The discussion centers on the use of Lorentz transformations versus time dilation and length contraction equations in solving problems related to special relativity. Participants unanimously agree that the Lorentz transformation equations, such as x' = γ(x - vt) and t' = γ(t - (v/c²)x), should be the primary method employed, as time dilation and length contraction are derived from these transformations. A specific example involving a rocket traveling at v = 0.6c illustrates the application of these equations, confirming that using the Lorentz transformation yields consistent results across various scenarios. The consensus emphasizes that while time dilation and length contraction can be useful, they are insufficient for addressing the relativity of simultaneity.
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NiallBucks said:I'm doing a class on special relativity and when doing some problems, I'm never sure whether I should be using the Lorentz transformations (Eg. x' = γ(x-vt) or t'=γ(t- (v/c^2)x)) or the Time dilation and Length contraction equations to find t or x! Can anyone explain if there's any way of knowing or am I missing something really simple?
NiallBucks said:Well, for example;
A rocket passes the Earth at v=0.6c and both the rocket and Earth agree it's 12:00. At t'=13:00 the rocket passes a space station. Show that the rocket passes the space station at 13:15 in the Earth's frame.
Here γ=5/4
Which would I use here? Is it correct to say T=γTo so then if you sub To as 1 you'll get 1.25 which is an hour and a quarter (ie 13:15) or am I misunderstanding something?
No, not at all. The Lorentz transformation is more fundamental in SR than time dilation and length contraction. You will only run into conceptual issues if you think otherwise.MachPrincipe said:If you do so, you will gain a much deeper understanding of relativity.
It might seem easy to work your way through some problems without using the full Lorentz transformation, but you'll most definitely run into hot water if you try solving anything different from those "standard" relativity questions using the TD and LC formulae only.MachPrincipe said:With practice either method will be as easy as the other.
I completely disagree with this. Time dilation and length contraction alone cannot be used to solve problems involving the relativity of simultaneity. If your physics 101 course did not include exercises on the relativity of simultaneity then it was not enough of a curriculum to even be considered an introduction to relativity.MachPrincipe said:Contrary to what the other posters say, you can perfectly go with the time dilation and length contraction formulae. I solved every single exercise that way in Physics 101, including relations with momentum and energy which transform in a similar way. If you do so, you will gain a much deeper understanding of relativity. The only caveat is that you must use proper time instead of coordinate time, which is achieved finding a clock which travels with the particle or placed baside the event taking place, and also computing the time that light uses to reach all of the observers involved. More ellaborate but will give you a better insight. With practice either method will be as easy as the other.
The course was relativdly good :) It was me who didn't want to use the Lorentz transf. after understanding them. The problems included the barn and pole apparent paradox, and I solved with time dilation and length contraction alone. As said, you only need to take into account the travel time of light rays, which is the faster way of communicating events, and what lies beneath the reason of the relativity of simultaneity (Einstein original paper).DaleSpam said:I completely disagree with this. Time dilation and length contraction alone cannot be used to solve problems involving the relativity of simultaneity. If your physics 101 course did not include exercises on the relativity of simultaneity then it was not enough of a curriculum to even be considered an introduction to relativity.
That is an indication of a deficiency in the course, not an indication of the sufficiency of length contraction and time dilation.
I doubt it.MachPrincipe said:I have studied GR at the faculty, and no need of using Lorentz transform
You can take my word. As for special relativity, think of a problem and send me a message or post it here. I will use time dilation and length contraction formulaae alone. It is funny. Even with cuadrivector p_i , E... I solved by this method though they wefe a little harder.PWiz said:I doubt it.
Does your knowledge of SR extend to 4-vectors and energy/momentum transformations?MachPrincipe said:You can take my word. As for special relativity, think of a problem and send me a message or post it here. I will use time dilation and length contraction formulaae alone. It is funny. Even with cuadrivector p_i , E... I solved by this method though they wefe a little harder.
PeroK said:Does your knowledge of SR extend to 4-vectors and energy/momentum transformations?
PeroK said:Does your knowledge of SR extend to 4-vectors and energy/momentum transformations?
Physcis 101,-introduction to. SR.PeroK said:Does your knowledge of SR extend to 4-vectors and energy/momentum transformations?
MachPrincipe said:The problems included the barn and pole apparent paradox, and I solved with time dilation and length contraction alone. As said, you only need to take into account the travel time of light rays, which is the faster way of communicating events, and what lies beneath the reason of the relativity of simultaneity (Einstein original paper).
That would be energy dilation and momentum contraction then!MachPrincipe said:Physcis 101,-introduction to. SR.
Quantum physics - SR with attention to particle physics, matter-antimatter aniquilation, Compton effect, Thomas precession.
General Relativity as a semester included in Astrophysics subject.
Analytical Mechanics and Relativity.
And yes, I solved (E,pc) problems by using time dilation and length contraction relationships. Very funny and very useful to understand relativity.
Haha... Nobel prize for me, then. :)PeroK said:That would be energy dilation and momentum contraction then!
I'm curious as to how you can use that formula without acknowledging the fact that you're utilizing the Lorentz transformation.MachPrincipe said:you could use velocity transfor. formulae,
Keep reading til the end of my sentence: just because I din't allow myself to use Lorentz, I did use v=e/t or the differential relationship.PWiz said:I'm curious as to how you can use that formula without acknowledging the fact that you're utilizing the Lorentz transformation.
More importantly for the purposes of this forum, please provide a professional reference that supports/explains your claim because the way you are explaining it does not make any sense.MachPrincipe said:Just choose any SR problem,
http://scitation.aip.org/content/aapt/journal/ajp/51/12/10.1119/1.13322DaleSpam said:More importantly for the purposes of this forum, please provide a professional reference that supports/explains your claim because the way you are explaining it does not make any sense.
This citation does NOT support anything even remotely like what you have suggested. It does not use length contraction and time dilation in place of the Lorentz transform as you have proposed above. It also makes no claim that the method is applicable to all problems.MachPrincipe said: