Velocity v & c^2: Simultaneous Events

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In summary, 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. This means that on a space-time diagram, the slope of a line representing simultaneous events is c^2/v. However, this is not possible for actual particles as they cannot move at velocities faster than light. Additionally, in the I inertial frame, the simultaneous events in the K' frame occur on the world line described by the Lorentz-Einstein transformations. This may seem like magic when t'=0, but it is simply due to the geometric locus of points where velocities are the same in a uniformly accelerating reference frame.
  • #1
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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  • #2
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.
 
  • #3
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).
 
  • #4
So if such a fictitious particle really existed, it would appear to be everywhere between x1' and x2' simultaneously
 
  • #5
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.
 
  • #6
But consider the formula t'=gamma*(t-vx/cc)

Set t'=0 and watch the magic happen!
 
  • #7
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?
 
  • #8
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
 
  • #9
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??
 

1. What is velocity?

Velocity is a measure of the rate at which an object changes its position in a specific direction over time. It is a vector quantity, meaning it has both magnitude (speed) and direction.

2. What is the equation for velocity?

The equation for velocity is v = Δx/Δt, where v is the velocity, Δx is the change in position, and Δt is the change in time. This equation is commonly written as v = dx/dt, where dx is the infinitesimal change in position and dt is the infinitesimal change in time.

3. What is the relationship between velocity and speed?

Velocity and speed are often used interchangeably, but they have different meanings. Speed is a scalar quantity that only measures the magnitude of an object's motion, while velocity is a vector quantity that also takes into account the direction of motion.

4. What is c^2 in the context of velocity and simultaneous events?

In the context of velocity and simultaneous events, c^2 refers to the speed of light squared. This value is a fundamental constant in physics and is equal to approximately 9 x 10^16 meters squared per second squared.

5. How are simultaneous events related to velocity and c^2?

In Einstein's theory of relativity, the concept of simultaneity is relative and depends on the observer's frame of reference. The speed of light, c, is the same for all observers regardless of their velocity. This means that the value of c^2 is constant and plays a crucial role in understanding the relationship between simultaneous events and velocity.

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