B Can we take a shrinking frame of reference?

[farolero]

I know the Galileo invariance don't allow us to take rotational or accelerating frame reference but an shrinking frame reference wouldn't be neither of this.

so would be allowed to take an shrinking frame reference?

 

[A.T.]

I know the Galileo invariance don't allow us to take rotational or accelerating frame reference but an shrinking frame reference wouldn't be neither of this.

so would be allowed to take an shrinking frame reference?

What do you think? Would Newton's Laws still apply, without modifications (adding fictitious forces)?

 

[farolero]

Well it becomes a very complex reference frame, a straight trajectory with a fixed size frame reference now wouldn't become a parabole? or maybe an ellipse?

Newtons laws would apply of course and the center of the reference frame wouldn't be neither rotating nor accelerating.

 

[A.T.]

...a straight trajectory with a fixed size frame reference now wouldn't become a parabole? or maybe an ellipse?... Newtons laws would apply of course...

How can Newtons 1st apply if a force free trajectory is not straight?

 

[farolero]

Because this frame reference results in a curved space.

You see the main point of this shrinking frame reference is that what is a straight line in a fixed size reference frame becomes a curve in an shrinking reference frame and Newton is true to fixed size reference frame which implies its true its curved in an shrinking frame reference.

So what this frame reference does is curve space and Einstein backs me up on this:

Im not sure of the maths and that's why i ask:

I think that if if you double the radius the reference grows at doublespeed the trajectory will be a parabole but if as you double the radius of the frame reference speed multiplies by square root of two the trajectory will be an ellipse.

Wouldnt this be correct? I am just trying to understand how space is curved according einstein and what valid reference frame could account for this.

 

[A.T.]

im just trying to understand how space is curved according einstein

Then ask about that. In curved space-time inertial frames are only approximations valid for areas small enough, that the curvature has negligible effects.

 

[Nugatory]

Wouldnt this be correct? I am just trying to understand how space is curved according einstein and what valid reference frame could account for this.

Frames have nothing to do with curvature; a frame is little more than a rule for attaching numbers (which are called "coordinates") to points. An example from one of your other threads would be the object sitting on a one-meter high table in a room 100 meters above sea level. In one frame (most convenient for an observer at sea level) the object is 101 meters high; in another frame (most convenient for an observer in the room) the object is one meter high. But it's the exact same physics either way.

Your "shrinking" reference frame is just what would happen if we decided to use shrinking rulers to assign coordinates. If our rulers shrank by fifty percent every day, then an object that was at rest ten meters away from me today would be twenty meters away tomorrow, and even the simplest laws of physics like "distance traveled equals speed times travel time" would become insanely complicated - but the actual physics, the behavior of objects, would be unchanged.

Be aware also that Einstein's general relativity does not say that space is curved, it says that spacetime is curved. That's a big difference.

 

[farolero]

i see thanks a lot, yes youre right space time is curved not just space and this frame reference shrinks with time,

please check this out.

" Soon afterwards, Einstein began thinking about what his new theory of gravity would mean for understanding the whole universe. To his surprise, his equations suggested that space could be expanding or shrinking. "

from:

https://www.sciencenewsforstudents.org/article/einstein-taught-us-its-all-relative

 

[farolero]

Also is kind of intuitive that the time of this frame reference would be slowing down from a fixed size frame reference

If you double the radius speed multiplies by two but if you half the rate of time momentum is conserved

So the cordenates velocities would increase at a rate of square root of two as you double radius froma fixed size reference and time would divide by two

In two seconds time from a fixed size reference time all eternity could happen in an shrinking time frame reference:

So:

Fixed size reference time------- shrinking frame time
1 second----------------1 second
1.5 second---------------2 second
1.75 second------------4 second
...
2 seconds... eternity

The mathematical geometry of this would be this:
X
A road in perspective that goes to infinity and beyond.

 

[Nugatory]

https://www.sciencenewsforstudents.org/article/einstein-taught-us-its-all-relative

Please take a moment to review the Physics Forums rules on acceptable sources. That writeup is better than a lot of the stuff out there, but it's still not real science, it's an oversimplified summary intended for people who either lack the mathematical tools or the willingness to learn what Einstein really said.

 

[farolero]

Sorry my apologies, I did a quick google, Ill try to search for more acceptable sources.

edit:

The frame reference I am trying to take its pretty simple actually

As you double radius time slows down by half, that's all the rules of this frame refernce

Its center is not accelerating nor spinning.

Would it be allowed to take this frame reference to see fictitious forces as just inertial?

 

[Nugatory]

In two seconds time from a fixed size reference time all eternity could happen in an shrinking time frame reference:
So:

F ixed size reference time------- shrinking frame time
1 second----------------1 second
1.5 second---------------2 second
1.75 second------------4 second
...
2 second... eternity

Sure, but those are just numbers. Let's try thinking about what they mean:

You are sitting there looking at a stopwatch counting milliseconds. You set it to zero at the moment that the "fixed size time" frame (I'll call it "FST") labels time 1. This is also the instant that the "shrinking time" frame (I'll call it "ST") labels time 1. A bit later you look at the stopwatch and see that it read 500; we label that instant 1.5 FST and 2.0 ST. So far, so good... but a bit later you look at your stopwatch again and it reads 1000, and then you look yet again and it reads 2000. This isn't a problem for FST; it labels those two instants time 2 and time 3 and we're happy. But if we try to use ST to label those instants, we have a problem - it cannot provide a label.

But the physics doesn't care about this problem. The physics is that we have a stopwatch with some electronics inside; the electronics are displaying a number on the face of the stopwatch and adding one to the number every millisecond. That's happening whether we use ST or FST to label the instants when the display reads 0, 500, 1000, 2000, and so forth; the electronics really don't care who is watching and what frames they're using to label these events. And of particular importance... you can't find an ST coordinate for the moment when the stopwatch reads 1000, nor for any higher value - but that doesn't mean these events don't happen, it just means that ST is a really poor choice to use in this problem.

 

[farolero]

When the FST marks 10,000 miliseconds the ST is unexistent that universe doesn't exist any more, you could adapt the cyclic universe model to this and consider each aeon is an eternity that from a FST just lasts two seconds.

edit:

You can see what i mean by analyzing this symbol:

X

From a FST from top to bottom of the symbol there are 4 seconds but for a ST time there are two eternities.

Just consider the distance run by an shrinking reference point from a fixed reference point

It runs double distance in half the time each step.

This is ungraspagle and bogles the mind of course.

Edit:

Maybe you know the joke: Chuck Norris counted to infinity twice.

Edit:

If i take an shrinking frame reference around big masses i should set one as well one around the moon with the right rate according her mass

But this would, both frames combined,imply there's a place in the cog moon Earth where the frame is inflating.

So you would expect on this place the opposite effect to gravity.

I was wondering if wormholes are accepted by mainstream cause this reference frame would expect to find one in the cog Earth moon and another in the cog Earth sun.

 

[Nugatory]

When the FST marks 10,000 miliseconds the ST is unexistent that universe doesn't exist any more, you could adapt the cyclic universe model to this and consider each aeon is an eternity that from a FST just lasts two seconds

Stop it! You're still trying to assign meaning to the coordinates instead of the underlying physics! Next thing I know, you'll be trying to tell me that, based on this picture, the island of Greenland is larger than the entire continent of South America... Or that I can stretch space by walking towards one of the poles.

You could design a wristwatch that displays ST time (it's easier with an old-fashioned analog wristwatch with hands - instead of moving the hands a constant distance with every tick, you'd move them a fixed fraction of the distance left around the face) and decide to use it to tell time. But that wouldn't miraculously propel you into a cyclic universe, and it wouldn't mean that the an eternity passed for you during one second of FST time. It would mean that you had designed a wristwatch that is useless after one second.

Much of physics is about finding things that are true in all frames, then choosing a frame that makes it easy to do the calculations and interpret the results.

 

[farolero]

For me its easier to visualize curved space time like this:

Than like this:

edit:

Also i was wondering how to face mathematically that from a fixed size and time reference you take a reference that doubles radius in half the time

That would lead to a transfinite space run per certain unit of fixed size and time reference.

And hence to a transfinite velocity that would be faster than anything misterious and etereal with an infinite velocity.

Does anybody know of any transfinite maths i could learn?

Or its not accepted by mainstream.

 

[farolero]

You could design a wristwatch that displays ST time (it's easier with an old-fashioned analog wristwatch with hands - instead of moving the hands a constant distance with every tick, you'd move them a fixed fraction of the distance left around the face) and decide to use it to tell time. But that wouldn't miraculously propel you into a cyclic universe, and it wouldn't mean that the an eternity passed for you during one second of FST time. It would mean that you had designed a wristwatch that is useless after one second.

But if you combine this clock with another that each time displays double time and combine them you have this X, I think the concept just can be expressed geometrically

basically for each unit of slowing time clock you take an unit of accelerating time clock
so:
1-1
1.5-2
1.75-4
...

Of course neither the slowing clock can be built with infinite precision nor the acelerating clock you could get the needle to turn fast enough.

This is kind of like achiles turtle paradox

edit:

Well i hope we can agree that if you double radius as you half time of the shrinking frame from the fixed frame one spot of the frame from the other will acquire transfinite speed of course energy is conserved in the universe relative to you but relative to the other frame kinetic energy might not posibly be transfinite and when there's infinite potential fictitious energy due to the forces the bigbang explodes.

Im basing all this on what i read from Einstein, seems relativity helps to explain the bigbang

 

[Dale]

Einstein backs me up on this:

Be very careful claiming things like this before you actually understand the theory and have worked with it yourself.

Einstein backs you up that curved coordinates can be used. He does not back you up that Newton's first law applies in such coordinates. @A.T. is correct in pointing out to you that the fact that the lines are curved is a clear indication that the frame is not inertial.

 

[farolero]

I understand your point but what i mean is that Newton states an object goes straight trajectory unless a force is applied on him in a fixed size fixed time reference frame.

But if i change this reference frame what before was a straight line according the equation v=s*t becomes a curve.

I don't see Einstein and Newton disgree on this.

In fact i still fail to see any difference in expectations from Einstein model to Newton model.

What does the Einstein model expect that the Newton one doesn't if you were so kind to teach me?edit:

I think one of the best ways to see the consecuences of Einstein curved space time gradient is Zenos dichotomy paradox:

The turtle runs first one meter, then half meter then one quarter and so on forever.

Will the turtle reach destination?

You could wrongly argue the turtle will never reach destination as my high school teacher taught me because she would have to take infinite steps and this is not posible.

But the turtle advances one meter (in the first second) half meter (in next half second) and a quarter of m (in next quarter of second) and so on forever and still at second two is at the finish line.

 

[A.T.]

Newton states an object goes straight trajectory unless a force is applied on him in a fixed size fixed time reference frame.

They are called inertial frames. If the trajectory is not straight, the frame is not inertial and Galilean invariance doesn't apply. That was the original question.

 

[farolero]

I see thanks so a frame reference that is going straight at constant speed is called inertial frame while one making a curve or acelerating is called non inertial where fictitious force appear.

 

[Dale]

But if i change this reference frame what before was a straight line according the equation v=s*t becomes a curve.

Again, this is exactly the key feature which makes such a reference frame non-inertial.

dont see Einstein and Newton disgree on this

On this they do agree with each other (insofar as it is possible for Newton to agree with concepts that came many years after his death), but both disagree with you. Neither would call such a frame "inertial".

In fact i still fail to see any difference in expectations from Einstein model to Newton model

The main difference between the two is that by Einstein's time the mathematical framework for doing physics in arbitrary coordinates had been developed. Newton did not have the math available, so he may not have been able to express physics in your non inertial frame.

I think one of the best ways to see the consecuences of Einstein curved space time gradient is Zenos dichotomy paradox:

Here is a long thread where this idea is discussed in depth

https://www.physicsforums.com/threads/on-the-nature-of-the-infinite-fall-toward-the-eh.656805/

 

[A.T.]

I see thanks so a frame reference that is going straight at constant speed is called inertial frame

A frame where a force free object is not going straight at constant speed, is not inertial.