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Author | Topic: The Twins Paradox and the speed of light | |||||||||||||||||||||||
lyx2no Member (Idle past 4716 days) Posts: 1277 From: A vast, undifferentiated plane. Joined: |
If dt is larger then ds you'd have dτ2 = dt2 - ds2, and would be calculating proper time rather than proper distance.
AbE: It looks like farther down in the tread ds has been used for time while I've been thinking of it as d(spatial). Sorry if I've confused the issue. Or maybe I'm confused now. Edited by lyx2no, : No reason given. Kindly Everyone deserves a neatly dug grave. It is the timing that's in dispute.
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Son Goku Inactive Member |
No, if the ds^2 is negative between two points in spacetime it indicates that they cannot be reached from one another or influence each other.
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New Cat's Eye Inactive Member |
So if you move around a lot, but arrive at Point B in space-time, then you had to have had spent less time doing it. That makes sense. Thanks randman!
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cavediver Member (Idle past 3644 days) Posts: 4129 From: UK Joined: |
That makes sense. Yes, Randman's idea does seem to make sense and sort of reproduces the desired effect. Unfortunately, it has nothing to do with relativity and the twins "paradox". Multiplying 2 by 2 gives the correct answer 4, despite the question being "what do you get if you raise 2 to the power of 2?"... Edited by cavediver, : No reason given.
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cavediver Member (Idle past 3644 days) Posts: 4129 From: UK Joined: |
Thank you SG. That is simple and clear. What is more, we can essentially derive the entirety of Special Relativity just from our simple metric, ds^2 = dt^2 - dx^2 - dy^2 - dz^2. General Relativity then follows by allowing us to generalise the metric to ds^2 = A()dt^2 - B()dx^2 - C()dy^2 - D()dz^2 where A, B, C and D are functions of t,x,y,z. (there can also be cross-terms in general, dt.dx, etc, though we can diagonalise them away at a point). The Einstein Equation tells us what A, B, C, and D can be based upon the matter distribution of the space-time. Beautiful in its simplicity
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Jester4kicks Junior Member (Idle past 5496 days) Posts: 33 Joined: |
Wow! Ok... I think I'm catching on!
I guess I had never thought about time in terms of distance... I always just thought it was more of a constant. Now, before I get even more confused.... you mentioned a seconds->meters conversion. I believe it was 1 second = 300,000,000 meters.... however, you qualified it with the terms "temporal direction". I guess this is where I'm getting a little hung up. Does this mean that if something travels faster than 300,000,000 meters in 1 second... that it traveled faster than time? I think I'm getting even more confused in my attempt to explain my confusion. I love the equations... but in order for me to understand why an equation proves a scenario, I need to understand where the values in the equation came from. How did we determine that 1 second = 300,000,000 meters? BTW, Thanks everyone! This is about the closest I've been to ever understanding this thing. I don't doubt that Einstein was right... but I've got this annoying curiousity that simply will not leave me alone until I understand WHY he was right.
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NosyNed Member Posts: 8996 From: Canada Joined: |
How did we determine that 1 second = 300,000,000 meters? That is c, the speed of light in a vacuum. It isn't a coincidence.
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cavediver Member (Idle past 3644 days) Posts: 4129 From: UK Joined: |
Does this mean that if something travels faster than 300,000,000 meters in 1 second... Hmmm... now what travels 300,000,000 metres in 1 second Oh, yes of course! All things travel at the speed of light *ALL THE TIME* - it's just that mostly we travel in the temporal direction, so we don't notice anything other than time passing. What we call *speed*, is us rotating our speed-of-light velocity slightly out of the temporal direction and slightly into the spatial durections. The most *speed* we can ever achieve is what we get by rotating our speed-of-light velocity completely into the spatial directions... and surprise surprise, we see the greatest *speed* is the speed of light. Our velocity is ALWAYS the speed of light - so it is impossible to talk about going *faster*, just as it is impossible to talk about going *slower*
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New Cat's Eye Inactive Member |
That makes sense. Yes, Randman's idea does seem to make sense and sort of reproduces the desired effect. Unfortunately, it has nothing to do with relativity and the twins "paradox". Multiplying 2 by 2 gives the correct answer 4, despite the question being "what do you get if you raise 2 to the power of 2?"...
I didn't understand him to be answering the actual "paradox". It was about how traveling in space can make the time distance shorter. As I understand it, if you're traveling between two points in spacetime, you have a time component and a space component. The total distance between the two points is the same whether you move in space or not (because they are the same points regardless). So therefore, if you don't move through space then all of the distance is from the time component. However, if you do move through space, then the time component of the total distance must be less because the total distance remains the same. That makes sense to me. Is it accurate? Edited by Catholic Scientist, : typo
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onifre Member (Idle past 2951 days) Posts: 4854 From: Dark Side of the Moon Joined: |
As I understand it, if you're traveling between two points in spacetime, you have a time component and a space component. The total distance between the two points is the same whether you move in space or not (because they are the same points regardless). So therefore, if you don't move through space then all of the distance is from the time component. However, if you do move through space, then the time component of the total distance must be less because the total distance remains the same. That makes sense to me. Is it accurate?
I hope its accurate too because your explanation cleared up for me perfectly. Lets repet it over and over again like a chant, maybe it'll finally sink into my brain All great truths begin as blasphemies I smoke pot. If this bothers anyone, I suggest you look around at the world in which we live and shut your mouth.
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cavediver Member (Idle past 3644 days) Posts: 4129 From: UK Joined: |
It was about how traveling in space can make the time distance shorter. Yes, I know.
That makes sense to me. I know, it does sort of make sense, but...
Is it accurate? Absolutely not, hence my warning. This is not how space-time works, and it is making a large confusion of time experienced with what we call coordinate time.
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New Cat's Eye Inactive Member |
How does coordinate time differ from time experienced?
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cavediver Member (Idle past 3644 days) Posts: 4129 From: UK Joined: |
Time experienced is given by the ds term - it's an inifnitessimal so it needs integrating along your path through space-time, to given you the time experienced along that path. The dt is coordinate time, and is merely a way of puting a chart or map down on space-time in order to make calculations - rather like latitude and longitude on the Earth - they are merely calculating conventions to ease measurement on the 2d surface of the Earth. The 2d surface is real, as is the physical distance between two points, but the actual lat/long grid is purely arbitrary. The 4d of space-time is real, as is the time experienced along a particular path, but the dt, dx, dy, dz grid you use to decribe it is (fairly) arbitrary.
Edited by cavediver, : No reason given.
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New Cat's Eye Inactive Member |
Time experienced is given by the ds term So then it seems that it should be the same regardless of whether or not you travel though space.
The dt is coordinate time, and is merely a way of puting a chart or map down on space-time in order to make calculations So then it seems that having the difference in the space component of the distance makes it so dt is less than if there was no space component. But if experienced time, ds, is the same between the two spacetime coordinates regardless of the space component of the distance, then how can traveling through space affect the experienced time?
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Jester4kicks Junior Member (Idle past 5496 days) Posts: 33 Joined: |
ROFL! I can't believe I didn't immediately make the connection with the 300,000,000 meters-> 1 second thing!
I think I'm getting closer to understanding this. Let me see if I can simplify it just a bit (understatement of the year). You're saying we are always "traveling" at the speed of light... but that most of our "speed" is in the temporal direction. (Gonna be using a lot of terms like "speed" in completely the wrong way... so bear with me) So... standing still:Temporal speed (let's call it Ts) = 300,000,000 m/s Spatial speed (let's call it Ss) = 0 m/s Total speed = 300,000,000 m/s Now... to over-simplify it even further... (and based on my understanding of your last post to indicate that we are always "traveling" at the speed of light) Ts + Ss = Speed of light (300,000,000 m/s) I REALLY hope I'm on the right track here... if I am, I now understand this... if I'm going in entirely the wrong direction, I'm screwed. But... presuming I'm on-track here... as we increase our spatial "speed", we accordingly decrease our temporal "speed", so that the equation always equals 300,000,000 m/s. However, since our typical spatial speeds are so low, the impact on our temporal speed is virtually non-existent. However, if we got on our hypothetical space ship and traveled at NEAR the speed of light... in order for the equation to still equal 300,000,000 m/s, our temporal "speed" would need to be VERY low! Example:Ss = 295,000,000 m/s Total speed = 300,000,000 m/s 295,000,000 m/s - Ts = 300,000,000Ts = 5,000,000 m/s Now... here's what I'm REALLY excited about... If I'm on track here, this also explains why faster-than-light travel is impossible... because it would either result in a negative temporal speed, or it would simply "break" the equation. PLEASE say I'm right here... cause if so, you guys managed to explain something that I've never been able to understand.
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