# Lorentz factor as a source of infinities/singularities in the relativity theory?

Discussion in 'Physics & Math' started by Ultron, Sep 21, 2021.

1. ### UltronRegistered Senior Member

Messages:
243
First some short introduction about infinities and singularities. For example lets imagine some company which is manufacturing computer chips and is planning the increase of production in next years. They have some equation which is producing the increasing number of chips based on some production parameters. And they get number like 150 mil, 180 mil following year, 250 mil and then they get infinity for the next year. They know for sure, that there is some error in the equation or in parameters and they will find it and fix it.

On the other hand in physics the situation is not that simple. Some physicist have the opinion, that if you get infinity aka singularity, the equation is wrong and it has to be reworked. For example Dirac was a proponent of this direction. Then there are pragmatic people like for example Feynman, who removed infinities by dividing infinity by infinity, but the usage of such nasty tricks is quite limited. And then there are kind of priests of physics, who preach kind of divine mystery of infinities or singularities and present it like special magic thing to wide audience in popular media. These are people who are perfectly OK for example with the infinite density of black holes.

Personally, I think that the main source of infinities in relativity is Lorentz factor:

This equation was tested many times and always passed the tests, so we can be quite confident that it is quite right. But the way it is constructed is always leading to infinities if the speed or the process related to speed reaches c. I think, there could be some better version, which would still be in line with observations/experiments and would not lead to infinities. In such improved version you have to ditch c and replace it with some other value, lets call it X, which would serve as a temporary value until it would be identified if there is some physics meaning of it and converting it to a new constant. The idea is to replace Lorentz factor with new equation which would give almost identical shape of the graph until you reach c, and then it would give some extremely high number, but not infinity. The main question is how to construct a new equation, which would give such shape of graph and deviate only at speed of c and above. Is there some tool out there which could help with such task? I have tried it with GeoGebra, but was not successful yet.

3. ### originHeading towards oblivionValued Senior Member

Messages:
11,506
No you never have an issue with infinities with the Lorentz factor. First of all you cannot achieve the speed of light so v cannot equal c and secondly if you make v equal to c you get 1/0 which is not infinity, it is an undefined result.

exchemist likes this.

5. ### UltronRegistered Senior Member

Messages:
243
From purely mathematical point of view, you are right. 1/0 is undefined. But from the viewpoint of physics the answer is rather infinity. I will give an example. Today we know, that neutrino has mass. The mass is extremely small, but it has some mass. In observations of neutrinos in experiments or in observations from the astronomical sources, we are not able to measure any difference of c and the speed which neutrinos achieve. I dont know the exact number, but it is something like this, it was measured that neutrinos can reach at least 99,999999999999% of c. So with every further digit nearing to 100% we get exponentially higher energy required to accelerate it further. And the answer to question what amount of energy you would theoretically need to accelerate neutrino to 100% speed of light is not undefined, but infinite. Sure theoretically it is impossible to get 100%, but this is the answer from the physics point of view.

I do believe, that it is possible for neutrino to achieve c, but you would need a lot of energy. And to describe it, a new equation would be needed. So does anybody here know, how to get a equation which produces similar graph as Lorentz factor, but it would be without getting 1/0 at c?

Last edited: Sep 21, 2021

7. ### Beer w/StrawTranscendental Ignorance!Valued Senior Member

Messages:
6,364
You do have to work better on explaining yourself. Is that not an itching time bomb in your mind?

8. ### DaveC426913Valued Senior Member

Messages:
16,518
No it isn't.

No it isn't.

You need to study limits.

Last edited: Sep 21, 2021
9. ### originHeading towards oblivionValued Senior Member

Messages:
11,506
Well it can't, so no equation is needed.

10. ### phytiRegistered Senior Member

Messages:
612
Ultron;

First, 'infinite' means 'without limit or boundary'. It's a state or condition.
It is NOT a number or quantifier.

We can make a larger integer, but not a largest integer.
The human experience with 'infinite' has never happened nor will it ever happen.

From my short list of special quotes:
Wittgenstein denies Hume's principle, arguing that our concept of number depends essentially on counting. "Where the nonsense starts is with our habit of thinking of a large number as closer to infinity than a small one".
(He could have included the popular phrase for limits, 'as it approaches infinity'.)

Energy is transferred in space at light speed c. The faster an object moves the more time required to transfer energy. It’s not now much energy but how much time is required. I.e., if a process requires an 'infinite' amount of time, it never happens!

11. ### James RJust this guy, you know?Staff Member

Messages:
36,974
If neutrinos have mass - and there's some good evidence that they do - then relativity tells us that it is impossible for them to travel at the speed of light.

Given that, what leads you to believe that it is possible for a neutrino to travel at the speed of light?

Do you have a disproof of relativity, perhaps? Or good evidence that neutrinos are massless after all? Or is it something else? Better than a guess, I hope.

12. ### UltronRegistered Senior Member

Messages:
243
Current experimental and astronomical measurements of speed of neutrinos give the result c. So in measurements or observations there is no difference between speed of neutrino and speed of light. It could be caused by simple fact, that the observation gives not sufficiently accurate speed and the expected difference in speed is minuscule. On the other hand there is also not any real world proof, that neutrino cant reach speed of light. So from observational point of view my speculative Lorentz factor replacement could be right.

Sure there are billions of observations which are not in line with General relativity theory. One type of observations is related to "Dark energy" and other to fictional "Dark matter". Also the results of Bell inequality experiment are not in line with GRT.

13. ### DaveC426913Valued Senior Member

Messages:
16,518
No.
It is within a few parts per billion. That may seem small, but it's not zero.

Yes there is. It's a few parts per billion.

That makes for a Lorentz factor of approximately 20,000. Big but not infinite.

Last edited: Sep 24, 2021
14. ### UltronRegistered Senior Member

Messages:
243
Theoretically you are right, but in real life the observed speed is c. No difference detected. The best observational case is
https://en.wikipedia.org/wiki/SN_1987A

Approximately two to three hours before the visible light from SN 1987A reached Earth, a burst of neutrinos was observed at three neutrino observatories. This was likely due to neutrino emission, which occurs simultaneously with core collapse, but before visible light is emitted. Visible light is transmitted only after the shock wave reaches the stellar surface.

So after 168 000 light-years, photons were not able to catch up to neutrinos which had few hours head start. And this observation is far better than anything scientists can measure in lab.

Last edited: Sep 24, 2021
15. ### DaveC426913Valued Senior Member

Messages:
16,518
Small difference is not no difference.

16. ### DaveC426913Valued Senior Member

Messages:
16,518
Relativity is not a theory of everything. The phenomena you mention do not refute relativity.

17. ### UltronRegistered Senior Member

Messages:
243
Where do you see your small difference? NO difference is measured. In other words the best measurement we have, gives the speed of neutrinos to be at least the same or even faster than speed of light.

18. ### DaveC426913Valued Senior Member

Messages:
16,518
No it doesnt.

Provide a reference.

19. ### UltronRegistered Senior Member

Messages:
243
I dont know if you did not read the entire text in the point 11, or did not understand it.

The best real world measurements of the speed of neutrinos gave the speed as the same or slightly above the speed of light aka c. If you think there are some measurements which gave less than c, please provide link.

https://en.wikipedia.org/wiki/Measurements_of_neutrino_speed

The most precise agreement with the speed of light (as of 2012) was determined in 1987 by the observation of electron antineutrinos of energies between 7.5 and 35 MeV originated at the Supernova 1987A at a distance of 157000 ± 16000 light years. The upper limit for deviations from light speed was:

thus 1.000000002 times the speed of light. This value was obtained by comparing the arrival times of light and neutrinos. The difference of approximately three hours was explained by the circumstance, that the almost noninteracting neutrinos could pass the supernova unhindered while light required a longer time

20. ### DaveC426913Valued Senior Member

Messages:
16,518
Yes. Your source is quite a few years out of date, in a field of very active research. Find a resource that's a little less dusty.

There was a well known kerfuffle a decade or so ago, thats been since debunked as an error in timing.

21. ### UltronRegistered Senior Member

Messages:
243
The result from 2012 analysis of 1987A supernova is still the best. And you could not be able to give link to any measurement which would have other result than c.

Regarding the error in measurement, which resulted in speed significantly higher than speed of light, that was an error in experiment technical setup which was corrected long ago and this is different topic.

https://en.wikipedia.org/wiki/Faster-than-light_neutrino_anomaly

But is seems to me, you just repeat your invalid argument without actually reading what Im writing or linking.

22. ### DaveC426913Valued Senior Member

Messages:
16,518
According to whom? You?

Define 'best'. The one that lets you make claims that are years out-of-date?

I'm reading it, and I'm saying your information is years out-of-date in a very active field of research.

The fact that you don't like it doesn't make it invalid.

Last edited: Sep 25, 2021
23. ### DaveC426913Valued Senior Member

Messages:
16,518
Consider the following analogous setup:

The Marine GPS on my boat has a resolution of +/-5m. That includes altitude. It cannot locate my position any more accurately than that. As far as it is concerned, I am an (opaque) sphere 5m in radius that is centred 2m above water level.

Within its margin of error, I could very well be located as much as 7m above water or 3m underwater (2+5, 2-5).

To put it in terms of your neutrinos:

"in measurements or observations there is no difference between altitude of GPS and level of lake."

Does that margin of error in my detection equipment mean it is possible for my GPS to be awash, or 3m underwater?

No. Known laws of physics (such as the fact that radio signals won't pass the air-water boundary, and the fact water short-circuits electricity), rules out anything at- or below- water level.

Does the margin of error in my detection device magically allow me to violate physics? No.

Margin of error in detection equipment doesn't "rule-in" possibilities that are otherwise ruled out.

Last edited: Sep 27, 2021