Is the Time Dilation Formula Incorrect?

[NordicLight]

Time dilation not correct?

Hello

First, I would like to start with the simple fact that I am not a physicist/mathematician so please bear with me if I ask somewhat simple/stupid questions. I did however have some exposure of maths during my university years but not so much so that I can answer the following question myself. Only recently I have begun to look at the equations that lie behind everything (when time permits me to do so).

Few weeks ago, I have stumbled across a website with an online transcription of a book where the author tries to dispute the correctness of Einstein’s conclusions with equations that according to him, support his claims. Needless to say, to me it all sounds ludicrous as his conclusions are as far as I know not supported by any experiments so it must be that his calculus is flawed somewhere. I have a hunch about where that could be but I would be very grateful if somebody could look at one chapter of the book about the time dilation maybe try to find where that fault might be.

His conclusion is that the correct $$\gamma$$ should be
http://users.net.yu/~mrp/formula18.301.gif

and not

http://users.net.yu/~mrp/formula18.302.gif

Here is the link: <snipped>

You might ask why I bother. Well, I just want to understand and in order to do so it is sometimes necessary to look at things that (I presume) contain errors.

Thank you for stopping buy.

 

[confinement]

The equation x' = c t' is taken out of context, and in particular this equation only applies to light and should not be combined with the lorentz transormations as this author has done.

The probem with this author's proposed gamma facor is that it differs greatly from the gamma factor that is used in trillions of calculations in particle colliders around the world.

At 3/4 of the speed of light this fellows Gamma is 2.6, and the real Gamma is 1.5.

 

[Vanadium 50]

it all sounds ludicrous as his conclusions are as far as I know not supported by any experiments so it must be that his calculus is flawed somewhere.

And that's the right attitude. If his ideas are unsupported by data, they are wrong. Full stop.

 

[NordicLight]

Thanks guys for the quick replies and for the words of encouragement :)
I took a closer look and I think I understand.

I also checked some other chapters of his "work" and realized that it is a pile of junk. Pure waste of time. Because of that and the small warning I got I'll try to remove the link.

 

[Naty1]

I don't know what the "warning" was about but we SHOULD be able to question a document we happen to find when we either don't understand or doubt its accuracy...

How is one SUPPOSED to verify the accuracy of a document statement ?? If I happen to quote something from, say, Wikipedia because I believe it is correct and answers a question from someone else, do I get in trouble if the quote contains an error??

I have posted several quotes from books I have read asking essentially "what does the author mean ??" ..in other words ,I don't even understand enough to draw a conclusion regarding accuracy...

 

[NordicLight]

@Naty1
I got the warning because "discussion or "free advertisement" to crackpot website is not allowed. Warnings serve as a reminder to you of the forum's rules, which you are expected to understand and follow". I didn't read them before I made the thread and I am sorry. That pretty much sums it up. I am not the one who decides the forum rules and it is not my intention to pollute this forum (which I find very interesting). Therefore I asked for the link to be removed. I can PM it to you if you are interested, however it won't make you much happier because as far as I can see it lacks connections with the real world.

 

[Phrak]

His conclusion is that the correct $$\gamma$$ should be
http://users.net.yu/~mrp/formula18.301.gif

That's the Lorentz transform of the x+ct coordinate for a boost in the x direction, isn't it? It looks a bit familiar. If so, it would just be a reformulation of relativity.

 

[bernhard.rothenstein]

His conclusion is that the correct $$\gamma$$ should be
http://users.net.yu/~mrp/formula18.301.gif

That's the Lorentz transform of the x+ct coordinate for a boost in the x direction, isn't it? It looks a bit familiar. If so, it would just be a reformulation of relativity.

I would mention that the Lorentz factor relates a proper time interval to a coordinate time interval whereas the Doppler factor relates two proper time intervals measured in the I and in the I' inertial reference frames. Once that difference is mentioned the discusion could be closed.

 

[Phrak]

I would mention that the Lorentz factor relates a proper time interval to a coordinate time interval whereas the Doppler factor relates two proper time intervals measured in the I and in the I' inertial reference frames. Once that difference is mentioned the discusion could be closed.

If you say so. What's the Lorentz transform matrix of coordinates for a boost in the x direction?

I think you've missed the point. What is the physical significance of this term in the context of special relativity?

 

[bernhard.rothenstein]

If you say so. What's the Lorentz transform matrix of coordinates for a boost in the x direction?

I think you've missed the point. What is the physical significance of this term in the context of special relativity?

If I have understood correctly the question was about the validity of the time dilation formula. As far as I know the time dilation formula could be derived without using the Lorentz transformatios (light clock) relating via $$\gamma$$ a proper time interval measured say in I and a coordinate time interval measured in I' or vice versa.
The formula which accounts for the Doppler shift could be derived without without using the Lorentz transformations,but using the formula which accounts for the time dilation. The Doppler shift formula relates via the Doppler factor, mentioned in the first thread, two proper time intervals measured in the two involved inertial reference frames respectively.
Please explain me in more detail your point of view.
Kind regards.

 

[Phrak]

The formula which accounts for the Doppler shift could be derived without without using the Lorentz transformations,but using the formula which accounts for the time dilation. The Doppler shift formula relates via the Doppler factor, mentioned in the first thread, two proper time intervals measured in the two involved inertial reference frames respectively.
Please explain me in more detail your point of view.
Kind regards.

I hadn't recognised the Doppler equation. I only noticed an odd coincidence of formula.

The relativistic Doppler equations for wavelength and frequency are

$$\lambda_o = \lambda_s \sqrt{\frac{c+v}{c-v}}$$

$$f_o = f_s \sqrt{\frac{c-v}{c+v}}$$

s -- source
o -- observer

Now, we can try to make the Lorentz transformation of coordinates a little more elegant by changing coordinates along eigenvectors. (ct, x, y, z) --> (ct+x, ct-x, y, z)

$$X_{-}{}' = X_{-} \sqrt{\frac{c+v}{c-v}}$$

$$X_{+}{}' = X_{+} \sqrt{\frac{c-v}{c+v}}$$

X_{-} = ct-x
X_{+} = ct+x

An interesting coincidence, but I'm sure this has nothing to do with the millionth attempt to replace special relativity.

 

[bernhard.rothenstein]

I hadn't recognised the Doppler equation. I only noticed an odd coincidence of formula.

The relativistic Doppler equations for wavelength and frequency are

$$\lambda_o = \lambda_s \sqrt{\frac{c+v}{c-v}}$$

$$f_o = f_s \sqrt{\frac{c-v}{c+v}}$$

s -- source
o -- observer

Now, we can try to make the Lorentz transformation of coordinates a little more elegant by changing coordinates along eigenvectors. (ct, x, y, z) --> (ct+x, ct-x, y, z)

$$X_{-}{}' = X_{-} \sqrt{\frac{c+v}{c-v}}$$

$$X_{+}{}' = X_{+} \sqrt{\frac{c-v}{c+v}}$$

X_{-} = ct-x
X_{+} = ct+x

An interesting coincidence, but I'm sure this has nothing to do with the millionth attempt to replace special relativity.

Interesting, but I think that you should mention that the derivation of the relativistic Doppler shift formula implies the knowledge of the formula that accounts for the time dilation. I subscribe your last sentence.

 

[Bob S]

Here is an observation that directly applies to the topic of this forum "Time dilation not correct?". The positive muon has a lifetime of about 2.197 microseconds. Bunches of muons have been accelerated to about gamma = 100 and stored in magnetic "storage" rings such that the time-dilated lifetime should be about 2 milliseconds (in our rest frame) according to special relativity. Indeed it is, within the accuracy of measurement.