TakenItSeriously

The way that I understand it, which I admit is still a bit fuzzy in spots is that special relativity linked space and time together by virtue of the speed of light being constant and the fact that nothing can go faster than the speed of light. The most obvious example of this is that when we look at any celestial body that is n light years away, we are looking at it as it existed n years in the past because that's how long the light took to arrive here. Other examples that they are linked has to do with the relativistic effects when traveling near the speed of light, e.g. Time dilation and length contraction, seem to go hand in hand.

Actually the formula used (revolutions/min)² which I changed to (Revolutions/sec)² to fit the units for g of m/s². I figured the distance traveled per revolution is just the circumference or 2πr

Yeah, I noticed that from Janus's post. I admit that I did take a big Liberty with my usage of the formula only because it was the closest my searches were able to find for some reason. I likely wasn't using the correct terminology which might be related to my using the term "centrifugal force" which seems to now have a different usage than what I was taught in high school physics around 1980. Any way, the formula was for calculating the g-force for a centrifuge. I thought that the situation was equivalent enough that it should still work but clearly, I was wrong about that. I have been trying to understand why modeling it like a centrifuge could be so wrong though. I noticed the .000001118 term as well, for which no explanation was given so I thought maybe it was a conversion factor of some kind. The fact that the answer is 11181 seems to just be an odd coincidence. I started trying permutations of different units but then I noticed the radius factor was inverted. So clearly there is something more fundamentally wrong with trying to use centrifuge model than I can understand. Note that the centrifuge formula does use angular velocity instead of velocity but I figured that could be handled by multiplying revolutions by the circumference. Edit to add: I'm beginning to wonder if that formula was some kind of curve fit equation with a huge fudge factor BTW, 6 orders of magnitude off makes me laugh at myself. Talk about biggest blunders!

True but the encryption key that could decrypt the email was shared instantaneously.

I ran the calculations and find that at the point of experiencing 2 g's of centripetal force or a net force of 1g pointing away from the planet, the ship is moving at 66,344,000 m/s Perhaps I made a mistake. Can you point to the post you were referring to?

Well some people think of solving interstellar travel as more than mildly interesting but to each their own.

I set the limit at 2 g's of centripetal force for practical matters of manned space travel. Another words, at 2 g's we cut the power and let the ship coast in a straight line away from the planet*. Treat the earth like a centrifuge and calculate the revolutions per second to find the speed based on the circumference of the Earth. Radius of the Earth: r = 6,371,000 Circumference of the Earth: C = 2πr Centripetal force: g-force = 2 * 9.8m/s² The equation for g-forces of a centrifuge: g-force = 0.000001118r(RPS)² or RPS = SQRT(g-force/0.000001118r) Convert revolutions/s to m/s Speed = C * RPS So Speed = 2π * 6,371,000 * SQRT[2 * 9.8/(0.000001118 * 6,371,000)] Note that at 2 g's centripetal force away from the planet and considering the 1g of gravity towards the planet, people inside the ship should experience something like anti-gravity or a 1g force radiating from the planet. Thus I used a four rail track with two below and 2 above to suspend the ship between the maglev rails. *I did address the problem of hitting the atmosphere at this speed in another post, where we could build the catapult on the moon rather than try to maintain a vacuum all the way to outer space on the earth. For the radius of the moon, I calculated the speed at 2 g's centripetal force to be around 11% of c. .

By free, I meant free from the perspective of the intestellar travelers who have serious payload budget issues, especially if the vast majority of their payload must be fuel. So if an intestellar space crew can get all of their speed right from the grid it's free relative to their payload budget. Economies of scale are a very complicated issue that goes well beyond the scope of this thread. This is why I tried to keep it to what was theoretically possible, though a first order approximation of what might be practical is fine. Beyond that the speculation grows exponentially. That electricity bill of $73 mil/Kg seems a bit high. Did you account for removing drag? It depends on the time frame you are choosing. Let's assume 1 g of constant acceleration since that's a popular choice for interstellar travel as well as a practical number for the acceleration of a maglev train in a vacuum. I didn't run the calculations myself, since math is not my strong suit but when looking at others numbers, I think the timeframe for reaching 22% C is roughly on the order of a year or two.

i) hint: do a search for the combin function to find your solution ii) hint: how many different groups can you and your enemy create and how does knowing this help you find your answer. ii) hint: for finding the probability, you are looking for the ratio of a smaller group within the total number of all possible groups. You need to figure out what group they are talking about and figure out its size.

I have a similar point of view to this but I've always thought of it this way. Imagine a universe of just you and me. Then the universe consists of the two of us and the space in between us because our presence defines that space as a two dimensional distance. We can measure it, watch it shrink or expand according to our movements, etc. Add a third person and now we have just added another dimension to our space because we can now calculate the area defined between the three of us which we could not do before. But if I turn around and look into the empty void behind me, it is completely lacking any point of reference, we have no appreciation of scale, no depth or width or height or or even motion to gauge time on for that matter. There is nothing what so ever that we could use to define any single property of the void, therefore it must not exist.

Good point, I was referencing mobile devices, but changing the monitor settings hue or tint to warmer colors should reduce eye strain for PC's which I hadn't thought of doing. Possibly some graphics driver settings could work as well.

Nice catch, I think the g-force at 75% C is somewhere in the twenties so I'm off the rails and it's a bad example. I originally had the g-force capped at 2 g's (centripetal force)for a couple of reasons. Any thing higher would be too uncomfortable for people to deal with over extended periods of time since g-forces at this scale would change over periods of months. Also I could deal with a 2 g force mechanically by using a four rail track that had a par of rails above and a pair below specifically to keep the ship from derailing, when centripetal forces first kicked in. So if we only accelerate the ship to 2 g's then, the initial speed for our ship is 22% the speed of light which is still a pretty respectable speed that we get for free so to speak. Edit to add: Also note that as the circumference of the track gets larger the initial speed we start out at also climbs. In that respect it's like a super collider for spaceships instead of particles. (For acceleration, not collisions) I came up with an idea of creating a maglev track that was in orbit and spinning at orbital speeds, then we would require a counter acceleration so that accelerating our ship didn't slow down the track which would cause it to collapse, but that seemed too unstable. Also I realized that the instant we left a vacuum, our ship would hit the atmosphere at a ridiculous speed that would first obliterate us then burn us up like flash paper. Better to choose a planet without an atmosphere such as the moon but the sacrifice is our initial speed drops to around 11% the speed of light.

Actually, there is an example of how entanglement can transmit useful information instantaneously over distance. Say Bob and Alice were at the opposite receiving ends of a stream of entangled particles. Bob observes the stream of particles as a series of 1s and 0s that he puts together to create a truly random binary key he uses to encrypt his emails that he sends to Alice. Alice instantly receives the key and uses it to decrypt Bobs messages. Therefore Bob did send Alice useful information that she (and only she) can use can use to decrypt his messages.

Actually the light in question has more to do with the high frequency, high energy, blue light that can cause eye strain over time which I tend to suffer from at the end of very long sessions but then I'm older and geekier than most. Twenty years ago, I'm sure I would have thought it was all just a gimmick to sell stuff like cheap glasses with yellow lenses. It's still true and they are just cheap glasses with yellow lenses but there is at least some kernel of truth behind them. There is often a separate setting for adjusting a blue light filter that I find helps more than just turning down the intensity. If you are reading a kindle or a book, reflected light is generally not as bad because the pages are often not that bright a white or have a yellowish tint to them, so the reflected light is a lower frequency light. Also, reading using incandescent bulbs helps a great deal except they are so damn inefficient. When I used an old incandescent bulb one time because that's all I had left as a replacement bulb I was amazed at how easy on the eyes it was compared to the newer bulbs.

Assume we adapted our interstellar space ship to use a maglev propulsion system (like those used for high speed trains) only over tracks surrounded by a sealed tube in order to create a perfect vacuum so that we travel in a frictionless state. Assume ideal tracks that encircle the Earth at the equator and are always perfectly level and straight. Wouldn't supplying a steady state power supply create a steady state acceleration given the frictionless state? Theoretically, what prevents us from accelerating the ship to close to light speed over a period of years before releasing the ship to coast towards a destination star system light years away at say, *22% of the speed of light without using any of the ships resources for propulsion. It seems like it's too easy but I can't think of any reasons that would prevent it from working, at least theoretically. Thanks. *changed from 75% thanks to Swansots pointing out of an error where centripetal g-forces would be too high to stay on the tracks at that speed

Thanks for the link, it looks like a great source for getting a basic grasp of the formalism which I lack. However I think the confusion lies with the fact that curved space time tends to reference how space time curves locally, but since it's local, we tend to ignore the fact that time is curved as well unless dealing with black holes because, it's a small effect and it's difficult to conceptualize curved time. What I was asking about is the effect on time that gravity has on us from distant objects such as other stars or even galaxies, and if that might relate to gravitational time dilation, but when I think about it in this context, it doesn't seem like it's related. If we go back to the past light cone example, then the gravity from all those distant bodies would seem to more or less cancel out in terms of space as far as its impact on us since they surround us in every direction, but in terms of time, gravity can only reach us from the past and if space and time is linked for gravity than the accumulative drag on time seems like it should be significant.

I understand, but any mass we can observe is always located in our past light cone. So to say that gravity is causing our movement towards an object that is located in our past seems to imply that at least gravity is slowing our forward progress through time which we already know is true. I was only wondering if that was the mechanism for gravitational time dilation.

If space and time are linked for gravity, wouldn't that imply that the direction of a gravitational force emanating from a distant massive body is towards the past in time as well as towards some distant point in space? Sorry, I meant to post this in the Relativity forum

I clearly made a mess of this post, and my attempts to rewrite aren't going well. Therefore, I'm going to take some extra time using some of the queues already given and work on my syntactic form before trying to clean up this mess. Live and learn. Thanks for your patience.

Yes, but for both conditions:free fall = inertial motion standing on the surface = inertial acceleration If we look at the example for an observer standing on the surface of the planet and the equivalence of the observers inertial acceleration through empty space, then your right: Einstein had concluded that if we remove the gravity field then we can replace it with an inertial reference frame that was accelerating past the observer locally. However, what he may have failed to consider were the implications of what happens in the other reference frame of the observer's inertial acceleration through empty space. In that case, If I'm right, the inertial observer is always accelerating away from the planet through empty space. It doesn't matter where on the planet the observer is standing, or even where you chose your empty space. This is the point that resonates with me. Apparently, equivalence is telling us that gravity doesn't only have a near field attractive effect over time but that it also seems to have a far field repellant effect over distance. This is very similar to the current view of expansion in the universe. It's expanding at an increasing rate with distance, and expanding at a decreasing rate over time. BTW, the sense I got from my reading was that the current method of using curved spacetime was adopted from Einstein's idea of an accelerated reference frame, not a start from scratch, but I don't know this for sure. I'm sure there are good reasons for using curved spacetime over using an accelerated reference frame. As I said, the math is beyond me. But I don't think flat vs curved frame is mutually exclusive in terms of their validity. From various readings, I think either is accepted in terms of their own validity, but there are limitations to what a flat frame could do. Again, I freely accept that I could be wrong but out of hand dismissals seems a bit undue at this point. I noticed the article is for isotropic cases. However from an observers view point within a gravity field, I doesn't seem like an accurate assumption since gravity is unidirectional. For instance, a view of gravity from an observer on the ground is different than that from an observer several miles higher. Is that assessment an incorrect application of isotropic?

I'm not sure why, but the quote button (iPad) bunched the entire post it all into a single paragraph. I'm basing this post on an early version of the Equivalence Principle described in the Wikipedia article under that name. It used an accelerated reference frame of 1g moving radially towards the planet to adapt gravity to a form that could be treated by SR. I'm not sure if there's an official name for this framework. To my knowledge it's still a valid method that predicts the bending of light or the lens effect, but there's much that was added to GR later, I'm sure. I like it because it's the only intuitive model I could find for understanding the Equivalence Principle and the modern version involving curved spacetime and tensors goes over my head on the math. I'm also sure this was how Einstein first thought about GR. I believe the article mentioned it was changed by a friend to use the modern framework to make it compatible for testing against other gravity theories of the time. Here's a relevant quote from Einstein that expresses a corollary to the quote you gave. I think your right in that its probably best represented as the weak Principle of Equivalence in modern physics. The models I was referring to were Einsteins mental models that included observers in white rooms for comparing a person in free fall or standing on the surface of a planet to their equivalents in inertial empty space which is roughly speaking a person who is floating or drifting and a person who is in uniform acceleration of 1g respectively. My arguement was that those models of equivalence didn't seem to be complete without including the vectors of motion since gravity vectors would always be a force of attraction as you put it. Sorry I struggle with finding the correct verbiage to use as I'm not a physicist. Once we add those vectors, then making those comparisons always results in the inertial free space frame being accelerated 1g away from the planet, unless I made a mistake, and which seemed to have striking implications about the expansion of the universe.

Could the principle of equivalence explain the apparent rate of expansion in the universe so that we don't need DE? I'm not a physicist but I'm good with logical constructs. The equivalence model for a body at rest on the surface of the Earth is a body accelerating at 1g through inertial free space. The property of equivalence has proven to hold up well under GR, so let's assume for now that it's true. I think it's easier to see if we just use equivalence to model gravity as the acceleration of local spacetime in towards the planet, as opposed to curved spacetime. We have always just thought of the inertial free space equivalence model as a hypothetical and completely isolated arbitrary system but in reality, I think any claims involving gravity must also involve vectors. It's an integral part of gravity because, gravity is always pointing in. If we take vectors into account then we would now say that a body at rest on the surface of a planet is equivalent to a body in freespace accelerating away from the planet at a rate of 1g. No matter how we think about equivalence, for free fall or at rest on the surface, it has to involve a vector of 1g in recession. Notice that this change doesn't change anything about the behavior of local spacetime so all evidence which was used to verify GR still applies. The only difference that happens when considering vectors is that space at a distance should now be accelerating away at 1g for any particular body in space. I also noticed that as we replace a gravity field with an accelerated inertial field, it doesn't make any changes to how we should treat time in local spacetime. All adjustments involve space only. For example, the rate of acceleration at the surface of the Earth is always 9.8m/s² but their is no velocity that changes over time because velocity relative to the gravitational frame is always 0. So it would appear that when we look at the behavior of gravity, it's primarily a local attractive inwards force over time, but after including vectors, it's also an expanding outwards force over distance. Even the units would only be an inverse unit of time which is one way we think about the Hubble constant which of course is a key constant for measuring the kind of expansion over distance that they have found. So, while I have no idea how much this would impact the calculations for DE it sure seems like all the units, vectors, and even dimensions seem to align properly. Am I making a mistake in the way I'm understanding the principle of equivalence? Is there a specific reason vectors shouldn't be considered with the principle of equivalence? Thanks.

Great, thanks for all the help!

I somehow missed or forgot this statement after I let myself get lost in the discussion. This does answer one original question, so thanks very much for that. Also, I see that when using percentage of growth instead of units of growth, that makes it consistent with the an increasing rate of expansion. Just to note that using percentage of growth makes it an exponential growth isn't that correct? So just to make sure I have the correct understanding. To put it another way, Is it fair to say: In lookback time the rate of change for distances between galaxies are increasing. While the rate of change for their respective velocities are decreasing over time. Therefore, there must be some yet unknown property which we call dark energy that must explain how distances are increasing or getting stretched faster than their respective velocities should allow? This is why the look back distances relative to us may increase faster than the speed of light. BTW I chose to use lookback time to make sure the effect at least extrapolates back to the state we are taking measurements from. And that the observable universe also demonstrates this property and it's not just limited to viewing the universe in a state of consistent density (at least in the last 5billion years) So galaxies at the edge of the observable universe could eventually fall the outside of the observable universe which we previously thought couldn't happen.

Ok, I see where I got at least one thing wrong. Every time I mentioned proper time, I was thinking of the definition for proper distance. I'm pretty sure I got the right definition for Hubble's law though (proper distance =fixed timeframe for the universe) even though I was calling it the wrong thing. This still has me worried since that's the time frame that I have a problem with. Also I'm pretty sure I got lost in click drift hitting too many links and may have got the wrong idea about a few things when reading the wrong page. I'm really embarrassed! Sorry for the confusion, and thanks for your help guys. I've got a lot of re-reading to do.