TakenItSeriously

Not sure where you got this, bit it's wrong. By a lot.

 

1 meter radius at 1 revolution per second should give 39.4 m/s^2 of acceleration (~4 g's). Your equation says 0.000001118 in whatever units it's supposed to have. So that's where ~6 orders of magnitude of error come into it.

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!

emails are not instantaneous.

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

After reading the previous posts, do you still think of this idea as a "solution"? If so, I think you need to work through the calculations again.

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?

The price of building those bridges, with or without PV or wind turbines to supply power, would add something to the costs too I would imagine1

 

As a thought experiment it's mildly interesting. As a physics exam question - how much energy to reach x% of c, what centripetal acceleration - it may have some application. I'm not convinced interstellar travel is a reasonable goal, let alone an achievable one for a human civilisation, even if it makes for engaging fiction.

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

Imperial percentages!

 

How did you compute this 22%? (Compute the percentage more carefully and I guarantee you the 'aha moment' you will not forget.)

The centripetal acceleration is a function of speed and radius. You do not get to choose it independently.

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.

 

 

 

.

For "free"? Even at 100% efficiency, the cost of getting a mass up to 22% of c would be $73,000,000 per kg(At 12 cents per kwh). And such a system couldn't come even close to achieving that kind of efficiency, even in operational costs.

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?

 

 

Even more striking... at 22% of the light speed the g-force would be some seventy million g... gee.

 

(Now I wonder how much my result is off if proper, relativistic, computation is used instead. Can anyone make and educated guess, please?)

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.

The way I see things...

 

The universe is now aged at 13.7 billion years isn't it now??

But the universe is too big to have grown this much in that time, then they introduced this "inflation stage" of development and everything fitted into place again. Back then it could expand quicker than it does now.

 

What's outside the universe?? I LOVE this one!!

You can't say there is a void or just nothing outside our universe. Because even nothing not even a void could exist outside it.

So to be accurate you've got to say, there's nothing at all not even nothing outside out universe, haven't you??

 

 

What if there was a galaxy right on the edge of the universe??

I think if I was on a planet in that galaxy I'd be packing my bags and legging it as far away as possible. So maybe we'll find out about the edge of the universe when the fleet of alien ships come whizzing by, stopping to tell us we're going the wrong way.

 

 

Another theory I have is that any particles trying to become a part of this nothing that's not even nothing, will be repelled with more force than it went in with.

But I mentioned that in another thread about tachyons.

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.

It is possible to change the colour temperature of PC screens etc

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.

Sort of... information cannot be transmitted by any means faster than the speed of light. For instance, using quantum entangelment does not allow faster than light communication. In this sense, the speed of light defines causality.

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

The curvature is (in the simple case) static, so I don't see why that would be relevant.

 

This site provides an explanation of the maths in fairly easy to understand language: http://math.ucr.edu/home/baez/einstein/

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.

What we perceive as the force of gravity s caused by the changing curvature of space time. This curvature causes things (light as well as objects) to move towards a mass.

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.

You mean free fall = inertial motion?

Yes, but for both conditions:

free fall = inertial motion

standing on the surface = inertial acceleration

 

I am not really following what you are trying to say.

 

You can use the equivalence principle locally, [...]

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.

To add some details the FLRW metric models the Universe in terms of a fundamental observer

Ned Wright has a decent coverage.

https://ned.ipac.caltech.edu/level5/Peacock/Peacock3_1.html.

Essentially we take our local conditions into consideration.

Now in the Einstein field equations the Universe is modelled as an ideal gas. So each contributor has an equation of state.

The equation of state for the Cosmological constant being w=-1.

Expansion occurs when the kinetic energy of each contributor overcomes its self gravity.

You don't need the cosmological constant to have expansion. Its only needed to explain the added rate of expansion. Essentially it's a placeholder until we can determine the process of the added expansion rate.

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?

Here I think you are using just the weak equivalence principle. I am not sure what the highlighted means.What model is this? I an not aware of a model with this name.Vectors are essential across physics. And by 'gravity is always pointing in' you mean that gravity is always attractive?The modern understanding would be the weak equivalence principle which states (in the form to what you are using)'The local effects of gravitation (curvature of space-time) are indistinguishable from those of an accelerated observer in flat space.'A slightly stronger statement was given by Einstein as the above holds and'Any local non-gravitational experiment in a freely falling laboratory is independent of the velocity of the laboratory and its location in space-time.'The first statement means that locally, so in a small enough region, space-time is flat. This is mathematically the statement that space-time is a (pseudo)Riemaniann manifold. The second part added by Einstein says that in a small enough region the non-gravitational laws of physics reduce to their special relativistic form.I do not sure why vectors are no included already in once sense, and in another I am not sure that they have anything to do with the equivalence principle.

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.

 

we [...] assume the complete physical equivalence of a gravitational field and a corresponding acceleration of the reference system.

 Einstein, 1907

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.

not bad you have the concept. A better terminology would be the acceleration is an acceleration of the seperation distance, not the rate of expansion per Mpc.

 

 

 

 

 

 

the universe will expand without DE, just to be clear the DE is needed to expalin why the rate between galaxies or Observable universe radius isnt slowing down.

 

we can measure a relative velocity faster than c above the Hubble horizon which is c* age of the universe.

 

Yuo already know recesive velocity is only an apparent but not real velocity.

 

well done. +1

Great, thanks for all the help!

If you measure expansion as per Hubbles parameter km/s/Mpc the rate of expansion is slowing down. Since the CMB it's slowed down considerably.)

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.

 

If however you measure expansion via the radius of the observable universe it's accelerating. This is because of the gained Mpc.

Let's say expansion growth is 100% increase for each Mpc.

measure radius.

1

2

4

8

16.

But the rate per Mpc is still 100%.

(Basically the two terms are due to seperation distance between measurement a and b.)

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.

No. Apart from anything else, the proper velocity of these distant galaxies is effectively zero. That is why the increasing speed with distance is not due to acceleration. The accelerating expansion means that the scale factor is changing with time.

 

 

 

Proper time is local by definition. If you are worried about light propagation time, you are probably not dealing with proper time.

 

 

 

I know of no physics that assumes zero travel time (for significant distances)

When I get a chance later I'll post the proper distance formula, how Hubbles constant evolves with time.

You can check my signature on the Cosmo calc. Which is all done to proper distance. If you look under advanced users the formulas are given though they are slightly modified to use Stretch. Which is the inverse of the scale factor.

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.

Any simplistic explanation is probably going to be wrong.

 

I don't understand, so was the method I described involving Hubble's law and scale factors to solve for v₀ not the correct method?

 

 

You don't believe in the time that your watch shows? Extraordinary.

Well, when light speed creates an insignificant delay, it's effectively fine.

 

However for large distances, it doesn't exist since it allows 0 time for information to travel.

I had brothers that taught me about QM, GR, and cosmology at the age of 7 and I understood it though I probably didn't know much beyond simple arithmetic at that age.

 

I think my age actually made it easier to understand before life experiences had biased my intuition too much against accepting the unintuitive. I'm still not very good at math though.

 

An open mind is the biggest hurdle for understanding science IMO, and math is mostly useful for proofs or sometimes problem solving.

 

In college, there was a non-math physics class for all majors that weren't technical in nature and they even used the same text.