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Author | Topic: What's the Fabric of space made out of? | |||||||||||||||||||||||||||
Sylas Member (Idle past 5250 days) Posts: 766 From: Newcastle, Australia Joined: |
Is the reason you can't use the train/vacuum train/non vacuum thought experiment is because it won't make your point. You will get different velocities as stated in the experiment both ways? My point will be made whether you are in a vacuum or not. The differences in values obtained are trivial. I was trying to give an example in which there is something (photons in a vacuum) moving at the same speed for all observers. But we can calculate for other examples if you prefer. Let's forget photons and consider the eagle example.
Like if you're flying in an airliner, you see an eagle flying in the opposite direction of your plane out the window. It appears he's flying at his normal speed/velocity plus the speed your plane is going. But if you could expand the size of your cabin and the eagle flew past you within your aircraft, he would be moving at his normal speed only. Is this relativity of the eagle within or without the cabin in any way analogous to your experiment? This is a different example, but we can solve it. You have a aircraft flying at 900 km/hr. An eagle inside the cabin flies down the aisle at 100 km/hr (from the cabin's perspective). The question is... how fast is the eagle moving relative to the Earth outside the cabin? Newtonian physics says 1000 km/hr (900 + 100). Einsteinian physics says 999.999999999999923 km/hr Which one do you think is closer to correct? How do you decide? Try actually answering this question. Just give it a shot. Cheers -- Sylas PS. By the way, you get the same numbers for the eagle flying outside the plane and in the opposite direction. If a plane is flying East at 900 km/hr, and an eagle is flying West at 100 km/hr, then the speed of the eagle relative to the plane is 999.999999999999923 km/hr; not 1000 km/hr. PPS. Just for fun; the exact formula used get the relativistic "addition" of velocities x and y given in km/hr is(x + y) / (1 + xy / 1164786711642915661.44) PPPS. Thanks MangyTiger; I have edited this post in response to your reply. In my first "PS" I originally had the eagle flying east. Have now corrected it to read "West". This message has been edited by Sylas, 03-26-2005 03:38 AM
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Trae Member (Idle past 4296 days) Posts: 442 From: Fremont, CA, USA Joined: |
quote: Does it take energy for nothing to expand? Since you seem to have a handle on it, what exactly is energy. I've been trying to get a better grasp on the concept.
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MangyTiger Member (Idle past 6343 days) Posts: 989 From: Leicester, UK Joined: |
If a plane is flying East at 900 km/hr, and an eagle is flying east Shouldn't one be flying East and the other West ? Confused ? You will be...
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Percy Member Posts: 22359 From: New Hampshire Joined: Member Rating: 4.7 |
Sylas writes: PPS. Just for fun; the exact formula used get the relativistic "addition" of velocities x and y given in km/hr is(x + y) / (1 + xy / 1164786711642915661.44) You've lost me. I see a vague resemblance to the Lorentz coefficient, but I don't really know what this is. The plane and earth agree they are traveling relative to each other at 900 km/hr. The people on the plane see an eagle flying down the corridor from the rear of the plane toward the cockpit at 100 km/hr. They believe that the speed of the eagle relative to the ground is 900 km/hr + 100 km/hr = 1000 km/hr. But the people on the ground see an airplane shorted in the direction of motion, and so would see the eagle taking longer to travel, say, a meter as determined from the ground versus a meter as determined on the plane. I would have simply calculated the Lorentz coefficient (sqrt(1-v2/c2)) using the airplane's speed relative to the ground and used that as the proportion of the 100 km/hr speed of the eagle to add to the speed of the airplane. Doing this I get 1, which shows the precision limits of Google. Moving to a different calculator (which unfortunately unlike Google doesn't do automatic units conversion for me) I get .99999999999965230, and applying this to the the 100 km/hr of the eagle I get a velocity of the eagle as measured from the ground of 999.999999999965230 km/hr, which is somewhat slower than your 999.999999999999923 km/hr by 0.000000000034693 km/hr. I'm probably doing something wrong, but I can't figure out what. Do you see the error? --Percy
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Buzsaw Inactive Member |
Hi Trae.
Does it take energy for nothing to expand? Since you seem to have a handle on it, what exactly is energy. I've been trying to get a better grasp on the concept. My "handle" is logical and scientific, as per thermodynamic laws and it will be limited solely as pertaining to the topic of space so as not to be off topic. Concerning the "fabric" or properties of space, neither I nor, imo, my counterparts have yet offered any properties capable of being energetic, nor of the capability of expansion. Space is static and unbounded, existing area in which energy and matter exist. The immeasurable present is forever consuming the eternal future and extending the infinite past. buzsaw
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Sylas Member (Idle past 5250 days) Posts: 766 From: Newcastle, Australia Joined: |
The basic formula to use is the Lorentz transformation. Use this, rather than trying to work with length and time contraction.
We locate things in spacetime with Cartesian co-ordinates. I'll use x for east/west distance and t for time. Let (x,t) be the co-ordinates for one observer, and let (x',t') be co-ordinates for another observer who sees the first observer moving at speed v in the x direction. Both co-ordinate systems are synchronized to a common origin (0,0) Then the Galilean transform (used in Newtonian physics) for mapping from one to the other is
x' = x + vt
Using c for speed of light, and γ = 1/sqrt(1 — v2/c2), the Lorentz transform is
t' = t
x' = γ (x + vt) t’ = γ (t + vx/c2) Suppose the first observer sees something (like an eagle) moving from the origin (0,0) at velocity u. Then at any time t, they see the eagle at location and time (ut,t) The second observer (who sees the first moving at speed v), sees the eagle at
γ (ut + vt) , γ(t + uvt/c2)
Velocity of the eagle is distance divided by time, the gamma factors cancel as does the t, and you are left with
(u + v) / (1 + uv/c2) Our first observer is in the aircraft. Our second observer is on the ground, seeing the first observer moving at v = 900 km/hr. Speed of light is exactly 1079252848.8 km/hr, and c2 is the factor I gave in my previous post. Now let’s do the same thing the hard way! Working with dilation factors is very error prone, since it is very easy to slip in an assumption of common simultaneity and get the wrong answer. You need to take three factors into account to get the right answer. These factors are all at odds with normal intuition, and I give them in order of increasing weirdness.
In the aircraft, the eagle gets up to flying speed in the galley, and enters the cabin aisle at its cruising speed. It maintains a fixed velocity until it crashes into the wall at the far end. All clocks on board read zero at the instant that the eagle enters the aisle at its cruising speed. The length of the aisle is x, and the eagle hits the end wall at time t. All clocks on the aircraft read t at the instant of this collision. The velocity of the eagle is therefore x/t. Let this velocity be u. From outside, the length of the aisle is x/γ. The eagle starts flying at time 0, and crashes into the end wall when the end clock reads t. But the end clock took γt seconds to get from 0 to t, and it was reading zero γvx/c2 seconds after the eagle started. Thus the time of the eagle’s ill-fated journey is
t’ = γt + γvx/c2 = γ(t + vx/c2) = γ(t + uvt/c2)
During this time, the plane flies at speed v, covering distance vt’. The eagle flies an additional distance x/γ which is the length of the aisle. The total distance from start to finish is thus
x’ = vt’ + x/γ = γ(vt + v2x/c2) + x/γ = γ(vt + v2x/c2 + x - xv2/c2) = γ(vt + x) = γ(vt + ut) These are the same formulae obtained form the Lorentz transformations directly, and so we proceed as before. Cheers -- Sylas
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Buzsaw Inactive Member |
My point will be made whether you are in a vacuum or not. Why then did you use a vacuum model for the space visual? I was puzzled about that and trying to figure the significance of it as I thought on this. I am assuming that the space shooter is also in space in the area of the spaceship. Is that correct? The immeasurable present is forever consuming the eternal future and extending the infinite past. buzsaw
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Sylas Member (Idle past 5250 days) Posts: 766 From: Newcastle, Australia Joined: |
Why then did you use a vacuum model for the space visual? I was puzzled about that and trying to figure the significance of it as I thought on this. I am assuming that the space shooter is also in space in the area of the spaceship. Is that correct? That is correct. The reason I used vacuum is because the speed of light in a vacuum is the same for all observers. This means we can answer the question without doing any calculations. But the effects of air on light are so small that it makes no real difference, and so the point stands whether you are in a vacuum or not. The speed of photons fired at a train or a spaceship are the same from the perspective of the train, and from the perspective of the person holding the photon source. If you are moving towards a photon source, or away from it, you still see the photons moving at the same speed. This is not what we would expect in Newtonian physics. This is relevant to the fabric of space topic. Before Einstein, it was commonly thought that light was waves in the fabric of space, called the ether. Many experiements have confirmed that this ether model fails. However, space can still be curved. The examples we are considering here don't deal with curvature yet; but they are a necessary pre-requisit, and they do show that "logic" or "intuition" that assumes some kind of absolute space give the wrong answers. Cheers -- Sylas
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Funkaloyd Inactive Member |
quote: Even if a laser is fired at a spaceship from the surface of Earth and up through our atmosphere to the vacuum of space, the observer in space will still get the same measurement of the speed of light whether (s)he's speeding towards the source of the beam, away from it or perpendicular to it. But it's much easier to just set the thought experiment in space to begin with. It should be noted that the mechanism through which light slows down in air isn't the same as wind resistance acting on a material object.
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Buzsaw Inactive Member |
Thanks Sylas and Funkaloyd.
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Sylas Member (Idle past 5250 days) Posts: 766 From: Newcastle, Australia Joined: |
You're welcome buzsaw. Now, can you please try answering a simple question?
Here are four examples of combined velocities.
You’ve used the word logical a lot. Tell me, are the statements above logical? The idea is to determine what logical really means when you say something is or is not logical. Even if I disagree with your answer, I promise not to merely laugh at you. I know that this stuff is bewildering, but it will really help if you can just answer the question clearly. Thanks -- Sylas
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Percy Member Posts: 22359 From: New Hampshire Joined: Member Rating: 4.7 |
Thanks, Sylas. I can see that you're right, but I feel uncomfortable with not having an intuitive grasp for where t’ = γ (t + vx/c2) comes from. There's an appendix in Einstein's Relativity that covers derivation of the Lorentz transformation, and I'll work through it when I have a spare moment.
--Percy
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NosyNed Member Posts: 8996 From: Canada Joined: |
I took my daughter thourgh it for Physics 11 last year. I can help via email if you want. It would be good to refresh me yet again.
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No Moon Inactive Member |
By definition, space is just the abscence of stuff but it has the capacity to have stuff put in it.
But people assume that space has to have time in it for it to be space. Our universe we occupy is fundamentally made of four dimensions, length, width, depth, and time, (and about 8 or 9 more other weird dimensions but basically four). But that's just the universe, if we could temporarily imagine the universe wasn't created and there is only nothingness then allowed for length width and depth as qualities of this nothingness, then we could put stuff in that space if there were time to allow the stuff to fill in that space. Space doesn't expand, the stuff inside of it does. But if you ask the question you really are trying to ask, "what is length, width, and depth?" then it gets really abstract like a kid who keep asking "why?" after every answer you give him or her. So what is length width and depth, and I don't mean the measurement of these dimensions, i mean really, what is it about our universe that allows us to move in any direction? What is a spatial dimension?
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Percy Member Posts: 22359 From: New Hampshire Joined: Member Rating: 4.7 |
No Moon writes: But that's just the universe, if we could temporarily imagine the universe wasn't created and there is only nothingness then allowed for length width and depth as qualities of this nothingness, then we could put stuff in that space if there were time to allow the stuff to fill in that space. Space doesn't expand, the stuff inside of it does. I'm not actually sure what you're trying to say here, but space *does* expand. "Expanding space" is not just another way of saying objects in the universe are moving away from each other. Space really is expanding. One of the most effective ways of convincing yourself of this is to contrast motion through space with motion due to the expansion of space. If you're an observer watching someone whiz by at .866 times the speed of light (.866c), then you'll see the second hand of his watch ticking off the seconds at half the rate of your own. But if you observe a watch in a distant galaxy receding from us at the same rate of .866c then you'll see the second hand ticking off seconds at the same rate as your own. This is because Einsteinian relativity only applies to relative motion through space. It does not apply to relative motion due to the expansion of space. The distant galaxy's motion through space relative to us is negligible compared to c, and so its clock appears unaffected. Its apparent motion due to expanding space is large, and so there is a red shift of the arriving light, but its motion through space relative to us is small, and so its clock runs at roughly the same rate as our own. If our nearby speedster's motion of .866c were away from us, his red shift would equal the distant galaxy's *and* has watch would run half as fast. This difference between motion through space and motion due to the expansion of space confirms that space *does* expand. --Percy
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