Velocity v & c^2: Simultaneous Events

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Discussion Overview

The discussion revolves around the concept of simultaneous events as perceived by observers moving at different velocities, particularly in the context of special relativity. Participants explore the implications of Lorentz transformations and the hypothetical existence of particles moving at velocities derived from the speed of light.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants propose that the set of events simultaneous to a person moving with velocity v corresponds to those occupied by a hypothetical particle moving at (c^2)/v.
  • Others argue that the slope of a line representing simultaneous events on a space-time diagram should be expressed as c^2/v to avoid implications of faster-than-light travel.
  • A participant presents Lorentz transformations to describe how simultaneous events in one frame relate to another, leading to a mathematical expression for the separation of events.
  • There is a suggestion that if such a fictitious particle existed, it would appear to occupy all points between two simultaneous events, although this is later corrected to specify that the events are only simultaneous at specific coordinates.
  • Some participants discuss the implications of setting t' to zero in the Lorentz transformation, questioning whether this leads to a meaningful interpretation of simultaneity.
  • There is a debate about the interpretation of "magic" in the context of mathematical results derived from the transformations, with some expressing skepticism about the conclusions drawn from setting variables to zero.
  • One participant mentions the geometric locus of points in uniformly accelerating frames, suggesting that it results in a straight line with a slope of c^2/v.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of simultaneous events and the implications of Lorentz transformations. There is no consensus on the existence of the hypothetical particle or the implications of setting t' to zero, indicating ongoing debate and exploration of the topic.

Contextual Notes

Some discussions involve assumptions about the nature of simultaneity and the behavior of particles at relativistic speeds, which may not be fully resolved within the thread. The mathematical steps and interpretations presented are subject to varying interpretations among participants.

actionintegral
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The set of events that are simultaneous to a person moving with velocity v is the same set of events that would be occupied by a hypothetical particle moving at
(c^2)/v
 
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My $.02 - close, but no cigar.

Particles can't move at velocities faster than light. I would say, instead "on a space-time diagram, the slope of a line representing simultaneous events is c^2/v" to avoid the issue.
 
actionintegral said:
The set of events that are simultaneous to a person moving with velocity v is the same set of events that would be occupied by a hypothetical particle moving at
(c^2)/v
Let I’ be the rest frame of the mentioned person and ( ,t’) and ( ,t’) the space-time coordinates of two simultaneous events. The same events, detected from the I inertial frame relative to which I’ moves with speed V are (x1,t1) and (x2,t2) respectively. We have in accordance with the Lorentz-Einstein transformations
t'=g(t1-Vx1/cc (1)
t'=g(t2-V x2/cc (2)
Combining (1) and (2) we obtain
x2-x1=cc(t2-t1)/V (3)
i,e. in I the simultaneous events in K’ take place on the world line described by (3).
 
So if such a fictitious particle really existed, it would appear to be everywhere between x1' and x2' simultaneously
 
discussion please

actionintegral said:
So if such a fictitious particle really existed, it would appear to be everywhere between x1' and x2' simultaneously
No! A typing error occurred due to the fact that the forum has no a formula editor. The two events are simultaneous only at x'1 and x'2 and not elsewhere.
 
But consider the formula t'=gamma*(t-vx/cc)

Set t'=0 and watch the magic happen!
 
magic?

actionintegral said:
But consider the formula t'=gamma*(t-vx/cc)

Set t'=0 and watch the magic happen!
Do you mean that the problem has something in common with events not causaly related?
 
bernhard.rothenstein said:
Do you mean that the problem has something in common with events not causaly related?

Sounds interesting - i'll open a new thread
 
actionintegral said:
But consider the formula t'=gamma*(t-vx/cc)

Set t'=0 and watch the magic happen!
Magic -- what Magic??
And please don't open another thread over this! (You'd do better to delete this entire thread)
When is the change in t' equal zero? -- when the change in t is zero.
That is t=0
What will "x" be? -- the same place or zero!
So you consider it magic to multiply gamma by zero and get 0!?

You’re comparing the starting point "zero" to the same starting point "zero" in both time and location.
ALL reference systems will measure this one event measured as two events as being simultaneous; with the identical separation both in time and distance for all reference frames; zero!
 
  • #10
RandallB said:
Magic -- what Magic??
And please don't open another thread over this! (You'd do better to delete this entire thread)
When is the change in t' equal zero? -- when the change in t is zero.
That is t=0
What will "x" be? -- the same place or zero!
So you consider it magic to multiply gamma by zero and get 0!?

You’re comparing the starting point "zero" to the same starting point "zero" in both time and location.
ALL reference systems will measure this one event measured as two events as being simultaneous; with the identical separation both in time and distance for all reference frames; zero!

Hi Randall,

I must respectfully disagree. If you take the lorentz transfromation for time (t'), and set t'=0, you will come up with the set of events for which t'=0. There are an infinite number of these events. You might have heard this set referred to as the "line of simultaneity".
 
  • #11
cc/v what is that?

actionintegral said:
The set of events that are simultaneous to a person moving with velocity v is the same set of events that would be occupied by a hypothetical particle moving at
(c^2)/v
Interesting enough, if you consider, in the uniformly accelerating reference frame, the observers who move with all possible proper accelerations and you try to find out the geometric locus of the points where theirs velocities are the same, you find out that it is a straight line the slope of which is c^2/v.
 
  • #12
actionintegral said:
Hi Randall,

I must respectfully disagree. If you take the lorentz transfromation for time (t'), and set t'=0, you will come up with the set of events for which t'=0. There are an infinite number of these events. You might have heard this set referred to as the "line of simultaneity".
SO
At displaced x' values with t' =0 give non simultaneous times t and x values don't match either, that’s what SR gamma is for --- Standard Ordinary even classical Special Relativity; what magic??
 

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