# Special relativity

1. May 30, 2010

### CHUKKY

if two events are simultaneous in an inertial frame, then they would not be simultaneous in another inertial frame as long as they are separated in space.Equally the vice versa is valid.Does this not imply that it would be possible for one to see someone to be born and to be dead at the same time?

2. May 30, 2010

### matheinste

The event of a person's birth and the event of a person's death are two events joined by a timelike vector. The same is true of all events on a person's "worldline". There is no inertial frame in which two events joined by a timelike vector can be simultaneous.

Matheinse.

3. May 30, 2010

### CHUKKY

so can you give me examples of events that are not connected by a timelike vector.

4. May 30, 2010

### matheinste

The ends of a rod. They are not joined by a timelike vector but by a spacelike vector. For events joined by a spacelike vector an inertial frame can always be found in which they, that is the events, are simultaneous.

Matheinste.

5. May 30, 2010

### CHUKKY

Matheinste-do you mean that whatever is joined by a timelike vector even if joined by a spacelike vector would never be simultaneous in any other frame.

6. May 30, 2010

### matheinste

Two events joined by timelike vector can never be joined by a spacelike vector and vice versa. Check out the definitions of timelike, spacelike and null vectors.

Matheinste.

7. May 30, 2010

### CHUKKY

Matheinste- i am just about to enter college and am trying to understand special relativity pretty confused about relative simultsneity and mass increase.Ccould you be of help to me?

8. May 30, 2010

### matheinste

There are many people on this forum who will be willing to help you. Just ask any questions no matter how basic.

Matheinste.

9. May 30, 2010

### CHUKKY

how can you prove to me mathematically that mass increases with speed by the relativistic factor.(freshman)

10. May 30, 2010

### CHUKKY

how can you also show that simultaneity is relative?

11. May 30, 2010

### matheinste

I think I'll pass that question on to someone else.

Matheinste.

12. May 30, 2010

### proculation

Not at the 'same' time. But, in two infinitesimally close moments, yes. Theoretically.

13. May 30, 2010

### matheinste

See Einstein's train and embankment demonstration for an explanation of the relativity of simultaneity. If there is anything you do not understand about it after reding it just ask.

Matheinste.

14. May 30, 2010

### Fredrik

Staff Emeritus
See this post. Physicists who use the term "mass" are talking about the "m" in my post, which is independent of speed. The quantity $\gamma m$ on the other hand, depends on the speed, because $\gamma$ does. Some people call $\gamma m$ the "mass". That terminology is considered obsolete and useless by a lot of people, including me. If I have to use a term for $\gamma m$ and I'm not allowed to use units such that c=1, I'll call it "relativistic mass". In units such that c=1, the relativistic mass is equal to the total energy $\gamma mc^2$, so I can just call it "total energy" instead.

15. May 31, 2010

### CHUKKY

What if the midpoints of the train and the embankment did not meet, at the point when the two flashes went out.Would it not be possible for him to also see it at the same time?or would he conclude that he knew that he was closer to one event than the order and hence that explains why the events were simultaneous to him?
please could you direct me to an explanation for mass increase? and could you mathematically prove to me that with the knowledge of relative simultaneity time order reversal would be impossible.

16. May 31, 2010

### Fredrik

Staff Emeritus
Uhh...you just got one. :uhh:

17. May 31, 2010

### matheinste

Regarding mass increase, there is presently a discussion in another thread.

When the endpoints of the train and the defined points on the embankment coincide it follows that the midpoints of train and embankment must also coincide. It is necessary for this set up to be as it is to demonstrate the relativity of simultaneity.

If the strikes were simultaneous in the train frame then observers would expect the llight fronts from the emissions to meet at the midpoint of the train rather than at the midpoint of the embankment.

As regards time order reversal, what is important is if one event can cause or influence a second event in the future, that is whether or not the events a re causally related. For two events joined by a timelike vector, it is impossible to find a reference frame where the time order of the events is reversed. For a spacelike vector it is possible to find a reference frame in which the time order of the events is reversed. The events joined by timelike vectors are causally related while those joined by spacelike vectors are not and so the time order for spacelike separated events, as far as causality is concerned, is irrelevant. The third type of spacetime vectors are null vectors and these represent the wordlines of photons and they are the same in all inertial frames. The mathematics is relatively simple but at the moment I am too lazy to play about with symbols.

Check out the light cone as this is a good demonstation of the relationship between these vectors.

Matheinste.

18. Jun 21, 2010

### CHUKKY

Thank you for all the information. I really appreciate it. Well I need help on the relativistic mass increase.Remember, like I earlier said I am just a beginner. Could you direct me to any link like you did on relative simultaneity

19. Jun 21, 2010

### Fredrik

Staff Emeritus
You said that twice (posts #7 and #9), and you got a good answer in #14. But you ignored that and asked the same question again (post #15). I directed you to #14, and you ignored that too. Why are you asking the same thing a fourth time when your question was answered after the second time?

20. Jun 22, 2010

### Mike_Fontenot

Depends on what you mean by "see", and on what you mean by "at the same time".

You won't see a received TV image of the simultaneous birth and death of someone far away. Simultaneity is not about an image you are currently receiving, but rather, it's about the CURRENT age of that distance person at the instant you receive that image from them, TAKING INTO ACCOUNT THE FACT THAT THEY HAVE AGED DURING THE TRANSIT TIME OF THAT IMAGE. And it turns out that that amount of ageing of the distant person, during the image transit, depends on the relative velocity of the observer and distant person, at the instant that the observer receives the image.

If you imagine a bunch of other observers, all momentarily co-located at the position of the first observer when he receives the image (and all receiving that same image at that instant), and with the different observers having different velocities, then they will all come to DIFFERENT conclusions about the amount of ageing of the distant person during the message transit, and therefore about her current age.

And if you imagine that the observer is rapidly and repeatedly changing his velocity, in essentailly zero time, then the observer will be rapidly and repeatedly changing his conclusion about the distance person's ageing during the image transit. And so the observer will be rapidly and repeatedly changing his conclusion about the current age of the distant person, all at roughly the same instant of the observer's life.

This effect gets more and more pronounced as their separation increases. And, a qualitatively similar effect occurs for finite accelerations, for sufficiently large separations. For a specific example with a sequence of 1g accelerations (sometimes separated by coasting segments, sometimes back-to-back), see my webpage:

http://home.comcast.net/~mlfasf [Broken]

Last edited by a moderator: May 4, 2017
21. Jun 23, 2010

### CHUKKY

Please could you explain or prove the relativistic mass increase formula for me.Thank you.I know that mass has to increase but I cannot prove the Lorentz formula for mass increase. I am just a beginner in special relativity

22. Jun 23, 2010

### Fredrik

Staff Emeritus
You can define the "relativistic mass" as $\gamma m$, where m is the mass and

$$\gamma=\frac{1}{\sqrt{1-v^2}}$$

And if you do, the relativistic mass depends on speed by definition. (I'm using units such that c=1. If you want to include c explicitly, replace every velocity in the formulas I type with velocity/c).

If you don't want to define it explicitly, you still have to define something, and take that as the starting point. For example, you can define the four-momentum p' in the comoving inertial frame as mass times the four-velocity u'=(1,0,0,0). p'=mu'=(m,0,0,0). (I'm putting a prime on the four-vectors in the comoving inertial frame, and I'm dropping the primes for the same four-vectors in the other frame). In an inertial frame that moves with velocity $$-\vec v$$ relative to the particle (so that the velocity of the particle is $$\vec v$$), the four-velocity is $$u=\gamma(1,\vec v)$$. (You get this result by applying a Lorentz transformation to (1,0,0,0)). So the four-momentum in this frame is $$(E,\vec p)=p=m\gamma(1,\vec v)=(\gamma m,\gamma m \vec v)$$. This can be interpreted as a "derivation" of relativistic mass, because it shows that $$\vec p=\gamma m\vec v$$, instead of $$=m\vec v$$ as we might have expected.

Last edited: Jun 23, 2010
23. Jun 23, 2010

### CHUKKY

what i mean is the mathematical proof that mass increases according to the lorentz formula

24. Jun 23, 2010

### Fredrik

Staff Emeritus
Now you're asking the same question a sixth time, and you still haven't said a word about the answers you got. I don't know why you think this is an acceptable way to behave in a forum.

You seem to be forgetting that what a proof tells you isn't that the theorem is true. What it tells you is that if the axioms are true and the terms used in the theorem are defined in a specific way, then the theorem is true. Is there some specific set of definitions that you insist on using? (I assume that special relativity is the axiom).

I don't understand what sort of answer you expect. Maybe you're just asking why the function

$$v\mapsto\frac{1}{\sqrt{1-v^2}}$$

is increasing. I have no idea since you're ignoring the answers you're getting.

25. Jul 17, 2010

### CHUKKY

Please can you give me a very elementary prove for relativistic mass increase.thank you