Science Forums

# Relativity And Simple Algebra

## Recommended Posts

I've been away at another forum because they don't kick off people who discuss personal theories in the physics forum. Of course it's polluted with the same type of parrot that pollutes every physics forum but I have been learning a lot there of how right my theory is. But I was introduced to the new wrinkle of circular motion that no one can answer my questions to. There are two variants to this circular motion scenario:

One is the relative velocity and resulting time dilation of the circumference of a centrifuge to its center. This is similar to the HafelKeating Experiment (HKX) if there was a guy at the center of the Earth conducting it. The other is the HKX where two planes leave an airport at the north pole in opposite longitudinal orbits around the Earth neglecting gravitational effects.

Now on this forum we discussed closing speed as not being relative velocity. An example of closing speed would be orbits parallel to yours on Earth where the orbiting satellite maintains the same distance from you. There is no linear vector between you and the satellite so the relative velocity between the two of you should always be zero. This should be the same relative velocity between a rotational centrifuge and its center. But here is some irrefutable mathe from John Rennie on the PSX who proves that assertion not true.

"Suppose you're whirling about a pivot with velocity v at a radius r and I'm watching you from the pivot. I'm going to measure your position using polar coordinates (t,r,θ,ϕ), and in polar coordinates the line interval is given by (I'm leaving c in the equation this time):

ds2=c2dt2+dr2+r2(dθ2+sin2θdϕ2)ds2=−c2dt2+dr2+r2(dθ2+sin2⁡θdϕ2)

Note that this is just the flat space, i.e. Minkowski metric, in polar coordinates. We're using the flat space metric because there are no masses around to curve spacetime (we'll assume you and I have been on a diet :-). We can choose our axes so you are rotating in the plane θ=π/2θ=π/2, and you're moving at constant radius so both dr and  are zero. The metric simplifies to:

ds2=c2dt2+r2dϕ2ds2=−c2dt2+r2dϕ2

We can simplify this further because in my frame you're moving at velocity v so  is given by:

dϕ=vrdtdϕ=vrdt

and therefore:

ds2=c2dt2+v2dt2=(v2c2)dt2ds2=−c2dt2+v2dt2=(v2−c2)dt2

In your frame you're at rest, so ds2=c2dt2ds2=−c2dt′2, and equating this to my value for ds2 gives:

c2dt2=(v2c2)dt2−c2dt′2=(v2−c2)dt2

or:

dt2=(1v2c2)dt2dt′2=(1−v2c2)dt2

or:

dt=dtγ

which you should immediately recognise as the usual expression for time dilation in SR. Note that the centripetal force/acceleration does not appear in this expression. The time dilation is just due to our relative velocities and not to your acceleration towards the pivot."

One of the blowhards on my new forum who doesn't understand the reciprocal time dilation is not the same as permanent age difference caused by the twin paradox, insists that for every revolution, the time difference between the center and the guy on the circumference is accumulating. Basically the centrifuge has become a Jules Verne time machine.

So I drew a Minkowski diagram (Md) to support reciprocal time dilation between the two but it fell apart when I tried to stop the centrifuge to compare clocks to establish permanent age difference between the two. The fact remained no matter how many orbits the centrifuge performed, when stopped, the only separation between them was always just the length of the radius. In normal linear twin paradox, the total age difference greatly increases the farther the separation between them when a change in velocity is made. So I asked the blowhard to draw me an Md that supported his theory. Of course these philosophers have no way to back up their opinions with math so he left in a huff calling me a mentally ill liar. I got an even worse reaction on the PSX to this question and I'm not allowed to ask any more questions.

There is just one more question. The only difference between the HKX and centrifuge scenarios is the participants begin separated in the centrifuge and begin together in the HKX. Otherwise they could be both modelled as circular motion. Except the HKX is free to expand into ever larger and more pointed elliptical motion which would at some point be the same as the linear twin paradox scenario which ends in permanent age difference, not reciprocal time dilation like the centrifuge scenario. So I also asked for an Md for the circular HKX which I assume is not an example of reciprocal time dilation but is always an example of the round trip twin paradox. Of course, no one understands this question either.

• Replies 1.3k
• Created

#### Popular Posts

As a side note, Tegmark and others have presented papers showing that the signature 3+1 is the only one compatible with sentient observers — quite an interesting find, if true. One can logically imagi

Theory:  I have three chickens, Using nothing but a strobe light, they will change into a woman, because of my math equations which I am still sorting out a bit.   Now please don't be critical of my t

Ralf;     [Not true. The MMX requires length contraction to explain the results. If nothing changed in the setup, the x axis would require more light time for a round trip than the p (perpendicular)

#### Posted Images

Can I ask if "differential equations" are algebraic expressions of relativity?

I am not sure if that is of any interest, but the question occurred to me. Perhaps it may clarify some unrealized cognition in my mind.....😁

##### Share on other sites
Posted (edited)

Diff eqs are calculus which can handle curves while algebra is about lines. Are you suggesting I can't apply algebra in the form of minkowski diagrams to circular motion as only calculus applies to curves like circular motion? I've never had to apply calculus to SR.

Edited by ralfcis
##### Share on other sites
Posted (edited)
1 hour ago, ralfcis said:

Diff eqs are calculus which can handle curves while algebra is about lines. Are you suggesting I can't apply algebra in the form of minkowski diagrams to circular motion as only calculus applies to curves like circular motion? I've never had to apply calculus to SR.

Not at all, it was an honest question about perspective.

When I think of the term "differential", for some reason the image of "relativity" comes to mind.

I do know that an equation is an algebraic formula. Question was if it was related to the concept of relativity in any way.

I am trying to follow David Bohm's  complaint that science is becoming fractured into little specialized bits and pieces and is losing view of the common denominators that make up the "wholeness".

Edited by write4u
##### Share on other sites
Posted (edited)
On 8/4/2020 at 5:24 PM, marcospolo said:

Mathematics is NOT PHYSICS, and cant "explain" the Physical universe in any way.

Tell that to Max Tegmark.

Do you deny that the universal values and functions have some mathematical properties?

Tegmark argues that the Universe has only mathematical properties. Reality is expressed in mathematical patterns of matter formed in various shapes and densities.

If not what else is there beside what we call mathematics?

Edited by write4u
##### Share on other sites
Posted (edited)

24 minutes ago, TheProdigalProdigy said:

Give her a chance.

Thanks for the link, it is now in my library.

This little lecture may seem simplistic but contains some profound messages for the interested novice like myself.

Edited by write4u
##### Share on other sites
15 minutes ago, TheProdigalProdigy said:

Okay all bs aside there are two ways to do calculus. A right and a wrong. For instance, putting a flattened sphere at the bottom of an equilateral triangle will seem to the lake like the discovery of three dimensions in computational. But it is one of the infinite wrong ways to do it.

I don't think he was doing maths, but rather demonstrating relative perspectives to gain a deeper understanding of the relational properties of spacetime.

##### Share on other sites

Go away, both of you. Start your own thread and talk all the philosophy you want there.

##### Share on other sites

sorry, it was just a question....😒

##### Share on other sites
4 hours ago, TheProdigalProdigy said:

##### Share on other sites

I'm really not too pleased with the movie buffs who've invaded this forum. The idea that you can express your gut feelings when there is actual math you can argue to support your philosophical ideas, turns this place into even more of a looney bin than it was before. My last thread was thrown into the looney bin even though it was mathematically supported while these guys are allowed to run amuck, drown legitimate discussions with their video droppings and unsupported musings. Get rid of them or stop pretending this is any kind of a physics forum (and re-instate my last thread). Also answer my last serious post which is now buried in their garbage.

##### Share on other sites
On 3/23/2021 at 6:56 PM, ralfcis said:

"I've been away at another forum because they don't kick off people who discuss personal theories in the physics forum. Of course it's polluted with the same type of parrot that pollutes every physics forum"

I hope you realize how ironic that is!

##### Share on other sites
On 3/28/2021 at 12:15 PM, ralfcis said:

I'm really not too pleased with the movie buffs who've invaded this forum. The idea that you can express your gut feelings when there is actual math you can argue to support your philosophical ideas, turns this place into even more of a looney bin than it was before. My last thread was thrown into the looney bin even though it was mathematically supported while these guys are allowed to run amuck, drown legitimate discussions with their video droppings and unsupported musings. Get rid of them or stop pretending this is any kind of a physics forum (and re-instate my last thread). Also answer my last serious post which is now buried in their garbage.

##### Share on other sites
On 4/1/2021 at 12:42 PM, HallsofIvy said:

I hope you realize how ironic that is!

I don't because I'm talking about personal physics theories not all personal theories about anything.

##### Share on other sites
On 3/24/2021 at 1:56 AM, ralfcis said:

One is the relative velocity and resulting time dilation of the circumference of a centrifuge to its center. This is similar to the HafelKeating Experiment (HKX) if there was a guy at the center of the Earth conducting it. The other is the HKX where two planes leave an airport at the north pole in opposite longitudinal orbits around the Earth neglecting gravitational effects.

Now on this forum we discussed closing speed as not being relative velocity. An example of closing speed would be orbits parallel to yours on Earth where the orbiting satellite maintains the same distance from you. There is no linear vector between you and the satellite so the relative velocity between the two of you should always be zero. This should be the same relative velocity between a rotational centrifuge and its center. But here is some irrefutable mathe from John Rennie on the PSX who proves that assertion not true.

"Suppose you're whirling about a pivot with velocity v at a radius r and I'm watching you from the pivot. I'm going to measure your position using polar coordinates (t,r,θ,ϕ), and in polar coordinates the line interval is given by (I'm leaving c in the equation this time):

ds2=c2dt2+dr2+r2(dθ2+sin2θdϕ2)ds2=−c2dt2+dr2+r2(dθ2+sin2⁡θdϕ2)

Note that this is just the flat space, i.e. Minkowski metric, in polar coordinates. We're using the flat space metric because there are no masses around to curve spacetime (we'll assume you and I have been on a diet :-). We can choose our axes so you are rotating in the plane θ=π/2θ=π/2, and you're moving at constant radius so both dr and  are zero. The metric simplifies to:

ds2=c2dt2+r2dϕ2ds2=−c2dt2+r2dϕ2

We can simplify this further because in my frame you're moving at velocity v so  is given by:

dϕ=vrdtdϕ=vrdt

and therefore:

ds2=c2dt2+v2dt2=(v2c2)dt2ds2=−c2dt2+v2dt2=(v2−c2)dt2

In your frame you're at rest, so ds2=c2dt2ds2=−c2dt′2, and equating this to my value for ds2 gives:

c2dt2=(v2c2)dt2−c2dt′2=(v2−c2)dt2

or:

dt2=(1v2c2)dt2dt′2=(1−v2c2)dt2

or:

dt=dtγ

which you should immediately recognise as the usual expression for time dilation in SR. Note that the centripetal force/acceleration does not appear in this expression. The time dilation is just due to our relative velocities and not to your acceleration towards the pivot."

One of the blowhards on my new forum who doesn't understand the reciprocal time dilation is not the same as permanent age difference caused by the twin paradox, insists that for every revolution, the time difference between the center and the guy on the circumference is accumulating. Basically the centrifuge has become a Jules Verne time machine.

So I drew a Minkowski diagram (Md) to support reciprocal time dilation between the two but it fell apart when I tried to stop the centrifuge to compare clocks to establish permanent age difference between the two. The fact remained no matter how many orbits the centrifuge performed, when stopped, the only separation between them was always just the length of the radius. In normal linear twin paradox, the total age difference greatly increases the farther the separation between them when a change in velocity is made. So I asked the blowhard to draw me an Md that supported his theory. Of course these philosophers have no way to back up their opinions with math so he left in a huff calling me a mentally ill liar. I got an even worse reaction on the PSX to this question and I'm not allowed to ask any more questions.

Hi Ralfcis,

Yeah, there's couple of details here worth considering really carefully, as John's mistake there is the same that the entire physics community has been merrily making for the past 100 years.

First let me voice out a very obvious disclaimer - dropping out acceleration (/gravity) effects makes this a rather unrealistic example to discuss in terms of time dilation (because one or the other participant would always either feel acceleration, or sit deeper in a gravitational well, both of which possibly* imply time dilation), but let's anyway discuss the kinematic term of the time dilation here because that's where the mistake is.

The reason why your analysis shows no time difference is that it considers r, which is not changing. John's analysis considers velocity around the circumference via equating it to a linear velocity - which is a (common) mistake and leads to an erroneous conclusion.

This is directly connected to Ehrenfest paradox, and here he is accepting a paradoxical situation as if it's perfectly valid - easy mistake to make because the centrifugal acceleration would yield time dilation. But the velocity alone does not - in actual fact the rotating observer agrees completely with the simultaneity notion of the observer in the center.

I wrote a little article about the length contraction side of this problem just recently, see the link in this post:

Also see the few first posts of the thread to see my rebuttal to a whole collection of laughable attempts to solve that paradox. Most people just think of the whole problem from completely wrong perspective; they think length contraction is something that occurs to objects themselves, as oppose to what happens to our own coordinate representation of reality when we change simultaneity notion. These are quite different things. (I blame poor education)

It is common that people apply linear velocity analysis on this situation, and pretend that it's okay to imagine a set of "very very short measuring sticks". What they miss is that it's easy to show velocities where that measuring stick would become longer than the entire diameter of the wheel it's attached to - this is simply invalid approach.

At this point it's common that people abstract that measuring stick as having infinitesimally small length. What they forget is that length contraction occurs because of adjusting simultaneity notion across a representation, which yields different events as simultaneous as you move further away from the observer. That means you consider different simultaneity as defining the shape of an object - not that the object somehow changes. That means you need to have multiple events to choose from along the length of an object. An infinitesimally small object is a single event - a single event cannot transform closer to itself.

Now I mention somewhere in there on few occasions how this connects to time dilation (in kinematic terms). The simple fact is that clocks placed on the circumference of the spinning disk are easy to synchronize with the center (i.e. with the lab frame), and thus they are synchronized between one another as well. If the linear analysis about circumference velocity was correct, it would yield a time discontinuity after boosting around the circumference once - this is paradoxical and occurs because the analysis itself is logically invalid.

This means that in terms of SR (in terms of a kinematic analysis), I'm fairly confident that there is no length contraction nor time dilation. Ehrenfest Paradox is the thought experiment that proves this right. Almost the entire physics community disagrees and accepts paradoxical situations instead.

In terms of acceleration though, there is time dilation expectation. Traditionally "time" has been defined in somewhat awkwardly manner - it's used as an interaction term (to determine whether particles meet), as well as time term. These two uses are inconsistent and can bite people in the arse if they don't realize it (See above :D). So just to avoid that confusion, let me point out that if we use time as an interaction term, then "clocks" should not be thought of as measuring "time". They should be thought of counting oscillation cycles. This makes it much easier to avoid logical mistakes here.

Now consider a simple clock as just a light oscillator (two mirrors and light bouncing between). It doesn't measure time, it measures light cycle count. The "clock" that is being rotated on a rope is experiencing a constant acceleration, so the path of the light that is actually bouncing between the mirrors looks curved (when plotted inside an accelerated frame). That means it's effective path becomes longer - it's cycle count becomes lower. But this is the only reason why I'd expect time dilation, not because of the kinematic term.

-Anssi

*I say "possibly" because I have never been at the center of the earth with an accurate clock, and I have my doubts.

##### Share on other sites
Posted (edited)
On 3/24/2021 at 6:56 AM, ralfcis said:

I've been away at another forum because they don't kick off people who discuss personal theories in the physics forum. Of course it's polluted with the same type of parrot that pollutes every physics forum but I have been learning a lot there of how right my theory is. But I was introduced to the new wrinkle of circular motion that no one can answer my questions to. There are two variants to this circular motion scenario:

One is the relative velocity and resulting time dilation of the circumference of a centrifuge to its center. This is similar to the HafelKeating Experiment (HKX) if there was a guy at the center of the Earth conducting it. The other is the HKX where two planes leave an airport at the north pole in opposite longitudinal orbits around the Earth neglecting gravitational effects.

Now on this forum we discussed closing speed as not being relative velocity. An example of closing speed would be orbits parallel to yours on Earth where the orbiting satellite maintains the same distance from you. There is no linear vector between you and the satellite so the relative velocity between the two of you should always be zero. This should be the same relative velocity between a rotational centrifuge and its center. But here is some irrefutable mathe from John Rennie on the PSX who proves that assertion not true.

"Suppose you're whirling about a pivot with velocity v at a radius r and I'm watching you from the pivot. I'm going to measure your position using polar coordinates (t,r,θ,ϕ), and in polar coordinates the line interval is given by (I'm leaving c in the equation this time):

ds2=c2dt2+dr2+r2(dθ2+sin2θdϕ2)ds2=−c2dt2+dr2+r2(dθ2+sin2⁡θdϕ2)

Note that this is just the flat space, i.e. Minkowski metric, in polar coordinates. We're using the flat space metric because there are no masses around to curve spacetime (we'll assume you and I have been on a diet :-). We can choose our axes so you are rotating in the plane θ=π/2θ=π/2, and you're moving at constant radius so both dr and  are zero. The metric simplifies to:

ds2=c2dt2+r2dϕ2ds2=−c2dt2+r2dϕ2

We can simplify this further because in my frame you're moving at velocity v so  is given by:

dϕ=vrdtdϕ=vrdt

and therefore:

ds2=c2dt2+v2dt2=(v2c2)dt2ds2=−c2dt2+v2dt2=(v2−c2)dt2

In your frame you're at rest, so ds2=c2dt2ds2=−c2dt′2, and equating this to my value for ds2 gives:

c2dt2=(v2c2)dt2−c2dt′2=(v2−c2)dt2

or:

dt2=(1v2c2)dt2dt′2=(1−v2c2)dt2

or:

dt=dtγ

which you should immediately recognise as the usual expression for time dilation in SR. Note that the centripetal force/acceleration does not appear in this expression. The time dilation is just due to our relative velocities and not to your acceleration towards the pivot."

One of the blowhards on my new forum who doesn't understand the reciprocal time dilation is not the same as permanent age difference caused by the twin paradox, insists that for every revolution, the time difference between the center and the guy on the circumference is accumulating. Basically the centrifuge has become a Jules Verne time machine.

So I drew a Minkowski diagram (Md) to support reciprocal time dilation between the two but it fell apart when I tried to stop the centrifuge to compare clocks to establish permanent age difference between the two. The fact remained no matter how many orbits the centrifuge performed, when stopped, the only separation between them was always just the length of the radius. In normal linear twin paradox, the total age difference greatly increases the farther the separation between them when a change in velocity is made. So I asked the blowhard to draw me an Md that supported his theory. Of course these philosophers have no way to back up their opinions with math so he left in a huff calling me a mentally ill liar. I got an even worse reaction on the PSX to this question and I'm not allowed to ask any more questions.

There is just one more question. The only difference between the HKX and centrifuge scenarios is the participants begin separated in the centrifuge and begin together in the HKX. Otherwise they could be both modelled as circular motion. Except the HKX is free to expand into ever larger and more pointed elliptical motion which would at some point be the same as the linear twin paradox scenario which ends in permanent age difference, not reciprocal time dilation like the centrifuge scenario. So I also asked for an Md for the circular HKX which I assume is not an example of reciprocal time dilation but is always an example of the round trip twin paradox. Of course, no one understands this question either.

First of all, you were not kicked off this forum. The proof is, you are still posting!

Secondly, it was a big mistake I made by moving your other thread to Alternative Theories, while leaving this thread under Physics and Mathematics.

So, please allow me to correct that mistake and now move this thread into Alternative Theories also. You can thank me later.

Quote

Edited by OceanBreeze

## Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

×   Pasted as rich text.   Paste as plain text instead

Only 75 emoji are allowed.

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.