Uniform acceleration in relativity, #3/3

[deathpass422]

Okay, i am a high school student and i understand most of the terminology described in the theories of relativity as well as the many ideals and various parts involved. However, I'm having a though time learning to understand the many equations. This video helped (I think) but to me, it is very difficult due to the fact that i have never taken a calculus class nor ever taught differential equations...any suggestions as to how to learn to get started learning the 'ligo' of relativity?

[trondreitan]

Thanks for the message! As to calculus, the lingo of relativity (and Newtonian physics also), I guess there's no way to avoid picking up a book on calculus. Which is a shame, because such books are usually bone dry and pretty heavy, both in terms of content and gravitational pull... :)

Perhaps it is possible to get hold of a calculus intro book which combines the theory with example from physics? Hopefully some other viewers watching this can give a tip.

[trondreitan]

The equations are not so much different as symmetric. The reason why this can be so is that the equation referes to time interval for two events that are at rest in one system and thus happen at the same location. This will not be the case for another system. When an observer in that other system sees two events at the same location but at different times, the roles will be reversed.

[BrunoTheQuestionable]

Thanks - I'm starting to get there. Time dilation is defined using events on the x'=0 axis, but length contraction is defined using events on the t=0 axis. I still don't see why its necessary to consider different systems in the two experiments.

[trondreitan]

Hmm, not quite sure if I get where the difficulty lies, so it would be helpful if you could describe it in more detail. A short answer of what I think the question is, is that x'=0 describes the marked system at rest, while x=0 describes the unmarked system. Possibly, I could make a video describing time dilation.

[BrunoTheQuestionable]

If time dilation is calculated using events on the x'=0 axis, then why isn't length contraction calculated using events on the t'=0 axis ? Why aren't the space and the time dimensions treated in the same way ? The only reason I can see is, the normal methods give the correct answer.

[trondreitan]

In measuring time intervals, the time difference between two events are found, if the events are found at the same location or not. When measuring length, the difference in position at a given time local to any inertial system is found. These two definitions differ in how time and length measurements are done, even if the Lorentz transformations themselves are symmetric in time and space.

[BrunoTheQuestionable]

Yes, exactly !

As you indicated in your first reply, there is an asymmetry entering the situation somehow. My difficulty is in seeing where the asymmetry comes from. My only thought so far is, it might be related to the handedness of the co-ordinate systems.

[trondreitan]

Hope this cleared things up. Still, it might be fun to make a video about the subject someday, though I probably will not do so in the immediate future.

[BrunoTheQuestionable]

I'm working on a video which will attempt to explain SR using only geometry (no equations!). I guess I'll have to use the conventional measurements of "time dilation" and "length contraction" without fully understanding why they work (like everyone else does).

Thanks for the discussion.

[trondreitan]

I'm looking forward to it!

[crawhip2]

I just wamted to know if there are two separate types of transformation equations when dealing with (accelerated frames) and one for (rotating frames). both accel. frames and rotating framess are categorized under non-inertial fames etc...

[crawhip2]

I am well aware of the fact that the original time dilation equation can only be applied to inertial frames. In fact time dilation for inertial frame has been proven with a light clock experiment, but how has time dilation been proven for accelerating frames, I've always wanted to know

[BrunoTheQuestionable]

Great video.

I have a question.

As the Lorentz transformations are symmetrical from the point of view of the space and time dimensions, how can the form of the "time dilation" and "length contraction" equations be different ?

I'll send a message with more detail.

[jas2754]

Thanks for your clear description of Special Relativity. I enjoyed it a great deal  John

[jas2754]

Thank You for your clear description of Special Relativity. I enjoyed it immensely. John

[trondreitan]

Thanks, John! It's comments like that which makes the effort worth while.

[yessingno]

Wahey! Good job! Hopefully more people will see it. I did like the Lego by the way.

[trondreitan]

Thanks! I think most videos could've been improved with a little Lego.