What reference frame is used for the velocity v in the Lorentz transformation?

[Dale]

My point is that there is no absolutely stationary reference frame. We can choose any reference frame to measure the speed of an object.

Yes. That is correct. In fact it is one of the underlying assumptions of the Lorentz transform

The Lorentz transformation then becomes meaningless

This is wrong. The fact that there is no absolutely stationary reference frame is one of the foundational assumptions of relativity. The correctness of its assumptions is precisely what makes the Lorentz transform meaningful. So this is completely backwards. It would be finding an absolutely stationary reference frame that would make the transform meaningless.

 

[Dale]

Perhaps I really don't understand relativity, but that doesn't mean we can't question and doubt authoritative theories.

Not here. The place for questioning and doubting authoritative theories is the professional scientific literature. PhyscisForums is an educational site that teaches about currently accepted science.

However, you should be made aware that your objections here are wrong. Relativity may eventually be found to be incorrect, but it will be through new experimental evidence.

Only new experimental evidence will disprove relativity. Do you have that? If so then please publish it in the scientific literature and then we can discuss it here once it is published. If not, then the purpose of this thread is to help you correct your misunderstandings.

The kinds of objections you are raising are just typical misunderstandings of introductory students. Your misunderstandings are a teaching and a learning challenge, not a challenge to the science.

 

[Ibix]

You solve this problem using mathematics

I can do this easily (except for the bits you haven't specified l, discussed below). The point is for you to familiarise yourself with relativity.

If a pair of twins were 20 years old at 8:00 on January 1, 2015. Then the elder brother went on a space journey and returned to Earth, and his clock showed 8:00 on January 1, 2020. So did he witness the events that happened on January 1, 2020 on Earth or the events that occurred on Earth in 2025? Could he see his younger brother on January 1, 2025?

You haven't specified the problem well. What speed is the elder brother travelling at relative to the Earth and are we assuming that he travels at constant speed (i.e., with instant acceleration)? Once you've specified that can you calculate the Lorentz gamma factor the Earth measures for the elder brother? Once you've done that, using the Earth frame, what does the maths tell you the clocks on Earth will show at the elder brother's return if his clocks showed 2015 when he left and 2020 when he returned?

 

[Dale]

You solve this problem using mathematics: If a pair of twins were 20 years old at 8:00 on January 1, 2015. Then the elder brother went on a space journey and returned to Earth, and his clock showed 8:00 on January 1, 2020. So did he witness the events that happened on January 1, 2020 on Earth or the events that occurred on Earth in 2025? Could he see his younger brother on January 1, 2025?

Yes. $2020-2015$ is $5$ years and $2025-2015$ is $10$ years. So the mathematical question is, do there exist two timelike worldlines, $x_1(t)$ and $x_2(t)$ that intersect at two events such that one timelike worldline is $\tau_1=10$ years long and the other is $\tau_2=5$ years long?

In any inertial coordinates using units where $c=1$, the length of a worldline can be calculated by $$\tau=\int_{t_i}^{t_f}\sqrt{1-v(t)^2}\ dt$$ where $v(t)=|\dot {\vec x}(t)|$.

So, if $v_1(t)=0$ and $v_2(t)=\sqrt{3}/2=0.866$ then $$\tau_1= \int_{0}^{10}\sqrt{1-0^2}\ dt=10$$ and $$\tau_2=\int_{0}^{10}\sqrt{1-\left(\frac{\sqrt{3}}{2}\right)^2}\ dt=5$$

Thus the problem is solved. The elder brother can leave in 2015 and return in 2025 with his own clock showing 2020 provided he spent the entire trip at a constant speed of $0.866 \ c$ in the inertial frame where his younger brother is at rest.

Now, that we have established the math, the next step is to establish your understanding of the math. Please look over what I have posted and ask any questions about any part of the math that you do not understand. But do so with the clear understanding that the purpose of this exercise is your education and learning, not to give you space to make claims that relativity is wrong. Such claims would require new experimental evidence published in the professional scientific literature.

 

[Nugatory]

You solve this problem using mathematics: If a pair of twins were 20 years old at 8:00 on January 1, 2015. Then the elder brother went on a space journey and returned to Earth, and his clock showed 8:00 on January 1, 2020. So did he witness the events that happened on January 1, 2020 on Earth or the events that occurred on Earth in 2025? Could he see his younger brother on January 1, 2025?

You might want to start by working through the Twin Paradox FAQ: https://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html

 

[Huangdongcheng]

Yes. $2020-2015$ is $5$ years and $2025-2015$ is $10$ years. So the mathematical question is, do there exist two timelike worldlines, $x_1(t)$ and $x_2(t)$ that intersect at two events such that one timelike worldline is $\tau_1=10$ years long and the other is $\tau_2=5$ years long?

In any inertial coordinates using units where $c=1$, the length of a worldline can be calculated by $$\tau=\int_{t_i}^{t_f}\sqrt{1-v(t)^2}\ dt$$ where $v(t)=|\dot {\vec x}(t)|$.

So, if $v_1(t)=0$ and $v_2(t)=\sqrt{3}/2=0.866$ then $$\tau_1= \int_{0}^{10}\sqrt{1-0^2}\ dt=10$$ and $$\tau_2=\int_{0}^{10}\sqrt{1-\left(\frac{\sqrt{3}}{2}\right)^2}\ dt=5$$

Thus the problem is solved. The elder brother can leave in 2015 and return in 2025 with his own clock showing 2020 provided he spent the entire trip at a constant speed of $0.866 \ c$ in the inertial frame where his younger brother is at rest.

Now, that we have established the math, the next step is to establish your understanding of the math. Please look over what I have posted and ask any questions about any part of the math that you do not understand. But do so with the clear understanding that the purpose of this exercise is your education and learning, not to give you space to make claims that relativity is wrong. Such claims would require new experimental evidence published in the professional scientific literature.

It seems that you haven't realized the complexity of this issue. Some problems can be solved using mathematics, but some cannot be simply addressed by mathematics alone. For instance, whether the calculated results are consistent with reality.

 

[Ibix]

For instance, whether the calculated results are consistent with reality.

For that, you'd have to do the experiment.

 

[weirdoguy]

It seems that you haven't realized the complexity of this issue.

It seems that you're not here to learn, but to argue. Telling physiscists that they haven't realized the complexity of issue when you haven't even grasped the very basics of the topic is rude.

Special relativity is consistent with reality as hundreds of thousands of experiments and observations show. So, again, what do you want to achieve here?

 

[Huangdongcheng]

Yes. $2020-2015$ is $5$ years and $2025-2015$ is $10$ years. So the mathematical question is, do there exist two timelike worldlines, $x_1(t)$ and $x_2(t)$ that intersect at two events such that one timelike worldline is $\tau_1=10$ years long and the other is $\tau_2=5$ years long?

In any inertial coordinates using units where $c=1$, the length of a worldline can be calculated by $$\tau=\int_{t_i}^{t_f}\sqrt{1-v(t)^2}\ dt$$ where $v(t)=|\dot {\vec x}(t)|$.

So, if $v_1(t)=0$ and $v_2(t)=\sqrt{3}/2=0.866$ then $$\tau_1= \int_{0}^{10}\sqrt{1-0^2}\ dt=10$$ and $$\tau_2=\int_{0}^{10}\sqrt{1-\left(\frac{\sqrt{3}}{2}\right)^2}\ dt=5$$

Thus the problem is solved. The elder brother can leave in 2015 and return in 2025 with his own clock showing 2020 provided he spent the entire trip at a constant speed of $0.866 \ c$ in the inertial frame where his younger brother is at rest.

Now, that we have established the math, the next step is to establish your understanding of the math. Please look over what I have posted and ask any questions about any part of the math that you do not understand. But do so with the clear understanding that the purpose of this exercise is your education and learning, not to give you space to make claims that relativity is wrong. Such claims would require new experimental evidence published in the professional scientific literature.

It seems that you haven't realized the complexity of this issue. Some problems can be solved using mathematics, but some cannot be simply addressed by mathematics alone. For instance, whether the calculated results are consistent with reality.

It seems that you're not here to learn, but to argue. Telling physiscists that they haven't realized the complexity of issue when you haven't even grasped the very basics of the topic is rude.

Special relativity is consistent with reality as hundreds of thousands of experiments and observations show. So, again, what do you want to achieve here?

Suppose the elder brother left the Earth at 8:00 on January 1, 2015, when they were both 20 years old. When he returned to Earth, his clock showed 8:00 on January 1, 2020, and he looked like a 25-year-old. While the younger brother's clock showed 8:00 on January 1, 2025, and he looked like a 30-year-old.

1. At two different times, 8:00 on January 1, 2020 and 8:00 on January 1, 2025, were the Earth in the universe at the same position? Should a moving Earth be at different positions at different times? Did the Earth that the elder brother stepped on in 2020 return to be in the same position as the Earth that the younger brother stepped on in 2025 in the universe?

2. If the elder brother's time passed slowly only because the reading on his clock was small and his body grew slowly, was it unrelated to what happened around him? If the elder brother's time was 8:00 on January 1, 2020, why could he stand together with the younger brother who was 8:00 on January 1, 2025 and see what happened around him in 2025?

If we follow this logical reasoning, if the younger brother was 30 years old in 2025, imagine he went back to 2020, his clock showed 2020, and he looked like a 25-year-old. But he didn't see what happened in 2020, and what he saw was still what happened in 2025. That is to say, he and his clock returned to the state of 2020, but the clocks of all the people around him showed 2025 instead of 2020. Do you think it's okay?

3. If one person's time passed slowly and showed 2020, and another person's time passed quickly and showed 2030, but they saw each other and saw all the other clocks showing 2025, do you think there's no problem?

 

[Dale]

Some problems can be solved using mathematics, but some cannot be simply addressed by mathematics alone. For instance, whether the calculated results are consistent with reality.

Indeed. That requires experiments.

The calculated results are consistent with a large amount of experimental data. In particular

Bailey et al., Nature 268 (July 28, 1977) pg 301.
Bailey et al., Nuclear Physics B 150 pg 1–79 (1979).
Hafele and Keating. Science Vol. 177 pg 166–170 (1972).

All three of those tested some version of your scenario, but the Bailey ones are conceptually simpler as the effect of gravity is negligible.

So now we have both the relevant math and a small sample of some of the most relevant experiments. Are you ready to start learning?

 

[Ibix]

1. At two different times, 8:00 on January 1, 2020 and 8:00 on January 1, 2025, were the Earth in the universe at the same position?

Why do you think the universe cares that their clocks don't show the same time? They are at the same event.

The maths you are refusing to do would eventually show you that the time you experience is a measure of a "distance" through spacetime that you have travelled, and just like with distance through space the elapsed time depends on the route taken. The elder brother found a shortcut, so his clock advanced less, but both brothers started at the same event and ended at the same event.

 

[Huangdongcheng]

Why do you think the universe cares that their clocks don't show the same time? They are at the same event.

The maths you are refusing to do would eventually show you that the time you experience is a measure of a "distance" through spacetime that you have travelled, and just like with distance through space the elapsed time depends on the route taken. The elder brother found a shortcut, so his clock advanced less, but both brothers started at the same event and ended at the same event.

In reality, do you think that what happens in time has no connection with what occurs in the universe? Do you think that exactly the same events could take place in different times within the universe?

 

[Dale]

In reality, do you think that what happens in time has no connection with what occurs in the universe? Do you think that exactly the same events could take place in different times within the universe?

It doesn't matter what you or he thinks about reality. What matters is what actually happens in reality. This is confirmed by experiments as linked above

 

[Huangdongcheng]

It doesn't matter what you or he thinks about reality. What matters is what actually happens in reality. This is confirmed by experiments as linked above

Have you really thought about these questions seriously? Suppose the elder brother left the Earth at 8:00 on January 1, 2015, when they were both 20 years old. When he returned to Earth, his clock showed 8:00 on January 1, 2020, and he looked like a 25-year-old. While the younger brother's clock showed 8:00 on January 1, 2025, and he looked like a 30-year-old.

1. At two different times, 8:00 on January 1, 2020 and 8:00 on January 1, 2025, were the Earth in the universe at the same position? Should a moving Earth be at different positions at different times? Did the Earth that the elder brother stepped on in 2020 and the Earth that the younger brother stepped on in 2025 have the same position in the universe space?

2. If the elder brother's time passed slowly was only because the reading on the clock was small and his body grew slowly, was it unrelated to what happened around him? Was the elder brother's time at 8:00 on January 1, 2020, able to stand together with the younger brother at 8:00 on January 1, 2025 and see what happened around in 2025? If reasoning like this is followed, why couldn't the younger brother, who was 30 years old in 2025, return to 2020 and have his clock show 2020, look like a 25-year-old, but not see what happened in 2020, but still see what happened in 2025? That is to say, he and his clock returned to the state of 2020, but the clocks of all the people around him showed 2025 instead of 2020. Do you think it's okay?

3. If one person's time passed slowly and showed 2020, and another person's time passed quickly and showed 2030, but they saw each other and saw all the clocks showing 2025, do you think there's no problem?

 

[weirdoguy]

do you think there's no problem?

Yes, because that's how reality/universe works. It's you that have problem with reality, because it does not work the way you want it to.

 

[weirdoguy]

Have you really thought about these questions seriously?

I've been teaching physics since 2008, and I've spent 5 hard years becoming a physicist. We all here thought about these questions seriously multiple times. You have not and you're wasting our time. You are not here to learn. This thread is going nowhere.

 

[Ibix]

Do you think that exactly the same events could take place in different times within the universe?

This is your problem. You think that there is a global time, so you think that the only way (non-broken) clocks can measure different times is if they are at different global times. This is wrong.

Relativity shows us that the time you experience is analogous to distance travelled through space. So two clocks showing different times is no more confusing or impossible than two odometers showing different distances.

 

[Herman Trivilino]

In reality, do you think that what happens in time has no connection with what occurs in the universe? Do you think that exactly the same events could take place in different times within the universe?

Your comments seem to indicate that you have a newtonian view of time. That there is the equivalent of a giant clock in the sky keeping track of a universal time that is the same everywhere. It's been shown repeatedly throughout the last 120 years that such a view is not right.

If the engineers who operate the GPS satellite clocks held that belief, the GPS system would not be precise enough to tell you what street intersection you are at, but instead perhaps only the city you were in. Each of the GPS clocks measure their own proper time, and engineers have to account for the fact that each clock reports a different amount of elapsed time between events.

 

[Ibix]

Have you really thought about these questions seriously?

Every single one of us answering your questions has thought about it. We were all where you are once, but we studied and learned how the universe actually works. Your intuition is wrong, although in a way that will make milliseconds of difference over your life. Once you start studying high speed phenomena, though, you have to accept that you are wrong because that's what the experiments say.

 

[Dale]

Have you really thought about these questions seriously?

Yes, I have, and they do not matter in the end. They are the standard questions that most students ask as distractions from the actual important learning. We have all asked these. I was stuck on my version for about 7 years before I understood.

Have you understood the math and the experiments?

 

[Huangdongcheng]

I've been teaching physics since 2008, and I've spent 5 hard years becoming a physicist. We all here thought about these questions seriously multiple times. You have not and you're wasting our time. You are not here to learn. This thread is going nowhere.

This is the problem I encountered when studying physics. Then I presented the problem for discussion!

 

[weirdoguy]

Then I presented the problem for discussion!

And people pointed MULTIPLE TIMES how to resolve your problem. You did nothing with that. In the end, experiments falsify your point of view. And that's what matters.

 

[PeterDonis]

Thread closed for moderation.

 

[Dale]

After a very brief discussion among the mentors, we will leave this thread closed.

As @weirdoguy mentioned, we have shown how the math and theory solve the problems raised by the OP, and we have referred to experimental evidence showing that the math and theory are correct. At this point the only productive thing is for the OP to review the provided math and experiment. If they have specific new questions after doing so, then they may open a new thread for help.