Galilean transformation equations and relativity.

[uncool]

Well, it is not really as difficult as you are trying to make it.

I don't think I'm making it difficult. What I am doing is asking you to actually explain what you mean by x', y', z', and t'. What precisely are they supposed to be?

If the coordinates in K are (x,y,z,t) and the coordinates in K' are (x',y',z',t'), all you do is provide the coordinates for the event. Suppose that the event takes place at (5 light sec,0,0,1 sec) in K. K' is traveling at ,25 light sec/sec relative to K. Then according to the Galilean transformation equations

 

x'=(5 light sec-.25 light sec/sec(1 sec))=4.75 light sec

y'=0

z'=0

t'= 4 sec

I think you mean 1 sec. And while providing examples is generally a good idea, I do understand the Galilean transformation.

t' is not shown by a clock in K'.

Do you mean by a clock that is at rest relative to K'? Or do you think that objects are "in" one frame and not another?

 

Further, if t' is not shown by a clock in K', then what is it supposed to represent? Why do we care about it at all?

It is shown by a clock in K. The clock in K' is irrelevant to these equations.

Err. That's not correct, if I've understood you correctly. A clock is supposed to tell us the time coordinate. In other words, a clock that is comoving with K' is supposed to tell us the time relative to K', which is the fourth coordinate. And a transform is supposed to tell us how to transform from one set of coordinates to another - so t', the result of the transform, is precisely what should be on the clock.

But you want to know what a clock in K' would read.

Well, yes, that's the idea of what a transform is supposed to do, assuming I've understood what you mean by "clock in K'", and as I've shown above.

Well, that depends on what is being used as the standard for time in K'. It could be related to t in K. For example, scientists say t2' would equal (t-vx/c^2)/sqrt(1-v^2/c^2) and figure the value for t2' from the Lorentz equations. It does not matter how t2' relates to t. The Galilean transformation equations work for any standard of time.

But not for any "standard of space and time". Specifically, they cannot account for the actual first premise of relativity, which is that the speed of light is both isotropic (the same in all directions) and frame invariant (the same relative to all inertial frames). The Galilean transformation that you are suggesting would contradict that, as I can show if you want.

For instance if the clock in K' was faster than the one in K and was twice as fast, we would just compute the value of t2' from t2'=2t. Scientists claim they can determine what t2' would be at the coordinates given if t= 1 sec from General Relativity or the Lorentz equations. That is fine with me. I don't care what a clock in K' reads when a clock in K reads 1 sec. It reads something. Let scientists determine it by experiment. My own estimate would be about .75 sec using Galilean transformation equations to estimate the time. Maybe it is more. Maybe it is less. Let scientists determine it by experiment, and then they cannot complain about it. But since we do not have any scientists,

This is false; many of the members of this site actually are scientists. You may want to rephrase this.

we will just use .75 sec for purposes of showing how the equations work. So using the Galilean transformation equations as seen by an observer in K' using a clock in K',

 

x=x'+v'(t2')

5 light sec=4.75 light sec + v'(.75sec)

v'=.33333 light sec/sec

Why is v' 0.3333... light sec/sec? Have you chosen this specifically to deal with the change between t2 and t2'?

0=y'

0=z'

t2=.75 sec

 

So the observer in K' sees K' traveling with a speed of .333333 light sec/sec instead of the .25 light sec/sec seen by an observer in K, and his clock is slower, which is what reality would also indicate.

As I said before, in order to find fault with these equations, you are going to have to do more than take times from the second set of equations and try to get them to work in the first equations. The standard of time in the first equations is faster than the standard of time in the second set of equations.

That is correct; what you are in effect doing is putting in a generalization of the Galilean transformation where you are allowed arbitrary time dilations (but not space dilations).

Now I understand that scientists have all kinds of shortcuts which require this kind of improper mathematics dating back to the time when James Clerk Maxwell and other scientists were deriving equations using the Galilean equations and absolute time, which had the speed the same measured from either frame of reference, but whenever you do it with these equations, I am just going to say, There are two different speeds. You cannot do it.

Cannot do what? And what "improper mathematics" are you referring to?

 

I'd prefer that you specifically answer the question about what t' is supposed to be, if it's not the time for a clock that is comoving relative to K'.

=Uncool-

Edited October 14, 2013 by uncool

[rbwinn]

You can define time however you want to, but it still remains a rate which can be measured an infinite number of ways. You can measure time by rotations of the earth. You can measure time by rotations of the planet Jupiter. You can measure time by transitions of a cesium isotope atom. You can measure time by ticks of a clock. You can measure time by the orbit of the planet Mars. It is not difficult to see your mistake. You define a second as a certain number of transitions of a cesium isotope atom and then say that the transitions slow down compared to the transitions of another cesium isotope atom which scientists define to be at rest. Then you set a second counted by slower transitions equal to a second counted by faster transitions in equations and wonder why distances are distorted. I told you what x,y,z, and t were. They are coordinates in K. If you do not know what a coordinate is, study up on it. If you want to keep pretending that you do not understand how coordinates work, I am just going to have to conclude that you really do not know.

I think I have explained enough times that t'=t, t2'=t2, etc. so that anyone who had any intelligence at all could understand what is meant by the two little horizontal lines between the two variables. I think I have said that t'=t represents the time of a clock in K enough times so that anyone who is not pretending to be stupid could grasp what that means.

So here is what I will say about it. If you want to discuss the equations I posted, let's discuss them. If you want to discuss wave theory that dates by to James Clerk Maxwell and his work using the Galilean transformation equations and absolute time adapted to the Lorentz equations by means of a length contraction, I am not really interested in it any more than I would be interested in discussing equations for epicycles in Ptolemaic astronomy.

I will tell you how I regard modern scientists. You are a bunch of parrots who can recite dogma, but you cannot think. You are like Muslim extremists who were taught how to explode a suicide bomb. You are very accomplished at what you were taught. You can do what you were taught. But you cannot even discuss anything else. So go ahead and do what you were taught. I see no reason to try to stop you.

I have stated enough times what you are doing wrong. If you want to discuss it, let's discuss it. if not, then there is no reason for me to waste my time with you. I have given the equations. If you want to discuss them, let's discuss them. If not, there is no reason I can see to discuss epicycles.

[ajb]

What we need to do is go back to Einstein's description of how he was going to solve this with the Lorentz equations. There are a few mathematical problems with what he did, but if it is good enough for mathematicians and scientists, for the present time it is good enough for me.

My advice is not to go back to Einstein's original papers as we have had over 100 years of special relativity and nearly the same of general relativity. Many very bright physicists and mathematicians have restructured Einstein's original ideas into the modern theory we use today. Any mistakes or misunderstandings that Einstein may or may not have made are irrelevant here. We have learned so much more since Einstein left this world.

[uncool]

You can define time however you want to, but it still remains a rate which can be measured an infinite number of ways. You can measure time by rotations of the earth. You can measure time by rotations of the planet Jupiter. You can measure time by transitions of a cesium isotope atom. You can measure time by ticks of a clock. You can measure time by the orbit of the planet Mars. It is not difficult to see your mistake. You define a second as a certain number of transitions of a cesium isotope atom and then say that the transitions slow down compared to the transitions of another cesium isotope atom which scientists define to be at rest. Then you set a second counted by slower transitions equal to a second counted by faster transitions in equations and wonder why distances are distorted.

Once again, this can easily hide many misunderstandings, and is most likely a strawman of relativity.

I told you what x,y,z, and t were. They are coordinates in K. If you do not know what a coordinate is, study up on it. If you want to keep pretending that you do not understand how coordinates work, I am just going to have to conclude that you really do not know.

I know what coordinates are. I know how they work. I am not pretending to not understand how coordinates work. That's not what I've been asking you. What I've been asking you is what x', y', z', and t' represent. You still haven't answered that question.

I think I have explained enough times that t'=t, t2'=t2, etc. so that anyone who had any intelligence at all could understand what is meant by the two little horizontal lines between the two variables. I think I have said that t'=t represents the time of a clock in K enough times so that anyone who is not pretending to be stupid could grasp what that means.

Just because you are repeating something doesn't mean that you have explained it. Why should we care about x', y', z', and t' if they aren't what the clock that is at rest with respect to K' shows? Once again, what do they represent - not what are they equal to, but what do they represent?

So here is what I will say about it. If you want to discuss the equations I posted, let's discuss them. If you want to discuss wave theory that dates by to James Clerk Maxwell and his work using the Galilean transformation equations and absolute time adapted to the Lorentz equations by means of a length contraction, I am not really interested in it any more than I would be interested in discussing equations for epicycles in Ptolemaic astronomy.

Then you will struggle in vain. Those who were trying to replace epicycles still had to understand them in order to replace them, and to show how what they were doing made more sense. I am asking you to explain what you are trying to do with Galilean transformations, and you are refusing to do so.

I will tell you how I regard modern scientists.

I don't care. I'm discussing precisely what you've stated.

 

So once again, I ask you: what are x', y', z', and t'? What do they represent? I'm not asking you what they are equal to, I'm asking you what they represent. Why are they important? I can answer this for special relativity. x', y', z', and t' are the coordinates with respect to frame K'; t' is what a clock that is at rest with respect to K' will show.

 

On a quick side note:

Posting these equations in the newsgroup, sci.physics.relativity resulted only in obscenities, profanity and insults. I am posting them in other forums with the hope that some more rational discussion of them might take place.

From what I've seen here, you are the one who is partaking in insults. Please practice what you preach and stick to the questions, rather than the insults. I've asked a direct question that seems to me to be very relevant. Please attempt to answer it. What do x', y', z', and t' represent? That is, why should we care about these numbers that satisfy the equations you've posted?

=Uncool-

[rbwinn]

I have already stated what I find wrong with modern science. Using two different lengths of time for a second and calling them equal is the same as saying that one rotation of the planet Mars and one rotation of the planet Neptune are equal because they are both days. No scientist has answered this or attempted to explain why slow transitions of a moving cesium isotope atom are considered to be the same as faster transitions of a cesium isotope atom at rest. So until science is willing to address this problem, I will just assume that we are going to have centuries more of the same. This kind of attitude permeates every aspect of human thought today. People who have been to school are considered to be more intelligent than people who work for a living. So let's just leave it at that. Science of today will just continue to be a show with no answers.

[Phi for All]

I think I have explained enough times that t'=t, t2'=t2, etc. so that anyone who had any intelligence at all could understand what is meant by the two little horizontal lines between the two variables. I think I have said that t'=t represents the time of a clock in K enough times so that anyone who is not pretending to be stupid could grasp what that means...

 

[snip]

 

You are a bunch of parrots who can recite dogma, but you cannot think. You are like Muslim extremists who were taught how to explode a suicide bomb. You are very accomplished at what you were taught. You can do what you were taught. But you cannot even discuss anything else. So go ahead and do what you were taught. I see no reason to try to stop you.

 

!

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[swansont]

I have already stated what I find wrong with modern science. Using two different lengths of time for a second and calling them equal is the same as saying that one rotation of the planet Mars and one rotation of the planet Neptune are equal because they are both days. No scientist has answered this or attempted to explain why slow transitions of a moving cesium isotope atom are considered to be the same as faster transitions of a cesium isotope atom at rest. So until science is willing to address this problem, I will just assume that we are going to have centuries more of the same. This kind of attitude permeates every aspect of human thought today. People who have been to school are considered to be more intelligent than people who work for a living. So let's just leave it at that. Science of today will just continue to be a show with no answers.

 

Equal lengths of time is what a Galilean transform does. A Lorentz transform has unequal times. Your entire premise seems to be based on a misunderstanding of the theory. (which makes your critique just a case of glass houses and stones as projectiles)

 

Bottom line here is that GPS works and GPS is based on relativity being correct. Also, the Hafele-Keating experiment (and the later repeats of it)

[uncool]

I have already stated what I find wrong with modern science.

And once again, I don't care. Are you going to answer the question or not? What do x', y', z', and t' represent? Why should we care about them?

[Bignose]

I have stated enough times what you are doing wrong. If you want to discuss it, let's discuss it.

You keep saying this, yet fail to demonstrate it using the data that is out there. If it is so easy to say that the current theory is wrong, shouldn't it be easy to demonstrate that your idea makes better predictions? Why do you keep ignoring this request?

[rbwinn]

I did not ignore that request. I pointed out that reality shows that if a second is longer in K' than in K, an observer in K' will get a faster speed between frames of reference than an observer in K. I have pointed this out at least ten times. Run the experiment. You can prove using an old slow propeller airplane that a moving cesium clock is slower than a cesium clock at rest. Now do the arithmetic. If this experiment was done on a plane going from New York to San Francisco, then you divide the number of miles between New York and San Francisco by the time each clock says it took to make the trip, and, by some strange chance, the time of the slower clock says that the plane made the trip faster than the faster clock indicates. This experiment agrees with my equations, not yours. That is just the way it is. If you do not want to discuss this, it is your choice to not discuss it, not mine.

x',y',z' and t' are coordinates in K'. Einstein defined them that way. I defined them that way. Did you have any other questions about coordinates?

Here is the problem I think you are having. The two little parrallel lines between t and t' have a meaning. They are not just there to separate the two variables. Think of the algebraic expression t'=t as a sentence with meaning. The algebraic expression says something about t' and t. Let's see if there are any scientists who can guess what the expression means.

OK, now if there are any such scientists, let's move on to the next step. If t' is the same time as t, then, obviously, it cannot be the time on a slower clock. So the slower clock in K' is not showing t' in the Galilean transformation equations. That does not mean the Galilean transformation equations are wrong. It means that you cannot use two different rates of time in the Galilean transformation equations. It is no different from saying that earth rotates in 24 hours, and Mars rotates in 24.6 hours, so day on Mars is the same as a day on earth because they are both one rotation of a planet. You cannot do it because you are saying two different rates of time are the same thing.

[uncool]

I did not ignore that request. I pointed out that reality shows that if a second is longer in K' than in K, an observer in K' will get a faster speed between frames of reference than an observer in K.

You have hidden one assumption there, which is that a meter in K is the same as a meter in K' (which is one of the assumptions of Galilean relativity). If the length of a meter is changed proportionally, then they will not get a faster speed between frames of reference.

I have pointed this out at least ten times.

Even when no one has asked you to. That may be a hint that you should stop doing so and try to figure out what they are actually asking you for.

Run the experiment. You can prove using an old slow propeller airplane that a moving cesium clock is slower than a cesium clock at rest. Now do the arithmetic. If this experiment was done on a plane going from New York to San Francisco, then you divide the number of miles between New York and San Francisco by the time each clock says it took to make the trip, and, by some strange chance, the time of the slower clock says that the plane made the trip faster than the faster clock indicates. This experiment agrees with my equations, not yours. That is just the way it is. If you do not want to discuss this, it is your choice to not discuss it, not mine.

Not ours? Would you mind doing the math using "our equations" to demonstrate that? You have made a claim about relativity; now please back it up. What time will the clock on the airplane show?

 

Further, how much faster will it go? Can you predict that precisely? Relativity can, in terms of the velocity of the airplane.

x',y',z' and t' are coordinates in K'. Einstein defined them that way. I defined them that way. Did you have any other questions about coordinates?

OK, so they are coordinates in (that is, relative to) K'. Why, then, wouldn't a clock in (that is, at rest relative to) K' show those as the time?

Here is the problem I think you are having.

You aren't a very good mind reader. Please stop trying, and simply answer the questions that have been asked, rather than the imaginary questions you think you've been asked.

The two little parrallel lines between t and t' have a meaning.

I know what an equals sign is. Please stop being condescending. This is part of the reason that you get insults - people respond in a way that matches what you do.

 

OK, now if there are any such scientists, let's move on to the next step. If t' is the same time as t, then, obviously, it cannot be the time on a slower clock. So the slower clock in K' is not showing t' in the Galilean transformation equations. That does not mean the Galilean transformation equations are wrong. It means that you cannot use two different rates of time in the Galilean transformation equations. It is no different from saying that earth rotates in 24 hours, and Mars rotates in 24.6 hours, so day on Mars is the same as a day on earth because they are both one rotation of a planet. You cannot do it because you are saying two different rates of time are the same thing.

You've repeated this several times now. It isn't answering the question that you've actually been asked. Please stop repeating until it's actually relevant to the question being asked; it makes trying to have a conversation impossible.

=Uncool-

[Bignose]

Ok, then, please find the papers written about the Hafele–Keating experiment and show how your equations make predictions that agree better with the experimental results than the predictions from SR & GR. (The experiment is exactly what you are describing with the planes, the experimental results matched very well with the predictions from relativity, and was the basis of the corrections we apply to our GPS systems today that also seem to be working pretty well.)

Edited October 14, 2013 by Bignose

[ydoaPs]

Well, that is fairly easy to do because the Lorentz equations predict that a slower clock in K' will show the same speed between frames of reference as a faster clock in K. This is accomplished by means of a length contraction in the frame of reference in motion. What reality shows is that if a clock in K' is slower, then an observer in K' will believe the speed of K relative to K' is faster than an observer in K would believe the speed of K' relative to K to be.

But aside from that, if t'=(t-vx/c^2)/sqrt(1-v^2/c^2) gives a correct representation of the time in K as compared to the time in K', then the correct representation of relativity would be to use the Galilean transformation equations for each rate of time as I have done. All I get from scientists is that this cannot be true because there is no length contraction. So if you want to believe that your car gets shorter every time you step on the accellerator, then it seems to me that you are free to do that. I don't really think it does.

'nuh uh' isn't very persuasive.

[rbwinn]

OK, since scientists cannot work the math, I will do it. You claim I cannot do what you do. So we will take the fastest observable speed I know about, the speed of the planet Mercury, and say that is the velocity of K' relative to K. The speed of the planet Mercury is 30 miles /sec. So you say you want to know how much a second in K is compared to a second in K'.

 

x'=x-vt

x=ct

x'=ct2'

 

ct2'=ct-vt

t2'=t(1-v/c)

t2'= 1sec(1-30/186,000)= 1 sec(1-.00016) =.999839 sec.

 

x=x'+v'(t2')

1 light sec= .999839 light sec + v'(.999839 sec)

.000161 light sec=v'(.999839 sec)

v'=.000161 light sec/sec=30 mi/sec

v' is actually slightly faster than v, but at this speed not enough to notice. So there is how much difference there is in time betweein a clock in K and a clock in K' according to the Galilean transformation equations. I do not say this is more than an estimate. These equations have some of the same inherent problems that the Lorentz equations have with regard to the speed of light being equal in both frames of reference.

[uncool]

OK, since scientists cannot work the math, I will do it.

You have once again managed to fail at mindreading. Please, stop trying.

You claim I cannot do what you do.

Please quote the specific part where we said this. You have a tendency not to quote what you are referring to, and it means that we have no idea what you are responding to. This makes it very difficult to figure out what you are trying to say sometimes. So please quote what you are referring to. Is this your attempt to use "our equations", or are you answering "Further, how much faster will it go? Can you predict that precisely? "

So we will take the fastest observable speed I know about, the speed of the planet Mercury, and say that is the velocity of K' relative to K. The speed of the planet Mercury is 30 miles /sec. So you say you want to know how much a second in K is compared to a second in K'.

 

x'=x-vt

x=ct

x'=ct2'

This is here to make sure that the speed of light is the same relative to this frame, right?

ct2'=ct-vt

t2'=t(1-v/c)

t2'= 1sec(1-30/186,000)= 1 sec(1-.00016) =.999839 sec.

 

x=x'+v'(t2')

1 light sec= .999839 light sec + v'(.999839 sec)

.000161 light sec=v'(.999839 sec)

v'=.000161 light sec/sec=30 mi/sec

v' is actually slightly faster than v, but at this speed not enough to notice. So there is how much difference there is in time betweein a clock in K and a clock in K' according to the Galilean transformation equations. I do not say this is more than an estimate. These equations have some of the same inherent problems that the Lorentz equations have with regard to the speed of light being equal in both frames of reference.

Actually, they have more problems. Because while you've managed to get the speed of light that is moving in one direction to be invariant, you have not done so for all of them. For example:

 

You've said that t2' = t (1 - v/c); at t = 1 sec, t2' = 1 - 30/186000. Now, let's take a look at light travelling in the opposite direction from the original lightbeam that you looked at. We then have that x = -ct. By the equations that you've repeated and repeated and repeated, x' = x - vt = - (v + c) t = - (v + c) t2'/(1 - v/c) = -c ((1 + v/c)/(1 - v/c))t2'. So at t = 1 sec, we have t' = 1 - 30/186000 sec, x' = -186000 - 30, which gives us a speed that is not equal to that of light. So we actually get that the speed of light relative to this frame is not isotropic, which contradicts everything we've ever tested.

 

What you've basically done is expand the group of transformations allowed to include time dilations without spatial dilations. If we choose one direction, we can preserve the speed of light in that one direction, at a cost of the speed of light in every other direction by using this group - which isn't enough.

 

Of course, I may have misunderstood what you've said, or made a mathematical mistake. Please point out any mistakes or misunderstandings I've made.

=Uncool-

[rbwinn]

Baloney. The speed of light is still c in the -x direction. There is a problem with it, which is that in order for light to be going at c in both frames of reference in that direction, the clock in K' has to be faster than the clock in K. The Lorentz equations have exactly the same problem.

[swansont]

OK, since scientists cannot work the math

 

Yes, it's incredible how scientists have been able to make progress while being unable to do math.

 

Or — and this is just a wild speculation — maybe it's you who are misinterpreting the math and the scientists actually have it right. With their silly experiments that actually work, and all that.

[rbwinn]

So tell me what progress scientists have made. I think they just set themselves up as some kind of super-intelligences who do nothing useful any more and are required to be supported by the slavery of the people.

[uncool]

Baloney. The speed of light is still c in the -x direction. There is a problem with it, which is that in order for light to be going at c in both frames of reference in that direction, the clock in K' has to be faster than the clock in K. The Lorentz equations have exactly the same problem.

I asked you to identify the error in what I posted. You are simply saying that the conclusion is wrong without identifying any mistake I've made. That isn't a sufficient objection. Did I perform your transform incorrectly? Did I make a mathematical mistake somewhere? Did I misunderstand something?

 

Further, the Lorentz equations do not have the same problem - that is, something moving at the speed of light in either (and in fact, any) direction remains at the speed of light after a transform, which is what I just demonstrated your expansion of the Galilean transform can't do. Do you want me to demonstrate?

 

So tell me what progress scientists have made. I think they just set themselves up as some kind of super-intelligences who do nothing useful any more and are required to be supported by the slavery of the people.

Before answering this question, I'd like to clarify. Which scientists are you referring to? Theoretical (mathematical) physicists?

=Uncool-

Edited October 15, 2013 by uncool

[swansont]

So tell me what progress scientists have made. I think they just set themselves up as some kind of super-intelligences who do nothing useful any more and are required to be supported by the slavery of the people.

 

GPS. Which works.

 

There's a bunch more, including the very internet you used to post your inquiry, in case you are tempted to try the "is that all?" gambit, but the massive success of the GPS system should be sufficient to address the silly claim that relativity is somehow wrong.

[Bignose]

So tell me what progress scientists have made. I think they just set themselves up as some kind of super-intelligences who do nothing useful any more and are required to be supported by the slavery of the people.

Wow, this just took a hugely negative turn. It would have been nice of you to actually read some of the supporting links that have been posted -- again I refer to the paper I posted which demonstrates the pretty excellent agreement between experiment and the predictions made by SR & GR.

 

Which, as swansont posted, has lead to some pretty useful things like GPS. The beginnings of which were discovered in the Hafele–Keating experiment I also have already referred to.

 

In other words, I am starting to have doubts about your expressed desire to have a conversation. Because it really shouldn't have been that hard to at least acknowledge the successes SR & GR have had. It is not impossible that your idea could be even better, but we'll never know until you compare your predictions to these other ones. I do not get this reluctance to compare your calculations to the tried and true published results. Unless you know your predictions will be wrong. In which case, then your tactic would be to lash out instead of actually supporting your position.

 

I hope I am wrong on this last sentence, and I hope you will show us how your calculations compare to the published results. But, I am really having doubts that that will ever happen.

[rbwinn]

In the first place, I am not a scientist. I do not have unlimited funds available to me for "research". Secondly, if scientists are so super-intelligent, why are they attempting to use speed of light in the negative direction as a proof that the Galilean transformation equations are incorrect? Even the Lorentz equations use velocity of light. That is why the equations remain in an unreduced form after Einstein introduced the equation x=ct. If x=ct, why say t'=(t-vx/c^2)gamma? The reason is that if light is directed in the -x direction, the velocity of the light is -186,000 miles per second, not +186,000 miles per second. So the Galilean transformation equations show light going in the -x direction at c in both frames of reference the same as the Lorentz equations.

 

-ct2'=-ct-vt

 

The problem scientists have is that this shows the same thing the Lorentz equations show. In order for this to happen, it takes a faster clock in K' and a slower clock in K. Experiment shows that the clock in K' is slower.

[swansont]

In the first place, I am not a scientist. I do not have unlimited funds available to me for "research". Secondly, if scientists are so super-intelligent, why are they attempting to use speed of light in the negative direction as a proof that the Galilean transformation equations are incorrect? Even the Lorentz equations use velocity of light. That is why the equations remain in an unreduced form after Einstein introduced the equation x=ct. If x=ct, why say t'=(t-vx/c^2)gamma? The reason is that if light is directed in the -x direction, the velocity of the light is -186,000 miles per second, not +186,000 miles per second. So the Galilean transformation equations show light going in the -x direction at c in both frames of reference the same as the Lorentz equations.

 

-ct2'=-ct-vt

 

The problem scientists have is that this shows the same thing the Lorentz equations show. In order for this to happen, it takes a faster clock in K' and a slower clock in K. Experiment shows that the clock in K' is slower.

 

It requires no funding to go onto the internet and do some research on relativity experiments. Complaining about funds is irrelevant.

 

The Lorentz transforms do not include a direction for light travel, since there is no requirement for light to be involved. It's two observers, one in each frame. Any negative signs come from the coordinate system set-up and sign convention; it is assumed that the primed observer moving at a speed v > 0 is moving in the +x direction of the unprimed observer's frame.

[Bignose]

I do not have unlimited funds available to me for "research".

The first link I gave you, the one with the extensive discussion of the comparing how GR's prediction agree really well with measurements, the full text of that paper is free.

Edited October 15, 2013 by Bignose

[uncool]

In the first place, I am not a scientist. I do not have unlimited funds available to me for "research".

As it happens, neither do scientists.

Secondly, if scientists are so super-intelligent,

Who said that they were?

why are they attempting to use speed of light in the negative direction as a proof that the Galilean transformation equations are incorrect?

Not that they are incorrect. That they have problems with experiments. The problem is that experiments have shown that the speed of light is isotropic relative to every inertial frame that has been tested. In layman's terms, that means that the speed of light is the same in every direction. So a transformation would have to preserve that property - if something is moving with speed c relative to frame K, then its transform should be something moving with speed c relative to frame K'.

Even the Lorentz equations use velocity of light.

Yes, they do. I don't understand your point here.

That is why the equations remain in an unreduced form after Einstein introduced the equation x=ct. If x=ct, why say t'=(t-vx/c^2)gamma? The reason is that if light is directed in the -x direction, the velocity of the light is -186,000 miles per second, not +186,000 miles per second.

But the speed is still 186000 miles per second. Speed doesn't have a direction - it's simply a number. And experiments have shown that it's the speed of light that is the same relative to every frame, in every direction.

So the Galilean transformation equations show light going in the -x direction at c in both frames of reference the same as the Lorentz equations.

 

-ct2'=-ct-vt

 

The problem scientists have is that this shows the same thing the Lorentz equations show. In order for this to happen, it takes a faster clock in K' and a slower clock in K. Experiment shows that the clock in K' is slower.

The equation you've written here is not what the Lorentz equations say. So no, this is not the same as the Lorentz equations.

=Uncool-