately because it is half of c.


OK, I kind of thought that's what you were going to say.

I don't know why you think our time would change because I've specified our speed relative to some arbitrary object. Note that I can give you my speed relative to multiple objects simultaneously. How are you going to calculate our speed of time if I give you speeds relative to six different galaxies?

Our time is 1s per s.

Wasted math? Truth is never a waist.

Had you just posted the speed I would have given you a simple answer. However, using the center of our Galaxy as the reference point makes much more sense. That's why I modified your number to one that fits that reference point. Of course you can see that our speed in relation to the center of the Galaxy is in constant flux. Thus our 'speed of time' is in constant flux.

Thank you for bringing up the idea of multiple galaxies. The best reference point for determining our speed of time is the center of the universe. When we can measure all the speed vectors (actually only three more than I have already added..one of which is known)
then we can accurately determine the speed of our time and any galaxy. It would be in the unit of UT (Universal Time).

Finally, time is 1s/s only at a point of reference. If you consider yourself as the only real point of reference, then yes you are right. That does come across a little egocentric though.