I Are the Lorentz Transformations False?

[Dale]

While the equation $\Delta t'=\gamma \Delta t$ was merely distasteful, the equation

$$\Delta t'= \gamma (\Delta t - v\Delta x)$$

Is totally repugnant.

In the former equation, $\Delta t'$ isn't a function of the coordinates of a point in the unprimed frame. In the latter equation $\Delta t'$ is a function of the coordinates of a point in the unprimed frame. That goes against all common sense.

Ok, thanks, that is helpful. The term you are objecting to is the relativity of simultaneity. It is indeed the most challenging concept in special relativity and the one that most directly disagrees with student’s intuition and “common sense”. Nevertheless, nature is relativistic.

What this term represents is not that the passage of time depends on location. It is that there is a location-dependent offset to synchronized clocks.

In other words, if you have synchronized two clocks in your frame then in my frame they are desynchronized by an amount given by that term. Both clocks tick at the same rate in my frame, but they are not synchronized in my frame despite being synchronized in yours.

 

[PeterDonis]

In the former equation, $\Delta t'$ isn't a function of the coordinates of a point in the unprimed frame.

Yes, it is. $t$ is a coordinate. Frames in relativity describe spacetime.

That goes against all common sense.

So does a lot of modern physics. If you think relativity goes against your common sense, try quantum mechanics.

However, relativity and QM are confirmed by many, many experiments; in some cases the confirmation goes to as much as 13 decimal places. So your common sense is outvoted. The only way to deal with it is to retrain your common sense; that is probably the hardest part of learning modern physics.

 

[Dale]

The thread is reopened after deleting a brief tangent about QM.

@Leepappas your personal feelings about relativity are not relevant. You can discuss the theory and experiments without editorializing. We understand that this is a difficult concept. And now you have a good summary of the experimental facts that establish it anyway. So let’s focus on the science and not opinions.

 

[Leepappas]

The thread is reopened after deleting a brief tangent about QM.

@Leepappas your personal feelings about relativity are not relevant. You can discuss the theory and experiments without editorializing. We understand that this is a difficult concept. And now you have a good summary of the experimental facts that establish it anyway. So let’s focus on the science and not opinions.

Fair enough.

 

[Leepappas]

If $t' = \gamma(t-vx)$ then space is two dimensional.
Point 1: (0,0)
Point 2: (a,t)
We have established that for these two points in spacetime we have
$\Delta t' = \gamma(\Delta t - v\Delta x)$

Therefore, for these two points
Point 1: (0,0)
Point 2: (a,0)
We have:
$0 = \gamma(0- va)$
Since $v \neq 0$ it follows that $a=0$.
The y and z coordinates are not constrained to be any particular value but the x coordinate is constrained to be equal to zero. Therefore space is two dimensional if the Lorentz transformations are true.

 

[Dale]

for these two points
Point 1: (0,0)
Point 2: (a,0)
We have:
$0 = \gamma(0- va)$

No. By the Lorentz transform we have:
$\Delta t’=\gamma(0-va)$

 

[Bosko]

TL;DR Summary: SR just doesn't make sense.

Consider the Lorentz transformations with c=1, and consider any point in space whose x coordinate isn't zero, starting from

$t_{inital }= t'_{inital }=0$

I will place the origin of the primed coordinate system in that point. So the initial conditions are
$t_0=t'_0=0$
and
$x_0 \neq x'_0=0$

$t' =\gamma (t-xv)$

You need to adapt this formula to the changed initial conditions.

Otherwise, for $t_0=t'_0=0$ it would be
$t'_0 =\gamma (t_0-x_0v)$
$0 =\gamma (0-x_0v)$
$0 =-x_0v$

Do you want to try with :
$$t' =\gamma (t-(x-x_0)v)$$

I drew the coordinate systems

Edit: Be careful because $t=0$ and $t'=0$ are not the same moment ( they are not simultaneous )
$t'=0$ is on $x'$ axis. When $x=0$ and $t=0$ (check drawing) $t' \gt 0$

 

[Leepappas]

No. By the Lorentz transform we have:
$\Delta t’=\gamma(0-va)$

If the change in $\Delta t$ is zero, then how can time pass in another inertial reference frame?

 

[Dale]

If the change in $\Delta t$ is zero, then how can time pass in another inertial reference frame?

The two events are simultaneous in one frame, but not in the other frame.

According to the primed frame the events happened at different times. According to the unprimed frame the primed clocks are offset.

 

[Orodruin]

Since that old thread I have familiarized myself with the relativity of simultaneity

The following tells me you have not understood the relativity of simultaneity:

If the change in $\Delta t$ is zero, then how can time pass in another inertial reference frame?

That $\Delta t’$ is non-zero for events with $\Delta t = 0$ is the relativity of simultaneity. Two events that are simultaneous in the unprimed frame are not simultaneous in the primed frame. What you have just done is to derive an expression for how much they differ.

 

[PeroK]

If the change in $\Delta t$ is zero, then how can time pass in another inertial reference frame?

The real problem.is that you've fundamentally set your mind against relativity. This thread is more about tackling that psychology than about science or mathematics.

 

[Ibix]

Since that old thread I have familiarized myself with the relativity of simultaneity and Minkowski world lines.

The key realisation is that the Lorentz transforms are very closely analogous to rotations in Euclidean space. Rotating your coordinate system on a Euclidean plane can't lead to contradictions because all you are doing is picking a different way of labelling points. You can be sloppy and do it wrong, but that's not the fault of the maths. Similarly, boosting your coordinate system can't lead to contradictions because all you are doing is changing your system for labelling events.

Minkowski diagrams can help with this because you can draw a diagram of some arbitrary scenario and superpose the coordinate grid of any frame you like. The diagram never changes, only the coordinate grid. So how can you have a contradiction? Then you can imagine stretching the diagram so that one of the other coordinate grids is now orthonormal. It's a smooth deformation (no points need to cross or anything nasty like that) so, again, how can there be a contradiction?

I found that visualisation helpful enough to have written some Javascript. It doesn't work very well on touch screens (they weren't as ubiquitous when I wrote this), but the buttons at the bottom of the page set up some simple scenarios. You can then choose another frame and it animates the boost.

 

[Orodruin]

The universe, alas, is not required to conform to your intuition. You're just not that important.

This is something that should be repeated and repeated and repeated and … well, you get the picture.

The bottom line is that anybody’s ”common sense” or ”intuition” is based on their general experience. In everyday life most people will not come into contact with relativistic effects and so they will feel unfamiliar or counter-intuitive. The Universe however is not restricted to abide by anyone’s ”common sense”. This is why in physics we make experiments to test how the Universe behaves in extreme situations. Regardless of whether someone likes it or not, the results of such tests are what will tell you how things work, not ”common sense” or thought experiments.

The good news is that intuition for the theory can be built by working with it to the point that it does seem familiar.

 

[Leepappas]

The following tells me you have not understood the relativity of simultaneity:

That $\Delta t’$ is non-zero for events with $\Delta t = 0$ is the relativity of simultaneity. Two events that are simultaneous in the unprimed frame are not simultaneous in the primed frame. What you have just done is to derive an expression for how much they differ.

That is counterintuitive and a contradiction. One moment in time in the unprimed frame, corresponds to an infinite number of moments in time in the primed frame. The relativity of simultaneity is what's wrong with special relativity.

 

[Orodruin]

The relativity of simultaneity is what's wrong with special relativity.

There is nothing conceptually wrong with relativity of simultaneity. Counterintuitive, perhaps, but that is an artefact of your intuition, which the Universe is not obliged to care about. Contradictory, no - the theory is consistent. As little as there is something wrong with saying that two points that have the same x-coordinate in one frame has different x-coordinates in a frame that is rotated relative to the first. So no, there is no actual logical fallacy.

You may not like it or be able to make sense out of it personally, but that’s how the world works as confirmed by countless experiments. You can choose not to believe it, but your beliefs would be in direct conflict with empirical data.

The idea that you have found a logical gap in the theory that has been missed by many thousands of physicists over the last 100 years is, quite frankly, ludicrous. In particular as what you say is a known fallacy among students that have difficulty grasping the relativity of simultaneity (and there are a lot of them - hence my forum signature).

 

[Leepappas]

The two events are simultaneous in one frame, but not in the other frame.

According to the primed frame the events happened at different times. According to the unprimed frame the primed clocks are offset.

Ok that's counterintuitive. One moment in time in the unprimed frame corresponds to two moments in time in the primed frame.

 

[Leepappas]

There is nothing conceptually wrong with relativity of simultaneity. Counterintuitive, perhaps, but that is an artefact of your intuition, which the Universe is not obliged to care about. Contradictory, no - the theory is consistent. As little as there is something wrong with saying that two points that have the same x-coordinate in one frame has different x-coordinates in a frame that is rotated relative to the first. So no, there is no actual logical fallacy.

You may not like it or be able to make sense out of it personally, but that’s how the world works as confirmed by countless experiments. You can choose not to believe it, but your beliefs would be in direct conflict with empirical data.

The idea that you have found a logical gap in the theory that has been missed by many thousands of physicists over the last 100 years is, quite frankly, ludicrous. In particular as what you say is a known fallacy among students that have difficulty grasping the relativity of simultaneity (and there are a lot of them - hence my forum signature).

Why can't you see SR is wrong?

 

[Orodruin]

Ok that's counterintuitive. One moment in time in the unprimed frame corresponds to two moments in time in the primed frame.

Again: Counterintuitive does not mean that the Universe needs to oblige by your intuition. Regardless of how counterintuitive, experiments that test these limits confirm it. The correct reaction is to realize you need better intuition.

 

[Orodruin]

Why can't see SR is wrong?

Because it has been confirmed as a better model than classical mechanics by countless experiments. That is what is used to judge, not what you happen to find intuitive.

 

[Dale]

One moment in time in the unprimed frame corresponds to two moments in time in the primed frame.

Yes. Also one position in space in the unprimed frame corresponds to multiple positions in space in the primed frame.

Although this is a challenging concept, there is nothing particularly new about it. That happens routinely with coordinate transforms in space. The only new thing is that it happens with time as well as space. This is not a problem or flaw with relativity, it is just a coordinate transform on spacetime instead of just space.

 

[Herman Trivilino]

Why can't you see SR is wrong?

That was the response of most physicists when the theory was first created in 1905. It took a decade or two of experimental confirmation for the theory to gain acceptance. Moreover, and obvious in hindsight, the theory is self-consistent.

 

[ersmith]

Ok that's counterintuitive. One moment in time in the unprimed frame corresponds to two moments in time in the primed frame.

Sure, just like one point in space for the "moving" frame sometimes corresponds to two points in space for the "stationary" frame. For me, on the train, I haven't left my seat -- I've been in the same place the whole time. Yet someone on the ground says I've moved from New York to Washington. Is that a contradiction?

 

[Vanadium 50]

On the one hand, we have the experimental evidence summarized here: https://www.physicsforums.com/threads/faq-experimental-basis-of-special-relativity.229034/

On the other, we have arguments described (correctly IMHO) as :sloppy" and "wrong" and by the time we got to the bottom of things, it boiled down to not liking the theory. So far as I can tell, he never read the above message, nor for that matter much of what was posted in his two threads.

Not sure if there is anything else useful to be said.

 

[Orodruin]

Sure, just like one point in space for the "moving" frame sometimes corresponds to two points in space for the "stationary" frame. For me, on the train, I haven't left my seat -- I've been in the same place the whole time. Yet someone on the ground says I've moved from New York to Washington. Is that a contradiction?

At the train platform, Einstein walks over to the station master and asks:
- Excuse me, young man. Can you tell me if Boston stops at this train?

 

[PeterDonis]

And on that note, this thread is closed. Thanks to all who participated.