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Posts posted by TakenItSeriously


Swansont,
Thank you for your reply.
You asked some difficult questions all of which I may not be able to answer to your complete satisfaction right now despite having thought about this problem for over two decades but I will do my best to answer what I can and perhaps I, or others, will be able to contribute more at a later time.
Iv’e often wondered if it could ever be 100% finished or would there always be more questions that needed answering?
Perhaps the later is the case because it seems unlikely to me that mankind was ever meant to know everything. Perhaps we are only meant to forever struggle to increase our knowledge by just enough to solve the latest problems that we’re confronted with in order to survive as a species.
6 hours ago, swansont said:How would that be deterministic? You seem to imply it depends on entanglement. Once the entanglement is broken (i.e. once a state is determined), you don't get it back.
6 hours ago, swansont said:If you have entangled particles you don't know their state. That information is already "hidden"
You have to understand that it’s only deterministic from a point of view from someone who exists outside of time.
From the point of view of an observer in either universe, they cannot know their future precisely because according to Heisenbergs uncertainty principle, we can only know half of the information needed for a single particle.
Only an omniscient being who exists outside of time can entirely have access to complete information. That’s what I mean by sharing a single deterministic future. They would not be two independent universes like we might think with the many worlds interpretation, but be linked by their entanglement and exist together like two sides of the same coin.
Once entanglement is broken, then the information each universe has may be more definitive and less probabilistic but each universe still only has access to half of the information needed to precisely predict the future.
6 hours ago, swansont said:Your earlier diagram implies that this is not what is going on, though. We do interference without entangled antiparticles, and they happen at one time, not two different times — your depiction has the entangled particles moving in opposite time directions.
I’m not entirely sure what you mean. I can say that the two cones represents two opposite directions in time, not two opposite directions in space. Also, you shouldn’t think of them as two arbitrary different times but a single differential time.
So, in essence the antiverse exists everywhere around us only in differential time with half of it phase shifted by 180° causing it to be hidden from direct observation except through the evidence of how they interact through their electromagnetic fields in their exhibiting quantum spin or intrinsic dipole moments.
6 hours ago, swansont said:Again, how? With your description of time, and all the rest of physics, how do they orbit? Even without that, why don't they just deexcite and annihilate? What prevents it?
They exist in a virtual dual orbit due to their electromagnetic fields and entanglement interacting with both particles at once.
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Now that I just posited that relativistic effects are directional:
Are relativistic effects directional?
If that were true and length contraction represents one side while time dilation represents the other side and the top half represents the universe while the bottom half represents the antiverse.
Then, in that case, the full plot of α vs β makes sense as a unit circle:
I didn’t want to introduce this plot in the other thread because I didn’t want to suggest that positive/negative α represented directionality. positive/negative β represents directionality.
The Penrose diagram shows the role of the antiverse with black holes.
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My hypothesis of an antiverse which I first posted about here:
Why would we expect an antiuniverse to be detectable?
and written about many times since elsewhere, is getting the attention of cosmologists:
Our Universe has antimatter partner on the other side of the Big Bang
My hypothesis, in part:
The first mystery of the Universe that is still unresolved today is what happened to all the antimatter created by the Big Bang?
Quantum Mechanics tells us that matter and antimatter was created in equal parts as entangled pairs by the big bang at the beginning of time yet there is absolutely no evidence of the existence of all that antimatter today.
One theory suggests that it was all annihilated and due to an imbalance of more matter than antimatter, or 1 extra particle of matter per billion matter/antimatter pairs was enough to leave us with all the matter in the universe today.
However, all attempts to prove this imbalance have failed and, in fact, all evidence thus far seems to suggest that their was no imbalance.
Instead the following noted works seem to suggest something else:
 CPT symmetry mathematically proves that an antiverse must include symmetries of charge conjugation, parity transformation, and time reversal.
 Noether’s theorem had mathematically proved that the Universe must be symmetrical according to the laws of conservation.
 Richard Feynman had once posited that antimatter is exactly like matter existing in reverse time.
Imagine for a moment that Feynman's statement was literally true?
If the antimatter created by the big bang did exist in a state of reverse time, then if you think about it carefully, reverse time starting from the beginning of time would be a separate dimension of negative time.
Another words if you count forwards from zero you get positive numbers but if you count backwards from zero you get negative numbers.
..., 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, +1, +2, +3, +4, +5, +6, +7, +8, +9, +10, ...
These two equal and opposite time lines (or more accurately time rays) would never overlap and so it wouldn’t be like reverse time as we normally think of it in terms of decreasing entropy like a broken glass reassembling itself and falling up to a table top. Therefore, it would not allow for paradoxes such as the grandfathers paradox.
Both dimensions would be dimensions of an expanding universe and increasing entropy.
Instead the hidden extradimension of negative time would be perfectly symmetrical to our universe in positive time due to its entanglement with our universe.
Figure 1: A dual big bang model where matter expands in a dimension of positive time and the entangled antimatter expands in a hidden dimension of negative time.
These two dimensions of time would not be two independent universes. Instead they would be linked to share single deterministic future by their entanglement. So as a whole, they would have a shared determinism.
However, from the perspective of an observer in either dimension, half of all information would be hidden in the opposite dimension and uncertainty would prevent us from ever being able to predict our future. Another words, outside of time, the two halves together would constitute a deterministic universe but from the perspective of an observer in either half, there must be uncertainty and therefore we would have free will.
So what would this antiverse look like? According to CPT symmetry, to an observer in negative time, it would be indistinguishable from that of an observer in positive time.
The consequences of a dual universe could explain all the weirdness of quantum mechanics to not seem so weird.
For instance, in the dual slit experiment for every particle that goes through one slit an entangled antiparticle would go through the opposite slit and their entanglement would impart the information of both slits to both particles causing the wave distribution pattern. If a particle is observed going through a specific slit, entanglement would be broken and the result would be a dual distribution of particles.
It would also answer how light particle/waves could propagate forever in a vacuum.
Figure 2: An unobserved particle and antiparticle would exist together in a virtual dual orbit connected by their entanglement. This would immediately explain the properties of spin having a much larger radius of angular momentum that the size of the particle or why particles with a single charge would behave like spinning dipoles.
The differential waves together would explain how they could propagate through a vacuum forever.
Spooky action at a distance could be explained for particles in opposite dimensions of time, time would cancel out and the actions between two entangled particles would cancel out and much more.
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5 minutes ago, Janus said:
If you think that someone has made a slip, say, typing "Alice" when they likely meant "Carole" ( something very easy to do when writing a long explanation involving a number of actors), you can ask them to clarify, or point out that they might have slipped up there. What you do not do is just throw out a blanket comment about it being "nonsensical", which can pretty much mean anything.
That’s what I was trying to do.
As I said, I meant to say the sentence was nonsensical as written, not the entire post, and I did say that I assumed it must contain some typos.
Edit to add:
I apologize for any confusion.
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Janus
Theres some confusion here on what was posted that I’d like to clarify before it gets out of hand.
First, please refer to this post:
When I was saying it was nonsensical I was referring to the particular sentence I quoted, not your entire post.
After I posted it, I realized what you must have meant to say....
You used an ambiguous reference of “her” which could have meant Carole or Alice. I assumed you meant Carole’s point of view when I saw you refer to Alice in the same sentence. The problem was compounded when you mistakenly referenced that Alice was catching up to Bob. It’s a minor error, but when speaking in the context of SR, it becomes very confusing and that’s why I said it was nonsensical as written.
I waited a while before replying trying to avoid a cross post. Unfortunately you were busy writing a long reply so my waiting only backfired.
After rethinking the problem with the corrected sentence I compounded the cross edit with a cross post before seeing your long reply and posted an encapsulation of what I thought you were trying to say.
So having said this, is that what you were trying to say, mor or less.
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Edit to further add:
So in the corrected context, I think the point you may be trying to make is that all three points of view on the problem tells a very different story which I agree happens a lot in SR. Kind of like the simultaneity thought experiments. So how valid could any conclusion be unless they all meet at some point which is impossible without adding acceleration into the problem.
Is that about it?
1 minute ago, Janus said:It make perfect sense by the rules of Relativity.
Here's the whole scenario in spacetime diagrams. For the sake of keeping things less cluttered, we'll have Bob start at Year 0 rather than 2020.
Alice also sets her clock to 0 When she is by Bob. Carole. likewise sets her clock to zero when, according to her, Bob's and Alice's Clocks read zero.
Because of this, we will first consider Carole's frame:
The Blue line represents Bob, the Red Alice, and the Green Carole. the numbers on each line represent years ticking off for each. Time for Carole is the vertical axis. Horizontal lines are lines of simultaneity. Draw a horizontal line and it will pass through events that are simultaneous for Carole, such as Bob's, Alice's, and Carole's clocks all reading 0
Go up to the gray horizontal line, and you see the when Bob's clock read 10 years according to Alice, Her own clock reads between 16 and 17 years and Alice's reads between 3 and 4 years. where the Red and Green lines cross is when Alice and Carole meet. Carole's clock reads 27 1/3 years, Alice's 6, and Bob's 16.4 years.
6 years later, Carole meets Bob, Her clock reads 33 1/3 years, Bobs 20 years and Alice's somewhere after 7 yrs
If we transform to Bob's frame, we get this:
Bob's and Alice's clock still read 0 at the same time, however, Carole's clock already reads past 21 years. This is a consequence of the Relativity of simultaneity; events that are simultaneous for Carole( all three clocks reading 0) are not so for Bob ( or as we will see later, Alice)
When Bob's clock reads 10 yrs, Alice and Carole are meeting, Alice's clock reads 6 yrs and Carol's 27 1/3 yrs. Bob agree with Carol as to what time Both Alice's and Carole's clocks read when they meet, but disagrees with Alice as what time is on his own clock when this happens.
Carole's meets Bob when his clock reads 20 and hers has added another 6 yrs and reads 33 1/3 years.
Again Bob and Alice's clocks both start at 0 when they are together, but Carole's clock already read almost 26 yrs. In 6 yrs according to Alice, she meets up with Carole. Carole's clock has advanced to 27 1/3 yrs, and Bob's to 3.6 yrs. it takes another 27 1/3 years By Alice's clock for Carol and Bob to meet, during which Bob's clock advances by 16.4 years and reads 20 years, and Carole's advances another 6 yrs to read 33 1/3 years.
Everyone agrees as to what times passing clocks had, how much time ticked away Alice's clock between leaving Bob, and meeting Carole, and how much time passed on Carole's clock between passing Alice and meeting Bob. They just don't always agree on when these events occurred by their own clock.
If this seems "nonsense" to you, that's on you. It is more an indication of your lack of understanding Relativity than anything else.
Just because you personally don't understand something or find it difficult to wrap your mind around it doesn't, in of itself, make it "nonsense".
While there are some things that, at first blush, seem nonsensical, and upon further examination do prove to be so, there are also things that, at first blush seem nonsensical, but in the end turns out to not be so.
The second scenario is what one meaning for "Paradox" is: "Something that seems like it shouldn't be true, but actually is".
And this is the usage of "paradox" in the term "the Twin Paradox".
Ugh, cross posted.
Sorry, I can take a while wile pondering the problem.
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1 hour ago, Janus said:
From her perspective, after that, Bob continues to recede at 0.8c, and Alice is catching up to him traveling at 0.97561.. c ,
I assume this contains some kind of typos.
I mean I think your saying that Alice’s perspective on Carole’s speed is 0.97561... c and vice versa which I understand without doing the math myself but the rest is nonsensical as written.
Edit to add, after reading it a few times more I think you’re trying to say the following:
From Alice’s perspective after passing Carole, Bob is receding at 0.8c and Carole is catching up to him at roughly 0.98c.
Is that correct?
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5 hours ago, Janus said:
Thus between Bob's 2020 at Bob ( when Alice Leaves) and 2040 ( when Carole arrives, Alice must measure 20/0.6 yrs by her clock or 33 1/3 years.
Sorry, I think you made a mistake here.
From Alices perspective:
Alices travel distance on the outbound leg due to length contraction should only be 8 Ly*0.6 = 4.8 Ly
therefore her travel time is 4.8/0.8 = 6 years.
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2 hours ago, Janus said:
As far as Carole is concerned it is 12.8 years later for Bob as she passes Alice than it for Alice.
For example if Alice left Bob when it was the year 2020 for Bob, when Alice and Carole meet, according to Alice it is a bit past the middle of 2023 for Bob, but for Carole it is already almost halfway into 2016 for Bob. According to Carole, Alice left Bob 27 1/3 years before Alice and Carole meet, and during that time advanced at a rate of 0.6 that of her own, and thus advanced from 2020 to 2016 in those years in the next 6 years, Bob's clock advances another 3.6 years to read 2020 when Carole arrives. In other words, for Carole, Bob ages 20 years between Alice leaving him and Carole arriving, while Carol herself ages 33 1/3 years.
For Alice, Bob ages 3.6 yrs between the time she leaves him and meets up with Carole, it will take another 27 1/3 years by her clock for Carol and Bob to meet during which time Bob ages 16.4 years, and Carol 6 years ( the relative speed between Carole and Alice is 0.97561.. and Carole's clock ticks at 0.21951... her own clocks rate)
The whole transferring the Alice's info of distance and time to Carole is just a redherring and doesn't give you anything equivalent to a total accumulated time For Bob, as you are jumping from a frame where it is 2023 for Bob to one where it is already 2016.
Whether or not the central clock(A) is rotating is of no consequence.
The second clock(B) is traveling in circle around the central clock.
The third clock(C) is traveling in straight line that runs tangent to B's path at one point.
Ok, I got it.
For sure acceleration adds a ton of complexity to this problem. BTW it’s not a stable model unless you add a balancing mass on the opposite side of B, say B’ but thats getting a little nit picky.
It reminds me of an even simpler model of two astronauts tethered together in flat space.
Someone gives them a push and they start spinning apart putting tension on the tether and ending up in a dual orbit kind of like a binary star system.
So what happens if you remove the surrounding universe from this model. They would have no reference frame to know that they’re even spinning and it would then seem as if they were just drifting in the void with a strange repulsive force that is pushing them apart.
Others would argue that their would no longer be a repulsive force and they would just be floating together in the void with the tether limp between them.
The point is that I agree that gravity or acceleration adds a ton of complexity to the problem. That’s why the three observer thought experiment (not mine BTW) was modified to only involve drift speeds taking acceleration out of the problem all together.
https://en.wikipedia.org/wiki/Twin_paradox?wprov=sfti1.
I will respond to your analysis of that problem next.
46 minutes ago, TakenItSeriously said:As far as Carole is concerned it is 12.8 years later for Bob as she passes Alice than it for Alice.
For example if Alice left Bob when it was the year 2020 for Bob, when Alice and Carole meet, according to Alice it is a bit past the middle of 2023 for Bob, but for Carole it is already almost halfway into 2016 for Bob. According to Carole, Alice left Bob 27 1/3 years before Alice and Carole meet, and during that time advanced at a rate of 0.6 that of her own, and thus advanced from 2020 to 2016 in those years in the next 6 years, Bob's clock advances another 3.6 years to read 2020 when Carole arrives. In other words, for Carole, Bob ages 20 years between Alice leaving him and Carole arriving, while Carol herself ages 33 1/3 years.
For Alice, Bob ages 3.6 yrs between the time she leaves him and meets up with Carole, it will take another 27 1/3 years by her clock for Carol and Bob to meet during which time Bob ages 16.4 years, and Carol 6 years ( the relative speed between Carole and Alice is 0.97561.. and Carole's clock ticks at 0.21951... her own clocks rate)
The whole transferring the Alice's info of distance and time to Carole is just a redherring and doesn't give you anything equivalent to a total accumulated time For Bob, as you are jumping from a frame where it is 2023 for Bob to one where it is already 2016.
I set the model up to be equivalent with the TP example you gave initially:
Bob’s time on Earth is still 20 years.
Essentially Alice’s travel time is 6 years, Carole’s travel time is a symmetrical 6 years so the total is12 years which is 60% of Bob’s time of 20 years.
I can’t see how you derived the numbers in your analysis. Can you please clarify?
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1 hour ago, studiot said:
Depends upon who is looking at them.
And all inertial frames extend throught all space. i.e. they cover the same region.I agree, it can become a confusing mess. That’s why I like to break problems down to their simplest forms possible while still considering all relevant variables and points of view.
2 hours ago, Janus said:No. You are overgeneralizing a particular conclusion about the role of acceleration beyond its meaning.
The conclusion is based on the "clock postulate". Basically it states that local acceleration has no effect on the operation of a clock. In other words, if you take a clock and put it in a high speed centrifuge and spin it up, the fact that the clock is experiencing a high value of acceleration has no additional effect on the rate of the clock ticking as measured from the lab frame. The clock will tick slow, but only by an amount due to its velocity relative to the lab frame.
This is not the same as saying that acceleration plays no role in the resolution of the Twin paradox. The clock postulate only deals with how an inertial frame measures the accelerating clock, and does not deal with what would be measured from the accelerating frame itself.
So for example, assume we have clock sitting at the center of the centrifuge in the lab frame. In addition to the clock spinning in the centrifuge, and the central clock, we have a third clock and observer traveling in an inertial frame at the same speed as the centrifuge clock and at a tangent to it such that its path and the centrifuge clock just touch at one point, so that if the two clocks were at that point at the same moment, they would have identical instantaneous velocities. The difference being that the centrifuge clock has an acceleration toward the center clock,a and the third clock doesn't.
If we compare what these two clock conclude as to what is happening two the center clock at that moment, they would come to different conclusions. the inertially moving clock would say that the central clock is running slow, while the centrifuge clock, which is under acceleration, would say that the central clock runs fast.
If a physicist says that acceleration is not the reason for the time difference they mean that in a specific way, and you are trying to infer a much broader meaning beyond that which they meant.
I’m a little confused about what each clock is doing.
Is it that the central clock is spinning around at the center point of centrifuge A.
Another clock is revolving around the spinning clock at some radius on the perimeter of A
A third clock is revolving around a separate centrifuge B and the two circular paths meet up like two spinning gears?
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10 hours ago, swansont said:
#5 — without an acceleration, there is no deviation. It's not the source of time dilation, but it is the reason for the asymmetry in the effects.
#6 is correct, and verified, making #7 wrong (not the part about it being what you think, but the physics). Take the HafeleKeating experiment. Time dilation depended on movement of East vs West, which boils down to faster or slower as compared to an inertial frame. Not moving toward or moving away, as they spent half of their time doing each, with respect to the clocks on the ground.
Damn, I lost my entire last post due to an outage. Hopefully I’m back now.
#5 Regarding acceleration. I mostly agree especially with how it plays no role in explaining the time deviation experienced by the twins. Perhaps not as much as with the asymmetry of the other effects.
Acceleration, while once accepted as the underlying cause, has since been refuted because of a modified TP thought experiment which removed all acceleration from the problem and you still end up with the same results.
It adds a complex asymmetric effect to be sure but it’s irrelevant to the simple form of the problem when using only velocity.
You can look it up here: https://en.wikipedia.org/wiki/Twin_paradox?wprov=sfti1
Under Twin Paradox subtitle: the Role of Acceleration.
A synopses of the modified version includes three observers
 Bob at rest on Earth.
 Alice drifting past the Earth at 80%c on her way to the star 8 ly away.
 Carole drifting in the opposite direction at 80%c passes the star at the same time Alice passes it.
Carole collects Alices information such as travel time, travel distance from the Earth, observations on Bobs time, etc. She then proceeds to Earth and passes all of Alices information as well as her own to Bob and the time experienced by both travelers only adds up to 60% of the time experienced by Bob.
#6 I recall the HafleKeating experiment using jet airliners and atomic clocks and I agree that it does seem to represent a bit of a conundrum. However, I would question whether the time dilation measured was due to gravity or velocity. For example, I’ve been told that the time dilation calibrated for in GPS satellites is almost entirely due to gravity. I know, different elevations and speeds, but I just get the feeling that gravity still dominated time dilation in that experiment but IDK for sure.
In any case, I’ve tried to consider how to adapt orbital information into the TP and it’s just beyond me so I let it drop and left the question to smarter minds to ponder than my own.
Now we already agree that time dilation is the cause of the relativistic component of relativistic red shift.
So how I would explain the cause behind the relativistic blue shift effect:
Using the original example, Alice has just turned around and is headed for Earth.
From Bob’s PoV:
Alice is racing her own light traveling at 100%c while she is moving at 80%c. Another words it takes the light 8 years to reach Earth while it takes her ship 10 years. Therefore all of her transmissions on the return leg must be compressed into only two years. So this blue shift effect can all be explained by simple lagtime for the light to travel such a distance just like communications in our own solar system.
No time dilation involved.
However there is still the difference between relativistic blue shift and normal blue shift so what explains this difference.
Well, Bob would expect Alices return leg to take 10 years which is squeezed into 2 years. However, after he meets Alice and counts the pings, he sees that there was only 4.8 years of pings compressed into those 2 years.
As I mentioned before, the 60% of the time she experienced on her journey home is due to traveling only 60% of the distance due to length contraction.
To look at it another way, we agree that:
 light waves from Alices ship exist in the space between Alice and the Earth.
 We agree that information is conserved and no waves (or pings) are either inserted or deleted.
 We agree that from Alices PoV the distance between the Star and Earth is length contracted to only 4.8 ly
So what do you think happens to those light waves in length contracted space?
The waves themselves must also be contracted...well at least those waves that are received from their sibling.You see the waves that are emanating from Alice’s ship are all part of the ships inertial reference frame.The waves that are emanating from Bob are all part of the Earth’s inertial reference frame.So from Bob’s PoV, the waves transmitted from Alice are length contracted.From Alices PoV, the waves transmitted from Bob are length contracted.Note that the waves coming from their own transponders are always pinging at 1 sec per sec. Another words the waves transmitted from their own transponders are all in each twins own respective inertial reference frame regardless of where they are in space.QED0 
3 minutes ago, swansont said:
You realize the fact that it's not a vector and uses scalars works against your position, right?
The directionality I refer to is the relative type as in moving away from the observer vs moving towards the observer.
In the problem
from Alices point of view, you calculate length contraction for the distance Alice has to travel (in the direction of motion.)
from Bobs point of view he knows the distance is 8 ly but he could calculate time dilation of a receding ship.
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5 minutes ago, studiot said:
Having a sign or not having a sign does not make something a vector, neither does it prevent something being one.
You yourself have already posted statements acknowledging this, unless you can convince me that a square root satisfies the 9 vector axioms.
I agree and I’m not trying to say that it does.
Strange was the one who was trying to assign meaning to the sign of the Lorentz factor.
I only tried to tell him it doesn’t apply that way.
2 minutes ago, swansont said:#5 — without an acceleration, there is no deviation. It's not the source of time dilation, but it is the reason for the asymmetry in the effects.
#6 is correct, and verified, making #7 wrong (not the part about it being what you think, but the physics). Take the HafeleKeating experiment. Time dilation depended on movement of East vs West, which boils down to faster or slower as compared to an inertial frame. Not moving toward or moving away, as they spent half of their time doing each, with respect to the clocks on the ground.
Thanks.
I’m going to have to get some sleep now.
I’ll get back to this later.
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Because I guess he was associating the sign with directionality or something.
The Lorentz factor as used in the TP doesn’t require a sign because it’s not a vector.
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2 minutes ago, uncool said:
No, you did. You are the one who said "Besides that the Lorentz factor is not a vector." I'm asking you, who said it, how that statement is relevant.
This post and the next post is where strange brought it up.
I didn’t understand why.
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6 minutes ago, Eise said:
But first, this is physics, not mathematics. One must always check if both solutions make sense physically.
Second, the direction of the velocity has nothing to do with the choice of the positive or the negative result, as Strange already showed, because you must use v^{2}.
So third, what do you get if you take the negative value as possible outcome? Say you compare two sticks, one flying in the opposite direction of the other, with the same speed. Due to the length contraction, one stick has for you a length of 0.5L, the other +0.5L. Which one is longer? 😈
So what is the physical meaning of a negative length?
The directionality I’m talking about in the title is the relative velocity as in moving closer vs moving away or as in relativistic red shift which I link to time dilation vs relativistic blue shift which I link to length contraction.
Strange claimed that the kind directionality I was positing wasn't consistent with the math.
I showed him why it was consistent.
He then accused me of lying and then brought up the signs for the Lorentz factor for some reason.
I told him that the Lorentz factor as applied to the TP doesn’t have a sign because its not a vector.
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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.
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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 = √(1β²) = 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.
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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.
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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.
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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 = √(1β²) = 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
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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.
 Light waves exist in space between source and observer as opposed to the Newtonian view where the SOL is instantaneous.
 The speed of light is constant to all observers but the frequency of light is frame dependent according to the relativistic doppler effect.
 If you agree with Janus, the causality of the relativistic component of relativistic redshift can be explained by time dilation.
 So far we don’t agree on the causality of the relativistic component of relativistic blueshift.
 Acceleration has been largely refuted by the physics community as the reason for the time deviation experienced by the twins.
 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.
 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.
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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
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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 redshifted fro the outbound trip and blueshifted during the return. However, he will see the redshift for a longer than he sees the redshift. He has to wait until the light from Alice's turnaround to reach until the he starts to see the Blueshift.
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 redshift 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 redshifted on the outbound trip and Blueshift 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 redshifted on the outbound trip and Blueshift 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.
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Corona virus general questions mega thread
in Microbiology and Immunology
Posted · Edited by TakenItSeriously
According to worldometers.info on 03222020 @12:30 afternoon which is the top site from a google search of “coronavirus numbers”
Total Cases: 321,278
Active cases: 211,573
Recovered: 96,006
Deaths:13,629
First of all, I am not a doctor nor am I mathematician. However, I was tested as profoundly gifted at logic in college which means that I have a knack for problem solving.
These numbers are based on only what we know as reported by governments around the world. Of course the numbers may not be accurate due to political fudging and of course testing is not anywhere close to 100%.
However, it seems to me that the odds of dying after testing positive is not really around 4% as reported by most media outlets.
This number seems to be a best possible spin of the numbers i.e. # of deaths divided by total cases:
13,629/321,278 = 4.264%
I believe this is the wrong way to calculate the numbers because it includes the 211,573 of active cases which are uncertain as to whether they will result in a recovery or a death.
If you test positive and you ask the question: what are the odds of coming out alive when all is said and done then a more accurate prediction should be the number of deaths divided by (the number recovered plus the number of deaths).
13,629/(96,006+13,629) = 13,629/109,705 = 12.49%
Now to be fair, there is quite a large lagtime between the number dead to the number recovered because it’s early in a growth dynamic scenario where death generally occurs much more quickly than recovery so we can probably assume the recovery number should be much higher but still, I think the most accurate number should be something like somewhere between 4.3% and 12.5%.
Thoughts?