relativity time dilation questions

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Hi,

To calculate time dilation in the following example using
relative velocities of objects on a line:

mass A: at rest
mass B: traveling left at 0.999C
mass C: traveling right at 0.999C

Using this online calculator for time dilation:

http://www.emc2-explained.info/Dilation-Calc/

Relative to mass A, time for mass B and C should
be slowed down to about 4.47%.

Now if another mass is added, mass D, and mass A
is traveling left at 0.999C as seen from mass A.

mass D: at rest
mass A: traveling left at 0.999C
mass B: traveling left at 0.999C relative to mass A
mass C: traveling right at 0.999C relative to mass A

 From the first example, mass C and D time is slowed
down to about 4.47% relative to mass A still.

Also mass A should now have time slowed down to about
4.47% relative to mass D now.

So the rest mass D has no time dilation, mass A has
time slowed down to 4.47% of mass D, and mass B and C,
have time slowed down to 4.47% of mass A still, meaning
4.47% of 4.47% of mass D, or in other relative to mass D,
time is slowed down for mass B and C to 0.199% of mass D.


However another way to look at this, is mass D is not
at rest and is traveling at 0.999C to the right relative to mass A,
which is still at rest.  Using mass A as the rest mass
would give mass B and D both traveling at 0.999C to the
right, giving the same time dilation answers as in the first
example, of 4.47%.  I don't think time dilation is arbitrary depending
on which mass is called the rest mass, so would appreciate
an explanation of my error in understanding this! :D

cheers,
Jamie


Re: relativity time dilation questions
On 1/21/19 8:39 AM, Jamie M wrote:
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Changing the rest frame isn't just a matter of labelling, because your  
time and distance measurements depend on what frame they're made in.  
Even the time ordering of events can change.

The classical example of the latter is the relativistic garage.  Say you  
have a garage with a door at each end.  The garage is 20 feet long, and  
you have a very fast limo that's 30 feet long in its rest frame.  If  
you're standing next to the garage as the limo approaches at 0.9c,  
you'll measure its length as 30*sqrt(1-.9**2) = 13 feet long, so it will  
easily fit in the garage (albeit briefly), and you can (conceptually)  
close both doors at once.

If you were driving the car, you'd see the car as 30 feet long, and the  
garage as 20*sqrt(1-.9**2) = 8.7 feet long--far too short to fit the  
whole car.  But in that frame, the doors don't close simultaneously--the  
second one opens again before the first one closes.

Cheers

Phil Hobbs

--  
Dr Philip C D Hobbs
Principal Consultant
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Re: relativity time dilation questions
On Monday, January 21, 2019 at 10:36:31 AM UTC-5, Phil Hobbs wrote:
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What Phil said,
Space time Physics by Taylor and Wheeler is a great intro to special  
relativity.  
(You can find it as a free PDF on the web)  

George H.  

Re: relativity time dilation questions
On 2019/01/21 7:44 a.m., George Herold wrote:
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Yeah, I really should have spent some time getting my head around  
Special Relativity back when I could do the math...

One thing that always bothered me was regarding the red shift and speed  
of light. If objects at the furthest point in the universe are receding  
from us at close to C then we too are receding from them at the same  
speed. Therefore the speed of light in our neighbourhood is determined  
by the base line which is already close to C. Which means the actual  
speed of light could be much faster IF you could figure out what the  
base reference point was.

How on earth do you get a base reference point then? Certainly the  
rubber sheet doesn't answer this.

I'm sure I'm missing something and to be quite honest have done no  
research on the matter as busy with my regular life and businesses...

I guess I better track down that book by Taylor & Wheeler.

And Archive.org rides to the rescue once again:

https://archive.org/details/SpacetimePhysicsIntroductionToSpecialRelativityTaylorWheelerPDF/page/n3

Just wasting time - sorry!

John :-#)#

Re: relativity time dilation questions
On Monday, January 21, 2019 at 11:36:33 AM UTC-5, John Robertson wrote:
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There is no base reference point.  Both the star at the edge of the universe
and we, agree that we are moving away from each other at some speed.  
You can pick either one as your reference frame to measure things from.  

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That's it.  
George H.  

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Re: relativity time dilation questions
On 21/01/2019 16:36, John Robertson wrote:

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IIRC the speed of light is postulated to be the same for any observer in  
a non accelerating frame of reference.

It is directly from that coupled with a "light beam in a spacecraft"  
thought experiment that you can derive the formula for Lorentz  
contraction (which is also the formula for time dialation and mass change).

I could probably work that out again, given long enough.

I cannot remember how E=mc2 is derived (being vaguely related), but I  
know I did work that out when I was about 17 using 2 sides of A4 paper  
and no more than British A Level maths (which was very slightly more  
advanced than today's highschool pre-university stuff).

The thought experiments are hard, but the maths is not terrible. Unlike  
general Relativity that I never understood.

--  
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Re: relativity time dilation questions

On 21/01/2019 16:36, John Robertson wrote:

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There is a somewhat novel way to derive the form of E=MC2 based on  
conservation of energy.

http://www.kevinaylward.co.uk/gr/emc2/emc2.html


-- Kevin Aylward
http://www.anasoft.co.uk - SuperSpice
http://www.kevinaylward.co.uk/ee/index.html


Re: relativity time dilation questions
Phil Hobbs wrote:
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I was going to say, great example but what always gets me is: When the  
car stops and both observers are in the same frame, then who has aged  
more?

But then I thought of another question about the example.  If you are  
inside the garage and the first door is receding and the second is  
approaching, then it makes sense that you would see the first close  
after the second.  But if you're riding in the trunk (or just more than  
8.7 feet from the front end) then both doors are approaching.  So why  
would you see the first door delayed?




Re: relativity time dilation questions
On Monday, January 21, 2019 at 1:55:35 PM UTC-5, Tom Del Rosso wrote:
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Time runs slower for the person traveling near light speed.  
(We measure the lifetime of muons (2 u sec) that are created in the upper
atmosphere.  (cosmic ray collisions.) If you look at the muon flux as  
a function of height, there is very little change... because the 'clock'
on the muons is running much slower.  If they decayed in 2 u sec. regardless
of speed, then you'd have 1/2 left after ~600 m (c * 2 u sec.) But almost  
all of them make it to the Earths surface for us to observe.)
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It's mostly just that the door closings happen at different times.
(not simultaneously.)    
Try reading some of the Taylor/ Wheeler book.  

George H.  

Re: relativity time dilation questions
"George Herold"  wrote in message  

On Monday, January 21, 2019 at 1:55:35 PM UTC-5, Tom Del Rosso wrote:
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According to standard Special Relativity, whilst pop accounts typical  
explain it this way, it is incorrect.

According to SR, time does not run slow for the object moving relatively.  
The accepted description is that the object takes a "longer path in  
space-time". For example, traveling a straight path from LA to San Francisco  
will take X miles. Traveling via Reno, will take longer. The odometer reads  
different, not because its calibration changes with the straight line  
distance, but because it took a longer path. A clock is equivalent to the  
odometer .



-- Kevin Aylward
http://www.anasoft.co.uk - SuperSpice
http://www.kevinaylward.co.uk/ee/index.html


Re: relativity time dilation questions
On Monday, January 21, 2019 at 2:56:42 PM UTC-5, Kevin Aylward wrote:
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Ahh OK... I really only have a pop-sci understanding anyway.  

I guess you can also say the muon (traveling near light speed)  
sees a shorter distance to the surface of the earth.  
(That's how I would describe it when 'travelling' with the muon.)

George H.  
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Re: relativity time dilation questions
"George Herold"  wrote in message  

On Monday, January 21, 2019 at 2:56:42 PM UTC-5, Kevin Aylward wrote:
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One should note though that "space-time" is only a *MODEL*.  It allows a  
description of *how * physical objects move, but not *why*.

It assumes that time and space actually exists independently of the objects  
in the universe. That is, it is a pure mathematical construct.

Clearly, this is false in physical reality. The *only* way to define  
distance is to have physical objects to mark out locations. The *only* way  
to define time, is to have objects change their position.   There has to be  
a real, physical process to create a clock, i.e. time.

-- Kevin Aylward
http://www.anasoft.co.uk - SuperSpice
http://www.kevinaylward.co.uk/ee/index.html


Re: relativity time dilation questions
On 1/21/19 2:56 PM, Kevin Aylward wrote:

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You'd be better off sticking to oscillators. ;)

Cheers

Phil Hobbs

--  
Dr Philip C D Hobbs
Principal Consultant
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Re: relativity time dilation questions

On 1/21/19 2:56 PM, Kevin Aylward wrote:
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I also have a more accessible description of mass-curving space as  
well....:-)

http://www.kevinaylward.co.uk/gr/einstien/einstien.html

Well, the 1st paragraph anyway...

-- Kevin Aylward
http://www.anasoft.co.uk - SuperSpice
http://www.kevinaylward.co.uk/ee/index.html


Re: relativity time dilation questions
On Monday, January 21, 2019 at 2:26:58 PM UTC-5, George Herold wrote:
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Just to be clear, it is not that the muon clock runs fast or slow, the muon clock *appears* to us to run slow.  The muon sees the clock running at normal speed and anyone going in the same direction at the same speed will also see that.  

  Rick C.

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Re: relativity time dilation questions
On Monday, January 21, 2019 at 1:55:35 PM UTC-5, Tom Del Rosso wrote:
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The aging is not caused by the relative speed since both observers see time slow for the other one.  The aging is faster for the one who does not accelerate.  The one who endures the acceleration has less time pass.  

So to get the two into the same speed frame, which one accelerates to make that happen?  


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I don't think it has to do with the direction of motion.  

  Rick C.

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Re: relativity time dilation questions
On 1/21/19 1:55 PM, Tom Del Rosso wrote:
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That's a form of the 'twin paradox'.  If I take a relativistic  
spacecraft and fly a year out from Earth and then back again, I'll have  
aged less than you.  But that isn't a paradox at all, because our  
histories are not comparable--I've accelerated to and from relativistic  
speed three times and you haven't.

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The car doesn't collide with the doors in either reference frame.  
Simultaneity doesn't apply in relativity.

Cheers

Phil Hobbs

--  
Dr Philip C D Hobbs
Principal Consultant
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Re: relativity time dilation questions
On 22/01/2019 5:55 am, Tom Del Rosso wrote:
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It turns out that your question is ill-defined, because it contains the  
false implicit assumption that you can define the instant when both  
observers start measuring, so as to determine later how much they aged,  
even though the two observers are spatially separated.

Sylvia.

Re: relativity time dilation questions
On Monday, January 21, 2019 at 10:36:31 AM UTC-5, Phil Hobbs wrote:
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l  
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Great thought experiment.  Say the garage doors can open and close very qui
ckly.  The second door (furthest away from the approaching limo) is already
 closed.  The first door is already open.  The car reaches the garage and u
pon the end of the car clearing the first door sends a signal to open the s
econd door.  I suppose the issue is that the open signal can't travel faste
r than c, so it does not arrive in time to open the second door...  but, if
 it could travel instantly...  would the door be opened in time?  What woul
d the observer at the garage see?  What would the driver see?  Would the ca
r plow through the door?  

  Rick C.

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Re: relativity time dilation questions
On 1/21/19 3:28 PM, snipped-for-privacy@gmail.com wrote:
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It's just a thought experiment.  A 3000-kg limo moving at 0.9c would  
have a kinetic energy of

KE = 3000 kg * (3e8 m/s)**2 * (1/sqrt(1-0.9**2) -1) = 3.5E20 J, a little  
matter of 83,600 megatons (*).  Just the gammas from the impact fusion  
of air molecules would fry you if you were anywhere nearby, never mind  
the blast wave.

Cheers

Phil Hobbs

(*) A megaton is defined as 1E15 calories, or 4.18E15 joules.

--  
Dr Philip C D Hobbs
Principal Consultant
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