# The Naked Scientists Forum

### Author Topic: Special Relativity & Time Dilation Question  (Read 5622 times)

#### latebind

• Sr. Member
• Posts: 248
• Hello World
##### Special Relativity & Time Dilation Question
« on: 20/04/2009 18:32:27 »
My question is about time dilation of connected objects.

I think a good example is a whip http://en.wikipedia.org/wiki/Whip. When it cracks, the popper on the end breaks the sound barrier.
So in relation to the handle the popper actually has moved backward in time a fraction according to special relativity.

The fraction is obviously infinitely small and cannot be noticed but suppose we cracked the whip, oh, about 1000000 trillion times (or cracked it at the speed of light a few times), then what would be the result?

Thats my question. The rest (below) is my own speculation

From what I can see there is pretty much just 2 outcomes(I wont pick any side though)

1) The popper has moved backward in time and is now younger than the handle.

This implies that although the objects are connected and are synchronized in 3 dimensions of space, they are not synchronized in the fourth dimension of time. The whip would probably look and feel fine but I dont want to guess how it would act

2 The whole whip has moved backward in time relative to the stationary environment around it.

We know that the popper moves fast, and goes backward in time first, but somehow this outcome implies that the information of the popper time dilation is transmitted to the rest of the whip.

« Last Edit: 20/04/2009 19:43:05 by latebind »

#### Vern

• Neilep Level Member
• Posts: 2072
##### Re: Special Relativity & Time Dilation Question
« Reply #1 on: 20/04/2009 19:27:04 »
I think you have (1 backwards. Time moves more slowly for a fast moving object. The tip of the whip would simply be younger than other parts IMHO

Edit: I see that you changed it
« Last Edit: 20/04/2009 20:41:16 by Vern »

#### latebind

• Sr. Member
• Posts: 248
• Hello World
##### Re: Special Relativity & Time Dilation Question
« Reply #2 on: 20/04/2009 19:38:58 »
Just reverse the effects, the question is still valid. I'll edit it now though.

thanks Vern
« Last Edit: 20/04/2009 19:43:48 by latebind »

#### Vern

• Neilep Level Member
• Posts: 2072
##### Special Relativity & Time Dilation Question
« Reply #3 on: 20/04/2009 20:43:08 »
Just reverse the effects, the question is still valid. I'll edit it now though.

thanks Vern

I think your analysis is now correct. But why is there a problem? All portions of the whip need not experience time the same as all other portions.

#### latebind

• Sr. Member
• Posts: 248
• Hello World
##### Special Relativity & Time Dilation Question
« Reply #4 on: 20/04/2009 21:01:14 »
Suppose the popper was back in time 12 hours, this must have some strange effect of delayed reaction?

« Last Edit: 20/04/2009 21:08:07 by latebind »

#### Vern

• Neilep Level Member
• Posts: 2072
##### Special Relativity & Time Dilation Question
« Reply #5 on: 20/04/2009 21:51:08 »
I still don't see a problem. Fast moving parts of the whip are then younger than other parts. Younger only means that the patterns repeating in the constituent atoms have accumulated less cycles. We define a second as the time required for a caesium atom to complete a certain number of state changes.

The notion of time warping comes from Einstein's theories of relativity. In that case you can twist your mind up quite easily. The Lorentz version of relativity phenomena does not warp time. Material objects experience time differently because of an easily understandable cause. Vibrations in moving atoms must travel farther to repeat their patterns. So material objects experience time as slower when moving.

Cesium Atom clock
A "cesium(-beam) atomic clock" (or "cesium-beam frequency standard") is a device that uses as a reference the exact frequency of the microwave spectral line emitted by atoms of the metallic element cesium, in particular its isotope of atomic weight 133 ("Cs-133"). The integral of frequency is time, so this frequency, 9,192,631,770 hertz (Hz = cycles/second), provides the fundamental unit of time, which may thus be measured by cesium clocks.

Quote
In 1967, the 13th General Conference on Weights and Measures first defined the International System (SI) unit of time, the second, in terms of atomic time rather than the motion of the Earth. Specifically, a second was defined as the duration of 9,192,631,770 cycles of microwave light absorbed or emitted by the hyperfine transition of cesium-133 atoms in their ground state undisturbed by external fields.
« Last Edit: 20/04/2009 22:15:41 by Vern »

#### J4B

• First timers
• Posts: 3
##### Special Relativity & Time Dilation Question
« Reply #6 on: 15/06/2009 12:32:12 »
Agree

There is no problem but conceptual.
What is in question is 'parts'.
We wish to define 'parts' in a dynamic >tau enviroment.

Conceptual analysis rules in these situations.. Lets let
Einstein be heard.. Imagination is far more.........

The tip of the whip is at tau X the handle at Y.
The relationship between the 2 is beyond human understanding, ATM.
This is called growing up.

J4B

#### LeeE

• Neilep Level Member
• Posts: 3382
##### Special Relativity & Time Dilation Question
« Reply #7 on: 16/06/2009 00:09:44 »
Suppose the popper was back in time 12 hours, this must have some strange effect of delayed reaction?

The popper being twelve hours younger than the rest of the whip doesn't mean that it's twelve hours back in time; both the popper and the rest of the whip are here now, at the same moment in time, it's just the the popper is younger than the rest of the whip.

#### Atomic-S

• Hero Member
• Posts: 935
• Thanked: 19 times
##### Special Relativity & Time Dilation Question
« Reply #8 on: 20/06/2009 07:17:41 »
An important feature of this problem, that is, this problem in which different parts of an object undergo different time dilations, is that such a time, or age, gradient alters the nature of the quantum wave functions across the entire object in a certain way that creates a directional bias.  This bias is not simply of academic interest, but has dynamic consequences. The dynamic consequences are that the wave functions become "wound up" much like a string one end of which is spun at a different rate than the other, resulting in an ever shortening overall wavelength, which, interestingly enough, implies an ever increasing momentum in the direction of the time gradient. (Basic wavelength-momentum relationship of quantum mechanics). Actually, this very situation is an important feature of General Relativity, in relation to the way time behaves in the vicinity of massive objects: time moves more slowly near the object, so that any object near it experiences precisely this phenomenon -- differential aging with respect to radial distance -- having the result that the object acquires a quantum momentum in the direction of the larger object -- i.e., GRAVITATION.  Therefore, a proper analysis of the cracking whip phenomenon must involve the concept of accelerational forces from one end to the other. Of course, acceleration is an intrinsic property of any cracking whip whose overall length remains within some definite limits. So we might say at first that all we learn from this study is that a cracking whip accelerates; however to expound the matter propertly, we would have to examine the dynamics of the whip under general relativity.

#### LeeE

• Neilep Level Member
• Posts: 3382
##### Special Relativity & Time Dilation Question
« Reply #9 on: 20/06/2009 20:33:20 »
Interesting comments Atomic-S.  I'm not sure what you mean by the wave functions being 'wound-up' though.  If there was a single wave function that spanned the entire object then I think I could see what you mean but as the wave functions will apply at the particle level  then we'll just have a gradient across many wave functions, which doesn't sound too problematic.

As something that's simply rotating should show the same effects, I thought I'd try working out how much time dilation could accrue in such a spinning object.

I've picked a large water turbine to work with as they can have diameters > 10 metres, rotate quite quickly and can run for decades.  I couldn't find any specific size/rotation combinations, just a rotation speed range of between 60-720 rpm (Steam turbines spin much faster and will give greater time dilation but I couldn't find good numbers for rotational speed & diameter, and nor for how long they're likely to run)

So working with 10 m diameter @ 60 rpm...

Circumference = pi*d = 31.4159265359m

because we're using 60 rpm

Linear speed v at the rotor tip = 31.4159265359 m/s

The time dilation factor will be √1-(v2/c2)

which equals (by using all my fingers and toes  ):

0.999999999999994

So the rotor tips should be younger than the center of the rotor by a factor of 0.999999999999994

Over, let's say 30 (non-leap year) years (some have run for 60 years afaik) we get:

946080000 seconds

which will be the age of the center of the rotor, whereas the age of the rotor tips will only be:

946080000 * 0.999999999999994 = 946079999.999995 seconds

so the rotor tips will be 0.00000524520874023438 (5.25E-006) seconds younger

#### tychobrahe

• Jr. Member
• Posts: 15
##### Special Relativity & Time Dilation Question
« Reply #10 on: 19/07/2009 15:17:57 »
I think you could use already established relativistic effects on geosynchronous satellites as a model for this.  Even though there is no physical link between the satellite and the ground (though there could be if a space elevator is ever built) the satellite and any position on earth move as if there was some physical link between them even though the satellite is moving much faster in its orbit.
So if a space elevator is ever built, its tip out in space would be like the tip of the whip you're talking about, and would go slower through time as it is moving at a speed closer to the speed of light.  Outcome 1 is what would happen, and Outcome 2 is false and a good example of why the universe under the rules of general relativity doesn't allow for completely rigid objects.

#### Stefanb

• Full Member
• Posts: 75
##### Special Relativity & Time Dilation Question
« Reply #11 on: 10/08/2009 04:04:26 »
The end of the whip would not go backwards in time.
Instead, the portions of the whip moving faster than other parts- relative to the universe- would not go through time as quickly as the slower moving parts- again, relative to the universe.

As an effect, the fastest moving part of the whip would not age as quickly as the other part and after many trillions of whippings would probably be much darker brown than the end you are holding  (Assuming you are using a brown leather whip!  )

#### lyner

• Guest
##### Special Relativity & Time Dilation Question
« Reply #12 on: 10/08/2009 09:07:31 »
Why are you all using the term  "younger"?
The only difference between the two objects, moving at different speeds, is that they are aging at different rates. They are both older than they were when the experiment started. Neither has gone backwards in time.
They are both 'sliding down the hill'. One just takes longer to get to the bottom. Neither has 'gone up'.
Films of sky divers seem (to the uninformed) to imply that the one opening his chute goes up but he still hits the ground and they will both see thi happen.
The 'younger' so called time traveller cannot  take any advantage of this aging rate difference to affect his own situation, except to save money on Oil Of Olay.

#### Soul Surfer

• Neilep Level Member
• Posts: 3345
• keep banging the rocks together
##### Special Relativity & Time Dilation Question
« Reply #13 on: 10/08/2009 22:58:12 »
Most simple and complex objects do not contain precise synchronised clocks to allow their effective ageing since some defined incident in the past to be measured with a very high accuracy so therefore any conceptual difference in aging is purely academic and has no effect on anything.

#### The Naked Scientists Forum

##### Special Relativity & Time Dilation Question
« Reply #13 on: 10/08/2009 22:58:12 »