Are relativistic effects directional?

[TakenItSeriously]

I’d like to keep this thread focused on the Janus discussion if you don’t mind which I left off here:

 

[Janus]

2 hours ago, TakenItSeriously said:

I agree.

Again I agree. I wasn’t trying to assert that time must be running faster. I was only trying to assert that you can no longer link time dilation as the cause for the relativistic blue shift.

You mean classical distance effect? In that the distance is decreasing classically due to motion?

I wasn’t trying imply anything about that. I was trying to say that relativistic blue shift must be due to length contraction of the distance. i.e. from Alices point of view at the turn around, her distance to the Earth is 0.6*4 ly or 2.4 ly due to length contraction.

Ok, here is where it gets super tricky.and deviates from what most people assume is happening so please try to keep an open mind.

From Alices point of view, is time still dilated on the return leg when Alice is now approaching Bob?

Empirically, we can’t conclude this because both clocks now seem to be running faster so I’m saying that time is not progressing faster or slower.

I’m saying that length contraction is nothing more than time dilation except as seen from the other side.

Again, relativistic redshift is due to time dilation of the frequency.

Relativistic blueshift is due to length contraction of the wavelength.

Edit to add:

If this has got you thinking, there are more consequences to it that can resolve a whopping mystery, but you kind of need to accept this step first.

 

You have fallen into a common trap: assuming that there is only one correct way to explain the time difference between the two twins when they meet up again. 

According to Bob, Alice's clock always runs slow by the time dilation factor both on the outbound and return trip.  He see Her clock red-shifted fro the outbound trip and blue-shifted  during the return.  However, he will see the red-shift for a longer than he sees the blue-shift.  He has to wait until the light from Alice's turnaround to reach until the he starts to see the Blue-shift.

Thus at 0.8c, it would take Alice 10 yrs to travel to a turn around point 8 ly distant. This means that Bob sees a red-shift coming from Alice for 18yrs at a factor of 1/3 ( during that 18 years, he would visually see Alice age 6 yrs.  From the time of turn around, it will take another 10 yrs for Alice to return to Bob, Ergo, Alice arrives back at Bob just 2 yrs after he first see's Alice's light shift from red to Blue shift. Thus he visually watches Alice age at a factor of 3 for 2 years or another 6 years.   After twenty years by his own clock, he sees Alice age 12 yrs.

No length contraction involved.

Alice, also sees Bob red-shifted on the outbound trip and Blue-shift during the return.  For Alice, she travels out to a distance of 6 ly from Bob before returning.  Thus she sees Bob aging at a rate of 1/3 for 6 yrs or aging 2 yrs before she turns around.  Right after turn around She will see Bob age at a factor of 3, this holds for the entire 6 years for the return trip, and sees him age another 18 yrs.   After returning to Bob he will have seen him age a total of 20 years while she aged 12 yrs. The difference being that Alice see the shift from red to blue shift immediately upon turnaround, and doesn't have to wait.  This is because Alice is the one undergoing an acceleration in order to change velocity and sees the effect of this change immediately.

As far as what happens to Bob's clock during the outbound and return trips:  According to Alice it runs slow during both legs due to time dilation. ( it is important here to distinguish between time dilation, which is the comparison of clock rates between relatively moving frames, and Accumulated time difference, which can be the result of time dilation, length contraction and the relativity of simultaneity).

Bob, indeed measures less elapsed time due to length contraction, as the 6 ly distance he measures is shorter than the 10 measured by Bob.  But this applies to both legs of the trip, and has no bearing in terms of red or blue shift.

The reason that Alice ends up agreeing that less total time accumulated for her is due to the fact that She had to undergo an acceleration in switching between outbound and inbound legs,  and doing so invokes a new set of rules as to what she concludes happens to Bob's clock.  She will conclude that during this acceleration Bob's age advanced by a great deal (12.8 years), so that even though he only aged 3.6 years during the outbound leg, and 3.6 years during the return leg, He aged a total of 20 yrs for the whole trip.

The empirical data only tells us the difference in their ages when they meet up again. It say nothing about how that difference came about.

Bob will say that it was because Alice aged slower during the whole trip, While Alice will say that Bob aged slower for large part of the trip, but aged a great deal for a brief part of the trip.

Both of these views are equally correct.

The upshot is simply that Alice and Bob measure time differently during the different parts of the trip, but come up with the same end conclusion.

Time measurement is frame dependent, and there is no absolute measure of who's clock was "really" ticking slower than the others at any one point.  There is no single "reason" why Alice returns younger than Bob, every frame will have a different reason and they all are equally valid.

This is simply the way things are.

Edited November 26, 2019 by Janus

[studiot]

12 minutes ago, Janus said:

According to Bob, Alice's clock always runs slow by the time dilation factor both on the outbound and return trip.  He see Her clock red-shifted fro the outbound trip and blue-shifted  during the return.  However, he will see the red-shift for a longer than he sees the red-shift.  He has to wait until the light from Alice's turnaround to reach until the he starts to see the Blue-shift.

A little bit of editing required ?

 

[TakenItSeriously]

35 minutes ago, Janus said:

You have fallen into a common trap: assuming that there is only one correct way to explain the time difference between the two twins when they meet up again. 

According to Bob, Alice's clock always runs slow by the time dilation factor both on the outbound and return trip.  He see Her clock red-shifted fro the outbound trip and blue-shifted  during the return.  However, he will see the red-shift for a longer than he sees the red-shift.  He has to wait until the light from Alice's turnaround to reach until the he starts to see the Blue-shift.

Thus at 0.8c, it would take Alice 10 yrs to travel to a turn around point 8 ly distant. This means that Bob sees a red-shift coming from Alice for 18yrs at a factor of 1/3 ( during that 18 years, he would visually see Alice age 6 yrs.  From the time of turn around, it will take another 10 yrs for Alice to return to Bob, Ergo, Alice arrives back at Bob just 2 yrs after he first see's Alice's light shift from red to Blue shift. Thus he visually watches Alice age at a factor of 3 for 2 years or another 6 years.   After twenty years by his own clock, he sees Alice age 12 yrs.

No length contraction involved.

Alice, also sees Bob red-shifted on the outbound trip and Blue-shift during the return.  For Alice, she travels out to a distance of 6 ly from Bob before returning.  Thus she sees Bob aging at a rate of 1/3 for 6 yrs or aging 2 yrs before she turns around.  Right after turn around She will see Bob age at a factor of 3, this holds for the entire 6 years for the return trip, and sees him age another 18 yrs.   After returning to Bob he will have seen him age a total of 20 years while she aged 12 yrs. The difference being that Alice see the shift from red to blue shift immediately upon turnaround, and doesn't have to wait.  This is because Alice is the one undergoing an acceleration in order to change velocity and sees the effect of this change immediately.

As far as what happens to Bob's clock during the outbound and return trips:  According to Alice it runs slow during both legs due to time dilation. ( it is important here to distinguish between time dilation, which is the comparison of clock rates between relatively moving frames, and Accumulated time difference, which can be the result of time dilation, length contraction and the relativity of simultaneity).

Bob, indeed measures less elapsed time due to length contraction, as the 6 ly distance he measures is shorter than the 10 measured by Bob.  But this applies to both legs of the trip, and has no bearing in terms of red or blue shift.

The reason that Alice ends up agreeing that less total time accumulated for her is due to the fact that She had to undergo an acceleration in switching between outbound and inbound legs,  and doing so invokes a new set of rules as to what she concludes happens to Bob's clock.  She will conclude that during this acceleration Bob's age advanced by a great deal (12.8 years), so that even though he only aged 3.6 years during the outbound leg, and 3.6 years during the return leg, He aged a total of 20 yrs for the whole trip.

The empirical data only tells us the difference in their ages when they meet up again. It say nothing about how that difference came about.

Bob will say that it was because Alice aged slower during the whole trip, While Alice will say that Bob aged slower for large part of the trip, but aged a great deal for a brief part of the trip.

Both of these views are equally correct.

The upshot is simply that Alice and Bob measure time differently during the different parts of the trip, but come up with the same end conclusion.

Time measurement is frame dependent, and there is no absolute measure of who's clock was "really" ticking slower than the others at any one point.  There is no single "reason" why Alice returns younger than Bob, every frame will have a different reason and they all are equally valid.

This is simply the way things are.

 

22 minutes ago, studiot said:

A little bit of editing required ?

 

I agree. (respectfully)

To keep things relatively simple can we use the Wikipedia example so that the problem has a known reliable baseline that we can check results to:

https://en.wikipedia.org/wiki/Twin_paradox?wprov=sfti1

This example problem uses a proper distance of 4 light years each way and traveling at 80%c.

If you like, I could outline the solution to save you some time or if you’d prefer to adapt your solution that’s fine as well.

Edited November 25, 2019 by TakenItSeriously

[iNow]

What’s the point? You’re wrong and many people here have corrected you. Why waste their or our time any further?

[TakenItSeriously]

1 minute ago, iNow said:

What’s the point? You’re wrong and many people here have corrected you. Why waste their or our time any further?

I don’t completely agree with his results.

That’s why I’d like to use a trusted third party results in the Wikipedia example.

[iNow]

6 minutes ago, TakenItSeriously said:

I don’t completely agree with his results.

Science doesn’t give a shit what you believe 

[Janus]

55 minutes ago, studiot said:

A little bit of editing required ?

 

 Got it, Thanks.   I really should take the time and go back and re-read what I wrote to catch these things.  Though that doesn't always work either.  A lot of the time when you re-read your own words that you just wrote, when you come to the mistype, you automatically read what you meant to say rather than what you actually typed.

[TakenItSeriously]

1 hour ago, Janus said:

You have fallen into a common trap: assuming that there is only one correct way to explain the time difference between the two twins when they meet up again. 

According to Bob, Alice's clock always runs slow by the time dilation factor both on the outbound and return trip.  He see Her clock red-shifted fro the outbound trip and blue-shifted  during the return.  However, he will see the red-shift for a longer than he sees the red-shift.  He has to wait until the light from Alice's turnaround to reach until the he starts to see the Blue-shift.

Thus at 0.8c, it would take Alice 10 yrs to travel to a turn around point 8 ly distant. This means that Bob sees a red-shift coming from Alice for 18yrs at a factor of 1/3 ( during that 18 years, he would visually see Alice age 6 yrs.  From the time of turn around, it will take another 10 yrs for Alice to return to Bob, Ergo, Alice arrives back at Bob just 2 yrs after he first see's Alice's light shift from red to Blue shift. Thus he visually watches Alice age at a factor of 3 for 2 years or another 6 years.   After twenty years by his own clock, he sees Alice age 12 yrs.

No length contraction involved.

Alice, also sees Bob red-shifted on the outbound trip and Blue-shift during the return.  For Alice, she travels out to a distance of 6 ly from Bob before returning.  Thus she sees Bob aging at a rate of 1/3 for 6 yrs or aging 2 yrs before she turns around.  Right after turn around She will see Bob age at a factor of 3, this holds for the entire 6 years for the return trip, and sees him age another 18 yrs.   After returning to Bob he will have seen him age a total of 20 years while she aged 12 yrs. The difference being that Alice see the shift from red to blue shift immediately upon turnaround, and doesn't have to wait.  This is because Alice is the one undergoing an acceleration in order to change velocity and sees the effect of this change immediately.

As far as what happens to Bob's clock during the outbound and return trips:  According to Alice it runs slow during both legs due to time dilation. ( it is important here to distinguish between time dilation, which is the comparison of clock rates between relatively moving frames, and Accumulated time difference, which can be the result of time dilation, length contraction and the relativity of simultaneity).

Bob, indeed measures less elapsed time due to length contraction, as the 6 ly distance he measures is shorter than the 10 measured by Bob.  But this applies to both legs of the trip, and has no bearing in terms of red or blue shift.

The reason that Alice ends up agreeing that less total time accumulated for her is due to the fact that She had to undergo an acceleration in switching between outbound and inbound legs,  and doing so invokes a new set of rules as to what she concludes happens to Bob's clock.  She will conclude that during this acceleration Bob's age advanced by a great deal (12.8 years), so that even though he only aged 3.6 years during the outbound leg, and 3.6 years during the return leg, He aged a total of 20 yrs for the whole trip.

The empirical data only tells us the difference in their ages when they meet up again. It say nothing about how that difference came about.

Bob will say that it was because Alice aged slower during the whole trip, While Alice will say that Bob aged slower for large part of the trip, but aged a great deal for a brief part of the trip.

Both of these views are equally correct.

The upshot is simply that Alice and Bob measure time differently during the different parts of the trip, but come up with the same end conclusion.

Time measurement is frame dependent, and there is no absolute measure of who's clock was "really" ticking slower than the others at any one point.  There is no single "reason" why Alice returns younger than Bob, every frame will have a different reason and they all are equally valid.

This is simply the way things are.

Ok, I originally misread the problem but these numbers seem fine to me now.

From Bob’s point of view, I agree Bob ages 20 years and he sees Alice age 10+2 = 12 years.

Just something I’d like to point out about Alices point of view:

1 hour ago, Janus said:

Alice, also sees Bob red-shifted on the outbound trip and Blue-shift during the return.  For Alice, she travels out to a distance of 6 ly from Bob before returning.  Thus she sees Bob aging at a rate of 1/3 for 6 yrs or aging 2 yrs before she turns around.  Right after turn around She will see Bob age at a factor of 3, this holds for the entire 6 years for the return trip, and sees him age another 18 yrs.   After returning to Bob he will have seen him age a total of 20 years while she aged 12 yrs. The difference being that Alice see the shift from red to blue shift immediately upon turnaround, and doesn't have to wait.  This is because Alice is the one undergoing an acceleration in order to change velocity and sees the effect of this change immediately.

Notice that you start with the assumption that Alice travels for 6 years on the outbound leg and 6 years on the inbound leg which I agree with but you neglected to say why it’s only 6 years each way.

It’s due to length contraction of the 8 light year distance:

The Lorentz factor α = 0.6

0.6*8Ly = 4.8Ly each way

so her travel time becomes:

4.8Ly/0.8 = 6 years each way or 12 years total.

So the reason for the deviation in time experienced by each twin is due to length contraction! Another words Alice had only 60% of the distance to travel from her point of view so it only took 60% of the time to travel it.

 

Edited November 26, 2019 by TakenItSeriously

[Janus]

1 hour ago, TakenItSeriously said:

So the reason for the deviation in time experienced by each twin is due to length contraction! Another words Alice had only 60% of the distance to travel from her point of view so it only took 60% of the time to travel it.

 

You've only covered Why Alice says that her clock only accumulated 12 total years.   You can't just stop there and claim a full solution.  You also have to deal with why Alice would say that Bob's clock accumulated 20 years.   It's not enough to just deal with how much time each of them says passed on their own clocks,  You also have to account for what each of them says is happening to the other persons clocks.

You can't say you have the answer when you only solve half the problem.

[TakenItSeriously]

1 hour ago, Janus said:

You've only covered Why Alice says that her clock only accumulated 12 total years.   You can't just stop there and claim a full solution.  You also have to deal with why Alice would say that Bob's clock accumulated 20 years.   It's not enough to just deal with how much time each of them says passed on their own clocks,  You also have to account for what each of them says is happening to the other persons clocks.

You can't say you have the answer when you only solve half the problem.

Sure, ok.

So the question that needs to be addressed, or the paradoxical perspective is that each twin should have symmetrical views of the other twins time, which is true (the each see the others time at 1/3 normal on the outbound trip and as 3x on the inbound trip) so how can they have experienced different amounts of time?

The asymmetry of this problem is the asymmetry of their inertial frames of reference and therefore the asymmetrical results that length contraction of those frames contributes to the problem.

Another words, from Bob’s perspective, only the ship, Alice and the rest of it’s contents become length contracted as the moving reference frame which contributes no additional information to their travel time.

From Alices perspective, Bob’s inertial reference frame includes Bob, the Earth, the destination of some star that’s 8 light years away, and the distance between the Earth and that Star.

So when that inertial reference frame becomes contracted, it shortens the distance she has to travel and therefore the time she has to travel by 60%. Thats why she experiences 12 years compared to Bob’s 20 years.

Edit to add:

If you can see this solution now and it just seems too obvious to be true, please don’t feel bad because it’s not. Once you fully understand any problem, no matter how difficult, the solution always seems simple in hindsight.

 

Quote

“If you can’t explain something simply, you don’t understand it well enough.”

-Albert Einstein

 

Edited November 26, 2019 by TakenItSeriously

[swansont]

15 hours ago, TakenItSeriously said:

Thanks for replying.

This is what I’m saying.

You need to assign a negative sign to the approaching direction which suggests directionality.

Not for length contraction or time dilation. The sign wouldn't matter.

[Janus]

13 hours ago, TakenItSeriously said:

Sure, ok.

So the question that needs to be addressed, or the paradoxical perspective is that each twin should have symmetrical views of the other twins time, which is true (the each see the others time at 1/3 normal on the outbound trip and as 3x on the inbound trip) so how can they have experienced different amounts of time?

The asymmetry of this problem is the asymmetry of their inertial frames of reference and therefore the asymmetrical results that length contraction of those frames contributes to the problem.

Another words, from Bob’s perspective, only the ship, Alice and the rest of it’s contents become length contracted as the moving reference frame which contributes no additional information to their travel time.

From Alices perspective, Bob’s inertial reference frame includes Bob, the Earth, the destination of some star that’s 8 light years away, and the distance between the Earth and that Star.

So when that inertial reference frame becomes contracted, it shortens the distance she has to travel and therefore the time she has to travel by 60%. Thats why she experiences 12 years compared to Bob’s 20 years.

Edit to add:

If you can see this solution now and it just seems too obvious to be true, please don’t feel bad because it’s not. Once you fully understand any problem, no matter how difficult, the solution always seems simple in hindsight.

 

 

I already covered how the observers resolve the their total elapsed times with the Doppler shift observations.  Bob sees a Red-shift from Alice for 18 years and then 2 years of Blue shift, While Alice sees and equal time of red shift and blue shift from Bob.  The difference being due to the fact that Alice actively changes her velocity and Bob doesn't.

While length contraction is a piece of the puzzle towards a full solution, it is only one piece and not the answer in total.  Yes, Alice measures the distance traveled as being only being 4.8 ly out and back. But that is only true from her perspective, and her perspective isn't any more valid than Bob's who says she traveled 8 ly out and back.

Your "simple" solution relies on just sweeping the meaty part of the problem under the rug and pretending that it doesn't exist.

And it is this "meaty" part that make the problem interesting, because it is the part that force ones to accept  that the very nature of time and space isn't what we thought it was under Newton's physics.

By ignoring the deeper issues in the scenario, you are just opting for the easy way out, so that you don't have to think outside of the mental box you've built for yourself.

[studiot]

46 minutes ago, Janus said:

And it is this "meaty" part that make the problem interesting, because it is the part that force ones to accept  that the very nature of time and space isn't what we thought it was under Newton's physics.

+1

I still like Eddington's interpretation that it is the configuration, set up as a network of links composed of invariants between points, that is important, not the frame-subjective distances and times.

Edited November 26, 2019 by studiot

[TakenItSeriously]

12 hours ago, swansont said:

Not for length contraction or time dilation. The sign wouldn't matter.

Ok, you’re right. That was a bad example.

Let me try to explain it another way but first allow me to outline what I think we do and don’t agree on so we can get on the same page. Some of this may be trivial to you but I’m just trying to cover all the relevant bases.

1. Light waves exist in space between source and observer as opposed to the Newtonian view where the SOL is instantaneous.
2. The speed of light is constant to all observers but the frequency of light is frame dependent according to the relativistic doppler effect.
3. If you agree with Janus, the causality of the relativistic component of relativistic redshift can be explained by time dilation.
4. So far we don’t agree on the causality of the relativistic component of relativistic blueshift.
5. Acceleration has been largely refuted by the physics community as the reason for the time deviation experienced by the twins.
6. You think that both length contraction and time dilation are true in moving frames regardless of whether the light source is moving towards an observer or away from an observer.
7. I think that time dilation is only true in frames where the light source is moving away and length contraction is only true in frames that are moving towards an observer.

Would you agree with the list above?

Please correct anything that’s wrong or feel free to add anything else you feel is pertinent.

Edited November 26, 2019 by TakenItSeriously

[Strange]

3 minutes ago, TakenItSeriously said:

• If you agree with Janus, the causality of the relativistic component of relativistic redshift can be explained by time dilation.

You can't separate time dilation and length contraction. They both always occur together and bth contribute to any solution.

4 minutes ago, TakenItSeriously said:

So far we don’t agree on the causality of the relativistic component of relativistic blueshift.

Because you are wrong / don't understand relativity.

5 minutes ago, TakenItSeriously said:

I think that time dilation is only true in frames where the light source is moving away and length contraction is only true in frames that are moving towards an observer.

Trying to think of a polite way to answer this. How about: you are wrong.

There is absolutely no reason to think this is the case. It is contradicted by SR and SR is (a) derived mathematically from existing theory and (b) confirmed by all experiments.

Your mistaken belief is not supported by the mathematics of SR and is contradicted by all experiments.

[TakenItSeriously]

7 hours ago, Strange said:

You can't separate time dilation and length contraction. They both always occur together and bth contribute to any solution.

Because you are wrong / don't understand relativity.

Trying to think of a polite way to answer this. How about: you are wrong.

There is absolutely no reason to think this is the case. It is contradicted by SR and SR is (a) derived mathematically from existing theory and (b) confirmed by all experiments.

Your mistaken belief is not supported by the mathematics of SR and is contradicted by all experiments.

Actually it’s consistent.

When you calculate the travel time and distance to the destination when traveling at 80%c, for the math to be consistent, you must only apply the Lorentz transform only once.

e.g., in this example, the proper distance to the destination is 8 ly.

Alice is moving at 80%c

D₀ = 8 ly

β = v/c = 0.8

the Lorentz factor:

α = √(1-β²) = 0.6

So from Alices point of view her length contracted distance is:

D’ = αD₀ = 0.6*8 = 4.8 ly

Alices travel time is next calculated directly from D’ without using the Lorentz factor:

T’ = D’/β = 4.8/0.8 = 6 yr 

 

Edited November 27, 2019 by TakenItSeriously

[TakenItSeriously]

I would add that the math is also consistent from Bob’s perspective as well.

Recall that from Alices point of view we apply the factor for length contraction to her destination.

From Bob’s point of view, he knows the star is 8 ly away so he would apply the factor only to time dilation not lrngth contraction.

T’ = 0.6·(8/0.8) = 6 yr each way.

Edited November 27, 2019 by TakenItSeriously

[Strange]

2 hours ago, TakenItSeriously said:

Actually it’s consistent.

It very obviously isn't. Just look at the equations for length contraction and time dilation: they are independent of the sign of the velocity.

 

2 hours ago, TakenItSeriously said:

Alice is moving at 80%c

D₀ = 8 ly

β = v/c = 0.8

the Lorentz factor:

α = √(1-β²) = 0.6

So from Alices point of view her length contracted distance is:

D’ = αD₀ = 0.6*8 = 4.8 ly

Alices travel time is next calculated directly from D’ without using the Lorentz factor:

T’ = D’/β = 4.8/0.8 = 6 yr 

Note that changing the sign of the velocity does not change either the length contraction or the time dilation. So you have shown that your claim is wrong.

[TakenItSeriously]

2 minutes ago, Strange said:

It very obviously isn't. Just look at the equations for length contraction and time dilation: they are independent of the sign of the velocity.

 

Note that changing the sign of the velocity does not change either the length contraction or the time dilation. So you have shown that your claim is wrong.

Not at all.

From Alices point of view length contraction is calculated for the distance to Alices destination that she is moving towards.

From Bob’s point of view her time is dilated as she moves away from him.

[Strange]

9 minutes ago, TakenItSeriously said:

Not at all.

From Alices point of view length contraction is calculated for the distance to Alices destination that she is moving towards.

From Bob’s point of view her time is dilated as she moves away from him.

You can keep saying that but it is very obviously not what the math says. Put +0.8c and -0.8c in the equations and tell us what the result is.

If you are just going to keep repeating blatantly false (and provably false) statements like this, then I don't think there is much point this thread staying open.

[Strange]

3 hours ago, TakenItSeriously said:

β = v/c = 0.8

the Lorentz factor:

α = √(1-β²) = 0.6

Now do the same for the velocity in the other direction:

β = v/c = -0.8

the Lorentz factor:

α = √(1-β²) = 0.6 (the same value)

So the effect on length contraction and time dilation is identical.

[TakenItSeriously]

33 minutes ago, Strange said:

Now do the same for the velocity in the other direction:

β = v/c = -0.8

the Lorentz factor:

α = √(1-β²) = 0.6 (the same value)

So the effect on length contraction and time dilation is identical.

Your kidding right?

You do realize that when you take the square root of any number you get a positive and negative result right?

e.g. √4 = +2 & -2

Besides that the Lorentz factor is not a vector. It doesn't even have units.

Edited November 27, 2019 by TakenItSeriously

[uncool]

The Lorentz factor is always taken to be positive. 

How does the Lorentz factor being a scalar affect this argument?

[TakenItSeriously]

6 minutes ago, uncool said:

The Lorentz factor is always taken to be positive. 

How does the Lorentz factor being a scalar affect this argument?

I really don’t know. Ask Strange, he brought it up.