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Why does Einstein say that a clock slows when it is moving? 
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#1
Dec2709, 04:30 AM

PF Gold
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In Chapter XII Einstein says the following:
That 1 proper second in the reference frame K is equal to gamma proper seconds in the moving frame K_{0}, leading to the conclusion that the seconds in K are larger than the seconds in K_{0} and that therefore the moving clock slows? No it isn't that, for the proper seconds in K_{0} have been transformed by the application of the Lorentz Transformation equations into coordinate time (as we term it), so he is saying that 1 proper second in the reference frame K is equal to gamma coordinate seconds in the moving frame K_{0}. So Einstein is actually describing a conversion from one set of units to another; that conversion being performed using the Lorentz Factor. And does the moving clock slow? Well, no, for what we see is that 1 unit of time in the reference frame K is equal to gamma coordinate units, so if anything one would say that the moving clock goes faster, albeit in smaller seconds. Grimble 


#2
Dec2709, 04:42 AM

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What he is saying is that a person in frame K sees t'= 1 second tick off a clock in frame K_{0} while he sees [tex]t = \frac{1}{\sqrt{1  \frac{v^2}{c^2}}}[/tex] tick off his own. t and t' do NOT measure "how long a second is", they measure what time is shown on a clock. Since t is larger than t', a clock in K_{0} shows time changing more slowly than in K.



#3
Dec2709, 05:04 AM

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#4
Dec2709, 05:08 AM

PF Gold
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Why does Einstein say that a clock slows when it is moving?
t' = 1 second, the units remain



#5
Dec2709, 07:53 AM

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[tex]\frac{1}{\sqrt{1 \frac{v^2}{c^2}}}[/tex] Both sides have dimensions of time. (Surely you are not thinking that "setting t= 1" removes the time units on the right? t is a time measure. Setting t= 1 means setting t equal to "1 second" or "1 minute" or "1 hour".) 


#6
Dec2709, 06:53 PM

PF Gold
P: 252

Wait a minute there, you cannot be suggesting that an equation that has units of days on one side and milliseconds on the other has the same units, just because they both are units of time, can you? For that would be the equivalent of saying we could have feet on one side of an equation and centimetres on the other and that would be valid, as they are both dimensions of distance. No, what the formula is saying is that 1 unit of proper time is equal to gamma seconds of coordinate time, that is coordinate time has units that are smaller than proper units by a factor of gamma. Grimble 


#7
Dec2709, 07:30 PM

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Eugene. 


#8
Dec2709, 07:49 PM

P: 451

Have I stated this correctly? Velocity is relative yes? 


#9
Dec2709, 07:56 PM

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#10
Dec2709, 08:03 PM

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Hello Grimble
All this has already been addressed at length in a thread started by you entitled, as far as I can remember, Time Dilation Formula. Matheinste 


#11
Dec2709, 08:31 PM

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Observation versus clock count. I see how both parties see the frequency of light flashes emitted by the other as slower due to their relative velocity away from each other. But suppose both observers agree to fire retro rockets after 1 million flashes (one flash per second) locally in their own frame and come to a mutual relative velocity of zero. And at that point they both agree to turn off the flasher. How many total flashes will each see before they see the flashing stop? I say both will count 1 million flashes. So what do you mean when you say a different amount of time passes in one frame versus the other?



#12
Dec3109, 05:18 AM

PF Gold
P: 252

Let us say we have two identical clocks, one in system A, and one in system B.
Clock A records 10 seconds while clock B records only 8 seconds. So for clock B more time is passing between successive 'ticks' (as Einstein put it): clock B is running slow. But is it? Or is time running faster? If more time is passing between two ticks of an identical clock does that not imply that it is time passing at a faster rate? 


#13
Dec3109, 05:40 AM

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#14
Dec3109, 05:43 AM

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#15
Dec3109, 05:47 AM

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#16
Dec3109, 06:37 AM

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Matheinste. 


#17
Dec3109, 10:31 AM

PF Gold
P: 252

A measure, of any kind, is surely based upon some standard, and that standard is what measurements are relative to? Then if the length of a second is different for two observers, yet is still equal to one second in each case, then the standard second for each observer has to be different? And if the standard is different for each observer, then, surely, they must be measuring time on separate scales that are appliccable to each observer? Or are you saying that there is, somehow a single "universal" second, or somekind of "Absolute" second that is measured differently by observer's moving at different relative velocities? If a second has different durations, depending on the conditions under which it is measured the does this not imply defferent scales depending on those conditions? And if all seconds are the same then where do the concepts of proper time and coordinate time come from? Grimble 


#18
Jan110, 02:00 PM

P: 451

Let's say we made ten clocks all the same and tested them while they were all in the same inertia frame. We find they all run at the same rate. We then send all ten into unique inertia frames. In each frame we do various low speed physics experiments we will find that physics is working as expected when we use our local copy of the clock. Each local clock, each local time is as expected in terms of physical/chemical/biological processes. If we want to translate between frames we can. The amount of local clock time in frame A (call it T_{a}) will be different than the amount of local clock time in frame B (T_{b}). All our experience is in a slow Newtonian world we have no intuitive understanding of the relativistic mix of time and place. We have to use the math. We can always translate time and place in frame X into time and place in frame Y. It just feels wrong. 


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