Quick calculation check please

[name123]

Modify just the $t'$ equation using the latter.

With the gamma equation you gave wouldn't it be wrong if $w$ = 0, and I divided $v^2$ by $c$ instead of $c^2$? By wrong I mean different to the normal equation for a single boost.

 

[PeterDonis]

With the gamma equation you gave wouldn't it be wrong if $w = 0$, and I divided $v^2$ by $c$ instead of $c^2$?

I don't think I ever said to divide $v^2$ by $c$ anywhere, but you are correct that you do have to include $c$ in the $\gamma$ equation, and I should have mentioned that. The correct equation with $c$ included is

$$
\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2} - \frac{w^2}{c^2}}}
$$

 

[name123]

I don't think I ever said to divide $v^2$ by $c$ anywhere, but you are correct that you do have to include $c$ in the $\gamma$ equation, and I should have mentioned that. The correct equation with $c$ included is

$$
\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2} - \frac{w^2}{c^2}}}
$$

Could you just include c with the others, I'm sure I'm not the only one that would find it useful?

 

[PeterDonis]

Could you just include c with the others

The $x'$ and $y'$ equations are unchanged. The $t'$ equation becomes

$$
t' = \gamma \left( t - \frac{v}{c^2} x - \frac{w}{c^2} y \right)
$$

 

[name123]

Thanks, and when looking at it from the B-Team's perspective are they considering the A-Team to be going at $-v$,$-w$?

 

[PeterDonis]

when looking at it from the B-Team's perspective are they considering the A-Team to be going at $-v$,$-w$?

Yes.

 

[name123]

That was great thanks, I the figures were pretty much the same, but I could see the gap (one A-Team member at a lower y and one at a higher y than the B-Team members).

Regarding a point earlier, regarding "now" I had said:

Now does have an absolute meaning for you personally though doesn't it? And would have for the next team A observer down. So can you see how it could true that simultaneously to you experiencing, a team A member was experiencing simultaneously to the team B member opposite to it who was experiencing simultaneously with another team B member experiencing who was simultaneously experiencing with you in the future?

If by "now" you mean "what is happening to me at a given reading on my clock", then yes, of course. But I don't see what that has to do with the rest of what you said.

I'm slightly confused, for me, while I can imagine all the clock times that I will be alive for, there will only ever be one "now". Are you saying that you think the way that "now" should be understood given relativity, is that any clock time in your life has equal right for the claim of being now?

Also with your understanding of relativity would it be true to say that everything the human you experience being has ever done exists in spacetime, so in theory if you could travel to those spacetime coordinates you could see yourself?

 

[PeterDonis]

while I can imagine all the clock times that I will be alive for, there will only ever be one "now"

But which clock time is "now" to you, on this definition of "now", is continually changing.

Are you saying that you think the way that "now" should be understood given relativity, is that any clock time in your life has equal right for the claim of being now?

No. It's true that, since each of them is your "now" when it's your "now", each of them has an equal claim to the term "now". This concept of "now" is just a label that means "whichever instant of my clock time I'm experiencing". But none of this has anything to do with relativity. Your entire worldline is represented in the spacetime model used in relativity; which instant you want to label "now" has nothing to do with the model.

with your understanding of relativity would it be true to say that everything the human you experience being has ever done exists in spacetime

Relativity models spacetime this way, yes. But relativity does not talk about what "exists" except in the sense that it's all there in the model.

in theory if you could travel to those spacetime coordinates you could see yourself?

In theory, yes. But the "if" there is a big "if". Traveling to spacetime coordinates that you've already visited once requires what are called "closed timelike curves", and while they are possible mathematically, pretty much all physicists believe that they aren't physically possible. Spacetimes which include them have a number of properties that don't appear to be physically reasonable.

 

[name123]

But which clock time is "now" to you, on this definition of "now", is continually changing.

The way I mean it if I were to always wear a watch (which had the date and always kept time) only one of its times would ever be "now".

Are you saying that you think the way that "now" should be understood given relativity, is that any clock time in your life has equal right for the claim of being now?

No. It's true that, since each of them is your "now" when it's your "now", each of them has an equal claim to the term "now". This concept of "now" is just a label that means "whichever instant of my clock time I'm experiencing". But none of this has anything to do with relativity. Your entire worldline is represented in the spacetime model used in relativity; which instant you want to label "now" has nothing to do with the model.

Reality has to do with what instant I label "now". Do you think that an interpretation of a model should take into account the reality of the situation?

What is moving along your worldline in the spacetime model used in relativity?

Also with your understanding of relativity would it be true to say that everything the human you experience being has ever done exists in spacetime, so in theory if you could travel to those spacetime coordinates you could see yourself?

In theory, yes. But the "if" there is a big "if". Traveling to spacetime coordinates that you've already visited once requires what are called "closed timelike curves", and while they are possible mathematically, pretty much all physicists believe that they aren't physically possible. Spacetimes which include them have a number of properties that don't appear to be physically reasonable.

Can my history change? (without me visiting it again)

 

[PeterDonis]

The way I mean it if I were to always wear a watch (which had the date and always kept time) only one of its times would ever be "now".

The way you are saying this makes me think that either you are confused or I'm misunderstanding you. The time you call "now" is whatever time your watch says it is when you look at it. But that time isn't always the same, right? Look at your watch today, it tells you one time and date. Look at your watch tomorrow, it tells you a different time and date. Both of those times and dates are "now" when you look at them, but they're not the same. Is this what you're trying to say? Or is it something else?

Reality has to do with what instant I label "now".

Why? This does not seem to me to be a statement about physics; it seems to be a statement about philosophy or metaphysics, both of which are off topic for this forum.

What is moving along your worldline in the spacetime model used in relativity?

Taking the model by itself, nothing. Nothing "moves" in spacetime; spacetime is just a 4-dimensional geometric object that is what it is. Your particular history is just a particular curve in this 4-dimensional geometry. Saying that you and I are "moving" relative to each other is just an informal way of saying that our two histories are described by different curves.

Can my history change? (without me visiting it again)

No, not even if you do visit it again--at least, not according to the way relativity models the universe. As above, your "history" is just a particular curve in the 4-dimensional geometry of the universe; it can't "change", because the 4-dimensional geometry doesn't "change", it just is what it is.

 

[Dale]

if I were to always wear a watch (which had the date and always kept time) only one of its times would ever be "now".

Reality has to do with what instant I label "now".

The first statement is obviously wrong, and the second is just philosophy. Since you have resolved your physics questions, it is a good time to close the thread.