SamBridge

If you look at integrals or derivatives or really any concept in calculus, doesn't it seem to suggest that there's cases where infinity and "potential" infinity can be treated as the same thing? Like since I have to add literally an infinite amount of boxes to get the exact area, or get literally infinitely close to a point to get a perfectly accurate derivative. The main problem I think is defining where the difference is between mathematics and the way reality actually works. If I walk two meters per second, did some invisible point on an invisible number line actually get infinitely close to some other invisible point that represents my velocity? Not that I see, but that derivative model can still work. If you have space, and you say "there's no limit to space," why not just treat that as an infinite amount of space? Limits are just loop-holes to originally not being able to deal with infinity, they exist just so that we can get a sense of what a situation is actually like when some variable is infinite because we have no real mathematical way of modeling what infinity really is since we can only define it as a man-made concept and not an inherent part of mathematical logic. Like there's no "infinity" on a number line, there's no defined answer if I say "what's 1/infinity?"

 

There is no energy gain, so there doesn't need to be a mechanism for energy gain.

 

The speed remains constant, but the oscillations will be observed to be happening faster if you're moving toward the photon. It's the Doppler shift, just like in sound.

See, that conflicts with something that you yourself said while ago in some other topic, which is that you can't actually physically model a photon that way, and it's because of the property I already described which you also described at a previous point. When you measure a photon, you are not observing millions of atoms over time like a wave, you're observing a single point of a collapsed wave function and you shouldn't have any knowledge of exact position or energy outside of a mathematical model generated by some computer, it's not the same as matter on the macroscopic scale and you yourself said that, I know you have a different explanation that makes more sense, or at least one that doesn't contradict other things you said.

Prior to measurement, sure, you can measure a photon's probability as a time evolution oscillation or a wave packet, but that probability model itself isn't doesn't work the same way as macroscopic substances, and I know you know that and that's why I never understand why you keep doing this, I don't know if you're just screwing with me or what.

 

It breaks the symmetry. It allows you to know whose clock was running slow; while the symmetry exists there is no answer to that.

So you're implying that prior to that turn around it is symmetrical, both observers would observe the same dilation of each other and we wouldn't know which one had "actually" accelerated to get to near the speed of light until one bothered to turn around and come back?

 

 

It doesn't gain energy, per se. Energy is not a quantity that stays the same in different frames of reference, i.e. it's not invariant.

 

This is trivially true of classical kinetic energy. Take your example of running into a brick wall. In the wall's frame, you might have 1 unit of KE. But from your frame, the wall (and the entire earth) is moving, having a much larger KE. There is no part of physics that says that the values should be the same in different frames of reference.

So what about everything else I said like where the physical mechanism for the energy gain comes from? I understand that if you move towards a photon, you will measure it blue shifting compared to if you measured it while stationary, but what I don't understand is the physical mechanism for how that happens specifically with photons, they aren't exactly brick walls.

 

We just went through this. The asymmetry is the acceleration, which is not relative. One twin accelerates. The other does not.

So say we do know which one accelerates, but what about that small acceleration changes everything? Or is it actually asymmetrical prior to that as well as md6 was flip-flopping with?

Something about red/blue shifting seems illusionary, or in a way physically non-nonsensical. If I travel towards a photon that's a light year away with 0 matter and energy in between me and the photon, and a source another light-year away said before the experiment began that the photon is red, when I finally run into it, I will measure it has blue shifted. But, where did it gain the energy? If I knew it gained the energy, how did I not measure it before the amount of time it would have taken light and violate causality? The only way I can think it works is some way of modeling is the energy you put into moving towards the photon is in some way proportional to the relative energy you measure it having, more like running into a brick wall at 20kph rather than 1kph, but, I still can't figure out how that physically works. There's also something weird with a physical mechanism for the frequency increase too. A photon doesn't seem to oscillate in a completely physical way, and when you measure one, you have a quantum eraser effect where the rest of the mathematical model of the photon appears to vanish since you narrowed down its position to a single point. So, how can we even possibly measure a photon's "oscillation over time" like a wave in the water when all definite photon measurements only give you a single point and not multiple points over time and essentially erase the rest of the spacial probabilistic distribution of the photon?

The acceleration allows you to declare who was actually moving and who was stationary. In essence, it lifts the "relative" part of relativity. We know the rocket twin was the one moving, we know his/her clock (i.e. time) ran slow. Absent an acceleration, both can claim those things about the other.

Right, that's what I got, but like what physical effect is there? If someone is in an accelerated frame of reference, they might experience, say, a fictitious force that causes a different measurement. What is that force in this scenario? What about turning around and that instantaneously small moment of acceleration that makes the entire situation asymmetric? Or how about before they turned around? They had to accelerate to get to near the speed of light but still stayed at a constant velocity once they got to that speed?

 

Acceleration. In the basic scenario, only one of them accelerates. Acceleration is not relative.

Yes many others have made that point, but still not a clear explanation. What about acceleration does this to create the asymmetric situation? Why is it that everyone agrees a certain object is accelerating, and what about this agreement makes the situation asymmetrical when the traveling twin observes the environment and Earth accelerating instead?

 

What makes you think the situation is symmetrical at all in the first place?

Normal relativity. The concept that everyone is stationary from their own frame of reference and only see other things moving.

The mutual observations of clocks are symmetrical, but demonstrate doppler shifts, not aging or accumulated time. Aging can only be determined when the clocks are reunited.

In the simple case, The cast is A(naut) and E(arth).

E records: A leaves, moves inertially for t1, reverses direction (due to rocket) for t2, and returns in t3.

A records: E leaves, moves inertially for t1', reverses direction (due to g-field) for t2', and returns in t3'.

Note, each has an explanation for the non inertial part of the trip, and A senses it, using the equivalence principle, and E does not.

The A times will be less, since his speed profile varies from the constant speed of E.

This is the point where you have to avoid the road map interpretation of the Minkowski drawing. It's not necessarily a longer path. It's a different speed profile or path, and the relation is t = x/v, i.e., faster speed, less time. (At least one segment will be faster than that of E.)

Consider acceleration as establishing the rate of time dilation.

Acceleration is not fictitious, since it can be measured (every time you weigh yourself).

What if A and B are both anauts in ships, and at max separation, each accelerates to rejoin, which one counts?

 

This is an example showing acceleration is not a factor.

twin clocks-no accel140402.doc

The equivalence principal isn't necessary to describe it and that link I posted didn't use it, so an explanation with out it should be simpler, ultimately. But, otherwise the only other way I could maybe see it making sense with it is if you create an additional distortion in space-time around the traveling twin like a gravity field itself to show the traveling twin's acceleration put them in a higher degree of curvature away from Earth's frame of reference. But the same previous problem arises where if say, I'm 1/3 of a radian away in curvature from someone, then that someone will observe me being 1/3 of a radian away from them (not that it works that simply) and so there's still no clear place where the asymmetry comes from. Someone mentioned previously that it was symmetrical for the first half of the trip which if true would mean there's a more real component to the Doppler effect, and if not, back to square one.

What it seems like is:

Intuition gives you a weighted idea of reasonable possibilities based on patterns you know.

Objective logic narrow's down the pool of possibilities you chose from to only a few, sometimes one, as fitting the patterns you observed. That is why although a mechanic would hear something wrong with a motor intuitively, they wouldn't know exactly what was wrong with it until they had a look and reasoned through what part is missing or damaged and how it affected the rest of the motor.

If it helps david, he can think of intuition as the "hypothesis" when starting a scientific experiment since you can't point science in any useful direction without already having some already established notion of what you should be testing in the first place.

Though, it would still not be logical to equate logic with reality, which, is why not every logical idea turns out to be true.

You keep ignoring the "third leg" of the SR stool: The Relativity of Simultaneity.

 

Assume the traveling twin flies by the Earth at 0.6 c. He is heading towards a planet 10 ly from Earth (as measured from Earth). when he is next to the planet, he reverses and heads back towards Earth, both he and the Earth set their clock to zero at the moment they pass each other. The planet and the Earth has previously synced their own clocks.

 

We will distinguish between the time each observer visually sees,and the the "real-time" on the clock. So for example if two clocks are 1 light hr apart and motionless with respect to each other, and one visually reads a time of 1 hr on the other clock, he knows that the real-time on the other clock is actually 2 hrs, because it took 1hr for the reading on the clock to reach him from the other clock.

 

According to the Earth, the traveler takes 16 2/3 yrs to reach the planet (Both the clocks on Earth and on the Planet read 16 2/3 yrs real-time upon his arrival) and 16 2/3 years to return for a total trip time of 33 1/3 yrs. During which time, the traveler ages at a rate of 0.8(time dilation) and has aged 26 2/3 yrs on his return.

 

That's the easy part.

 

According to the traveler, the Distance from Earth to planet is 8 light yrs. (length contraction), also due to the Relativity of Simultaneity, the clock on the Planet does not read 0 (real-time) as he passes the Earth, but already reads a time of 6 yrs(real-time).

 

I'll explain that last bit. As the traveler passes the Earth, he visually sees the same time reading for the other planet (-10 yrs). Now for someone on the Earth, all they have to do is add 10 yrs to this to get what the "real-time" it is at that moment on the planet. They can do this because the planet and the Earth do not move with respect to each other.

 

However, in the case of the Traveler, things are different. He knows that the planet is 0.8 light yrs away as he passes the Earth. (or, at the very least, will know when he reaches it in 13 1/3 years at 0.6c) But that means it had to be further away when the light he sees left it. By backtracking both the light he sees(which travels at c with respect to him) and the planet's motion of 0.6 c with respect to him, he can determine how far away the planet was from him when the light left the planet and how long ago by his clock. He also knows that due to time dilation, the Planet's clock ticks slower than his own by a factor of 0.8 Putting this all together (the -10 yrs reading he sees, how long ago by his clock the light carrying that information left the planet and the time dilation factor for the planet's clock), he can determine what real-time it is at the planet the moment he passes the Earth. This will not be the same answer as someone on the Earth.

 

Okay, so now it will take 13 1/3 years by clock to cross the light years between Earth and planet (or if you prefer for the Planet to cross the distance to come to him.) The planet's clock ticks off 0.8 x 13 1/3 year = 10 2/3 years during this time. Since it started at 6 yrs when the traveler left Earth, it now reads 16 2/3 yrs. The Earth clocks has also ticked off 10 2/3 years and reads 10 2/3 yrs ar this moment. Both traveler and planet will visually see the Earth clock as reading 6 2/3 years

 

The traveler changes velocity so that he and the Earth are now moving towards each other at 0.6c We will assume that he does it in so short a time that he never leaves the vicinity of the planet. The planet clock still reads 16 2/3 yrs, the traveler clock, 13 1/3 yrs and both still read 6 2/3 years on the Earth clock.

 

However, as before, when leaving Earth, while the real-time readings on the Earth and planet clock are the same according to someone on either Earth and Planet, they are not so according to the traveler; there will be a 6 year difference in the real-time readings of the two clocks. And since he is now heading towards the Earth, it will the Earth clock that reads 6 yrs ahead of the planet one, again due to the Relativity of Simultaneity. So, according to real-time, it is now 12 2/3 years on Earth.

 

It again takes 13 1/3 years by the traveler's clock for he and Earth to meet up again,during which time, the Earth clock undergoes time dilation and ticks off 10 2/3 years, and reads 33 1/3 years for his 26 2/3 years when they meet back up.

 

The point is that due to the Relativity of Simultaneity, if you have two clocks separated by distance, inertial frames with different velocities that run parallel to the line separating the clocks will disagree as to the real-time difference in the reading of those clocks. And you have to include the Relativity of Simultaneity into any discussion of the Twin paradox.

It will take some to read over to interpret everything you said correctly, but initially what it sounds like is one of the important differences is that the traveling twin says it's a shorter distance due to the relativistic effects which is maybe how we could say the traveling twin is younger though the asymmetry. The thing is, I just can't help but think about the fact that the traveling twin still sees Earth traveling away at the same speed, and then observes Earth to be returning and then heading towards themselves and why that situation alone is asymmetrical, like if the distance didn't matter, just in any scenario, why the symmetry is broken in reality and not via illusion because of a photon delay in those two instances alone. Earth twin see's traveling twin heading away, traveling twin see's Earth twin heading away at the same speed, and they both see each move in a semi circle around the star when the direction is changing, then both see each other heading towards one another, and in that scenario events, how do we know only the traveling twin has experienced more time dilation or traveled dramatically less measured distance to make them younger?

Waves don't necessary need to have minimum caused by the amplitude that extends below 0. For instance, if I describe a wave through time as x=sin(t) + 1, it only ranges from 0 to 2. And, just as you have mass or no mass but not negative mass, you also have gravity or no gravity but not negative gravity since gravity is directly related to mass, anti gravity would simply require a completely different force.

The only asymmetry that matters is the difference in speed profiles, as drawn on a Minkowski diagram. The profile (path) that varies from the the constant speed (straight line) one, loses more time. It's permanent and results in a differnce in aging.

In the common simple case, only one twin changes speed, thus the speed change has to be assigned to that profile.

But that argument alone doesn't work because of relativity itself. If I observe someone traveling away from me, they will observe me traveling away from them.The traveling twin should still measure Earth's clock slowing down because the traveling twin see's Earth accelerating away from them to near speed of light even if everyone on Earth isn't being pushed into their seats, and if the clock didn't slow down and length didn't contract, there wouldn't be a reason for Earth not to accelerate right past the speed of light. It has to be more complicated than that.

The Doppler shift drawn in Minkowski space only seems to account for the illusion that the Earth twin sees of the traveling twin and not an actual real, physical component of what's happening.

Now if I "assumed" special relativity didn't work in the other direction, it might make sense to say everyone can agree, even the traveling twin, that only the traveling twin is traveling. But I know the spacial and temporal metric contractions work both ways based on what different sources have been saying and the traveling twin doesn't see themselves traveling, only their environment and outside objects.

Someone said something about "only one is accelerating like when someone gets pushed into the seat of your car." The supposed force that "pushes you into the seat of your car" is a fictitious force caused by an accelerated frame of reference, that's why I asked what the "fictitious force" of this scenario is, what is the thing that could only happen if someone was accelerating for sure that would account for the age difference as an additional effect that Earth couldn't be afflicted by? We know lorentz's transformations work the same in both directions, so both have to observe each other being affected from relativistic effects in some way, but Earth confirms the twin is younger from these effects, similar to being in a higher gravitational field (though it is not necessary to explain it as such) because of the addition effect of _______________ (fill in the blank) caused by the traveling twin's acceleration.

I can't say what would happen if there was no delay of light.

But that's like saying you can't figure out what would happen with gravity in a perfect sphere just because perfect spheres don't exist in reality. With your knowledge of mathematics, when you set the speed of light equal to infinity or if you take a limit with it approaching infinity in this scenario, what happens? How do the other variables change?

is the light cone (https://en.wikipedia.org/wiki/Light_cone).

Just out of curiosity, is there meaning to different conic sections of light cones? I haven't encountered many useful things with the actual cone that you can model parabolas and ellipses coming from.

Not really. You don't need photons at all, just the velocities. If the twins separate and exchange no information until they reunite, their clocks will show the same difference in aging that you'd get if they were constantly observing each other.

 

Their paths through spacetime really are asymmetrical, whether watched or not.

 

Edit: Or, to interpret what you said a different way: If the delay of light wasn't what it is, relativity wouldn't work the way it does. So I don't know if you could meaningfully describe the scenario without a delay of light.

 

 

I guess that looking for the resolution only in the long durations of relative velocity is like considering only time dilation, and looking only at the turnaround is like looking only at relativity of simultaneity. The resolution of the paradox is in all of these things considered together. What occurs, how it's seen, who feels it, what the clocks say, these are all related and tell the whole story in a consistent way, but no one of these aspect makes sense isolated from the others.

Ok so just to be clear, it's because there is delay in how long the information takes to reach Earth that is the reason we see the asymmetry? Otherwise if the information reached Earth instantaneously, it would show symmetry?

Is it possible to even more closely relate the phenomena to the Doppler effect by going on to say that the information relayed to Earth on the frequency of events (like the periodic ticking of a clock) that takes place "piles up" in a sort of temporal blue shift which would account for what you called "ticking faster," similar only in concept to conventional blue shifting of a photon's actual frequency?

Sorry for the confusion. There is a difference between what "is" a clocks tick rate and the rate at which one "sees it appear" to tick. I incorrectly assumed that this was well understood and clearly stated.

 

The relativistic Doppler effect and Lorentz transformation agree with each other. If you want to understand why, maybe look to the math.

 

The most important factors are time dilation, length contraction (and thus relative velocity), and relativity of simultaneity (and thus asymmetrical paths). The difference in appearance and any difference in proper acceleration will be there because of the asymmetry, and they *should* by now make it clear that the observers aren't symmetric, but they do not directly show how the paradox is resolved. Time dilation, length contraction, and relativity of simultaneity resolve the paradox. The "paradox" only arises in the predictions of SR, and you really have to look at those details to resolve it, instead of looking for some answer that is not relativity of time, length, and simultaneity.

Right, you obviously can't just do away with the relativistic effects, but what I mean is, the thing that makes the difference between being symmetric and asymmetric with different directions is those things but with the added Doppler effect, right? Because otherwise if you don't factor in the delay with light and the seeming delay in the photons you use to measure events, its the same as the scenario I was talking about before where they both see each other's clocks exactly the same.

@sam

i guess that what i am trying to convey to you is that while argument is a vital tool for the progression of science, it is pointless to argue if you cannot reach a consensus. this is my contribution to you.

you still win though.

and there is nothing you can do about it.

at that level, i will discontinue answering this thread.

good luck.

Most of what I said multiple times is "we don't know everything, don't assume dark energy is 100% correct, don't assume we know the nature of the big bang" does that honestly sound irrational to you? Because if you agree with that statement I quoted, you had no reason to argue with me.

 

he does not realize that you do not have to argue to have effective communication

I do when you ignore my point after I repeat it countless times.

And for the record, you have in fact given rep points in the past.

Actually, I had a different staff member tell me otherwise to make sure of it. The only way it could have happened is by accident in recent times. In fact, you tell me which posts I rated in which ways and I'll go undo them.

I fear you may be mixing up the relativistic Doppler effect and the Lorentz transformation. Others are right, time dilation and length contraction are the same whether you're receding or approaching. The Doppler effect is different because of the way things change during the travel time of light. The Doppler effect simply shows how it looks, and how the two observers cannot see the described situation symmetrically.

 

You may be satisfied with that --- the outbound and return trip look different --- but that's not describing things according to the Lorentz transformation, independently of how things look from a particular viewpoint within an inertial frame. Once you accept that the situation is not symmetrical, the details still come down to time dilation, length contraction, and relativity of simultaneity. The relativistic Doppler effect includes those, but also includes delay of light, but it doesn't make sense without those first 3 things.

So if they're the same, why did you say the rocket twin's clock is "ticking faster" in post #57 when they head towards Earth if the light delay alone can account for the asymmetry and not time dilation or length contraction? If time dilation was the same in both directions, why didn't you say the clock was still slowing down? I knew I should have brought that up, it still make sense that observers on Earth would see their clock slow down no matter what, every time I decide not to argue some point it creates confusion later on. But either way, the way manner in which photons are measured relativistic-ally with their delay is the most important factor for resolving the paradox is what it seems. If you were trying to equate the measured time dilation with the Doppler effect, that's where I'm confused now, because time dilation works the same in both directions, but the Doppler effect as you put it, doesn't.

 

just make sure you get a few of those rep points along the way.

Rep points have nothing to do with science, I have no regard for them.

Sam, I'm sorry, I think you're trolling for a reaction and you have confirmed my opinion by denying the Big Bang.

I confirmed you're trolling by the fact that you said I was "denying" the big bang. Either that or you entirely missed the point of every single thing I said which I don't see how you could given my over-emphasis on being open minded to different possibilities. We don't know for sure a big bang even happened, even with some evidence, there's still gaps to fill in about ANY model that uses a big bang or any model without the bang bang or really just any model about the universe at all, and that's completely different than saying "the big bang could never have ever happened." Why would I even waste my time "trolling for a reaction?" Reaction for what? I don't want you to just "react", I want you to actually use your head and see a different view. What you call "common sense" is merely an illusion created by taking causes for fundamental properties for granted, causes which many scientists and mathematicians are trying to investigate which you can easily see in number theory where 1+1=2 is 3 pages more complicated than you expected.