# Lorentz Transformations or Dilation/Contraction?

• NiallBucks
In summary: I did not memorize a single formulae. I just used the invariance of the interval. You can do the same.In summary, the conversation discusses the use of Lorentz transformations and Time dilation and Length contraction equations in solving problems related to special relativity. While some suggest using only the Lorentz transformation, others argue that using both methods can provide a better understanding of relativity. It is also mentioned that the relativity of simultaneity cannot be solved using time dilation and length contraction alone. Finally, one person claims to have solved all problems using only time dilation and length contraction, even in their studies of general relativity.

#### NiallBucks

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?

You should always use the Lorentz transformation first. Time dilation and length contraction are just special cases of the transformation.

bcrowell
I agree with PWiz. Always use the Lorentz transform. The length contraction and time dilation formulas will automatically fall out when appropriate.

BvU
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?

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?

Why not do both? Two different solutions to a problem that agree are better than one!

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?

The perfect example! Do it both ways and check you get the same answer.

NiallBucks
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.

MachPrincipe said:
If you do so, you will gain a much deeper understanding of relativity.
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:
With practice either method will be as easy as the other.
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.

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bcrowell
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.
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.

bcrowell
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.
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).

I have studied GR at the faculty, and no need of using Lorentz transform. never in my life. Why the academical books insist on this historical and rather artificial approach is beyond my understanding.

MachPrincipe said:
I have studied GR at the faculty, and no need of using Lorentz transform
I doubt it.

PWiz said:
I doubt it.
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.

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.
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?
PeroK said:
Does your knowledge of SR extend to 4-vectors and energy/momentum transformations?

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.

PeroK said:
Does your knowledge of SR extend to 4-vectors and energy/momentum transformations?
Physcis 101,-introduction to. SR.
Quantum physics - SR with attention to particle physics, matter-antimatter annihilation, 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.

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).

This just sounds wrong.

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.
That would be energy dilation and momentum contraction then!

PeroK said:
That would be energy dilation and momentum contraction then!
Haha... Nobel prize for me, then. :)
You can make p = mv. E = mc^2. m=m_0 * gamma.
Now you just get the v' for a particle and you are done. For v' you could use velocity transfor. formulae, but I didn't myself to use Lorentz, can be done
.with v=x/t alone for constant speed. Just think a little: it is just «low level Relativity».
s

MachPrincipe said:
you could use velocity transfor. formulae,
I'm curious as to how you can use that formula without acknowledging the fact that you're utilizing the Lorentz transformation.

PWiz said:
I'm curious as to how you can use that formula without acknowledging the fact that you're utilizing the Lorentz transformation.
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.

Just choose any SR problem, send it to me, and allow for aboutp 24 hours so I s

MachPrincipe said:
Just choose any SR problem,
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.

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MachPrincipe said:
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.

## 1. What are Lorentz Transformations?

Lorentz Transformations are mathematical equations used in special relativity to describe the relationship between space and time in different reference frames. They were first developed by Dutch physicist Hendrik Lorentz in the late 19th century.

## 2. What is time dilation in special relativity?

Time dilation is a phenomenon in which time appears to pass slower for objects moving at high speeds. This is a consequence of the theory of special relativity, which states that time is relative and can be affected by the speed of an object.

## 3. How does length contraction work in special relativity?

Length contraction is the phenomenon in which an object appears shorter when it is moving at high speeds. This is due to the fact that space and time are interconnected and can be affected by an object's velocity.

## 4. What are the applications of Lorentz Transformations?

Lorentz Transformations have many practical applications, such as in GPS technology, particle accelerators, and the study of high-speed particles. They are also essential in understanding the effects of time and space in special relativity.

## 5. How do Lorentz Transformations differ from Galilean Transformations?

Lorentz Transformations are a more accurate and comprehensive mathematical model than Galilean Transformations. They take into account the effects of relativity, while Galilean Transformations assume that time and space are absolute and independent of an observer's frame of reference.