What is time dilation and how does it relate to Einstein's theory?

[MeJennifer]

Strictly speaking, you could replace Einstein's first postulate by the postulate that the speed of light is isotropic in every inertial frame (ie every inertial frame will measure the speed of light to be the same in all directions in that frame, without assuming from the start that different frames will measure the value of that speed to be the same), and still derive the Lorentz transform and the rest of SR from that.

Yes, but then that is not longer Einstein's theory of specal relativity.

In Einstein's theory of special relativity all laws of physics are the same for all inertial frames, and the includes the measured speed of light.

So for ether theories you can hold that position but not for special relativity.

 

[JesseM]

Observer A & observer B at 0.866c relative, so gamma=2. The B frame per the A frame (B is contracted by 50%) ...

300,000 km/sec x [ (length contraction) / (time contraction) ] = 300,000 km/sec

300,000 km/sec x [ (0.5km/1km) / (0.5sec/1sec) ] = 300,000 km/sec

pess

At 0.866c a moving 1-meter stick only appears to be 0.5 meters relative to our own rulers, and a moving clock only ticks 0.5 seconds in 1 second of our time, so the numbers pess5 gave are correct

Actually I take it back, I think pess5's answer here is wrong. If "0.5sec/1sec" means "0.5sec of the moving clock is equal to 1 sec of the stationary one (as measured in the stationary frame)", then for consistency it should be "2km/1km", since "2 meters on the moving ruler is equal to 1 meter on the stationary one (as measured in the stationary frame)". So to really understand how the math works out and both frames measure the same speed of light, it is essential that you take into account the relativity of simultaneity.

 

[JesseM]

Yes, but then that is not longer Einstein's theory of specal relativity.

In Einstein's theory of special relativity all laws of physics are the same for all inertial frames, and the includes the measured speed of light.

So for ether theories you can hold that position but not for special relativity.

True, if you include the laws of electromagnetism in the fundamental laws of physics, then the second postulate already requires that the speed of light must be measured to be the same in every frame. Of course, in this sense you don't actually need both postulates to derive SR, the first postulate is totally redundant. I'm not sure what Einstein's reasons for including them both were, I suspect he wanted to show that even if you don't include Maxwell's laws as one of the fundamental laws of physics from the start, allowing the possibility that they could just be defined relative to the rest frame of the ether (in the same way that laws governing sound propagation are not considered fundamental but are defined relative to the rest frame of the air or whatever medium the sound waves are moving through), then you end up concluding that Maxwell's laws will work exactly in every frame, so it's a kind of reductio ad absurdum for the idea that the ether could be physically meaningful (assuming the second postulate is correct and that all the other laws do work the same way in each frame, of course).

 

[pmb_phy]

True, if you include the laws of electromagnetism in the fundamental laws of physics, then the second postulate already requires that the speed of light must be measured to be the same in every frame.

Not neccesarily. The laws of EM can be derived from a Lagrangian. If one uses the Proca Lagrangian with a finite value for photon proper mass then it no longer becomes true that the speed of light is invariant. The speed of light is invariant if and only if the photon's proper mass is zero. And as of yet the photon proper mass has not measured to be zero. The experimenta error margins will not allow this to be measured to exactly zero. So one either postulates that the photon mass is zero or postulate that the speed of light is a constant.

I'm not sure what Einstein's reasons for including them both were, ..

Perhaps he was lacking proof that the permitivity of free space was not invariant. As such he'd have to postulate the invariance of the speed of light to be constant.

Best wishes

Pete

 

[JesseM]

Not neccesarily. The laws of EM can be derived from a Lagrangian. If one uses the Proca Lagrangian with a finite value for photon proper mass then it no longer becomes true that the speed of light is invariant. The speed of light is invariant if and only if the photon's proper mass is zero. And as of yet the photon proper mass has not measured to be zero. The experimenta error margins will not allow this to be measured to exactly zero. So one either postulates that the photon mass is zero or postulate that the speed of light is a constant.

Is the "Proca Lagrangian" based on quantum electrodynamics or classical electromagnetism? In classical EM there are no photons, only electromagnetic waves, would it make sense to talk about the proper mass of an electromagnetic wave? And of course, when Einstein invented SR there was no quantum theory of electromagnetism.

Perhaps he was lacking proof that the permitivity of free space was not invariant. As such he'd have to postulate the invariance of the speed of light to be constant.

Yes, that could be it as well.

 

[petm1]

Anyway, I'm just trying to show petm1 how the math works out if you take for granted the basic features of relativity like length contraction and time dilation and the relativity of simultaneity, not to explain how these features were actually derived.

JesseM,
I know that the math works out; I think that SR works, what I am talking about is how every frame sees them as being at rest with the speed of light being the same. Part of my point is that even though Einstein sees time dilation for objects with more motion in SR, what he was talking about with time dilation in gravity GR is in fact time contraction the opposite of time dilation. I see time dilation as associated with increase in movement, time contraction is less motion and we feel it as gravity. I am trying to show that using SR you can see how we "see" 3-d rest frames through the movement of a light wave in 4-d. The only new concept is with time contraction and length dilation the opposite effects of what Einstein was talking about. Even the trouble with the basic math of how to fit length contraction / time dilation into the speed of light helps point us to this concept

 

[JesseM]

JesseM,
I know that the math works out; I think that SR works, what I am talking about is how every frame sees them as being at rest with the speed of light being the same.

But the fact that "every frame sees them as being at rest with the speed of light being the same" is part of SR--do you agree that the math works out here too, that if time dilation and length contraction and the relativity of simultaneity are all assumed true, that is enough to guarantee that each frame will measure the speed of a light beam to be c? If you do agree with this, then what was the point of your objection about the fractions?

 

[petm1]

But the fact that "every frame sees them as being at rest with the speed of light being the same" is part of SR--do you agree that the math works out here too, that if time dilation and length contraction and the relativity of simultaneity are all assumed true, that is enough to guarantee that each frame will measure the speed of a light beam to be c? If you do agree with this, then what was the point of your objection about the fractions?

My objection is in the apparent discrepancy when you try to put the finished product back into the speed of light, ie (300,000k) (meter/second) (length contraction/time dilation).

 

[JesseM]

My objection is in the apparent discrepancy when you try to put the finished product back into the speed of light, ie (300,000k) (meter/second) (length contraction/time dilation).

So did you look at the details of my example, which was meant to help you understand why you must also take into account the relativity of simultaneity (the fact that clocks which are synchronized in one frame appear out-of-sync in other frames) in order to see why each frame measures the same speed of light using their own rulers and clocks? This is important because each observer measures the speed of light using two synchronized clocks at different locations--if the light is emitted at the 0-light-second mark on my ruler and the clock there reads 0 seconds, then later the light beam hits a detector at the 100-light-second mark and the clock there reads 100 seconds, then that tells me the light beam was moving at 1 light-second per second in my frame. And the second observer will be using a ruler that seems shrunk and clocks that appear slow in my frame, but the clock at the 0-light-second mark of his ruler seems out-of-sync with the clock at the 50-light-second mark in my frame, in just the right way so that the light beam is emitted at the 0-light-second mark of his ruler with the clock there reading 0 seconds, and it is absorbed at the 50-light-second mark of his ruler with the clock there reading 50 seconds, so he also concludes the light was moving at 1 light-second per second according to his own measurements.

 

[JesseM]

Actually, beyond the relativity of simultaneity, your argument also doesn't make sense because it ignores the fact that the ruler is moving in my frame. Again, I measure the position and time of light being emitted from a source at rest in my frame, and the position and time of the same light beam being absorbed by a detector in my frame, and I conclude that the difference in positions is 100 light-seconds and the difference in times is 100 seconds. Your argument that the speed measured by the moving observer would be "(300,000k) (meter/second) (length contraction/time dilation)" means that in this example, you think the moving observer should measure the distance to be (100 ls)*1.25 = 125 light-seconds, and the time to be (100 s)/1.25 = 80 seconds, right?

Well, the 80 seconds would be wrong because of the relativity of simultaneity, but the 125 light-second distance would also be wrong, because the ruler has moved between the time its back end was at the same position as the emitter (at the same moment the light was being emitted) and the time its front end was at the same position as the detector (at the same moment the light was being absorbed). And since the moving observer considers his ruler to be at rest, for him the distance between the absorption and emission event is just the difference between the position on his ruler that the emission was next to and the position on his ruler the absorption was next to. So despite the fact that his ruler is only 40 light-seconds long in my frame, it has also moved forward by 60 light-seconds in between the event of emission and the event of absorption, so that the back end could be at the same position as the emission when it happened and the front end at the same position as the absorption when it happened, which means that in his frame the distance between the events is just the distance between the back and front of his ruler, which is 50 light-seconds in his frame.

 

[petm1]

SR talks about length contraction and time dilation, I have added length dilation and time contraction just to show the two sides or if you will the duality of SR. Length contraction LC/TC time contraction shows less motion while length dilation LD/TD time dilation shows more motion, meter per second is relative to us in our 3-d finite visible universe, The twist we see in the fact that SR says we see LC/TD when our motion increases and I think that we feel the other twist of LD/TC in gravity. Granted we do not know our true motion and can only tell our motion as compared to some other frame but none the less we do see time constriction the deeper we travel into the gravity well we call earth, and we see time dilation the faster we leave it.

Light exists almost exclusively in 4-d, while we exist almost exclusively in 3-d, and only at very high speeds and very low speeds do we notice the twist that we see through the 4-d of a light wave all the time.

 

[JesseM]

SR talks about length contraction and time dilation, I have added length dilation and time contraction just to show the two sides or if you will the duality of SR.

Did you pay any attention to what I just wrote, and do you have anything to say to it? Do you understand why you can't just do c*(length contraction)/(time dilation) for the speed of light in a different frame, since in my example the distance between light-emission and light-absorption would be 100 light-seconds and the time between these events would be 100 seconds, but the distance and time between these events as measured on the ruler/clock system which is moving at 0.6c in my frame would not be 125 light-seconds and 80 seconds? Do you understand how this is a consequence of both the fact that the ruler is moving in my frame (so the ruler's position is different at the moment the light is absorbed than it was when it was emitted) and the fact that clocks at either end of the ruler are out-of-sync in my frame?

Again, if you have trouble understanding the example, I can draw a diagram to help make it more clear. But please don't just keep ignoring it and repeating the same old incorrect arguments!

 

[petm1]

Actually, beyond the relativity of simultaneity, your argument also doesn't make sense because it ignores the fact that the ruler is moving in my frame. Again, I measure the position and time of light being emitted from a source at rest in my frame, and the position and time of the same being being absorbed by a detector in my frame{/QUOTE]

But Jesse your frame is moving too. Your rest frame is an illusion brought to you from a light wave traveling through 4-d space. The light in your light clock, while appearing to be moving in a straight line up and down is not. We always see light from the outside looking in and it always appears to travel in straight lines and to each of us it appears to be moving at c relative to us, but when viewing another observer who is in motion it appears to have changed. I know that we each can measure and we each can figure out the changes but, why is it that I am always in a rest frame. Could it be because we feel our 3-d frame and see other 3-d frames through a 4-d filter called light? We can show how we all measure light to be the same speed but there is a difference as proven by the moving twins’ age. What is the change each of us makes seamlessly so that we do not feel that difference? I am looking for the answer that will tie everything together and I believe that it will be the little clues that will make it happen.

 

[nakurusil]

Is the "Proca Lagrangian" based on quantum electrodynamics or classical electromagnetism?

QED.
The Procal EM theory plays an important role in setting up the experiments that determine the limits on the photon mass.

 

[JesseM]

But Jesse your frame is moving too.

To talk about whether a frame is "moving" in an absolute sense is meaningless in relativity, you can only talk about whether something is moving relative to another thing, or relative to another frame. In my example, I just used the phrase "moving ruler" to mean "moving relative to myself". It is equally true that an observer at rest on that ruler would consider me to be moving in his frame, and therefore would measure my ruler to be shrunk relative to his, and my clocks to be slowed-down relative to his.

Your rest frame is an illusion brought to you from a light wave traveling through 4-d space. The light in your light clock, while appearing to be moving in a straight line up and down is not. We always see light from the outside looking in and it always appears to travel in straight lines and to each of us it appears to be moving at c relative to us, but when viewing another observer who is in motion it appears to have changed. I know that we each can measure and we each can figure out the changes but, why is it that I am always in a rest frame. Could it be because we feel our 3-d frame and see other 3-d frames through a 4-d filter called light? We can show how we all measure light to be the same speed but there is a difference as proven by the moving twins’ age. What is the change each of us makes seamlessly so that we do not feel that difference? I am looking for the answer that will tie everything together and I believe that it will be the little clues that will make it happen.

Again, questions about what is "really" moving or "really" at rest are meaningless in the context of relativity. All relativity deals with is the practical issue of what different observers will measure if they use rulers and clocks at rest relative to themselves. For an object to be "at rest" in an observer's frame just means it stays lined up with the same mark on his ruler as time passes, for an object to be "moving" in an observer's frame just means the object is passing different marks on his ruler at different times.

So, do you agree that just in terms of measurements, it does make sense that each observer will measure the speed of a light beam (defined in terms of [change in position on his ruler between emission and absorption]/[change in time on his clocks between emission and absorption]) to be c, even though each observer measures the other observer's ruler to be shrunk and the other observer's clocks to be slowed down and out of sync?

 

[petm1]

Motion is the change, more motion gives us time dilation and I do not believe the deeper we travel into gravity well gives us more motion, it gives us less, hence time contraction. It "looks" the same as time dilation but it is not, can we put it is a graph to compare it to time dilation, yes. I wrote it out as a proportional equation, (LC/TC<meter/second<LD/TD) if you think of light being a twist we see all the time, then for more motion we see objects as LC/TD and for less motion we feel and see them as LD/TC.

 

[petm1]

Does this view hold for a full range of numbers in our equation, well when we are talking about motion I think it does, the more motion away makes things appear to follow LC/TD things appear to contract getting smaller as they move away with little change to their time till their speed get high enough, what about the other side, as things get closer and their speeds slow to match ours they do appear to get larger LD/TC, and as their speed matches our Earth's their time does appear to contract the deeper they go into the gravity well.

 

[JesseM]

petm1, this isn't the forum for you to be talking about your own personal theories (and your ideas seem too vague anyway--can you explain how 'length dilation' or 'time contraction' would be measured on actual physical rulers and clocks?). If you have questions about relativity that's fine, if you wish to construct your own alternatives you should submit to the Independent Research forum.

 

[Doc Al]

Well said, JesseM. And on that note, I think it's time to close this thread.