How to explain Einstein's Special theory of Relativity.

[John Huang]

You should start with the title of that paper... Einstein introduced Special Relativity to resolve the great unsolved problem of the second half of the 19th century, namely the incompatibilities between Galilean relativity and Newtonian mechanics on the one hand, and Maxwell's theory of electricity and magnetism on the other hand.

Thanks. Do you think the "time dilation equation" is the solution created by Einstein?

No one else mentioned about it, right? At least I don't know who else mentioned about it. That is why I assign that solution (the time dilation equation) as the main purpose of SR.

 

[John Huang]

The time equation of SR is LT. the lorentz transforms are a set of equations for transforming from one reference frame to another. They are a part of SR.

If you think LT is part of SR, that's fine. Now, we have two "time dilation" equations.

As I know, SR can be used for two systems with constant relative speed; however, in case of constant relative velocity SR should be correct as well. I mean, in cases of constant relative velocity, should I use LT or SR? Do you have website where I can find the answer of it? Thanks.

 

[Vorde]

There is a lot in SR. The Lorentz Transformations were a set of coordinate transformations that Lorentz first developed with regards to electromagnetism. It was Einstein who first used them to describe space itself, and the time dilation and length contraction equations come directly from the lorentz transformations.

You keep saying that LT and SR are seemingly two distinct things, which is completely wrong. The Lorentz Transformations are a part of SR. To ask whether to use Special Relativity or the Lorentz Transformations is like to ask whether to use Newtonian Mechanics or Newton's Second Law; the question doesn't make sense.

 

[tensor33]

If you think LT is part of SR, that's fine. Now, we have two "time dilation" equations.

As I know, SR can be used for two systems with constant relative speed; however, in case of constant relative velocity SR should be correct as well. I mean, in cases of constant relative velocity, should I use LT or SR? Do you have website where I can find the answer of it? Thanks.

I'm not quite sure I understand your question. When you say "Should I use LT or SR?", it makes no sense. It is my understanding that LT is a part of LR. There is no need to choose between the two.
Maybe if you gave me an example of what you consider to be an equation of SR and an equation of LT I would better understand your question.

 

[Mentz114]

Thanks for the comment. I know that Einstein also supported LT and he claimed that he proved LT by 2 postulates. Actually I also know that after Einstein introduced his SR in the section 3 of his 6/30/1905 paper, he extended SR from "constant relative velocity" to "constant relative speed" in the section 4 right away. Even with the new expansion, I think SR should continue its support to the situation of "constant relative velocity".

The changing of the term 'velocity' and 'speed' makes no operational difference. Speed is defined as s = √(v_x²+v_y²+v_z²) where the v terms are the magnitudes of the x,y and z velocities. It is always possible to rotate the coordinates so only one component is non-zero in these coords.

What difference do you think it makes ?

 

[Dale]

Thanks for the comment. I know that Einstein also supported LT and he claimed that he proved LT by 2 postulates. Actually I also know that after Einstein introduced his SR in the section 3 of his 6/30/1905 paper

In that section he clearly derived the LT from his two postulates. Therefore, the LT is part of SR, and has been from the beginning of SR.

he extended SR from "constant relative velocity" to "constant relative speed" in the section 4 right away.

In section four he derives the time dilation equation from the LT with the additional restriction that the other clock is "at rest relative to the moving system, to be located at the origin". I.e. That is the only time that derived formula applies.

So, could you explain why in the situation that {the observed event happened at a location other than O'} we should use LT, not SR?

Can you explain in playing football why you should use your leg, not your foot?

I think the main purpose of SR is to introduce the time dilation equation. However, if you could show me what else SR has provided to people, I will appreciate and study it.

Please re read the 1905 paper. Clearly he includes more than just the time dilation equation. So for you to make this statement is absurd. Furthermore, going beyond Einstein, SR now includes also Minkowski's spacetime, and even pseudo-Riemannian geometry on flat manifolds.

 

[Dale]

If you think LT is part of SR, that's fine. Now, we have two "time dilation" equations.

No, you have the LT which simplifies to the time dilation equation under specific circumstances. When the circumstances match then you can use the simplified equation or the LT equally since they agree. When the circumstances don't match then you cannot use the simplified equation since it doesn't apply.

 

[John Huang]

That is the best answer I have received so far. Thanks. Do you mean, only when x'=0 we can use SR, otherwise, we should apply LT?

 

[John Huang]

The changing of the term 'velocity' and 'speed' makes no operational difference. Speed is defined as s = √(v_x²+v_y²+v_z²) where the v terms are the magnitudes of the x,y and z velocities. It is always possible to rotate the coordinates so only one component is non-zero in these coords.

What difference do you think it makes ?

With constant velocity, LT works for inertial systems only; with constant speed, SR can expand to circling or any kind of constant speed situation.

 

[John Huang]

You keep saying that LT and SR are seemingly two distinct things, which is completely wrong. The Lorentz Transformations are a part of SR. To ask whether to use Special Relativity or the Lorentz Transformations is like to ask whether to use Newtonian Mechanics or Newton's Second Law; the question doesn't make sense.

According to # 42, my understanding is that SR is part of LT. What do you think?

 

[John Huang]

I'm not quite sure I understand your question. When you say "Should I use LT or SR?", it makes no sense. It is my understanding that LT is a part of LR. There is no need to choose between the two.
Maybe if you gave me an example of what you consider to be an equation of SR and an equation of LT I would better understand your question.

For example, if we focus on the events happen at the origin point of the stationary system, the point O, then we will have x=0. If LT is part of SR, then, both of the time equations in LT and SR should apply and under this situation, the time equations are inverse. Which one should apply?

 

[Doc Al]

According to # 42, my understanding is that SR is part of LT. What do you think?

Realize that in common usage SR means "Special Relativity". The LT is part of SR, of course.

You seem to be using "SR" to mean the time dilation formula, which is a special case of the LT (as has been explained). Your non-standard use of "SR" is creating some confusion.

 

[Doc Al]

For example, if we focus on the events happen at the origin point of the stationary system, the point O, then we will have x=0. If LT is part of SR, then, both of the time equations in LT and SR should apply and under this situation, the time equations are inverse. Which one should apply?

If you want to convert measurements from one frame to another you can always use the LT. In certain cases the simplified 'time dilation' formula can be applied.

In this example, since the events in question all take place at x = 0, you can convert the time between them (Δt) to the moving frame (Δt') using the time dilation formula: Δt' = γΔt. But that's just an application of the LT.

What's your point?

 

[Dale]

Do you mean, only when x'=0 we can use SR, otherwise, we should apply LT?

No, I mean what I said. The LT is part of SR. The time dilation formula (which is part of the LT) only applies when x'=0.

You continue to identify SR with only the time dilation formula. That is simply WRONG.

 

[Dale]

According to # 42, my understanding is that SR is part of LT. What do you think?

No, you have this backwards. The LT is part of SR.

I think there is some language barrier. Perhaps this will help:
$SR \supset LT \supset time \; dilation$
$SR \neq time \; dilation$

 

[John Huang]

If you want to convert measurements from one frame to another you can always use the LT. In certain cases the simplified 'time dilation' formula can be applied.

In this example, since the events in question all take place at x = 0, you can convert the time between them (Δt) to the moving frame (Δt') using the time dilation formula: Δt' = γΔt. But that's just an application of the LT.

What's your point?

My point is a logical issue.

In above example, two systems have constant relative velocity so that the speed of time in the moving system t' and the speed of time in the stationary system t should be decided once we select the point O as the stationary point, and the O' as the moving point. Under this SPECIFIC arrangement, when we talk about a period of time for ONE SPECIFIC EVENT then we should have ONLY ONE event period Δt as recorded in the stationary system and ONLY ONE event period Δt' as recorded in the moving system.

Now, what SR claims is Δt' = Δt/γ and what LT claims is Δt' = γΔt for the ABOVE example. Logically speaking, this should not happen UNLESS γ=1, isn't it? How do you explain this logical issue?

If you like the event to stay in the moving system, then you may let x'=1.

 

[tensor33]

Now, what SR claims is Δt' = Δt/γ and what LT claims is Δt' = γΔt for the ABOVE example. Logically speaking, this should not happen UNLESS γ=1, isn't it? How do you explain this logical issue?

I don't know where you got this idea. In SR Δt' = γΔt not Δt/γ. It is the same for LT. That is where your confusion lies.

 

[Vorde]

You are wrong with these equations. In both LT and SR (it seems stupid as I previously mentioned to distinguish between the two like that but I'll cave for argument's sake), $\Delta t'=\Delta t \gamma$. You may be confusing the time dilation equation with the length contraction equation, which is $\Delta L'= \frac{\Delta L}{\gamma}$

 

[Doc Al]

Now, what SR claims is Δt' = Δt/γ and what LT claims is Δt' = γΔt for the ABOVE example. Logically speaking, this should not happen UNLESS γ=1, isn't it? How do you explain this logical issue?

The simple explanation is that you do not understand how and when to apply the time dilation formula. (And please stop saying "SR claims...".)

Events that happen at x = 0 can be treated similar to a clock at that point that is stationary in the unprimed frame. From the primed frame, that clock is moving and obeys the 'time dilation' formula (which is derived from the LT). You'll get Δt' = γΔt no matter how you slice it.

 

[Dale]

Now, what SR claims is Δt' = Δt/γ and what LT claims is Δt' = γΔt for the ABOVE example. Logically speaking, this should not happen UNLESS γ=1, isn't it? How do you explain this logical issue?

The explanation is easy: You made a mistake.

SR claims the same as the LT claims, specifically that in any given inertial frame a moving clock will tick more slowly. Your assertion to the contrary is simply a mistake on your part.

 

[John Huang]

The simple explanation is that you do not understand how and when to apply the time dilation formula. (And please stop saying "SR claims...".)

Events that happen at x = 0 can be treated similar to a clock at that point that is stationary in the unprimed frame. From the primed frame, that clock is moving and obeys the 'time dilation' formula (which is derived from the LT). You'll get Δt' = γΔt no matter how you slice it.

I knew that you might claim the event at x=0 would reverse the moving and stationary status. I also mentioned "If you like the event to stay in the moving system, then you may let x'=1." in my response. When the event happens at x'=1, the time dilation equation of SR remains the same Δt' = Δt/γ but the time dilation equation of LT will include the variable x.

Now, we have a SPECIFIC event happens at x'=1, the SPECIFIC event period measured at two systems, Δt' and Δt, should be SPECIFIC as well. That means, logically speaking, we have three possible answers for this logical issue: 1) SR is correct, 2) LT is correct or 3) both of them are wrong. That is my logical issue. Could you please explain this logical issue? Thanks.

 

[Vorde]

I knew that you might claim the event at x=0 would reverse the moving and stationary status. I also mentioned "If you like the event to stay in the moving system, then you may let x'=1." in my response. When the event happens at x'=1, the time dilation equation of SR remains the same Δt' = Δt/γ but the time dilation equation of LT will include the variable x.

Now, we have a SPECIFIC event happens at x'=1, the SPECIFIC event period measured at two systems, Δt' and Δt, should be SPECIFIC as well. That means, logically speaking, we have three possible answers for this logical issue: 1) SR is correct, 2) LT is correct or 3) both of them are wrong. That is my logical issue. Could you please explain this logical issue? Thanks.

You are not listening to the rest of us. You have your equations wrong, and you are going to continue to be wrong until you acknowledge and fix that. I don't want to repeat what has been posted already by several people, so I would go back and read their posts. Furthermore, it seems you are confusing the time dilation equation with the lorentz boost in the time dimension, which are two separate (not competing) equations.

 

[John Huang]

You are not listening to the rest of us. You have your equations wrong, and you are going to continue to be wrong until you acknowledge and fix that. I don't want to repeat what has been posted already by several people, so I would go back and read their posts. Furthermore, it seems you are confusing the time dilation equation with the lorentz boost in the time dimension, which are two separate (not competing) equations.

Thanks for your comment. But I did listen, otherwise, how could I respond?

You said that ".. it seems you are confusing the time dilation equation with the lorentz boost in the time dimension,..". I think SR is independent to the Lorentz boost. A Lorentz boost in any direction can be turned and moved to match the boost in the x-direction mathematically. I think I am fine with the term of boost.

 

[Vorde]

No, you are misunderstanding the equations. A lorentz boost, given the input of a time coordinate of an event for one observer, and the x-value and velocity of a second observer, will tell you the time coordinate of the event for the second observer.

The time dilation equation, given an input of an interval of time and the velocity of a second observer, will give you the interval of time measured by the second observer.

They are two totally different equations, and one can be derived from the other, so it's preposterous to claim one is true and the other isn't.

 

[John Huang]

No, you have this backwards. The LT is part of SR.

I think there is some language barrier. Perhaps this will help:
$SR \supset LT \supset time \; dilation$
$SR \neq time \; dilation$

Your "No," after your quote of my response {If you think LT is part of SR, that's fine. Now, we have two "time dilation" equations.} in the # 42 confused me. Now I know your "No," is for my second statement in your quote. Thanks for the clarification.

 

[JesseM]

My point is a logical issue.

In above example, two systems have constant relative velocity so that the speed of time in the moving system t' and the speed of time in the stationary system t

SR, and the time dilation equation, do not say anything about "the speed of time", that's your misconception right there. The time dilation equation is about the rate of a clock as perceived in a frame where it's moving at speed v; nothing more. If you take two events on a clock's worldline and Δt is the time between them as measured by the clock, then naturally Δt is also the time between those events in the frame where the clock is at rest, where Δx for that pair of events is 0. If you plug Δx=0 into the Lorentz transformation equation Δt' = γ(Δt - vΔx/c²), you get the equation Δt' = γΔt, which is the time dilation equation (here Δt is the time between two events on a clock's worldline as measured by the clock itself, and Δt' is the dilated time between those same two events in an inertial frame where the clock is moving at speed v. So, in this frame the clock takes a time of Δt' to tick forward by a time increment Δt, and this is the only case that the time dilation equation was ever intended to cover).

 

[John Huang]

No, you are misunderstanding the equations. A lorentz boost, given the input of a time coordinate of an event for one observer, and the x-value and velocity of a second observer, will tell you the time coordinate of the event for the second observer.

The time dilation equation, given an input of an interval of time and the velocity of a second observer, will give you the interval of time measured by the second observer.

They are two totally different equations, and one can be derived from the other, so it's preposterous to claim one is true and the other isn't.

Thanks. Now I found out SR is just for the event periods, it is not designed for the event time. Even if we let t=t'=0 when O=O', SR is not for event time due to the simultaneity issue. I should not ask the time equation of SR to tell event time, it is for the time period. My mistake.

If I use x'=1 for the location of an event, then, the variable of x will be canceled out and the event period calculated by LT will be the same as the event period calculated by SR.

 

[HomogenousCow]

I recommend the intro in Schutz

 

[harrylin]

My point is a logical issue.

In above example, two systems have constant relative velocity so that the speed of time in the moving system t' and the speed of time in the stationary system t should be decided once we select the point O as the stationary point, and the O' as the moving point. Under this SPECIFIC arrangement, when we talk about a period of time for ONE SPECIFIC EVENT then we should have ONLY ONE event period Δt as recorded in the stationary system and ONLY ONE event period Δt' as recorded in the moving system.

Now, what SR claims is Δt' = Δt/γ and what LT claims is Δt' = γΔt for the ABOVE example. Logically speaking, this should not happen UNLESS γ=1, isn't it? How do you explain this logical issue?

If you like the event to stay in the moving system, then you may let x'=1.

Of course, LT is part of SR. The apparent contradiction is perhaps due to an important point that you may have missed: you cannot directly measure the rate of a moving clock with a single stationary clock, as the moving clock can only be at negligible distance from a single stationary clock at one moment - for comparing two time periods you need to use for example two clocks in the "stationary" system, one at x1 and one at x2 (there are other means, but this is the simplest to picture). According to the LT:

1. For x1'=x2' (Δx'=0, clock at rest in S', moving in S): Δt' = Δt/γ
2. For x1=x2 (Δx=0, clock at rest in S, moving in S'): Δt' = γΔt

I think that you selected situation 1. In that situation we compare the clock readings of a clock that is moving relative to S with the readings of clocks that are rest relative to S. For simplicity you can choose that "moving" clock at be positioned at O'. SR says simply what the LT say for each situation.

If I correctly recall it, I did not fully understand how this works until I actually derived that myself and made sketches of the physical meanings of 1. and 2. And it is necessary to understand relativity of simultaneity.

PS I see that others already gave roughly the same explanation with different words, but one never knows which one is the easiest to understand and regretfully some gave mistaken and even wrong answers. Probably such mistaken answers are the cause of your confusion. I may have identified the cause of your confusion and advice to ignore those answers that did not clarify if they took Δx or Δx' zero, or what they took as "moving".

 

[Doc Al]

I knew that you might claim the event at x=0 would reverse the moving and stationary status.

I hope you realize that the 'stationary' status is purely relative. Each frame considers themselves to be the stationary one. Better to use the distinctions of primed and unprimed.

I also mentioned "If you like the event to stay in the moving system, then you may let x'=1." in my response.

You seem to be confused about what an 'event' is. Events happen in all frames. (Their coordinates are different in different frames.)

When the event happens at x'=1, the time dilation equation of SR remains the same Δt' = Δt/γ but the time dilation equation of LT will include the variable x.

In order to discuss a time interval between events you need at least two events. What are they? I thought you wanted the events to all take place at x = 0?

Now, we have a SPECIFIC event happens at x'=1, the SPECIFIC event period measured at two systems, Δt' and Δt, should be SPECIFIC as well.

You seem to be mixing up two sets of events (as far as I can decipher):

(1) Events that occur at the same place in the unprimed frame with coordinates in that frame of (0,0) and (0, t). The interval between them is Δt. As measured in the primed frame, the interval between those same events is Δt' = γΔt.

(2) Events that occur at the same place in the primed frame with coordinates in that frame of (0,0) and (0, t'). The interval between them is Δt'. As measured in the unprimed frame, the interval between those same events is Δt = γΔt'.

Please take note of the symmetry here.

That means, logically speaking, we have three possible answers for this logical issue: 1) SR is correct, 2) LT is correct or 3) both of them are wrong. That is my logical issue. Could you please explain this logical issue?

Again, you insist on conflating the time dilation formula (which is only part of SR) with SR itself. That will always be wrong. Please stop, as it just makes you seem silly.

So assuming that what you are actually asking about is the time dilation formula compared to the LT: You are applying the time dilation formula incorrectly! Used correctly, they will always yield the same results (in those special cases where the time dilation formula applies).

 

[John Huang]

Ok. How does SR define an event time for an event moving in the moving system?

For example, if an event moves at speed v to the positive x direction relative to the O', then to LT, it is easy. It is x'=OO'=vt so that x2'-x1' is not zero.

For that moving event, we will get a different event period for this moving event from LT than from SR if SR still use the same equation for this moving event. If SR will use different equation for that moving event, what could that equation be? I don't know, do you have idea?

 

[Doc Al]

Ok. How does SR define an event time for an event moving in the moving system?

That doesn't make sense. Events don't move. An event is something that happens at a specific place and time (with respect to some frame of reference).

Objects can move. Is that what you mean?

For example, if an event moves at speed v to the positive x direction relative to the O', then to LT, it is easy. It is x'=OO'=vt so that x2'-x1' is not zero.

So, you have some object (I presume) moving with speed v relative to some frame. So the events might be the start of the object (at x = 0, t = 0) and the arrival of the object at some later point (vt, t). Is that what you mean? What about it?

In order to proceed in any sensible fashion to apply the LT (or the time dilation formula), first define the events you want to describe.

For that moving event, we will get a different event period for this moving event from LT than from SR if SR still use the same equation for this moving event. If SR will use different equation for that moving event, what could that equation be? I don't know, do you have idea?

Again: Events don't move (objects do). Stop saying "SR" when you mean the time dilation formula. (If this thread keeps going in circles, it will be shut down.)

Define the two events you would like to talk about. Then we can discuss how the time interval between them will be measured in each frame.

 

[Dale]

the event period calculated by LT will be the same as the event period calculated by SR.

For the 5th or 6th time. LT is part of SR. What you are saying is literally nonsense.

 

[Dale]

Ok. How does SR define an event time for an event moving in the moving system?

It uses the LT.

if an event moves at speed v

A little bit of terminology here. Events don't move, objects move.

An event is something that happens at a specific time and place, i.e. an event is a point in a 4D spacetime. Events have 4 coordinates (t,x,y,z). SR uses the LT to transform those coordinates from one inertial frame to another.

we will get a different event period for this moving event from LT than from SR

No, you won't. SR uses the LT to calculate the coordinates of events in different frames.

 

[harrylin]

Ok.

Sorry but... can you please give a little more feedback? For example, did you follow my post #64? Was I right about the situation that you presented? For if I understood you correctly, then several others gave a wrong answer that may have confused you.

How does SR define an event time for an event moving in the moving system?
For example, if an event moves at speed v to the positive x direction relative to the O', then to LT, it is easy. It is x'=OO'=vt so that x2'-x1' is not zero.

There is somewhat of a language problem... an object is not an event.
I suppose that you mean the time of a physical process, and you give as example an object. But your coordinates are all mixed up, I'm afraid that you'll never get anywhere like that. Try this:

An object moves at speed v in the positive x' direction from O' starting at t'=0. Then we can describe its x' coordinate as function of time as x'=v't'. And if we relate to a system in which the object is in rest at O (in the rest system S), then in S the object is simply at O which has as x-coordinate x=0.

Likely you meant something like that, but the question is not clear. Perhaps you can rephrase it using the above notation, and without repeating the error that LT is different from SR. In fact, "Ok" would mean that you would not write that error; your last post was a self contradiction.